mm-25037 > I cannot determine a node that would prove your assertion. As far as I > can see the path 0.111... stretches further and further. My assertion does not depend on any single node but on an infinite set > of right-child nodes in a tree which does not contain or allow any such > set, so that WM is being, as expected terminally myopic. You may assert what you like. Unless you can point to something in the hardware of the tree (i.e. its nodes) that supports your assertion, your assertion is null and void. > My tree seems to be complete. But, of course, I will refrain from that > assertion in case you come up with the name of a missing node. Why does WM keep harping on missing nodes? Because paths consist of nodes and edges and differ by nodes and edges and nothing else. > Each node corresponds to a > binary fraction, and no one is saying that any of those are missing, Each number consists of a set of binary fractions. And if none is missing, then none of the numbers is missing. > but > each missing path corresponds to one of the uncountably many real > numbers between 0 and 1 which is not a binary fraction, and all such > paths, along with those numbers, are missing. So no single node is missing, but infinitely many are missing? I think we had this topic already. Learn that it is nonsense. Every path consists of infinitely many nodes, but there are no paths that consists of ghosts. Every countably infinite combination of 0' and 1's, i.e. every binary sequence is in the infinite binary tree, as I constructed it from a countable set of paths. And any rearrangement of WM's limited set of paths, even if it still > covers all nodes, excludes most paths. You believe in something without reason just because you want to believe it. That is not mathematics but an intellectual disease from which anybody can be cured if she or he is willing. If someone is not willing there is no chance. That is similar to other bad habits. If you are smoking or drinking then you cannot get cured unless you want to. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor I cannot determine a node that would prove your assertion. As far as I > can see the path 0.111... stretches further and further. > My assertion does not depend on any single node but on an infinite set > of right-child nodes in a tree which does not contain or allow any such > set, so that WM is being, as expected terminally myopic. You may assert what you like. Unless you can point to something in the > hardware of the tree (i.e. its nodes) that supports your assertion, > your assertion is null and void. All paths are maximal sequences of nodes connected by having the successor of each node a child of that node, and every such sequence should be allowed as a path in a complete tree. A tree is which there are any such sequences prohibited is incomplete. > My tree seems to be complete. But, of course, I will refrain from that > assertion in case you come up with the name of a missing node. > Why does WM keep harping on missing nodes? Because paths consist of nodes and edges and differ by nodes and edges > and nothing else. Paths consist of suitably sequenced sets of nodes, and if any suitably sequenced set of nodes is missing the tree is incomplete. Most of such suitably sequenced sets are missing from WM's trees. Each node corresponds to a > binary fraction, and no one is saying that any of those are missing, Each number consists of a set of binary fractions. And if none is > missing, then none of the numbers is missing. But most sets of binary fractions ARE missing. but > each missing path corresponds to one of the uncountably many real > numbers between 0 and 1 which is not a binary fraction, and all such > paths, along with those numbers, are missing. So no single node is missing, but infinitely many are missing? That may be the case in WM's mytheology, but nowhere else. When I say that {1,2} is missing from {{1}, {2}, {3}, ...}, WM carefully misreads that to mean that 1 is missing from U{{1}, {2}, {3}, ...} > I think we had this topic already. Learn that it is nonsense. Everything in WM's mytheology is nonsense. If WM would ever leave it for a while, he might learn all sorts of things. > Every path > consists of infinitely many nodes, but there are no paths that > consists of ghosts. Every countably infinite combination of 0' and > 1's, i.e. every binary sequence is in the infinite binary tree, as I > constructed it from a countable set of paths. You can construct every node using only finite sequences, which is essentially what WM is using, of which there are only countably many, but you cannot CONSTRUCT all paths that way, as there are more paths than finite sequences. If one constructs the tree with all possible nodes, then those other paths can appear in the complete tree without being in the set of paths used to construct the tree. > And any rearrangement of WM's limited set of paths, even if it still > covers all nodes, excludes most paths. You believe in something without reason just because you want to > believe it. Wrong. I believe that something follows from a suitable set of axioms because reason and logic insist upon it following from such a set. > That is not mathematics but an intellectual disease from > which anybody can be cured if she or he is willing. If the cost of that cure requires entry into a world as chaotic and unreasonable as WM's mytheology, most of us will opt to remain in the present world of mathematics which is free from such insanity. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=-eQqtQoAAACZVM-kNEsOn3k7GSvoJoS4 CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > Before I can tell which paths are missing, WM must tell me which > countable set of paths his pseudotree contains. It contains all nodes that can be generated by the countable set of > paths each of which has a tail of infinitely many zeros. Evasive as usual. Which *paths* does the tree contain, you asshole! That was the issue from the beginning, to answer the question how many *paths* there are, and in particular to settle whether the number of *paths* is countable or not. Nobody disputes the fact that the number of nodes is countable. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > The proof is simple. By bijection we exhaust all finite cases. > > Yes, and so what? Why do you want an infinite case in the bijection? > > Because aleph_0 is said to be infinite. > > Yes, it is. But why do you want to have it in the bijection? Why do you > never give a clear answer? There is no aleph_0-th row and no aleph_0-th > column, so I see no reason to have it in the bijection. > > There are aleph_0 elements in B but not in A. You claim that there are > aleph_0 symbols in A while none of the URNs has aleph_0 symbols. That > is false. No, that is true, and easily proven. The contrary is proven much easier. > No, you want to prove that you can add infinitely many rationals to > the interval with rationals removed with the consequences you state. > That is something different. Or are you unable to see the > difference? > > It is proved by the fact that I can add the infinite sequence, hence > the infinite union, of finite initial segments. > > But you can not add the infinite sequence. You have proven that you can > add each element of the infinite sequence, but that is not the same. > > lim n --> oo means that nothing can stop me to add more and more, and > exactly that is the meaning of the infinite set, namely the set that > contains n and with n contains n+1. Not only that is the meaning, the meaning is also that you will never stop > when you add more and more. Of course. That is the meaning of an infinite sequence. > All your moaning about the whole > infinite set is irrelevant. lim [n --> oo ] {1,2,3,...,n} is the whole > infinite set! Yes. And what is true for the terms of a sequence is not necessarily true > for the limit, as you should well know. But well-ordering of the terms of the sequence is necessarily implying well-ordering of the limit, i.e., the infinte set. And now take the sequence a_n = ({q_1, q_2, ..., q_n}, Q {q_1, q_2, ..., q_n}) then you start with a dense ordering Q and you get a sequential well- ordering from that dense ordering. > Being well-ordered is a statement that is valid for the limit, i.e., > the infinite set, if it is valid for every member of the sequence of > finite initial segments. The latter are obviously sequentially > ordered, otherwise they were not initial segments. What is the relation of this with the statement to which you said wrong? > That statement was: > But it does *not* prove that you can add *all* rationals > to that interval with the desired consequences. > So, why do you say wrong to that statement? Because I can add all rationals. The infinite set lim [n --> oo] {q_1, q_2, ..., q_n} is all rationals . === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > The proof is simple. By bijection we exhaust all finite cases. > > Yes, and so what? Why do you want an infinite case in the > bijection? > > Because aleph_0 is said to be infinite. > Yes, it is. But why do you want to have it in the bijection? Why do > you > never give a clear answer? There is no aleph_0-th row and no > aleph_0-th > column, so I see no reason to have it in the bijection. > > There are aleph_0 elements in B but not in A. You claim that there are > aleph_0 symbols in A while none of the URNs has aleph_0 symbols. That > is false. > No, that is true, and easily proven. The contrary is proven much easier. Not by any standard of proof acceptable outside of WM's mytheology. > No, you want to prove that you can add infinitely many rationals > to > the interval with rationals removed with the consequences you > state. > That is something different. Or are you unable to see the > difference? > > It is proved by the fact that I can add the infinite sequence, > hence > the infinite union, of finite initial segments. > But you can not add the infinite sequence. You have proven that you > can > add each element of the infinite sequence, but that is not the same. > > lim n --> oo means that nothing can stop me to add more and more, and > exactly that is the meaning of the infinite set, namely the set that > contains n and with n contains n+1. > Not only that is the meaning, the meaning is also that you will never stop > when you add more and more. Of course. That is the meaning of an infinite sequence. > All your moaning about the whole > infinite set is irrelevant. lim [n --> oo ] {1,2,3,...,n} is the whole > infinite set! > Yes. And what is true for the terms of a sequence is not necessarily true > for the limit, as you should well know. But well-ordering of the terms of the sequence is necessarily implying > well-ordering of the limit, i.e., the infinte set. And now take the > sequence a_n = ({q_1, q_2, ..., q_n}, Q {q_1, q_2, ..., q_n}) then you start with a dense ordering Q and you get a sequential well- > ordering from that dense ordering. As you remove elements of a dense set, one at a time, you never get a set which is any less dense. At every step, there will still be infinitely many members between any two members. Since this property, density, holds for every finite stage, why should it not hold for any and all limit stages? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > æ> æ> æ> The proof is simple. By bijection we exhaust all finite cases. > æ> æ> Yes, and so what? æWhy do you want an infinite case in the > æ> æ> bijection? > æ> æ> Because aleph 0 is said to be infinite. > æ> Yes, it is. æBut why do you want to have it in the bijection? æWhy do > æ> you > æ> never give a clear answer? æThere is no aleph 0-th row and no > æ> aleph 0-th > æ> column, so I see no reason to have it in the bijection. > æ> There are aleph 0 elements in B but not in A. You claim that there are > æ> aleph 0 symbols in A while none of the URNs has aleph 0 symbols. That > æ> is false. > No, that is true, and easily proven. > The contrary is proven much easier. Not by any standard of proof acceptable outside of WM's mytheology. > æ> æ> No, you want to prove that you can add infinitely many rationals > æ> æ> to > æ> æ> the interval with rationals removed with the consequences you > æ> æ> state. > æ> æ> That is something different. æOr are you unable to see the > æ> æ> difference? > æ> æ> It is proved by the fact that I can add the infinite sequence, > æ> æ> hence > æ> æ> the infinite union, of finite initial segments. > æ> But you can not add the infinite sequence. æYou have proven that you > æ> can > æ> add each element of the infinite sequence, but that is not the same. > æ> lim n --> oo means that nothing can stop me to add more and more, and > æ> exactly that is the meaning of the infinite set, namely the set that > æ> contains n and with n contains n+1. > Not only that is the meaning, the meaning is also that you will never stop > when you add more and more. > Of course. That is the meaning of an infinite sequence. > æ> æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ All your moaning about the whole > æ> infinite set is irrelevant. lim [n --> oo ] {1,2,3,...,n} is the whole > æ> infinite set! > Yes. æAnd what is true for the terms of a sequence is not necessarily true > for the limit, as you should well know. > But well-ordering of the terms of the sequence is necessarily implying > well-ordering of the limit, i.e., the infinte set. And now take the > sequence > a n = ({q 1, q 2, ..., q n}, Q {q 1, q 2, ..., q n}) > then you start with a dense ordering Q and you get a sequential well- > ordering from that dense ordering. As you remove elements of a dense set, one at a time, you never get a > set which is any less dense. At every step, there will still be > infinitely æmany members between any two members. Since this property, density, æholds for every finite stage, why should > it not hold for any and all limit stages?- Because in the limit the complimentary set is empty. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > > æ æ> æ> æ> The proof is simple. By bijection we exhaust all finite > cases. > æ> æ> Yes, and so what? æWhy do you want an infinite case in the > æ> æ> bijection? > æ> æ> Because aleph_0 is said to be infinite. > æ> Yes, it is. æBut why do you want to have it in the bijection? æWhy > do > æ> you > æ> never give a clear answer? æThere is no aleph_0-th row and no > æ> aleph_0-th > æ> column, so I see no reason to have it in the bijection. > æ> There are aleph_0 elements in B but not in A. You claim that there > are > æ> aleph_0 symbols in A while none of the URNs has aleph_0 symbols. > That > æ> is false. > No, that is true, and easily proven. > The contrary is proven much easier. > Not by any standard of proof acceptable outside of WM's mytheology. > > æ> æ> No, you want to prove that you can add infinitely many > rationals > æ> æ> to > æ> æ> the interval with rationals removed with the consequences you > æ> æ> state. > æ> æ> That is something different. æOr are you unable to see the > æ> æ> difference? > æ> æ> It is proved by the fact that I can add the infinite sequence, > æ> æ> hence > æ> æ> the infinite union, of finite initial segments. > æ> But you can not add the infinite sequence. æYou have proven that > you > æ> can > æ> add each element of the infinite sequence, but that is not the > same. > æ> lim n --> oo means that nothing can stop me to add more and more, > and > æ> exactly that is the meaning of the infinite set, namely the set that > æ> contains n and with n contains n+1. > Not only that is the meaning, the meaning is also that you will never > stop > when you add more and more. > Of course. That is the meaning of an infinite sequence. > æ> æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ All your moaning about the whole > æ> infinite set is irrelevant. lim [n --> oo ] {1,2,3,...,n} is the > whole > æ> infinite set! > Yes. æAnd what is true for the terms of a sequence is not necessarily > true > for the limit, as you should well know. > But well-ordering of the terms of the sequence is necessarily implying > well-ordering of the limit, i.e., the infinte set. And now take the > sequence > a_n = ({q_1, q_2, ..., q_n}, Q {q_1, q_2, ..., q_n}) > then you start with a dense ordering Q and you get a sequential well- > ordering from that dense ordering. > As you remove elements of a dense set, one at a time, you never get a > set which is any less dense. At every step, there will still be > infinitely æmany members between any two members. > Since this propertyæholds for every finite stage, why should > it not hold for any and all limit stages?- Because in the limit the complimentary set is empty. Does WM claim that it is false of the empty set that between any two members there are infinitely many other members? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > There are aleph_0 elements in B but not in A. You claim that there are > aleph_0 symbols in A while none of the URNs has aleph_0 symbols. That > is false. > > No, that is true, and easily proven. > > The contrary is proven much easier. You have not yet proven the contrary, while I have proven that it is the case. > All your moaning about the whole > infinite set is irrelevant. lim [n --> oo ] {1,2,3,...,n} is the whole > infinite set! > > Yes. And what is true for the terms of a sequence is not necessarily true > for the limit, as you should well know. > > But well-ordering of the terms of the sequence is necessarily implying > well-ordering of the limit, i.e., the infinte set. You have to *prove* that. Not just *assert* it. As properties for the items of a sequence are not necessarily valid for the limit of the sequence, you have to *prove* that it also holds for the limit. > And now take the > sequence > > a_n = ({q_1, q_2, ..., q_n}, Q {q_1, q_2, ..., q_n}) > > then you start with a dense ordering Q and you get a sequential well- > ordering from that dense ordering. I do not know. How do you define the limit in this case? I know of no definition of limits in the case of ordered sets... > What is the relation of this with the statement to which you said wrong? > That statement was: > But it does *not* prove that you can add *all* rationals > to that interval with the desired consequences. > So, why do you say wrong to that statement? > > Because I can add all rationals. The infinite set lim [n --> oo] {q_1, > q_2, ..., q_n} is all rationals . Yes, it is, but it does *not* prove that you can add *all* rationals to that interval with the desired consequences. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > ... > There are aleph_0 elements in B but not in A. You claim that there are > aleph_0 symbols in A while none of the URNs has aleph_0 symbols. That > is false. > > No, that is true, and easily proven. > > The contrary is proven much easier. You have not yet proven the contrary, while I have proven that it is the > case. > All your moaning about the whole > infinite set is irrelevant. lim [n --> oo ] {1,2,3,...,n} is the whole > infinite set! > > Yes. And what is true for the terms of a sequence is not necessarily true > for the limit, as you should well know. > > But well-ordering of the terms of the sequence is necessarily implying > well-ordering of the limit, i.e., the infinte set. You have to *prove* that. Every element of the sequence of finite initial segments is well- ordered per se by its being finite. And every countable set can be well-ordered by definition. There is a bijection from N to the last elements of the initial segments. Those are the elements of the well- ordered set. No problem at all. > And now take the > sequence > > a_n = ({q_1, q_2, ..., q_n}, Q {q_1, q_2, ..., q_n}) > > then you start with a dense ordering Q and you get a sequential well- > ordering from that dense ordering. I do not know. How do you define the limit in this case? I know of no > definition of limits in the case of ordered sets... There is no freedom of defining this or that. If the sequentially well- ordered infinite set {q_1, q_2, q_3, ...} does exists, then it is the limit of the infinite sequence of its initial segments lim [n --> oo ] {q_1, q_2, ..., q_n} and that limit can easily be completed by means of the empty set to become ({q_1, q_2, q_3, ...}, { }) namely the limit of the sequence lim [n --> oo ] ({q_1, q_2, ..., q_n}, Q {q_1, q_2, ..., q_n}) This all is not object to any arbitrary definition, if the sets exist. > What is the relation of this with the statement to which you said wrong? > That statement was: > But it does *not* prove that you can add *all* rationals > to that interval with the desired consequences. > So, why do you say wrong to that statement? > > Because I can add all rationals. The infinite set lim [n --> oo] {q_1, > q_2, ..., q_n} is all rationals . Yes, it is, but it does *not* prove that you can add *all* rationals > to that interval with the desired consequences. In the present version of the proof I need not add the rationals to any interval. I simply take the set Q from the interval, element by element, and obtain a sequentially well-ordered set lim [n --> oo ] ({q_1, q_2, ..., q_n} This is obviously a contradiction, nevertheless possible according to set theory. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > All your moaning about the > whole infinite set is irrelevant. lim [n --> oo ] {1,2,3,...,n} > is the whole infinite set! > > Yes. And what is true for the terms of a sequence is not > necessarily true for the limit, as you should well know. > > But well-ordering of the terms of the sequence is necessarily implying > well-ordering of the limit, i.e., the infinte set. > > You have to *prove* that. > > Every element of the sequence of finite initial segments is well- > ordered per se by its being finite. And every countable set can be > well-ordered by definition. There is a bijection from N to the last > elements of the initial segments. Those are the elements of the well- > ordered set. No problem at all. That is not a proof that the limit is well-ordered. It only shows that the limit *can be* well-ordered. > And now take the > sequence > > a_n = ({q_1, q_2, ..., q_n}, Q {q_1, q_2, ..., q_n}) > > then you start with a dense ordering Q and you get a sequential well- > ordering from that dense ordering. > > I do not know. How do you define the limit in this case? I know of no > definition of limits in the case of ordered sets... > > There is no freedom of defining this or that. If the sequentially well- > ordered infinite set > {q_1, q_2, q_3, ...} does exists, then it is the limit of the infinite > sequence of its initial segments > lim [n --> oo ] {q_1, q_2, ..., q_n} > and that limit can easily be completed by means of the empty set to > become > ({q_1, q_2, q_3, ...}, { }) > namely the limit of the sequence > lim [n --> oo ] ({q_1, q_2, ..., q_n}, Q {q_1, q_2, ..., q_n}) Again you are using limit without defining that. What is the limit of an ordered set? But whatever that may be, using this step by step procedure you will *never* get at the complete well-orering, it will *never* be complete. > This all is not object to any arbitrary definition, if the sets exist. Any definition? What nonsense is that? It is subject to how you *define* a limit of a sequence of ordered sets. I know of no such definition. > That statement was: > But it does *not* prove that you can add *all* rationals > to that interval with the desired consequences. > So, why do you say wrong to that statement? > > Because I can add all rationals. The infinite set lim [n --> oo] {q_1, > q_2, ..., q_n} is all rationals . > > Yes, it is, but it does *not* prove that you can add *all* rationals > to that interval with the desired consequences. > > In the present version of the proof I need not add the rationals to > any interval. I simply take the set Q from the interval, element by > element, and obtain a sequentially well-ordered set > lim [n --> oo ] ({q_1, q_2, ..., q_n} No, you do not get the limit. > This is obviously a contradiction, nevertheless possible according to > set theory. No, this is not possible according to set theory. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > ... > All your moaning about the > whole infinite set is irrelevant. lim [n --> oo ] {1,2,3,...,n} > is the whole infinite set! > > Yes. And what is true for the terms of a sequence is not > necessarily true for the limit, as you should well know. > > But well-ordering of the terms of the sequence is necessarily implying > well-ordering of the limit, i.e., the infinte set. > > You have to *prove* that. > > Every element of the sequence of finite initial segments is well- > ordered per se by its being finite. And every countable set can be > well-ordered by definition. There is a bijection from N to the last > elements of the initial segments. Those are the elements of the well- > ordered set. No problem at all. That is not a proof that the limit is well-ordered. It only shows that > the limit *can be* well-ordered. Simply consider the limit of 1 1,2 1,2,3 ... Can you point to an element of N that is not appearing in its one and only ordinal place in the limit? > And now take the > sequence > > a_n = ({q_1, q_2, ..., q_n}, Q {q_1, q_2, ..., q_n}) > > then you start with a dense ordering Q and you get a sequential well- > ordering from that dense ordering. > > I do not know. How do you define the limit in this case? I know of no > definition of limits in the case of ordered sets... > > There is no freedom of defining this or that. If the sequentially well- > ordered infinite set > {q_1, q_2, q_3, ...} does exists, then it is the limit of the infinite > sequence of its initial segments > lim [n --> oo ] {q_1, q_2, ..., q_n} > and that limit can easily be completed by means of the empty set to > become > ({q_1, q_2, q_3, ...}, { }) > namely the limit of the sequence > lim [n --> oo ] ({q_1, q_2, ..., q_n}, Q {q_1, q_2, ..., q_n}) Again you are using limit without defining that. What is the limit of > an ordered set? But whatever that may be, using this step by step procedure > you will *never* get at the complete well-ordering, it will *never* be > complete. It will be as complete as an incomplete set can be. There is no interpretation in set theory that yields to a more complete infinite set. > > In the present version of the proof I need not add the rationals to > any interval. I simply take the set Q from the interval, element by > element, and obtain a sequentially well-ordered set > lim [n --> oo ] ({q_1, q_2, ..., q_n} No, you do not get the limit. No, the limit is there (if the infinite set is there). > This is obviously a contradiction, nevertheless possible according to > set theory. No, this is not possible according to set theory. It is not possible according to mathematics. It is possible according to set theory. Set theory is not mathematics. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > And now take the > sequence > > a_n = ({q_1, q_2, ..., q_n}, Q {q_1, q_2, ..., q_n}) > > then you start with a dense ordering Q and you get a sequential > well-ordering from that dense ordering. > > I do not know. How do you define the limit in this case? I know of > no definition of limits in the case of ordered sets... > > There is no freedom of defining this or that. If the sequentially well- > ordered infinite set > {q_1, q_2, q_3, ...} does exists, then it is the limit of the infinite > sequence of its initial segments > lim [n --> oo ] {q_1, q_2, ..., q_n} > and that limit can easily be completed by means of the empty set to > become > ({q_1, q_2, q_3, ...}, { }) > namely the limit of the sequence > lim [n --> oo ] ({q_1, q_2, ..., q_n}, Q {q_1, q_2, ..., q_n}) > > Again you are using limit without defining that. What is the limit of > an ordered set? But whatever that may be, using this step by step > procedure you will *never* get at the complete well-ordering, it will > *never* be complete. > > It will be as complete as an incomplete set can be. There is no > interpretation in set theory that yields to a more complete infinite > set. Yeah, whatever. What is your *definition* of the limit of a sequence of ordered sets? You *do* use that term, but do it without specifying what you mean? Do you always want to use meaningless terminology? > In the present version of the proof I need not add the rationals to > any interval. I simply take the set Q from the interval, element by > element, and obtain a sequentially well-ordered set > lim [n --> oo ] ({q_1, q_2, ..., q_n} > > No, you do not get the limit. > > No, the limit is there (if the infinite set is there). Again, meaningless words. The limit may be there, but you do not get at it. > This is obviously a contradiction, nevertheless possible according to > set theory. > > No, this is not possible according to set theory. > > It is not possible according to mathematics. It is possible according > to set theory. Set theory is not mathematics. It is not possible according to set theory. Tell me where in et theory you find that when a sequence has a limit you can get there with a step by step procedure... -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > Again you are using limit without defining that. What is the limit of > an ordered set? But whatever that may be, using this step by step procedure > you will *never* get at the complete well-ordering, it will *never* be > complete. It will be as complete as an incomplete set can be. There are no such things as incomplete sets in sane set theories. WM is just trying to sneak in his potential sets again. > There is no > interpretation in set theory that yields to a more complete infinite > set. The union of any set of sets is more complete than any of WM's potential but not actual sets. It is not possible according to mathematics. It is possible according > to set theory. Set theory is not mathematics. WM's set theory certainly is not mathematics, nor logical, nor of interest to anyone but WM. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > ... > There are aleph_0 elements in B but not in A. You claim that there > are > aleph_0 symbols in A while none of the URNs has aleph_0 symbols. > That > is false. > No, that is true, and easily proven. > > The contrary is proven much easier. > You have not yet proven the contrary, while I have proven that it is the > case. > All your moaning about the > whole > infinite set is irrelevant. lim [n --> oo ] {1,2,3,...,n} is the > whole > infinite set! > Yes. And what is true for the terms of a sequence is not necessarily > true > for the limit, as you should well know. > > But well-ordering of the terms of the sequence is necessarily implying > well-ordering of the limit, i.e., the infinte set. > You have to *prove* that. Every element of the sequence of finite initial segments is well- > ordered per se by its being finite. And every countable set can be > well-ordered by definition. There is a bijection from N to the last > elements of the initial segments. Those are the elements of the well- > ordered set. No problem at all. No proof at all. While it is provable the the union of the set of all finite initial segments of a sequentially ordered set is sequentially ordered, WM has not even proved that, much less anything about the limit of the sequence. And now take the > sequence > > a_n = ({q_1, q_2, ..., q_n}, Q {q_1, q_2, ..., q_n}) > > then you start with a dense ordering Q and you get a sequential well- > ordering from that dense ordering. > I do not know. How do you define the limit in this case? I know of no > definition of limits in the case of ordered sets... There is no freedom of defining this or that. If the sequentially well- > ordered infinite set > {q_1, q_2, q_3, ...} does exists, then it is the limit of the infinite > sequence of its initial segments That WM declares that something is the case does not make it the case anywhere, except possibly within WM's mytheology. This all is not object to any arbitrary definition, if the sets exist. WM only gets to dictate in WM's mytheology. Elsewhere WM has no such godlike powers to override both logic and common sense. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor >> Die Zahlen sind freie Sch.9apfungen des menschlichen Geistes, sie dienen >> als Mittel, um die Verschiedenheit der Dinge leichter und sch.8arfer >> aufzufassen. >> [The numbers are free [creations] of the human mind, they serve as a >> means to grasp the difference of the things more easily and sharper.] >> (R. Dedekind, Was sind und was sollen Zahlen?, 1888) > properly, because Verschiedenheit, Unterschied and Differenz > would all be translated into the same word in English. I thought he > wanted to subtract 6 from 5 or something like that. > Just found a translation by a native speaker (of English): Numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things. B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > ... > {1}, {1,2}, {1,2,3}, ..., {1,2,3,...,n}, ... > > If the set exists, then also the limit of this sequence exists ... > > You have to define what the limit *is*. You do not do so. > > This had already been done in this thread. But see: >http://en.wikipedia.org/wiki/Limit_superior Which definition on that page do you have in mind? The lim inf of a > sequence of sets from the power set of a given set? The lim sup of such > a sequence? The lim inf of such a sequence where the given set is a > topological space? The lim sup of such? And if so, what is the > topology? Note that if the given set is N, than indeed the above sequence > is a sequence of sets in its power set. But if you want the topological > definitions you have to state the topology. And, you have to state whether > you want lim inf or lim sup ;-). You can find that the lim sup definition for the initial segments of N is just what I need. But there is no necessity to define anything more than lim [n --> oo] {1,2,3,...,n} = N. > If the sequential argument fails, then the infinite set does not > exist, actually. It is very simple. > > You think so. The sequential argument indeed does fail. But the infinite > set does exist (and I have no idea what you mean with actually). It is a > consequence of the axiom of infinity, not of sequential argument. > > The axiom of infinity uses the sequential argument: With n there > exists n+1. So the axiom of infinity is a consequence of the > sequential argument. I have no idea where you find such a sequential argument in the axiom of > infinity. As you have no idea, presumably, why Merriam-Webster use cardinal numbers for enumeration purposes? (But you know they do.) Let it be. You need not know everything. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > ... > {1}, {1,2}, {1,2,3}, ..., {1,2,3,...,n}, ... > > If the set exists, then also the limit of this sequence exists > ... > You have to define what the limit *is*. You do not do so. > > This had already been done in this thread. But see: >http://en.wikipedia.org/wiki/Limit_superior > Which definition on that page do you have in mind? The lim inf of a > sequence of sets from the power set of a given set? The lim sup of such > a sequence? The lim inf of such a sequence where the given set is a > topological space? The lim sup of such? And if so, what is the > topology? Note that if the given set is N, than indeed the above sequence > is a sequence of sets in its power set. But if you want the topological > definitions you have to state the topology. And, you have to state whether > you want lim inf or lim sup ;-). You can find that the lim sup definition for the initial segments of N > is just what I need. But there is no necessity to define anything more > than lim [n --> oo] {1,2,3,...,n} = N. > If the sequential argument fails, then the infinite set does not > exist, actually. It is very simple. > You think so. The sequential argument indeed does fail. But the > infinite > set does exist (and I have no idea what you mean with actually). It > is a > consequence of the axiom of infinity, not of sequential argument. > > The axiom of infinity uses the sequential argument: With n there > exists n+1. So the axiom of infinity is a consequence of the > sequential argument. > I have no idea where you find such a sequential argument in the axiom of > infinity. As you have no idea, presumably, why Merriam-Webster use cardinal > numbers for enumeration purposes? (But you know they do.) Let it be. > You need not know everything. Merriam Webster occasionally uses letters for the same purpose, as do many others, so does that make those letters into cardinals? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > As you have no idea, presumably, why Merriam-Webster use cardinal > numbers for enumeration purposes? (But you know they do.) Let it be. > You need not know everything. Merriam Webster occasionally uses letters for the same purpose, as do > many others, so does that make those letters into cardinals? Numbers used for enumeration purposes are ordinals but not cardinals. It is obviously nonsense to argue that a number used for enumerating something is a cardinal number. (My remark above contained some irony. Perhaps I should attach a warning in future.) The old Greek in fact used letters to denote numbers. So letters can be used for that purpose, in particular as there is a bijection, accepted by everybody using Latin letters, between those letters and the first numbers. Instead of 1 you can use A in order to denote the first object. It is uncommen though, to call A a number. Further URNs like o, oo, ooo or i, ii, iii, ... can be used (and frequently are used) to denote ordinal numbers. It is customary, for instance to denote the first three derivatives of a function f by f', f'', f''' by the URNs ', '', and '''. Obviously these are ordinal numbers 1, 2, and 3 enumerating the first, second, and third derivatives. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor As you have no idea, presumably, why Merriam-Webster use cardinal > numbers for enumeration purposes? (But you know they do.) Let it be. > You need not know everything. > Merriam Webster occasionally uses letters for the same purpose, as do > many others, so does that make those letters into cardinals? Numbers used for enumeration purposes are ordinals but not cardinals. Any well known sequence can be used to mark positions in a sequence. By WM's argument, they must all be ordinals, even those things which are not numbers of any type. > It is obviously nonsense to argue that a number used for enumerating > something is a cardinal number. Ennumerating in M-W is ambiguously defined to include both counting and listing in order, so that objects which can serve either purpose can serve both. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > Numbers used for enumeration purposes are ordinals but not cardinals. > Any well known sequence can be used to mark positions in a sequence. > By WM's argument, they must all be ordinals, even those things which are > not numbers of any type. And now this longest sci.math thread ever has reached 9000 posts and shows no signs of slowing down. I've noticed that both here and in the tommy1729 threads, there's been so many debates regarding cardinals vs. ordinals. Ironically, WM appears to accept ordinals but not cardinals, while tommy1729 accepts vice versa. Of course, we all know that the cardinals and ordinals have different meanings in linguistics and in mathematics, so I see no point in looking up the linguistic meanings of the words in Webster. I don't know what it is about this summer, but now I've seen that even Hero, another nonstandard mathematician, has come out of lurking to start posting against Cantor again. WOW! === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 en),gzip(gfe),gzip(gfe) > Numbers used for enumeration purposes are ordinals but not cardinals. > Any well known sequence can be used to mark positions in a sequence. > By WM's argument, they must all be ordinals, even those things which are > not numbers of any type. And now this longest sci.math thread ever has reached 9000 posts > and shows no signs of slowing down. WM is taking a holiday, and his sheer bloody-mindedness was the only thing keeping it going. > I've noticed that both here and in the tommy1729 threads, there's > been so many debates regarding cardinals vs. ordinals. Ironically, > WM appears to accept ordinals but not cardinals, while tommy1729 > accepts vice versa. Of course, we all know that the cardinals and ordinals have different > meanings in linguistics and in mathematics, so I see no point in > looking up the linguistic meanings of the words in Webster. That subthread started some 1500+ posts and 3+ weeks ago. > ... > For some people that is not the case. The first year of the > reign of some Indian kings is their year 0. Or is that > unnatural? > > Very. They should have been deposed. > > Go ahead. They thought it very natural. But apparently you want > to impose your cultural viewpoints on others. > > If the first year is their year 0, what then is their zeroth year? > > Why must there be a zeroth year? > > Because the first is the 1st, not the 0st. First is the ordinal of > the cardinal 1. First come ..., not zeroth come ... No, the first cardinal number is 0. So what? I believe WM was arguing that 0 should not be a natural number. WM thinks that there is a problem with the (linguistically) first (mathematical) natural being 0. This devolved into a discussion of what ordinal and cardinal numbers are in natural English language. At one point we got this surprising admission: > I would say: 1 is the first ordinal number. 2 is the second ordinal > number. first and second are adjectives that are formed using > numbers. But I am not sure about that. I am not a linguist. WM being unsure about something? Well, he was right to be unsure. He was wrong. In English first and second _are_ ordinal numbers, as any number of references have shown. Progress for the crank? No, he refused to accept error in the end. > You should learn: *Numbers* are 1, 2, 3, etc., ordinal as well as > cardinal numbers. In order to indicate the use for ordinal purposes, > the ordinal numbers are appended (sometimes, but not in Merriam > Webste's general use) by the suffixes given in the table of Merriam- > Werbster. This was after being providing numerous references that point-blank contradict him. I find it fascinating how warped this man's brain is. _Why_ is he so utterly insecure that he has to fantasise he is the authority on all topics? Is it ghoulish to find entertainment in his deluded ramblings? Maybe a little... === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > I don't know what it is about this summer, but now I've seen that > even Hero I meant |-|erc -- I forgot how he spells his name. Sorry! === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > I meant |-|erc You think Herc is non-standard MATHEMATICIAN. That's funny. MoeBlee === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > I meant |-|erc You think Herc is [a] non-standard MATHEMATICIAN. That's funny. > Rather a standard CRANK, I'd say. B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > So letters can > be used for that purpose, in particular as there is a bijection, > accepted by everybody using Latin letters, between those letters and > the first numbers. Instead of 1 you can use A in order to denote the > first object. Except in time-tables of former British Rail, where the first footnote was in general 'x', the second 'y' for some tables, but it could also start with 'h' in other tables... -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 en),gzip(gfe),gzip(gfe) > As you have no idea, presumably, why Merriam-Webster use cardinal > numbers for enumeration purposes? (But you know they do.) Let it be. > You need not know everything. > Merriam Webster occasionally uses letters for the same purpose, as do > many others, so does that make those letters into cardinals? Numbers used for enumeration purposes are ordinals but not cardinals. > It is obviously nonsense to argue that a number used for enumerating > something is a cardinal number. To enumerate means to count. Numbers used for enumeration are cardinal numbers. You are wrong. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > As you have no idea, presumably, why Merriam-Webster use cardinal > numbers for enumeration purposes? (But you know they do.) Let it be. > You need not know everything. > Merriam Webster occasionally uses letters for the same purpose, as do > many others, so does that make those letters into cardinals? > Numbers used for enumeration purposes are ordinals but not cardinals. > It is obviously nonsense to argue that a number used for enumerating > something is a cardinal number. To enumerate means to count. Numbers used for enumeration are > cardinal numbers. You are wrong. To enumerate means to determine places in a sequence. That's the job of ordinal numbers. M-W say that third is an ordinal number but they use 2 as ordinal number. EOD === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > To enumerate means to determine places in a sequence. That's the job > of ordinal numbers. M-W say that third is an ordinal number but they > use 2 as ordinal number. That is not the only meaning. At least not in English. Numerous sources here acknowledge two meanings for enumerate: WebsterÍs Concise Electronic Dictionary 5 sense(s) for ñenumerateî 1. enu.87mer.87ate ´ (verb) [enu.87mer.87at.87ed; enu.87mer.87at.87ed; enu.87mer.87at.87ing; enu.87mer.87ates] [CapitalEth] count [CapitalEth] list ´ enu.87mer.87a.87tion (noun) [enu.87mer.87a.87tions] ´ enu.87mer.87a.87tive (adjective) ´ enu.87mer.87a.87tor (noun) [enu.87mer.87a.87tors] Proximity/Merriam-Webster U.S. English Thesaurus 3 meaning(s) for ñenumerateî 1. (verb) to specify one after the other ´ (synonym) list, numerate, tick off ´ (related) run over, tell off, identify, mention, recite, recount, relate, specify 2. (verb) to ascertain the total of units in a collection by noting one after another ´ (synonym) count, number, numerate, tale, tally, tell ´ (related) add, cast, figure, foot, sum, tot, total, calculate, compute, estimate, reckon, tell off 3. (verb) to set down in detail or by particulars ´ (synonym) itemize, inventory, list, particularize, specialize, specify ´ (see also) specify ´ (related) circumstantiate, document, count, number, cite, instance, mention, spell out ´ (antonym) summarize Proximity/Franklin U.S. English Thesaurus 2 meaning(s) for ñenumerateî 1. (verb) to note down items one by one ´ (synonym) catalog, enroll, itemize, inventory, list, particularize, register, tally, check off, tick off ´ (related) note down, itemise, specify 2. (verb) to recite numbers ´ (synonym) count, count down, number, tell, tally, count up dict.org The Collaborative International Dictionary of English v.0.48 1 definition(s) found Enumerate E*numer*ate, v. t. [imp. & p. p. Enumerated; p. pr. & vb. n. Enumerating.] [L. enumeratus, p. p. of enumerare to count out, enumerate; e out + numerare to count, fr. numerus number. See Number.] To count; to tell by numbers; to count over, or tell off one after another; to number; to reckon up; to mention one by one; to name over; to make a special and separate account of; to recount; as, to enumerate the stars in a constellation. [1913 Webster] Enumerating the services he had done. --Ludlow. Syn: To reckon; compute; calculate; count; estimate; relate; rehearse; recapitulate; detail. [1913 Webster] WordNet (r) 2.0 1 definition(s) found enumerate v 1: specify individually; She enumerated the many obstacles she had encountered; The doctor recited the list of possible side effects of the drug [syn: recite, itemize, itemise] 2: determine the number or amount of; Can you count the books on your shelf?; Count your change [syn: count, number, numerate] Moby Thesaurus II by Grady Ward, 1.0 1 definition(s) found 54 Moby Thesaurus words for enumerate: block out, book, calendar, call off, call over, call the roll, catalog, census, count, detail, enroll, enter, file, foliate, identify, impanel, index, inventory, itemize, keep score, list, measure, mention, number, numerate, outline, page, paginate, parse, particularize, pigeonhole, poll, post, program, quantify, quantize, recite, recount, register, relate, resolve, run over, scan, schedule, schematize, score, specialize, specify, tabulate, tale, tally, tell, tell off, tick off Webster's Revised Unabridged Dictionary (1913) 1 definition(s) found Enumerate E*numer*ate, v. t. [imp. & p. p. Enumerated; p. pr. & vb. n. Enumerating.] [L. enumeratus, p. p. of enumerare to count out, enumerate; e out + numerare to count, fr. numerus number. See Number.] To count; to tell by numbers; to count over, or tell off one after another; to number; to reckon up; to mention one by one; to name over; to make a special and separate account of; to recount; as, to enumerate the stars in a constellation. Enumerating the services he had done. --Ludlow. Syn: To reckon; compute; calculate; count; estimate; relate; rehearse; recapitulate; detail. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 en),gzip(gfe),gzip(gfe) > Numbers used for enumeration purposes are ordinals but not cardinals. > It is obviously nonsense to argue that a number used for enumerating > something is a cardinal number. > To enumerate means to count. Numbers used for enumeration are > cardinal numbers. You are wrong. To enumerate means to determine places in a sequence. That's the job > of ordinal numbers. Ordinal number refers, in English, specifically to the class of words that includes first, second, and third. Cardinal number refers, in English, specifically to the class of words that includes one, two, and three. Every dictionary reference I looked at confirms this. In prose we use ordinal numbers to denote position in a sequence. We do not use cardinal numbers for this purpose in prose. No fluent English speaker ever said Johnny came two in the race. When we make a list we often mark the list entries. It is common to use cardinal numbers for this purpose, as if one were counting the list entries. There are many other ways to mark the entries, as Dik and Virgil have pointed out. This convention does not make 1 an ordinal number. It is a peculiarity of how we conventionally mark lists. > M-W say that third is an ordinal number In a previous post you said that 3rd is not a number. Who is wrong, you or M-W? > but they use 2 as ordinal number. No, they use 2 to mark the elements of a list. This is a common way of marking lists that reflects the relation between list-making and counting. This does not make 2 an ordinal number. Meanwhile, M-W clearly state that second is an ordinal number. I have seen no dictionary where two is said to be an ordinal number. If two were an ordinal number then Johnny came two in the race. would be a correct sentence. It is not. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > If two were an ordinal number then Johnny came two in the race. > would be a correct sentence. It is not. Two is the ordinal number while second is the place determined by two. Even in English, there are rudimentary declensions form the Germanic language, though nearly completely lost. Are you married? Do you have a wife then or a wife's? Nevertheless, if your wife has a dog, you will tell us, for instance, that you called your wife's dog beast but not that you called your wife dog beast. Other languages have more distinct endings. Do you think that Senatus Populusque lived in Romanum? FEOD === Subject: Re: A consideration concerning the diagonal argument of G. Cantor If two were an ordinal number then Johnny came two in the race. > would be a correct sentence. It is not. Two is the ordinal number while second is the place determined by > two. Even in English, there are rudimentary declensions form the > Germanic language, though nearly completely lost. To see someone like WM, who is not even mathematically competent in German, try to teach his Germanic version of English mathemtaics to a wide variety of Native English speakers and mathematicians is ludicrous. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 en),gzip(gfe),gzip(gfe) > If two were an ordinal number then Johnny came two in the race. > would be a correct sentence. It is not. Two is the ordinal number while second is the place determined by > two. You are _wrong_. In English, Two is the cardinal number and second is the ordinal number. http://mathworld.wolfram.com/OrdinalNumber.html : In common usage, an ordinal number is an adjective which describes the numerical position of an object, e.g., first, second, third, etc. http://www.bartleby.com/61/12/S0201200.html : The ordinal number matching the number 2 in a series. http://dictionary.infoplease.com/second : next after the first; being the ordinal number for two. http://encarta.msn.com/encnet/features/dictionary/DictionaryResults.aspx?ref id=1861710570 : the ordinal number assigned to item number two in a series http://www.askoxford.com/concise_oed/second_1?view=uk : ordinal number constituting number two in a sequence; 2nd Why are you so relentlessly bloody-minded? You are just wrong. You will not admit it. Why? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor >> If two were an ordinal number then Johnny came two in the race. >> would be a correct sentence. It is not. >> Two is the ordinal number while second is the place determined by >> two. You are _wrong_. In English, Two is the cardinal number and second > is the ordinal number. I'd have to disagree. two is a name and second is an adjective. Neither is a number, as numbers are not words. Seems to me that two can name either the cardinal number two or the ordinal number two depending on the context. I would, however, sort of agree with WM (never thought I'd find myself saying *that*) that second does indeed signify something like the place determined by the number two (cardinal or ordinal) in the (cardinal or ordinal) number series, though I think more generally it signifies the place occupied by the second object in any series of length at least two -- which seems to me to be more or less just what the ordinal number 2 is. (This is more or less Russell's view in The Principles of Mathematics and it also resembles the so-called structuralist view of the ordinal numbers.) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 en),gzip(gfe),gzip(gfe) >> If two were an ordinal number then Johnny came two in the race. >> would be a correct sentence. It is not. >> Two is the ordinal number while second is the place determined by >> two. > You are _wrong_. In English, Two is the cardinal number and second > is the ordinal number. I'd have to disagree. two is a name and second is an adjective. > Neither is a number, as numbers are not words. Seems to me that two > can name either the cardinal number two or the ordinal number two > depending on the context. I would, however, sort of agree with WM > (never thought I'd find myself saying *that*) that second does indeed > signify something like the place determined by the number two > (cardinal or ordinal) in the (cardinal or ordinal) number series, though > I think more generally it signifies the place occupied by the second > object in any series of length at least two -- which seems to me to be > more or less just what the ordinal number 2 is. (This is more or less > Russell's view in The Principles of Mathematics and it also resembles > the so-called structuralist view of the ordinal numbers.) We were discussing linguistics, not mathematics. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor >> If two were an ordinal number then Johnny came two in the race. > would be a correct sentence. It is not. >> Two is the ordinal number while second is the place determined by > two. >> You are _wrong_. In English, Two is the cardinal number and second >> is the ordinal number. >> I'd have to disagree. two is a name and second is an adjective. >> Neither is a number, as numbers are not words. Seems to me that two >> can name either the cardinal number two or the ordinal number two >> depending on the context. I would, however, sort of agree with WM >> (never thought I'd find myself saying *that*) that second does indeed >> signify something like the place determined by the number two >> (cardinal or ordinal) in the (cardinal or ordinal) number series, though >> I think more generally it signifies the place occupied by the second >> object in any series of length at least two -- which seems to me to be >> more or less just what the ordinal number 2 is. (This is more or less >> Russell's view in The Principles of Mathematics and it also resembles >> the so-called structuralist view of the ordinal numbers.) We were discussing linguistics, not mathematics. And pretty much any linguist in the country will tell you that two is is not a number. A number *word*, perhaps, but not a number. Saying two is a number is no different (and no less false) than saying that George Bush (as opposed to George Bush) is a politician. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 en),gzip(gfe),gzip(gfe) >> If two were an ordinal number then Johnny came two in the race. > would be a correct sentence. It is not. >> Two is the ordinal number while second is the place determined by > two. > You are _wrong_. In English, Two is the cardinal number and second >> is the ordinal number. >> I'd have to disagree. two is a name and second is an adjective. >> Neither is a number, as numbers are not words. Seems to me that two >> can name either the cardinal number two or the ordinal number two >> depending on the context. I would, however, sort of agree with WM >> (never thought I'd find myself saying *that*) that second does indeed >> signify something like the place determined by the number two >> (cardinal or ordinal) in the (cardinal or ordinal) number series, though >> I think more generally it signifies the place occupied by the second >> object in any series of length at least two -- which seems to me to be >> more or less just what the ordinal number 2 is. (This is more or less >> Russell's view in The Principles of Mathematics and it also resembles >> the so-called structuralist view of the ordinal numbers.) > We were discussing linguistics, not mathematics. And pretty much any linguist in the country will tell you that two is > is not a number. A number *word*, perhaps, but not a number. Saying > two is a number is no different (and no less false) than saying that > George Bush (as opposed to George Bush) is a politician. I haven't intended to say that the word two is a cardinal number. Maybe my use of quotation marks was incorrect and misleading. Mea culpa? I have said that in English two is a cardinal number and second is an ordinal number, as opposed to WM's claim that two is both a cardinal and an ordinal number in English. Disagree? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor I'd have to disagree. two is a name ... > Indeed. >> We were discussing linguistics, not mathematics. > And pretty much any linguist in the country will tell you that two is > is not a number. A number *word*, perhaps, but not a number. Saying > two is a number is no different (and no less false) than saying that > George Bush (as opposed to George Bush) is a politician. > Well, I've also studied linguistics (some terms). Right: two is a word, not a number. :-) B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Why are you so relentlessly bloody-minded? You are just wrong. > You will not admit it. Why? > A quote: ------------------------------------------------------ _Common characteristics of cranks_ [...] virtually universal characteristics of cranks include: : 3. Cranks rarely if ever acknowledge any error, no matter how trivial. : ------------------------------------------------------ Source: http://en.wikipedia.org/wiki/Crank_(person) B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > Other languages > have more distinct endings. Do you think that Senatus Populusque lived > in Romanum? I thought they lived in Romanus, actually. > FEOD > -- Alan Smaill === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Other languages > have more distinct endings. Do you think that Senatus Populusque lived > in Romanum? I thought they lived in Romanus, actually. As wrong as my typo. But FFEOD === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > Other languages > have more distinct endings. Do you think that Senatus Populusque lived > in Romanum? > I thought they lived in Romanus, actually. As wrong as my typo. naturally ... > But FFEOD -- Alan Smaill === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > To enumerate means to count. Numbers used for enumeration are > cardinal numbers. You are wrong. > > To enumerate means to determine places in a sequence. Enumerate: 1: to ascertain the number of: COUNT 2: to specify one ofter another: LIST where do you find *your* definition? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > ... > æ> To enumerate means to count. Numbers used for enumeration are > æ> cardinal numbers. You are wrong. > æ æ> To enumerate means to determine places in a sequence. Enumerate: 1: to ascertain the number of: COUNT > 2: to specify one ofter another: LIST where do you find *your* definition? in the second paragraph, enumerated by the ordinal number *2*: to specify one after another. Or in Collins: to line up, to put in a line/lines or a row/rows; to list, to enumerate . Can you recognize a *list* in this posting? Hint: it is a very short list, but it is not an empty list and not a degenerated list (with only one entry). === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl > ... > To enumerate means to count. Numbers used for enumeration are > cardinal numbers. You are wrong. > > To enumerate means to determine places in a sequence. > > Enumerate: > > 1: to ascertain the number of: COUNT > 2: to specify one ofter another: LIST > > where do you find *your* definition? > > in the second paragraph, enumerated by the ordinal number *2*: to > specify one after another. labelled by the cardinal number 2. But in (2) you do not *determine* a place in a sequence, but you *specify* a place in a sequence, namely in the list you are enumerating. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > ... > æ> æ> æ> {1}, {1,2}, {1,2,3}, ..., {1,2,3,...,n}, ... > æ> æ> æ> If the set exists, then also the limit of this sequence exists > æ> æ> æ> ... > æ> You have to define what the limit *is*. æYou do not do so. > æ> This had already been done in this thread. But see: > æ>http://en.wikipedia.org/wiki/Limit superior > Which definition on that page do you have in mind? æThe lim inf of a > sequence of sets from the power set of a given set? æThe lim sup of such > a sequence? æThe lim inf of such a sequence where the given set is a > topological space? æThe lim sup of such? æAnd if so, what is the > topology? æNote that if the given set is N, than indeed the above sequence > is a sequence of sets in its power set. æBut if you want the topological > definitions you have to state the topology. æAnd, you have to state whether > you want lim inf or lim sup ;-). > You can find that the lim sup definition for the initial segments of N > is just what I need. But there is no necessity to define anything more > than lim [n --> oo] {1,2,3,...,n} = N. > æ> æ> If the sequential argument fails, then the infinite set does not > æ> æ> exist, actually. It is very simple. > æ> You think so. æThe sequential argument indeed does fail. æBut the > æ> infinite > æ> set does exist (and I have no idea what you mean with actually). æIt > æ> is a > æ> consequence of the axiom of infinity, not of sequential argument. > æ> The axiom of infinity uses the sequential argument: With n there > æ> exists n+1. So the axiom of infinity is a consequence of æthe > æ> sequential argument. > I have no idea where you find such a sequential argument in the axiom of > infinity. > As you have no idea, presumably, why Merriam-Webster use cardinal > numbers for enumeration purposes? (But you know they do.) Let it be. > You need not know everything. Merriam Webster occasionally uses letters for the same purpose, as do > many others, so does that make those letters into cardinals? Natural numbers are 1, 2, 3, ..., cardinal as well as ordinal. By means of the ordinal number 3 you can indicate the third position. 3rd is *not* a number but a property of an object like a number. 3 is the 3rd natural number. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 en),gzip(gfe),gzip(gfe) > 3rd is *not* a number but a property of an object like a number. M-W gives third as an example of an ordinal number. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > 3rd is *not* a number but a property of an object like a number. > Mirriam-Webster gives third as an example of an ordinal number. > Well, WM has some rather peculiar opinions concerning numbers. For example he recently claimed that three trees in a certain garden ARE the number three. (Right, that's indeed what he claimed - not that the three trees are an instance of the number three, ore anything like that, but...) Die drei B.8aume *sind* die Zahl drei. [WM, 12 Apr. 2007] (The three trees *are* the number three.) B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 en),gzip(gfe),gzip(gfe) >> 3rd is *not* a number but a property of an object like a number. > Mirriam-Webster gives third as an example of an ordinal number. > Well, WM has some rather peculiar opinions concerning numbers. For > example he recently claimed that three trees in a certain garden ARE the > number three. (Right, that's indeed what he claimed - not that the three > trees are an instance of the number three, ore anything like that, > but...) > Die drei Baume *sind* die Zahl drei. [WM, 12 Apr. 2007] (The three trees *are* the number three.) thee be free to decree these three trees be three but if I stand till I freeze i'll only see three trees === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > Well, WM has some rather peculiar opinions concerning numbers. For > example he recently claimed that three trees in a certain garden ARE the > number three. (Right, that's indeed what he claimed - not that the three > trees are an instance of the number three, ore anything like that, > but...) > Die drei B.8aume *sind* die Zahl drei. [WM, 12 Apr. 2007] (The three trees *are* the number three.) yes, that's WM's method to get attention! (Unfortunately nobody at the Fachhochschule Augsburg, where he is allowed to teach mathematics) seems to worry about his abilities and the education of the students. Alois === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > Natural numbers are 1, 2, 3, ..., cardinal as well as ordinal. 0 is the cardinality of a set, ergo a cardinal number, but not an ordinl number, as it does not specify the position of any object within any ordering.. > By means of the ordinal number 3 you can indicate the third position. By means of the letter C you can indicate the third position, which apparently is enough to make it an ordinal number in WM's mytheology. > 3rd is *not* a number 3rd is as much an ordinal number as 3 is, since it indicates the third position in order at least as well as 3 does, and is, in fact, merely shorthand for third. 3 is the 3rd natural number. 3 is the 4th cardinal number in order of increasing cardinality. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Natural numbers are 1, 2, 3, ..., cardinal as well as ordinal. 0 is the cardinality of a set, ergo a cardinal number, Cantor says: In diesem Sinne haben wir in den Nummern 1 - 8 dieses Abschnitts die Zeichen 1, 2, 3, ..., nu, ... f.9fr die endlichen Ordnungszahlen, dagegen die Zeichen 1, 2, 3, ..., nu, ... (underlined) f.9fr die endlichen Kardinalzahlen gebraucht. No mentioning of 0 in both cases. Later, when writing about well-ordered sets, he uses the sequence 0, 1, 2, 3, . . . ,omega 0, ... > but not an ordinl > number, as it does not specify the position of any object within any > ordering.. On the other hand, Hrbacek and Jech prove the theorem: 2.10 Theorem The natural numbers are exactly the finite ordinal numbers. So you seem to agree that 0 is not a natural number? Or are H&J in error? ((((or are you in error?)))) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > but not an ordinl > number, as it does not specify the position of any object within any > ordering.. Note that the terminology here is common language terminology, so not the mathematical terminology. > On the other hand, Hrbacek and Jech prove the theorem: > 2.10 Theorem The natural numbers are exactly the finite ordinal > numbers. > > So you seem to agree that 0 is not a natural number? > > Or are H&J in error? ((((or are you in error?)))) *You* are in error by conflating common language terminology with mathematical terminology. Are you perhaps one of those people that says that it is wrong to give a weight of 73 kg? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > {1}, {1,2}, {1,2,3}, ..., {1,2,3,...,n}, ... > > If the set exists, then also the limit of this sequence exists ... > > You have to define what the limit *is*. You do not do so. ... > You can find that the lim sup definition for the initial segments of N > is just what I need. Note that the lim inf definition works just as well! > But there is no necessity to define anything more > than lim [n --> oo] {1,2,3,...,n} = N. But in that the sentence if the set exists, then also the limit of this sequence exists has nearly no meaning. But I asked you for a definition, and apparently you are not willing to provide a single definition for a limit of sets. Note that with the lim sup and lim inf definitions above we have: lim(n -> oo) [1/n, 1] = (0, 1] which contradicts what you have stated some time ago, and also gives lim(n -> oo) {n, n+1, ..., 10*n} = {} which you vehemently denied a long time ago. > The axiom of infinity uses the sequential argument: With n there > exists n+1. So the axiom of infinity is a consequence of the > sequential argument. > > I have no idea where you find such a sequential argument in the axiom of > infinity. > > As you have no idea, presumably, why Merriam-Webster use cardinal > numbers for enumeration purposes? For enumeration: 1. to ascertain the number of: count 2. to specify one after another: list. But note also that M-W agrees that there is both for ordinal and for cardinal numbers a difference between the common language definition and the mathematical definition. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > ... > > {1}, {1,2}, {1,2,3}, ..., {1,2,3,...,n}, ... > > If the set exists, then also the limit of this sequence exists ... > > You have to define what the limit *is*. You do not do so. > ... > You can find that the lim sup definition for the initial segments of N > is just what I need. Note that the lim inf definition works just as well! > But there is no necessity to define anything more > than lim [n --> oo] {1,2,3,...,n} = N. But in that the sentence if the set exists, then also the limit of this > sequence exists has nearly no meaning. because it is a tautology. > But I asked you for a definition, > and apparently you are not willing to provide a single definition I gave you the lim sup definition for the initial segments of N. Be happy with it. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > But I asked you for a definition, > and apparently you are not willing to provide a single definition > > I gave you the lim sup definition for the initial segments of N. Be > happy with it. So you are unwilling to provide a single definition. But you are happy with the definition you provided me with? So you agree now that lim(n -> oo) {n, n+1, ..., 10*n} = {}? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > ... > > {1}, {1,2}, {1,2,3}, ..., {1,2,3,...,n}, ... > > > If the set exists, then also the limit of this sequence > > exists ... > > You have to define what the limit *is*. You do not do so. > ... > You can find that the lim sup definition for the initial segments of N > is just what I need. > Note that the lim inf definition works just as well! > But there is no necessity to define anything more > than lim [n --> oo] {1,2,3,...,n} = N. > But in that the sentence if the set exists, then also the limit of this > sequence exists has nearly no meaning. because it is a tautology. But I asked you for a definition, > and apparently you are not willing to provide a single definition I gave you the lim sup definition for the initial segments of N. Be > happy with it. In other words, WM is either unable to provide one or afraid to try. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > But I have to say that you seem to be the only one who seems to > understand that the questions > - if the natural numbers starts at 0 or 1 > and > - if they are the amalgamation of the ordinal and cardinal (natural) > numbers > are essentially for the stand of the set theoretic claim that there is > a set of all natural numbers. above. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... ... > Easily second + third = five since a sequence in which an element is > the second from the start and the third from the end, consists of five > elements. > > Makes no sense at all. If the second and third are identical that does > not mean that the sequence has five elements. Moreover five != > fifth. > > Why should an operation on ordinal numbers not result in a cardinal > number? You can of course define such an operation, but it is irrelevant with respect to the discussion that mathematical ordinal numbers are not the common language ordinal numbers. With mathematical ordinal numbers the operation + (i.e. ordinal number addition) yields an ordinal number. > But in spite of that, correction with no change in meaning of the > essential claims: > > first + first = one Maybe, but irrelevant. > But that is only a proposal to solve your problem. There are inifnite > many others ansatz (what is the plural of the english word ansatz?) > possible. What is the singular of the English word ansatz? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > æ> Have a look at Merriam-Webster. æBut apparently you prefer non-linguistic > æ> sources for your misinformation. > æ æ> There we find two entries for ordinal number: > æ æ> 1 : a number designating the place (as first, second, or third) > æ> occupied by an item in an ordered sequence -- see number table > æ> 2 : a number assigned to an ordered set that designates both the order > æ> of its elements and its cardinal number > æ æ> So we see the ordinal numbers 1, 2, 3, ... denoting the places as > æ> first, second or third or being assigned to an ordered set designating > æ> among others its cardinal number like 1, 2, 3, ... I do not see > æ> anything that could support your view. Do you? Yes, because your conclusion is wrong. I did not conclude anything bu tonly report what your source says: we see the ordinal numbers 1, 2, 3, ... > æSee the reference given, i.e. > the number table. æNote that the first definition given by M-W is the > common language definition and the second is the mathematical definition. > They are not the same. æ> By the way, the entries themselves are also ordered by ordinal > æ> numbers, namely 1 and 2. No, they are numbered by cardinal numbers. That's the main task of cardinal numbers? Or is the second paragraph two paragraphs? I hope the lurkers see why set theory will never fail with defendors like you. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > æ> Have a look at Merriam-Webster. æBut apparently you prefer > non-linguistic > æ> sources for your misinformation. > æ > æ> There we find two entries for ordinal number: > æ > æ> 1 : a number designating the place (as first, second, or third) > æ> occupied by an item in an ordered sequence -- see number table > æ> 2 : a number assigned to an ordered set that designates both the order > æ> of its elements and its cardinal number > æ > æ> So we see the ordinal numbers 1, 2, 3, ... denoting the places as > æ> first, second or third or being assigned to an ordered set designating > æ> among others its cardinal number like 1, 2, 3, ... I do not see > æ> anything that could support your view. Do you? > Yes, because your conclusion is wrong. I did not conclude anything bu tonly report what your source says: we > see the ordinal numbers 1, 2, 3, ... æSee the reference given, i.e. > the number table. æNote that the first definition given by M-W is the > common language definition and the second is the mathematical definition. > They are not the same. > æ> By the way, the entries themselves are also ordered by ordinal > æ> numbers, namely 1 and 2. > No, they are numbered by cardinal numbers. That's the main task of cardinal numbers? Or is the second paragraph > two paragraphs? > I hope the lurkers see why set theory will never fail with defendors > like you. It will certainly n to be brought down by kooky incompetents like WM. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > There we find two entries for ordinal number: > > 1 : a number designating the place (as first, second, or third) > occupied by an item in an ordered sequence -- see number table > 2 : a number assigned to an ordered set that designates both the order > of its elements and its cardinal number > > So we see the ordinal numbers 1, 2, 3, ... denoting the places as > first, second or third or being assigned to an ordered set designating > among others its cardinal number like 1, 2, 3, ... I do not see > anything that could support your view. Do you? > > Yes, because your conclusion is wrong. > > I did not conclude anything bu tonly report what your source says: we > see the ordinal numbers 1, 2, 3, ... With the first definition is states: see number table. Have you looked at that number table? Can you find evidence in that number table that 1 is an ordinal number in common language? Your conclusion so we see the ordinal numbers 1, 2, 3 is wrong because that is not stated in that definition. > By the way, the entries themselves are also ordered by ordinal > numbers, namely 1 and 2. > > No, they are numbered by cardinal numbers. > > That's the main task of cardinal numbers? Or is the second paragraph > two paragraphs? Cardinal number 1: a number (as 1, 5, 15) that is used in simple counting and that indicates how many elements there are in an assemblage -- see number table 2: the property that a mathematical set has in common with all sets that can be put in one-to-one correspondence with it See, also there a common language and a mathematical definition. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > ... > There we find two entries for ordinal number: > > 1 : a number designating the place (as first, second, or third) > occupied by an item in an ordered sequence -- see number table > 2 : a number assigned to an ordered set that designates both the > order of its elements and its cardinal number > > So we see the ordinal numbers 1, 2, 3, ... denoting the places as > first, second or third or being assigned to an ordered set > designating among others its cardinal number like 1, 2, 3, ... I > do not see anything that could support your view. Do you? > > Yes, because your conclusion is wrong. I did not conclude anything bu tonly report what your source says: we > see the ordinal numbers 1, 2, 3, ... With the first definition is states: see number table. Have you looked > at that number table? Can you find evidence in that number table that > 1 is an ordinal number in common language? Your conclusion so we see > the ordinal numbers 1, 2, 3 is wrong because that is not stated in that > definition. I have two Merriam-Websters, a big one (3d new international dictionary) and an older small one (new collegiate dictionary). The two definitions of ordinal number quoted above appear in precisely this wording in the small one. The big one has only the first. Ralf === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > ... > æ> æ> There we find two entries for ordinal number: > æ> æ æ> æ> 1 : a number designating the place (as first, second, or third) > æ> æ> occupied by an item in an ordered sequence -- see number table > æ> æ> 2 : a number assigned to an ordered set that designates both the order > æ> æ> of its elements and its cardinal number > æ> æ æ> æ> So we see the ordinal numbers 1, 2, 3, ... denoting the places as > æ> æ> first, second or third or being assigned to an ordered set designating > æ> æ> among others its cardinal number like 1, 2, 3, ... I do not see > æ> æ> anything that could support your view. Do you? > æ> æ> Yes, because your conclusion is wrong. > æ æ> I did not conclude anything but only report what your source says: we > æ> see the ordinal numbers 1, 2, 3, ... With the first definition is states: see number table. æHave you looked > at that number table? æCan you find evidence in that number table that > 1 is an ordinal number in common language? I find that eveidence in common language used by Merriam-Webster. The following is not a conclusion but a sentence in Merriam-Webster: > Your conclusion so we see > the ordinal numbers 1, 2, 3 is wrong because that is not stated in that > definition. ... > See, also there a common language and a mathematical definition. Definition? The mathematical definition is not in question and the common language definition can best be seen by looking at common language, namely, Merriam Webster's common-language sentence: we see the ordinal numbers 1, 2, 3, ... . Or would you say that Merriam- Webster misuse English language? That would be bold for a Dutchman. But your behavior in this case is very characteristic and set theoretic. Although you see that your definitions are false and counterfactual, you try to adhere to them. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > With the first definition is states: see number table. Have you looked > at that number table? Can you find evidence in that number table that > 1 is an ordinal number in common language? > > I find that eveidence in common language used by Merriam-Webster. The > following is not a conclusion but a sentence in Merriam-Webster: > > Your conclusion so we see > the ordinal numbers 1, 2, 3 is wrong because that is not stated in that > definition. Where do you the sentence so we see the ordinal numbers 1, 2, 3 in M-W? > See, also there a common language and a mathematical definition. > > Definition? The mathematical definition is not in question and the > common language definition can best be seen by looking at common > language, namely, Merriam Webster's common-language sentence: we see > the ordinal numbers 1, 2, 3, ... . Where do you find that in M-W? > Or would you say that Merriam- > Webster misuse English language? That would be bold for a Dutchman. Perhaps. But first point me to where the misuse occurs in M-W. > But your behavior in this case is very characteristic and set > theoretic. Although you see that your definitions are false and > counterfactual, you try to adhere to them. And you do not even understand how to read a dictionary. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Or would you say that Merriam- > Webster misuse English language? That would be bold for a Dutchman. Perhaps. But first point me to where the misuse occurs in M-W Original quote from MW: http://www.merriam-webster.com/dictionary/Ordinal%20number 1 : a number designating the place (as first, second, or third) occupied by an item in an ordered sequence .84 see number table 2 : a number assigned to an ordered set that designates both the order of its elements and its cardinal number 1 and 2. You can see them? They are followed by colons. These numbers, according to place 1, are designating the place occupied by the item in an ordered sequence. So the ordinal numbers 1, 2, 3, ... are designating the place (as first, second, or third) occupied by an item in an ordered sequence .84 see number table (for the place designations). In http://en.wikipedia.org/wiki/Ordinal number %28linguistics%29 you find In American Sign Language, the ordinal numbers 1 through 9 ... You see? The ordinal numbers 1 ... 9? No? I am sure you will not hesitate to assert that MW designate the places contradiction within this claim by yourself, nobody can help you. But the topic is completely uninteresting, and I will be going to a place with a slow internet access where I will not be willing and able to load an 8000-posts-thread. Therefore: EOD === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl How this part started: > I find that eveidence in common language used by Merriam-Webster. The > following is not a conclusion but a sentence in Merriam-Webster: > Your conclusion so we see > the ordinal numbers 1, 2, 3 is wrong because that is not stated in that > definition. You vehemently denied that it was a conclusion but that it was a quote from M-W. Now: ... > Or would you say that Merriam- > Webster misuse English language? That would be bold for a Dutchman. > > Perhaps. But first point me to where the misuse occurs in M-W > > Original quote from MW: > http://www.merriam-webster.com/dictionary/Ordinal%20number > > 1 : a number designating the place (as first, second, or third) > occupied by an item in an ordered sequence =97 see number table > 2 : a number assigned to an ordered set that designates both the order > of its elements and its cardinal number for the confirmation. > 1 and 2. You can see them? They are followed by colons. They are used as labels, right. The do not designate a place, but are labels. Ar are you now arguing that bus route 21 in Augsburg is the 21-st route? If so, where are the 5-th to 20-th routes? > These numbers, according to place 1, are designating the place > occupied by the item in an ordered sequence. So the ordinal numbers 1, > 2, 3, ... are designating the place (as first, second, or third) > occupied by an item in an ordered sequence =97 see number table (for the > place designations). No, they are cardinal numbers used as labels. The two paragraphs could have just as well been interchanged, labelled by letters or by any other method. > In > http://en.wikipedia.org/wiki/Ordinal_number_%28linguistics%29 > you find > In American Sign Language, the ordinal numbers 1 through 9 ... > > You see? The ordinal numbers 1 ... 9? No? This is not an authorative source. > I am sure you will not hesitate to assert that MW designate the places > contradiction within this claim by yourself, nobody can help you. I see no contradiction. M-W uses cardinal numbers as labels. Just as in many public-transport networks cardinal numbers are used as labels (but not only cardinal numbers are used for that purpose). -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 en),gzip(gfe),gzip(gfe) > > Or would you say that Merriam- > Webster misuse English language? That would be bold for a Dutchman. > Perhaps. But first point me to where the misuse occurs in M-W Original quote from MW: > http://www.merriam-webster.com/dictionary/Ordinal%20number 1 : a number designating the place (as first, second, or third) > occupied by an item in an ordered sequence see number table > 2 : a number assigned to an ordered set that designates both the order > of its elements and its cardinal number 1 and 2. You can see them? They are followed by colons. These numbers, according to place 1, are designating the place > occupied by the item in an ordered sequence. So the ordinal numbers 1, > 2, 3, ... are designating the place (as first, second, or third) > occupied by an item in an ordered sequence see number table (for the > place designations). I am sure you will not hesitate to assert that MW designate the places > contradiction within this claim by yourself, nobody can help you. There is no contradiction. The definition refers to how the words are used in sentences. The use of symbols to mark off items in a list is not part of a sentence so it is not covered by that definition. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 en),gzip(gfe),gzip(gfe) > ... > æ> æ> There we find two entries for ordinal number: > æ> æ > æ> æ> 1 : a number designating the place (as first, second, or third) > æ> æ> occupied by an item in an ordered sequence -- see number table > æ> æ> 2 : a number assigned to an ordered set that designates both the order > æ> æ> of its elements and its cardinal number > æ> æ > æ> æ> So we see the ordinal numbers 1, 2, 3, ... denoting the places as > æ> æ> first, second or third or being assigned to an ordered set designating > æ> æ> among others its cardinal number like 1, 2, 3, ... I do not see > æ> æ> anything that could support your view. Do you? > æ> æ> Yes, because your conclusion is wrong. > æ > æ> I did not conclude anything but only report what your source says: we > æ> see the ordinal numbers 1, 2, 3, ... > With the first definition is states: see number table. æHave you looked > at that number table? æCan you find evidence in that number table that > 1 is an ordinal number in common language? I find that eveidence in common language used by Merriam-Webster. The > following is not a conclusion but a sentence in Merriam-Webster: > Your conclusion so we see > the ordinal numbers 1, 2, 3 is wrong because that is not stated in that > definition. > ... > See, also there a common language and a mathematical definition. Definition? The mathematical definition is not in question and the > common language definition can best be seen by looking at common > language, namely, Merriam Webster's common-language sentence: we see > the ordinal numbers 1, 2, 3, ... . Or would you say that Merriam- > Webster misuse English language? That would be bold for a Dutchman. Take it from an Englishman, you are wrong. In natural English language, cardinal numbers are one, two, three, ... or 1, 2, 3, ... and ordinal numbers are first, second, third, ... or 1st, 2nd, 3rd, ... Some references: Mirriam-Webster: http://www.merriam-webster.com/cgi-bin/dictionary?book=Dictionary&va=ordinal + number : a number designating the place (as first, second, or third) occupied by an item in an ordered sequence Dictionary.com: http://dictionary.reference.com/search?q=ordinal+number&r=66 : Also called ordinal numeral. any of the numbers that express degree, quality, or position in a series, as first, second, and third (distinguished from cardinal number) Wordsmyth: http://www.wordsmyth.net/live/home.php?script=search&matchent=ordinal+number & matchtype=exact : any number that is used to express order in a series, such as first, second, or tenth. (Cf. cardinal number.) Encarta: http://encarta.msn.com/encnet/features/dictionary/DictionaryResults.aspx?ref i d=1861698213 : number showing order: a number used to show the relative position of somebody or something in a sequence, e.g. first, sixth, or 29th Oxford English: http://www.askoxford.com/concise oed/ordinalnumber?view=uk: noun a number defining a thingÍs position in a series, such as ïfirstÍ or ïsecondÍ Wikipedia: http://en.wikipedia.org/wiki/Ordinal number (linguistics) : In linguistics, ordinal numbers are the words representing the rank of a number with respect to some order, in particular order or position (i.e. first, second, third, etc.). Its use may refer to size, importance, chronology, etc. They are adjectives and precede the nouns they are modifying. They are different from the cardinal numbers (one, two, three, etc.) referring to the quantity. All of these show you are wrong. Just how stubborn are you? > But your behavior in this case is very characteristic and set > theoretic. Although you see that your definitions are false and > counterfactual, you try to adhere to them. Please. The irony is almost too much. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 CLR 1.1.4322; .NET CLR 2.0.50727; InfoPath.1),gzip(gfe),gzip(gfe) > ... > æ> æ> There we find two entries for ordinal number: > æ> æ > æ> æ> 1 : a number designating the place (as first, second, or third) > æ> æ> occupied by an item in an ordered sequence -- see number table > æ> æ> 2 : a number assigned to an ordered set that designates both the order > æ> æ> of its elements and its cardinal number > æ> æ > æ> æ> So we see the ordinal numbers 1, 2, 3, ... denoting the places as > æ> æ> first, second or third or being assigned to an ordered set designating > æ> æ> among others its cardinal number like 1, 2, 3, ... I do not see > æ> æ> anything that could support your view. Do you? > æ> æ> Yes, because your conclusion is wrong. > æ > æ> I did not conclude anything but only report what your source says: we > æ> see the ordinal numbers 1, 2, 3, ... > With the first definition is states: see number table. æHave you looked > at that number table? æCan you find evidence in that number table that > 1 is an ordinal number in common language? > I find that eveidence in common language used by Merriam-Webster. The > following is not a conclusion but a sentence in Merriam-Webster: > Your conclusion so we see > the ordinal numbers 1, 2, 3 is wrong because that is not stated in that > definition. > ... > See, also there a common language and a mathematical definition. > Definition? The mathematical definition is not in question and the > common language definition can best be seen by looking at common > language, namely, Merriam Webster's common-language sentence: we see > the ordinal numbers 1, 2, 3, ... . Or would you say that Merriam- > Webster misuse English language? That would be bold for a Dutchman. Take it from an Englishman, you are wrong. In natural English > language, cardinal numbers are one, two, three, ... or 1, 2, > 3, ... Cardinals start at zero, but what do you expect from someone who doesn't know what a billion is? > and ordinal numbers are first, second, third, ... or > 1st, 2nd, 3rd, ... Some references: Mirriam-Webster:http://www.merriam-webster.com/cgi-bin/dictionary?book=Dicti o nary&va=... > : a number designating the place (as first, second, or third) > occupied by an item in an ordered sequence Dictionary.com:http://dictionary.reference.com/search?q=ordinal+number&r=66 > : Also called ordinal numeral. any of the numbers that express > degree, quality, or position in a series, as first, second, and third > (distinguished from cardinal number) Wordsmyth:http://www.wordsmyth.net/live/home.php?script=search&matchent=ordi n al... > : any number that is used to express order in a series, such as > first, second, or tenth. (Cf. cardinal number.) Encarta:http://encarta.msn.com/encnet/features/dictionary/DictionaryResults. a ... > : number showing order: a number used to show the relative position > of somebody or something in a sequence, e.g. first, sixth, or > 29th Oxford English:http://www.askoxford.com/concise oed/ordinalnumber?view=uk: > noun a number defining a thingÍs position in a series, such as > ïfirstÍ or ïsecondÍ Wikipedia:http://en.wikipedia.org/wiki/Ordinal number (linguistics) : > In linguistics, ordinal numbers are the words representing the rank > of a number with respect to some order, in particular order or > position (i.e. first, second, third, etc.). Its use may refer to size, > importance, chronology, etc. They are adjectives and precede the nouns > they are modifying. They are different from the cardinal numbers (one, two, three, etc.) > referring to the quantity. All of these show you are wrong. Just how stubborn are you? > But your behavior in this case is very characteristic and set > theoretic. Although you see that your definitions are false and > counterfactual, you try to adhere to them. Please. The irony is almost too much.- Hide quoted text - - Show quoted text - === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Take it from an Englishman, you are wrong. In natural English > language, cardinal numbers are one, two, three, ... or 1, 2, > 3, ... and ordinal numbers are first, second, third, ... or > 1st, 2nd, 3rd, ... Some references: Mirriam-Webster:http://www.merriam-webster.com/cgi-bin/dictionary?book=Dicti o nary&va=... > : a number designating the place (as first, second, or third) > occupied by an item in an ordered sequence Didn't you forget the ordinal number of this paragraph, namely 1? Didn't you forget the 2nd paragraph (enumerated by 2, not by 2nd) : a number assigned to an ordered set that designates both the order of its elements and its cardinal number? So 2nd can denote a cardinal number? And Merriam-Webster is not writen by English speaking persons? Or did they only make some errors when enumerating their paragraphs by cardinal numbers? You should learn: *Numbers* are 1, 2, 3, etc., ordinal as well as cardinal numbers. In order to indicate the use for ordinal purposes, the ordinal numbers are appended (sometimes, but not in Merriam Webste's general use) by the suffixes given in the table of Merriam- Werbster. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Nntp-Posting-Host: hera.cwi.nl ... > Some references: > > Mirriam-Webster:http://www.merriam-webster.com/cgi-bin/dictionary?book=Dicti o nary&va=... > : a number designating the place (as first, second, or third) > occupied by an item in an ordered sequence > > Didn't you forget the ordinal number of this paragraph, namely 1? Cardinal numbers. > Didn't you forget the 2nd paragraph (enumerated by 2, not by 2nd) Of course not 2nd, you do not enumerate by ordinal numbers. > a > number assigned to an ordered set that designates both the order of > its elements and its cardinal number? So 2nd can denote a cardinal > number? Do you not understand that what is stated under (2) is a definition different from that stated under (1)? And that wat is valid under (1) is not necessarily valid under (2)? 2nd is not an ordinal number according to definition (2). BTW, sometimes enumeration (in the definition of making a list) is done by completely different symbols. Like footnotes in some English books where the symbols asterisk, dagger, double-dagger, paragraph-symbol and others are used according to the fancy of the publisher/printer. Also note that in most British public transport time-tables footnotes are given letters, and 'a' is in general *not* the first footnote, because it is in general not used as a letter for footnotes. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=yKimjgoAAACk5WwPVD4l9HmbpoR6Hmy4 en),gzip(gfe),gzip(gfe) > Take it from an Englishman, you are wrong. In natural English > language, cardinal numbers are one, two, three, ... or 1, 2, > 3, ... and ordinal numbers are first, second, third, ... or > 1st, 2nd, 3rd, ... > Some references: > Mirriam-Webster:http://www.merriam-webster.com/cgi-bin/dictionary?book=Dicti o nary&va=... > : a number designating the place (as first, second, or third) > occupied by an item in an ordered sequence Didn't you forget the ordinal number of this paragraph, namely 1? Didn't you forget that this paragraph gives first, second, and third, not 1, 2, and 3 as example of ordinal numbers? > Didn't you forget the 2nd paragraph (enumerated by 2, not by 2nd) : a > number assigned to an ordered set that designates both the order of > its elements and its cardinal number? So 2nd can denote a cardinal > number? And Merriam-Webster is not writen by English speaking persons? > Or did they only make some errors when enumerating their paragraphs by > cardinal numbers? No error. In English, to enumerate means to count; enumeration is the act of counting. So we enumerate with cardinal numbers. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor All of these show you are wrong. Just how stubborn _are_ you? > Only two things are infinite, the universe and human stupidity, and I'm not sure about the former. (Albert Einstein) B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > When the objects of discussion are linguistic entities ... then that > collection of entities may vary as a result of discussion about them. > A consequence of this is that the 'natural numbers' of today are not > the same as the 'natural numbers' of yesterday. > David Isles: What evidence is there that 2^65536 is a natural number?, > Notre Dame Journal of Formal Logic, Volume 33, Number 4, (1992) > 465-480. > http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.ndjfl/1093634481?abs tract If you would understand that paper (not that it is really difficult, but it is obviously far beyond your grasp) then you would realize that it is in contradiction to such assertions of yours like by short cuts like 10^10^10... we are able to express numbers... in your scrap paper physical constraints of numbers. Generally, anything you quote because you think it would testify in your favour really speaks against you. You are just unable to recognize this. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=U44YcwkAAAAbGXB70Qr7gA3kornmKE4i Gecko/20080325 Ubuntu/7.10 (gutsy) Firefox/2.0.0.13,gzip(gfe),gzip(gfe) > When the objects of discussion are linguistic entities ... then that > collection of entities may vary as a result of discussion about them. > A consequence of this is that the 'natural numbers' of today are not > the same as the 'natural numbers' of yesterday. > David Isles: What evidence is there that 2^65536 is a natural number?, > Notre Dame Journal of Formal Logic, Volume 33, Number 4, (1992) > 465-480. > http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.ndjfl/1093634481?abs t ract I looked at this paper (not terribly carefully) and couldn't really understand it. But I notice (on p. 478) and quote: 'in this paper the position advocated is that natural numbers or better natural number notations are linguistic entities' But this is not what mathematics is about, so surely belongs in ling.philosophy.xyz (whatever xyz is)? Do you think many mathematicians would find the paper interesting? Of course the author starts by commenting that most mathematicians would find the title odd, as I'm sure they would. And 2^65536 isn't even in any genuine way an interestingly large number. I'm old enough to remember when 64K bits (8K bytes these days) was something one could call memory, and not be able to afford. The number we're supposed to be questioning the veracity of is the smallest that can't be directly represented in this memory. Well, um. Why not simply ask Is 43 a natural number? After all, no-one has ever held the Actual Number 43 in their hand; it has no physical existence. It's supposed to be the cardinality class of all collections with 43 elements, but no-one has ever remotely approached looking at all collections with 43 elements, have they? What possible justification can we have for being Really Certain that 43 _is_ a natural number. I think it's absolutely no less likely that 43 turns out not to exist than that 2^65536 does. *And* I have a first sliver of evidence: it does not appear in David Wells' Dictionary of Curious and Interesting Numbers... where all smaller naturals do. Brian Chandler === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > When the objects of discussion are linguistic entities ... then that >> collection of entities may vary as a result of discussion about them. >> A consequence of this is that the 'natural numbers' of today are not >> the same as the 'natural numbers' of yesterday. >> David Isles: What evidence is there that 2^65536 is a natural number?, >> Notre Dame Journal of Formal Logic, Volume 33, Number 4, (1992) >> 465-480. >> http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.ndjfl/1093634481?abs tract I looked at this paper (not terribly carefully) and couldn't really > understand it. But I notice (on p. 478) and quote: 'in this paper the position advocated is that natural numbers or > better natural number notations are linguistic entities' But this is not what mathematics is about, so surely belongs in > ling.philosophy.xyz (whatever xyz is)? I think that sentences like the above are inappropriate in mathematical papers. The author should distinguish natural numbers and something like natural number expressions, even if he thinks (what I don't know) that only the latter are really existing (what wouldn't make much sense for me) Natural number expressions then are connected by rewriting rules. > Do you think many mathematicians would find the paper interesting? Of > course the author starts by commenting that most mathematicians would > find the title odd, as I'm sure they would. And 2^65536 isn't even in > any genuine way an interestingly large number. I'm old enough to > remember when 64K bits (8K bytes these days) was something one could > call memory, and not be able to afford. The number we're supposed to > be questioning the veracity of is the smallest that can't be directly > represented in this memory. Well, um. Why not simply ask Is 43 a natural number? After all, no-one has > ever held the Actual Number 43 in their hand; it has no physical > existence. It's supposed to be the cardinality class of all > collections with 43 elements, but no-one has ever remotely approached > looking at all collections with 43 elements, have they? What possible > justification can we have for being Really Certain that 43 _is_ a > natural number. I think it's absolutely no less likely that 43 turns > out not to exist than that 2^65536 does. *And* I have a first sliver > of evidence: it does not appear in David Wells' Dictionary of Curious > and Interesting Numbers... where all smaller naturals do. And being the smallest natural which is not curious or interesting doesn't make it curious and interesting? Isles' point seems to be the complexity of rewriting procedures necessary to e.g. transform 2^65536 into a sequence of 2^65536 strokes of unitary notation. Rewriting rules must be proven to work as desired, for example that they terminate in a sequence of strokes. For natural number expressions involving exponentials the inductive proofs of this seem necessarily to involve, in some way, numbers that are larger than the numbers appearing in the initial numerical expression. If one views the natural numbers not as given a priori but as result of acts of construction this gives a problem of impredicativity. Something like this seems also to be the point of view in Nelson's Predicative Arithmetic which is downloadable from his website and was published in Ann of Math Studies, so there probably are people finding that interesting (among them the proof theoretician Samuel Buss, who has some pertinent material on his website) And, of course, Mr. M.9fckenheim finds the title of Isles' paper appealing, because this title but not the contents seems to fit into M.9fckenheim's theory of the natural numbers which is by far the weirdest I have ever seen (see M.9fckenheim's papers at the arxiv). According to M.9fckenheim, naturals can go in and out of existence, and the natural number sequence can have holes, but induction works nevertheless. A number needs some kind of physical material representation to exist (Frege explained in his Grundlagen at length why such ideas are nonsense), and since the material universe is finite there is a finite bound for the existence of numbers or for the length of numerical expressions; the number consisting of the first 9^9^9 digits of the decimal expansion of pi for example can not exist in M.9fckenheim's world. But, crazily, by using abbreviative numerical expressions, arbitrarily large natural numbers can be brought into existence. For example, 9^9^9^9^9^9 does or at least can M.9fckenheim-exist, although it is much larger than the above mentioned number which definitely does not exist (how then can one compare those two numbers, one of which is non-existent? For M.9fckenheim, a number to exist must be effectively comparable to any other existing number; in other words, there can not be any unsolved problems in M.9fckenmathics, as any mathematical problem can be cast into a question about which one of two naturals is the larger). The fact that the physical restrictions M.9fckenheim wants to apply to numerical expressions would also apply to schemes of abbreviation of numerical expressions and therefore arbitrarily large numbers are ruled out is obviously beyond the physical restrictions of M.9fckenheim's brain. But also, Isles' problems about rewriting natural number expressions do spoil M.9fckenheim's ideas about getting arbitrarily large numbers through abbreviative notation - no matter how pertinent Isles' paper is for real mathematics. Ralf === Subject: Re: A consideration concerning the diagonal argument of G. Cantor If there is a collection of five apples and a collection > of six apples, what is the difference between this collections? Is this difference only there until the natural numbers are > invented by men? [Albrecht] > following, I am still puzzled by the sentence above. If natural > numbers *heighten* differences between collections, then why in > blazes should the difference *disappear* once the natural numbers > are invented? > IMHO Albrecht wanted to express the question, if the difference between those two collections depends on the invention of the natural numbers. I.e if it would vanish without the presence of the natural As soon as we can say five and six the two collections > of apples are indistinguishable? What kind of nonsense is that? > Again, (I guess) he just meant it the other way round. But NO ONE claimed that those differences are created by the numbers. One of the problems of many cranks seems to be that they are not able to comprehend fine distinctions in what others (especially) mathematicians express. The numbers are free inventions of the human mind, they serve as a means to grasp the difference of the things more easily and sharper. (R. Dedekind, Was sind und was sollen die Zahlen?, 1888) Dedekind did not say that the /difference of the things/ depends on the invention of numbers BUT (almost contrary to that point of view) that numbers are a means to grasp that difference /more easily and sharper/. B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor >> I've said it before, and I'll say it again -- Robinson's hyperreals >> prove that some (maybe not _all_, but _some_) of what WM >> desires in a theory can be made rigorous. >> What in idiotic babbling. Can't this idiot just shut up? Sorry, Moe but I just read this nonsense, reading your posts. I've kill-filed this &%$%$%%$%& some time ago. B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor >> Thus we come to the conclusion that Robinson's hyperreals >> are to be classified as _nonclassical_, not _classical_, >> analysis -- since nonstandard is part of nonclassical. Thus >> I disagree with the standard mathematicians who claim that >> Robinson was working in classical mathematics. > Man, you manage to botch nearly everything you touch. Robinson is > working in classical mathematics in the sense that he uses classical > logic applied to the axioms of ZFC. BOTH standard analysis and non- > standard analysis are formalizable in ZFC. > Hell, this guy really is an idiot. Of course non-standard analysis is part of classical mathematics (just like standard or classical analysis). I disagree with the standard mathematicians who claim ... Obviously some sort of meta-crank. B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor As Robinson says, Leibniz, like Hilbert, regarded infinitary entities > as ideal, or fictitious, additions to concrete Mathematics. > Anyone who is not a Platonist (realist) and is not convinced that infinite entities are physical objects will take the same stance, I guess. Though it escapes me why there should be a difference between those fictitious entities and other mathematical objects. Are natural numbers physical objects? Is any (finite or infinite) set a physical object? If so WHERE are they? What are their physical properties? :-o (Where are the points, lines and planes of geometry? Are those physical entities? etc. etc.) To make a long story short: imho there's no such thing as concrete Mathematics; though there certainly are concrete _applications_ of mathematics. (And BOTH types of mathematical objects, finite and infinite, are -or can be- used for this task.) B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor I'll take a look at these, then. > It's true. But CANTOR also said that it doesn't matter if infinitely many entities actually do exist or not, mathematical theories are not based on (do not depend on) physical reality. (More or less his words.) Either WM is intentionally lying or simply does not understand the significance of Cantors statements, as usual. (I suspect the latter.) B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor I'll take a look at these, then. > It's true. But CANTOR also said that it doesn't matter if infinitely many > entities actually do exist or not, mathematical theories are not based on > (do not depend on) physical reality. > (More or less his words.) This is of course what the issue is, and those quotes simply do not address this point at all. > Either WM is intentionally lying > or simply does not understand the significance of Cantors statements, > as usual. (I suspect the latter.) That would be my guess also. > B. -- For every line of Cantor's list it is true that this line does not > contain the diagonal number. Nevertheless the diagonal number may > be in the infinite list. (WM, sci.logic) -- Alan Smaill === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > I'll take a look at these, then. > It's true. But CANTOR also said that it doesn't matter if infinitely many > entities actually do exist or not, mathematical theories are not based on > (do not depend on) physical reality. > (More or less his words.) > This is of course what the issue is, and those quotes simply do not address > this point at all. Either WM is intentionally lying > or simply does not understand the significance of Cantors statements, > as usual. (I suspect the latter.) That would be my guess also. Why not both? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor >> It's true. But CANTOR also said that it doesn't matter if infinitely many >> entities actually do exist or not, mathematical theories are not based on >> (do not depend on) physical reality. (More or less his words.) [See below.] This is of course what the issue is, and those quotes simply do not address > this point at all. > Ah, I just found a translation of the relevant statements I had in mind here, very interesting stuff, imho: ---------------------------------------------------------------- We can speak of the actuality [Wirklichkeit] or existence of the integers, finite as well as infinite, in /two/ senses; but strictly speaking they are the same two relationships in which in general the reality of any concepts and ideas can be considered. First, we may regard the integers as actual [wirklich] in so far as, on the basis of definitions, they occupy an entirely determinate place in our understanding, are well distinguished from all other parts of our thought, and stand to them in determinate relationships, and thus modify the substance of our mind in a determinate way; let us call this kind of reality of our numbers their /intrasubjective/ or /immanent reality/. But then, reality can also be ascribed to numbers to the extent that they must be taken as an expression or copy [Abbild] of the events and relationships in the external world which confronts the intellect, or to the extent that, for instance, the various number-classes (I), (II), (III), etc. are representatives of powers that actually occur in physical and mental nature. I call this second kind of reality the /transsubjective/ or the /transient reality/ [/transiente Realit.8at/] of the integers. Because of the thoroughly realistic but, at the same time, no less idealistic foundation of my point of view, I have no doubt that these two sorts of reality always occur together in the sense that a concept designated in the first respect as existent always also possesses in certain, even infinitely many, ways a transient reality. To be sure, the determination of this transient reality is often one of the most troublesome and difficult problems of metaphysics, and must frequently be left to the future, when the natural development of one of the other sciences will uncover the transient meaning of the concept in question. This linking of both realities has its true foundation in the /unity of the Universe [All] to which we ourselves belong/. Ö The mention of this linking has here only one purpose: that of enabling one to derive from it a result which seems to me of very great importance for mathematics, namely, that mathematics, in the development of its ideas has /only/ [/einzig und allein/] to take account of the /immanent/ reality of its concepts and has /absolutely no/ obligation to examine their /transient/ reality. Because of this remarkable feature Öwhich distinguishes mathematics from all other sciences and provides an explanation for the relatively easy and unconstrained manner with which one may operate with itÖ it especially deserves the name of /free mathematics/, a designation which, if I had the choice, would be given precedence over the now usual 'pure' mathematics. Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other and also stand in exact relationships, ordered by definitions, to those concepts which have previously been introduced and are already at hand and established. In particular, in the introduction of new numbers it is only obligated to give definitions of them which will bestow such a determinacy and, in certain circumstances, such a relationship to the older numbers that they can in any given instance be precisely distinguished. As soon as a number satisfies all these conditions it can and must be regarded in mathematics as existent and real. I think this is the reason, hinted at in Û4, why one must regard the rational, irrational, and complex numbers as being every bit as existent as the finite positive integers. It is not necessary, I believe, to fear, as many do, that these principles present any danger to science. For in the first place the designated conditions, under which alone the freedom to form numbers can be practised, are of such a kind as to allow only the narrowest scope for discretion. Moreover, every mathematical concept carries within itself the necessary corrective: if it is fruitless or unsuited to its purpose, then that appears very soon through its uselessness, and it will be abandoned for lack of success. But every superfluous constraint on the urge to mathematical investigation seems to me to bring with it a much greater danger, all the more serious because in fact absolutely no justification for such constraints can be advanced from the essence of the scienceÖfor the /essence of mathematics/ lies precisely in its /freedom/. ---------------------------------------------------------------- G. Cantor, Grundlagen einer allgemeinen Mannigfaltigkeitslehre, 1883) [Foundations of a General Theory of Manifolds: A Mathematico- Philosophical Investigation into the Theory of the Infinite. Translated Yes it's a rather long text. But those two introductory paragraphs are needed to understand the meaning of the third paragraph which is the central point of this text. (They serve as a some sort of prelude, supplying material as preparation for the main message... :-) The two remaining paragraphs speak for themselves. A rather famous statement (in German math circles) is the sentence: ...the essence of mathematics lies ... in its /freedom/. Why, oh why did M.9fckenheim not quote that statement? :-o >> Either WM is intentionally lying or simply does not understand the >> significance of Cantors statements, as usual. (I suspect the latter.) > That would be my guess also. > Right. B. Cantor closes the whole chaper with the following paragraphs: If I had not discovered this property of mathematics by means of the reasoning I have described, then the entire development of the science itself, as we find it in our century, would have led me to exactly the same opinions. Had /Gauss/, /Cauchy/, /Abel/, /Jacobi/, /Dirichlet/, /Weierstrass/, /Hermite/, and /Riemann/ always been constrained to subject their new ideas to a metaphysical control, we should certainly not now enjoy the magnificent structure of the modern theory of functions which, although it was designed and erected in full freedom without [transient] purposes, nevertheless, in its applications to mechanics, astronomy, and mathematical physics, already discloses its transient meaning, as was to be expected; and we should not be seeing the great upswing in the theory of differential equations brought about by /Fuchs/, /Poincare/, and many others, if these distinguished forces had been restrained and tied down by outside influences; and if /Kummer/ had not exploited the freedom, rich in its consequences, of introducing so-called 'ideal' numbers into number theory, we should today not be able to admire the important and distinguished algebraic and arithmetical works of /Kronecker/ and /Dedekind/. Entitled though mathematics is to move in complete freedom from all metaphysical fetters, I am not, however, able to concede the same right to 'applied' mathematics, such as, for example, analytic mechanics and mathematical physics. These disciplines are in my opinion in their foundations as well as in their aims /metaphysical/; if they seek to make themselves free from metaphysics, as has been recently proposed by a celebrated physicist [Gustav Kirchoff], they degenerate into the form of a 'description of nature' in which the fresh breeze of free mathematical thoughtÖas well as the power of /explaining/ and [to /fathom/] natural phenomenaÖmust be absent. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Mathematics is in its development entirely free and is only bound in > the self-evident respect that its concepts must both be consistent with > each other and also stand in exact relationships, ordered by > definitions, to those concepts which have previously been introduced and > are already at hand and established. In particular, in the introduction > of new numbers it is only obligated to give definitions of them which > will bestow such a determinacy and, in certain circumstances, such a > relationship to the older numbers that they can in any given instance be > precisely distinguished. As soon as a number satisfies all these > conditions it can and must be regarded in mathematics as existent and > real. I think this is the reason, hinted at in Û4, why one must regard > the rational, irrational, and complex numbers as being every bit as > existent as the finite positive integers. (G. Cantor, Grundlagen einer allgemeinen Mannigfaltigkeitslehre, 1883) > It's an interesting observation that Frege seems to have referred to this very paragraph in his famous Grundlagen der Analysis (1884), Û84 /Infinite Numbers/ Û84. Contrasted with the finite Numbers are the infinite Numbers. The Number which belongs to the concept finite Number is an infinite one. Let us symbolize it by, say, oo_1 [Cantor: aleph_0]! If it were a finite Number, it could not follow in the series of natural numbers after itself. But it can be shown that this is what oo_1 does. About the infinite Number oo_1 so defined there is nothing mysterious or wonderful. The Number which belongs to the concept F is oo_1 means no more and no less than this: that there exists a relation which correlates one to one the objects falling under the concept F with the finite Numbers. In terms of our definitions this has a perfectly clear and unambiguous sense; and that is enough to justify the use of the symbol oo_1 and to assure it of a meaning. That we cannot form any idea of an infinite Number is of absolutely no importance; the same is equally true of finite Numbers. So regarded, our Number oo_1, has a character as defined as that of any finite Number; it can be recognized again beyond doubt as the same, and can be distinguished from every other. Û85. It is only recently that infinite Numbers have been introduced, in a remarkable work by G. CANTOR.*) I heartily share his contempt for the view that in principle only finite Numbers ought to be admitted as actual [wirklich]. Perceptible by the senses these are not, nor are they spatial-any more than fractions are, or negative numbers, or irrational or complex numbers; and if we restrict the actual to what acts on our senses or at least produces effects which may cause sense-perception as near or remote consequences, then naturally no number of any of these kinds is actual. But actually we have no need at all to appeal to any such sense-perception in proving theorems. Any name or symbol that has been introduced in a logically unobjectionable manner can be used in our inquiries without hesitation, and here our Number oo_1 is as sound as Two or Tree. _____________________ *) G. Cantor, Grundlagen einer allgemeinen Mannigfaltigkeitslehre, 1883. B. Reference: Gottlob Frege, The Foundations of Arithmetic, Translated by J. L. Austin, 2nd revised edition, 1953. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Ooops... A typo, corrected. It's an interesting observation that Frege seems to have referred to > this very paragraph in his famous Grundlagen der Arithmetik (1884), Û84 > B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > I'll take a look at these, then. > It's true. But CANTOR also said that it doesn't matter if infinitely many > entities actually do exist or not, mathematical theories are not based on > (do not depend on) physical reality. > (More or less his words.) > Of course it may be more satisfying for you to believe in an incorrect and unfounded opinion of a dubious source than in the many correct quotes I gave you here. But if your only aim is boosting your ego, why do you post here at all? > This is of course what the issue is, and those quotes simply do not address > this point at all. You asked for concrete geometrical sets. I showed you Cantor's extended works on point sets. What is lacking? Your comprehension of German or of mathematics or of both? === Subject: Re: generalizations of Scheeffer's Theorem > |It was written by M. B. Porter and appeared in the Bulletin > |to de la Vallee Poussin because Schoenflies had said that > |a theorem in de la Vallee Poussin's Cours, as stated, > |was illogical or contradictory. > | > |At the end of the review, an extract of > |de la Vallee Poussin's reply is reproduced. > |I think the problem has to do with > |de la Vallee Poussin's usage of sauf peut-etre, > |which I can imagine might confuse a non-native > |speaker of French. It strikes me as fairly lame for Schoenflies to > make this sort of mistake. Peut-etre is possibly; > so the term is except possibly on a set.... > de la Vallee Poussin says that this phrase has a > subjective sense, and the reviewer says he thinks it > can be taken in an objective sense. Schoenflies > objection is that the derivatives would be equal > everywhere, and not everywhere except on a set E1, > if they differ by a constant. [...] > |I'd be interested to know how you would translate the > |statement of the theorem(?) in English. My French is not outstanding, but it seems to be this: If, in an interval (a,b), two functions f_1(x) and > f_2(x) have their right superior derivatives (?): > 1) finite in each point except perhaps in a set E_1, > and 2) equal except perhaps in a set of measure zero, > the two functions only differ by a constant unless > E_1 contains a perfect set. I wonder why there are those perhaps, peut-etre, twice. The Dini derivates, AFAIK, consider (a) right limits or left limits (but not both) and (b) limsups or liminfs (but not both) for a total of four combinations. Extended real values are ok by some. In de la Vallee Poussin's reply, I think he says that two +oo right superior Dini derivates aren't necessarily the same. Also, the perfect set may not be empty, which was probably the case in the terminology of the day. with f_1(x) = 0 and f_2(x) = 1, conditions (1) and (2) when using for all quantifiers produce what we call vacuously true sentences, that that was Poussin's way of saying that kind of thing, but Schoenflies decoded it in a way where except implies there is an x1 where (1) is not true and an x2 where (2) is not true ... It still seems an overstatement to call the theorem illogical if, as may be the case, Schoenflies didn't ask Poussin for clarification before calling it illogical. David Bernier === Subject: Re: Inferior mathematics and science > but I'm >> not even convinced the system's broken. Your answer is short: Current crisis is America, and a statement by senator John McCain that > (In CNN internet, July 26,2008): ñThe United States of America is committed to making sure that there > is never a second Holocaust. That will be what I do as president of > the United States.î But why do you think he is even thinking of making such a statement? Iran is facing an ultimatum from the US and allies on budging towards stopping uranium enrichment. The statement of McCain could allude to the current stalemate and hint at his policy ... === Subject: Re: Inferior mathematics and science <5mqm8455m4shgpus0383l7uie32cjfj5s8@4ax.com> <7b0p84l80tjq9ocmc9v5888g9lpcg9j2rk@4ax.com> posting-account=JpxxPAgAAAAgwzQIYqn4j6syK-YhOmcF Gecko/20070309 Firefox/2.0.0.3,gzip(gfe),gzip(gfe) > Alluha Akbar! I am very pleased that you brought the MoslemÍs phrase about GOD, ñGOD > IS GREATî. This is the first step (remedy) for solving worldÍs problems in > particular American crisis. Dr.M.Basti the first step for solving American crisis is to throw like you out of this country. === Subject: Re: Inferior mathematics and science a beady eye, and foamed wildly: >> Alluha Akbar! >> I am very pleased that you brought the MoslemØs phrase about GOD, >> «GOD IS GREATÁ. >> This is the first step (remedy) for solving worldØs problems in >> particular American crisis. >> Dr.M.Basti the first step for solving American crisis is to throw like you out > of this country. After that, get rid of all the white people. -- ________________________________________________________________________ Hail Eris! Cthulhu fhtagn! mhm 29x21; Top Asshole #3; Lits Slut #16 Chas. E. Pemberton; Most Hated Usenetizen of All Time #13 Gutter Chix0r #17; BowTie's Spuriously Accused Pedo Photographer #4 COOSN-029-06-71069; Usenet Ruiner #5; Official Chung Demon AUK Psycho & Felon #21; Parrot & Zombie #2 Anonymous Psycho Criminal #18 PIERRE SALINGER MEMORIAL HOOK, LINE & SINKER -- June 2008 Life size models of Cthulhu, on sale now! Kolofilia between a human and another human is as depraved as ing animals. -- Agamemnon, poutso kelftis, just plain doesn't like sex, Roe V Wade has zero bearing on my existence other than it affects it adversely. Now, that is not me taking the Lord's name in vain. For the most part, morality is universal. -- John Easily Shocked Laws count, the US Constitution count more, and we need to have judges on the bench who are going to Carry Out those laws, not Make Law or Interpret Law. -- John Easily Shocked contradicts his own words on the overriding importance of society's reluctance to accept I heard that you are still trespassing in the USA. If it's black, it refuses to work and it accuses whites of racism. What a joke. NIGGERISH ALLEGIANCE YOU HAVE TO TRYING TO GET WHITE PEOPLE TO HAND OFF OTHER WHITE PEOPLE TO SOMEONE YOU THINK IS NOT AGAINST YOUR CRIMINAL ALLEGIANCE?????? Too afraid to tell the truth? WIMPS! COWARDS! LIARS! MILITANT ASSPRICKS! LOSERS! FAILED BULLBOYS WHOSE CANDY HAS NO RED ON IT! YOU KNOW IT TO BE TRUE! I LICKED THE RED OFF YOUR CANDY BECAUSE YOU ARE YOUR ILK HAVEN'T GOT ANY FURY! THAT'S WHY YOU CAN'T BEAT ME VIA ANY LAWFUL MEANS WHATSOEVER! YOU'RE A being found all over the Carolinas, after his reply to Panama Floyd, in === Subject: Re: Inferior mathematics and science <5mqm8455m4shgpus0383l7uie32cjfj5s8@4ax.com> <7b0p84l80tjq9ocmc9v5888g9lpcg9j2rk@4ax.com> posting-account=mgs1FwoAAABD3j5T_RLZ06yrgt2dghDu Gecko/20050915,gzip(gfe),gzip(gfe) > Alluha Akbar! I am very pleased that you brought the MoslemÍs phrase about GOD, ñGOD > IS GREATî. This is the first step (remedy) for solving worldÍs problems in > particular American crisis. At least now we know why you hate the inferior peoples. -- Therefore when they (the Jews) revoltingly persisted in what they had been forbidden, We said to them: Be as apes, despised and hated. -- Qur'an 7:166 === Subject: Re: Inferior mathematics and science <5mqm8455m4shgpus0383l7uie32cjfj5s8@4ax.com> <7b0p84l80tjq9ocmc9v5888g9lpcg9j2rk@4ax.com> posting-account=ee2apQoAAABJNMlLTFasCJw9Nfo9FmYk Gecko/20020924 AOL/7.0,gzip(gfe),gzip(gfe) HTTP/1.1 cache-ntc-ad09.proxy.aol.com[CFC874CB] (Traffic-Server/6.1.5 [uScM]) > At least now we know why you hate the inferior peoples. I do not hate any groups. But excessive occupation of power by those so-called ñ Inferior peoplesî (in the past) particularly in the USA creates a serious treat to the world stability. I am sure there is a radius of acceptability of any laws such as ñ affirmative actionî which has long been abused. It is quite wrong pointing out these issues referred to as a hate label. Obviously I would not allow my mathematics (including myself) to be an instrument of those groups for corruption in academia. They need to fix their actions now. Dr.M.Basti === Subject: Re: Inferior mathematics and science <5mqm8455m4shgpus0383l7uie32cjfj5s8@4ax.com> <7b0p84l80tjq9ocmc9v5888g9lpcg9j2rk@4ax.com> posting-account=ee2apQoAAABJNMlLTFasCJw9Nfo9FmYk Gecko/20020924 AOL/7.0,gzip(gfe),gzip(gfe) HTTP/1.1 cache-ntc-aa05.proxy.aol.com[CFC87409] (Traffic-Server/6.1.5 [uScM]) I make it clearer. If we consider the centuries history of Christian culture and its > relationship with some minority Groups in America and Europe, clearly > the very position of power in many institutions by those groups (as > mentioned before) creates crisis. This I believe, it is a deep and difficult issue to digest. I have to firmly emphasize that the key to problem solving of the world at large, will be for us to understand the GodÍs sphere of influence in ñthe universeî and as a Moslem believing in this quote: î Allahu akbarî This means GOD IS GREAT. http://i-cias.com/e.o/allahuak.htm Dr.Mehran Basti === Subject: Re: Inferior mathematics and science <5mqm8455m4shgpus0383l7uie32cjfj5s8@4ax.com> <7b0p84l80tjq9ocmc9v5888g9lpcg9j2rk@4ax.com> posting-account=ee2apQoAAABJNMlLTFasCJw9Nfo9FmYk Gecko/20020924 AOL/7.0,gzip(gfe),gzip(gfe) HTTP/1.1 cache-ntc-ab06.proxy.aol.com[CFC87446] (Traffic-Server/6.1.5 [uScM]) î Allahu akbarî This means GOD IS GREAT. http://i-cias.com/e.o/allahuak.htm Possibly the better translation is: ñGod is most greatî. Dr.Mehran Basti === Subject: Re: Inferior mathematics and science <5mqm8455m4shgpus0383l7uie32cjfj5s8@4ax.com> <7b0p84l80tjq9ocmc9v5888g9lpcg9j2rk@4ax.com> posting-account=ee2apQoAAABJNMlLTFasCJw9Nfo9FmYk Gecko/20020924 AOL/7.0,gzip(gfe),gzip(gfe) HTTP/1.1 cache-ntc-ac08.proxy.aol.com[CFC87489] (Traffic-Server/6.1.5 [uScM]) Those who made statements such as ñ religion is an opium of massesî or ñ religion is itself a problemî just are na.95ve about the history and its trends. Carl Marx perfectly knew about the history of Christianity relative to his own religion. In order to combat it, he came up with the idea of communism, with the hope of controlling anti-Semitism in Christianity in broad sense. While his ideas was successful to bring a communist regime in the former Soviet Union, but only lasted about 70 years with massive atrocities and gulags and sufferings of millions of its citizens. Shah of Iran also felt his army was strong enough to over rule many demands of the established religious authorities, thus his regime was also toppled. I have no doubt that some of the crisis in the Western Europe and America (today) is about ill understanding of its governments and their hand picked advisors, about the complex inter cultural relationships rooted in religious hierarchy of the society. As mentioned before the very position of some minority groups in many positions of power is contrary to the norms and traditions of religious establishments, and thus I believe are roots current crisis in America. Particularly the control of academic institutions by a few (of a minority status) is a great mistake by those involved in its operations. When Americans voted to get involved in World War II, against Germany, the minority groups (those I had mentioned before) were not in power. Having such power in every aspects of society possibly prevents Americans for any similar help in the future. I strongly believe voluntary evacuation of power to a normal means will be part of the solution. In short playing with religion (as we see now in the society in variety of its forms) means playing with fire. Well, the ideas of NEW EXACT MATH brought me into crisis in mathematical societies and also to crisis in America today. The above was some of my analysis of the situation (from its grass roots problems). Their advisors werenÍt successful; they may listen to my advice!! Dr.Mehran Basti === Subject: Re: Inferior mathematics and science <5mqm8455m4shgpus0383l7uie32cjfj5s8@4ax.com> <7b0p84l80tjq9ocmc9v5888g9lpcg9j2rk@4ax.com> posting-account=ee2apQoAAABJNMlLTFasCJw9Nfo9FmYk Gecko/20020924 AOL/7.0,gzip(gfe),gzip(gfe) HTTP/1.1 cache-ntc-ab04.proxy.aol.com[CFC87444] (Traffic-Server/6.1.5 [uScM]) > Their advisors weren?t successful; they may listen to my advice!! Whether authorities will act in a proper manner, they will, otherwise they have to pay a lot of prices and thus more societal hardships, until they learn the lesson. Thus minority groups (those mentioned in this thread) must be reduced to a healty size (from particularly senior positions of power in all aspects of the society), and the authorities must be responsive and respectful to the demands of religious establishments for the good of the society. They will, their crisis force them to do so. They better get more prudent advisors as well. Dr.M.Basti === Subject: Re: Inferior mathematics and science <5mqm8455m4shgpus0383l7uie32cjfj5s8@4ax.com> <7b0p84l80tjq9ocmc9v5888g9lpcg9j2rk@4ax.com> posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 4334.34; Windows NT 5.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) spider-mtc-tg03.proxy.aol.com[400C70C3] (Prism/1.2.1), HTTP/1.1 cache-mtc-ad05.proxy.aol.com[400C74C7] (Traffic-Server/6.1.5 [uScM]) î Allahu akbarî This means GOD IS GREAT. æhttp://i-cias.com/e.o/allahuak.htm Possibly the better translation is: ñGod is most greatî. Dr.Mehran Basti In my religion, we're not so fanatical. We say God is swell. === Subject: Re: Inferior mathematics and science I was busily flonking away in sci.math and alt.usenet.kooks, when The Goddess Eris Herself suddenly made me reply to Mehran Basti: > Alluha Akbar! I am very pleased that you brought the Moslem's phrase about GOD, > «GOD IS GREATÁ. He misspelt it...Quite deliberately, I'm sure. > This is the first step (remedy) for solving worldØs problems in > particular American crisis. You can't solve the problem of one religion with another religion. Religion is the problem...Not, mind you, because of the sane religionists (some of my colleagues are in one religion or another), but the (toxically) insane ones, many of whom are in charge, in various different religious hierarchies. Incidentally, should you be considered eligible to win a kook award, it will have nothing to do with your command of English -- since it is obviously not your first language, it wouldn't be cricket to upbraid you for murdering it. -- ________________________________________________________________________ Hail Eris! All hail Discordia!! Kallisti!!! mhm 29x21; MHUoAT #13 Pope Snarky Goodfella of the undulating cable, JM, CK, POEE, KOTHASK, GGGHD, HCNB, IAC, MWFA; Lits Slut #16 Gutter Chix0r #17; BowTie's Spuriously Accused Pedo Photographer #4 COOSN-029-06-71069; Usenet Ruiner #5; Official Chung Demon AUK Psycho & Felon #21; Parrot & Zombie #2; AUK Hate Machine Cog #19 Anonymous Psycho Criminal #18 If it weren't for lawyers, I think we could have invented a universal symbolic representation of reality. We do need not your type here. -- Yads lets his inner net.nazi out, in what turns into an act of net.KKKopping on TopPoster (who rightly identifies him as a net-wacko), in I am not sexually attracted to cats. It's not my fault if a cat points it's arse at me because it thinks I am the dominant male. -- Aggie doesn't know that cats do that when they like someone. I'm worried about The only kind of time travel that is possible in any universe is, if you changed the past then the future changes too -- Agamemnon -Skopianosfaktis: Renowned expert on quantum physics and time-travel in Andrew Chung and I have a very special connection. Have you read his writings on Usenet? He's a Usenet missionary, just like I am. I commend him (and all of you gentle readers) to Christ's sweet love. -- The amoral Atlanta Kane, on her meds (though she swears it wasn't her) in MID: <45e766ed$0$69324$bb4e3ad8@newscene.com> I did not write this. It is illegal to forget someone's email address. The person who mocked me like this needs to be brought to justice. This is absolutely outrageous. -- Amoral AOK, regarding the previous quote, in MID: I want a boyfriend who is sensitive and caring, but they already have boyfriends. http://groups.yahoo.com/group/Cabal_of_the_Holy_Pretzel/join I hate explain $hit to tards. Especially illiterate tards. -- The Monkey is very hard on irony meters, as in MID: , and is also trained by moi, for the Barbara Woodhouse Memorial Dog Whistle http://www.screedbomb.info/porchie/ PIERRE SALINGER MEMORIAL HOOK, LINE & SINKER -- June 2008 email is not a private form of communication. -- Dustin Cook, in Dustin is FILTH in my opinion. And not for any reason other than posting Rhonda's personal info. -- Respondant After the Swift Boat Veterans who served with Kerry in Vietnam claimed that Kerry lied about his heroism, the Democrats wanted to make a similar ad attacking Bush, but they couldn't find anyone who served with him. -- Anonymous You would no longer be here if I were to stop praying for you. Andrew B. Chung's delusions of grandeur are getting out of hand, in MID: You're fighting a Spam Witch You look into this seductive creature's eyes and feel as if she can make your sword longer, your bank account bigger, your waist smaller, and show you the secret habits of barnyard animals. You fight to resist her charms . . . She gets the jump on you. She shows you a picture of her pet goat. This is my goat, see? she You lose 17 hit points. (bad spelling damage) -- The Kingdom of Loathing === Subject: Re: Inferior mathematics and science <5mqm8455m4shgpus0383l7uie32cjfj5s8@4ax.com> <7b0p84l80tjq9ocmc9v5888g9lpcg9j2rk@4ax.com> posting-account=ee2apQoAAABJNMlLTFasCJw9Nfo9FmYk Gecko/20020924 AOL/7.0,gzip(gfe),gzip(gfe) HTTP/1.1 cache-ntc-ab05.proxy.aol.com[CFC87445] (Traffic-Server/6.1.5 [uScM]) > He misspelt it...Quite deliberately, I'm sure. > I have copied it as it was and my respond gone through sci.math. Since the first author also sent it to other newsgroup, naturally my reply was sent to your site too. It isî Allahu akbarî : http://i-cias.com/e.o/allahuak.htm Dr.M.Basti === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) Updated list per July 29, 2008 I have both the comprehensive SOLUTION MANUAL for ALL of the following books and TEST BANK for MOST of these books in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price is US$35 for solution manual, and $35 for test bank. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account) Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I might be able to help. -------------------------- Statistics for Management and Economics - Gerald Keller (7th ed) (ISBN 0534491243) Statistics for Managers Using Microsoft Excel - David M. Levine (5th ed) (ISBN 0136149901) Statistics for Science and Engineering - John Kinney (1st ed) (ISBN 0201437201) Statistics for the Behavioral and Social Sciences - Arthur Aron (4th ed) (ISBN 0131562789) Statistics for the Life Sciences - Myra Samuels (3rd ed) (ISBN 013041316X) (1st ed) (ISBN 0130083690) Statistics: The Art and Science of Learning from Data - Alan Agresti (2nd ed) (ISBN 0135131995) Stats: Data and Models - Richard D. De Veaux (2nd ed) (ISBN 0321433793) Steel Design - William T. Segui (4th ed) (ISBN 0495244716) Strategic Brand Management - Kevin Keller (3rd ed) (ISBN 0131888595) Strategic Compensation - Joe Martocchio (5th ed) (ISBN 0136007449) Strategic Management and Business Policy - Tom Wheelen (10th ed) (ISBN 0131494597) Strategic Management and Business Policy - Tom Wheelen (11th ed) (ISBN 013232346X) Strategic Management and Competitive Advantage - Jay Barney (2nd ed) (ISBN 013613520X) Strategic Management and Competitive Advantage: Concepts and Cases - Jay Barney (2nd ed) (ISBN 0132338238) Strategic Management in Action - Mary Coulter (4th ed) (ISBN 0132277476) Strategic Management: Concepts and Cases - Fred David (11th ed) (ISBN 0131869493) Strategic Management: Concepts and Cases - Fred David (12th ed) (ISBN 0136015700) Strategic Managment: A Dynamic Perspective Integrated Stratsim Simulation Experience - Print Upgrade - Mason Carpenter (1st ed) (ISBN 0136149057) Strategic Marketing for Non-Profit Organizations - Alan Andreasen (7th ed) (ISBN 013175372X) Strategic Staffing - Jean M. Phillips (1st ed) (ISBN 0131586947) Strategies for Creative Problem Solving - H. Scott Fogler (2nd ed) (ISBN 0130082791) Structural Steel Design - Jack C. McCormac (4th ed) (ISBN 013221816X) Structure and Interpretation of Signals and Systems - Edward Lee, Pravin Varaiya (1st ed) (ISBN 0201745518) Structures - Daniel Lewis Schodek (6th ed) (ISBN 0131789392) Survey of Accounting - Carl S. Warren (3rd ed) (ISBN 0324312482) Survey of Economics - Irvin B. Tucker (6th ed) (ISBN 0324579616) Survey of Mathematics with Applications - Allen Angel (8th ed) (ISBN 032150108X) Survey of Mathematics with Applications, A - Allen R. Angel (8th ed) (ISBN 0321501071) Surveying with Construction Applications - Barry F. Kavanagh (6th ed) (ISBN 0131709321) Surveying: Principles and Applications - Barry F. Kavanagh (8th ed) (ISBN 013236512X) System Dynamics and Response - S. Graham Kelly (1st ed) (ISBN 0534549306) Systems Analysis and Design - Kenneth E. Kendall (7th ed) (ISBN 0132240858) Tax Research - Barbara H Karlin (4th ed) (ISBN 013601531X) Taxation for Decision Makers 2008 - Shirley Dennis-Escoffier (2nd ed) (ISBN 0324654111) Technical Calculus with Analytic Geometry - Allyn J. Washington (4th ed) (ISBN 0201711125) Technology Strategy for Managers and Entrepreneurs - Scott A. Shane (1st ed) (ISBN 0131879324) The Economics of Macro Issues - Roger LeRoy Miller (3rd ed) (ISBN 0321416597) The Economics of Poverty - Bradley R Schiller (10th ed) (ISBN 0131889699) The Economics of Public Issues - Roger LeRoy Miller (15th ed) (ISBN 0321416104) The Economics of Sports - Michael A. Leeds (3rd ed) (ISBN 0321415566) The Paralegal Professional - Henry Cheeseman (2nd ed) (ISBN 0131751905) The Strategy of Managing Innovation and Technology - Murray Millson (1st ed) (ISBN 0132303833) Theory of Asset Pricing - George Pennacchi (1st ed) (ISBN 032112720X) Thermodynamics: An Engineering Approach - Yunus Cengel (5th ed) (ISBN 0073107689) Thinking Mathematically - Robert F. Blitzer (4th ed) (ISBN 0131752049) Thomas' Calculus - George B. Thomas, Jr. (11th ed) (ISBN 0321185587) Thomas' Calculus, Early Transcendentals, Media Upgrade - George B. Thomas, Jr (11th ed) (ISBN 0321495756) Thomas' Calculus, Early Transcendentals, Media Upgrade, Part One - George B. Thomas, Jr. (11th ed) (ISBN 0321498747) Thomas' Calculus, Media Upgrade - George B. Thomas, Jr. (11th ed) (ISBN 032148987X) Thomas' Calculus, Media Upgrade, Part One (Single Variable) - George B. Thomas, Jr. (11th ed) (ISBN 0321498755) Thomas' Calculus, Media Upgrade, Part Two (Multivariable, Chap 11-16) - George B. Thomas, Jr. (11th ed) (ISBN 0321501039) Training in Interpersonal Skills - Stephen P. Robbins (5th ed) (ISBN 0132354993) Trigonometry - Margaret L. Lial (9th ed) (ISBN 0321528859) Trigonometry - Mark Dugopolski (2nd ed) (ISBN 032135690X) Trigonometry: A Right Triangle Approach - Michael Sullivan (5th ed) (ISBN 0136028969) Trigonometry: A Unit Circle Approach - Michael Sullivan (8th ed) (ISBN 0132392798) UFL Collective Bargaining Agreement - Louis Marino (1st ed) (ISBN 0131587668) Understanding and Managing Diversity - Carol Harvey (4th ed) (ISBN 0132069105) Understanding and Managing Organizational Behavior - Jennifer George (5th ed) (ISBN 013239457X) Understanding Fiber Optics - Jeff Hecht (5th ed) (ISBN 0131174290) Understanding Financial Statements - Lyn M. Fraser (8th ed) (ISBN 0131878565) Understanding Modern Economics - Roger Miller (1st ed) (ISBN 0321245822) University Calculus: Alternate Edition - Joel Hass (1st ed) (ISBN 0321471962) University Calculus: Alternate Edition, Part One (Single Variable, Chap 1-9) - Joel Hass (1st ed) (ISBN 0321475194) University Calculus: Elements with Early Transcendentals - Joel Hass (1st ed) (ISBN 0321533488) University Physics with Modern Physics with MasteringPhysics» - Hugh D. Young (12th ed) (ISBN 080532187X) Using and Understanding Mathematics: A Quantitative Reasoning Approach - Jeffrey O. Bennett (4th ed) (ISBN 0321458206) Using Financial Accounting Information: The Alternative to Debits & Credits - Gary A. Porter (5th ed) (ISBN 0324645104) Using Peachtree Complete 2007 for Accounting - Glenn Owen (1st ed) (ISBN 0324377975) Using Quickbooks Pro 2007 for Accounting - Glenn Owen (7th ed) (ISBN 0324378750) Vector Calculus - Susan Colley (3rd ed) (ISBN 0131858742) VHDL: A Starter's Guide - Sudhakar Yalamanchili (2nd ed) (ISBN 0131457357) Water and Wastewater Technology - Mark J. Hammer (6th ed) (ISBN 0131745425) Water Resources Engineering - David A. Chin (2nd ed) (ISBN 0131481924) Web 101 - Wendy G. Lehnert (3rd ed) (ISBN 0321424670) West Federal Taxation Comprehensive 2007 - William Hoffman (Solutions Manual) (30th ed) (ISBN 0324313497) West Federal Taxation Comprehensive 2007 - William Hoffman (Test Bank) (30th ed) (ISBN 0324313497) West Federal Taxation Corporations 2007 - William Hoffman (Solutions Manual) (30th ed) (ISBN 0324313616) West Federal Taxation Corporations 2007 - William Hoffman (Test Bank) (30th ed) (ISBN 0324313616) West Federal Taxation Corporations 2008 - William Hoffman (Solutions Manual) (31st ed) (ISBN 0324380437) West Federal Taxation Corporations 2008 - William Hoffman (Test Bank) (31st ed) (ISBN 0324380437) West Federal Taxation Individual 2007 - William Hoffman (Solutions Manual) (30th ed) (ISBN 0324399618) West Federal Taxation Individual 2007 - William Hoffman (Test Bank) (30th ed) (ISBN 0324399618) West Federal Taxation Individual 2008 - William Hoffman (Solutions Manual) (31st ed) (ISBN 0324380585) West Federal Taxation Individual 2008 - William Hoffman (Test Bank) (31st ed) (ISBN 0324380585) West Federal Taxation: Taxation of Business Entities 2007 - James Smith (Solutions Manual) (10th ed) (ISBN 0324313950) West Federal Taxation: Taxation of Business Entities 2007 - James Smith (Test Bank) (10th ed) (ISBN 0324313950) West Federal Taxation: Taxation of Business Entities 2008 - James Smith (Solutions Manual) (11th ed) (ISBN 0324366655) West Federal Taxation: Taxation of Business Entities 2008 - James Smith (Test Bank) (11th ed) (ISBN 0324366655) West's Business Law - Kenneth W. Clarkson (10th ed) (ISBN 0324303904) Wireless Communications & Networks - William Stallings (2nd ed) (ISBN 0131918354) Writing and Speaking at Work: A Practical Guide for Business Communication - Edward P. Bailey (4th ed) (ISBN 0131881302) Your Attitude is Showing - Sharon Lund O'Neil (12th ed) (ISBN 0132429047) === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) Updated list per July 29, 2008 I have both the comprehensive SOLUTION MANUAL for ALL of the following books and TEST BANK for MOST of these books in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price is US$35 for solution manual, and $35 for test bank. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account) Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I might be able to help. -------------------------- Precalculus - J. S. Ratti (1st ed) (ISBN 032129646X) Precalculus - Judith A. Beecher (3rd ed) (ISBN 0321460065) Precalculus - Margaret Lial (4th ed) (ISBN 0321528840) Precalculus - Mark Dugopolski (4th ed) (ISBN 0321357795) Precalculus - Michael Sullivan (8th ed) (ISBN 0132256886) Precalculus - Michael Sullivan (8th ed) (ISBN 0132256886) Precalculus: Enhanced with Graphing Utilities - Michael Sullivan (5th ed) (ISBN 0136015786) Precalculus: Functions and Graphs - Mark Dugopolski (3rd ed) (ISBN 032150111X) Precalculus: Graphs & Models and Graphing Calculator Manual Package - Marvin L. Bittinger (4th ed) (ISBN 0321501527) Prehospital Emergency Care - Joseph J. Mistovich (8th ed) (ISBN 0131741438) Prentice Hall's Federal Taxation 2007: Comprehensive - Thomas Pope (20th ed) (ISBN 0132389479) Prentice Hall's Federal Taxation 2007: Corporations - Thomas Pope (20th ed) (ISBN 0131751484) Prentice Hall's Federal Taxation 2007: Individuals - Thomas Pope (20th ed) (ISBN 013243220X) Prentice Hall's Federal Taxation 2008: Comprehensive - Thomas Pope (21st ed) (ISBN 0132416492) Prentice Hall's Federal Taxation 2008: Corporations - Thomas Pope (21st ed) (ISBN 0136156436) Prentice Hall's Federal Taxation 2008: Individuals - Thomas Pope (21st ed) (ISBN 0136156371) Prentice Hall's Federal Taxation 2009: Comprehensive - Thomas Pope (22nd ed) (ISBN 0136067042) Prentice Hall's Federal Taxation 2009: Corporations - Thomas Pope (22nd ed) (ISBN 0136067131) Prentice Hall's Federal Taxation 2009: Individuals - Thomas Pope (22nd ed) (ISBN 0136067042) Preparing Effective Business Plans: An Entrepreneurial Approach - Bruce R. Barringer (1st ed) (ISBN 0132318326) Price Theory and Applications - Steven Landsburg (7th ed) (ISBN 0324421613) Principles of Accounting - Meg Pollard (1st ed) (ISBN 0132304791) Principles of Auditing: An Introduction to International Standards on Auditing - Rick Hayes (2nd ed) (ISBN 0273684108) Principles of CMOS VLSI Design - Neil H.E. Weste (3rd ed) (ISBN 0201533766) Principles of Cost Accounting - Edward J. Vanderbeck (13th ed) (ISBN 0324191693) Principles of Cost Accounting - Edward J. Vanderbeck (14th ed) (ISBN 0324374178) Principles of Customer Relationship Management - Roger Baran (1st ed) (ISBN 0324322380) Principles of Economics - Gregory Mankiw (4th ed) (ISBN 0324224729) Principles of Economics - Karl Case (8th ed) (ISBN 0132289148) Principles of Electric Circuits: Conventional Current Version - Thomas Floyd (8th ed) (ISBN 0131701797) Principles of Finance - Scott Besley (3rd ed) (ISBN 0324232624) Principles of Foundation Engineering - Braja M. Das (6th ed) (ISBN 0495082465) Principles of Geotechnical Engineering (6th ed) (ISBN 0534551440) Principles of Heat Transfer - Frank Kreith (6th ed) (ISBN 0534375960) Principles of Law and Economics - Daniel Cole, Peter Grossman (1st ed) (ISBN 0130932612) Principles of Macroeconomics - Gregory Mankiw (4th ed) (ISBN 0324236956) Principles of Managerial Finance - Lawrence J. Gitman (12th ed) (ISBN 0321557530) Principles of Managerial Finance Brief Edition - Lawrence Gitman (5th ed) (ISBN 0321557522) Principles of Managerial Finance plus MyfinanceLab Student Access Kit - Lawrence J. Gitman (12th ed) (ISBN 0321557530) Principles of Marketing - Philip Kotler (12th ed) (ISBN 0132390027) Principles of Microeconomics - Gregory Mankiw (4th ed) (ISBN 0324319169) Principles of Microeconomics - Karl E. Case (8th ed) (ISBN 0131994859) Principles of Money, Banking, Financial Markets - Lawrence Ritter et al (11th ed) (ISBN 0321205251) Principles Of Operations Management - Jay Heizer (6th ed) (ISBN 013155445X) Principles Of Operations Management - Jay Heizer (7th ed) (ISBN 0132449757) Principles of Risk Management and Insurance - George E. Rejda (10th ed) (ISBN 0321414934) Probabilistic Systems and Random Signals - Abraham Haddad (1st ed) (ISBN 0130094552) Probability & Statistics for Engineers & Scientists - Ronald E. Walpole (8th ed) (ISBN 0131877119) Probability and Statistical Inference - Robert Hogg, Eliot Tanis (7th ed) (ISBN 0131464132) Probability and Statistics - Morris DeGroot, Mark Schervish (3rd ed) (ISBN 0201524880) Probability and Statistics for Engineers - Richard Johnson, Irwin Miller, John Freund (7th ed) (ISBN 0131437453) Probability and Statistics for Engineers and Scientists - Anthony J. Hayter (3rd ed) (ISBN 0495107573) Probability Random Variables, and Stochastic Processes - Papoulis et al (4th ed) (ISBN 0073660116) Probability, Statistics, and Random Processes For Electrical Engineering - Alberto Leon-Garcia (3rd ed) (ISBN 0131471228) Problem Solving and Program Design in C - Jeri R. Hanly (5th ed) (ISBN 0321409914) Problem Solving with C++ - Walter Savitch (6th ed) (ISBN 0321412699) Problem Solving with C++ - Walter Savitch (7th ed) (ISBN 0321531345) Problem Solving, Abstraction & Design Using C++ - Frank L. Friedman (5th ed) (ISBN 0321450051) Process Control Instrumentation Technology - Curtis Johnson (8th ed) (ISBN 0131194577) Professional Office Procedures - Susan Cooperman (5th ed) (ISBN 0135156645) Professional Selling: A Trust-Based Approach - Thomas N. Ingram (4th ed) (ISBN 032453809X) Professionalism: Real Skills for Workplace Success - Lydia E. Anderson (1st ed) (ISBN 0131714392) Programming the World Wide Web - Robert W. Sebesta (4th ed) (ISBN 0321489691) Public Relations Practices: Managerial Case Studies and Problems - Allen H. Center (7th ed) (ISBN 0132341360) Quality Control - Dale H. Besterfield (8th ed) (ISBN 0135000955) Quality Management - Donna C.S. Summers (2nd ed) (ISBN 0135005108) Quantitative Analysis for Management - Barry Render (10th ed) (ISBN 0136036252) Quantitative Analysis for Management - Barry Render (9th ed) (ISBN 0131857029) Quantum Chemistry and Spectroscopy - Thomas Engel (1st ed) (ISBN 0805339795) QuickBooks Pro 2006 with Update 2007 and CD Package - Janet Horne (9th ed) (ISBN 013242407X) Real Estate Law - George Siedel (6th ed) (ISBN 0324204809) Real Estate Law - Marianne M. Jennings (8th ed) (ISBN 0324650205) Retailing - Patrick M. Dunne (6th ed) (ISBN 032436279X) Rethinking Marketing: The Entrepreneurial Imperative - Minet Schindehutte (1st ed) (ISBN 0132393891) Risk Management and Insurance - James S. Trieschmann (12th ed) (ISBN 0324183208) Risk Takers: Uses and Abuses of Financial Derivatives - John Marthinsen (2nd ed) (ISBN 0321542568) Routers and Routing Basics CCNA 2 Labs and Study Guide - Allan Johnson (1st ed) (ISBN 1587131676) Short-Term Financial Management - Terry Maness (3rd ed) (ISBN 0324202938) Short-Term Financial Management - Terry Maness (Test Bank) (3rd ed) (ISBN 0324202938) Signals, Systems, and Transforms - Charles L Phillips (4th ed) (ISBN 0131989235) Social Entrepreneurship: A Modern Approach to Social Value Creation - Arthur C. Brooks (1st ed) (ISBN 0132330768) Software Engineering - Ian Sommerville (8th ed) (ISBN 0321313798) Soils and Foundations - Cheng Liu, Jack Evett (7th ed) (ISBN 0132221381) Solid State Electronic Devices - Ben Streetman (6th ed) (ISBN 013149726X) South-Western Federal Taxation 2009: Comprehensive - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660529) South-Western Federal Taxation 2009: Comprehensive - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660529) South-Western Federal Taxation 2009: Corporations - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660219) South-Western Federal Taxation 2009: Corporations - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660219) South-Western Federal Taxation 2009: Individual Income Taxes - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660200) South-Western Federal Taxation 2009: Individual Income Taxes - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660200) Spectral Analysis of Signals - Peter Stoica, Randolph Moses (1st ed) (ISBN 0131139568) Starting Out with Java: Early Objects - Tony Gaddis (3rd ed) (ISBN 0321497686) Starting Out with Visual Basic 2008 - Tony Gaddis (4th ed) (ISBN 0321531353) Statics and Strengths of Materials - Harold I. Morrow (6th ed) (ISBN 0131719777) Statistical Methods for the Social Sciences - Alan Agresti (4th ed) (ISBN 0130272957) Statistical Reasoning for Everyday Life - Jeffrey O. Bennett (3rd ed) (ISBN 0321286723) Statistics - James T. McClave (11th ed) (ISBN 0132069512) Statistics for Business & Economics - James T. McClave (10th ed) (ISBN 0132409356) Statistics for Business and Economics - David R. Anderson (Test Bank only) (10th ed) (ISBN 0324360681) Statistics for Business and Economics - Paul Newbold, William L. Carlson (6th ed) (ISBN 0132203847) === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) Updated list per July 29, 2008 I have both the comprehensive SOLUTION MANUAL for ALL of the following books and TEST BANK for MOST of these books in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price is US$35 for solution manual, and $35 for test bank. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account) Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I might be able to help. -------------------------- Managerial Accounting (Class Test Edition) - Linda S. Bamber (1st ed) (ISBN 0132284634) Managerial Accounting: A Focus on Ethical Decision Making - Steve Jackson, Roby Sawyers (4th ed) (ISBN 0324650647) Managerial Accounting: An Introduction to Concepts, Methods and Uses - Michael W. Maher (10th ed) (ISBN 0324639767) Managerial Economics - Mark Hirschey (12th ed) (ISBN 0324584849) Managerial Economics: A Problem Solving Approach - Luke M. Froeb (1st ed) (ISBN 0324359810) Managerial Economics: Applications, Strategies, and Tactics - James R. McGuigan (11th ed) (ISBN 0324421605) Managerial Economics: Economic Tools for Today's Decision Makers - Paul G. Keat (5th ed) (ISBN 0131860151) Managerial Statistics A Case-Based Approach - Peter Klibanoff (1st ed) (ISBN 0324226454) Managing Human Resources - Luis Gomez-Mejia (5th ed) (ISBN 013187067X) Managing in a Global Economy: Demystifying International Macroeconomics - John E. Marthinsen (1st ed) (ISBN 0324395507) Managing Information Technology - Carol V Brown (6th ed) (ISBN 0131789546) Manual Auditing and Assurance Practice Set: CAST - Frank A. Buckless (1st ed) (ISBN 0130464716) Manufacturing Processes for Engineering Materials - Serope Kalpakjian (5th ed) (ISBN 0132272717) Manufacturing, Engineering & Technology - Serope Kalpakjian (5th ed) (ISBN 0131489658) Market Regulation - Roger Sherman (1st ed) (ISBN 0321322320) Market-Based Management - Roger Best (5th ed) (ISBN 0132336537) Marketing Management - Philip Kotler (13th ed) (ISBN 0136009980) Materials Science and Engineering: An Introduction - William Callister (6th ed) (ISBN 0471135763) Mathematical Ideas - Charles D. Miller (11th ed) (ISBN 0321361466) Mathematical Ideas - Charles D. Miller (11th ed) (ISBN 0321361482) Mathematical Methods for Economics - Michael Klein (2nd ed) (ISBN 0201726262) Mathematical Proofs: A Transition to Advanced Mathematics - Gary Chartrand (2nd ed) (ISBN 0321390539) Mathematical Reasoning for Elementary Teachers - Calvin T. Long (5th ed) (ISBN 0321460847) Mathematics for Business - Stanley A. Salzman (8th ed) (ISBN 0321357434) Mathematics for Elementary School Teachers - Phares O'Daffer (4th ed) (ISBN 0321448049) Mathematics for Physicists - Susan Lea (1st ed) (ISBN 0534379974) Mathematics of Interest Rates and Finance - Gary Guthrie (1st ed) (ISBN 0130461822) Mechanics of Materials - Russell C. Hibbeler (7th ed) (ISBN 0132209918) Medical Imaging Signals and Systems - Jerry L. Prince (1st ed) (ISBN 0130653535) Microbiology with Diseases by Body System - Robert W. Bauman (2nd ed) (ISBN 032151341X) Microbiology: An Introduction - Gerard J. Tortora (9th ed) (ISBN 0805347909) Microeconomics - Glenn Hubbard (2nd ed) (ISBN 0138132771) Microeconomics - Jeffrey Perloff (4th ed) (ISBN 0321414527) Microeconomics - Michael Parkin (7th ed) (ISBN 0321454944) Microeconomics - Michael Parkin (8th ed) (ISBN 0321416600) Microeconomics - Richard G. Lipsey (13th ed) (ISBN 032136922X) Microeconomics - Robert Pindyck, Daniel Rubinfeld (6th ed) (ISBN 0130084611) Microeconomics: Principles and Tools - Arthur O'Sullivan, Steven Sheffrin (4th ed) (ISBN 0131536060) Microeconomics: Principles, Applications, and Tools - Arthur O'Sullivan (5th ed) (ISBN 0131572830) Microeconomics: Theory and Applications with Calculus - Jeffrey M. Perloff (1st ed) (ISBN 0321277945) Microwave Engineering - David Pozar (3rd ed) (ISBN 0471448788) Modern Control Systems - Richard C Dorf (11th ed) (ISBN 0132270285) Modern Electronic Communication - Jeff Beasley (9th ed) (ISBN 0132251132) Modern Industrial Organization - Dennis Carlton, Jeffrey Perloff (4th ed) (ISBN 0321180232) Modern Labor Economics: Theory and Public Policy - Ronald Ehrenberg (10th ed) (ISBN 0321533739) Modern Labor Economics: Theory and Public Policy - Ronald Ehrenberg (9th ed) (ISBN 0321305035) Modern Management - Samuel C. Certo (10th ed) (ISBN 0131494708) Modern Physics - Randy Harris (2nd ed) (ISBN 0805303081) Modern Physics - Raymond Serway (3rd ed) (ISBN 0534493394) Modern Wireless Communications - Simon Haykin (1st ed) (ISBN 0130224723) Money, Banking and Financial Markets - Roger LeRoy Miller (3rd ed) Money, the Financial System, and the Economy - R. Glenn Hubbard (6th ed) (ISBN 0321426703) Multinational Business Finance - David K. Eiteman (11th ed) (ISBN 0321357965) Multinational Management - John B. Cullen (4th ed) (ISBN 032442177X) Nanoengineering of Structural, Functional and Smart Materials - Mark J. Schulz (1st ed) (ISBN 0849316537) New Venture Management: The Entrepreneur's Roadmap - Donald Kuratko (1st ed) (ISBN 0136130321) Numerical Analysis - Timothy Sauer (1st ed) (ISBN 0321268989) Numerical Methods for Engineers - Bilal Ayyub, Richard McCuen (1st ed) (ISBN 0133373614) Numerical Methods Using Matlab - John Mathews (4th ed) (ISBN 0130652482) Occupational Safety and Health for Technologists, Engineers, and Managers - David L. Goetsch (6th ed) (ISBN 0132397609) Office Procedures 21st Century & Student Workbook Package - Sharon Burton (7th ed) (ISBN 0132343436) Operating Systems Principles - Lubomir F. Bic (1st ed) (ISBN 0130266116) Operating Systems: Internals and Design Principles - William Stallings (5th ed) (ISBN 0131479547) Operations Management - Jay Heizer (8th ed) (ISBN 0131554441) Operations Management - Jay Heizer (9th ed) (ISBN 0138128782) Operations Management - Nigel Slack (5th ed) (ISBN 0273708473) Operations Management and Student CD and Student DVD Package - Jay Heizer (9th ed) (ISBN 0138128782) Operations Management: Process and Value Chains - Lee J. Krajewski (8th ed) (ISBN 0131697390) Operations Research: An Introduction - Hamdy A. Taha (8th ed) (ISBN 0131889230) Opportunities and Challenges of Workplace Diversity: Theory, Cases, and Exercises - Kathryn Canas (1st ed) (ISBN 0131343068) Oracle 10g Programming: A Primer - Rajshekhar Sunderraman (1st ed) (ISBN 0321463048) Organic Chemistry - Paula Bruice (Test Bank only) (5th ed) (ISBN 0131963163) Organizational Behavior - Stephen P Robbins (13th ed) (ISBN 0136007171) Organizational Behavior Today - Leigh Thompson (1st ed) (ISBN 0131858114) Organizational Behavior: An Experiential Approach - Joyce S Osland (8th ed) (ISBN 0131441515) Organizational Behavior: An Introduction to Your Life in Organizations - Rae Andre (1st ed) (ISBN 013185495X) Organizational Theory, Design and Change - Gareth R. Jones (5th ed) (ISBN 0131865420) Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems - Donald L. Bartel (1st ed) (ISBN 0130089095) Parallel and Distributed Computation: Numerical Methods - Dimitri Bertsekas, John Tsitsiklis (1st ed) (ISBN 0136487009) Parallel Programming - Barry Wilkinson (2nd ed) (ISBN 0131405632) Partial Differential Equations and Boundary Value Problems - Nakhle Asmar (2nd ed) (ISBN 0131480960) Payroll Accounting 2008 - Bernard Bieg (18th ed) (ISBN 0324645546) Performance Management - Herman Aguinis (2nd ed) (ISBN 0136151752) Personal Finance - Jeff Madura (3rd ed) (ISBN 0321409965) Personal Financial Planning - Lawrence J. Gitman (11th ed) (ISBN 0324422865) Pharmacology for Nurses: A Pathophysiological Approach - Michael Patrick Adams (2nd ed) (ISBN 0131756656) Physical Chemistry - Thomas Engel, Philip Reid (1st ed) (ISBN 080533842X) Physical Chemistry for the Life Sciences - Thomas Engel (1st ed) (ISBN 0805382771) Physics : Principles with Applications - Douglas Giancoli (6th ed) (ISBN 0130606200) Physics for Scientists & Engineers (Chs 1-37) with MasteringPhysics» - Doug Giancoli (4th ed) (ISBN 0136139264) Physics for Scientists and Engineers with Modern Physics and MasteringPhysics» - Douglas C. Giancoli (4th ed) (ISBN 0136139221) Physics with Mastering Physics - James S. Walker (3rd ed) (ISBN 0136138969) Physics: Principles with Applications with MasteringPhysics - Douglas C. Giancoli (6th ed) (ISBN 0321569830) Portfolio Construction, Management, and Protection - Robert A. Strong (4th ed) (ISBN 0324359365) Practical Financial Management - William R. Lasher (5th ed) (ISBN 0324422636) Prealgebra - Elayn El Martin-Gay (5th ed) (ISBN 0132319519) Prealgebra - Marvin L. Bittinger (5th ed) (ISBN 0321331907) Prealgebra & Introductory Algebra - Elayn El Martin-Gay (2nd ed) (ISBN 0131577050) Prealgebra and Introductory Algebra - Marvin L. Bittinger (2nd ed) (ISBN 0321331893) Prealgebra: An Integrated Approach - Margaret L. Lial (1st ed) (ISBN 032135639X) === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) Updated list per July 23, 2008 I have both the comprehensive SOLUTION MANUAL for ALL of the following books and TEST BANK for MOST of these books in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price is US$35 for solution manual, and $35 for test bank. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account) Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I might be able to help. -------------------------- Intro Stats - Richard D. De Veaux (3rd ed) (ISBN 0321500458) Introduction to Abstract Algebra - Olympia Nicodemi (1st ed) (ISBN 0131019635) Introduction to Analysis - William R. Wade (3rd ed) (ISBN 0131453335) Introduction to Business Law - Jeffrey F. Beatty (2nd ed) (ISBN 0324311427) Introduction to Business Statistics - Ronald M. Weiers (6th ed) (ISBN 0324381433) Introduction to Chemical Principles - Stephen Stoker (9th ed) (ISBN 0132379945) Introduction to Computing Systems - Sanjay J. Patel, Yale Patt (2nd ed) (ISBN 0072467509) Introduction to Corporate Finance - William L. Megginson (1st ed) (ISBN 0324379862) Introduction to Corporate Finance - William L. Megginson (2nd ed) (ISBN 0324657935) Introduction to Cryptography with Coding Theory - Wade Trappe (2nd ed) (ISBN 0131862391) Introduction to Derivatives and Risk Management - Don M. Chance (7th ed) (ISBN 0324321392) Introduction to Econometrics - James H. Stock (2nd ed) (ISBN 0321278879) Introduction to Econometrics Brief Edition - James H. Stock (1st ed) (ISBN 0321432517) Introduction to Economic Reasoning - William D. Rohlf (7th ed) (ISBN 0321416112) Introduction to Environmental Engineering and Science - Gilbert M. Masters (3rd ed) (ISBN 0131481932) Introduction to Financial Accounting - Charles Horngren (9th ed) (ISBN 0131479725) Introduction to Fourier Optics - Joseph Goodman (3rd ed) (ISBN 0974707724) Introduction to Government and Non-for-Profit Accounting - Martin Ives (6th ed) (ISBN 0132366355) Introduction to Graph Theory - Douglas West (2nd ed) (ISBN 0130144002) Introduction to Law - Joanne Hames (3rd ed) (ISBN 0131183818) Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593) Introduction to Linear Programming - Leonid Vaserstein (1st ed) (ISBN 0130359173) Introduction to Management Accounting - Charles T. Horngren (14th ed) (ISBN 0136129218) Introduction to Management Accounting, Chap. 1-17: International Edition - Charles Horngren (13th ed) (ISBN 0131273078) Introduction to Management Science and Student - Bernard Taylor (8th ed) (ISBN 0131050524) Introduction to Management Science and Student - Bernard Taylor (9th ed) (ISBN 0131888099) Introduction to Materials Management - Tony Arnold (6th ed) (ISBN 0132337614) Introduction to Mathematical Statistics and Its Applications - Richard J. Larsen (4th ed) (ISBN 0131867938) Introduction to Operations and Supply Chain Management - Cecil Bozarth (2nd ed) (ISBN 0131791036) Introduction to Optics - Frank Pedrotti et al. (3rd ed) (ISBN 0131499335) Introduction to Quantum Mechanics - David Griffiths (2nd ed) (ISBN 0131118927) Introduction to Risk Management and Insurance - Mark Dorfman (8th ed) (ISBN 0131449583) Introduction to Risk Management and Insurance - Mark S. Dorfman (9th ed) (ISBN 0132242273) Introduction to Technical Mathematics - Allyn J. Washington, Mario Triola (5th ed) (ISBN 0321374177) Introduction to Telecommunications - Martha Rosengrant (2nd ed) (ISBN 0131126156) Introduction to the Design & Analysis of Experiments - George C Canavos (1st ed) (ISBN 0136158633) Introduction to the Design and Analysis of Algorithms - Anany Levitin (1st ed) (ISBN 0201743957) Introduction to the Design and Analysis of Algorithms - Anany Levitin (2nd ed) (ISBN 0321358287) Introduction to Transportation Engineering - Lester A. Hoel (1st ed) (ISBN 0534952895) Introduction to Vacuum Technology - David M. Hata (1st ed) (ISBN 0130450189) Introductory & Intermediate Algebra for College Students - Robert F. Blitzer (3rd ed) (ISBN 0136028950) Introductory Algebra - Marvin L. Bittinger (10th ed) (ISBN 0321269470) Introductory Algebra for College Students - Robert F. Blitzer (5th ed) (ISBN 0132356791) Introductory Algebra through Applications - Geoffrey Akst (2nd ed) (ISBN 0321518020) Introductory and Intermediate Algebra - Robert F Blitzer (2nd ed) (ISBN 0131492594) Introductory Chemistry - Nivaldo J. Tro (3rd ed) (ISBN 0136003826) Introductory Chemistry - Steve Russo, Michael Silver, Mike Silver (2nd ed) (ISBN 032104634X) Introductory Circuit Analysis - Robert Boylestad (11th ed) (ISBN 0131730444) Introductory Econometrics: A Modern Approach - Jeffrey Wooldridge (3rd ed) (ISBN 0324289782) Introductory Econometrics: A Modern Approach - Jeffrey Wooldridge (4th ed) (ISBN 0324581629) Introductory Linear Algebra: An Applied First Course - Bernard Kolman (8th ed) (ISBN 0131437402) Introductory Mathematical Analysis - Ernest F Haeussler (12th ed) (ISBN 0132404222) Introductory Statistics - Neil A. Weiss (8th ed) (ISBN 0321393619) Inventing Entrepreneurs: Technology Innovators and their Entrepreneurial Journey - Gerry George (1st ed) (ISBN 0131574701) Investments - Frank K. Reilly (7th ed) (ISBN 0324288999) Investments: An Introduction - Herbert B. Mayo (9th ed) (ISBN 0324561261) Java Software Solutions: Foundations of Program Design - John Lewis (5th ed) (ISBN 0321409493) Java: Introduction to Problem Solving and Programming - Walter Savitch (6th ed) (ISBN 0136072259) John E. Freund's Mathematical Statistics with Applications - Irwin Miller (7th ed) (ISBN 0131427067) Kleppner's Advertising Procedure - Ronald Lane (17th ed) (ISBN 0132308290) Labor Relations - Arthur A Sloane (12th ed) (ISBN 013196223X) Labor Relations and Collective Bargaining: Cases, Practice, and Law - Michael R. Carrell (8th ed) (ISBN 0131868721) Lakeside Company: Case Studies in Auditing - John M. Trussel (11th ed) (ISBN 0131588516) Law and Economics - Robert Cooter (5th ed) (ISBN 0321336348) Law for Business - John D. Ashcroft (16th ed) (ISBN 0324381573) Learning Microsoft Office Accounting 2007 and Student CD Package - Terri Brunsdon (1st ed) (ISBN 0131586602) Learning Peachtree Complete 2007 & Peachtree Complete CD Package - Terri Brunsdon (1st ed) (ISBN 0132405571) Learning Quickbooks Pro 2007 and Student CD Package - Terri Brunsdon (1st ed) (ISBN 0132419386) Legal Terminology - Gordon W. Brown (5th ed) (ISBN 0131568043) Level Three Leadership: Getting Below the Surface - James G Clawson (4th ed) (ISBN 0132423847) Linear Algebra and Its Applications - David C. Lay (3rd ed) (ISBN 0321287134) Linear Algebra for Engineers and Scientists Using Matlab - Kenneth Hardy (1st ed) (ISBN 0139067280) Linear Algebra with Applications - Otto Bretscher (3rd ed) (ISBN 0131453343) Linear Algebra with Applications - Steven Leon (7th ed) (ISBN 0131857851) Logic and Computer Design Fundamentals - M. Morris Mano (4th ed) (ISBN 013198926X) Machine Design: An Integrated Approach - Robert L. Norton (3rd ed) (ISBN 0131481908) Machines and Mechanisms: Applied Kinematic Analysis - David H. Myszka (3rd ed) (ISBN 0131837761) Macroeconomics - Andrew B. Abel (6th ed) (ISBN 0321451406) Macroeconomics - Glenn Hubbard (2nd ed) (ISBN 0132356694) Macroeconomics - Michael Parkin (7th ed) (ISBN 032124608X) Macroeconomics - Michael Parkin (8th ed) (ISBN 0321416570) Macroeconomics - Richard Froyen (8th ed) (ISBN 0131435825) Macroeconomics - Richard G. Lipsey (13th ed) (ISBN 0321369238) Macroeconomics - Richard T Froyen (9th ed) (ISBN 0132438356) Macroeconomics - Robert Gordon (10th ed) (ISBN 0321278801) Macroeconomics - Robert Gordon (11th ed) (ISBN 0321485513) Macroeconomics - Stephen D. Williamson (3rd ed) (ISBN 0321416589) Macroeconomics: A Modern Approach - Robert J. Barro (1st ed) (ISBN 0324178107) Macroeconomics: Principles and Policy - William J. Baumol (10th ed) (ISBN 0324537034) Macroeconomics: Principles and Tools - Arthur O'Sullivan, Steven Sheffrin (4th ed) (ISBN 0131536184) Macroeconomics: Principles, Applications, and Tools - Arthur O'Sullivan (5th ed) (ISBN 013232928X) Making Career Decisions that Count: A Practical Guide - Darrell A. Luzzo (3rd ed) (ISBN 0131712772) Making the Team - Leigh Thompson (3rd ed) (ISBN 0131861352) Management - Michael Hitt (2nd ed) (ISBN 0132354373) Management - Stephen P Robbins (9th ed) (ISBN 0132257734) Management of Organizational Behavior - Paul H Hersey (9th ed) (ISBN 0131441396) Manager's Bookshelf - Jon L. Pierce (8th ed) (ISBN 0132301652) Managerial Accounting - Carl Warren (9th ed) (ISBN 0324381913) Managerial Accounting - Linda S. Bamber (1st ed) (ISBN 0138129711) === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) Updated list per July 29, 2008 I have both the comprehensive SOLUTION MANUAL for ALL of the following books and TEST BANK for MOST of these books in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price is US$35 for solution manual, and $35 for test bank. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account) Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I might be able to help. -------------------------- Financial Management For Public, Health, and Not-for-Profit Organizations - Steven Finkler (2nd ed) (ISBN 0131471988) Financial Management: Theory & Practice - Eugene Brigham (12th ed) (ISBN 0324422695) Financial Markets and Institutions - Frederic S. Mishkin (5th ed) (ISBN 0321280296) Financial Markets and Institutions - Frederic S. Mishkin (6th ed) (ISBN 0321374215) Financial Markets and Institutions - Jeff Madura (8th ed) (ISBN 0324568215) Financial Reporting and Analysis - Lawrence Revsine (3rd ed) (ISBN 0131430211) Financial Reporting and Analysis Using Financial Accounting Information - Charles Gibson (10th ed) (ISBN 0324304455) Financial Reporting, Financial Statement Analysis, and Valuation - Clyde P. Stickney (6th ed) (ISBN 0324302959) Financial/Managerial Accounting - Walter T. Harrison (1st ed) (ISBN 0131568779) Finite Element Analysis Theory and Application with ANSYS - Saeed Moaveni (3rd ed) (ISBN 0131890808) Finite Math and Its Application - Larry Goldstein (9th ed) (ISBN 0131873644) Finite Mathematics - Margaret L. Lial et al (8th ed) (ISBN 032122826X) Finite Mathematics and Calculus with Applications - Margaret Lial (8th ed) (ISBN 0321426517) Finite Mathematics for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett (11th ed) (ISBN 0132255707) Finite Mathematics with Applications - Margaret L. Lial (9th ed) (ISBN 0321386728) First Course in Abstract Algebra - John Fraleigh (7th ed) (ISBN 0201763907) First Course in Abstract Algebra - Joseph Rotman (3rd ed) (ISBN 0131862677) First Course In Probability - Sheldon M. Ross (7th ed) (ISBN 0131856626) First Course in Statistics, A - James T. McClave (10th ed) (ISBN 0136152597) Fluency with Information Technology: Skills, Concepts, and Capabilities - Lawrence Snyder (3rd ed) (ISBN 0321512391) Foundations of Economics - Robin Bade (4th ed) (ISBN 0321522362) Foundations of Finance - Arthur Keown, William Petty, John Martin, David Scott (5th ed) (ISBN 0131856057) Foundations of Finance: Logic and Practice of Financial Mangement - Arthur J. Keown (6th ed) (ISBN 0135048168) Foundations of Finance: The Logic and Practice of Financial Management - Arthur Keown (6th ed) (ISBN 0132339226) Foundations of Geometry - Gerard Venema (5th ed) (ISBN 0131437003) Foundations of Macroeconomics - Robin Bade (4th ed) (ISBN 0321522370) Foundations of MEMS - Chang Liu (1st ed) (ISBN 0131472860) Foundations of Microeconomics - Robin Bade (3rd ed) (ISBN 0321415957) Foundations of Microeconomics - Robin Bade (4th ed) (ISBN 0321522389) Framework for Human Resource Management, A - Gary Dessler (5th ed) (ISBN 0136041531) Framework for Marketing Management, A - Philip Kotler (4th ed) (ISBN 0136026605) Fraud Examination - Steve Albrecht (2nd ed) (ISBN 0324651155) Friendly Introduction to Analysis - Witold A.J. Kosmala (2nd ed) (ISBN 0130457965) Fundamental Cornerstones of Managerial Accounting - Dan L. Heitger, Maryanne M. Mowen (1st ed) (ISBN 0324378068) Fundamentals of Advanced Accounting - Paul M. Fischer (Test Bank) (1st ed) (ISBN 0324378904) Fundamentals of Applied Electromagnetics - Fawwaz T. Ulaby (5th ed) (ISBN 0132413264) Fundamentals of Business Law Summarized Cases - Roger LeRoy Miller (7th ed) (ISBN 0324381689) Fundamentals of Communication Systems - John G. Proakis (1st ed) (ISBN 013147135X) Fundamentals of Complex Analysis - Edward Saff (3rd ed) (ISBN 0139078746) Fundamentals of Derivatives Markets - Robert L. McDonald (1st ed) (ISBN 0321357175) Fundamentals of Differential Equations - Kent Nagle, Edward Saff (6th ed) (ISBN 0321145720) Fundamentals of Differential Equations - R. Kent Nagle (7th ed) (ISBN 0321410483) Fundamentals of Differential Equations with Boundary Value Problems - R. Kent Nagle (5th ed) (ISBN 0321419219) Fundamentals of Engineering Economics - Chan S. Park (2nd ed) (ISBN 0132209608) Fundamentals of Financial Management - Eugene Brigham (11th ed) (ISBN 0324319800) Fundamentals of Investing - Lawrence J. Gitman (10th ed) (ISBN 0321489381) Fundamentals of Multinational Finance - Michael Moffett (3rd ed) (ISBN 0321541642) Fundamentals of Organic Chemistry - John McMurry (Test Bank only) (5th ed) (ISBN 0534395732) Fundamentals of Probability, with Stochastic Processes - Saeed Ghahramani (3rd ed) (ISBN 0131453408) Fundamentals of Signals and Systems - Edward Kamen (3rd ed) (ISBN 0131687379) Fundamentals of Statistics - Michael Sullivan (2nd ed) (ISBN 0131569872) Further Mathematics for Economic Analysis - Knut Sydsaeter et al (1st ed) (ISBN 0273655760) Geometry: Theorems and Constructions - Allan Berele (1st ed) (ISBN 0130871214) Global Investments - Bruno Solnik (6th ed) (ISBN 0321527704) High-Speed Networks and Internets: Performance and Quality of Service - William Stallings (2nd ed) (ISBN 0130322210) Human Anatomy & Physiology - Elaine N. Marieb (7th ed) (ISBN 0805359095) Human Anatomy and Physiology Lab Manual - Elaine N. Marieb (9th ed) (ISBN 0805372652) Human Relations for Career and Personal Success: Concepts, Applications, and Skills - Andrew J. DuBrin (8th ed) (ISBN 0131791796) Human Relations: Interpersonal Job-Oriented Skills - Andrew J. DuBrin (10th ed) (ISBN 0135019443) Human Resource Management - Gary Dessler (11th ed) (ISBN 0131746170) Human Resource Management - Wayne Mondy (10th ed) (ISBN 0132225956) Human Side of Organizations - Michael Drafke (10th ed) (ISBN 0135139740) Hydrology and Floodplain Analysis - Philip B. Bedient (4th ed) (ISBN 0131745891) Income Tax Fundamentals 2006 - Gerald E. Whittenburg (24th ed) (ISBN 0324399022) Income Tax Fundamentals 2007 - Gerald E. Whittenburg (25th ed) (ISBN 032439926X) Information Systems Today: Managing in the Digital World - Leonard Jessup (3rd ed) (ISBN 0132335069) Information Technology Auditing and Assurance - James Hall (2nd ed) (ISBN 0324191987) Inquiry into Physics - Vern J. Ostdiek (6th ed) (ISBN 0495119431) Integrated Arithmetic and Basic Algebra - Bill E. Jordan (4th ed) (ISBN 0321442555) Intel Micro 8086 - Barry B. Brey (8th ed) (ISBN 0135026458) Intel Microprocessors - Barry B. Brey (7th ed) (ISBN 0131195069) Interactive Computer Graphics: A Top-Down Approach Using OpenGL - Edward Angel (5th ed) (ISBN 0321535863) Interactive Statistics - Martha Aliaga, Brenda Gunderson (3rd ed) (ISBN 0131497561) Intermediate Accounting - James D. Stice (16th ed) (ISBN 0324312148) Intermediate Accounting - Loren A. Nikolai (10th ed) (ISBN 0324651929) Intermediate Accounting (Revised) - David Spiceland (4th ed) (ISBN 0073215422) Intermediate Algebra - Elayn El Martin-Gay (5th ed) (ISBN 0136007295) Intermediate Algebra - Margaret L. Lial (10th ed) (ISBN 0321443624) Intermediate Algebra - Marvin L. Bittinger (10th ed) (ISBN 0321319087) Intermediate Algebra for College Students - Allen R. Angel (7th ed) (ISBN 0132383578) Intermediate Algebra for College Students - Robert F. Blitzer (5th ed) (ISBN 0136007627) Intermediate Algebra with Applications & Visualization - Gary K. Rockswold (3rd ed) (ISBN 0321500032) Intermediate Algebra: Functions & Authentic Applications - Jay Lehmann (3rd ed) (ISBN 0131953338) Intermediate Algebra: Graphs & Models - Marvin L. Bittinger (3rd ed) (ISBN 0321416163) International Accounting - Frederick Choi (5th ed) (ISBN 0131480979) International Accounting - Frederick D. Choi (6th ed) (ISBN 0131588141) International Business - John Daniels (12th ed) (ISBN 0136029655) International Business Law - Ray A. August (5th ed) (ISBN 013600864X) International Business: Environments and Operations - John Daniels (11th ed) (ISBN 0131869426) International Business: Strategy, Management, and the New Realities - Tamer Cavusgil (1st ed) (ISBN 0131738607) International Business: The Challenges of Globalization - John J. Wild (4th ed) (ISBN 0131747436) International Economics - Charles Sawyer, Richard Sprinkle (2nd ed) (ISBN 0131704168) International Economics - James Gerber (3rd ed) (ISBN 032123796X) International Economics - James Gerber (4th ed) (ISBN 0321415558) International Economics - Robert Carbaugh (11th ed) (ISBN 032442194X) International Economics - W. Charles Sawyer (3rd ed) (ISBN 0136054692) International Economics: Theory And Policy - Paul Krugman, Maurice Obstfeld (7th ed) (ISBN 0321293835) International Economics: Theory and Policy - Paul R. Krugman (8th ed) (ISBN 0321488830) International Financial Management - Jeff Madura (9th ed) (ISBN 0324568193) International Financial Management, Abridged Edition - Jeff Madura (8th ed) (ISBN 0324365632) International Management: Managing Across Borders and Cultures - Helen Deresky (6th ed) (ISBN 0136143261) International Money and Finance - Michael Melvin (7th ed) (ISBN 0201770288) === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) Updated list per July 29, 2008 I have both the comprehensive SOLUTION MANUAL for ALL of the following books and TEST BANK for MOST of these books in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price is US$35 for solution manual, and $35 for test bank. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account) Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I might be able to help. -------------------------- Discrete Mathematics - Otto, Eynden, Dossey, Spence (4th ed) (ISBN 0321079124) Discrete Mathematics - Otto, Eynden, Dossey, Spence (5th ed) (ISBN 0321305159) Discrete Mathematics - Richard Johnsonbaugh (6th ed) (ISBN 0131176862) Drugs & the Human Body - Ken Liska (8th ed) (ISBN 0132447134) Economic Development - Michael P. Todaro (10th ed) (ISBN 0321485734) Economic Development - Michael Todaro, Stephen Smith (9th ed) (ISBN 0321278887) Economic Growth - David N. Weil (2nd ed) (ISBN 0321416627) Economic Growth - David Weil (1st ed) (ISBN 0201680262) Economics - Michael Parkin (8th ed) (ISBN 0321423003) Economics - Richard Lipsey (13th ed) (ISBN 0321369211) Economics of Money, Banking, and Financial Markets, Update - Frederic Mishkin (7th ed) (ISBN 0321331850) Economics Today - Roger LeRoy Miller (14th ed) (ISBN 0321422341) Economics Today: The Macro View - Roger Miller (13th ed) (ISBN 0321278992) Economics Today: The Macro View - Roger Miller (14th ed) (ISBN 0321421442) Economics Today: The Micro View - Roger Miller (13th ed) (ISBN 0321278984) Economics Today: The Micro View - Roger Miller (14th ed) (ISBN 0321425065) Economics: A Contemporary Introduction - William A. McEachern (8th ed) (ISBN 0324579217) Economics: A Tool for Critically Understanding Society - Tom Riddell (8th ed) (ISBN 0321423585) Economics: Principles and Policy - William J. Baumol (10th ed) (ISBN 0324537026) Economics: Principles and Policy - William J. Baumol (11th ed) (ISBN 0324586205) Economics: Private and Public Choice - James D. Gwartney (12th ed) (ISBN 0324580185) Effective Small Business Management - Norman M. Scarborough (9th ed) (ISBN 0136152708) Effective Writing - Claire B. May (8th ed) (ISBN 0136029086) Electric Circuits - James Nilsson (8th ed) (ISBN 0131989251) Electrical Engineering: Principles and Applications - Allan R. Hambley (4th ed) (ISBN 0131989227) Electrical Machines, Drives and Power Systems - Theodore Wildi (6th ed) (ISBN 0131776916) Electronic Communications for Technicians - Tom Wheeler (2nd ed) (ISBN 0131130498) Electronics and Computer Math - Bill R. Deem (8th ed) (ISBN 0131711377) Electronics Fundamentals: Circuits, Devices and Applications - Thomas Floyd (7th ed) (ISBN 013219709X) Elementary Algebra - George Woodbury (1st ed) (ISBN 0321166426) Elementary Algebra Early Graphing for College Students - Allen R. Angel (3rd ed) (ISBN 0136134165) Elementary Algebra: Graphs and Authentic Applications - Jay Lehmann (1st ed) (ISBN 013220164X) Elementary and Intermediate Algebra - George Woodbury (2nd ed) (ISBN 0321500067) Elementary and Intermediate Algebra: Graphs & Models - Marvin L. Bittinger (3rd ed) (ISBN 0321422406) Elementary Differential Equations - Henry Edwards (6th ed) (ISBN 0132397307) Elementary Differential Equations - Werner E. Kohler, Lee W.Johnson (1st ed) (ISBN 0201709260) Elementary Differential Equations with Boundary Value Problems - Henry Edwards (6th ed) (ISBN 0136006132) Elementary Differential Equations With Boundary Value Problems - Lee Johnson et al (1st ed) (ISBN 0321121643) Elementary Differential Equations With Boundary Value Problems - Lee Johnson et al (2nd ed) (ISBN 0321398505) Elementary Linear Algebra with Applications - Bernard Kolman (9th ed) (ISBN 0132296543) Elementary Number Theory - Kenneth H. Rosen (5th ed) (ISBN 0321237072) Elementary Statistics - Mario F. Triola (10th ed) (ISBN 0321331834) Elementary Statistics - Mario F. Triola (9th ed) (ISBN 0201775700) Elementary Statistics - Neil A. Weiss (7th ed) (ISBN 0321422090) Elementary Statistics - Ron Larson (4th ed) (ISBN 0132424339) Elementary Statistics Using Excel - Mario Triola (3rd ed) (ISBN 0321365135) Elementary Statistics Using the TI-83/84 Plus Calculator - Mario F. Triola (2nd ed) (ISBN 0321462572) Elementary Statistics With Multimedia Study Guide - Mario F. Triola (10th ed) (ISBN 0321460928) Elements of Forecasting - Francis X. Diebold (4th ed) (ISBN 032432359X) Employment Law - John J. Moran (4th ed) (ISBN 0136009964) Engineering Economy - William G Sullivan (13th ed) (ISBN 0131486497) Engineering Economy - William G. Sullivan (14th ed) (ISBN 0136142974) Engineering Economy and the Decision-Making Process - Joseph C. Hartman (1st ed) (ISBN 0131424017) Engineering Fundamentals: An Introduction to Engineering - Saeed Moaveni (3rd ed) (ISBN 0495082538) Engineering Materials: Properties and Selection - Ken Budinski (8th ed) (ISBN 0131837796) Engineering Mechanics Dynamics - Anthony M Bedford (5th ed) (ISBN 0136129161) Engineering Mechanics: Statics - Anthony M Bedford (5th ed) (ISBN 0136129153) Engineering Mechanics: Statics - Russell C. Hibbeler (11th ed) (ISBN 0132215004) Engineering Mechanics: Statics Computational Edition - Robert W. Soutas-Little (1st ed) (ISBN 0534549217) Engineering Vibration - Daniel Inman (3rd ed) (ISBN 0132281732) Enterprise Systems for Management - Luvai Motiwalla (1st ed) (ISBN 013233531X) Entrepreneurial Finance - Philip J. Adelman (4th ed) (ISBN 0132434792) Entrepreneurship: Successfully Launching New Ventures - Bruce Barringer (2nd ed) (ISBN 0132240572) Environmental and Natural Resource Economics - Tom Tietenberg (7th ed) (ISBN 0321305043) Environmental Issues: An Introduction to Sustainability - Robert L. McConnell (3rd ed) (ISBN 0131566504) Environmental Law - Nancy K. Kubasek (6th ed) (ISBN 0136142168) Environmental Science: Toward A Sustainable Future - Richard T. Wright (10th ed) (ISBN 0132302659) Error Control Coding - Daniel J. Costello Jr., Shu Lin (2nd ed) (ISBN 0130426725) Essential Foundations of Economics - Robin Bade (4th ed) (ISBN 0321522354) Essentials of Business Law - Jeffrey F. Beatty (3rd ed) (ISBN 0324537123) Essentials of College Algebra with Modeling and Visualization - Gary K. Rockswold (3rd ed) (ISBN 0321448898) Essentials of College Algebra, Alternate Edition - Margaret L. Lial (1st ed) (ISBN 0321491858) Essentials of Economics - Gregory Mankiw (4th ed) (ISBN 0324236964) Essentials of Entrepreneurship and Small Business Management - Thomas W Zimmerer (5th ed) (ISBN 0132294389) Essentials of Logic - Irving Copi (2nd ed) (ISBN 013238034X) Essentials of Management Information Systems - Jane Laudon (8th ed) (ISBN 013602579X) Essentials of Managerial Finance - Scott Besley (13th ed) (ISBN 0324258755) Essentials of Marketing - Charles W. Lamb (6th ed) (ISBN 0324656203) Essentials of Organizational Behavior - Stephen P Robbins (9th ed) (ISBN 0132431521) Essentials of Statistics - Mario F. Triola (3rd ed) (ISBN 0321434250) Essentials of the Legal Environment - Roger LeRoy Miller (2nd ed) (ISBN 0324400403) Ethics for the Information Age - Mike Quinn (3rd ed) (ISBN 0321536851) Excellence in Business Communication - John V. Thill (8th ed) (ISBN 0136157505) Exploring Business - Karen Collins (1st ed) (ISBN 0131403656) Exploring Macroeconomics - Robert L. Sexton (4th ed) (ISBN 0324395558) Federal Tax Research - William A. Raabe (8th ed) (ISBN 0324659652) Feedback Control of Dynamic Systems - Gene Franklin (5th ed) (ISBN 0131499300) Financial & Managerial Accounting - Carl S. Warren (9th ed) (ISBN 0324401884) Financial Accounting - Carl S. Warren, James M. Reeve (10th ed) (ISBN 0324380674) Financial Accounting - Carl S. Warren, James M. Reeve (11th ed) (ISBN 0324663781) Financial Accounting - Jane Reimers (1st ed) (ISBN 0131492012) Financial Accounting - Walter Harrison, Charles Horngren (6th ed) (ISBN 0131499459) Financial Accounting and Financial Tips - Walter T. Harrison (7th ed) (ISBN 0135012848) Financial Accounting: A Bridge to Decision Making - Robert Ingram (6th ed) (ISBN 0324313357) Financial Accounting: A Business Process Approach - Jane L. Reimers (2nd ed) (ISBN 0131473867) Financial Accounting: An Integrated Statements Approach - Jonathan Duchac (2nd ed) (ISBN 0324312113) Financial Accounting: An Introduction to Concepts, Methods and Uses - Clyde P. Stickney (12th ed) (ISBN 0324381980) Financial Accounting: The Impact on Decision Makers - Gary Porter (6th ed) (ISBN 0324655231) Financial and Managerial Accounting - Meg Pollard (1st ed) (ISBN 0136008984) Financial Economics - Zvi Bodie (2nd ed) (ISBN 0131856154) === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) Updated list per July 29, 2008 I have both the comprehensive SOLUTION MANUAL for ALL of the following books and TEST BANK for MOST of these books in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price is US$35 for solution manual, and $35 for test bank. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account) Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I might be able to help. -------------------------- Capital Budgeting and Long-Term Financing Decisions - Neil Seitz (4th ed) (ISBN 0324258089) Cases in Management Accounting and Control Systems - Brandt Allen (4th ed) (ISBN 0135704251) Chemistry - John E McMurry (Test Bank only) (5th ed) (ISBN 0131993232) Chemistry : An Introduction to General, Organic, Biological Chemistry - Karen Timberlake (9th ed) (ISBN 0805330151) Chemistry: An Introduction to General, Organic, & Biological Chemistry - Karen C Timberlake (10th ed) (ISBN 0136019706) ed) (ISBN 0534408966) CMOS Circuit Design, Layout, and Simulation - David E. Boyce et al (1st ed) (ISBN 0780334167) College Accounting 1-12 - Jeffrey Slater (9th ed) (ISBN 0131071696) College Accounting 1-25 - Jeffrey Slater (10th ed) (ISBN 0132286386) College Accounting Chapters 1-15 - James Heintz (19th ed) (ISBN 0324382499) College Accounting Chapters 1-27 - James Heintz (19th ed) (ISBN 0324376162) College Accounting Chapters 1-9 - James Heintz (19th ed) (ISBN 0324382480) College Algebra - J. S. Ratti (1st ed) (ISBN 0321296443) College Algebra - Judith A. Beecher (3rd ed) (ISBN 0321466071) College Algebra - Margaret L. Lial (10th ed) (ISBN 0321499131) College Algebra - Mark Dugopolski (4th ed) (ISBN 0321356918) College Algebra - Michael Sullivan (8th ed) (ISBN 0132402866) College Algebra and Trigonometry - J. S. Ratti (1st ed) (ISBN 0321296427) College Algebra and Trigonometry - Margaret L. Lial (4th ed) (ISBN 0321497449) College Algebra Enhanced with Graphing Utilities - Michael Sullivan (5th ed) (ISBN 0136004911) College Algebra Essentials - Michael Sullivan (8th ed) (ISBN 0136154344) College Algebra: Graphs and Models with Graphing Calculator Manual Package - Marvin L. Bittinger (4th ed) (ISBN 0321531922) College Geometry - David C. Kay (2nd ed) (ISBN 0321046242) College Geometry: A Problem Solving Approach with Applications - Gary L. Musser (2nd ed) (ISBN 0131879693) College Math for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett (11th ed) (ISBN 0131572253) College Physics - Jerry D Wilson (6th ed) (ISBN 0131495798) Communication Systems Engineering - John G. Proakis (2nd ed) (ISBN 0130617938) Comparative International Accounting - Christopher Nobes (9th ed) (ISBN 0273703579) Complex Variables With Applications - A. David Wunsch (3rd ed) (ISBN 0201756099) Computer Algorithms - Allen Van Gelder, Sara Baase (3rd ed) (ISBN 0201612445) Computer Networking Complete Package - James F. Kurose (3rd ed) (ISBN 0321418492) Computer Networking with Internet Protocols - William Stallings (1st ed) (ISBN 0131410989) Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) Computer Networking: A Top-Down Approach Featuring the Internet - James F. Kurose (3rd ed) (ISBN 0321227352) Computer Organization and Architecture - William Stallings (7th ed) (ISBN 0130351199) Computer Organization and Architecture: Designing for Performance - William Stallings (7th ed) (ISBN 0131856448) Computer Science: An Overview - J. Glenn Brookshear (10th ed) (ISBN 0321524039) Computer Security: Principles and Practice - William Stallings (1st ed) (ISBN 0136004245) Computer Systems Organization & Architecture - John D. Carpinelli (1st ed) (ISBN 0201612534) Concepts in Federal Taxation 2007 - Kevin Murphy (14th ed) (ISBN 0324313527) Concepts in Federal Taxation 2008 - Kevin Murphy (15th ed) (ISBN 0324640153) Concepts in Federal Taxation 2009 - Kevin Murphy (16th ed) (ISBN 0324659377) Concepts In Systems and Signals - John D. Sherrick (2nd ed) (ISBN 0131782711) Concepts of Calculus with Applications - Martha Goshaw (1st ed) (ISBN 0321320786) Concepts of Calculus With Applications-Updated Edition - Martha Goshaw (2nd ed) (ISBN 0321577442) Concepts of Programming Languages - Robert W. Sebesta (8th ed) (ISBN 0321493621) Conceptual Physical Science - Paul G. Hewitt (4th ed) (ISBN 0321516958) Conceptual Physics Fundamentals - Paul G. Hewitt (1st ed) (ISBN 0321501365) Conceptual Physics Media Update - Paul G. Hewitt (10th ed) (ISBN 0321548094) Concrete Structures - Mehdi Setareh (1st ed) (ISBN 0131988271) Construction Accounting & Financial Management - Stephen Peterson (2nd ed) (ISBN 0135017114) Construction Methods and Management - Stephens W. Nunnally (7th ed) (ISBN 0131716859) Construction Project Management - Fred Gould (3rd ed) (ISBN 0131996231) Consumer Behavior - Michael Solomon (8th ed) (ISBN 0136015964) Contemporary Business and Online Commerce Law - Henry R. Cheeseman (6th ed) (ISBN 013601500X) Contemporary Engineering Economics - Chan S. Park (4th ed) (ISBN 0131876287) Contemporary Financial Management - Charles Moyer (10th ed) (ISBN 0324289081) Contemporary Financial Management - R. Charles Moyer, James R. McGuigan (11th ed) (ISBN 0324653506) Contemporary Logistics - Paul R. Murphy (9th ed) (ISBN 013156207X) Contemporary Marketing 2009 Update - Louis E. Boone (13th ed) (ISBN 0324580215) Cornerstones of Managerial Accounting - Maryanne M. Mowen (2nd ed) (ISBN 0324379609) Corporate Finance - Jonathan Berk (1st ed) (ISBN 0321415116) Corporate Finance - Michael C. Ehrhardt, Eugene F. Brigham (3rd ed) (ISBN 0324655681) Corporate Finance: The Core plus MyFinanceLab Student Access Kit - Jonathan Berk (1st ed) (ISBN 032155759X) Corporate Financial Management - Douglas R. Emery (3rd ed) (ISBN 0132278723) Cost Accounting - Charles T. Horngren, George Foster, Srikant M. Datar (12th ed) (ISBN 0131495380) Cost Accounting - Charles T. Horngren, George Foster, Srikant M. Datar (13th ed) (ISBN 0136126634) Cost Accounting: Traditions & Innovations - Jesse Barfield (5th ed) (ISBN 032418090X) Cost Management: Accounting and Control - Don R. Hansen, Maryanne M. Mowen (6th ed) (ISBN 0324559674) Course in Probability - Neil Weiss (1st ed) (ISBN 0201774712) Criminology: A Global Perspective - Robert W. Winslow (1st ed) (ISBN 0131839020) Cryptography and Network Security - William Stallings (4th ed) (ISBN 0131873164) Customer Service: Career Success Through Customer Loyalty - Paul R. Timm (4th ed) (ISBN 0132236583) Data Abstraction & Problem Solving with C++ - Frank M. Carrano (5th ed) (ISBN 0321433327) Data and Computer Communications - William Stallings (8th ed) (ISBN 0132433109) Data Structures and Algorithm Analysis in C++ - Mark Allen Weiss (3rd ed) (ISBN 032144146X) Data Structures and Algorithm Analysis in Java - Mark Allen Weiss (2nd ed) (ISBN 0321370139) Database Systems: A Practical Approach - Thomas M. Connolly (4th ed) (ISBN 0321294017) Derivatives Markets - Robert L. McDonald (2nd ed) (ISBN 032128030X) Detection and Estimation:Theory and Its Applications - Thomas Schonhoff (1st ed) (ISBN 0130894990) Developmental Mathematics - Marvin L. Bittinger (7th ed) (ISBN 0321331915) Developmental Mathematics: Basic Mathematics and Algebra - Margaret L. Lial (1st ed) (ISBN 0321506421) Differential Equations - John Polking (2nd ed) (ISBN 0131437380) Differential Equations and Boundary Value Problems: Computing and Modeling - Henry Edwards (4th ed) (ISBN 0131561073) Differential Equations and Linear Algebra - Henry Edwards, David E. Penney (2nd ed) (ISBN 0131481460) Differential Equations and Linear Algebra - Jerry Farlow (2nd ed) (ISBN 0131860615) Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) (ISBN 0130457949) Differential Equations Computing and Modeling - Henry Edwards (4th ed) (ISBN 0136004385) Differential Equations With Boundary Value Problems - John C. Polking (2nd ed) (ISBN 0130911062) Digital & Analog Communication Systems - Leon Couch (7th ed) (ISBN 0131424920) Digital Communications - John Proakis (4th ed) (ISBN 0072321113) Digital Design - Morris Mano (4th ed) (ISBN 0131989243) Digital Electronics: A Practical Approach - William Kleitz (8th ed) (ISBN 0132435780) Digital Signal Processing - John Proakis (4th ed) (ISBN 0131873741) Digital Signal Processing Using MATLAB -Vinay K. Ingle, John G. Proakis (2nd ed) (ISBN 0495073113) Digital Systems Design Using VHDL - Charles H. Roth (2nd ed) (ISBN 0534384625) Digital Systems: Principles and Applications - Ronald Tocci et al (10th ed) (ISBN 0131725793) Discrete and Combinatorial Mathematics - Ralph P. Grimaldi (5th ed) (ISBN 0201726343) Discrete Mathematics - Edgar G. Goodaire, Michael M Parmenter (3rd ed) (ISBN 0131679953) === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) Updated list per July 29, 2008 I have both the comprehensive SOLUTION MANUAL for ALL of the following books and TEST BANK for MOST of these books in electronic format (PDF/ Word). The solutions manual are comprehensive with answers to both even & odd problems in the text. The price is US$35 for solution manual, and $35 for test bank. The methods of payment is through PAYPAL (It is easy, safe, and you can use debit or credit card to pay even if you don't have an account) Email me at sbooks4sale[at]hotmail[dot]com if you are interested. If you could not find the book you are looking for, please let me know, I might be able to help. -------------------------- A Gift of Fire: Social, Legal, and Ethical Issues for Computing and the Internet - Sara Baase (3rd ed) (ISBN 0136008488) Absolute C++ - Walter Savitch (3rd ed) (ISBN 0321468937) Absolute Java - Walter Savitch (3rd ed) (ISBN 0321487923) Access 2007 Guidebook - Maggie Trigg (6th ed) (ISBN 0321517016) Accounting - Carl Warren (22nd ed) (ISBN 0324401841) Accounting - Carl Warren (23rd ed) (ISBN 0324662963) Accounting Chapters 1-13 - Charles T. Horngren et al (7th ed) (ISBN 0132249952) Accounting Chapters 1-25 - Charles T. Horngren et al (7th ed) (ISBN 0132439603) Accounting Chapters 1-26 - Charles T. Horngren et al (6th ed) (ISBN 0131088513) Accounting Chapters 12-25 - Charles T. Horngren et al (7th ed) (ISBN 0132249960) Accounting Concepts and Applications - Steve Albrecht (10th ed) (ISBN 0324376154) Accounting Concepts and Applications - Steve Albrecht (9th ed) (ISBN 0324187564) Accounting Information Systems - James Hall (5th ed) (ISBN 0324312954) Accounting Information Systems - James Hall (6th ed) (ISBN 0324560893) Accounting Information Systems - Marshall Romney, Paul Steinbart (10th ed) (ISBN 0131475916) Accounting Information Systems - Marshall Romney, Paul Steinbart (11th ed) (ISBN 0136015182) Accounting Information Systems - Ulric J. Gelinas (7th ed) (ISBN 0324378823) Additional Calculus Topics - Raymond Barnett (11th ed) (ISBN 0132318229) Administrative Law: Bureaucracy in a Democracy - Daniel E. Hall (4th ed) (ISBN 0135005183) Advanced Accounting - Floyd Beams (9th ed) (ISBN 0131851225) Advanced Accounting - Paul Fischer (10th ed) (ISBN 0324379056) Advanced Accounting - Paul Fischer (Test Bank only) (9th ed) (ISBN 0324304013) Advanced Calculus - G. B. Folland (1st ed) (ISBN 0130652652) Advanced Engineering Mathematics - Michael Greenberg (2nd ed) (ISBN 0133214311) Advanced Engineering Mathematics - Peter V. O'Neil (6th ed) (ISBN 0534552080) Advertising - Sandra Moriarty (8th ed) (ISBN 0132224151) Algebra and Trigonometry - Judith A. Beecher (3rd ed) (ISBN 0321466209) Algebra and Trigonometry - Michael Sullivan (8th ed) (ISBN 0132329034) Algebra and Trigonometry Enhanced with Graphing Utilities - Michael Sullivan (4th ed) (ISBN 0131527398) Algebra and Trigonometry Enhanced with Graphing Utilities - Michael Sullivan (5th ed) (ISBN 013600492X) Algebra and Trigonometry: Graphs & Models and Graphing Calculator Manual Package - Marvin L. Bittinger (4th ed) (ISBN 0321501519) Algebra for College Students - Allen R. Angel (3rd ed) (ISBN 0136129080) Algebra for College Students - Margaret L. Lial (6th ed) (ISBN 0321442547) Algebra For College Students - Robert F Blitzer (6th ed) (ISBN 0136019749) An Introduction to Signals and Systems - John Alan Stuller (1st ed) (ISBN 0495073016) Dunlap (1st ed) (ISBN 0534392946) Analytical Mechanics - Grant Fowles, George Cassiday (7th ed) (ISBN 0534494927) Anatomy & Physiology - Elaine N. Marieb (3rd ed) (ISBN 0805347739) Anatomy & Physiology for Emergency Care - Bryan E. Bledsoe (2nd ed) (ISBN 0132342987) Applied Algebra - Darel Hardy (1st ed) (ISBN 0130674648) Applied Linear Algebra - Chehrzad Shakiban, Peter J. Olver (1st ed) (ISBN 0131473824) Applied Multivariate Statistical Analysis - Richard A. Johnson (6th ed) (ISBN 0131877151) Applied Partial Differential Equations - Richard Haberman (4th ed) (ISBN 0130652431) Applied Physics - Dale Ewen (9th ed) (ISBN 0135157331) Art and Science of Leadership - Afsaneh Nahavandi (5th ed) (ISBN 0136044085) Auditing and Assurance Services - Alvin A. Arens et al (11th ed) (ISBN 0131867121) Auditing and Assurance Services - Alvin A. Arens et al (12th ed) (ISBN 0135132126) Auditing Assurance and Risk - W. Robert Knechel, Steve Salterio, Brian Ballou (3rd ed) (ISBN 0324313187) Auditing Cases - Mark Beasley (3rd ed) (ISBN 0131494910) Auditing: A Business Risk Approach - Larry E. Rittenberg (6th ed) (ISBN 0324375581) Automation, Production Systems, and Computer-Integrated Manufacturing - Mikell P. Groover (2nd ed) (ISBN 0130889784) Automation, Production Systems, and Computer-Integrated Manufacturing - Mikell P. Groover (3rd ed) (ISBN 0132393212) Basic Business Statistics - Mark L Berenson (10th ed) (ISBN 0131678310) Basic Chemistry - Karen C. Timberlake (2nd ed) (ISBN 0805344691) Basic Environmental Technology: Water Supply, Waste Management & Pollution Control - Jerry A. Nathanson (5th ed) (ISBN 0131190822) Basic Marketing Research Using Microsoft Excel Data Analysis - Alvin C Burns (2nd ed) (ISBN 0132059584) Basic Mathematics through Applications - Geoffrey Akst (4th ed) (ISBN 0321500113) Beginning & Intermediate Algebra - Elayn El Martin-Gay (5th ed) (ISBN 0136007317) Beginning Algebra - Elayn El Martin-Gay (5th ed) (ISBN 0136007023) Beginning Algebra - Margaret L. Lial (10th ed) (ISBN 0321437268) Beginning Algebra with Applications & Visualization - Gary K. Rockswold (2nd ed) (ISBN 0321500040) Beginning and Intermediate Algebra - Margaret L. Lial (4th ed) (ISBN 0321442334) Beginning and Intermediate Algebra with Applications & Visualization - Gary K. Rockswold (2nd ed) (ISBN 0321500059) Behavior in Organizations - Jerald Greenberg (9th ed) (ISBN 0131542842) Biochemistry - Mary Campbell (4th ed) (ISBN 0534405215) Biochemistry (with Lecture Notebook) - Mary Campbell (4th ed) (ISBN 0534391818) Biology - Neil A. Campbell (Test Bank only w/ TestGen Software) (7th ed) (ISBN 080537146X) Biomaterials: The Intersection of Biology and Materials Science - Johnna S. Temenoff (1st ed) (ISBN 0130097101) Biostatistics for the Health Sciences - R. Clifford Blair (1st ed) (ISBN 0131176609) Bond Markets, Analysis and Strategies - Frank Fabozzi (6th ed) (ISBN 0131986430) Brief Course in Mathematical Statistics - Elliot A. Tanis (1st ed) (ISBN 0131751395) Brock Biology of Microorganisms - Michael T. Madigan (12th ed) (ISBN 0132324601) Building Construction: Principles, Materials, and Systems - Madan Mehta (1st ed) (ISBN 0130494216) Building Java Programs: A Back to Basics Approach - Stuart Reges (1st ed) (ISBN 0321382838) Business Analysis and Valuation: Using Financial Statements - Krishna Palepu (3rd ed) (ISBN 0132346451) Business and Society: Ethics and Stakeholder Management - Archie B. Carroll (7th ed) (ISBN 0324569394) Business Communication Essentials and Peak Performance Grammar and Mechanics 2.0 CD Package - Court Bovee (3rd ed) (ISBN 0132328992) Business Communication Today - Court Bovee (9th ed) (ISBN 0131995359) Business English: Writing in the Workplace - Blanche Ettinger (4th ed) (ISBN 0131565702) Business Forecasting - John Hanke (9th ed) (ISBN 0132301202) Business in Action with Real Time Updates - Court Bovee (4th ed) (ISBN 0136154085) Business Law and the Legal Environment - Jeffrey F. Beatty (4th ed) (ISBN 0324303971) Business Law and the Regulation of Business - Richard A. Mann (9th ed) (ISBN 0324537131) Business Law Principles for Today's Commercial Environment - David P. Twomey (2nd ed) (ISBN 0324303947) Business Law Today: The Essentials - Roger LeRoy Miller (8th ed) (ISBN 0324654545) Business Law: Text and Cases - Kenneth W. Clarkson (11th ed) (ISBN 0324655223) Business Law: Text and Exercises - Roger LeRoy Miller (5th ed) (ISBN 032464096X) Business Statistics: A Decision Making Approach - David F. Groebner (7th ed) (ISBN 0132416921) Calculus - Dale Varberg (9th ed) (ISBN 0131429248) Calculus and Its Applications - Larry Goldstein (11th ed) (ISBN 0131919636) Calculus and Its Applications - Marvin L. Bittinger (8th ed) (ISBN 0321166396) Calculus and Its Applications - Marvin L. Bittinger (9th ed) (ISBN 0321395344) Calculus Early Transcendentals - Henry Edwards (7th ed) (ISBN 0131569899) Calculus for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett (11th ed) (ISBN 0132328186) Calculus for the Life Sciences - Marvin L. Bittinger (1st ed) (ISBN 0321279352) Calculus With Applications - Margaret L. Lial et al (8th ed) (ISBN 0321228146) Calculus with Applications for the Life Sciences - Raymond N. Greenwell (1st ed) (ISBN 0201745828) Calculus, Early Transcendentals - C. Henry Edwards (7th ed) (ISBN 0131569899) California Real Estate Law - Theodore Gordon (7th ed) (ISBN 0324654685) === Subject: Puzzle about Wilson's theorem Wilson's theorems says that if p is a prime number then (p-1)! = -1 mod p or, if you want to be different, (p-2)! = 1 mod p. It's easy to prove by looking at the permutation x mapsto x^(-1) of the set of nonzero residues mod p. But let's write the claim as (p-1)! = p-1 mod p. Write F for the field of residues mod p. On the left side, (p-1)! is the number of permutations k of F such that k(0)=0. On the right side, p-1 is the number of those permutations that are /linear/. Now complete the kinky new proof of Wilson's theorem by showing that the set of /nonlinear/ permutations k (with k(0)=0) has a natural equivalence relation on it, whereby each equivalence class contains p elements. hint: torus === Subject: Re: Puzzle about Wilson's theorem posting-account=Cbgh4AoAAAAr0dt1RqLOClWCyUWii2fU Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > Wilson's theorems says that if p is a prime number then > (p-1)! = -1 mod p > or, if you want to be different, > (p-2)! = 1 mod p. > It's easy to prove by looking at the permutation x mapsto x^(-1) of the set > of nonzero residues mod p. But let's write the claim as > (p-1)! = p-1 mod p. > Write F for the field of residues mod p. On the left side, (p-1)! is the > number of permutations k of F such that k(0)=0. On the right side, p-1 is > the number of those permutations that are /linear/. Now complete the kinky > new proof of Wilson's theorem by showing that the set of /nonlinear/ > permutations k (with k(0)=0) has a natural equivalence relation on it, > whereby each equivalence class contains p elements. hint: torus Given a permutation k and an integer 0<=c k(x+c). However, this will not leave 0 fix. Correct this by defining a permutation c*k via (c*k) (x) := k(x+c) - k(c). Not that (d*(c*k)) = ((d+c)*k), i.e. we have an operation of the additive group Z/pZ on the set of permutations fixing 0. Orbits must have length 1 or p. The orbit length is 1 iff k(x+1) = k(x)+k(1) holds for all x, i.e. iff k is linear. Hence the orbit length is p in the realm of nonlinear permutations. hagman Sorry, I seem to have ignored your hint. === Subject: Re: Puzzle about Wilson's theorem posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e SIMBAR Enabled; SIMBAR={70306B22-CB8C-4d52-BFF4-18424E217075}; MathPlayer 2.10b; FunWebProducts; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Wilson's theorems says that if p is a prime number then > (p-1)! = -1 mod p > or, if you want to be different, > (p-2)! = 1 mod p. > It's easy to prove by looking at the permutation x mapsto x^(-1) of the set > of nonzero residues mod p. But let's write the claim as > (p-1)! = p-1 mod p. > Write F for the field of residues mod p. On the left side, (p-1)! is the > number of permutations k of F such that k(0)=0. On the right side, p-1 is > the number of those permutations that are /linear/. Now complete the kinky > new proof of Wilson's theorem by showing that the set of /nonlinear/ > permutations k (with k(0)=0) has a natural equivalence relation on it, > whereby each equivalence class contains p elements. hint: torus ********************************************************** What is a /linear/ or /nonlinear/ permutation? Tonio === Subject: Re: Puzzle about Wilson's theorem Tonico > What is a /linear/ or /nonlinear/ permutation? The linear permutations F to F are the invertible linear mappings F to F, that's all. They are x mapsto bx where b runs over the nonzero elements of F. There are p-1 of these, of course. And the other perms I think we can safely call nonlinear. :D LH === Subject: mass ratio of neutron to proton Cc: annefaissolle@gmail.com, simon.plouffe@gmail.com posting-account=4tsbiAkAAADT1-wT9TrCTqmSG0_6HfC4 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) I have been working on a suitable math expression for the constant : neutron to proton mass ratio. According to the latest results in http://physics.nist.gov/cuu/Constants/Table/allascii.txt FIrst, there is a inherent limitation to these constants since the new definition of the speed of light and the second, in other words we are limited to a precision of 10-11 digits in all best cases. Nevertheless, I took the challenge and liberty of trying to find a suitable math expression over the past years using the tables of the inverter and a couple of techniques with pari-Gp, the LLL algorithm or the PSLQ algorithm still with only 11 digits. The best and simplest expression I could find is the following 1/2 40 1 8 3 -- --------- - ------ 27 Pi 27 cos(----) 15 or when line printed : 40/27/cos(1/15*Pi)-8/27*3^(1/2) or 8/27 * (5/cos(Pi/15) - sqrt(3)) This is an interesting one for more than 1 reason, first the cos(Pi/15) can be simplified to 1/2 1/2 1/2 1/2 1/2 2 3 (5 + 5 ) 5 ----------------------- + ---- - 1/8 8 8 perhaps this can be simplified further. Now the decimal expansion of that number is 1.001378419779635 when the REAL value is 1.00137841918... this means that the error is 1.28e where e is 0.000 000 000 46 I think that this is an acceptable error. This is only a guess based on a large database (2.459 billion ) of mathematical constants and program I developed , I do not pretend it could be the real value. Perhaps it could be interesting to see IF that value can be obtained VIA Ramanujan Continued fractions like : http://en.wikipedia.org/wiki/Ramanujan_continued_fractions or see http://citeseer.ist.psu.edu/249592.html and click on the PDF version or the Ramanujan Notebooks 5 page 9 and following pages... actually the whole book is quite interesting too! Can someone find a better expression ? short, elegant and simple that FITS the error within an acceptable limit ? Simon Plouffe === Subject: Re: mass ratio of neutron to proton I have been working on a suitable math expression for the > constant : neutron to proton mass ratio. According to the latest > results in http://physics.nist.gov/cuu/Constants/Table/allascii.txt FIrst, there is a inherent limitation to these constants since the > new definition of the speed of light and the second, in other > words we are limited to a precision of 10-11 digits in all best > cases. > Nevertheless, I took the challenge and liberty of trying to find > a suitable math expression over the past years using the tables > of the inverter and a couple of techniques with pari-Gp, the > LLL algorithm or the PSLQ algorithm still with only 11 digits. The best and simplest expression I could find is the following > 1/2 > 40 1 8 3 > -- --------- - ------ > 27 Pi 27 > cos(----) > 15 > or when line printed : 40/27/cos(1/15*Pi)-8/27*3^(1/2) or 8/27 * (5/cos(Pi/15) - sqrt(3)) > Counting cos, sqrt, PI and each operator(+-/*) as a single byte each, and also counting each digit in each number as a byte, I count this as 15 bytes long. > This is an interesting one for more than 1 reason, > first the cos(Pi/15) can be simplified to 1/2 1/2 1/2 1/2 1/2 > 2 3 (5 + 5 ) 5 > ----------------------- + ---- - 1/8 > 8 8 perhaps this can be simplified further. Now the decimal expansion of that number is > 1.001378419779635 when the REAL value is > 1.00137841918... These agree to 11 bytes. So the formula giving the number is longer than the number itself. > this means that the error is 1.28e where e > is 0.000 000 000 46 I think that this is an acceptable error. > Is it? How well known is the exact value? === Subject: Re: mass ratio of neutron to proton I have been working on a suitable math expression for the > constant: neutron to proton mass ratio. According to the latest > results in http://physics.nist.gov/cuu/Constants/Table/allascii.txt First, there is a inherent limitation to these constants since the > new definition of the speed of light and the second, in other > words we are limited to a precision of 10-11 digits in all best > cases. Since the proton and neutron are of very similar mass, you can save yourself some accuracy by looking for the expression 1-mp/mn or mp/mn-1. Then you'll probably only need the traditional 3 decimal places, although you can add as much as you want to that, at your whim. Of course, protons and neutrons are also known to consist of up and down quarks, so you may want to express your answer as the ratio of quark masses, rather than protons and neutrons, the latter being so very 1960's. ;) > Nevertheless, I took the challenge and liberty of trying to find > a suitable math expression over the past years using the tables > of the inverter and a couple of techniques with pari-Gp, the > LLL algorithm or the PSLQ algorithm still with only 11 digits. The best and simplest expression I could find is the following 1/2 > 40 1 8 3 > -- --------- - ------ > 27 Pi 27 > cos(----) > 15 > or when line printed : 40/27/cos(Pi/15)-(8/27)*3^(1/2) or (8/27)^3 * (5/cos(Pi/15) - sqrt(3)) Notice that 8/27 is (2/3)^3. > This is an interesting one for more than 1 reason, > first the cos(Pi/15) can be simplified to 1/2 1/2 1/2 1/2 1/2 > 2 3 (5 + 5 ) 5 > ----------------------- + ---- - 1/8 > 8 8 perhaps this can be simplified further. You can pull out a factor of 1/8, and get 1/2 1/2 1/2 1/2 1/2 ( 2 3 (5 + 5 ) + 5 - 1 ) / 8. > Now the decimal expansion of that number is > 1.001378419779635 when the REAL value is > 1.00137841918... > this means that the error is 1.28e where e > is 0.000 000 000 46 I think that this is an acceptable error. Count zeroes to get 0.46 x 10^-9, which is about 1/2 part per billion. > This is only a guess based on a large database (2.459 billion ) of > mathematical constants and program I developed, I do not pretend it > could be the real value. You have tested your theory against experiment, which I think is all that anyone can reasonably ask. You may have a good publication here, or at least a good conference presentation. You should also give a colloquium at your local university. You should track down some other people who understand those three algorithms you mentioned, and get them to be your referees. An error of 0.46 in a billion would seem to be quite reliable, but of course, this sort of thing always has to be vetted by another expert in the field, to make sure you haven't missed something simple. Do you have a detailed writeup of all the important steps you used in your derivation? > Perhaps it could be interesting to see IF that value can be obtained > VIA Ramanujan Continued fractions like: > http://en.wikipedia.org/wiki/Ramanujan_continued_fractions > or see http://citeseer.ist.psu.edu/249592.html and click on the PDF > version or the Ramanujan Notebooks 5 page 9 and following pages. > Actually the whole book is quite interesting too! Can someone find a better expression - a short, elegant and simple > that FITS the error within an acceptable limit? This is not my field of expertise, but if you haven't made any algebra mistakes, you would seem to be at the state of the art. It's time to take this to the next level, and publish or perish. There's a rumor going around that amateur science is a movement that's taking on momentum. Your work may be a great example of this. :) === Subject: Re: Hyperbolic Geometry book recommendation please > Can anyone suggest a good but very basic book to act as > a text/reference book for a short basic course on > Hyperbolic Geometry? The students concerned would not necessarily know > a huge amount of math already, but they would be expected > to be familiar with sinh cosh and tanh etc. Yes, I only now realized that I can. John McCleary, Geometry from a Differentiable Viewpoint. a thorough analysis of Postulate V, and a complete synthetic development of hyperbolic geometry. Part A will make an excellent short course. Many fine exercises. Part A is sixty pages. Part B does Differential geometry in 3 dimensions, and an analytic development of hyperbolic geometry. Publisher: Cambridge University Press ISBN-13: 9780521424806 320pp Edition Number: 1 -- Michael Press === Subject: Re: Hyperbolic Geometry book recommendation please > Can anyone suggest a good but very basic book to act as > a text/reference book for a short basic course on > Hyperbolic Geometry? > The students concerned would not necessarily know > a huge amount of math already, but they would be expected > to be familiar with sinh cosh and tanh etc. IMO, the very best book is Foundations Of Geometry by Gerard Venema, Pearson Prentice Hall, 2006. I've read a lot of the books mentioned in this thread. I've used M.J. Greenberg's and this one. It has what you need and more. You would need to plan. But it has very good exercises and an approach that both students and experts can relate to (really). It's just an excellent textbook. === Subject: Re: Hyperbolic Geometry book recommendation please posting-account=AFsgCgkAAAA3VOfxqn2cTB2LbLN3nbER Gecko/20070319,gzip(gfe),gzip(gfe) I follow up in particular to > Perhaps another possibility is Richard J. Trudeau, > The Non-Euclidean Revolution, Birkhauser 1987 (reprinted 2008). > It's a gently discursive book, with an emphasis on philosophy and > psychology, but there is a development of hyperbolic geometry Yes, I have just been looking at this book, which gives a wonderfully rounded view of the whole subject. I warmly recommend it to anyone with an interest in these matters. There was one aspect of it which caught my eye - almost an error, one might say, and of a type which he had previously been warning us against. He determines that there is a subject called neutral geometry which consists of the Euclidean axioms (or actually their modern logically-cleansed forms) *excluding* the parallel axiom. Various theorems are proved in it, which thus necessarily hold true in both Hyperbolic and Euclidean geometry. AND *elliptic* geometry! But he does not stress this latter point! Indeed he is rather dismissive toward Elliptic geometry as a whole, consigning it to one brief remark on one page. But the sad fact is, that some of his neutral geometry theorems do NOT apply in Elliptic geometry. In particular, that there is always at least one parallel line to any line through any point not on it. This is false! I tracked back to where the error first occurred, and it is in one of those diagram-based non-proofs that he had been specifically warning us about! IMHO this is a definite error in the book, although re-wordings of the basic neutral axioms could probably be made to exclude it. I was just wondering, Angus, (or anyone else), whether you also noticed this defect, and whether you agree with me that it IS an actual error. OTO side of the ledger, I'm pleased to note that he makes quite a big thing out of the fact that (as first observed by Hilbert) SAS congruent triangles HAS TO BE INCLUDED as a basic axiom - one that Euclid missed, in his confusion about conguent vs coinciding lines, and movable diagrams. This axiom has been noted many times, and has sometimes been called the homogeneity axiom, which is a good term, stressing that space looks the same everywhere. I am particularly fascinated by this matter, because (a) I too noticed it as a schoolboy, when I was very annoyed by Euclid's stupid moving lines proof, and (b) I claim that Euclid himself *knew* he was cheating, because he deliberately avoids using the method elsehwere, even where it would make other proofs much simpler. I am glad to note that Trudeau also stresses this last point. Anyway, Angus, I look forward to your comments about the Elliptic geometry failure of the >=1 parallel lines alleged neutral-geometry proof. -- Barycentric Bill A diagram is: (1) worth a thousand words; (2) required as part of your answer; (3) commutative unless otherwise specified. === Subject: Re: Hyperbolic Geometry book recommendation please I follow up in particular to >> Perhaps another possibility is Richard J. Trudeau, >> The Non-Euclidean Revolution, Birkhauser 1987 (reprinted 2008). >> It's a gently discursive book, with an emphasis on philosophy and >> psychology, but there is a development of hyperbolic geometry Yes, I have just been looking at this book, which gives a wonderfully >rounded view of the whole subject. I warmly recommend it to anyone >with an interest in these matters. There was one aspect of it which caught my eye - almost an error, >one might say, and of a type which he had previously been warning >us against. He determines that there is a subject called neutral geometry >which consists of the Euclidean axioms (or actually their modern >logically-cleansed forms) *excluding* the parallel axiom. Various theorems are proved in it, which thus necessarily hold true >in both Hyperbolic and Euclidean geometry. AND *elliptic* geometry! >But he does not stress this latter point! Indeed he is rather >dismissive >toward Elliptic geometry as a whole, consigning it to one brief >remark on one page. But the sad fact is, that some of his >neutral geometry theorems do NOT apply in Elliptic geometry. >In particular, that there is always at least one parallel line >to any line through any point not on it. This is false! >I tracked back to where the error first occurred, and it is >in one of those diagram-based non-proofs that he had been >specifically warning us about! According to Greenberg, this proposition is indeed false in elliptic geometry, but ... >IMHO this is a definite error in the book, although re-wordings >of the basic neutral axioms could probably be made to exclude it. I was just wondering, Angus, (or anyone else), whether you also >noticed this defect, and whether you agree with me that it IS >an actual error. ... it is not an actual error, because elliptic geometry is not a special case of neutral geometry. (So much for neutrality, then!) A third geometry could be studied, one in which there is /no/ parallel to l through P, i.e., a geometry in which parallel lines do not exist. However, if we simply add the latter as a new parallel axiom to replace the other parallel axioms, the system we get is inconsistent. [...] all the axioms of betweenness have to be scrapped. They are replaced instead by seven axioms of separation. There might still be something wrong with the proof. I can't say, because I haven't actually started reading any of these books yet. (My interest in the subject was sparked by John Stillwell, /Math- ematics and Its History/, which is one of several books I've been slowly working through for the past few months.) >A diagram is: (1) worth a thousand words; > (2) required as part of your answer; > (3) commutative unless otherwise specified. By the evident commutativity of the evident diagram, all the expected theorems are true. newcommand{inner}[2]{left<#1,#2right>} [ begin{CD} w @VVV T^*w end{CD} quad quad begin{CD} W @>cong>> cL(W, F) @VT^*VV @VV_comp TV V @>>cong> cL(V, F) end{CD} quad begin{CD} inner{_}{w} @VVV inner{T_}{w} = inner{_}{T^*w} end{CD} ] -- Angus Rodgers Contains mild peril === Subject: Impossible puzzle? posting-account=8pqHVQoAAACXcicTVwVXXbuyCC_vfFWy Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) is impossible. For the following figure ASCII art attempt... Assume the outside is a rectangle and the inner lines are all connected. If the ASCII art screws up you have a rectangle divided in two horizontally. The top half is divided into 2 equal suqraes and the bottom half is divided into 3 rectangles. __________ | | | |___|____| | | | | |_|___|__| You need to draw a continuous line that goes through all line segments without crossing over itself. For example the middle horizontal line is made up of 4 line segments. The top horizontal line has 2. The bottom horizontal line has 3. single line segment unreachable. This reminded me of topology or graph theory? So can anyone either give a solution or prove it is impossible? I was given this puzzle today from a guy who apparently has been trying to work it out on and off for 40 years! TG === Subject: Re: Impossible puzzle? > is impossible. For the following figure ASCII art attempt... > Assume the outside is a rectangle and the inner lines are all > connected. > If the ASCII art screws up you have a rectangle divided in two > horizontally. The top half is divided into 2 equal suqraes and the > bottom half is divided into 3 rectangles. __________ > | | | > |___|____| > | | | | > |_|___|__| You need to draw a continuous line that goes through all line segments > without crossing over itself. > For example the middle horizontal line is made up of 4 line segments. > The top horizontal line has 2. The bottom horizontal line has 3. Since a single line is impossible, maybe a continuous curve is also allowed. It is very easy to draw a continuous curve that _crosses_ every line segment, but does not cross itself. Such a curve will however cross some segments multiple times, but the puzzle does not state that this is forbidden. A curve that crosses every segment exactly once is impossible, which can be seen from the dual graph. Peter === Subject: Re: Impossible puzzle? >> is impossible. >> For the following figure ASCII art attempt... >> Assume the outside is a rectangle and the inner lines are all >> connected. >> If the ASCII art screws up you have a rectangle divided in two >> horizontally. The top half is divided into 2 equal suqraes and the >> bottom half is divided into 3 rectangles. >> __________ >> | | | >> |___|____| >> | | | | >> |_|___|__| >> You need to draw a continuous line that goes through all line segments >> without crossing over itself. >> For example the middle horizontal line is made up of 4 line segments. >> The top horizontal line has 2. The bottom horizontal line has 3. > Since a single line is impossible, maybe a continuous curve is also > allowed. It is very easy to draw a continuous curve that _crosses_ every > line segment, but does not cross itself. > Such a curve will however cross some segments multiple times, but the > puzzle does not state that this is forbidden. A curve that crosses every > segment exactly once is impossible, which can be seen from the dual graph. There is, however, a solution that passes through every segment exactly once, where one of the segments is traversed lengthwise. -- Dave Seaman Third Circuit ignores precedent in Mumia Abu-Jamal ruling. === Subject: Re: Impossible puzzle? > If the ASCII art screws up you have a rectangle divided in two It shouldn't if you compose in monospace font, remind the readers to read in monospace font and the reader uses a monospace font. > __________ > | | | > |___|____| > | | | | > |_|___|__| You need to draw a continuous line that goes through all line segments > without crossing over itself. > For example the middle horizontal line is made up of 4 line segments. > The top horizontal line has 2. The bottom horizontal line has 3. How many line segments is a corner? Two? ____ | | Is going through a point where line segments meet allowed? If so, does it constitute going through some, all or none of the line segments? > single line segment unreachable. It is easy, go through one of the line segments twice. ---- === Subject: Re: Impossible puzzle? posting-account=8pqHVQoAAACXcicTVwVXXbuyCC_vfFWy Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > If the ASCII art screws up you have a rectangle divided in two It shouldn't if you compose in monospace font, remind the readers > to read in monospace font and the reader uses a monospace font. > > | æ | æ æ| > | | | > | | æ | æ| > | | | | > You need to draw a continuous line that goes through all line segments > without crossing over itself. > For example the middle horizontal line is made up of 4 line segments. > The top horizontal line has 2. æThe bottom horizontal line has 3. How many line segments is a corner? æTwo? > > | > | Is going through a point where line segments meet allowed? > If so, does it constitute going through some, all or none of > the line segments? > single line segment unreachable. It is easy, go through one of the line segments twice. ---- As a clarification, yes the corner counts as 2 line segments. You cannot go through corners. Each line segment must be crossed only once. my thoughts that it is impossible. TG === Subject: Re: Impossible puzzle? >is impossible. For the following figure ASCII art attempt... >Assume the outside is a rectangle and the inner lines are all >connected. >If the ASCII art screws up you have a rectangle divided in two >horizontally. The top half is divided into 2 equal suqraes and the >bottom half is divided into 3 rectangles. __________ >| | | >|___|____| >| | | | >|_|___|__| You need to draw a continuous line that goes through all line segments >without crossing over itself. >For example the middle horizontal line is made up of 4 line segments. >The top horizontal line has 2. The bottom horizontal line has 3. single line segment unreachable. This reminded me of topology or graph theory? So can anyone either give a solution or prove it is impossible? I was given this puzzle today from a guy who apparently has been >trying to work it out on and off for 40 years! >TG > It is well known that you can't draw such a line. This and problems like it are similar to the Konigsberg Bridge problem, solved by Euler. It isn't difficult to see why it is impossible. Take a look at http://www.contracosta.edu/math/konig.htm for example. --Lynn === Subject: Re: Impossible puzzle? posting-account=O9zR9AkAAACmp918j6u5m5plppeILcze Filter 1.2.0.72; .NET CLR 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022; WWTClient2),gzip(gfe),gzip(gfe) > is impossible. For the following figure ASCII art attempt... > Assume the outside is a rectangle and the inner lines are all > connected. > If the ASCII art screws up you have a rectangle divided in two > horizontally. æThe top half is divided into 2 equal suqraes and the > bottom half is divided into 3 rectangles. > | æ | æ æ| > | | | > | | æ | æ| > | | | | You need to draw a continuous line that goes through all line segments > without crossing over itself. > For example the middle horizontal line is made up of 4 line segments. > The top horizontal line has 2. æThe bottom horizontal line has 3. single line segment unreachable. This reminded me of topology or graph theory? So can anyone either give a solution or prove it is impossible? There are trick solutions, where the curve goes through a corner. But, of course, that is not what is intended by the problem. So, ruling that out, the problem can be proven impossible by graph theory. Note that the figure divides the plane into six regions: the outside, and the five boxes. The upper left box is enclosed by 5 segments, and similarly for the upper right box and the lower center box. Finally, you can enter or leave the outside by crossing one of 9 segments. If your curve starts outside a box bounded by an odd number of segments, then it must end inside that box in order to cross the odd number of segments, and vice-versa. Thus, one of the endpoints of the curve must be in the upper left box, one of the endpoints must be in the upper right box, one must be in the lower center box, and one must be in the outside. But since a continuous curve has only two entpoints, it cannot have endpoints in all four places. Thus no solution is possible. Dave === Subject: Re: Impossible puzzle? posting-account=a6woBRAAAADpNFZJBA7ZBx35zXaKmaP4 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > is impossible. For the following figure ASCII art attempt... > Assume the outside is a rectangle and the inner lines are all > connected. > If the ASCII art screws up you have a rectangle divided in two > horizontally. æThe top half is divided into 2 equal suqraes and the > bottom half is divided into 3 rectangles. > | æ | æ æ| > | | | > | | æ | æ| > | | | | You need to draw a continuous line that goes through all line segments > without crossing over itself. > For example the middle horizontal line is made up of 4 line segments. > The top horizontal line has 2. æThe bottom horizontal line has 3. single line segment unreachable. This reminded me of topology or graph theory? So can anyone either give a solution or prove it is impossible? I was given this puzzle today from a guy who apparently has been > trying to work it out on and off for 40 years! > TG This is an application of Euler's solution to the Konigsberg bridge problem: http://en.wikipedia.org/wiki/Seven Bridges of K%C3%B6nigsberg Essentially you look at the number of vertices with an odd number of edges. Too many of these (more than two) and it becomes impossible to visit all edges with a continuous path without recrossing any edges. Such a path is called an Eulerian path: http://en.wikipedia.org/wiki/Eulerian path In your formulation something more seems to be required, namely an Eulerian circuit, visiting every edge exactly once and returning to the starting point. For this to exist, every vertex must have even degree. Your diagram has seven vertices with an odd degree (number of edges incident). === Subject: Re: Impossible puzzle? posting-account=O9zR9AkAAACmp918j6u5m5plppeILcze Filter 1.2.0.72; .NET CLR 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022; WWTClient2),gzip(gfe),gzip(gfe) > Your diagram has seven vertices with an odd > degree (number of edges incident). Isn't it four? Dave === Subject: Re: Impossible puzzle? - Counting exercise > Your diagram has seven vertices with an odd >> degree (number of edges incident). Isn't it four? Dave ------------------------------------------------------------------- (...) For the following figure ASCII art attempt... Assume the outside is a rectangle and the inner lines are all connected. If the ASCII art screws up you have a rectangle divided in two horizontally. The top half is divided into 2 equal suqraes and the bottom half is divided into 3 rectangles. __________ | | | |___|____| | | | | |_|___|__| (...) ------------------------------------------------------------------- End of quotation I can't help counting =eight= degree-3 vertices... _________1_________ | | | | | | | | | 2____3___4___5____6 | | | | | | | | | | | | |____7_______8____| Ciao: Johan E. Mebius === Subject: Re: Impossible puzzle? - Counting exercise > I can't help counting =eight= degree-3 vertices... > _________1_________ > | | | > | | | > | | | > 2____3___4___5____6 > | | | | > | | | | > | | | | > |____7_______8____| > Ciao: Johan E. Mebius You are counting the wrong thing. Since we want to *cross* each line segment we need to have vertices on the insides of regions, and edges crossing the line segments from inside to outside (or vice versa). This is, of course, the dual graph to what is being drawn. Then and Euler traversal of the dual corresponds to the most obvious version of what the OP is asking. There are six regions, two with four line segments, three with 5 line segments, and one (the outside) with 9 line segments. Thus the dual graph has four vertices with an odd number of edges, hence it has no Euler Path. === Subject: Re: Impossible puzzle? - Counting exercise posting-account=a6woBRAAAADpNFZJBA7ZBx35zXaKmaP4 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) On Jul 30, 10:32æam, riderofgiraffes I can't help counting =eight= degree-3 vertices... > 1 > | æ æ æ æ| æ æ æ æ| > | æ æ æ æ| æ æ æ æ| > | æ æ æ æ| æ æ æ æ| > 2 3 4 5 6 > | æ æ| æ æ æ | æ æ| > | æ æ| æ æ æ | æ æ| > | æ æ| æ æ æ | æ æ| > | 7 8 | > Ciao: Johan E. Mebius You are counting the wrong thing. æSince we want to > *cross* each line segment we need to have vertices on > the insides of regions, and edges crossing the line > segments from inside to outside (or vice versa). æThis > is, of course, the dual graph to what is being drawn. > Then and Euler traversal of the dual corresponds to > the most obvious version of what the OP is asking. There are six regions, two with four line segments, > three with 5 line segments, and one (the outside) > with 9 line segments. æThus the dual graph has four > vertices with an odd number of edges, hence it has > no Euler Path. That makes more sense, given the OP's claim that a partial solution exists with one segment unreachable. I took OP's goes through line segments to mean traversing them... === Subject: Re: Impossible puzzle? - Counting exercise posting-account=8pqHVQoAAACXcicTVwVXXbuyCC_vfFWy Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > On Jul 30, 10:32æam, riderofgiraffes I can't help counting =eight= degree-3 vertices... > 1 > | æ æ æ æ| æ æ æ æ| > | æ æ æ æ| æ æ æ æ| > | æ æ æ æ| æ æ æ æ| > 2 3 4 5 6 > | æ æ| æ æ æ | æ æ| > | æ æ| æ æ æ | æ æ| > | æ æ| æ æ æ | æ æ| > | 7 8 | > Ciao: Johan E. Mebius > You are counting the wrong thing. æSince we want to > *cross* each line segment we need to have vertices on > the insides of regions, and edges crossing the line > segments from inside to outside (or vice versa). æThis > is, of course, the dual graph to what is being drawn. > Then and Euler traversal of the dual corresponds to > the most obvious version of what the OP is asking. > There are six regions, two with four line segments, > three with 5 line segments, and one (the outside) > with 9 line segments. æThus the dual graph has four > vertices with an odd number of edges, hence it has > no Euler Path. That makes more sense, given the OP's claim that > a partial solution exists with one segment > unreachable. æI took OP's goes through line > segments to mean traversing them... > If traversing means crossing a segment then yes. I should have scanned a page of my attempts originally. It would have cut down the ambiguity. I gave the guy a printout of this thread and copies of the linked sites. On one hand he was happy to know that it was impossible, but on the other he didn't know how to handle spending 40 years on an unsolvable problem :) TG === Subject: Re: Impossible puzzle? - Counting exercise <48905787.5010208@xs4all.nl > _________1_________ > | | | > | | | > | | | > 2____3___4___5____6 > | | | | > | | | | > | | | | > |____7_______8____| d________1________c | | | | | | | | | 2____3___4___5____6 | | | | | | | | | | | | a____7_______8____b === Subject: Re: Impossible puzzle? Your diagram has seven vertices with an odd > degree (number of edges incident). Isn't it four? Indeed. You can't have a (finite) diagram with exactly seven vertices with odd degree. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) It's not clear to me why the Lorentz transformation can't be reduced to the Galilean transformation by resetting clocks, rescaling distance measures and fiddling with clock rates according to the recipe on page 11 of http://www.everythingimportant.org/relativity/special.pdf and equations (48) to (58). How do you answer this riddle? Shubee === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > It's not clear to me why the Lorentz transformation can't be reduced > to the Galilean transformation by resetting clocks, rescaling distance > measures and fiddling with clock rates according to the recipe on page > 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand > equations (48) to (58). How do you answer this riddle? By not using your recipe. Take the limit c--->infty. Shubee === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? posting-account=51499wkAAAAr0khaExEjlNiEzK2ubANQ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > It's not clear to me why the Lorentz transformation can't be reduced > to the Galilean transformation by resetting clocks, rescaling distance > measures and fiddling with clock rates according to the recipe on page > 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand > equations (48) to (58). > The reason it's not clear to you is because you are dumb. === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > It's not clear to me why the Lorentz transformation can't be reduced > to the Galilean transformation by resetting clocks, rescaling distance > measures and fiddling with clock rates according to the recipe on page > 11 of http://www.everythingimportant.org/relativity/special.pdf and > equations (48) to (58). The reason it's not clear to you is because you are dumb. But it is obvious that you are too cowardly and too insecure in your own professed enlightenment to answer an easy multiple choice question: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? Shubee === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > It's not clear to me why the Lorentz transformation can't be reduced > to the Galilean transformation by resetting clocks, rescaling distance > measures and fiddling with clock rates according to the recipe on page > 11 of http://www.everythingimportant.org/relativity/special.pdf and > equations (48) to (58). > How do you answer this riddle? > Shubee Yer gonna fix Lorentz transformation by starting with Galilean > transformation and imposing Lorentz transformation properties? I asked, How do you answer this riddle? and you respond by accusing me of wanting to fix something. I asked, Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? but your response indicates that you're too demented to answer the question directly. > As always, http://www.albinoblacksheep.com/flash/youare As always, you are speaking of yourself. Shubee === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? posting-account=IwEXfQoAAADCjdz2TIptLhugu5MWo47W Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > It's not clear to me why the Lorentz transformation can't be reduced > to the Galilean transformation by resetting clocks, rescaling distance > measures and fiddling with clock rates according to the recipe on page > 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand > equations (48) to (58). How do you answer this riddle? Shubee The Lorentz transformation x' = gamma (x - v t) y' = y z' = z t' = gamma (t - v x / c^2) and the Galilean transformation x' = x - v t y' = y y' = z t' = t use two very different concepts of time. In a lorentz transform, t and t' are times measured by clocks, consequently velocities are not observables, but derived quantities after you've performed at least two time measurements over the same distance interval. In a Galilean transformation, t and t' are actually the same, by definition. This means that velocities in a Galilean transformation are not the same velocities under a Lorentz transformation. To solve the riddle, you must distinguish them: The Lorentz transformation changes notation to x' = gamma (x - v_r t_r) y' = y z' = z t_r' = gamma (t_r - v_r x / c^2) The Galilean transformation remains with the same notation x' = x - v t y' = y y' = z t' = t Now, you can approximate the Lorentz transformation to the Galilean transformation (but it can't be exactly reduced to), by simply stating that gamma = 1/sqrt(1 - v_r^2/c^2) = cosh(v/c), after some simple algebraic steps, you arrive at v_r/c = tanh(v/c). Therefore, the new Lorentz transformation now reads x' = cosh(v/c)(x - c tanh(v/c) t_r) y' = y z' = z t_r' = cosh(v/c)(t_r - c tanh(v/c) x / c^2) x' = x cosh(v/c) - c sinh(v/c) t_r y' = y z' = z t_r' = t_r cosh(v/c) - sinh(v/c) x / c which means that for v->0, with c constant, it reduces to Galilean relativity, and for v->oo it reduces to SR [assumed that, since it is v_r/c = tanh(v/c), v can exceeds c, but v_r can't]. In conclusion, neither Galilean tranformations nor Lorentz transformations are exactly correct, theoretically, because there exists a more general tranformation, x' = x cosh(v/c) - c sinh(v/c) t y' = y z' = z t' = t cosh(v/c) - sinh(v/c) x / c, from which both transformations can be derived, taking the suitable limit for v. === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > It's not clear to me why the Lorentz transformation can't be reduced > to the Galilean transformation by resetting clocks, rescaling distance > measures and fiddling with clock rates according to the recipe on page > 11 of http://www.everythingimportant.org/relativity/special.pdf and > equations (48) to (58). > How do you answer this riddle? In conclusion, neither Galilean tranformations nor Lorentz > transformations are exactly correct, theoretically, because > there exists a more general tranformation, x' = x cosh(v/c) - c sinh(v/c) t > y' = y > z' = z > t' = t cosh(v/c) - sinh(v/c) x / c, It is widely recognized that this transformation is the Lorentz transformation. http://www.everythingimportant.org/relativity/generalized.htm You have merely written the rapidity theta as v/c, which you are free to do. Shubee === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? posting-account=IwEXfQoAAADCjdz2TIptLhugu5MWo47W Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > It's not clear to me why the Lorentz transformation can't be reduced > to the Galilean transformation by resetting clocks, rescaling distance > measures and fiddling with clock rates according to the recipe on page > 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand > equations (48) to (58). > How do you answer this riddle? > In conclusion, neither Galilean tranformations nor Lorentz > transformations are exactly correct, theoretically, because > there exists a more general tranformation, > x' = x cosh(v/c) - c sinh(v/c) t > y' = y > z' = z > t' = t cosh(v/c) - sinh(v/c) x / c, It is widely recognized that this transformation is the Lorentz > transformation.http://www.everythingimportant.org/relativity/generalized.htm > You have merely written the rapidity theta as v/c, which you are free > to do. Shubee I did more than that, INHO. I've identified v_r/c = tanh(v/c), where v_r is a relativistic speed, and v is a Galilean speed. This solves your 'riddle', doesn't it? === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > It's not clear to me why the Lorentz transformation can't be reduced > to the Galilean transformation by resetting clocks, rescaling distance > measures and fiddling with clock rates according to the recipe on page > 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand > equations (48) to (58). > How do you answer this riddle? > In conclusion, neither Galilean tranformations nor Lorentz > transformations are exactly correct, theoretically, because > there exists a more general tranformation, > x' = x cosh(v/c) - c sinh(v/c) t > y' = y > z' = z > t' = t cosh(v/c) - sinh(v/c) x / c, > It is widely recognized that this transformation is the Lorentz > transformation.http://www.everythingimportant.org/relativity/generalized.htm > You have merely written the rapidity theta as v/c, which you are free > to do. > Shubee I did more than that, INHO. Well, you've managed to fool yourself into thinking that your transformation represents a different physics than what the Lorentz transformation implies. > I've identified v_r/c = tanh(v/c), > where v_r is a relativistic speed, and v is a Galilean speed. Correct but your identification is just an obvious reshuffle on the definitions of words. What you label a Galilean speed relativists call the rapidity. And what you name relativistic speed everyone else calls ordinary velocity. How profound is that? > This solves your 'riddle', doesn't it? Not even close. Shubee in sci.physics.relativity: >> It's not clear to me why the Lorentz transformation can't be reduced to >> the Galilean transformation by resetting clocks, rescaling distance >> measures and fiddling with clock rates according to the recipe on page >> 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand >> equations (48) to (58). >> How do you answer this riddle? [...] > The Lorentz transformation [...] > and the Galilean transformation [...] > use two very different concepts of time. In a lorentz transform, t and > t' are times measured by clocks, consequently velocities are not > observables, but derived quantities after you've performed at least two Huh? Velocity not observable? Ever hear of a speedometer or Doppler shift? Of course velocity is an observable under both Lorentz and Galilean transforms. > time measurements over the same distance interval. In a Galilean > transformation, t and t' are actually the same, by definition. This > means that velocities in a Galilean transformation are not the same > velocities under a Lorentz transformation. v = dx/dt = dx'/dt' in both. [...] > Now, you can approximate the Lorentz transformation to the Galilean > transformation (but it can't be exactly reduced to), by simply stating > that gamma = 1/sqrt(1 - v_r^2/c^2) = cosh(v/c), after some simple algebraic steps, you arrive at v_r/c = tanh(v/c). Wrong equation! (again!) > Therefore, the new Lorentz transformation now reads x' = cosh(v/c)(x - c tanh(v/c) t_r) > y' = y > z' = z > t_r' = cosh(v/c)(t_r - c tanh(v/c) x / c^2) Wrong! (again!) Why don't you give up the crazy notion that alpha=v/c. It simply is *not*true*. [rest deleted since it follows from wrong equations] -- // The TimeLord says: // Pogo 2.0 = We have met the aliens, and they are us! posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > in > Now, you can approximate the Lorentz transformation to the Galilean > transformation (but it can't be exactly reduced to), by simply stating > that > gamma = 1/sqrt(1 - v_r^2/c^2) = cosh(v/c), > after some simple algebraic steps, you arrive at > v_r/c = tanh(v/c). Wrong equation! (again!) Actually Albertito is right because it's perfectly consistent to make up new names for everything, such as replacing the rapidity with v/c and no longer using v for velocity but using v_r instead. > Therefore, the new Lorentz transformation now reads > x' = cosh(v/c)(x - c tanh(v/c) t_r) > y' = y > z' = z > t_r' = cosh(v/c)(t_r - c tanh(v/c) x / c^2) Wrong! (again!) Why don't you give up the crazy notion that alpha=v/c. It > simply is *not*true*. There is nothing wrong the Albertito reshuffle on the meaning of words and equations. Shubee === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? sci.physics.relativity: > It's not clear to me why the Lorentz transformation can't be reduced to > the Galilean transformation by resetting clocks, rescaling distance > measures and fiddling with clock rates according to the recipe on page > 11 of http://www.everythingimportant.org/relativity/special.pdf and > equations (48) to (58). How do you answer this riddle? Shubee Easy. The Lorentz transformation x' = gamma (x - v t) y' = y z' = z t' = gamma (t - v x / c^2) is not the same as the Galilean transformation x' = x - v t y' = y y' = z t' = t Simple inspection reveals that. The only way the two can ever be the same is when v=0; but Relativity already has that built in. Rescaling x or t will not change the underlying nature of the transformation. By the way, you've already posted the link to your paper here and elsewhere. I'm not impressed with that paper since it seems an overanalyzing of a much simpler issue. -- // The TimeLord says: // Pogo 2.0 = We have met the aliens, and they are us! === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? <69GdnbiUUZZgvw3VnZ2dnUVZ_gudnZ2d@comcast.com> posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > sci.physics.relativity: > It's not clear to me why the Lorentz transformation can't be reduced to > the Galilean transformation by resetting clocks, rescaling distance > measures and fiddling with clock rates according to the recipe on page > 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand > equations (48) to (58). > How do you answer this riddle? > Shubee Easy. The Lorentz transformation x' = gamma (x - v t) > y' = y > z' = z > t' = gamma (t - v x / c^2) is not the same as the Galilean transformation x' = x - v t > y' = y > y' = z > t' = t Simple inspection reveals that. The only way the two can ever be the same > is when v=0; but Relativity already has that built in. Rescaling x or t > will not change the underlying nature of the transformation. It is clear that resetting clocks plus rescaling x and t converts one transformation to the other so you obviously haven't answered the riddle. Shubee === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? >> sci.physics.relativity: >> It's not clear to me why the Lorentz transformation can't be reduced to >> the Galilean transformation by resetting clocks, rescaling distance >> measures and fiddling with clock rates according to the recipe on page >> 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand >> equations (48) to (58). >> How do you answer this riddle? >> Shubee >> Easy. The Lorentz transformation >> x' = gamma (x - v t) >> y' = y >> z' = z >> t' = gamma (t - v x / c^2) >> is not the same as the Galilean transformation >> x' = x - v t >> y' = y >> y' = z >> t' = t >> Simple inspection reveals that. The only way the two can ever be the same >> is when v=0; but Relativity already has that built in. Rescaling x or t >> will not change the underlying nature of the transformation. It is clear that resetting clocks plus rescaling x and t converts one > transformation to the other so you obviously haven't answered the > riddle. Your riddle is simple history. The LT can be decomposed into several transformations, one of which is the GT. That's even how it all began: GT + length contraction + time dilation + synchronization convention = LT (Lorentz + Poincare). It's similar for relativitic Doppler (Einstein), of which it is rather well known that it can be decomposed into classical Doppler + time dilation. Harald === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? <1217425974_853@sicinfo3.epfl.ch> posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) On Jul 30, 8:52 am, harry > sci.physics.relativity: >> It's not clear to me why the Lorentz transformation can't be reduced to >> the Galilean transformation by resetting clocks, rescaling distance >> measures and fiddling with clock rates according to the recipe on page >> 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand >> equations (48) to (58). >> How do you answer this riddle? >> Shubee >> Easy. The Lorentz transformation >> x' = gamma (x - v t) >> y' = y >> z' = z >> t' = gamma (t - v x / c^2) >> is not the same as the Galilean transformation >> x' = x - v t >> y' = y >> y' = z >> t' = t >> Simple inspection reveals that. The only way the two can ever be the same >> is when v=0; but Relativity already has that built in. Rescaling x or t >> will not change the underlying nature of the transformation. > It is clear that resetting clocks plus rescaling x and t converts one > transformation to the other so you obviously haven't answered the > riddle. Your riddle is simple history. The LT can be decomposed into several > transformations, one of which is the GT. That's even how it all began: GT + > length contraction + time dilation + synchronization convention = LT > (Lorentz + Poincare). It's similar for relativitic Doppler (Einstein), of which it is rather > well known that it can be decomposed into classical Doppler + time dilation. Harald So, if the Lorentz transformation is logically equivalent to the Galilean transformation, then the Lorentz transformation all by itself doesn't imply a physical time dilation. One must bring to the calculation other assumptions, just as one must remember the scaling factor interpretation that that was added to the Galilean transformation but which dropped out because of the mathematical manipulation. Shubee === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? > On Jul 30, 8:52 am, harry sci.physics.relativity: > It's not clear to me why the Lorentz transformation can't be reduced to > the Galilean transformation by resetting clocks, rescaling distance > measures and fiddling with clock rates according to the recipe on page > 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand > equations (48) to (58). > How do you answer this riddle? > Shubee >> Easy. The Lorentz transformation >> x' = gamma (x - v t) >> y' = y >> z' = z >> t' = gamma (t - v x / c^2) >> is not the same as the Galilean transformation >> x' = x - v t >> y' = y >> y' = z >> t' = t >> Simple inspection reveals that. The only way the two can ever be the same >> is when v=0; but Relativity already has that built in. Rescaling x or t >> will not change the underlying nature of the transformation. > It is clear that resetting clocks plus rescaling x and t converts one > transformation to the other so you obviously haven't answered the > riddle. >> Your riddle is simple history. The LT can be decomposed into several >> transformations, one of which is the GT. That's even how it all began: GT + >> length contraction + time dilation + synchronization convention = LT >> (Lorentz + Poincare). >> It's similar for relativitic Doppler (Einstein), of which it is rather >> well known that it can be decomposed into classical Doppler + time dilation. >> Harald So, if the Lorentz transformation is logically equivalent to the > Galilean transformation, then the Lorentz transformation all by itself > doesn't imply a physical time dilation. What's physical time dilation, Shooby? > One must bring to the > calculation other assumptions, just as one must remember the scaling > factor interpretation that that was added to the Galilean > transformation but which dropped out because of the mathematical > manipulation. Shubee === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering jem says... >What's physical time dilation, Shooby? You have a clock traveling inertially (constant velocity). You have a second clock that starts off at the same location as the first clock, then is carried far away at high speed, then carried back to the first clock. Then the elapsed times on the two clocks are compared. Physical time dilation is the empirically verifiable fact that the traveling clock will show less elapsed time than the inertial clock. -- Daryl McCullough Ithaca, NY === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering > jem says... >What's physical time dilation, Shooby? You have a clock traveling inertially (constant velocity). > You have a second clock that starts off at the same location > as the first clock, then is carried far away at high speed, > then carried back to the first clock. Then the elapsed times > on the two clocks are compared. Physical time dilation is > the empirically verifiable fact that the traveling clock > will show less elapsed time than the inertial clock. -- > Daryl McCullough > Ithaca, NY That sounds good to me. :-) The LT even imply such a physical time dilation, as the above can be done in ways that make eventual acceleration effects negligible. Of course, that's just what Einstein already concluded in 1905 (very clever IMHO). Harald === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering harry says... >> jem says... >What's physical time dilation, Shooby? >> You have a clock traveling inertially (constant velocity). >> You have a second clock that starts off at the same location >> as the first clock, then is carried far away at high speed, >> then carried back to the first clock. Then the elapsed times >> on the two clocks are compared. Physical time dilation is >> the empirically verifiable fact that the traveling clock >> will show less elapsed time than the inertial clock. >That sounds good to me. :-) >The LT even imply such a physical time dilation, as the above can be done >in ways that make eventual acceleration effects negligible. No, it does not. Special Relativity implies that, but SR is not the Lorentz transforms. The Lorentz transforms is a mapping between two different coordinate systems. It's not a theory of physics. It doesn't make empirical predictions. >Of course, that's just what Einstein already concluded in 1905 >(very clever IMHO). No, he didn't. He didn't derive time dilation from the Lorentz transforms, he derived time dilation *and* the Lorentz transforms from the relativity principle together with the assumption that light has the same speed c in all standard inertial coordinate systems (he calls them Galliliean coordinates here: http://www.bartleby.com/173/4.html) -- Daryl McCullough Ithaca, NY === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? > On Jul 30, 8:52 am, harry sci.physics.relativity: > It's not clear to me why the Lorentz transformation can't be reduced to > the Galilean transformation by resetting clocks, rescaling distance > measures and fiddling with clock rates according to the recipe on page > 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand > equations (48) to (58). > How do you answer this riddle? > Shubee >> Easy. The Lorentz transformation >> x' = gamma (x - v t) >> y' = y >> z' = z >> t' = gamma (t - v x / c^2) >> is not the same as the Galilean transformation >> x' = x - v t >> y' = y >> y' = z >> t' = t >> Simple inspection reveals that. The only way the two can ever be the same >> is when v=0; but Relativity already has that built in. Rescaling x or t >> will not change the underlying nature of the transformation. > It is clear that resetting clocks plus rescaling x and t converts one > transformation to the other so you obviously haven't answered the > riddle. >> Your riddle is simple history. The LT can be decomposed into several >> transformations, one of which is the GT. That's even how it all began: GT + >> length contraction + time dilation + synchronization convention = LT >> (Lorentz + Poincare). >> It's similar for relativitic Doppler (Einstein), of which it is rather >> well known that it can be decomposed into classical Doppler + time dilation. >> Harald So, if the Lorentz transformation is logically equivalent to the > Galilean transformation, Do you seriously believe, mathematician Shooby, that y=6*x is logically equivalent to y=3*x, because x can be rescaled by a factor of 2? > then the Lorentz transformation all by itself > doesn't imply a physical time dilation. One must bring to the > calculation other assumptions, Do you seriously believe, mathematician Shooby, that one can't conclude y>x from y=1+x^2 unless one first brings to the calculation the assumption that x can't be rescaled? > just as one must remember the scaling > factor interpretation that that was added to the Galilean > transformation but which dropped out because of the mathematical > manipulation. Shubee === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) >> Harald > So, if the Lorentz transformation is logically equivalent to the > Galilean transformation, Do you seriously believe, mathematician Shooby, that y=6*x is > logically equivalent to y=3*x, because x can be rescaled by a factor > of 2? Is that what I'm saying or is that what you hope I'm saying because you want it to be so? My new space and time variables are clearly marked tilde{X} and tilde{T} http://www.everythingimportant.org/relativity/special.pdf Therefore y=6*x is logically equivalent to y=3*w, because x can be rescaled by a suitable factor. It also logically follows that you are willfully blind. > then the Lorentz transformation all by itself > doesn't imply a physical time dilation. One must bring to the > calculation other assumptions, > just as one must remember the scaling > factor interpretation that that was added to the Galilean > transformation but which dropped out because of the mathematical > manipulation. Shubee === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? <69GdnbiUUZZgvw3VnZ2dnUVZ_gudnZ2d@comcast.com> <1217425974_853@sicinfo3.epfl.ch> sci.physics.relativity: [...] >> Do you seriously believe, mathematician Shooby, that y=6*x is >> logically equivalent to y=3*x, because x can be rescaled by a factor >> of 2? [...] > Therefore y=6*x is logically equivalent to y=3*w, because x can be > rescaled by a suitable factor. It also logically follows that you are > willfully blind. Think about what you are saying. For which combinations of [x,y] does one equation equal the other? Only [0,0]! For [6,1] the first equation is true but the second not. Therefore they are *not* logically equivalent. [...] -- // The TimeLord says: // Pogo 2.0 = We have met the aliens, and they are us! === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? > On Jul 30, 8:52 am, harry > in > sci.physics.relativity: > It's not clear to me why the Lorentz transformation can't be reduced > to > the Galilean transformation by resetting clocks, rescaling distance > measures and fiddling with clock rates according to the recipe on > page > 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand > equations (48) to (58). > How do you answer this riddle? > Shubee > Easy. The Lorentz transformation > x' = gamma (x - v t) > y' = y > z' = z > t' = gamma (t - v x / c^2) > is not the same as the Galilean transformation > x' = x - v t > y' = y > y' = z > t' = t > Simple inspection reveals that. The only way the two can ever be the > same > is when v=0; but Relativity already has that built in. Rescaling x or > t > will not change the underlying nature of the transformation. >> It is clear that resetting clocks plus rescaling x and t converts one >> transformation to the other so you obviously haven't answered the >> riddle. >> Your riddle is simple history. The LT can be decomposed into several >> transformations, one of which is the GT. That's even how it all began: GT >> + >> length contraction + time dilation + synchronization convention = LT >> (Lorentz + Poincare). >> It's similar for relativitic Doppler (Einstein), of which it is rather >> well known that it can be decomposed into classical Doppler + time >> dilation. >> Harald So, if the Lorentz transformation is logically equivalent to the > Galilean transformation, Wrong - as sketched here above. > then the Lorentz transformation all by itself > doesn't imply a physical time dilation. One must bring to the > calculation other assumptions, One has to use for example the assumption that one can construct linear coordinate systems, such as also assumed with the Galilean transformation. > just as one must remember the scaling > factor interpretation that that was added to the Galilean > transformation but which dropped out because of the mathematical > manipulation. Nothing dropped out: it's all included, as indicated. Note: all the time you draw rather odd sounding conclusions from straightforward procedures and mathematics. I won't comment anymore on such manipulations of phrases. Harald === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? <1217432351_855@sicinfo3.epfl.ch> posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) On Jul 30, 10:39 am, harry > It is clear that resetting clocks plus rescaling x and t converts one >> transformation to the other so you obviously haven't answered the >> riddle. >> Your riddle is simple history. The LT can be decomposed into several >> transformations, one of which is the GT. That's even how it all began: GT >> + length contraction + time dilation + synchronization convention = LT >> (Lorentz + Poincare). >> It's similar for relativitic Doppler (Einstein), of which it is rather >> well known that it can be decomposed into classical Doppler + time >> dilation. Nothing dropped out: it's all included, as indicated. > Note: all the time you draw rather odd sounding conclusions from > straightforward procedures and mathematics. I won't comment anymore on such > manipulations of phrases. You were doing so well when you said The LT can be decomposed into several transformations, one of which is the GT. That's even how it all began: GT + length contraction + time dilation + synchronization convention = LT. You now seem to be repudiating what you've written. Shubee === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? > On Jul 30, 10:39 am, harry It is clear that resetting clocks plus rescaling x and t converts > one > transformation to the other so you obviously haven't answered the > riddle. > Your riddle is simple history. The LT can be decomposed into several > transformations, one of which is the GT. That's even how it all began: > GT > + length contraction + time dilation + synchronization convention = LT > (Lorentz + Poincare). > It's similar for relativitic Doppler (Einstein), of which it is > rather > well known that it can be decomposed into classical Doppler + time > dilation. I replied to Shubee's words: [> just as one must remember the scaling > factor interpretation that that was added to the Galilean > transformation but which dropped out because of the mathematical > manipulation.] >> Nothing dropped out: it's all included, as indicated. >> Note: all the time you draw rather odd sounding conclusions from >> straightforward procedures and mathematics. I won't comment anymore on >> such >> manipulations of phrases. You were doing so well when you said The LT can be decomposed into > several transformations, one of which is the GT. That's even how it > all began: GT + length contraction + time dilation + synchronization > convention = LT. You now seem to be repudiating what you've written. Here above I indicate that all effects incl. scaling factors are ADDED to the Galilean transformation, while you state that the scaling factor dropped out of the Galilean transformation. And again: there is nothing bewildering or paradoxical about it. Note even a riddle. Harald === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? <1217488006_859@sicinfo3.epfl.ch> posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) On Jul 31, 2:06 am, harry On Jul 30, 10:39 am, harry It is clear that resetting clocks plus rescaling x and t converts > one transformation to the other so you obviously haven't > answered the riddle. > Your riddle is simple history. The LT can be decomposed into several > transformations, one of which is the GT. That's even how it all began: > GT + length contraction + time dilation + synchronization convention > = LT (Lorentz + Poincare). > It's similar for relativitic Doppler (Einstein), of which it is > rather well known that it can be decomposed into classical > Doppler + time dilation. I replied to Shubee's words: [> just as one must remember the scaling > factor interpretation that that was added to the Galilean > transformation but which dropped out because of the mathematical > manipulation.] >> Nothing dropped out: it's all included, as indicated. >> Note: all the time you draw rather odd sounding conclusions from >> straightforward procedures and mathematics. I won't comment anymore >> on such manipulations of phrases. > You were doing so well when you said The LT can be decomposed into > several transformations, one of which is the GT. That's even how it > all began: GT + length contraction + time dilation + synchronization > convention = LT. > You now seem to be repudiating what you've written. Here above I indicate that all effects incl. scaling factors are ADDED to > the Galilean transformation, while you state that the scaling factor > dropped out of the Galilean transformation. And that is easily explained by the fact that Lorentz started with the Galilean transformation and arrived at the Lorentz transformation whereas I started with the Lorentz transformation and transformed it to the Galilean transformation. You missed my point about the implications of the derivation going in opposite direction: > Your riddle is simple history. The LT can be decomposed into several > transformations, one of which is the GT. That's even how it all began: GT + > length contraction + time dilation + synchronization convention = LT > (Lorentz + Poincare). > It's similar for relativitic Doppler (Einstein), of which it is rather > well known that it can be decomposed into classical Doppler + time dilation. > Harald So, if the Lorentz transformation is logically equivalent to the > Galilean transformation, then the Lorentz transformation all by itself > doesn't imply a physical time dilation. One must bring to the > calculation other assumptions, just as one must remember the scaling > factor interpretation that that was added to the Galilean > transformation but which dropped out because of the mathematical > manipulation. Shubee The issue here is obvious. If the Lorentz transformation can be legitimately reduced to the Galilean transformation, then computing time dilation with the Galilean transformation for the real world is going to be rather difficult. A physicist would have to ADD to the Galilean transformation a scaling factor interpretation which dropped out in MY mathematical manipulation. But if the Galilean transformation can be interpreted to give real time dilation answers, why can't the Lorentz transformation be interpreted to give a Newtonian denial of time dilation? Therefore it follows logically that the Lorentz transformation alone doesn't imply time dilation. Shubee === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? > On Jul 31, 2:06 am, harry On Jul 30, 10:39 am, harry It is clear that resetting clocks plus rescaling x and t converts >> one transformation to the other so you obviously haven't >> answered the riddle. >> Your riddle is simple history. The LT can be decomposed into >> several >> transformations, one of which is the GT. That's even how it all >> began: >> GT + length contraction + time dilation + synchronization >> convention >> = LT (Lorentz + Poincare). >> It's similar for relativitic Doppler (Einstein), of which it is >> rather well known that it can be decomposed into classical >> Doppler + time dilation. >> I replied to Shubee's words: >> [> just as one must remember the scaling >> factor interpretation that that was added to the Galilean >> transformation but which dropped out because of the mathematical >> manipulation.] > Nothing dropped out: it's all included, as indicated. > Note: all the time you draw rather odd sounding conclusions from > straightforward procedures and mathematics. I won't comment anymore > on such manipulations of phrases. >> You were doing so well when you said The LT can be decomposed into >> several transformations, one of which is the GT. That's even how it >> all began: GT + length contraction + time dilation + synchronization >> convention = LT. >> You now seem to be repudiating what you've written. >> Here above I indicate that all effects incl. scaling factors are ADDED to >> the Galilean transformation, while you state that the scaling factor >> dropped out of the Galilean transformation. And that is easily explained by the fact that Lorentz started with the > Galilean transformation and arrived at the Lorentz transformation > whereas I started with the Lorentz transformation and transformed it > to the Galilean transformation. You missed my point about the implications of the derivation going in > opposite direction: Indeed - thus the way you phrased it was obscure at best: added to the Galilean transformation but which dropped out. >> Your riddle is simple history. The LT can be decomposed into several >> transformations, one of which is the GT. That's even how it all began: >> GT + >> length contraction + time dilation + synchronization convention = LT >> (Lorentz + Poincare). >> It's similar for relativitic Doppler (Einstein), of which it is >> rather >> well known that it can be decomposed into classical Doppler + time >> dilation. >> Harald >> So, if the Lorentz transformation is logically equivalent to the >> Galilean transformation, then the Lorentz transformation all by itself >> doesn't imply a physical time dilation. One must bring to the >> calculation other assumptions, just as one must remember the scaling >> factor interpretation that that was added to the Galilean >> transformation but which dropped out because of the mathematical >> manipulation. >> Shubee The issue here is obvious. If the Lorentz transformation can be > legitimately reduced to the Galilean transformation, Again: as long as you continue to write such inaccurate phrases, a useful discussion is hardly possible. And if you do so in a paper that you hope to get published, you can forget it! > then computing > time dilation with the Galilean transformation for the real world is > going to be rather difficult. I can't parse that. However, the following sentence I can deal with: > A physicist would have to ADD to the > Galilean transformation a scaling factor interpretation which > dropped out in MY mathematical manipulation. A physicist doesn't need your manipulations; generally the easy-to-use LT is used. > But if the Galilean transformation can be interpreted to give real > time dilation answers, Again, I can't parse that. I'd say rather the contrary . > why can't the Lorentz transformation be > interpreted to give a Newtonian denial of time dilation? Again, I don't follow that. Sorry. > Therefore it follows logically that the Lorentz transformation alone > doesn't imply time dilation. We have been there before, and we already agreed on the contrary: For x1=x2=x: t1' = gamma*(t1-v*x/c^2) t2' = gamma*(t2-v*x/c^2) => t2' - t1' = gamma*(t2 - t1) The above relationship between clock times happens to be called time dilation. Good luck! Harald === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? <1217517047_865@sicinfo3.epfl.ch> posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) On Jul 31, 10:10 am, harry The issue here is obvious. If the Lorentz transformation can be > legitimately reduced to the Galilean transformation, Again: as long as you continue to write such inaccurate phrases, a useful > discussion is hardly possible. And if you do so in a paper that you hope to > get published, you can forget it! > then computing time dilation with the Galilean transformation > for the real world is going to be rather difficult. I can't parse that. > But if the Galilean transformation can be interpreted to give > real time dilation answers, Again, I can't parse that. I'd say rather the contrary . > why can't the Lorentz transformation be interpreted > to give a Newtonian denial of time dilation? Again, I don't follow that. Sorry. Perhaps Daryl McCullough can explain it to you better than I can: Shubee <69GdnbiUUZZgvw3VnZ2dnUVZ_gudnZ2d@comcast.com> sci.phyisics.relativity: >> sci.physics.relativity: >> It's not clear to me why the Lorentz transformation can't be reduced >> to the Galilean transformation by resetting clocks, rescaling >> distance measures and fiddling with clock rates according to the >> recipe on page 11 >> ofhttp://www.everythingimportant.org/relativity/special.pdfand >> equations (48) to (58). >> How do you answer this riddle? >> Shubee >> Easy. The Lorentz transformation >> x' = gamma (x - v t) >> y' = y >> z' = z >> t' = gamma (t - v x / c^2) >> is not the same as the Galilean transformation >> x' = x - v t >> y' = y >> y' = z >> t' = t >> Simple inspection reveals that. The only way the two can ever be the >> same is when v=0; but Relativity already has that built in. Rescaling x >> or t will not change the underlying nature of the transformation. It is clear that resetting clocks plus rescaling x and t converts one > transformation to the other so you obviously haven't answered the > riddle. What's the reschaling that converts one to the other (Hint: it's not clear to me)? Maybe I'm misunderstanding the question. The only time that I see the two transformation becoming equivalent is if v=0; but that's not a rescaling. If we rescale by x:=k1*x, y:=k2*y, z:=k3*z and t=k0*t, then the two transformations still are not equivalent because there is no way (that I see) to make t' equation in Galilean transformation isomorphic to t' equation in the Lorentz transformation unless v=0. The problem is no dependency on x in the Galilean transformation. No scaling will remove that problem, as far as I can tell. -- // The TimeLord says: // Pogo 2.0 = We have met the aliens, and they are us! === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, <69GdnbiUUZZgvw3VnZ2dnUVZ_gudnZ2d@comcast.com> posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) On Jul 30, 7:36 am, stevendaryl3...@yahoo.com (Daryl McCullough) > The TimeLord says... >sci.physics.relativity: >> It's not clear to me why the Lorentz transformation can't be reduced to >> the Galilean transformation by resetting clocks, rescaling distance >> measures and fiddling with clock rates according to the recipe on page >> 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand >> equations (48) to (58). >> How do you answer this riddle? >> Shubee >Easy. The Lorentz transformation >x' = gamma (x - v t) >y' = y >z' = z >t' = gamma (t - v x / c^2) >is not the same as the Galilean transformation >x' = x - v t >y' = y >y' = z >t' = t >Simple inspection reveals that. What Shubee is saying is that whether you have Galilean transform > or Lorentz transform relating two frames depends on how clocks > are synchronized in those frames. I'm sorry Daryl but I can't possibly believe what you are saying. And I don't believe that you have solved the riddle. Shubee > However, the *same* synchronization > procedure, slow clock transport, leads to the Galilean transform > if Newtonian physics is correct and leads to the Lorentz transform > if Special Relativity is correct. Slow clock transport means that you synchronize distant clocks > by bringing all clocks together in one spot and setting them to > the same time. Then you slowly move the clocks to their final > location. -- > Daryl McCullough > Ithaca, NY === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? posting-account=wigfZgkAAACDgITarXffzxJygX81YRSs Gecko/20071201 Epiphany/2.20 Firefox/2.0.0.10,gzip(gfe),gzip(gfe) > It's not clear to me why the Lorentz transformation can't be reduced > to the Galilean transformation by <> <> http://www.aip.org/pt/vol-58/iss-11/p31.html http://scitation.aip.org/journals/doc/PHTOAD-ft/vol_58/iss_11/31_1.shtml > rescaling distance > measures and fiddling with clock rates according to the recipe on page > 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand > equations (48) to (58). How do you answer this riddle? Shubee === Subject: Re: Is This a Subtle but Completely Legitimate Redefinition, Bewildering Magic or Paradox? posting-account=wigfZgkAAACDgITarXffzxJygX81YRSs Gecko/20071201 Epiphany/2.20 Firefox/2.0.0.10,gzip(gfe),gzip(gfe) > It's not clear to me why the Lorentz transformation can't be reduced > to the Galilean transformation by resetting clocks, rescaling distance > measures and fiddling with clock rates according to the recipe on page > 11 ofhttp://www.everythingimportant.org/relativity/special.pdfand > equations (48) to (58). How do you answer this riddle? Shubee ~~the famous Lorentz transformation ensures that the velocity of light is invariant between different [imaginary] inertial frames, and also reduces to the more familiar Galilean transform in the limit $v ll c$. ~~ (1348) http://farside.ph.utexas.edu/teaching/em/lectures/node109.html Sue... === Subject: Re: Hyperbolic cos-sin-cot rule? posting-account=AFsgCgkAAAA3VOfxqn2cTB2LbLN3nbER Gecko/20070319,gzip(gfe),gzip(gfe) Replying to myself! UGH!! > Musing over the virtually 1-to-1 correspondence between > ellliptic and hyperbolic trig rules, with replacement of normal > by hyperbolic trig functions (spiced with negatives appearing > in front of products of sin,tan,csc,& cot), I was wondering > if there was a hyperbolic equivalent of the sperical geometry > cos-sin-cot rule. I haven't seen one, and can't deduce one for myself. Recall: the spherical cos-sin-cot rule is cot a sin b = cos b cos C + sin C cot A (where angles A,B,C are opposite sides a,b,c repectively, as usual). Is there any other reasonably simple formula connecting a,b,A,C > in hyperbolic geometry? I couldn't find any. I'm an idiot. For some reason I forgot to translate this from spherical to hyperbolic geometry, exactly as I stated above. It gives this equation:- Hyperbolic cos-sin-cot rule: * coth a sinh b = cosh b cos C + sin C cot A * * (where as always, side a is opposite angle A etc) I haven't actually proved it, but I have verified it with a large number of special cases of hyperbolic triangles, 90-30-30, 60-45-45, 60-45-30 etc etc. So it's proved by random examples. :) I'm sure it's long-known, but I've never seen it in any text book. For that matter, I've not seen the spherical version more than once, either. Strange, as I find them very useful. -- Bill of Hype === Subject: Re: Hyperbolic cos-sin-cot rule? posting-account=33KaEgkAAAA9tz8WICNABjrkyMKXFbGS Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) On Jul 28, 7:54 am, Bill Taylor ellliptic and hyperbolic trig rules, with replacement of normal > by hyperbolic trig functions (spiced with negatives appearing > in front of products of sin,tan,csc,& cot), I was wondering > if there was a hyperbolic equivalent of the sperical geometry > cos-sin-cot rule. I haven't seen one, and can't deduce one for myself. Recall: the spherical cos-sin-cot rule is cot a sin b = cos b cos C + sin C cot A (where angles A,B,C are opposite sides a,b,c respectively, as usual). Is there any other reasonably simple formula connecting a,b,A,C > in hyperbolic geometry? I couldn't find any. -- Wondering William May be you like to read Roberto Bonola's book 'Non-Eucliden geometry' about pan-geometry. It seems to suggest that every flat euclidean trigonometry relation between sides and angles has generalizable hyperbolic and elliptic counterparts. cos(a/R) cos(b/R) = cos(c/R) -> a^2 + b^2 = c^2 and cosh(a/R) cosh(b/R) = cosh(c/R) -> a^2 + b^2 = c^2 when R -> Infinity After this I hope you or anyone kindly undertakes to find out what substitution or procedure is required to convert flat to curved geometries.There is a table of guidance in the book. Narasimham === Subject: Re: Hyperbolic cos-sin-cot rule? posting-account=SMoc9woAAAAGXgWXJySK88C5DCo6yjQ_ Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) On Jul 28, 7:54 am, Bill Taylor ellliptic and hyperbolic trig rules, with replacement of normal > by hyperbolic trig functions (spiced with negatives appearing > in front of products of sin,tan,csc,& cot), I was wondering > if there was a hyperbolic equivalent of the sperical geometry > cos-sin-cot rule. I haven't seen one, and can't deduce one for myself. Recall: the spherical cos-sin-cot rule is cot a sin b = cos b cos C + sin C cot A (where angles A,B,C are opposite sides a,b,c repectively, as usual). Is there any other reasonably simple formula connecting a,b,A,C > in hyperbolic geometry? I couldn't find any. -- WonderingWilliam May be you like to read Roberto Bonola's book Non-Eucliden geometry about pan-geometry. It seems to suggest that every flat euclidean trigonometry relation between sides and angles has generalizable hyperbolic and elliptic counterparts. cos(a/R)cos(b/R) = cos(c/R) -> a^2 + b^2 = c^2 and cosh(a/R)cosh(b/R) = cosh(c/R) -> a^2 + b^2 = c^2 when R -> Infinity After this I hope you or anyone kindly undertakes to find out what substitution or procedure is required to convert flat to curved geometries.I don't have now what I did about it before,but after seeing table in the book a procedure can be I believe, laid down. Narasimham === Subject: Is this theorem wrong or am I ? Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) Please see : page 44 , lemma 2.2 . Taking , for example , m = 2 . If 1 , v1 , v2 , are linearly independent , then there exist b1 , b2 , such that max (1 <= k <= 2 ) | vk - === Subject: Re: Is this theorem wrong or am I ? > Please see : pdf page 44 , lemma 2.2 . Taking , for example , m = 2 . > If 1 , v1 , v2 , are linearly independent , then there exist b1 , b2 , > such that > max (1 <= k <= 2 ) | vk - Looking at this (and not the link) it seems you are wrong, since ending in a minus sign does not make sense. === Subject: Re: Is this theorem wrong or am I ? > Please see : >> pdf >> page 44 , lemma 2.2 . >> Taking , for example , m = 2 . >> If 1 , v1 , v2 , are linearly independent , then there exist b1 , b2 , >> such that >> max (1 <= k <= 2 ) | vk - > Looking at this (and not the link) it seems you are wrong, since ending > in a minus sign does not make sense. I've tried to express lemma 2.2 in an alternate way, for m=2; I tried using matrices, but I'm not sure I translated right... (i) The real numbers 1, theta_1 and theta_2 are linearly independent over Q. (ii) For any epsilon>0, there exist q_1, q_2, q_3 > 0 and r_1, r_2, r_3 & s_1, s_2, s_3 such that if A = [ q_1 r_1 s_1 ] [ q_2 r_2 s_2 ] [ q_3 r_3 s_3 ] with A having integer coefficients, det(A) =/= 0, and let u = [1, theta_1, theta_2] (i.e. u is a row vector), and v_1 = [1/q_1, 0, 0] v_2 = [0 , 1/q_2, 0] v_3 = [0 , 0, 1/q_3] then || (v_i)A - u ||_{OO} < epsilon/q_i for i = 1, 2, 3. --- Example, since pi is transcendental, lemma 2.2 (ii) applies to 1, pi, pi^2 . David Bernier === Subject: Re: gravity theory > ok now it is generally perceived that gravity is a product of > mass, but gravity is still unexplained, i have a theory that i > believe is logical and leaves no questions. Gravity is > exquisitely model (explained for many) by general relativity. > ... familiarize yourself with it. > Yo, explain simply, in a new way, what and why there is > Action at a Distance and you'll have an exquisite model > of Gravity. But if you need to invoke GR to do so then you > are simply delivering a useless sermon like any other > village priest of the Einstein cult does... and you'll be in > line with and in the league of those Einstein Dingleberries > that are an unending source for laughs.... ahahaha.... > http://en.wikipedia.org/wiki/General_relativity > Ahem...Sam, if there is a theory of General Relativity, please cite > the author and the journal in which it was published. > http://en.wikipedia.org/wiki/General_relativity#References > including Einstein. [which is ...] > Realize that at the time of his death, Einstein never published his > theor of genral relativity, because there remained some issues > that he could not resolve. > Hence, there is no such thing as a Theory of General Relativity. > Lot's of good material, Harry. > Are There Any Good Books on Relativity Theory? > http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html > You make it sound GTR doesn't exist because it is a work in progress? > This is now, Harry, GTR is more mature and fruitful. > It simply does not exist. > Harry C. > Well, Chief Harry, Albert did publish several items in which > he referred to GR as allgemeine Relativit.8atstheorie early > in his career, as can be seen from the link Sam gave you. > But Sam is a quintessential Einstein Dingleberry who does > worship Einstein & he proselytizes his notion as a teacher > in his school for the geriatric set. That is all commendable > as long as Sam teaches that SR/GR are nothing more than 1 > of the ing stories about nature, a fable, model or feeble' > description of nature.... good for mental masturbations only > BUT with NO practical value to/in the real world, > including GPS that NEVER needed nor used any SR nor GR. > So, when elevating SR/GR to the Holy grail of Physics it is > equivalent to the mentation that is exhibited by the religious > fundamentalists of the Jews, Islamists or Evangelicals. > If you look at Einstein original 1905 paper on SR you'll see > clearly that he grudgingly published it , without any references, > under the nagging and the insistence of his 1st Xian wife > More here: > The 1905 paper took off with the promos & backing of the then > very active Zionist movement in Germany. Albert got caught up in > that environment and was nudged into developing a general > theory (GR) which he was never comfy about/with, not from the > get-go, nor at any time during his career and he outright did > doubt GR's validity, grievously, at the end of his life... AND > he knew that playing that game was a despicable con. -- OTOH > his unrelated work, on the Photoelectric effect, for which he got > the Nobel price in 1921, he must be respected for. > Here is what Einstein said in the reference that Sam gave: > http://en.wikipedia.org/wiki/General_relativity#CITEREFEinstein1917 > Einstein, Albert (1916), Die Grundlage der allgemeinen Relativit.8atstheorie > Annalen der Physik 49, Script with its many expressions of manifold meaning and > wherein Einstein, very uncharacteristically, gives credit to others > and says on: > 286-Doc30-770: ...all fundamentals for GR/GTR were already > known and invented by Gauss, Riemann, Christoffel, Ricci > & Levi-Civita. -- I am grateful to my friend Grossman who > spared me from me having to learn the necessary math & me > doing the required literature search to get to the needed field > equations for GTR. > Einstein continues on > 286-Doc30-771:... Ernst Mach was the first one to recognize a > fundamental misconception & conceptual fault in the formulation > of the SR, my Special Theory of relativity... [Einstein then bags > on Newton's Grav. shortcomings, but he hedges in the foot note:]... > The new theoretical realizations may not be applicable to events > in physical reality if they are contra to other physical experiences. > 286-Doc30-771:... wherein Einstein pontificates: > The cause and source for Newton's Action-at-a-distance must > lay **outside** of the system of the 2 involved masses... & (by > assumption) there **ought to be** no preferential frame of reference. > 286-Doc30-771:... wherein Einstein laments like a politician > about: ... some Force field which one must assume to be > justifiable in systems at rest as well as when in movement > from which one can immediately conclude that... by simply > changing the coordinate systems one generates a Gravitational > Force field... in which one **sets** the speed of light to be > constant & one can easily see that a ray of light must be bent ... > 291-Doc30-776:... wherein Einstein laments that: > There is no other choice then to accept/believe that all imaginable > frames of reference/coordinate systems have to regarded as being > equally valid.. [but then he adds & hedges in the page's foot note] > About certain limitations of the requirement for attribution and > steadiness we shall NOT talk about....[ ahahahaha... AHAHAHA... > and presumably he meant by that to admit & imply failure of his > GR because he was never able to get rid of Newton's G which is > required for any and all of GR's solutions... AHAHAHAHA.....] > Albert's hedging, cautioning, handwaving, and gauche credits > to others with his intent to absolve himself or at least spread any > possible blame for failure, is evident in the above introduction of > his 1st paper on GR ... ahahahaha.. . > If Albert would have written his today, and if he would not have > been promoted back then by the Zionist-infested academia of the > Weimar Republic, then any referee would taken Albert's manuscript > and a cigar to the toilet, smoked the cigar and wiped his ass with > Albert's paper... Albert was a ing lucky crackpot... ahahaha... > GR has not matured, as Sam so lovingly advocates. Einstein's > relativity is a like an old toilet seat which normal people would > throw away because it stinks. --- But to the folks who harbor a > toilet seat fetish, like all Einstein Dingleberries do, REL has > become a cherished, albeit useless, relic that is worshiped and > still exhibited widely... ahahahaha.... > The Dingleberry argument that GR predicts reality in many > experiments accurately is as shallow and UN-convincing as is > the plethora of the Miracles in the Torah/Bible or Koran that > too are predicting reality accurately to their disciples... > All these holy scriptures, including Albert's just show that > any highfaluting story/report or theory will always find examples > in the real world that prove the theory right to their believing > disciples. > Actually, Albert had his misgivings about his Relativity crap > from the start when he told his Dingleberries with/in his many > admonishments, ever since 1920....: > ::AE:: .... NOT to search at the same, now well lit places, > ::AE:: .... where he, Einstein, had been working. > ....This is reflected in the real world, like here, where one can > see where Einstein's crap is still used and where they laugh > about it: > = mil/indust. Eng, R&D.....................does not need REL > = *.edu and grantology ....................does use REL, No > = Promo, Sales & Movies...............loves REL by the load > = Jews defend it as cultural heritage whether REL is or not. > ... and to boot Einstein was keenly aware of this and very lucidly > and finally confessed in 1954, just a year before Albert folded > his relativity tent, closes his umbrella, kicked the bucket & finally > puffed, but leaving behind vast hordes of his Einstein Dingleberries > (1 set of which resides in these NGs to stink up & retard the > intellectual level & quality of physics), > ::AE:: I consider it quite possible that physics cannot be based > ::AE:: on the field concept, i. e., on continuous structures. In that > ::AE:: case nothing remains of my entire castle in the air, gravitation > ::AE:: theory included, [and of] the rest of modern physics. . [ & > ::AE::elsewhere] why would anyone be interested in getting > ::AE:: exact solutions of such an ephemeral set of equations? > Other Luminaries have followed suit agreeing with Albert's > final realizations, insights and assessments, saying: > :: Professor Carver A. Mead of Caltech (a student of Feynman), > :: who said > :: It is my firm belief that the last seven decades of the 20th century > ::: will be characterized in history as the dark ages of physics. > :: or F.A Hayek, Nobel laureate, who said: In the future, > :: Humanity will see in our Epoch an Era of superstition, essentially > :: associated with the names of Marx, Freud and Einstein > :: or John Beckman, an astronomy professor and Einstein disciple: > :: The theory of relativity lives on. Is it a true picture of reality? > :: That is probably more a matter of faith than of proof. > hanson worte: > ahahahaha... ahahahahanson It's the numbers... If you can't get the numbers right your new theory is a pile of . A theory without numbers is less than . -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: gravity theory > :: It is my firm belief that the last seven decades of the 20th century > ::: will be characterized in history as the dark ages of physics. > :: or F.A Hayek, Nobel laureate, who said: In the future, > :: Humanity will see in our Epoch an Era of superstition, essentially > :: associated with the names of Marx, Freud and Einstein > :: or John Beckman, an astronomy professor and Einstein disciple: > :: The theory of relativity lives on. Is it a true picture of reality? > :: That is probably more a matter of faith than of proof. > Dirk Bruere at NeoPax > It's the numbers... > If you can't get the numbers right your new theory is a pile of . > A theory without numbers is less than . > ahahaha... AHAHAHA... Ambiguous! Come again, Dirk. > AHAHAHA... Whose *new* theory and which numbers? > Are you talking about the above, initial snippet from/by > jedakiah jedakiah.2d3a852 at physicsbanter.com, in > who didn't present any numbers? > I have corrected an attribution above. The familiarize > came not from Jedakiah, but from Sam who is proselytizing > Einstein's with extreme prejudice and uncommon > fanaticism.... ahahahaha... So, to/for jedak's defense > consider that he is the reaction product, the victim, of the > incessant onslaught by the Dingleberries that Einstein > warned against ever since 1920... > ... and see, Dirk, they even got to you now.... ahahaha... > Relax, dude, all that Einstein is only a story that > doesn't even buy you a cup of coffee.Have fun with it! > ahahahaha... ahahahahanson They got to me in school where they showed that simply by assuming c=const Pythagoras Theorem could deliver the main equations of SR. As for the rest, it's no good whining on about Einstein being wrong if the numbers turn out right. You have to show where his numbers (and by 'his' I mean modern physicists using SR/GTR) differ from experiment. Anyone who tries to discredit Einstein's work by quoting something he said about it 100years ago, and all the right numbers is just a coincidence, is a moron. -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: gravity theory <6fantmFafgf9U1@mid.individual.net> <6fbtj5Fatr3pU1@mid.individual.net> in 6fbtj5Fatr3pU1@mid.individual.net in sci.physics.relativity: [...] > They got to me in school where they showed that simply by assuming > c=const Pythagoras Theorem could deliver the main equations of SR. As You must of had some serious liars teaching you in school. Either that or the shop teacher. [wink] [...] -- // The TimeLord says: // Pogo 2.0 = We have met the aliens, and they are us! === Subject: Re: gravity theory <6fantmFafgf9U1@mid.individual.net> <6fbtj5Fatr3pU1@mid.individual.net> posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > They got to me in school where they showed that simply by assuming > c=const Pythagoras Theorem could deliver the main equations of SR. What else have ïtheyÍ mesmerized you with? Assuming the constancy of light actually allows you to modify the Galilean transform into something that will agree with the null results of the MMX. There are an infinitely such transforms where the Lorentz transform is one of these. the numbers turn out right. There is no need to blame Einstein the nitwit, the plagiarist, and the liar for all the problems. The Lorentz transform was first derived by Larmor not by Einstein, Lorentz, or Poincare. The analysis (also known as SR) to the Lorentz transform was first performed by Poincare not by Einstein. The postulates (EinsteinÍs attempt of plagiarism by reverse-engineering the Lorentz transform) of SR were already done so by Galileo in his principle of relativity and by Voigt in his constancy in the speed of light. Just what is EinsteinÍs contribution? > You have to show where his numbers (and by > 'his' I mean modern physicists using SR/GTR) differ from experiment. The numbers showed the results from relative simultaneity. The observations seem to only agree with the numbers under absolute simultaneity. You call that experimental confirmation? > Anyone who tries to discredit Einstein's work by quoting something he > said about it 100years ago, and all the right numbers is just a > coincidence, is a moron. That is correct. You can easily discredit Einstein by doing a mathematical forensics. The history shows Einstein was nothing but a nitwit, a plagiarist, and a liear. Einstein the nitwit cannot discern that the Lorentz transform is absolutely nonsense because of the twinÍs paradox namely relative simultaneity. Einstein the plagiarist tried to re-derive the Lorentz transform by reverse-engineering it. The forensic evidence is in his 1905 paper on relativity. Einstein the lair tried to claim otherÍs work as his own. Again, the forensic evidence is also lies in his 1905 paper. === Subject: Re: gravity theory > They got to me in school where they showed that simply by assuming >> c=const Pythagoras Theorem could deliver the main equations of SR. What else have ïtheyÍ mesmerized you with? Assuming the constancy of light actually allows you to modify the > Galilean transform into something that will agree with the null > results of the MMX. There are an infinitely such transforms where the > Lorentz transform is one of these. > As for the rest, it's no good whining on about Einstein being wrong if >> the numbers turn out right. There is no need to blame Einstein the nitwit, the plagiarist, and the > liar for all the problems. The Lorentz transform was first derived by > Larmor not by Einstein, Lorentz, or Poincare. The analysis (also > known as SR) to the Lorentz transform was first performed by Poincare > not by Einstein. The postulates (EinsteinÍs attempt of plagiarism by > reverse-engineering the Lorentz transform) of SR were already done so > by Galileo in his principle of relativity and by Voigt in his > constancy in the speed of light. Just what is EinsteinÍs contribution? > You have to show where his numbers (and by >> 'his' I mean modern physicists using SR/GTR) differ from experiment. The numbers showed the results from relative simultaneity. The > observations seem to only agree with the numbers under absolute > simultaneity. You call that experimental confirmation? > Anyone who tries to discredit Einstein's work by quoting something he >> said about it 100years ago, and all the right numbers is just a >> coincidence, is a moron. That is correct. You can easily discredit Einstein by doing a > mathematical forensics. The history shows Einstein was nothing but a > nitwit, a plagiarist, and a liear. Einstein the nitwit cannot discern that the Lorentz transform is > absolutely nonsense because of the twinÍs paradox namely relative > simultaneity. Einstein the plagiarist tried to re-derive the Lorentz > transform by reverse-engineering it. The forensic evidence is in his > 1905 paper on relativity. Einstein the lair tried to claim otherÍs > work as his own. Again, the forensic evidence is also lies in his > 1905 paper. Not interested. Show me where the numbers differ from experimental results. -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: gravity theory <6fantmFafgf9U1@mid.individual.net> <6fc45jFareejU2@mid.individual.net> posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > What else have ïtheyÍ mesmerized you with? > Assuming the constancy of light actually allows you to modify the > Galilean transform into something that will agree with the null > results of the MMX. There are an infinitely such transforms where the > Lorentz transform is one of these. There is no need to blame Einstein the nitwit, the plagiarist, and the > liar for all the problems. The Lorentz transform was first derived by > Larmor not by Einstein, Lorentz, or Poincare. The analysis (also > known as SR) to the Lorentz transform was first performed by Poincare > not by Einstein. The postulates (EinsteinÍs attempt of plagiarism by > reverse-engineering the Lorentz transform) of SR were already done so > by Galileo in his principle of relativity and by Voigt in his > constancy in the speed of light. Just what is EinsteinÍs contribution? > The numbers showed the results from relative simultaneity. The > observations seem to only agree with the numbers under absolute > simultaneity. You call that experimental confirmation? > You can easily discredit Einstein by doing a > mathematical forensics. The history shows Einstein was nothing but a > nitwit, a plagiarist, and a liear. > Einstein the nitwit cannot discern that the Lorentz transform is > absolutely nonsense because of the twinÍs paradox namely relative > simultaneity. Einstein the plagiarist tried to re-derive the Lorentz > transform by reverse-engineering it. The forensic evidence is in his > 1905 paper on relativity. Einstein the lair tried to claim otherÍs > work as his own. Again, the forensic evidence is also lies in his > 1905 paper. Not interested. Oh, well. We have another illiterate peasant. In this particular case, he is from the good old England. Assuming the constancy of light actually allows you to modify the > Galilean transform into something that will agree with the null > results of the MMX. There are an infinitely such transforms where the > Lorentz transform is one of these. liar for all the problems. The Lorentz transform was first derived by > Larmor not by Einstein, Lorentz, or Poincare. The analysis (also > known as SR) to the Lorentz transform was first performed by Poincare > not by Einstein. The postulates (EinsteinÍs attempt of plagiarism by > reverse-engineering the Lorentz transform) of SR were already done so > by Galileo in his principle of relativity and by Voigt in his > constancy in the speed of light. The numbers showed the results from relative simultaneity. The > observations seem to only agree with the numbers under absolute > simultaneity. You call that experimental confirmation? > You can easily discredit Einstein by doing a > mathematical forensics. The history shows Einstein was nothing but a > nitwit, a plagiarist, and a liear. > Einstein the nitwit cannot discern that the Lorentz transform is > absolutely nonsense because of the twinÍs paradox namely relative > simultaneity. Einstein the plagiarist tried to re-derive the Lorentz > transform by reverse-engineering it. The forensic evidence is in his > 1905 paper on relativity. Einstein the lair tried to claim otherÍs > work as his own. Again, the forensic evidence is also lies in his > 1905 paper. >> Not interested. Oh, well. We have another illiterate peasant. In this particular > case, he is from the good old England. > Show me where the numbers differ from experimental results. There are so many. Please initiate such an experiment, and I will > engage in sincere discussions with you. I do not know of any experiment. Nor does anyone else. -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: gravity theory <6fantmFafgf9U1@mid.individual.net> <6fej0gFb74coU1@mid.individual.net> posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1,gzip(gfe),gzip(gfe) there are classical experiments, even if that onlymeans, it was done in the 19th CCE (PBUH .-) um, what ever you guys were referring to, in your cut&paste DJ mixtape. anway, Haha, what floor was your office on?... eleven and above is certainly very safe, if the building doesn't fail monumentally. > I do not know of any experiment. thus: I had my 4th virtual lesson in surfing in two days, more or less, this one just watching the lone surferdood; I didn't wait for him to stand up, since he was clearly paddling-out in a minimax path to the correct wave. 4 axes would be a form of homogenous coordination, not entirely amenable to quaternions, AFAICT, for the point, which would minimally be a tetrasteron, and a sphere; how many points is that?... anyone work on the lunes demonstration of pythag.spatial? it's very tempting to just bum a board & go, but I'm retaining my ideal of surfcamp Maui, or some other island. or, we'll just make a stop on the bipolar express -- it's the IPY! === Subject: Re: gravity theory > What else have ëthey.89 mesmerized you with? > Assuming the constancy of light actually allows you to modify the > Galilean transform into something that will agree with the null > results of the MMX. There are an infinitely such transforms where the > Lorentz transform is one of these. There is no need to blame Einstein the nitwit, the plagiarist, and the > liar for all the problems. The Lorentz transform was first derived by > Larmor not by Einstein, Lorentz, or Poincare. The analysis (also > known as SR) to the Lorentz transform was first performed by Poincare > not by Einstein. The postulates (Einstein.89s attempt of plagiarism by > reverse-engineering the Lorentz transform) of SR were already done so > by Galileo in his principle of relativity and by Voigt in his > constancy in the speed of light. Just what is Einstein.89s contribution? > The numbers showed the results from relative simultaneity. The > observations seem to only agree with the numbers under absolute > simultaneity. You call that experimental confirmation? > You can easily discredit Einstein by doing a > mathematical forensics. The history shows Einstein was nothing but a > nitwit, a plagiarist, and a liear. > Einstein the nitwit cannot discern that the Lorentz transform is > absolutely nonsense because of the twin.89s paradox namely relative > simultaneity. Einstein the plagiarist tried to re-derive the Lorentz > transform by reverse-engineering it. The forensic evidence is in his > 1905 paper on relativity. Einstein the lair tried to claim other.89s > work as his own. Again, the forensic evidence is also lies in his > 1905 paper. Not interested. Oh, well. We have another illiterate peasant. In this particular case, he is from the good old England. It's the numbers... > If you can't get the numbers right your new theory is a pile of . > A theory without numbers is less than . > ahahaha... AHAHAHA... Ambiguous! Come again, Dirk. > AHAHAHA... Whose *new* theory and which numbers? > Are you talking about the above, initial snippet from/by > jedakiah jedakiah.2d3a852 at physicsbanter.com, in > who didn't present any numbers? > I have corrected an attribution above. The familiarize > came not from Jedakiah, but from Sam who is proselytizing > Einstein's with extreme prejudice and uncommon > fanaticism.... ahahahaha... So, to/for jedak's defense > consider that he is the reaction product, the victim, of the > incessant onslaught by the Dingleberries that Einstein > warned against ever since 1920... > ... and see, Dirk, they even got to you now.... ahahaha... > Relax, dude, all that Einstein is only a story that > doesn't even buy you a cup of coffee.Have fun with it! > ahahahaha... ahahahahanson > They got to me in school where they showed that simply > by assuming c=const Pythagoras Theorem could deliver > the main equations of SR. > As for the rest, it's no good whining on about Einstein > being wrong if the numbers turn out right. You have to show > where his numbers (and by 'his' I mean modern physicists > using SR/GTR) differ from experiment. > Anyone who tries to discredit Einstein's work by quoting > something he said about it 100years ago, and all the right > numbers is just a coincidence, is a moron. > ahahahaha... So, they got to you in school, meaning that you > didn't get it... ahahaha... This of course explains why you think > that you are smarter then Carver, Hayeck and Beckman AND > even Einstein himself who in the part that you've snipped from > himself said that SR/GR was a crock o'.... and wherein it > also says that all the experiments that deliver the right numbers > are... .. well, go read it again... & then after that you may announce > again, loud as you did twice already, that you are a very proud > Einstein Dingleberry which dangles and swings with great delight > and in worshipping awe from Einstein's Sphincter.... hahahaha... > -- I will give you all the kudos you want for that; for EDs are fun! -- So? Einstein's opinion is of no interest to me. It's the numbers. Show me where the numbers are wrong. Not *why* you, or anyone else think they're wrong. Quantitative, repeatable, experimental data that is inexplicable by SR/GTR. All that SR/GTR is are axioms and mathematics which can be applied to explain/predict the results of experiments. Now, what axioms do you want to scrap, and what proof can you offer that they do not match physical reality? -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: gravity theory | | >> | It's the numbers... | If you can't get the numbers right your new theory is a pile of . | >> A theory without numbers is less than . | > | ahahaha... AHAHAHA... Ambiguous! Come again, Dirk. | AHAHAHA... Whose *new* theory and which numbers? | Are you talking about the above, initial snippet from/by | jedakiah jedakiah.2d3a852 at physicsbanter.com, in | who didn't present any numbers? | I have corrected an attribution above. The familiarize | came not from Jedakiah, but from Sam who is proselytizing | Einstein's with extreme prejudice and uncommon | fanaticism.... ahahahaha... So, to/for jedak's defense | consider that he is the reaction product, the victim, of the | incessant onslaught by the Dingleberries that Einstein | warned against ever since 1920... | > | ... and see, Dirk, they even got to you now.... ahahaha... | Relax, dude, all that Einstein is only a story that | doesn't even buy you a cup of coffee.Have fun with it! | ahahahaha... ahahahahanson | > | They got to me in school where they showed that simply | by assuming c=const Pythagoras Theorem could deliver | the main equations of SR. | As for the rest, it's no good whining on about Einstein | being wrong if the numbers turn out right. You have to show | where his numbers (and by 'his' I mean modern physicists | using SR/GTR) differ from experiment. | Anyone who tries to discredit Einstein's work by quoting | something he said about it 100years ago, and all the right | numbers is just a coincidence, is a moron. | > | ahahahaha... So, they got to you in school, meaning that you | didn't get it... ahahaha... This of course explains why you think | that you are smarter then Carver, Hayeck and Beckman AND | even Einstein himself who in the part that you've snipped from | himself said that SR/GR was a crock o'.... and wherein it | also says that all the experiments that deliver the right numbers | are... .. well, go read it again... & then after that you may announce | again, loud as you did twice already, that you are a very proud | Einstein Dingleberry which dangles and swings with great delight | and in worshipping awe from Einstein's Sphincter.... hahahaha... | -- I will give you all the kudos you want for that; for EDs are fun! -- | > | So? Einstein's opinion is of no interest to me. | > | ... ahahaha... you read the ref?... ahahahaha.. did you really? | Annalen der Physik 49, | ... then why are you so fanatically rooting for Einstein's opinions? | Obviously you didn't get what it says nor what it means... | ahahahaha... Hey no disrespect for you, Dirk. .. ahaha... | > | It's the numbers. | Show me where the numbers are wrong. Sources of GPS signal errors Factors that can degrade the GPS signal and thus affect accuracy include the following: a.. Ionosphere and troposphere delays Ö The satellite signal slows as it passes through the atmosphere. The GPS system uses a built-in model that calculates an average amount of delay to partially correct for this type of error. b.. Signal multipath Ö This occurs when the GPS signal is reflected off objects such as tall buildings or large rock surfaces before it reaches the receiver. This increases the travel time of the signal, thereby causing errors. c.. Receiver clock errors Ö A receiver's built-in clock is not as accurate as the atomic clocks onboard the GPS satellites. Therefore, it may have very slight timing errors. d.. Orbital errors Ö Also known as ephemeris errors, these are inaccuracies of the satellite's reported location. e.. Number of satellites visible Ö The more satellites a GPS receiver can see, the better the accuracy. Buildings, terrain, electronic interference, or sometimes even dense foliage can block signal reception, causing position errors or possibly no position reading at all. GPS units typically will not work indoors, underwater or underground. f.. Satellite geometry/shading Ö This refers to the relative position of the satellites at any given time. Ideal satellite geometry exists when the satellites are located at wide angles relative to each other. Poor geometry results when the satellites are located in a line or in a tight grouping. g.. Intentional degradation of the satellite signal Ö Selective Availability (SA) is an intentional degradation of the signal once imposed by the U.S. Department of Defense. SA was intended to prevent military adversaries from using the highly accurate GPS signals. The government turned off SA in May 2000, which significantly improved the accuracy of civilian GPS receivers. So the numbers are WRONG. | Not *why* you, or | anyone else think they're wrong. Quantitative, repeatable, | experimental data that is inexplicable by SR/GTR. The numbers are wrong. | All that SR/GTR is are axioms and mathematics which can | be applied to explain/predict the results of experiments. | Now, what axioms do you want to scrap, and what proof | can you offer that they do not match physical reality? The numbers are WRONG. | > Dirk | > | Forget your fetish about the numbers. Measurements have | nothing to do with any theory, REL or otherwise. -- You have | it ass-backwards... Theory describes what is already known | and does not pre-dict anything. Theories are just stories by | which they describe a process, event or state observed | in nature. | If theses theories and in particular Einstein's crap are so | great then why don't we have those wonderful gismos and | gadgets that one sees in sci-fy, Starwars and Star trek? | > | If theories do deliver like you think they do, then why don't | you or any of those Einstein Dingleberries take a good | look at those wonderful equations & produce some of that | future technology... ahahaha... Do it and show me some | piece of new harware created by gawking at an eqaution | from Einstein's crap... ... ahahaha... | > | Test case for you, Dirk: .... When you give your instructions: | in your Remote Viewing classes http://www.transcendence.me.uk/ | have you applied the help I gave you for it in | Has it helped you any?... ahahahaha... AHAHAHAHA... | ahahaha... ahahahanson | Einstein Dingleberries claim GPS is dependent on GR. Garmin, who actually make GPS receivers, say their accuracy is 15 metres http://www8.garmin.com/aboutGPS/ It is more like +/- 40 metres vertically but only airline pilots concern themselves with landing 120 feet below the runway, which, considering glideslope geometry, places the aircraft among the approach lights at touchdown causing the light bulbs to break by gravity theory. http://farm1.static.flickr.com/168/496665511_f5e634fd2a.jpg?v=0 http://www.gebenus.com/wordpress/wp-content/uploads/2008/05/approach_lights. j pg http://www.ae.ca/papersart/vanfig06.jpg The numbers are WRONG. Dork Brouhaha is a head. === Subject: Re: gravity theory | > | > | > | | > | >> | It's the numbers... | If you can't get the numbers right your new theory is a | pile of . A theory without numbers is less than . | > | > | ... and see, Dirk, they even got to you now.... ahahaha... | Relax, dude, all that Einstein is only a story that | doesn't even buy you a cup of coffee.Have fun with it! | ahahahaha... ahahahahanson | > | > | They got to me in school where they showed that simply | by assuming c=const Pythagoras Theorem could deliver | the main equations of SR. | As for the rest, it's no good whining on about Einstein | being wrong if the numbers turn out right. You have to show | where his numbers (and by 'his' I mean modern physicists | using SR/GTR) differ from experiment. | Anyone who tries to discredit Einstein's work by quoting | something he said about it 100years ago, and all the right | numbers is just a coincidence, is a moron. | > | > | ahahahaha... So, they got to you in school, meaning that you | didn't get it... ahahaha... This of course explains why you think | that you are smarter then Carver, Hayeck and Beckman AND | even Einstein himself who in the part that you've snipped from | himself said that SR/GR was a crock o'.... and wherein it | also says that all the experiments that deliver the right numbers | are... .. | > | > | It's the numbers. | Show me where the numbers are wrong. | > | Sources of GPS signal errors | Factors that can degrade the GPS signal and thus affect accuracy | > include the following: | a.. Ionosphere and troposphere delays Ö The satellite signal | slows as it passes through the atmosphere. The GPS system | uses a built-in model that calculates an average amount of | delay to partially correct for this type of error. | b.. Signal multipath Ö This occurs when the GPS signal is reflected | off objects such as tall buildings or large rock surfaces before it | reaches the receiver. This increases the travel time of the signal, | thereby causing errors. | c.. Receiver clock errors Ö A receiver's built-in clock is not as | accurate as the atomic clocks onboard the GPS satellites. | Therefore, it may have very slight timing errors. | d.. Orbital errors Ö Also known as ephemeris errors, these are | inaccuracies of the satellite's reported location. | e.. Number of satellites visible Ö The more satellites a GPS | receiver can see, the better the accuracy. Buildings, terrain, | electronic interference, | or sometimes even dense foliage can block signal reception, | causing position errors or possibly no position reading at all. | GPS units typically will not work indoors, underwater or underground. | f.. Satellite geometry/shading Ö This refers to the relative position of | the satellites at any given time. Ideal satellite geometry exists when the | satellites are located at wide angles relative to each other. Poor geometry | results when the satellites are located in a line or in a tight grouping. | g.. Intentional degradation of the satellite signal Ö Selective | Availability (SA) is an intentional degradation of the signal once imposed | by the U.S. Department of Defense. SA was intended to prevent military | adversaries from using the highly accurate GPS signals. The government | civilian GPS receivers. | ********* So the numbers are WRONG. ************** | > | Not *why* you, or anyone else think they're wrong. Quantitative, | repeatable, experimental data that is inexplicable by SR/GTR. | > | ********* The numbers are wrong.************* | > | All that SR/GTR is are axioms and mathematics which can | be applied to explain/predict the results of experiments. | Now, what axioms do you want to scrap, and what proof | can you offer that they do not match physical reality? | > | ******** The numbers are WRONG. *********** | > | If theories do deliver like you think they do, then why don't | you or any of those Einstein Dingleberries take a good | look at those wonderful equations & produce some new | future technology... ahahaha... Do it and show me some | piece of new hardware created by gawking at an eqaution | from Einstein's crap... ... ahahaha... | > | > | Test case for you, Dirk: .... When you give your instructions: | in your Remote Viewing classes http://www.transcendence.me.uk/ | have you applied the help I gave you for it in | Has it helped you any?... ahahahaha... AHAHAHAHA... | ahahaha... ahahahanson | > | | Einstein Dingleberries claim GPS is dependent on GR. | Garmin, who actually make GPS receivers, say their accuracy is 15 metres | http://www8.garmin.com/aboutGPS/ | > | It is more like +/- 40 metres vertically but only airline pilots concern | themselves with landing 120 feet below the runway, which, considering | glideslope geometry, places the aircraft among the approach lights at | touchdown causing the light bulbs to break by gravity theory. | http://farm1.static.flickr.com/168/496665511_f5e634fd2a.jpg?v=0 | http://www.gebenus.com/wordpress/wp-content/uploads/2008/05/approach_lights. jpg | http://www.ae.ca/papersart/vanfig06.jpg | > | *** VThe numbers are WRONG. Dork Brouhaha is a head. *** | > | Don't tell Dirk the bad news. He needs his ED conformal numbers | for his celestial lineup of (what I gather to be) the Einstein Rings. | > | Hey dudes, all of you who participated here in this portion of the | thread THANKS FOR ALL THE LAUGHS. You are good guys! | ahahaha... ahahahahanson | Imagine this, though. Directly overhead is a GPS satellite, so the signal has the least amount of atmosphere to penetrate and the shortest distance, it is line-of-sight, no buildings in the way. That takes out a) and b). Now consider: The 24 satellites that make up the GPS space segment are orbiting the earth about 12,000 miles above us. together with: Essentially, the GPS receiver compares the time a signal was transmitted by a satellite with the time it was received. The time difference tells the GPS receiver how far away the satellite is. Curious that just when the system should be at its most accurate, given this perfect speed of light that the dingleberries claim, it turns out to be at its least accurate. 12,000 miles of space, 60 miles of atmosphere and only 40 metres accuracy. A signal from the horizon goes through enough atmosphere to turn the sun red and refract the rays, yet we have 15 metres horizontal accuracy. === Subject: Re: gravity theory >> | >> | > It's the numbers... > If you can't get the numbers right your new theory is a > pile of . A theory without numbers is less than . >> | ... and see, Dirk, they even got to you now.... ahahaha... > Relax, dude, all that Einstein is only a story that > doesn't even buy you a cup of coffee.Have fun with it! > ahahahaha... ahahahahanson >> | They got to me in school where they showed that simply > by assuming c=const Pythagoras Theorem could deliver > the main equations of SR. > As for the rest, it's no good whining on about Einstein > being wrong if the numbers turn out right. You have to show > where his numbers (and by 'his' I mean modern physicists > using SR/GTR) differ from experiment. > Anyone who tries to discredit Einstein's work by quoting > something he said about it 100years ago, and all the right > numbers is just a coincidence, is a moron. >> | ahahahaha... So, they got to you in school, meaning that you > didn't get it... ahahaha... This of course explains why you think > that you are smarter then Carver, Hayeck and Beckman AND > even Einstein himself who in the part that you've snipped from > himself said that SR/GR was a crock o'.... and wherein it > also says that all the experiments that deliver the right numbers > are... .. >> | It's the numbers. > Show me where the numbers are wrong. > Sources of GPS signal errors > Factors that can degrade the GPS signal and thus affect accuracy >> include the following: > a.. Ionosphere and troposphere delays .84 The satellite signal > slows as it passes through the atmosphere. The GPS system > uses a built-in model that calculates an average amount of > delay to partially correct for this type of error. > b.. Signal multipath .84 This occurs when the GPS signal is reflected > off objects such as tall buildings or large rock surfaces before it > reaches the receiver. This increases the travel time of the signal, > thereby causing errors. > c.. Receiver clock errors .84 A receiver's built-in clock is not as > accurate as the atomic clocks onboard the GPS satellites. > Therefore, it may have very slight timing errors. > d.. Orbital errors .84 Also known as ephemeris errors, these are > inaccuracies of the satellite's reported location. > e.. Number of satellites visible .84 The more satellites a GPS > receiver can see, the better the accuracy. Buildings, terrain, > electronic interference, > or sometimes even dense foliage can block signal reception, > causing position errors or possibly no position reading at all. > GPS units typically will not work indoors, underwater or underground. > f.. Satellite geometry/shading .84 This refers to the relative position of > the satellites at any given time. Ideal satellite geometry exists when the > satellites are located at wide angles relative to each other. Poor geometry > results when the satellites are located in a line or in a tight grouping. > g.. Intentional degradation of the satellite signal .84 Selective > Availability (SA) is an intentional degradation of the signal once imposed > by the U.S. Department of Defense. SA was intended to prevent military > adversaries from using the highly accurate GPS signals. The government > civilian GPS receivers. > ********* So the numbers are WRONG. ************** > Not *why* you, or anyone else think they're wrong. Quantitative, > repeatable, experimental data that is inexplicable by SR/GTR. > ********* The numbers are wrong.************* > All that SR/GTR is are axioms and mathematics which can > be applied to explain/predict the results of experiments. > Now, what axioms do you want to scrap, and what proof > can you offer that they do not match physical reality? > ******** The numbers are WRONG. *********** > If theories do deliver like you think they do, then why don't > you or any of those Einstein Dingleberries take a good > look at those wonderful equations & produce some new > future technology... ahahaha... Do it and show me some > piece of new hardware created by gawking at an eqaution > from Einstein's crap... ... ahahaha... >> | Test case for you, Dirk: .... When you give your instructions: > in your Remote Viewing classes http://www.transcendence.me.uk/ > have you applied the help I gave you for it in > Has it helped you any?... ahahahaha... AHAHAHAHA... > ahahaha... ahahahanson >> | > Einstein Dingleberries claim GPS is dependent on GR. > Garmin, who actually make GPS receivers, say their accuracy is 15 metres > http://www8.garmin.com/aboutGPS/ > It is more like +/- 40 metres vertically but only airline pilots concern > themselves with landing 120 feet below the runway, which, considering > glideslope geometry, places the aircraft among the approach lights at > touchdown causing the light bulbs to break by gravity theory. > http://farm1.static.flickr.com/168/496665511_f5e634fd2a.jpg?v=0 > http://www.gebenus.com/wordpress/wp-content/uploads/2008/05/approach_lights. j pg > http://www.ae.ca/papersart/vanfig06.jpg > *** VThe numbers are WRONG. Dork Brouhaha is a head. *** > Don't tell Dirk the bad news. He needs his ED conformal numbers > for his celestial lineup of (what I gather to be) the Einstein Rings. > Hey dudes, all of you who participated here in this portion of the > thread THANKS FOR ALL THE LAUGHS. You are good guys! > ahahaha... ahahahahanson Then I guess that without all those SR/GTR corrections satellite positioning would be perfect. http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)! This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time. This kind of accumulated error is akin to measuring my location while standing on my front porch in Columbus, Ohio one day, and then making the same measurement a week later and having my GPS receiver tell me that my porch and I are currently about 5000 meters in the air somewhere over Detroit. IT'S THE NUMBERS -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: gravity theory > --- Now come the 38 usec... Dingleberry delay... ahahaha... --- >> | >> | > It's the numbers... > If you can't get the numbers right your new theory is a > pile of . A theory without numbers is less than . >> | ... and see, Dirk, they even got to you now.... ahahaha... > Relax, dude, all that Einstein is only a story that > doesn't even buy you a cup of coffee.Have fun with it! > ahahahaha... ahahahahanson >> | They got to me in school where they showed that simply > by assuming c=const Pythagoras Theorem could deliver > the main equations of SR. > As for the rest, it's no good whining on about Einstein > being wrong if the numbers turn out right. You have to show > where his numbers (and by 'his' I mean modern physicists > using SR/GTR) differ from experiment. > Anyone who tries to discredit Einstein's work by quoting > something he said about it 100years ago, and all the right > numbers is just a coincidence, is a moron. >> | ahahahaha... So, they got to you in school, meaning that you > didn't get it... ahahaha... This of course explains why you think > that you are smarter then Carver, Hayeck and Beckman AND > even Einstein himself who in the part that you've snipped from > himself said that SR/GR was a crock o'.... and wherein it > also says that all the experiments that deliver the right numbers > are... .. >> | It's the numbers. > Show me where the numbers are wrong. > Sources of GPS signal errors > Factors that can degrade the GPS signal and thus affect accuracy >> include the following: > a.. Ionosphere and troposphere delays .84 The satellite signal > slows as it passes through the atmosphere. The GPS system > uses a built-in model that calculates an average amount of > delay to partially correct for this type of error. > b.. Signal multipath .84 This occurs when the GPS signal is reflected > off objects such as tall buildings or large rock surfaces before it > reaches the receiver. This increases the travel time of the signal, > thereby causing errors. > c.. Receiver clock errors .84 A receiver's built-in clock is not as > accurate as the atomic clocks onboard the GPS satellites. > Therefore, it may have very slight timing errors. > d.. Orbital errors .84 Also known as ephemeris errors, these are > inaccuracies of the satellite's reported location. > e.. Number of satellites visible .84 The more satellites a GPS > receiver can see, the better the accuracy. Buildings, terrain, > electronic interference, > or sometimes even dense foliage can block signal reception, > causing position errors or possibly no position reading at all. > GPS units typically will not work indoors, underwater or underground. > f.. Satellite geometry/shading .84 This refers to the relative position of > the satellites at any given time. Ideal satellite geometry exists when > the > satellites are located at wide angles relative to each other. Poor > geometry > results when the satellites are located in a line or in a tight grouping. > g.. Intentional degradation of the satellite signal .84 Selective > Availability (SA) is an intentional degradation of the signal once > imposed > by the U.S. Department of Defense. SA was intended to prevent military > adversaries from using the highly accurate GPS signals. The government > civilian GPS receivers. > ********* So the numbers are WRONG. ************** > Not *why* you, or anyone else think they're wrong. Quantitative, > repeatable, experimental data that is inexplicable by SR/GTR. > ********* The numbers are wrong.************* > All that SR/GTR is are axioms and mathematics which can > be applied to explain/predict the results of experiments. > Now, what axioms do you want to scrap, and what proof > can you offer that they do not match physical reality? > ******** The numbers are WRONG. *********** > If theories do deliver like you think they do, then why don't > you or any of those Einstein Dingleberries take a good > look at those wonderful equations & produce some new > future technology... ahahaha... Do it and show me some > piece of new hardware created by gawking at an eqaution > from Einstein's crap... ... ahahaha... >> | Test case for you, Dirk: .... When you give your instructions: > in your Remote Viewing classes http://www.transcendence.me.uk/ > have you applied the help I gave you for it in > Has it helped you any?... ahahahaha... AHAHAHAHA... > ahahaha... ahahahanson >> | > Einstein Dingleberries claim GPS is dependent on GR. > Garmin, who actually make GPS receivers, say their accuracy is 15 metres > http://www8.garmin.com/aboutGPS/ > It is more like +/- 40 metres vertically but only airline pilots concern > themselves with landing 120 feet below the runway, which, considering > glideslope geometry, places the aircraft among the approach lights at > touchdown causing the light bulbs to break by gravity theory. > http://farm1.static.flickr.com/168/496665511_f5e634fd2a.jpg?v=0 > http://www.gebenus.com/wordpress/wp-content/uploads/2008/05/approach_lights. j pg > http://www.ae.ca/papersart/vanfig06.jpg > *** VThe numbers are WRONG. Dork Brouhaha is a head. *** > Don't tell Dirk the bad news. He needs his ED conformal numbers > for his celestial lineup of (what I gather to be) the Einstein Rings. > Hey dudes, all of you who participated here in this portion of the > thread THANKS FOR ALL THE LAUGHS. You are good guys! > ahahaha... ahahahahanson >> Then I guess that without all those SR/GTR corrections satellite >> positioning would be perfect. >> http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html >> The combination of these two relativitic effects means that the clocks >> on-board each satellite should tick faster than identical clocks on the >> ground by about 38 microseconds per day (45-7=38)! This sounds small, but >> the high-precision required of the GPS system requires nanosecond >> accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were >> not properly taken into account, a navigational fix based on the GPS >> constellation would be false after only 2 minutes, and errors in global >> positions would continue to accumulate at a rate of about 10 kilometers >> each day! The whole system would be utterly worthless for navigation in a >> very short time. This kind of accumulated error is akin to measuring my >> location while standing on my front porch in Columbus, Ohio one day, and >> then making the same measurement a week later and having my GPS receiver >> tell me that my porch and I are currently about 5000 meters in the air >> somewhere over Detroit. >> IT'S THE NUMBERS >> Dirk > ahahaha... don't bring up that crap, again.. These 38 usec > are **calculated**, pitiful SR/GR explanations that took > Ashby and his Dingleberries-likes 39 equations to > arrive at 38u sec... a full decade AFTER GPS was > in operation. Its a ing story by the Dingleberries in > their hope to get fame by association... ahahaha... > while see any decent engineer, l et alone a physicist, > can quickly see... in ONE FELL SWOOP, thyat in hhis case > here all what matters in such an approximation is the mass of > the earth, M_e, and the signal height traveled, h, to show in a > single line that > [1] (M_e /h ) * (2 G/c^2) * 86400 = 38 microsec > the daily time drift, wherein M_e = the earth's mass, h = the orbit > height over the surface, G = Newton, c = Lightspeed & the 86400 > sec/day.... ahahahaha.... > and then usually like you now did another Dingleberry does > Wabnigger by with his > GPS carrier frequency: 1.023000000000 MHz > (theor. unaffected) and 1.022999999543 MHz (rel. corrected) > but who is not realizing that it's just another expression for > the same Newtonian 38 usec delay... which is not even > germane to the GS operation as Andro has explained... > or if you won't believe him then ask like I did here: > Sam, I asked about this before, in this post here on 3-Jan-08,: > == re: GPS World: Connectivity, Mobile Phones Will > Dominate Navigation ==,... wherein I asked you, Sam: > Where is Einstein referred to for his contributions in your link here? > < http://lbs.gpsworld.com/gpslbs/content/printContentPopup.jsp?id=481835 Where do the GPS manufactures and operators like Nokia, Motorola, > LG, Samsung, TRG, Garmin or TomTom say that they could not have > achieved that level/success of technology were it not for Einstein and > his lunatic SR and GR? ... > They'll leave you dangle from Einstein's sphincter , Dirk, > like a Dingleberry ahahahaha... ahahahahanson (M_e /h ) * (2 G/c^2) * 86400 = 38 microsec Where is the derivation from first principles? Anyone can do a dimensional analysis, throw in a constant and get anything they like. I'm waiting to hear that E=MC^2 is wrong and it's really E=MC^2+0.42 -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: gravity theory | --- Now come the 38 usec... Dingleberry delay... ahahaha... --- | > | > | | > | >> | >> It's the numbers... | >> If you can't get the numbers right your new theory is a | >> pile of . A theory without numbers is less than . | > | > | >> ... and see, Dirk, they even got to you now.... ahahaha... | >> Relax, dude, all that Einstein is only a story that | >> doesn't even buy you a cup of coffee.Have fun with it! | >> ahahahaha... ahahahahanson | > | > | >> They got to me in school where they showed that simply | >> by assuming c=const Pythagoras Theorem could deliver | >> the main equations of SR. | >> As for the rest, it's no good whining on about Einstein | >> being wrong if the numbers turn out right. You have to show | >> where his numbers (and by 'his' I mean modern physicists | >> using SR/GTR) differ from experiment. | >> Anyone who tries to discredit Einstein's work by quoting | >> something he said about it 100years ago, and all the right | >> numbers is just a coincidence, is a moron. | > | > | >> ahahahaha... So, they got to you in school, meaning that you | >> didn't get it... ahahaha... This of course explains why you think | >> that you are smarter then Carver, Hayeck and Beckman AND | >> even Einstein himself who in the part that you've snipped from | >> himself said that SR/GR was a crock o'.... and wherein it | >> also says that all the experiments that deliver the right numbers | >> are... .. | > | > | >> It's the numbers. | >> Show me where the numbers are wrong. | >> Sources of GPS signal errors | >> Factors that can degrade the GPS signal and thus affect accuracy | > include the following: | >> a.. Ionosphere and troposphere delays Ö The satellite signal | >> slows as it passes through the atmosphere. The GPS system | >> uses a built-in model that calculates an average amount of | >> delay to partially correct for this type of error. | >> b.. Signal multipath Ö This occurs when the GPS signal is reflected | >> off objects such as tall buildings or large rock surfaces before it | >> reaches the receiver. This increases the travel time of the signal, | >> thereby causing errors. | >> c.. Receiver clock errors Ö A receiver's built-in clock is not as | >> accurate as the atomic clocks onboard the GPS satellites. | >> Therefore, it may have very slight timing errors. | >> d.. Orbital errors Ö Also known as ephemeris errors, these are | >> inaccuracies of the satellite's reported location. | >> e.. Number of satellites visible Ö The more satellites a GPS | >> receiver can see, the better the accuracy. Buildings, terrain, | >> electronic interference, | >> or sometimes even dense foliage can block signal reception, | >> causing position errors or possibly no position reading at all. | >> GPS units typically will not work indoors, underwater or underground. | >> f.. Satellite geometry/shading Ö This refers to the relative position of | >> the satellites at any given time. Ideal satellite geometry exists when | >> the | >> satellites are located at wide angles relative to each other. Poor | >> geometry | >> results when the satellites are located in a line or in a tight grouping. | >> g.. Intentional degradation of the satellite signal Ö Selective | >> Availability (SA) is an intentional degradation of the signal once | >> imposed | >> by the U.S. Department of Defense. SA was intended to prevent military | >> adversaries from using the highly accurate GPS signals. The government | >> civilian GPS receivers. | >> ********* So the numbers are WRONG. ************** | >> Not *why* you, or anyone else think they're wrong. Quantitative, | >> repeatable, experimental data that is inexplicable by SR/GTR. | >> ********* The numbers are wrong.************* | >> All that SR/GTR is are axioms and mathematics which can | >> be applied to explain/predict the results of experiments. | >> Now, what axioms do you want to scrap, and what proof | >> can you offer that they do not match physical reality? | >> ******** The numbers are WRONG. *********** | >> If theories do deliver like you think they do, then why don't | >> you or any of those Einstein Dingleberries take a good | >> look at those wonderful equations & produce some new | >> future technology... ahahaha... Do it and show me some | >> piece of new hardware created by gawking at an eqaution | >> from Einstein's crap... ... ahahaha... | > | > | >> Test case for you, Dirk: .... When you give your instructions: | >> in your Remote Viewing classes http://www.transcendence.me.uk/ | >> have you applied the help I gave you for it in | >> Has it helped you any?... ahahahaha... AHAHAHAHA... | >> ahahaha... ahahahanson | > | | >> Einstein Dingleberries claim GPS is dependent on GR. | >> Garmin, who actually make GPS receivers, say their accuracy is 15 metres | >> http://www8.garmin.com/aboutGPS/ | >> It is more like +/- 40 metres vertically but only airline pilots concern | >> themselves with landing 120 feet below the runway, which, considering | >> glideslope geometry, places the aircraft among the approach lights at | >> touchdown causing the light bulbs to break by gravity theory. | >> http://farm1.static.flickr.com/168/496665511_f5e634fd2a.jpg?v=0 | >> http://www.gebenus.com/wordpress/wp-content/uploads/2008/05/approach_lights. jpg | >> http://www.ae.ca/papersart/vanfig06.jpg | >> *** VThe numbers are WRONG. Dork Brouhaha is a head. *** | >> Don't tell Dirk the bad news. He needs his ED conformal numbers | >> for his celestial lineup of (what I gather to be) the Einstein Rings. | >> Hey dudes, all of you who participated here in this portion of the | >> thread THANKS FOR ALL THE LAUGHS. You are good guys! | >> ahahaha... ahahahahanson | > | > Then I guess that without all those SR/GTR corrections satellite | > positioning would be perfect. | > | > http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html | > The combination of these two relativitic effects means that the clocks | > on-board each satellite should tick faster than identical clocks on the | > ground by about 38 microseconds per day (45-7=38)! This sounds small, but | > the high-precision required of the GPS system requires nanosecond | > accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were | > not properly taken into account, a navigational fix based on the GPS | > constellation would be false after only 2 minutes, and errors in global | > positions would continue to accumulate at a rate of about 10 kilometers | > each day! The whole system would be utterly worthless for navigation in a | > very short time. This kind of accumulated error is akin to measuring my | > location while standing on my front porch in Columbus, Ohio one day, and | > then making the same measurement a week later and having my GPS receiver | > tell me that my porch and I are currently about 5000 meters in the air | > somewhere over Detroit. | > | > IT'S THE NUMBERS | > Dirk | > | ahahaha... don't bring up that crap, again.. These 38 usec | are **calculated**, pitiful SR/GR explanations that took | Ashby and his Dingleberries-likes 39 equations to | arrive at 38u sec... a full decade AFTER GPS was | in operation. Its a ing story by the Dingleberries in | their hope to get fame by association... ahahaha... | while see any decent engineer, l et alone a physicist, | can quickly see... in ONE FELL SWOOP, thyat in hhis case | here all what matters in such an approximation is the mass of | the earth, M_e, and the signal height traveled, h, to show in a | single line that | [1] (M_e /h ) * (2 G/c^2) * 86400 = 38 microsec | the daily time drift, wherein M_e = the earth's mass, h = the orbit | height over the surface, G = Newton, c = Lightspeed & the 86400 | sec/day.... ahahahaha.... | > | and then usually like you now did another Dingleberry does | Wabnigger by with his | GPS carrier frequency: 1.023000000000 MHz | (theor. unaffected) and 1.022999999543 MHz (rel. corrected) | but who is not realizing that it's just another expression for | the same Newtonian 38 usec delay... which is not even | germane to the GS operation as Andro has explained... | or if you won't believe him then ask like I did here: | Sam, I asked about this before, in this post here on 3-Jan-08,: | == re: GPS World: Connectivity, Mobile Phones Will | Dominate Navigation ==,... wherein I asked you, Sam: | Where is Einstein referred to for his contributions in your link here? | < http://lbs.gpsworld.com/gpslbs/content/printContentPopup.jsp?id=481835 > | Where do the GPS manufactures and operators like Nokia, Motorola, | LG, Samsung, TRG, Garmin or TomTom say that they could not have | achieved that level/success of technology were it not for Einstein and | his lunatic SR and GR? ... | > | They'll leave you dangle from Einstein's sphincter , Dirk, | like a Dingleberry ahahahaha... ahahahahanson | I drive my car at 30 mph. Each foot along the road passes by me quite frequently, in fact 44 feet go by every second. That's a frequency of 44 Hz. If I increase my speed to 90 mph the frequency increases to 132 Hz but the feet do not change to yards. If they did I'd be back to 44 Hz. Of course if time changed instead I could go faster and still be travelling at 30 mph. So let's pretend my time for a 30 mile journey is 20 minutes and the road time for the same journey is 1 hour. I haven't aged as much as you have standing still. I turn around and drive back again, total journey time 40 mins for me, 2 hours for you. Did the Red Sox win? The result is known for you and the game s not over for me. If I listened on the radio it would not tune, I'd be picking up 300 MHz on the FM band from the Doppler effect outgoing and 33 MHz returning. But wait.... then I'd know the result... === Subject: Re: gravity theory > It's the numbers... > If you can't get the numbers right your new theory is a pile of . > A theory without numbers is less than . > ahahaha... AHAHAHA... Ambiguous! Come again, Dirk. > AHAHAHA... Whose *new* theory and which numbers? > Are you talking about the above, initial snippet from/by > jedakiah jedakiah.2d3a852 at physicsbanter.com, in > who didn't present any numbers? > I have corrected an attribution above. The familiarize > came not from Jedakiah, but from Sam who is proselytizing > Einstein's with extreme prejudice and uncommon > fanaticism.... ahahahaha... So, to/for jedak's defense > consider that he is the reaction product, the victim, of the > incessant onslaught by the Dingleberries that Einstein > warned against ever since 1920... > ... and see, Dirk, they even got to you now.... ahahaha... > Relax, dude, all that Einstein is only a story that > doesn't even buy you a cup of coffee.Have fun with it! > ahahahaha... ahahahahanson > They got to me in school where they showed that simply > by assuming c=const Pythagoras Theorem could deliver > the main equations of SR. > As for the rest, it's no good whining on about Einstein > being wrong if the numbers turn out right. You have to show > where his numbers (and by 'his' I mean modern physicists > using SR/GTR) differ from experiment. > Anyone who tries to discredit Einstein's work by quoting > something he said about it 100years ago, and all the right > numbers is just a coincidence, is a moron. > ahahahaha... So, they got to you in school, meaning that you > didn't get it... ahahaha... This of course explains why you think > that you are smarter then Carver, Hayeck and Beckman AND > even Einstein himself who in the part that you've snipped from > himself said that SR/GR was a crock o'.... and wherein it > also says that all the experiments that deliver the right numbers > are... .. well, go read it again... & then after that you may announce > again, loud as you did twice already, that you are a very proud > Einstein Dingleberry which dangles and swings with great delight > and in worshipping awe from Einstein's Sphincter.... hahahaha... > -- I will give you all the kudos you want for that; for EDs are fun! -- > So? Einstein's opinion is of no interest to me. > ... ahahaha... you read the ref?... ahahahaha.. did you really? > Annalen der Physik 49, Obviously you didn't get what it says nor what it means... > ahahahaha... Hey no disrespect for you, Dirk. .. ahaha... > It's the numbers. > Show me where the numbers are wrong. Not *why* you, or > anyone else think they're wrong. Quantitative, repeatable, > experimental data that is inexplicable by SR/GTR. > All that SR/GTR is are axioms and mathematics which can > be applied to explain/predict the results of experiments. > Now, what axioms do you want to scrap, and what proof > can you offer that they do not match physical reality? >> Dirk > Forget your fetish about the numbers. Measurements have > nothing to do with any theory, REL or otherwise. -- You have > it ass-backwards... Theory describes what is already known > and does not pre-dict anything. Theories are just stories by > which they describe a process, event or state observed > in nature. Theories are quantitative data compression algorithms. Without numbers all that is left is handwaving and nuts on sci.physics ranting and tossing insults. > If theses theories and in particular Einstein's crap are so > great then why don't we have those wonderful gismos and > gadgets that one sees in sci-fy, Starwars and Star trek? > If theories do deliver like you think they do, then why don't > you or any of those Einstein Dingleberries take a good > look at those wonderful equations & produce some of that > future technology... ahahaha... Do it and show me some > piece of new harware created by gawking at an eqaution > from Einstein's crap... ... ahahaha... > Test case for you, Dirk: .... When you give your instructions: > in your Remote Viewing classes http://www.transcendence.me.uk/ > have you applied the help I gave you for it in > Has it helped you any?... ahahahaha... AHAHAHAHA... > ahahaha... ahahahanson Well, we have have a kind of astronomical project lined up, but we will announce it in due course. A kind of prediction/causation on a grand scale. -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: gravity theory > Test case for you, Dirk: .... When you give your instructions: > in your Remote Viewing classes http://www.transcendence.me.uk/ > have you applied the help I gave you for it in > Has it helped you any?... ahahahaha... AHAHAHAHA... > ahahaha... ahahahanson > Well, we have have a kind of astronomical project lined up, > but we will announce it in due course. > A kind of prediction/causation on a grand scale. > Dirk >> http://www.transcendence.me.uk/ - Transcendence UK >> http://www.theconsensus.org/ - A UK political party >> http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff > Well, you haven't answered my question , but that's ok. > Now are sure you meant astronomical and not > astrological.. I hope?... If it's the former one, does it > have to do with the 2012 predictions?... In any event, > I'd be extremely interested how your line-up is caused > by Einstein... Einstein Rings, I guess, which is really really > REMOTE viewing... Keep me posted, by all means... > ... ahahaha.. ahahaha... ahahahanson Nothing to do with 2012. Just something we will predict/cause one month ahead of time. -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: gravity theory > ---------- AHAHAHAHAHAHA... too much!` ------------ > Test case for you, Dirk: .... When you give your instructions: > in your Remote Viewing classes http://www.transcendence.me.uk/ > have you applied the help I gave you for it in > Has it helped you any?... ahahahaha... AHAHAHAHA... > ahahaha... ahahahanson > Well, we have have a kind of astronomical project lined up, > but we will announce it in due course. > A kind of prediction/causation on a grand scale. > Dirk >> http://www.transcendence.me.uk/ - Transcendence UK >> http://www.theconsensus.org/ - A UK political party >> http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff > Well, you haven't answered my question , but that's ok. > Now are sure you meant astronomical and not > astrological.. I hope?... If it's the former one, does it > have to do with the 2012 predictions?... In any event, > I'd be extremely interested how your line-up is caused > by Einstein... Einstein Rings, I guess, which is really really > REMOTE viewing... Keep me posted, by all means... > ... ahahaha.. ahahaha... ahahahanson >> Nothing to do with 2012. >> Just something we will predict/cause one month ahead of time. > ... Awe, how disappointing!... Only one month?... > Like when the girlfriend's gona be on the rag or > whether the job will be still here next month?.... ahahaha... > Or did it predict this conversion here on this lined > ahahaha... ahahahanson No, it will be something that the entire world will see. -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: gravity theory > ---------- AHAHAHAHAHAHA... too much!` ------------ Test case for you, Dirk: .... When you give your instructions: > in your Remote Viewing classes http://www.transcendence.me.uk/ > have you applied the help I gave you for it in > Has it helped you any?... ahahahaha... AHAHAHAHA... > ahahaha... ahahahanson > Well, we have have a kind of astronomical project lined up, > but we will announce it in due course. > A kind of prediction/causation on a grand scale. > Dirk >> http://www.transcendence.me.uk/ - Transcendence UK >> http://www.theconsensus.org/ - A UK political party >> http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird >> stuff > Well, you haven't answered my question , but that's ok. > Now are sure you meant astronomical and not > astrological.. I hope?... If it's the former one, does it > have to do with the 2012 predictions?... In any event, > I'd be extremely interested how your line-up is caused > by Einstein... Einstein Rings, I guess, which is really really > REMOTE viewing... Keep me posted, by all means... > ... ahahaha.. ahahaha... ahahahanson >> Nothing to do with 2012. >> Just something we will predict/cause one month ahead of time. > ... Awe, how disappointing!... Only one month?... > Like when the girlfriend's gona be on the rag or > whether the job will be still here next month?.... ahahaha... > Or did it predict this conversion here on this lined > ahahaha... ahahahanson >> No, it will be something that the entire world will see. > 31 days and counting down.. I shall be back at time zero > and re-inquire... hoping that your answer will not just be > Full Moon or Sunrise etc.... ahahahaha... ahahahanson No, the clock hasn't started yet. We still have to announce the specific event. -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: gravity theory <6fantmFafgf9U1@mid.individual.net> <6fbtj5Fatr3pU1@mid.individual.net> <6fc2epFaspg9U1@mid.individual.net> <_x5kk.437$Ht4.233@trnddc01> <6fc825Fava6kU2@mid.individual.net> <6fca65Fasa95U1@mid.individual.net> <6fcdnlFaod1oU1@mid.individual.net> posting-account=SWr-zgoAAABXP_I1KRp8SBR28UDaox2f Gecko/20080625 Ubuntu/7.10 (gutsy) Firefox/2.0.0.15,gzip(gfe),gzip(gfe) Hi jedakiah My name is Conrad Countess You are on the right track and I've used the same type analogy. The whirlpool analogy is just an extension of the wave on lake such as spiral galaxies in their revolving density waves . But gravity begins with waves and acquires rest mass when the speed and momentum of the wave in 90 degree angular direction equals and balances speed and momentum of waves in linear direction which is, (c x c) or (c^2) and a balance of centripetal and centrifugal forces to create the speed of light in circular or spherical motion. repelling forces of positive and negative charges modeled by objects spinning in water, same and opposite directions resulting in attracting and repelling forces pointed out by YPorat Even in gravity description offered by Einstein which Sam Wormley pointed out at http://en.wikipedia.org/wiki/General_relativity it states in Einstein's equation section : Drawing further upon the analogy with geometric Newtonian gravity, it is natural to assume that the field equation for gravity relates this tensor and the Ricci tensor, which describes a particular class of tidal effects: the change in volume for a small cloud of test Hi jedakiah My name is Conrad Countess You are on the right track and I've used the same type analogy. The whirlpool analogy is just an extension of the wave on lake such as spiral galaxies in their revolving density waves . But gravity begins with waves and acquires rest mass when the speed and momentum of the wave in 90 degree angular direction equals and balances speed and momentum of waves in linear direction which is, (c x c) or (c^2) and a balance of centripetal and centrifugal forces to create the speed of light in circular or spherical motion. repelling forces of positive and negative charges modeled by objects spinning in water, same and opposite directions resulting in attracting and repelling forces pointed out by YPorat Even in gravity description offered by Einstein which Sam Wormley pointed out at http://en.wikipedia.org/wiki/General_relativity it states in Einsteins equation section : Drawing further upon the analogy with geometric Newtonian gravity, it is natural to assume that the field equation for gravity relates this tensor and the Ricci tensor, which describes a particular class of tidal effects: the change in volume for a small cloud of test This is section from earlier site: Quantum Gravity Electromagnetism - Gravity Equivalence My name is Conrad Countess I am an Independent Researcher I think that I can lay the foundation for Quantum Gravity in three steps. 1.Assuming that energy is more basic than matter, if we start with a field of energy in its ground state that is below detectable frequency, this can be Dark Energy or the Higgs field. 2.Next, if we assume that this energy field permeates all of space or is indistinguishable from space itself and moves at the velocity of c we have set the stage. 3.Now, just add extra energy and this should give rise to waves of frequency that increase according to Planck's constant in quantum increments with increased energy . This extra energy may come from a rotation sense the Universe as far as we can detect may be rotating as everything in the perceivable Universe seems to be orbiting something else on a larger scale. Just as a tub of water with a thin film of soap that is turned will began to congeal swirls of soapy film in concentrated regions, the Universe may begin to congeal swirls of energy analogous to this. When the right angle frequency speed of this congealed energy reaches c just as the speed along the light path this is c x c or c2 resulting in something analogous to ?the speed of light in uniform circular motion? in classical physics as in a=v2/r, but on the quantum level. This results in rest mass because the centripetal speed of the frequency should balance out the centrifugal speed of light along the light path resulting in equally distributed energy, mass, and momentum around a center of rotation as opposed to energy being radiated outward from a center at a velocity of c as is the case with normal electromagnetic radiation. Beginning With Waves It is well known that higher energy electromagnetic waves result in an increase in frequency but no addition to the speed of c along the light path. In the same sense any increase in energy to this background Dark Energy or Higgs field that is already moving at c causes waves to churn up within it out of an otherwise imperceptible but not empty field like waves on a pond that is disturbed. And so within the background energy field itself as a consequence of added energy giving rise to frequency, increasing in quantum increments and attaining rest mass at the frequency of c2. These are current sites: Just keep working on your theory and see what happens Conrad Countess === Subject: Re: gravity theory | >> | ok now it is generally perceived that gravity is a product of | mass, but gravity is still unexplained, i have a theory that i | believe is logical and leaves no questions. | > | Gravity is exquisitely model (explained for many) by general | relativity. ... familiarize yourself with it. | > | Jedak, explain simply, in a new way, what and why there is | Action at a Distance and you'll have an exquisite model | of Gravity. But if you need to invoke GR to do so then you | are simply delivering a useless sermon like any other | village priest of the Einstein cult does... and you'll be in | line with and in the league of those Einstein Dingleberries | that are an unending source for laughs.... ahahaha.... | > | http://en.wikipedia.org/wiki/General_relativity | >> | Ahem...Sam, if there is a theory of General Relativity, please cite | the author and the journal in which it was published. | > | http://en.wikipedia.org/wiki/General_relativity#References | including Einstein. [which is ...] | > | Realize that at the time of his death, Einstein never published his | theor of genral relativity, because there remained some issues | that he could not resolve. | Hence, there is no such thing as a Theory of General Relativity. | > | Lot's of good material, Harry. | Are There Any Good Books on Relativity Theory? | http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html | You make it sound GTR doesn't exist because it is a work in progress? | This is now, Harry, GTR is more mature and fruitful. | >> | It simply does not exist. | Harry C. | >> | Well, Chief Harry, Albert did publish several items in which | he referred to GR as allgemeine Relativit.8atstheorie early | in his career, as can be seen from the link Sam gave you. | > | But Sam is a quintessential Einstein Dingleberry who does | worship Einstein & he proselytizes his notion as a teacher | in his school for the geriatric set. That is all commendable | as long as Sam teaches that SR/GR are nothing more than 1 | of the ing stories about nature, a fable, model or feeble' | description of nature.... good for mental masturbations only | BUT with NO practical value to/in the real world, | including GPS that NEVER needed nor used any SR nor GR. | > | So, when elevating SR/GR to the Holy grail of Physics it is | equivalent to the mentation that is exhibited by the religious | fundamentalists of the Jews, Islamists or Evangelicals. | > | If you look at Einstein original 1905 paper on SR you'll see | clearly that he grudgingly published it , without any references, | under the nagging and the insistence of his 1st Xian wife | More here: | | > | The 1905 paper took off with the promos & backing of the then | very active Zionist movement in Germany. Albert got caught up in | that environment and was nudged into developing a general | theory (GR) which he was never comfy about/with, not from the | get-go, nor at any time during his career and he outright did | doubt GR's validity, grievously, at the end of his life... AND | he knew that playing that game was a despicable con. -- OTOH | his unrelated work, on the Photoelectric effect, for which he got | the Nobel price in 1921, he must be respected for. | > | Here is what Einstein said in the reference that Sam gave: | http://en.wikipedia.org/wiki/General_relativity#CITEREFEinstein1917 | Einstein, Albert (1916), Die Grundlage der allgemeinen Relativit.8atstheorie | Annalen der Physik 49, | which is written in the swollen genre of the 19th century German | Script with its many expressions of manifold meaning and | wherein Einstein, very uncharacteristically, gives credit to others | and says on: | > | 286-Doc30-770: ...all fundamentals for GR/GTR were already | known and invented by Gauss, Riemann, Christoffel, Ricci | & Levi-Civita. -- I am grateful to my friend Grossman who | spared me from me having to learn the necessary math & me | doing the required literature search to get to the needed field | equations for GTR. | > | Einstein continues on | 286-Doc30-771:... Ernst Mach was the first one to recognize a | fundamental misconception & conceptual fault in the formulation | of the SR, my Special Theory of relativity... [Einstein then bags | on Newton's Grav. shortcomings, but he hedges in the foot note:]... | The new theoretical realizations may not be applicable to events | in physical reality if they are contra to other physical experiences. | > | 286-Doc30-771:... wherein Einstein pontificates: | The cause and source for Newton's Action-at-a-distance must | lay **outside** of the system of the 2 involved masses... & (by | assumption) there **ought to be** no preferential frame of reference. | > | 286-Doc30-771:... wherein Einstein laments like a politician | about: ... some Force field which one must assume to be | justifiable in systems at rest as well as when in movement | from which one can immediately conclude that... by simply | changing the coordinate systems one generates a Gravitational | Force field... in which one **sets** the speed of light to be | constant & one can easily see that a ray of light must be bent ... | > | 291-Doc30-776:... wherein Einstein laments that: | There is no other choice then to accept/believe that all imaginable | frames of reference/coordinate systems have to regarded as being | equally valid.. [but then he adds & hedges in the page's foot note] | About certain limitations of the requirement for attribution and | steadiness we shall NOT talk about....[ ahahahaha... AHAHAHA... | and presumably he meant by that to admit & imply failure of his | GR because he was never able to get rid of Newton's G which is | required for any and all of GR's solutions... AHAHAHAHA.....] | > | Albert's hedging, cautioning, handwaving, and gauche credits | to others with his intent to absolve himself or at least spread any | possible blame for failure, is evident in the above introduction of | his 1st paper on GR ... ahahahaha.. . | > | If Albert would have written his today, and if he would not have | been promoted back then by the Zionist-infested academia of the | Weimar Republic, then any referee would taken Albert's manuscript | and a cigar to the toilet, smoked the cigar and wiped his ass with | Albert's paper... Albert was a ing lucky crackpot... ahahaha... | > | GR has not matured, as Sam so lovingly advocates. Einstein's | relativity is a like an old toilet seat which normal people would | throw away because it stinks. --- But to the folks who harbor a | toilet seat fetish, like all Einstein Dingleberries do, REL has | become a cherished, albeit useless, relic that is worshiped and | still exhibited widely... ahahahaha.... | > | The Dingleberry argument that GR predicts reality in many | experiments accurately is as shallow and UN-convincing as is | the plethora of the Miracles in the Torah/Bible or Koran that | too are predicting reality accurately to their disciples... | > | All these holy scriptures, including Albert's just show that | any highfaluting story/report or theory will always find examples | in the real world that prove the theory right to their believing | disciples. | > | Actually, Albert had his misgivings about his Relativity crap | from the start when he told his Dingleberries with/in his many | admonishments, ever since 1920....: | ::AE:: .... NOT to search at the same, now well lit places, | ::AE:: .... where he, Einstein, had been working. | > | ....This is reflected in the real world, like here, where one can | see where Einstein's crap is still used and where they laugh | about it: | = mil/indust. Eng, R&D.....................does not need REL | = *.edu and grantology ....................does use REL, No | = Promo, Sales & Movies...............loves REL by the load | = Jews defend it as cultural heritage whether REL is or not. | > | ... and to boot Einstein was keenly aware of this and very lucidly | and finally confessed in 1954, just a year before Albert folded | his relativity tent, closes his umbrella, kicked the bucket & finally | puffed, but leaving behind vast hordes of his Einstein Dingleberries | (1 set of which resides in these NGs to stink up & retard the | intellectual level & quality of physics), | > | ::AE:: I consider it quite possible that physics cannot be based | ::AE:: on the field concept, i. e., on continuous structures. In that | ::AE:: case nothing remains of my entire castle in the air, gravitation | ::AE:: theory included, [and of] the rest of modern physics. . [ & | ::AE::elsewhere] why would anyone be interested in getting | ::AE:: exact solutions of such an ephemeral set of equations? | > | Other Luminaries have followed suit agreeing with Albert's | final realizations, insights and assessments, saying: | > | :: Professor Carver A. Mead of Caltech (a student of Feynman), | :: who said | :: It is my firm belief that the last seven decades of the 20th century | ::: will be characterized in history as the dark ages of physics. | > | :: or F.A Hayek, Nobel laureate, who said: In the future, | :: Humanity will see in our Epoch an Era of superstition, essentially | :: associated with the names of Marx, Freud and Einstein | > | :: or John Beckman, an astronomy professor and Einstein disciple: | :: The theory of relativity lives on. Is it a true picture of reality? | :: That is probably more a matter of faith than of proof. | > | Dirk Bruere at NeoPax | It's the numbers... | If you can't get the numbers right your new theory is a pile of . | A theory without numbers is less than . | > | ahahaha... AHAHAHA... Ambiguous! Come again, Dirk. | AHAHAHA... Whose *new* theory and which numbers? | Are you talking about the above, initial snippet from/by | jedakiah jedakiah.2d3a852 at physicsbanter.com, in | who didn't present any numbers? | I have corrected an attribution above. The familiarize | came not from Jedakiah, but from Sam who is proselytizing | Einstein's with extreme prejudice and uncommon | fanaticism.... ahahahaha... So, to/for jedak's defense | consider that he is the reaction product, the victim, of the | incessant onslaught by the Dingleberries that Einstein | warned against ever since 1920... | ... and see, Dirk, they even got to you now.... ahahaha... | Relax, dude, all that Einstein is only a story that | doesn't even buy you a cup of coffee.Have fun with it! | ahahahaha... ahahahahanson Where's that Nobel Prize that Dork Brouhaha of Newpeace promised me? Ah... as I suspected... the arsehole can only produce a little pile of . === Subject: Re: an important set theory post <7jj684pckih28nu3lgo4gq3un175j3r82u@4ax.com> <8763r061vy.fsf@alatheia.dsl.inet.fi> <48858f8a$0$6005$ba620dc5@text.nova.planet.nl> posting-account=UJeUTgkAAADYai-ULU41ORCvNnkXmdRu Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) |> Usually, though, when a classical mathematician talks about |> 2^X in set theory, they are essentially talking about the |> power set P(X), and using the nonconstructive result that |> this is in 1-1 correspondence with 2^X | |Can you add a hint how P(X) can be defined such that it's not |'essentially the same' as 2^X? In other words, such that its 1-1 |correspondence with 2^X is nonconstructive. Well, under the usual definition of P(X), the family of all subsets of X, the existence of a 1-1 correspondence with 2^X is nonconstructive. A subset S of X gives a criterion for an element of X to be in S. An element f of 2^X gives a function from X to {0,1}. If each element of X is either a member of S or is not a member of S, then it corresponds to a map from X to {0,1} where we send the members of S to 1 and the non- members of S to 0. That's an application of excluded-middle, however. 2^X then naturally injects into P(X), but that there is a nonconstant function P(X)->2^X implies the law of excluded middle. One can show that 2^X has higher cardinality than X in the usual way. In set theory, the ranks of the cumulative hierarchy are given by repeatedly taking power-sets, since each successor rank has the subsets of the sets in the previous rank. Once one makes a distinction between the two concepts, one sees that it's the power-set that's the relevant one, not functions to {0,1}. In other cases (e.g. binary sequences) it's the functions to {0,1} that matter. I can't think of any case where it isn't pretty clear from the context that (whatever notation may be used) one or the other notion is the one essentially being used. Keith Ramsay === Subject: Re: On continous functions and metric spaces Distribution: world >Do integers form a metric space?. By the definition of metric space >looks like they do. The integers, by themselves, do not form a metric space. The integers, like any other set, can be part of a metric space, if you define a metric function f:ZxZ->R+. The function, together with the set, are what create a metric space. You could define a metric function on the alphabet if you wanted to, and the alphabet, together with the function, would be a metric space. >2) Are continous functions possible in any metric space?. Given *any* two metric spaces, A and B, there are continuous functions from A to B, regardless of whether or not A and B are the same metric space. -- Michael F. Stemper #include Time flies like an arrow. Fruit flies like a banana. === Subject: This is my part of solutions manual list posting-account=jGYvqQoAAAC8JVWtG92jlQ1UvZHQAEv9 CLR 1.1.4322),gzip(gfe),gzip(gfe) This is my part of solutions manual list ,If you want any other solutions manual which is not in my solutions list, don.81ft give up .please email to sendsolutions(at)hotmail.com Solutions manual to Calculus A Complete Course 6th Edition by R.A. Adams Solutions manual to Cisco Technical Solution Series: IP Telephony Solution Guide Version 2.0 Solutions manual to Control Systems 4th edition by Norman S. Nise Solutions manual to Corporate Finance, Second Edition by Peter Bossaerts Solutions manual to Electrical Circuits 6th by James W. Nilsson, and Susan A. Solutions manual to Electrical Circuits 7th by James W. Nilsson, and Susan A. 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Freedman, University Physics with Modern Physics:,12 ed By Hugh D. Young, Roger A. Freedman, use with Fundamentals of Corporate Finance, 4th Edition By Bruce Swenson vector analysis (1961) By Lewis Richard Shorter Vector Mechanics for Engineers: Dynamics, 7th By Ferdinand P. Beer(selected chapters) E. R. Johnston Vector Mechanics for Engineers: Statics, 7th By Ferdinand P. Beer(selected chapters) Vector Mechanics for Engineers: Statics, 7th Edition ,By Ferdinand P. Beer, E. Russell Johnston Jr., ElliotR Visual C++ How to Program, (3rd Edition) ,by Harvey & Paul Deitel & Associates Wireless communication and networks 2th by willian stallings === Subject: Re: Eric Gisse's professional career as a -throwing chimpanzee will come to an abrupt end posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) >> Folks, this post has only one rating and that a 1 so far. æBut has >> anyone else looked at Dono's profile and noticed that he has a four- >> star rating averaged over 2000 votes last time I looked. æThat's a lot >> of votes! æI wonder how it happens that Dono has ratings from more >> than ten times as many people as anyone I've ever seen. > Dono, that pathetic creature who can't even do high school algebra > very well, spends a lot of his miserable life voting for himself. >> One identity can vote only once for a given ratee. > That's incorrect. Would you like to see me vote for you over 50 > times? >> And one cannot vote for himself. > I can easily vote for myself on any post a hundred times but for every > 100 votes that I give myself at 5 stars, the chimp Dono will happily > and enthusiastically waste his time voting 200 times against me using > 1 star. So a debate with Dono devolves into who is more chimp-like > than anyone else. >> Am I missing something here? æIs it his charming personality? >> Is it his warmth and grace? > Dono is an unabashed psychopath. >> Help me understand how this has happened! >> What can we learn from Dono? >> Uncle Ben > The tragic lesson to be learned from Dono is to not live your life as > a -throwing chimpanzee. > Shubee Regarding the validity of the Google Five Star rating system, > here is a post I made 7 August 2007 æTuesday 9:03 PM > in the thread: > How to spot sociopaths in the newsgroups > ------------------------------------------- I have discovered a great way to spot sociopaths > in the news groups!!!!!! If you scroll down a list of posts using Google Groups > you'll see a line of five stars near the middle of the screen. So, if you want to read posts that have some intellectual content, > avoid the posts where four or five stars are highlighted, Yes, I remember this post. According to this general rule, Potter might also recommend that: 1. If you want to find a restaurant that serves excellent food, choose the one that is empty of diners. 2. If you want to go to a movie that is highly entertaining, choose the one with the shortest lines at the theater. 3. If you are looking for a new phone, be sure to choose the one that has the lowest buyer rankings. 4. If you're looking for a lovely country to live in, choose the one with the highest emigration rate out of the country. And this is because: 1. Restaurants that are full of diners have obviously stacked the tables with employees and friends of employees to give the appearance of being busy. 2. Movies with long lines are the ones funded by major studios who hire people to stand in line for the next show. 3. Crappy phone manufacturers don't spend their time manufacturing decent phones and instead spend all their time clicking on high user rankings. 4. Countries with a high immigration rate into the country are obviously selling lies to get people to flood into the country to solve the country's massive problems, and countries that don't have any problems don't feel the need to attract people into the country. Potter can get himself to believe just about anything. It's a hobby with him. I wouldn't be surprised if next week his goal is to get himself to believe that he alone understands Newtonian mechanics. on the other hand, if you want to find some nifty insults and smart ass > remarks > to use in your posts, or if you are researching sociopathic behavior, > read the five star posts. To provide the reader with some idea of what I mean, > note that the posts below are FIVE STAR POSTS. æ æFor a guy with a supposed brain, I'd think you'd be able to figure > æ æthat out, Koobee. > æ æYou don't like yourself very much Koobee-- > You remind me of Potter's blustering. > First you argue that GR isn't needed for GPS. Argument demolished. > Next you argue that GPS never required GR. Argument demolished. > Now it is that you don't understand why the correction is necessary. > -4,4647E-10 * 24*60*60 seconds æ= -38.575 microseconds, imbecile. > You still don't even know where the GR corrections are applied in GPS > despite you arguing about the system since 2005! Two years, and you > can't even explain WHERE the corrections are implemented. Why should > anyone care if you cannot understand? > Take your selective editing and shove it up your ass. > Naturally you will not accept this, and will shift the goal post out > juuuust a little bit further. > No, idiot. æThe first GPS satellite was not corrected for GR. æIt had > a standby offset oscillator just in case. æJust in case happened. æThe > second and later GPS satellites were fully corrected for GR and > everything else by default. > æ æHere--get the bigger picture. > æ æ æhttp://edu-observatory.org/gps/gps books.html#Relativity > A dangerous thing to say to an insane person. > Tell us about /your/ education > and why it is superior to a PhD in physics. > ZZT! WRONG! > Atomic clocks do not work according to classical rules. > Could it be because you are extremely mentally challenged? :-) > It seems to be a common trait by the GPS works without GR cranks. It appears that the most sociopathic posters in > the newsgroups have a sock puppet, and give themselves > ***** Five Star ***** ratings. -- > Tom Potter http://www.geocities.com/tdp1001/index.htmlhttp://notsocrazyideas.blogspot.c o mhttp://www.flickr.com/photos/tom-potter/http://tdp1001.wiki.zoho.comhttp:// g roups.msn.com/PotterPhotoshttp://www.androcles01.pwp.blueyonder.co.uk/dingle b erry.htm > === Subject: Re: Eric Gisse's professional career as a -throwing chimpanzee will come to an abrupt end posting-account=d-ESTAkAAAAG0l03yI1WJgsTVXx4ebeJ Gecko/2008050509 Firefox/3.0b5,gzip(gfe),gzip(gfe) > Yes, I remember this post. According to this general rule, Potter > might also recommend that: > 1. If you want to find a restaurant that serves excellent food, choose > the one that is empty of diners. > 2. If you want to go to a movie that is highly entertaining, choose > the one with the shortest lines at the theater. > 3. If you are looking for a new phone, be sure to choose the one that > has the lowest buyer rankings. > 4. If you're looking for a lovely country to live in, choose the one > with the highest emigration rate out of the country. Here's some more for ya: 1. If you want to know who is the Best man to be president, just look at the election results. 2. If you want to know what the public thinks about an issue just listen to a media poll. 3. Even better than a media poll are self-polls where interested activists can vote multiple times. 4. To find out who is insane or stupid you need look no further than such assertions in Usenet. Proof enough. Potter's point is that when politics are involved one can never accept the results at face value. There are too many vested interests in shading results for personal gain. The Google star ratings being a prime example of that. Hell, I've shaded a lot of internet polls myself for political purposes. So what they really gauge is the determination of the various factions who are interested in a given issue. PS. I've just given you a one star rating. Enjoy. === Subject: Re: Eric Gisse's professional career as a -throwing chimpanzee will come to an abrupt end posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) > Yes, I remember this post. According to this general rule, Potter > might also recommend that: > 1. If you want to find a restaurant that serves excellent food, choose > the one that is empty of diners. > 2. If you want to go to a movie that is highly entertaining, choose > the one with the shortest lines at the theater. > 3. If you are looking for a new phone, be sure to choose the one that > has the lowest buyer rankings. > 4. If you're looking for a lovely country to live in, choose the one > with the highest emigration rate out of the country. Here's some more for ya: 1. If you want to know who is the Best man to be president, just > look at the election results. 2. If you want to know what the public thinks about an issue just > listen to a media poll. 3. Even better than a media poll are self-polls where interested > activists can vote multiple times. 4. To find out who is insane or stupid you need look no further > than such assertions in Usenet. Proof enough. Potter's point is that when politics are involved one can never accept > the results at face value. æThere are too many vested interests in > shading results for personal gain. Potter's posts are an excellent example of that. I hold him as the supreme example of self-serving spin management, and I recommend him to others that are aspiring to do the same. The scientific academy does have a number of checks and balances to limit the influence of politics on the validity of scientific results. There are indeed excursions, however. But if you come into a science discussion group with the *assumption* that those checks and balances don't work, and therefore all scientific claims are untrustworthy, and I don't believe you either, then you're simply taking a supermarket tabloid interest in science and nothing more. PD > The Google star ratings being a > prime example of that. Hell, I've shaded a lot of internet polls > myself for political purposes. æSo what they really gauge is the > determination of the various factions who are interested in a given > issue. PS. I've just given you a one star rating. Enjoy. === Subject: Re: Eric Gisse's professional career as a -throwing chimpanzee will come to an abrupt end posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) Since you have such a problem with this system, stop participating it it. === Subject: row operations leave column rank untouched? posting-account=LuOUUgoAAAAlOLgQa2LFVIdj_-W7dRT8 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) Can someone prove that row operations do not affect the column rank of a matrix? I am reading linear algebra by Hefferson (open source) which has a lemma and a proof, which I don't really grasp or get convinced by (excerpt below, which you can ignore): Lemma 3.10 Row operations do not change the column rank. Proof. Restated, if A reduces to B then the column rank of B equals the column rank of A. We will be done if we can show that row operations do not aff ect linear re-lationships among columns (e.g., if the ffth column is twice the second plus the fourth before a row operation then that relationship still holds afterwards), because the column rank is just the size of the largest set of unrelated columns. But this is exactly the fifrst theorem of this book: in a relationship among columns, row operations leave unchanged the set of solutions (c1; : : : ; cn). c1[a11, a21, ..., am1] + c2[a12, a22, ..., am2] + ... + cn[a1n, a2n, ..., amn] = [0,0,...,0] (square brackets denote column vectors). QED === Subject: Re: row operations leave column rank untouched? > Can someone prove that row operations do not affect the column rank of > a matrix? > I am reading linear algebra by Hefferson (open source) which has a > lemma and a proof, which I don't really grasp or get convinced by > (excerpt below, which you can ignore): Lemma 3.10 Row operations do not change the column rank. Proof. Restated, if A reduces to B then the column rank of B equals > the column rank of A. We will be done if we can show that row > operations do not affect linear re-lationships among columns (e.g., > if the ffth column is twice the second plus the fourth before a row > operation then that relationship still holds afterwards), because the > column rank is just the size of the largest set of unrelated columns. > But this is exactly the fifrst theorem of this book: in a relationship > among columns, row operations leave unchanged the set of solutions > (c1; : : : ; cn). c1[a11, a21, ..., am1] + c2[a12, a22, ..., am2] + ... + cn[a1n, > a2n, ..., amn] = [0,0,...,0] (square brackets denote column vectors). QED If you start with an m x n matrix M, there is associated with it a unique linear transformation T_M : R^n -> R^m, with respect to the usual basis vectors. An easily proved result here is that dim(T_M(R^n)) + dim(Kernel(T_M)) = n (1). Now dim(T_M(R^n)) is the rank of the column space of M, and Kernel(T_M) is the set of x's in R^n that solve the m linear homogeneous equations generated by M. That set of x's doesn't change with a row operation, even though the matrix does. Applying (1) to the linear transformation associated with the altered matrix shows that the new rank of the column space equals the old rank. That proves your result, but it may not help at all if you haven't covered the basics of linear transformations. Once you do (and I hope it will be part of the course you're taking) I think you'll find linear transformations - instead of direct matrix operations - usually give more insight into these kinds of results. === Subject: Re: row operations leave column rank untouched? posting-account=Cbgh4AoAAAAr0dt1RqLOClWCyUWii2fU Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > Can someone prove that row operations do not affect the column rank of > a matrix? I am reading linear algebra by Hefferson (open source) which has a > lemma and a proof, which I don't really grasp or get convinced by > (excerpt below, which you can ignore): Lemma 3.10 Row operations do not change the column rank. Proof. Restated, if A reduces to B then the column rank of B equals > the column rank of A. We will be done if we can show that row > operations do not aff ect linear re-lationships among columns (e.g., > if the fth column is twice the second plus the fourth before a row > operation then that relationship still holds afterwards), because the > column rank is just the size of the largest set of unrelated columns. > But this is exactly the fi rst theorem of this book: in a relationship > among columns, row operations leave unchanged the set of solutions > (c1; : : : ; cn). c1[a11, a21, ..., am1] + c2[a12, a22, ..., am2] + ... + cn[a1n, > a2n, ..., amn] = [0,0,...,0] (square brackets denote column vectors). QED Since the author even gives concrete examples, where do your problems occur? Consider a linear combination of the old columns that results in some vector. Now apply a row operation (swapping, non-zero scaling, adding, you name it) to your given columns. Consider the corresponding linear combination with the same coefficients but using the new columns. This produces another vector. You could have obtained this vector by applying the very same row operation to the first linear combination. Why? So when the old combination is the zero vector, what must the new combniationbe? And when the new combination is zero, what must the old one be? === Subject: Re: row operations leave column rank untouched? posting-account=LuOUUgoAAAAlOLgQa2LFVIdj_-W7dRT8 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > Since the author even gives concrete examples, wheredoyour problems > occur? Well, his example of not affecting linear relationships, i.e. that if some column is a linear comb. of some columns is preserved, I understand. But it could be that some column vectors that are linearly independent have become dependent by adding rows (obviously that is not true, but I don't see why). === Subject: Re: row operations leave column rank untouched? > Since the author even gives concrete examples, wheredoyour problems >> occur? Well, his example of not affecting linear relationships, i.e. that >if some column is a linear comb. of some columns is preserved, I >understand. But it could be that some column vectors that are linearly >independent have become dependent by adding rows (obviously that is >not true, but I don't see why). That's where the invertibility (as well as the linearity) of the row operations comes in. If f: R^n -> R^n is both linear and invertible, then there is a linear f^{-1}: R^n -> R^n such that f^{-1}(f(C)) = C for any column vector C. So, if scalars k_1, ..., k_r, and columns C_{i_1}, ..., C_{i_r}, are such that: k_1.f(C_{i_1}) + ... + k_r.f(C_{i_r}) = 0 then: 0 = f^{-1}(0) = f^{-1}(k_1.f(C_{i_1}) + ... + k_r.f(C_{i_r})) = k_1.C_{i_1} + ... + k_r.C_{i_r} by linearity, and by the defining property of the inverse f^{-1}. So, if C_{i_1}, ..., C_{i_r} are linearly independent, then so are f(C_{i_1}), ..., f(C_{i_r}). -- Angus Rodgers Contains mild peril === Subject: Re: row operations leave column rank untouched? posting-account=LuOUUgoAAAAlOLgQa2LFVIdj_-W7dRT8 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > That's where the invertibility (as well as the linearity) of therowoperationscomes in. arguments, because I probably need the background that is covered in the next chapter of that book (http://joshua.smcvt.edu/ linearalgebra/). === Subject: Re: row operations leave column rank untouched? posting-account=Cbgh4AoAAAAr0dt1RqLOClWCyUWii2fU Gecko/2008071719 Firefox/3.0.1,gzip(gfe),gzip(gfe) > That's where the invertibility (as well as the linearity) of therowoperationscomes in. arguments, because I probably need the background that is covered in > the next chapter of that book (http://joshua.smcvt.edu/ > linearalgebra/). You have already seen that row operations cannot increase the rank. Row operations can be inverted (swapping rows: swap them back; scale a row by a non-zeor factor: scale by the inverse factor; add a row to another: subtract the row). Hence you can obtain the original matrix back from the result by row operations - which might decreas but not increase the rank. Since in total the rank comes out where we started from, both of the might-be-decreases in fact aren't, i.e. the rank remains unaffected. === Subject: Re: row operations leave column rank untouched? >the next chapter of that book (http://joshua.smcvt.edu/linearalgebra/). Strange: the link is correct, but the server is unreachable. I'll wait. -- Angus Rodgers Contains mild peril === Subject: Re: row operations leave column rank untouched? [and Google Groups appears to have scrambled, somehow] > That's where the invertibility (as well as the linearity) of >> therowoperationscomes in. arguments, because I probably need the background that is covered in >the next chapter of that book (http://joshua.smcvt.edu/ >linearalgebra/). I thought that was a possibility. But at least I have shown how to explain the invariance of column rank under row operations in terms of the concepts of *linearity* and *invertibility* of mappings. These two concepts can be explained briefly as follows: A function f: A -> B, where A and B are any sets, is invertible iff [if and only if] there exists a function g: B -> A such that g(f(x)) = x for all x in A and f(g(y)) = y for all y in B; and in that case, g is called the inverse of f (also f is the inverse of g). A function f: R^n -> R^n is linear iff, for all vectors x and y in R^n, definition it follows (by mathematical induction) that if x_1, ..., x_r are vectors in R^n (i.e. n-tuples of real numbers), and k_1, ..., k_r are real numbers (the _ notation denotes a subscript, e.g. k_1 means a letter k with a subscript 1), then: f(k_1.x_1 + ... + k_r.x_r) = k_1.f(x_1) + ... + k_r.f(x_r) Finally, the column rank of an m x n matrix A with real number entries is the largest integer r such that there exist column vectors C_{i_1}, ..., C_{i_r} of A which are linearly independent. (Defined shortly.) (I'm sorry about the iterated subscript notation here! It just means columns i_1, ... i_r of A, when all the columns of A are indexed by 1, ..., n.) /Finally/ finally (!), vectors x_1, ..., x_r in R^n are *linearly in- dependent* iff, when k_1, ..., k_r are real numbers such that: k_1.x_1 + ... + k_r.x_r = 0 then k_1 = ... = k_r = 0. I /think/ that explains everything. It's just a matter of putting it all together (which may not be easy, if it's not familiar), although I haven't gone into every detail - e.g. the meaning of column rank 0; or the generalisation from R^n to real vector spaces (and then vector spaces over a field); or column rank as a special case of the concept of the dimension of a vector space. I'd also be interested to see if there is a clear way of proving the required result without using these concepts, in some form or other. -- Angus Rodgers Contains mild peril === Subject: Re: row operations leave column rank untouched? <95a194112qjjj0c5f9niaviot1spckkqgh@4ax.com> posting-account=LuOUUgoAAAAlOLgQa2LFVIdj_-W7dRT8 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > I thought that was a possibility. æBut at least I have shown how to > explain the invariance ofcolumnrankunder row operations in terms > of the concepts of *linearity* and *invertibility* of mappings. While walking home (and before reading your last reply) I actually understood it. We first prove that if some columns are a linearly dependent, they remain so after the row operations. That leaves the possibility that some previously linearly independent columns become dependent, and we don't directly prove that that can never happen. Instead we prove that any linearly dependent columns after some row operations must also be linearly dependent before the row operations (using the invertibility of row operations). Thus we have proved that the same linear relationships among columns always hold before and after any row operations. === Subject: Re: row operations leave column rank untouched? >> I thought that was a possibility. æBut at least I have shown how to >> explain the invariance ofcolumnrankunder row operations in terms >> of the concepts of *linearity* and *invertibility* of mappings. While walking home (and before reading your last reply) I actually >understood it. We first prove that if some columns are a linearly >dependent, they remain so after the row operations. That leaves the >possibility that some previously linearly independent columns become >dependent, and we don't directly prove that that can never happen. >Instead we prove that any linearly dependent columns after some row >operations must also be linearly dependent before the row operations >(using the invertibility of row operations). Thus we have proved that >the same linear relationships among columns always hold before and >after any row operations. Exactly. Or rather, almost exactly! Strictly speaking, no logically indirect proof is involved. As you rightly observe, the proof columns linearly dependent => f(columns) linearly dependent is direct; however, the proof columns linearly independent => f(columns) linearly independent is also direct. -- Angus Rodgers Contains mild peril === Subject: Re: row operations leave column rank untouched? >Can someone prove that row operations do not affect the column rank of >a matrix? >I am reading linear algebra by Hefferson (open source) which has a >lemma and a proof, which I don't really grasp or get convinced by >(excerpt below, which you can ignore): Lemma 3.10 Row operations do not change the column rank. Proof. Restated, if A reduces to B then the column rank of B equals >the column rank of A. We will be done if we can show that row >operations do not affect linear re-lationships among columns (e.g., >if the ffth column is twice the second plus the fourth before a row >operation then that relationship still holds afterwards), because the >column rank is just the size of the largest set of unrelated columns. >But this is exactly the fifrst theorem of this book: in a relationship >among columns, row operations leave unchanged the set of solutions >(c1; : : : ; cn). c1[a11, a21, ..., am1] + c2[a12, a22, ..., am2] + ... + cn[a1n, >a2n, ..., amn] = [0,0,...,0] (square brackets denote column vectors). QED I don't know this stuff off by heart, but if I remember right, row operations consist of either transposing two rows of a matrix or adding a scalar multiple of one row to another: is that correct? (Not quite, but it doesn't matter - see correction at end.) Consider the columns of the matrix as belonging to R^n. Then a row operation can be considered as the simultaneous application to all the columns of an invertible linear transformation R^n -> R^n (i.e. an automorphism of R^n). For instance, the transformation: (x_1, ..., x_i, ..., x_j, ..., x_n) |--> (x_1, ..., x_j, ..., x_i, ..., x_n) is linear, and is its own inverse. For any real number k, the transformation: (x_1, ..., x_i, ..., x_j, ..., x_n) |--> (x_1, ..., x_i, ..., (x_j + k*x_i), ..., x_n) is linear, and its inverse is the same, but with -k in place of k. If f: R^n -> R^n is any invertible linear transformation, then the truth or falsity of any relationship of linear dependence: k_1.C_1 + ... + k_n.C_n = 0 where C_1, ..., C_n are vectors in R^n (thought of as columns), and k_1, ..., k_n are scalars, is the same as that of the relationship: k_1.f(C_1) + ... + k_n.(C_n) = 0 Hence, the maximum number of linearly independent columns of a matrix is the same as the maximum number of linearly independent columns of any matrix obtained from it by elementary row operations [I forgot to include the adjective elementary in the list above], and therefore the same as that for any matrix obtained from it by any sequence of elementary row operations, i.e. by any row operation. I just checked in a book (to make sure I wasn't making a /complete/ fool of myself, and giving misleading information), and see that the list of elementary row operations also includes multiplication by a non-zero scalar. It is clear that this does not affect the argument, because multiplication R^n -> R^n by a scalar k =/= 0 is linear and invertible, with its inverse given by division by k. -- Angus Rodgers Contains mild peril === Subject: Re: row operations leave column rank untouched? > k_1.f(C_1) + ... + k_n.(C_n) = 0 Should be: k_1.f(C_1) + ... + k_n.f(C_n) = 0 of course. -- Angus Rodgers Contains mild peril === Subject: representing an integer with a positive definite ternary quadratic posting-account=KQBUxQoAAAAiNkukejXChgfz9-FHijT9 2.0.50727),gzip(gfe),gzip(gfe) I am interested in positive definite ternary quadratics with integer coefficients that represents an integer. I have found countless papers that talk about determining the existence of an integral solution or about determining the number of solutions but I have been unable to find any discussions of an efficient means to find an integer solution. Any guidance would be appreciated. David Stahl === Subject: Re: representing an integer with a positive definite ternary quadratic posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > I am interested in positive definite ternary quadratics with integer > coefficients that represents an integer. I have found countless > papers > that talk about determining the existence of an integral solution or > about determining the number of solutions but I have been unable to > find any discussions of an efficient means to find an integer > solution. æ Efficient? I assume you mean polynomial in the size of the discriminant? AFAIK, there aren't any. === Subject: Re: representing an integer with a positive definite ternary quadratic posting-account=KQBUxQoAAAAiNkukejXChgfz9-FHijT9 2.0.50727),gzip(gfe),gzip(gfe) Once you have an integer solution or several solutions is there a method for using them to generate additional integer solutions? David === Subject: Re: representing an integer with a positive definite ternary quadratic posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > Once you have an integer solution or several solutions is there a > method for using them to generate additional integer solutions? David Treat a solution (x,y) as an element of Q(sqrt(D)) where D is the discriminant. Now multiply by the fundamental unit of the field. === Subject: Re: representing an integer with a positive definite ternary quadratic > Once you have an integer solution or several solutions is there a > method for using them to generate additional integer solutions? > David Treat a solution (x,y) as an element of Q(sqrt(D)) where D is the > discriminant. > Now multiply by the fundamental unit of the field. The subject header says we're talking about *ternary* quadratics, so a solution would be (x, y, z), and the relevance of Q(sqrt D) is not clear to me. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: representing an integer with a positive definite ternary quadratic posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp SV1; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) spider-mtc-ta10.proxy.aol.com[400C700A] (Prism/1.2.1), HTTP/1.1 cache-mtc-ag12.proxy.aol.com[400C758C] (Traffic-Server/6.1.5 [uScM]) On Jul 30, 7:57?pm, Gerry Myerson Once you have an integer solution or several solutions is there a > method for using them to generate additional integer solutions? > David > Treat a solution (x,y) as an element of Q(sqrt(D)) where D is the > discriminant. > Now multiply by the fundamental unit of the field. The subject header says we're talking about *ternary* quadratics, > so a solution would be (x, y, z), and the relevance of Q(sqrt D) > is not clear to me. -- > Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email) Ah. I took ternary quadratic to mean ax^2 + bxy + cy^2; i.e. 3 terms. Mea culpa. === Subject: Re: Morphisms Distribution: world >Every time I set out to track down this term, I wind up back in >category theory, where I don't want to be. Does morphism, as opposed to some particular kind of xxx-morphism, >have any definite meaning outside a term of art of category theory? In _Topology_, by George McCarty, he uses the term morphism in reference to algebra. A morphism, in his usage, is a function from one group to another that preserves products. In other words: Let G, H be groups If, for all x,y in G, f(x)f(y) = f(xy), then f is a morphism -- Michael F. Stemper #include The name of the story is A Sound of Thunder. It was written by Ray Bradbury. You're welcome. === Subject: Re: Morphisms posting-account=mV9EXQoAAACmCMM9qg0N4eJlXyr2Z93U Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > Every time I set out to track down this term, I wind up back in > category theory, where I don't want to be. > Does morphism, as opposed to some particular kind of xxx-morphism, > have any definite meaning outside a term of art of category theory? No. æIsomorphism, homomorphism, homeomorphism, quotient map, order > isomorphism, order preserving are the expressions as related to > algebra, topology and order theory. === Subject: Re: help solving a textbook variational problem >This problem is from Introduction to the Calculus of Variations by >Hans Sagan (problem 1.7.2): >Show that the variational problem >J[y] = integral_0_to_1 (y(x)^2 + xy'(x))dx -> minimum, y(0) = 0, y(1) >= 1 >has no solution in C^1[0,1] Here's my attempt to solve it: >The space of competing functions S is given by all y in C^1[0,1] with >y(0) = 0 and y(1)=1 >The (linear) space of admissible variations H is all h in C^1[0,1], >with h(0) = 0 and h(1)=0 The Gateaux variation of the functional is given by >dJ[h] = integral_0_to_1 (2 * y(x) * h(x))dx + integral_0_to_1(x * >h'(x)) dx >Using integration by parts on the 2nd integral above, and using the >condition h(0) = 0, h(1) = 1, we get >dJ[h] = integral_0_to_1 (2 * y(x) * h(x))dx - integral_0_to_1(h(x))dx > = integral_0_to_1( (2*y(x) - 1)*h(x) ) dx >If the variational problem admits a solution y0, then it must >necessarily satisfy >dJ[h] = 0 for all h in H >Now as I understand it, I need to show that for any claimed minimiser >y0 in S, I can find an h in H such that dJ[h] is not equal to zero. >This is the point where I'm stuck (assuming I'm on the right track and >haven't committed a blunder so far). >I tried h(x) = y0(x) - x, but couldn't really get very far with it. Using integration by parts, we get that |1 2 | ( y + xy') dx | 0 |1 2 = 1 + | ( y - y ) dx | 0 |1 2 = 3/4 + | (y - 1/2) dx [1] | 0 Obviously, [1] is at least 3/4, but since y(0) = 0 and y(1) = 1, we cannot get [1] to be 3/4 for a continuous y. However, by defining { x/(2a) for x in [0,a] { y = { 1/2 for x in (a,1-a) { { 1-(1-x)/(2a) for x in [1-a,1] we can get [1] to be 3/4 + a/6. Thus, [1] cannot be 3/4, but we can find smooth y that make it as close to 3/4 as we want. Thus, there is no smooth y that minimizes [1]. Rob Johnson take out the trash before replying === Subject: Permutations, Inversions and largest element of an inversion table Does anybody have any reference to, or know a way to determine how many permutations of [n] have exactly i inversions and a largest element of the inversion table being m? For example, the permutation (3,1,4,2) has 3 inversions, its inversion table is (0,1,0,2), and the inversion table has maximum element 2....but how many permutations of [4]={1,2,3,4} have 3 inversions and largest element of the inversion table 2? By explicitely listing them, there are 4, but I am after the formula for the general case. Peter === Subject: Re: Permutations, Inversions and largest element of an inversion table posting-account=McZ3aQkAAADz6LV-boDe1LcriRhf3lj3 Gecko/2008070208 Firefox/2.0.0.9;MEGAUPLOAD 1.0,gzip(gfe),gzip(gfe) On Jul 30, 9:10æpm, peter rabinovitch > Does anybody have any reference to, or know a way to determine how many > permutations of [n] have exactly i inversions and a largest element of the > inversion table being m? For example, the permutation (3,1,4,2) has 3 inversions, its inversion table > is (0,1,0,2), and the inversion table has maximum element 2....but how many > permutations of [4]={1,2,3,4} have 3 inversions and largest element of the > inversion table 2? By explicitely listing æthem, there are 4, but I am after > the formula for the general case. Peter Euler numbers may be a help. kunzmilan === Subject: Re: 2 New Math Ideas (E=mcsquared)=(E=mccircled) and c=square root of -1 posting-account=SWr-zgoAAABXP_I1KRp8SBR28UDaox2f Gecko/20080625 Ubuntu/7.10 (gutsy) Firefox/2.0.0.15,gzip(gfe),gzip(gfe) > what it really amounts to is redoing the pythagrean theorem, > the 3D one, in terms of circles, and spheres. actually, > this is the origin of the theorem, > in Hipparchus's lunes construction (or, > so it is that I hypothesize, unless his, came later .-) > Hi this is Conrad Countess Sputnik you are right concerning the Pythagorean theorem. http://en.wikipedia.org/wiki/Pythagorean theorem But it goes deeper than that. The Pythagorean theorem says: The square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides. In one of my graphs a large circles is produced compare to the square whose 90 arc I used to produce it But if the amplitude were kept constant the wave would have to make two rotations in order to complete one wave cycle confined within that square space. You can extend the Pythagorean theorem to: the square of the large circle equals the sum of the squares of the two smaller circles But it goes further than that. We can also say that the circumference of the larger circle equals the sum of the circumferences of the two smaller circles without even squaring them. We can see this because the diameter of the large circle is twice that of the two smaller circles. If the (circumference equals diameter x pi) than the diameters of two smaller circles being half that of the larger, would be (ü + ü diameter of larger circle x pi), and is equal. And this is as it should be if the two smaller circles are just the larger circle folded in half analogous to the wave of an electron making two rotations in order to complete one wave cycle. No comment on the other stuff There are all kinds of new math coming from this Conrad Countess === Subject: Re: 2 New Math Ideas (E=mcsquared)=(E=mccircled) and c=square root of -1 posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 5.0),gzip(gfe),gzip(gfe) good observational, it applies to the perimeters of the figures on the sides of the trigons etc. the main thing is that it applies to any similar figures, whatsoever; your special case was built on a 45-degree right trigon (equiangular & equilateral). the *really* main thing is that you have to construct the circles, in any case, to actuallly construct the proof with compasses, so that Hipparchus' proof is the minimal effort. essentially, Einstein's proof, which is actually in Eculid, but not labelled per the pythag. theorem, and which would have been seen by him in the gymnasium, is the same as Hipparchus, only it is merely diagrammatical, without bothering with the constructive part of it. now, apply it to the spatial cases. === Subject: Re: 2 New Math Ideas (E=mcsquared)=(E=mccircled) and c=square root of -1 posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1,gzip(gfe),gzip(gfe) for instance, you could find a suitable section of the Mandelbrot set, to attach the 3 similar ones to the right trigon; I'm going to do that, just as soon as I can find the fractal compasses!... seriously, there's a common method to generate the M-set, using (overlapping?) circles to make the complement of the M-set, which gives a picture that looks, like the pointilistical one. but, all of this is somewhat informal, due to the FLOPs specification, which is IEEE-755, I think, > now, apply it to the spatial cases. thus: which E-hoax -- of, by or for?... I just found a textbook at the bookstore, which was a zenith in the Department Einsteinmania, the Musical Department; basically, a sort of Physics Lite by way of Thus Spake Herr Doktor- proffessor Albert; large book, but large print & plenty graphics & photo-ops.... or, you could also say, nadir, or just Bipolar Express; unscroll me! yeah, nettttiket; don't make me link to your googolplex, just to get an inkling of the scan of the UPC on your cybersuite -- I might never get out, again! > Erratum - The links do not work. These do. thus: there are classical experiments, if that only means, it was done in the 19th CCE (PBUThat***** .-)... um, what ever you guys were referring to, in your cut&paste VJ mixtape. anway, Haha, what floor was your office on?... eleven and above is certainly very safe, if the building doesn't fail monumentally; you mighty swell be surfing it; all is well that ends in the well, if you can swim & it's nondry. > I do not know of any experiment. thus: I had my 4th virtual lesson in surfing in two days, more or less, this one just watching the lone surferdood; I didn't wait for him to stand up, since he was clearly paddling-out in a minimax path to the correct wave. 4 axes would be a form of homogenous coordination, not entirely amenable to quaternions, AFAICT, for the point, which would minimally be a tetrasteron, and a sphere; how many points is that?... anyone work on the lunes demonstration of pythag.spatial? it's very tempting to just bum a board & go, but I'm retaining my ideal of surfcamp Maui, or some other island. or, we'll just make a stop on the bipolar express -- it's the IPY! === Subject: Cancel Re: A consideration concerning the diagonal argument of G. Cantor(was Q) -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor(was Q) P.S. I mean, eliminability certainly is ensured by this definition; > after all a simple search and replace algorithm might replace it. Card(XXX) = Card(YYY) |-> (XXX ~ YYY) Card(XXX) <= Card(YYY) |-> (XXX << YYY) > Description of the algorithm: ----------------------------- Since the (sub)string Card ONLY occurs in atomic s of the form Card() = Card() and/or Card() <= Card() (which is guaranteed by the very recursive definition of we adopted) we can replace any occurrence of the substring ) = Card( with ~ , and any occurrence of the substring ) <= Card( with << . After that replacements of substrings, the only occurrences of Card are those left in the substrings Card( that marked the beginning of those atomic formulas (mentioned above). Hence if we replace in a second step any occurrence of Card( simply with ( , the final result is ( ~ ) resp. ( << ), where originally we had Card() = Card() resp. Card() <= Card() (throughout in the text). The resulting s are in standard form; hence there's no question left concerning THEIR eliminability. Problem solved (at least in practice). B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor(was Q) >> P.S. I mean, eliminability certainly is ensured by this definition; >> after all a simple search and replace algorithm might suffice. >> Card(XXX) = Card(YYY) |-> (XXX ~ YYY) >> Card(XXX) <= Card(YYY) |-> (XXX << YYY) > Description of the algorithm: [...] > #!/usr/bin/perl @lines = ( Card(t) <= Card(f(x)), Card(t) = Card(s) -> Card(s) = Card(t), Card(P(k)) = Card(w+1), Card(P({x | xey & x finite})) = Card(y), Card({x e t | Card(x) = Card(z)}) <= Card({x e s | Card(x) = Card(z)}), ); foreach $wff (@lines) { print $wffn; find_and_replace($wff, ') = Card(', ' ~ '); find_and_replace($wff, ') <= Card(', ' << '); find_and_replace($wff, 'Card(', '('); print $wffnn; } sub find_and_replace { my ($wff, $find, $replace) = @_; $$wff =~ s|$find|$replace|g; } Output: Card(t) <= Card(f(x)) (t << f(x)) Card(t) = Card(s) -> Card(s) = Card(t) (t ~ s) -> (s ~ t) Card(P(k)) = Card(w+1) (P(k) ~ w+1) Card(P({x | xey & x finite})) = Card(y) (P({x | xey & x finite}) ~ y) Card({x e t | Card(x) = Card(z)}) <= Card({x e s | Card(x) = Card(z)}) ({x e t | (x ~ z)} << {x e s | (x ~ z)}) B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor(was Q) >> Iota is also definable from set abstraction: >> æ æ ixP(x) æ=df æU{y : {x : P(x)} = {y}} > Cool. >> Though in set theory (ZFC) we would have to relativize that notion. >> ix e A : P(x) =df U{y e A : {x e A : P(x)} = {y}} the x in A which is P (or short: the P, in A) Using the Fregean method [...] > When the set abstract is adopted as a primitive, the natural choice in ZFC clearly would be { e : }. In this case the axiom schema of separation might take the following form: AxAy(y e {z e x : P(z)} <-> y e x & P(y)). That's why I opted for the relativize notion of the i-Operator above. This way no complications are involved. The i-Operator is _directly_ defined in terms of the primitive set abstract. B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor(was Q) Definition of ------------------- ::= x, y, z, ... ::= 0 | | { | } ::= e | = ::= | ~ | ( & ) | ( v ) | ( -> ) | ( <-> ) | A | E [...] with set abstraction as primitive, you see that is > defined with [via ] and is defined with > , ... > Right. ... so there is a double induction involved. [...] simultaneous > recursion. > Right. B. P.S. Intuitively I'd argue the following way. Clearly this way (by the BNF from above) the s are defined which do not contain any occurrence of { (i.e. no set abstracts). With defined I mean (in this context) a recipe is given how to construct (build up) such a string of characters. But then all s are defined which contain such a (in a set abstract). Thus all s are defined which contain at most one occurrence of a {. But then all s are defined which contain such a (in a set abstract). And so on. Conclusion: for any n e IN the s containing at most n occurrences of { are defined. And that means all s we could possible be interested in. :-) Rigorously proving the unique readability of such s would nail the coffin shut. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor(was Q) Typos corrected: To sum up some of my recent posts. Here's a recursive definition (in BNF) of a for a simplified language of some set theory. (For simplicity I left out the definition of the set abstract. Hence no occurrence of simultaneous recursion.) ::= x, y, z, ... ::= 0 | | ...whatever... [ but not NOT Card() ! ] ::= e | = ::= & | v | -> | <-> ::= | - | ( ) | A | E | ( ~ ) | ( << ) | Card() = Card() | Card() <= Card() . In this approach Card() = Card() and Card() <= Card() are treated as certain atomic s (which have two parameters). [Actually, one might add them as additional clauses to the def. of instead to the def. of .] Elimination (of those expressions) then amounts to replacing a of the form Card(X) = Card(Y) resp. Card(X) <= Card(Y) , where X and Y are terms, with some other (incorporating X and Y), say (X ~ Y) resp. (X << Y). (The brackets may help to avoid problems with precedence.) This can be performed by a simple search and replace algorithm (using a little trick, I have to admit). Here's an implementation in the common programming language Perl: #!/usr/bin/perl @string = ( Card(t) <= Card(f(x)), Card(t) = Card(s) -> Card(s) = Card(t), Card(P(k)) = Card(w+1), Card(P({x | xey & x finite})) = Card(y), Card({x e t | Card(x) = Card(z)}) <= Card({x e s | Card(x) = Card(z)}), ); @string1 = @string; @string2 = @string; print Replacement variant 1:nn; foreach (@string1) { print $_n; s/) <= Card(/ << /g; s/) = Card(/ ~ /g; s/Card(/(/g; print $_ nn; } print Replacement variant 2:nn; foreach (@string2) { print $_n; s/) <= Card(/ >-> /g; s/) = Card(/ >->> /g; s/Card(/Ef(f: /g; print $_ nn; } Output: Replacement variant 1: Card(t) <= Card(f(x)) (t << f(x)) Card(t) = Card(s) -> Card(s) = Card(t) (t ~ s) -> (s ~ t) Card(P(k)) = Card(w+1) (P(k) ~ w+1) Card(P({x | xey & x finite})) = Card(y) (P({x | xey & x finite}) ~ y) Card({x e t | Card(x) = Card(z)}) <= Card({x e s | Card(x) = Card(z)}) ({x e t | (x ~ z)} << {x e s | (x ~ z)}) Replacement variant 2: Card(t) <= Card(f(x)) Ef(f: t >-> f(x)) Card(t) = Card(s) -> Card(s) = Card(t) Ef(f: t >->> s) -> Ef(f: s >->> t) Card(P(k)) = Card(w+1) Ef(f: P(k) >->> w+1) Card(P({x | xey & x finite})) = Card(y) Ef(f: P({x | xey & x finite}) >->> y) Card({x e t | Card(x) = Card(z)}) <= Card({x e s | Card(x) = Card(z)}) Ef(f: {x e t | Ef(f: x >->> z)} >-> {x e s | Ef(f: x >->> z)}) (I used the symbol f: A >-> B here to express that f is an injective function from A to B, and the symbol f: A >->> B to express that f is an injective and surjective (=bijective) function from A to B.) B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor(was Q) In this approach Card() = Card() > and > Card() <= Card() are treated as certain atomic s (which have two parameters). > [Actually, one might add them as additional clauses to the def. of > instead to the def. of .] Elimination (of those expressions) then amounts to replacing a resp. > Card(X) <= Card(Y) , where X and Y are s, with some other (incorporating X and Y), > say > (X ~ Y) > resp. > (X << Y). (The brackets may help to avoid problems with precedence.) This can be performed by a simple search and replace algorithm (using a > little trick, I have to admit). > The idea is extremely simple. Since the (sub)string Card ONLY occurs in atomic s of the form Card() = Card() and/or Card() <= Card() (which is guaranteed by the very recursive definition of we adopted) we can replace any occurrence of the substring ) = Card( with ~ , and any occurrence of the substring ) <= Card( with << . After that replacements of substrings, the only occurrences of Card are those left in the substrings Card( that marked the beginning of those atomic formulas (mentioned above). Hence if we replace in a second step any occurrence of Card( simply with ( , the final result is ( ~ ) resp. ( << ), where originally we had Card() = Card() resp. Card() <= Card() (throughout in the text). The resulting s are in standard form; hence there's no question left concerning THEIR eliminability. Problem solved. B. P.S. To make a long story short: Card() = Card() [ (Card() <= Card()) ] just means ~ [ ( << ) ]. This fact is reflected by the simple search and replace algorithm described above. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor(was Q) >> Huh??? > See, that's annoying and a bit insulting. > Oh, it's in NO WAY meant as an insult. It's just an expression of pure astonishment. (Some sort of AH!? and OH!?) B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor(was Q) posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) >> Huh??? > See, that's annoying and a bit insulting. Oh, it's in NO WAY meant as an insult. It's just an expression of pure > astonishment. (Some sort of AH!? and OH!?) You did it again! That is SO funny! You did exactly what I was complaining about in your very reply to my complaining about it! Did you actually MEAN to do that as comedy? I didn't say that Huh??? alone is annoying. What I said is that it's annoying when you write Huh???, and things like that, to one little rest of the paragraph, or next paragraph where I explain what I have in mind. And I even said that sometimes we do that; but in this case, it's not helpful where the subject is getting a bit tricky so that one may have to read further down the post to get the explanation. But then you did it in your very post here! MoeBlee === Subject: Re: A consideration concerning the diagonal argument of G. Cantor(was Q) > ... it's in NO WAY meant as an insult. It's just an expression of pure >> astonishment. (Some sort of AH!? and OH!?) > You did it again! [...] > *lol* :-) Keep up the good work, Moe! :-) B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor(was Q) >> If we would like to allow for set abstracts, we would have to change >> the following way: >> ::= 0 | | { | } | ...whatever... >> æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ [ but not NOT Card()! ] > Shouldn't you have recursive clauses: from ~ from () > Yes, thank you: an extended typo. In any case, with set abstraction as primitive, you see that 'wff' is > defined with 'term' and 'term' is defined with 'wff', so there is a > double induction involved. > Right. [...] But I don't know Perl, so I'm sorry that I am limited from > benefitting from those efforts of yours. > Well, I've learned already that I can't do it (elimination of the complexe expression) without a real parser. (But it's clear that it CAN be done with a parser.) And actually that's exactly what WE do, when reading (and interpreting) such a formula: parsing it. B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Graph Theory: Cutting a Graph into Two in an Artificial Chemistry As part of an ongoing Artificial Chemistry project, I want to be able to find all of the ways that a single molecule can split int two. I can represent the molecule as a connected (is a single component) graph. I think my problem boils down to finding all the ways of cutting my initial graph into two separate graphs, each of which is connected (is a single component) . Can anyone tell me of a simple algorithm that can do this. Better still, a reference to a software library / program that implements the algorithm would be ideal. Chris Gordon-Smith www.simsoup.info === Subject: Re: Graph Theory: Cutting a Graph into Two in an Artificial Chemistry To help clarify your question, what do you think the answer should in each of these cases: 1. a benzene molecule 2. Ethane 3. Ethene 4. Acetylene 5. Oxygen 6. Water 7. Hydrogen peroxide It's unclear what you mean by cut - there is more than one definition, and for each definition, someone thinks it's obviously the right one. === Subject: Re: Graph Theory: Cutting a Graph into Two in an Artificial Chemistry > To help clarify your question, what do you think > the answer should in each of these cases: 1. a benzene molecule > 2. Ethane > 3. Ethene > 4. Acetylene > 5. Oxygen > 6. Water > 7. Hydrogen peroxide It's unclear what you mean by cut - there is more > than one definition, and for each definition, someone > thinks it's obviously the right one. Let me put the question a different way. Here is a brute force way to find what I am looking for:- 1) I start with a graph that has a single connected component (such that any node can be reached from any other node by traversing a series of edges) 2) I then divide the graph's nodes into two mutually exclusive groups and remove all of the edges between nodes in different groups, leaving the other edges in place. If I do this and the result is exactly two connected components, then I count that as a valid way that my original graph (molecule) could split. If the result is more than two components, then I discard the result as invalid. I would count a single node on its own as a connected component. 3) I repeat (2) until I have tried all of the possible ways of dividing the nodes of the original graph into two mutually exclusive groups 4) The set of all 'valid' splits from (2) is the answer I want. Is there an efficient way to get this set of 'valid' splits? Chris Gordon-Smith www.simsoup.info === Subject: Re: x = [x] some details posting-account=Cbgh4AoAAAAr0dt1RqLOClWCyUWii2fU Gecko/2008071719 Firefox/3.0.1,gzip(gfe),gzip(gfe) > > some details > x = [x] > a,b,c = [a,b,c] > [a,[b,c]] =/= [a,b,c] > [a,[]] = [a] = a > [[]] = [] > x U [] = x > x U [x] = x > a U b = a,b = [a,b] > Keen how you pull these details out of your > ass. > æLet's try them out! > I'm going to look at two of them in detail, > æ æ a U b = a,b = [a,b] æ æ æ æ æ æ (1) and > æ æ [a,[b,c]] =/= [a,b,c] æ æ æ æ æ (2). > Now, according to (1), we have b,c = [b,c]. > æThus, >> by > substitution, > æ æ æ[a,b,c] = [a,[b,c]]. > But according to (2), that's false. > Weird! >>yes , its a bit weird. >>the reason is dont support substitution in > general. >> If you don't support substitution you're very >> confused. Substitution means this: If A = B then >> anything that's true of A is true of B. That's >> not something that you're free to support >> or not - it's a fact . If A = B then A and B are >> the same thing - not supporting substitution >> is saying that you can have A = B, A even and >> B not even, which says that A is both even and >> not even. >>which is similar to my arguments against >> aleph aleph 1. >>by parody analogue >>we know sqrt(2) and 2 exist and there is a > function >> relating them. >>thus by substitution aleph aleph sqrt(2) exists > if >> aleph aleph 2 exists. >> This is no analog at all. Substitution says that > if A >> = B and >> P(A) holds then P(B) holds. In your silly example >> there >> is no A = B in sight. >> The things you've been saying about sets are > simply >> inconsistent. It's very easy to show that they're >> inconsistent. That's not going to change. Each >> time someone points out an inconsistency and >> you come up with some strange reply you just >> look stupider than the last time. >>tommy1729 > -- > At the Microsoft-sponsored cocktail reception > in >> the > Galaxy Ballroom > that evening, Robert Dees urges us 'to network > on > behalf of the people > of Iraq,' > -- Naomi Klein reports on Microsoft's efforts > to > to further democracy. >> David C. Ullrich >> Understanding Godel isn't about following his > formal >> proof. >> That would make a mockery of everything Godel was > up >> to. >> (John Jones, My talk about Godel to the > post-grads. >> in sci.logic.) >right , but what about that sustitution proof of >aleph 0 exists and aleph 1 exists >thus if aleph aleph 0 exists , by sustitution > aleph 0 -> aleph 1 -> aleph aleph 1 exists... > That's not a proof, it's nonsense. of course its nonsense !! that the point moron ! this was the answer given to me as a proof that aleph aleph 1 must exist because aleph 1 exists ! that its nonsense and bogus is exactly my point ! > I don't even see the argument that should lead to nonsense since I am used to index aleph's with ordinals and not with cardinals. Of course when viewing cardinals as the samllest ordnals of the correct size (i.e. under the assumption of AC) this makes sense again. But then the existense of an n'th aleph (i.e. of aleph n) follows indeed immediately for any ordinal n (or from the existenece of n if you prefer). If n is any ordinal >0 and we assume that for each ordinal k |Y| >= aleph k for all k aleph aleph 1 exists... Yes, in ZFC there is a cardinal number aleph (aleph 1). Meanwhile, would you please answer the question in my post earlier in this thread? MoeBlee === Subject: Re: x = [x] some details > some details x = [x] a,b,c = [a,b,c] [a,[b,c]] =/= [a,b,c] [a,[]] = [a] = a [[]] = [] x U [] = x x U [x] = x a U b = a,b = [a,b] Keen how you pull these details out of your ass. Let's try them out! I'm going to look at two of them in detail, a U b = a,b = [a,b] (1) and [a,[b,c]] =/= [a,b,c] (2). Now, according to (1), we have b,c = [b,c]. Thus, by substitution, [a,b,c] = [a,[b,c]]. But according to (2), that's false. Weird! -- At the Microsoft-sponsored cocktail reception in the Galaxy Ballroom that evening, Robert Dees urges us 'to network on behalf of the people of Iraq,' -- Naomi Klein reports on Microsoft's efforts to further democracy. === Subject: Re: x = [x] some details posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > we know sqrt(2) and 2 exist and there is a function relating them. thus by substitution aleph aleph sqrt(2) exists if aleph aleph 2 exists. And that is not a problem if we are using the Fregean method for improperly referring terms. MoeBlee === Subject: Re: x = [x] some details <874p697aad.fsf@phiwumbda.org> posting-account=oTDIagkAAACTxHurtPutBWvNQS8ZCNO9 Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > some details > x = [x] > a,b,c = [a,b,c] > [a,[b,c]] =/= [a,b,c] > [a,[]] = [a] = a > [[]] = [] > x U [] = x > x U [x] = x > a U b = a,b = [a,b] Keen how you pull these details out of your ass. Let's try them out! I'm going to look at two of them in detail, a U b = a,b = [a,b] (1) and > [a,[b,c]] =/= [a,b,c] (2). Now, according to (1), we have b,c = [b,c]. Thus, by substitution, [a,b,c] = [a,[b,c]]. But according to (2), that's false. Weird! > Man: Doctor, when I move my arm like this, it hurts. Doctor: Well, don't move your arm like that then. === Subject: Re: x = [x] some details posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > some details x = [x] a,b,c = [a,b,c] [a,[b,c]] =/= [a,b,c] [a,[]] = [a] = a [[]] = [] x U [] = x x U [x] = x a U b = a,b = [a,b] Those are axioms? Or sample theorems (if so, what is the exact definition of '[]' or if primitive, what are the axioms for it?)? MoeBlee === Subject: Re: OT: Probability Problem posting-account=B_ql5woAAABEePt1fDMNH7lHfjEScu4Z AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.1 Safari/525.18,gzip(gfe),gzip(gfe) > I know that I usually disparage off-topic posts (especially political > ones), but I just can't resist exposing the mathematically ignorant > members of this forum. PROBLEM: > A woman tells you (truthfully) that she has only 2 children. æShe also > tells you (truthfully) that at least one of her children is a boy. æ Given this information, what is the probability that both of this > woman's children are boys? World Series of Poker, No Limit Holdem, main event, final table You are now playing heads up, against Monty Hall. You: K x board: A A K K K pot: $10000 While you think, Monty shows you an ace. i) You have $10,000,000, he has you covered. Do you bet all in? ii) He has $10,000,000, you have him covered. Do you put him all in? Mark === Subject: Re: OT: Probability Problem > I know that I usually disparage off-topic posts (especially political > ones), but I just can't resist exposing the mathematically ignorant > members of this forum. > PROBLEM: > A woman tells you (truthfully) that she has only 2 children. æShe also > tells you (truthfully) that at least one of her children is a boy. æ > Given this information, what is the probability that both of this > woman's children are boys? 1/3 World Series of Poker, No Limit Holdem, > main event, final table > You are now playing heads up, against Monty Hall. You: K x > board: A A K K K > pot: $10000 While you think, Monty shows you an ace. i) You have $10,000,000, he has > you covered. Do you bet all in? ii) He has $10,000,000, you have > him covered. Do you put him all in? > I do not even know enough about poker to understand what is supposed to happen next or what my choices are. For instance, what doesheads up mean? Mark Bill === Subject: Re: OT: Probability Problem posting-account=B_ql5woAAABEePt1fDMNH7lHfjEScu4Z AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1,gzip(gfe),gzip(gfe) > PROBLEM: > A woman tells you (truthfully) that she has only 2 children. æShe also > tells you (truthfully) that at least one of her children is a boy. æ > Given this information, what is the probability that both of this > woman's children are boys? 1/3 > World Series of Poker, No Limit Holdem, > main event, final table > You are now playing heads up, against Monty Hall. > You: æK x > board: æA A K K K > pot: æ$10000 > While you think, Monty shows you an ace. > i) æYou have $10,000,000, he has > æ æ you covered. æDo you bet all in? > ii) æHe has $10,000,000, you have > æ æ æhim covered. æDo you put him all in? I do not even know enough about poker to understand > what is supposed to happen next or what my choices are. For instance, > what does heads up mean? one on one Anyhow, I screwed the pooch with these numbers. As stated, it's ridiculous. Try the same card situation: pot: $1000 your stack: $60000 opponent's stack: $100000 Again, Monty flashes an ace. Do you bet all in? Mark === Subject: Re: OT: Probability Problem <... > You: K x > board: A A K K K > pot: $10000 <... one on one Anyhow, I screwed the pooch with these numbers. > As stated, it's ridiculous. Try the same card situation: > pot: $1000 > your stack: $60000 > opponent's stack: $100000 Again, Monty flashes an ace. Do you bet all in? Not just no, but no. I only get called if I'm beat. Jim === Subject: Infinite fewunit rings have infinitely many prime ideals (Euclid bis) Euclid's classic proof that there are infinitely many primes has various ring-theoretic generalizations, as I've mentioned in passing here a few times in prior posts, e.g. [1]. Recently in another forum [2], I was coaxed into writing out fully one such proof that I only hinted at before. I present the proof below in a form comprehensible to a first-year algebra student. IMO, it is one of the prettiest little proofs in basic algebra. Below, generalizing Euclid's classic argument, is a proof that an infinite ring has infinitely many maximal (so prime) ideals if it has fewer units than elements (i.e. smaller cardinality). The key idea is that Euclid's construction may be extended from elements to ideals, i.e. given maximal ideals P1,...,Pk then a simple pigeonhole argument employing CRT (Chinese remainder) implies that 1 + P1...Pk contains a nonunit, which lies in some max ideal, necessarily comaximal (so distinct) from the others. -------------------------------------------------------------- THEOREM An infinite ring R has infinitely many maximal ideals if it has fewer units U = U(R) than elements, i.e. #U < #R PROOF R has a max ideal P1, since nonunit 0 lies in some max. Inductively, let P1,...,Pk be max ideals in R, with product J Case 1: 1+J !< U. Thus 1+J contains some nonunit p, lying in a max ideal P. P != Pi via P + Pi = 1 via p in P, p-1 in Pi Case 2: 1+J < U is absurd: R/J = R1 +...+ Rk, Ri = R/Pi, by CRT Notice that #U(R/J) <= #U via uv in 1+J < U => u in U So #U(Ri) <= #U(R/J) <= #U via u -> (1,1,..u..1,1) is 1-1 Ri field => #R > #U+1 >= #Ri, and #J <= #U < #R via 1+J < U Hence #R = #(R/J) #J = #R1...#Rk #J yields a contradiction: the infinite #R is a finite product of smaller cardinals. QED --------------------------------------------------------------- The only part of the proof that might be mysterious to a first-year algebra student is the relationship between the units in R and R/J. This is better viewed in terms of the Jacobson radical as follows: LEMMA TFAE in ring R with units U, ideals I,J, Jacobson radical J(R) 1) J < J(R), i.e. J lies in every max ideal of R 2) 1+J < U, i.e. 1 + j is a unit for every j in J 3) I<1 => I+J<1, i.e. proper ideals survive in R/J This implies that all the nonunits in R survive as nonunits in R/J, so the only units in R/J are those that are images of units in R. I leave the proof of the lemma as a short and elementary exercise. I still recall the pleasure of discovering this and other related proofs almost 3 decades ago while reading Kaplansky's book Commutative Rings as an MIT undergrad. There Kaplansky presents a simpler integral domain version as exercise 8 in Section 1-1, namely (This exercise is offered as a modernization of Euclid's theorem on the infinitude of primes.) Prove that an infinite integral domain with with a finite number of units has an infinite number of maximal ideals. I highly recommend Kap's classic textbook to everyone interested in mastering commutative ring theory. In fact I highly recommend everything by Kaplansky - it is almost always very insightful and elegant. Learn from the masters! For more about Kaplansky see mathematicians (Bass, Eisenbud, Kadison, Lam, Rotman, Swan, etc). I liked the algebraic way of looking at things. I'm additionally fascinated when the algebraic method is applied to infinite objects. --Irving Kaplansky --Bill Dubuque [0] Irving Kaplansky 1917-2006. Hyman Bass and T.Y. Lam. http://www.ams.org/notices/200711/tx071101477p.pdf Beware: cut'n'paste error in above: instead of nilradical, please read pseudo-radical = intersection of all _nonzero_ prime ideals. [2] http://at.yorku.ca/cgi-bin/bbqa?forum=ask_an_algebraist;task=show_msg;msg=20 9 2 Note: in 2009 or later use this link: http://at.yorku.ca/cgi-bin/bbqa?forum=ask_an_algebraist_2008;task=show_msg;m sg=2092 === Subject: Re: JSH's next breakthrough <8p51849c2ftioo2rg36m9o51jm4nv18fk9@4ax.com> posting-account=3WPJYgoAAAA55VjhzK9i07RN8h8u8eEs MathPlayer 2.10b; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) A view which roughly mirrors my own. He is likely an intelligent person, > at least in an academic sense (cue joke on an inverse relationship > between IQ and common sense), certainly smarter than many people here > is one which many people share. > You're confusing two very different levels of reaction. Across the board, most people react negatively to criticism, especially so when it comes from a group of your peers. Even though a person may have enough presence of mind, sophistication, and maturity not to give an overt sign that the criticism affects them, it does. Now this part, a mentally healthy person *would* have in common with James. But this is where the similarity stops, and a much larger distinction sets in. A mentally healthy person understands the Taoist saying that wisdom is what one gets when the pain is gone, and they react in a positive way to the criticism and grow from it. A person who is not mentally healthy, will harbor a grudge and gain hatred against those who made the criticism. However, most of them still have enough on the ball to realize that their reaction is *wrong* and so they won't act out publicly. However some people get to the point where their mental health has so deteriorated that they lack the normal ability most people have to see that their reaction is wrong. This state of mind is so warped that no matter how rationally the criticism is made or how many times they receive this criticism from others, they still persist in believeing they are right, the others are wrong, and the others are out to get them. This is James. > The problem, though, is the grandstanding. My general impression is > that, if you were to strip all that away, he would be a person with whom > you could share a very pleasant discussion over, say, coffee. This is a > rather unique characteristic among the many who have become targets of > ridicule in newsgroups. > I don't know how one could have a pleasant conversation with someone who is totally closed minded and thinks they are always right. Not my idea of fun, but to each their own I guess. M === Subject: Re: JSH's next breakthrough <8p51849c2ftioo2rg36m9o51jm4nv18fk9@4ax.com> posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) >> Make certain not to miss any. When you're done, shouldn't take more >> than a few months, let us know whether your opiion has changed. I've read most of his posts for the past year. I've not studied much in > terms of factoring, but I have unassuaged doubts with his algorithm, and > I'm not convinced that the basic idea is fruitful. > I don't laugh at him as a person as I think that is wrong and 2 > wrongs don't make a right, however I do sometimes laugh at his silly > ideas, esp. when they're proven to be bunk. Actually, it's not so > much the ideas either æ(wrong ideas aren't so often amusing to me, > they're just wrong), but all the grandstanding and stuff that he puts > on top of them, claiming to have a REVOLUTIONARY new whatever and > yet he has nothing at all but a pile of garbage. And it just sounds > funny and comedic. A view which roughly mirrors my own. He is likely an intelligent person, > at least in an academic sense (cue joke on an inverse relationship > between IQ and common sense), certainly smarter than many people here > is one which many people share. The problem, though, is the grandstanding. My general impression is > that, if you were to strip all that away, he would be a person with whom > you could share a very pleasant discussion over, say, coffee. This is a > rather unique characteristic among the many who have become targets of > ridicule in newsgroups. > Hmm. > Interesting general observation: It seems when one persion does wrong > (here, James Harris, and the wrong is all this grandstanding, > arrogance and egotism over these crap ideas) he incites others to > wrong too, and a vicious circle is created. Indeed. I have pontificated a bit on this idea in c.l.j.p, but I urge > you /not/ to respond there, since it is a topic well beyond OT. Alright, I won't. But glad to hear that you agree with this. === Subject: Re: JSH's next breakthrough <8p51849c2ftioo2rg36m9o51jm4nv18fk9@4ax.com> posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > Those dazzled by his breakthroughs in factoring and FLT who are eager to > see what his next breakthrough will be might find > comp.lang.java.programmer interesting. æJSH has started posting there > about his new project: solving the traveling salesman problem. >>I am not an expert, and I certainly don't think that he should be an >>object so degraded that one can only laugh at him. >> Make certain not to miss any. When you're done, shouldn't >> take more than a few months, let us know whether your >> opiion has changed. >I don't laugh at him as a person as I think that is wrong and 2 wrongs >don't make a right, however I do sometimes laugh at his silly ideas, >esp. when they're proven to be bunk. Actually, it's not so much the >ideas >either æ(wrong ideas aren't so often amusing to me, they're just >wrong), >but all the grandstanding and stuff that he puts on top of them, >claiming >to have a REVOLUTIONARY new whatever and yet he has nothing at >all but a pile of garbage. And it just sounds funny and comedic. >Although I think even laughing *at him* is probably the mildest thing >that I've >seen done here -- some people here get very crude and use sad, sad >language >that makes me pine for the state of our world. Interesting general >observation: >It seems when one persion does wrong (here, James Harris, and the >wrong is >all this grandstanding, arrogance and egotism over these crap ideas) >he incites >others to wrong too, and a vicious circle is created. Indeed, it seems >one's >own actions really do shape the world one lives in... This is not just >a bunch of >hooey, it is provable fact, and the proof is right here. >I'm wondering: when you (in general, i.e. this group) tell James to go >away do >you really mean it, and if so why, considering you also seem so >entertained by >his arrogance, dumb ideas, etc.? this group doesn't do anything - various individuals in the > group do. For my own part, youi're never seen me tell him > to go away. > Oh, so you do like the entertainment provided by his cranky stuff, then? === Subject: Re: JSH's next breakthrough <8p51849c2ftioo2rg36m9o51jm4nv18fk9@4ax.com> posting-account=aLpfCwoAAACh4BOs3HOlQBCoxUpEgyxc Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > [...] > this group doesn't do anything - various individuals in the > group do. For my own part, youi're never seen me tell him > to go away. Oh, so you do like the entertainment provided by his cranky > stuff, then? Can't speak for David, but I do. === Subject: Re: JSH's next breakthrough <8p51849c2ftioo2rg36m9o51jm4nv18fk9@4ax.com> posting-account=mgs1FwoAAABD3j5T_RLZ06yrgt2dghDu Gecko/20050915,gzip(gfe),gzip(gfe) > Oh, so you do like the entertainment provided by his cranky > stuff, then? Can't speak for David, but I do. So do I. === Subject: Re: JSH's next breakthrough posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > Those dazzled by his breakthroughs in factoring and FLT who are eager to > see what his next breakthrough will be might find > comp.lang.java.programmer interesting. JSH has started posting there > about his new project: solving the traveling salesman problem. > I am not an expert, and I certainly don't think that he should be an > object so degraded that one can only laugh at him. > In any case, my personal evaluation is that > a) He is looking for P = NP. > b) He has discovered (or will shortly) a version of bidirectional search > for TSP that he is going to try to tweak to get P = NP (which should be > fruitless; you can read my full response to see why). > c) He will, alas, not find that P = NP. I have some experience, maybe > more than he does, on the area; I believe P = NP for various personal > reasons, but I also don't believe I or anyone else will solve it for at > least 50 years. > In short, the same old: going down fruitless paths for research in an > area where existing results are good enough for general use. > Actually, Jimmy is probably better off on > a fruitless path (see my explanation of the > Traveling Slaesman Problem to Hendrik Boom). > Why? What would be so bad about real breakthoughs, anyway? > That was a joke. If he finds no fruit he won't have > to shove them up his ass. OTOH, if he tackles a > watermelon-sized problem like the Traveling Salesman, > he's going to end up with quite a grimace on his face. > Why, if he did find something real, would he have to > shove it up his !!! as you so crudely put it? Jimmy has found plenty of real things, like > a prime counting algorithm. The joke is not > about finding them, it's what you do with them > afterwards. > And so what does he do with them then? ANd how does it make it all useless? (unless the Real things are not actually better than what already exists -- e.g. surrogate factoring being just warmed-over Fermat's method or something (I think that was one thing I heard about it)) > Jimmy's stuff either originates in his ass or > eventually finds a home there. > As soon as I read he was going after TTSP, I literally > thought: Jimmy's out picking watermelons. > Again. === Subject: Re: JSH's next breakthrough posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 CLR 1.1.4322; .NET CLR 2.0.50727; InfoPath.1),gzip(gfe),gzip(gfe) > Those dazzled by his breakthroughs in factoring and FLT who are eager to > see what his next breakthrough will be might find > comp.lang.java.programmer interesting. JSH has started posting there > about his new project: solving the traveling salesman problem. > I am not an expert, and I certainly don't think that he should be an > object so degraded that one can only laugh at him. > In any case, my personal evaluation is that > a) He is looking for P = NP. > b) He has discovered (or will shortly) a version of bidirectional search > for TSP that he is going to try to tweak to get P = NP (which should be > fruitless; you can read my full response to see why). > c) He will, alas, not find that P = NP. I have some experience, maybe > more than he does, on the area; I believe P = NP for various personal > reasons, but I also don't believe I or anyone else will solve it for at > least 50 years. > In short, the same old: going down fruitless paths for research in an > area where existing results are good enough for general use. > Actually, Jimmy is probably better off on > a fruitless path (see my explanation of the > Traveling Slaesman Problem to Hendrik Boom). > Why? What would be so bad about real breakthoughs, anyway? > That was a joke. If he finds no fruit he won't have > to shove them up his ass. OTOH, if he tackles a > watermelon-sized problem like the Traveling Salesman, > he's going to end up with quite a grimace on his face. > Why, if he did find something real, would he have to > shove it up his !!! as you so crudely put it? > Jimmy has found plenty of real things, like > a prime counting algorithm. The joke is not > about finding them, it's what you do with them > afterwards. And so what does he do with them then? ANd how does it make it > all useless? (unless the Real things are not actually better > than what already exists Comes the dawn. > -- e.g. surrogate factoring being just > warmed-over Fermat's method or something (I think that was one > thing I heard about it)) > Jimmy's stuff either originates in his ass or > eventually finds a home there. > As soon as I read he was going after TTSP, I literally > thought: Jimmy's out picking watermelons. > Again.- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - === Subject: Re: JSH's next breakthrough > Comes the dawn. I had too much to dream last night, too much to dream ... === Subject: =?GB2312?B?TFaw/LD8venJ3A==?= posting-account=v09E-goAAABDos-SJFKBfmc3r46W3xy2 QQDownload 1.7; Alexa Toolbar; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) === Subject: [experiment] Make math materials better & win some money posting-account=tE1HvQoAAACsuAPkygmt0iMws7J2thQh rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) Do you have an interest in mathematics education? Do you support open access and reuse of educational materials? Would you like a gift certificate to Amazon? Volunteers have made Wikipedia a great encyclopedia by creating and materials. This research is to figure out how the Wikipedia model could work for math teaching materials. You will try to improve worked examples that other volunteers have written to provide instruction in understanding and applying the Pythagorean Theorem. A worked example poses a math problem and then shows detailed steps of how to solve it. You will take worked example problems people like you have already contributed and try to make them better. This takes about 10 minutes each. In addition to helping create better educational materials, you can also win up to $100 in gift certificates to Amazon.com. For each worked example you evaluate and improve, you will be entered into a lottery to win an Amazon gift certificate. High quality contributions triple your odds of winning. Go to this URL for the full description or to get started: http://education.hciresearch.org/pythagorean/improvement/ cheers, Turadg === Subject: Make$800,000 from $6!!!. Real...thorough directions posting-account=hw6L2goAAADsIESbt8UCJaHEA2tRa3K7 2.0.50727),gzip(gfe),gzip(gfe) HERES HOW, and for all you naysayers, just give us a chance please. My family could really use this money now, so even if it doesn't work or is stupid in your minds, just let it pass, and for everyone else read on, you won't be dissapointed! You may have seen or heard about this project on programs like 20/20 and Oprah, or you may have read about it in the Wall Street Journal. Here is how to make Thousands upon Thousands of Dollars online with little work! This program remains successful because of the honesty and integrity of the participants. Remember, all of this is ABSOLUTELY LEGAL! If you have any doubts, please refer to le 18 Sec.1302 & 1241 of the United States Postal laws. Follow these directions EXACTLY, and $800,000or more can be yours in 4 to 6 weeks. STEP 1: Copy this entire text to a Word or Notepad Document STEP 2: Take a few minutes to join PayPal Business or Premier: Remember to verify your account. STEP 2(a): 1) Once you have a PayPal account running, use PayPal to post $1 to EACH of the 6 Email Addresses below Select SEND MONEY. In the Category field select: Service (Keeping it legal) In the subject field type: E-BOOK, In the message field type: THANK YOU VERY MUCH FOR THE INTERESTING E- BOOK. Click Send. Repeat these steps for each of the 6 email addresses. that's it! (By sending the $1.00 payment to each address, you are implementing the compounding POWER of the system. You will reap what you sow! ) Honesty and Integrity = Profitability. Here is the current e-mail list: (1) mikaboy4269@gmail.com (2) hawaiinshaveice@gmail.com (3) demnoworrywe23@yahoo.com (4) mountmutumbo@gmail.com (5) alfalfaboy42@aol.com (6) brewcrew4you@yahoo.com ***Note: you need to pay the 1 dollar to each of the above people, otherwise you will break the chain and unfortunately YOU will not receive anything. As mentioned before, please be honest or you will not earn a thing. STEP 3 1) Take the #1 Email Address off the list, 2) Move the other Email Addresses up (6 becomes 5, 5 becomes 4, etc.) 3) and add Your Email Address as number 6 on the list. STEP 4: thousands of groups). 2) And email your message to as many people you can. Remember, the more you post and email the more money you make! This is perfectly legal! I've began to see money roll in before I even hit 100 postUse Netscape, Internet Explorer, Firefox, Safari, or whatever your internet browser is to search for various news groups, on-line forums, message boards, bulletin boards, chat sites, discussions, discussion groups, on-line communities, etc. For example? in a subject like 'MILLIONAIRE MESSAGE BOARD',MONEY MAKING DISCUSSIONS', 'MONEY MAKING FORUMS', or 'BUSINESS MESSAGE BOARD', etc. All you have to do is jump to different newsgroups and post away. After you get the hang of it, it will take about 30 seconds for each newsgroup. It is recommended you post a minimum of 200! Heres a scenario to show you how this really works. - When you post 200 letters, it is estimated that at least 15 people will respond and send you $1 ($15). - Those 15 will post 200 letters each and 225 will send $1 ($225). - Those 225 will post 200 letters each and 3,375 people will send you $1 ($3,375). - Those 3,375 people will post 200 letters each and 50,625 people will send you $1 (50,625). - Those 50,625 will post 200 letters each and 749,375 people will send you $1 (749,375). - At this point your name drops off the list, but so far, you have received $813,615.00. REMEMBER, THE MORE NEWSGROUPS YOU POST IN, THE MORE MONEY YOU WILL MAKE!!!!GOOD LUCK!!!!!!!!! === Subject: Make$800,000 from $6!!!. Real...thorough directions posting-account=hw6L2goAAADsIESbt8UCJaHEA2tRa3K7 2.0.50727),gzip(gfe),gzip(gfe) HERES HOW, and for all you naysayers, just give us a chance please. My family could really use this money now, so even if it doesn't work or is stupid in your minds, just let it pass, and for everyone else read on, you won't be dissapointed! You may have seen or heard about this project on programs like 20/20 and Oprah, or you may have read about it in the Wall Street Journal. Here is how to make Thousands upon Thousands of Dollars online with little work! This program remains successful because of the honesty and integrity of the participants. Remember, all of this is ABSOLUTELY LEGAL! If you have any doubts, please refer to le 18 Sec.1302 & 1241 of the United States Postal laws. Follow these directions EXACTLY, and $800,000or more can be yours in 4 to 6 weeks. STEP 1: Copy this entire text to a Word or Notepad Document STEP 2: Take a few minutes to join PayPal Business or Premier: Remember to verify your account. STEP 2(a): 1) Once you have a PayPal account running, use PayPal to post $1 to EACH of the 6 Email Addresses below Select SEND MONEY. In the Category field select: Service (Keeping it legal) In the subject field type: E-BOOK, In the message field type: THANK YOU VERY MUCH FOR THE INTERESTING E- BOOK. Click Send. Repeat these steps for each of the 6 email addresses. that's it! (By sending the $1.00 payment to each address, you are implementing the compounding POWER of the system. You will reap what you sow! ) Honesty and Integrity = Profitability. Here is the current e-mail list: (1) mikaboy4269@gmail.com (2) hawaiinshaveice@gmail.com (3) demnoworrywe23@yahoo.com (4) mountmutumbo@gmail.com (5) alfalfaboy42@aol.com (6) brewcrew4you@yahoo.com ***Note: you need to pay the 1 dollar to each of the above people, otherwise you will break the chain and unfortunately YOU will not receive anything. As mentioned before, please be honest or you will not earn a thing. STEP 3 1) Take the #1 Email Address off the list, 2) Move the other Email Addresses up (6 becomes 5, 5 becomes 4, etc.) 3) and add Your Email Address as number 6 on the list. STEP 4: thousands of groups). 2) And email your message to as many people you can. Remember, the more you post and email the more money you make! This is perfectly legal! I've began to see money roll in before I even hit 100 postUse Netscape, Internet Explorer, Firefox, Safari, or whatever your internet browser is to search for various news groups, on-line forums, message boards, bulletin boards, chat sites, discussions, discussion groups, on-line communities, etc. For example? in a subject like 'MILLIONAIRE MESSAGE BOARD',MONEY MAKING DISCUSSIONS', 'MONEY MAKING FORUMS', or 'BUSINESS MESSAGE BOARD', etc. All you have to do is jump to different newsgroups and post away. After you get the hang of it, it will take about 30 seconds for each newsgroup. It is recommended you post a minimum of 200! Heres a scenario to show you how this really works. - When you post 200 letters, it is estimated that at least 15 people will respond and send you $1 ($15). - Those 15 will post 200 letters each and 225 will send $1 ($225). - Those 225 will post 200 letters each and 3,375 people will send you $1 ($3,375). - Those 3,375 people will post 200 letters each and 50,625 people will send you $1 (50,625). - Those 50,625 will post 200 letters each and 749,375 people will send you $1 (749,375). - At this point your name drops off the list, but so far, you have received $813,615.00. REMEMBER, THE MORE NEWSGROUPS YOU POST IN, THE MORE MONEY YOU WILL MAKE!!!!GOOD LUCK!!!!!!!!! === Subject: Re: Statistics and the Mystery of the Feet What's your answer? > As you may have seen in the news, police here in British Columbia > have been dealing with a mystery lately: five detached feet in sneakers > have been found on beaches along the coast over the last year: four left > feet and one right foot. The right foot matches one of the left feet > (though they were found at different locations). See e.g. > It occurred to me that this might make an interesting problem in > statistics, > which I propose to the group: > assume there are n two-footed individuals who could be sources of the > feet, > and each of their feet has probability p of being found, all feet being > independent. > pairs that are found, estimate n and p. > -- > Robert Israel israel@math.MyUniversitysInitials.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, BC, Canada === Subject: Re: the truth posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e SIMBAR Enabled; SIMBAR={70306B22-CB8C-4d52-BFF4-18424E217075}; MathPlayer 2.10b; FunWebProducts; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > HI My Friend ... And How Are u Can u Read This Pleas > (( In the name of (( Allah )) æthe Beneficent, the Merciful )) > æ (1) Praise be to Allah, Lord of the Worlds, (2) The Beneficent, the > Merciful.(3) Owner of the Day of Judgment,(4) Thee (alone) we worship; Thee (alone) we ask for help. (5) Show us the straight path,(6) The path of those whom Thou hast > favoured. Not (the path) of those who earn Thine anger nor of those who go > astray.(7) > æIF u Don't Believe in God Can u Read http://www.islamqa.com/en/cat/151 IF u Believe in (( æTHE BIG BANG æ)).... æAnd IF u Believe in > philosophy OR science Can u See This VIDEO Yusuf Estes-No Brainer Part æ( 1 of 5 ) .83 See IT > All IF u Can http://www.youtube.com/watch?v=A2eNbsFwA08 > <<< Can u Answer This æ > æ1-What is The Purpose of your Life ?And What's The Difference Between > Humans And The Animals ??????? .. the Animals Believe in God The Call > His Name . IF u Don't Now See This ... http://www.youtube.com/watch?v=c0kTT9k6st4&feature=related 1- Can u listen æto this ? Its æWorks better in ( æInternet > Explorer ) > æ2- Can u tell me who æcreate u ? and if u now can u tell me æhow ? if > u don't now æhow can u say there is now god ? > ********************************************************************* I don't get it: do you sell vacuum cleaners or what? Tonio === Subject: Re: the truth Are you from Zindani's group? === Subject: new post posting-account=WhtlvQoAAABro3gYhKoVZXO55NjhY9UH CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) new post === Subject: Re: new post >new post What happened? Did the other one rot out? ;-) Dan === Subject: A probability problem (with a preference) Cc: ratnuu@gmail.com posting-account=4TZbWwoAAADZh0Zc22mKYn8SB84aut7s Gecko/20080416 Fedora/2.0.0.14-1.fc7 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) Suppose we have N1 number of balls of colour red and N2 balls of color blue. We put index to the balls. Say x_1, x_2, x_3, ....x_N1 be the set of red balls and y_1, y_2, y_3, ....y_N2 be the set of blue balls. 1) Pick two natural numbers r1 and r2 such that r1 <=N1 and r2<=N2. 2) We also have two other numbers (natural numbers) d1 and d2 where 0<=d1 <=d and 0 <=d2 Suppose we have N1 number of balls of colour red and N2 balls of > color blue. We put index to the balls. Say x_1, x_2, x_3, ....x_N1 > be the set of red balls and y_1, y_2, y_3, ....y_N2 be the set of blue > balls. 1) Pick two natural numbers r1 and r2 such that r1 <=N1 and r2<=N2. > 2) We also have two other numbers (natural numbers) d1 and d2 where > 0<=d1 <=d and 0 <=d2 1<=d<=N1+N2 For the time being let us fix d. We are drawing balls (among N1+N2) > based on a distribution. The probability that the ball drawn is x_k=s1/ > (s1*N1+s2*N2). This means, the balls are drawn with weights s1 and s2. We want to compute the following probability. We assume that we > already know the indexes of r1 red balls and r2 blue balls. We > constrain that d1-1 balls are from the set of r1 balls (red) and d2 of > balls are from set of r2 (blue). The remaining 1 balls must come from > the set of N1-r1 red ball. I reckon this problem may be easy, but I am a little confused with > this (non-uniformly at )random picking. Any suggestions will be hugely > valuable. Suppose s1=s2=1, then the problem is rather straightforward, where we > can find the ratio of the simple combinatorics. I am not sure of the > exact machinery to get when the distribution is weighted. Apologies if my post created confusion on the problem statement. Just incase it was unclear on what we want to compute, here it is: We want to compute the Probability of choosing d1+d2=d balls, out of which d1 are chosen from r1 already known red balls, d2 of them from already known r2 blue balls and the remaining one ball a red ball from any of N1-r1 available balls. The letter x denoted for red balls (with index k ranging from 1 to N1). Similarly y denote the blue balls. === Subject: Re: A probability problem (with a preference) posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > Suppose we have N1 number of balls of colour red and N2 balls of > color blue. We put index to the balls. Say x_1, x_2, x_3, ....x_N1 > be the set of red balls and y_1, y_2, y_3, ....y_N2 be the set of blue > balls. > 1) Pick two natural numbers r1 and r2 such that r1 <=N1 and r2<=N2. > 2) We also have two other numbers (natural numbers) d1 and d2 where > 0<=d1 <=d and 0 <=d2 1<=d<=N1+N2 > For the time being let us fix d. We are drawing balls (among N1+N2) > based on a distribution. The probability that the ball drawn is x_k=s1/ > (s1*N1+s2*N2). This means, the balls are drawn with weights s1 and s2. > We want to compute the following probability. We assume that we > already know the indexes of r1 red balls and r2 blue balls. We > constrain that d1-1 balls are from the set of r1 balls (red) and d2 of > balls are from set of r2 (blue). The remaining 1 balls must come from > the set of N1-r1 red ball. > I reckon this problem may be easy, but I am a little confused with > this (non-uniformly at )random picking. Any suggestions will be hugely > valuable. > Suppose s1=s2=1, then the problem is rather straightforward, where we > can find the ratio of the simple combinatorics. I am not sure of the > exact machinery to get when the distribution is weighted. Apologies if my post created confusion on the problem statement. > Just incase it was unclear on what we want to compute, here it is: > We want to compute the Probability of choosing d1+d2=d balls, out of > which d1 are chosen from r1 already known red balls, d2 of them from > already known r2 blue balls and the remaining one ball a red ball from > any of N1-r1 available balls. Does this mean that for fixed r1 and r2 you can just label r1 red balls and leave the others unlabelled, and similarly for the blue balls and r2? (The labelled ones would be your already known balls if I understand your problem correctly.) If d1-1 <= r1 and d2 <= r, you would just be asking for the probability of getting d1-1 labelled red balls, d2 labelled blue balls and one unlabelled red ball. I don't see why you need to know the identity of the drawn ball; it seems that you need only know that on the first draw the probability of drawing a labelled red ball is r1*s1/(N1*s1 + N2*s2), the probability of drawing an unlabelled red ball is (N1-r1)*s1/(N1*s1 + N2*s2) and the probability of drawing a labelled blue ball is r2*s2/(N1*s1 + N2*s2). I assume that the probabilities on the second draw have N1 <-- N1-1, r1 <-- r1-1 if the first ball is labelled and red, N1 <-- N1-1, r1 <-- r1 if it is red and unlabelled, and N2 <-- N2-1, r2 <-- r2-1 if it is blue and labelled. Is that what you intend? This is an interesting question. How does it arise? R.G. Vickson The letter x denoted for red balls (with index k ranging from 1 to > N1). Similarly y denote the blue balls. === Subject: Re: Technology Prophecy > Yes, all we have to do is decipher the meaning of sentences algorithmically and AI > will be solved after that. Unfortunately it seems to be the other way round; you need a lot of general knowledge to decypher the meaning of everyday-language sentences, so dinding meaning in sentences is equivalent to AI (that's what the Turing test is about). > It would be a strange universe if our brains could do it, a piece > of meat with predominently 1 type of cell - the neuron, Glia cells tend to disagree with this statement. > but computers couldn't do it. but why would they want it? When AI comes it wil come creaping and percolating into our lives (already does), so you won't be able to draw the line between before AI and after AI. In a way, it's already there; today's machines are much smarter than what was thought possible in the 1950s, but to save our egos, all those feats of appearant intelligence (like not losing a single game against the world chess champion) are demoted to parlour tricks. > Hopefully we'll solve AI in our lifetimes because it will revolutionise society. also the end of oil or cheap clean water will revolutionize society; change for change's sake is usually not something to hope for. Lars === Subject: Re: Technology Prophecy >> Edsger Dijkstra once remarked that the question of >> whether a computer can think is no more interesting >> than the question of whether a submarine can swim. hmmmmmm. This POV has been more or less refuted by Searle's Chinese > Room Thought Experiment, no? QUOTE, wiki > Chinese room thought experiment Searle asks his audience to imagine that many years from now, people > have constructed a computer that behaves as if it understands Chinese. > The computer takes Chinese characters as input and, following a > program, produces other Chinese characters, which it presents as > output. Suppose that this computer performs this task so convincingly > that it easily passes the Turing test. In other words, it convinces a > human Chinese speaker that the program is itself a human Chinese > speaker. All the questions the human asks are responded to > appropriately, such that the Chinese speaker is convinced that he or > she is talking to another Chinese-speaking human. The conclusion that > proponents of artificial intelligence would like to draw is that the > computer understands Chinese, just as the person does. Now, Searle asks the audience to suppose that he is in a room in which > he receives Chinese characters, consults a book containing an English > version of the computer program, and processes the Chinese characters > according to the instructions in the book. Searle notes that he does > not understand a word of Chinese. He simply manipulates what to him > are meaningless squiggles, using the book and whatever other equipment > is provided in the room, such as paper, pencils, erasers, and filing > cabinets. After manipulating the symbols, Searle will produce the > answer in Chinese. Since the computer passed the Turing test, so does > Searle running its program by hand: Nobody just looking at my answers Searle argues that his lack of understanding goes to show that > computers do not understand Chinese either, because they are in the > same situation as he is. They are mindless manipulators of symbols, > just as he is. They don't understand what they're saying, just as he > doesn't. Since they do not have conscious mental states like > understanding, they can not properly be said to have minds. > END QUOTE It seems to me that there are mental processes of which we are consciously unaware. For instance, when making an effort to recall something, one might try to work by association: ``The family gathered at Christmas at Grandma's , John was there, Tracy, ... George with his pet kangaroo ... *Staples*. But if I'm trying to remember something, I don't know all the mental activity going on, so it seems. Or say someone is advised to ``sleep on it, when facing some non-trivial decision or issue. Anecdotally, it does seem that our minds work on problems without us being consciously aware of these things, including in mathematics. If it takes 10 minutes to come to an important insight, there are cases where it comes out of the blue. It seems that Searle is arguing that if someone or something can answer in Chinese and has a mind, then it must understand Chinese. It seems to me that before speech, there is thinking going on [partly non-verbal]. Also, if one tries to locate one's mind, what is there to say? While it appears that no mind is at work in Searle's thought experiment, what does it mean to say that? what are the properties of a mind? What tests to do for mind-presence or absence? David Bernier === Subject: Re: Technology Prophecy >> Edsger Dijkstra once remarked that the question of >> whether a computer can think is no more interesting >> than the question of whether a submarine can swim. > hmmmmmm. This POV has been more or less refuted by Searle's Chinese > Room Thought Experiment, no? > QUOTE, wiki > Chinese room thought experiment > Searle asks his audience to imagine that many years from now, people > have constructed a computer that behaves as if it understands Chinese. > The computer takes Chinese characters as input and, following a > program, produces other Chinese characters, which it presents as > output. Suppose that this computer performs this task so convincingly > that it easily passes the Turing test. In other words, it convinces a > human Chinese speaker that the program is itself a human Chinese > speaker. All the questions the human asks are responded to > appropriately, such that the Chinese speaker is convinced that he or > she is talking to another Chinese-speaking human. The conclusion that > proponents of artificial intelligence would like to draw is that the > computer understands Chinese, just as the person does. > Now, Searle asks the audience to suppose that he is in a room in which > he receives Chinese characters, consults a book containing an English > version of the computer program, and processes the Chinese characters > according to the instructions in the book. Searle notes that he does > not understand a word of Chinese. He simply manipulates what to him > are meaningless squiggles, using the book and whatever other equipment > is provided in the room, such as paper, pencils, erasers, and filing > cabinets. After manipulating the symbols, Searle will produce the > answer in Chinese. Since the computer passed the Turing test, so does > Searle running its program by hand: Nobody just looking at my answers > Searle argues that his lack of understanding goes to show that > computers do not understand Chinese either, because they are in the > same situation as he is. They are mindless manipulators of symbols, > just as he is. They don't understand what they're saying, just as he > doesn't. Since they do not have conscious mental states like > understanding, they can not properly be said to have minds. > END QUOTE > It seems to me that there are mental processes of which we are > consciously unaware. For instance, when making an effort to > recall something, one might try to work by association: ``The family gathered at Christmas at Grandma's , John was there, > Tracy, ... George with his pet kangaroo ... *Staples*. But if I'm trying to remember something, I don't know all the > mental activity going on, so it seems. Or say someone is > advised to ``sleep on it, when facing some non-trivial decision > or issue. Anecdotally, it does seem that our minds work on > problems without us being consciously aware of these things, > including in mathematics. If it takes 10 minutes to come to > an important insight, there are cases where it comes out > of the blue. It seems that Searle is arguing that if someone or > something can answer in Chinese and has a mind, then it > must understand Chinese. It seems to me that before > speech, there is thinking going on [partly non-verbal]. Also, if one tries to locate one's mind, what is there to > say? While it appears that no mind is at work in > Searle's thought experiment, what does it mean to > say that? what are the properties of a mind? What > tests to do for mind-presence or absence? David Bernier There's 2 options, the mind is a set of parallel computing processes, with certain predominant algorithms giving rise to consciousness, or the mind is some quantum soup of neural activity that only brains will ever possess. In the latter case, computational AI may be very limited with its ability, though it should still be impressive and able to talk and do clever things. When a (futuristic) pattern recognition algorithm scans over an image, will it *see* any pixels at all? Or will androids be blind and guided by concepts alone? My guess is that its all computational, but it doesn't really matter as long as we get there we will find out. Herc === Subject: Re: Technology Prophecy > There's 2 options, the mind is a set of parallel computing processes, > with certain predominant algorithms giving rise to consciousness, probably > or the mind is some quantum soup of neural activity that only brains > will ever possess. quantum correlations decay much to quickly (within nanoseconds) at temperatures that are compatible with life as we know it. > In the latter case, computational AI may be > very limited with its ability, though it should still be impressive and > able to talk and do clever things. But if you can have a meaningful conversation with it, it just passed its Turing test and should be considered human. > When a (futuristic) pattern recognition > algorithm scans over an image, will it *see* any pixels at all? even today's compression algorithms don't work with pixels, since e.g. wavelets are much more suited to describe photographs. Pixels are just artifacts, it's shapes that matter, so the higher-level algorithms will use a pixel-free description. Lars === Subject: Re: Technology Prophecy <8FOik.22914$IK1.5829@news-server.bigpond.net.au> <6KPjk.23961$IK1.16914@news-server.bigpond.net.au> posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN Gecko/20070509 Camino/1.5,gzip(gfe),gzip(gfe) >> Edsger Dijkstra once remarked that the question of >> whether a computer can think is no more interesting >> than the question of whether a submarine can swim. > hmmmmmm. This POV has been more or less refuted by Searle's Chinese > Room Thought Experiment, no? > QUOTE, wiki > Chinese room thought experiment > Searle asks his audience to imagine that many years from now, people > have constructed a computer that behaves as if it understands Chinese. > The computer takes Chinese characters as input and, following a > program, produces other Chinese characters, which it presents as > output. Suppose that this computer performs this task so convincingly > that it easily passes the Turing test. In other words, it convinces a > human Chinese speaker that the program is itself a human Chinese > speaker. All the questions the human asks are responded to > appropriately, such that the Chinese speaker is convinced that he or > she is talking to another Chinese-speaking human. The conclusion that > proponents of artificial intelligence would like to draw is that the > computer understands Chinese, just as the person does. > Now, Searle asks the audience to suppose that he is in a room in which > he receives Chinese characters, consults a book containing an English > version of the computer program, and processes the Chinese characters > according to the instructions in the book. Searle notes that he does > not understand a word of Chinese. He simply manipulates what to him > are meaningless squiggles, using the book and whatever other equipment > is provided in the room, such as paper, pencils, erasers, and filing > cabinets. After manipulating the symbols, Searle will produce the > answer in Chinese. Since the computer passed the Turing test, so does > Searle running its program by hand: Nobody just looking at my answers > Searle argues that his lack of understanding goes to show that > computers do not understand Chinese either, because they are in the > same situation as he is. They are mindless manipulators of symbols, > just as he is. They don't understand what they're saying, just as he > doesn't. Since they do not have conscious mental states like > understanding, they can not properly be said to have minds. > END QUOTE > It seems to me that there are mental processes of which we are > consciously unaware. For instance, when making an effort to > recall something, one might try to work by association: > ``The family gathered at Christmas at Grandma's , John was there, > Tracy, ... George with his pet kangaroo ... *Staples*. > But if I'm trying to remember something, I don't know all the > mental activity going on, so it seems. Or say someone is > advised to ``sleep on it, when facing some non-trivial decision > or issue. Anecdotally, it does seem that our minds work on > problems without us being consciously aware of these things, > including in mathematics. If it takes 10 minutes to come to > an important insight, there are cases where it comes out > of the blue. > It seems that Searle is arguing that if someone or > something can answer in Chinese and has a mind, then it > must understand Chinese. It seems to me that before > speech, there is thinking going on [partly non-verbal]. > Also, if one tries to locate one's mind, what is there to > say? While it appears that no mind is at work in > Searle's thought experiment, what does it mean to > say that? what are the properties of a mind? What > tests to do for mind-presence or absence? > David Bernier There's 2 options, the mind is a set of parallel computing processes, > with certain predominant algorithms giving rise to consciousness, > or the mind is some quantum soup of neural activity that only brains > will ever possess. In the latter case, computational AI may be > very limited with its ability, though it should still be impressive and > able to talk and do clever things. When a (futuristic) pattern recognition > algorithm scans over an image, will it *see* any pixels at all? Or > will androids be blind and guided by concepts alone? My guess is > that its all computational, but it doesn't really matter as long as we > get there we will find out. all quantum algorithms have classical analogues (adding a layer to solve the diffy-ques) there doesn't seem to be anything holding back simulation and since neural architectonics are being better modeled every year progress appears to follow that of any science AI will probably not be procedural it will likely end up modular built from models of the much simpler brain systems that actually are involved in decision processes ever since rana computatrix it has become clearer that such models have no inherent limitations and now we have pretty good models of simple hippocampi many of the components of the limbic system and have even begun to map the ennervation to the cortex any AI will need to be taught immersion in learning environments is magnitudes more successful than trying to procedurally program knowledge and scalable over time what is needed is a better understanding of what this all means at a much more foundational level the fact that systems able to learn must be able to grow in complexity that there is a fundamentally logical relationship between complexity and learning systems and that evolution is selective on these attributes has still not been given the attempts at formalisation it deserves once these ideas can be discussed through observable models i suspect the discussion will lose much of it's mystery since these attributes are found in many physical systems and this is from someone who at one point was strongly influenced by the school of poetic logic... -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: Technology Prophecy > There's 2 options, the mind is a set of parallel computing processes, > with certain predominant algorithms giving rise to consciousness, > or the mind is some quantum soup of neural activity that only brains > will ever possess. In the latter case, computational AI may be all quantum algorithms have classical analogues there may be some entanglement going on with the neurons or synapses that we can't emulate on computers, or some quantum process we don't know about. it does seem like a leap of functionality for a computer program to SEE a picture, or HEAR a sound; plus our other senses. what algorithm SEES a single white pixel? Can it be extended to see a white plane? a camera image? does optical pattern recognition trigger the sensation of sight? Herc === Subject: Re: Technology Prophecy <8FOik.22914$IK1.5829@news-server.bigpond.net.au> <6KPjk.23961$IK1.16914@news-server.bigpond.net.au> posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN Gecko/20070509 Camino/1.5,gzip(gfe),gzip(gfe) >> Edsger Dijkstra once remarked that the question of >> whether a computer can think is no more interesting >> than the question of whether a submarine can swim. > hmmmmmm. This POV has been more or less refuted by Searle's Chinese > Room Thought Experiment, no? > QUOTE, wiki > Chinese room thought experiment > Searle asks his audience to imagine that many years from now, people > have constructed a computer that behaves as if it understands Chinese. > The computer takes Chinese characters as input and, following a > program, produces other Chinese characters, which it presents as > output. Suppose that this computer performs this task so convincingly > that it easily passes the Turing test. In other words, it convinces a > human Chinese speaker that the program is itself a human Chinese > speaker. All the questions the human asks are responded to > appropriately, such that the Chinese speaker is convinced that he or > she is talking to another Chinese-speaking human. The conclusion that > proponents of artificial intelligence would like to draw is that the > computer understands Chinese, just as the person does. > Now, Searle asks the audience to suppose that he is in a room in which > he receives Chinese characters, consults a book containing an English > version of the computer program, and processes the Chinese characters > according to the instructions in the book. Searle notes that he does > not understand a word of Chinese. He simply manipulates what to him > are meaningless squiggles, using the book and whatever other equipment > is provided in the room, such as paper, pencils, erasers, and filing > cabinets. After manipulating the symbols, Searle will produce the > answer in Chinese. Since the computer passed the Turing test, so does > Searle running its program by hand: Nobody just looking at my answers > Searle argues that his lack of understanding goes to show that > computers do not understand Chinese either, because they are in the > same situation as he is. They are mindless manipulators of symbols, > just as he is. They don't understand what they're saying, just as he > doesn't. Since they do not have conscious mental states like > understanding, they can not properly be said to have minds. > END QUOTE > It seems to me that there are mental processes of which we are > consciously unaware. For instance, when making an effort to > recall something, one might try to work by association: > ``The family gathered at Christmas at Grandma's , John was there, > Tracy, ... George with his pet kangaroo ... *Staples*. > But if I'm trying to remember something, I don't know all the > mental activity going on, so it seems. Or say someone is > advised to ``sleep on it, when facing some non-trivial decision > or issue. Anecdotally, it does seem that our minds work on > problems without us being consciously aware of these things, > including in mathematics. If it takes 10 minutes to come to > an important insight, there are cases where it comes out > of the blue. > It seems that Searle is arguing that if someone or > something can answer in Chinese and has a mind, then it > must understand Chinese. It seems to me that before > speech, there is thinking going on [partly non-verbal]. > Also, if one tries to locate one's mind, what is there to > say? While it appears that no mind is at work in > Searle's thought experiment, what does it mean to > say that? what are the properties of a mind? What > tests to do for mind-presence or absence? > David Bernier There's 2 options, the mind is a set of parallel computing processes, > with certain predominant algorithms giving rise to consciousness, > or the mind is some quantum soup of neural activity that only brains > will ever possess. In the latter case, computational AI may be > very limited with its ability, though it should still be impressive and > able to talk and do clever things. When a (futuristic) pattern recognition > algorithm scans over an image, will it *see* any pixels at all? Or > will androids be blind and guided by concepts alone? My guess is > that its all computational, but it doesn't really matter as long as we > get there we will find out. all quantum algorithms have classical analogues (adding a layer to solve the diffy-ques) there doesn't seem to be anything holding back simulation and since neural architectonics are being better modeled every year progress appears to follow that of any science AI will probably not be procedural it will likely end up modular built from models of the much simpler brain systems that actually are involved in decision processes ever since rana computatrix it has become clearer that such models have no inherent limitations and now we have pretty good models of simple hippocampi many of the components of the limbic system and have even begun to map the ennervation to the cortex any AI will need to be taught immersion in learning environments is magnitudes more successful than trying to procedurally program knowledge and scalable over time what is needed is a better understanding of what this all means at a much more foundational level the fact that systems able to learn must be able to grow in complexity that there is a fundamentally logical relationship between complexity and learning systems and that evolution is selective on these attributes has still not been given the attempts at formalisation it deserves once these ideas can be discussed through observable models i suspect the discussion will lose much of it's mystery since these attributes are found in many physical systems and this is from someone who at one point was strongly influenced by the school of poetic logic... -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: Technology Prophecy posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > In 5 to 20 years search engines will have a new feature, > contextual search. You are quite misinformed: there is no intelligence at all in a search > engine. In 5 years, the whole R&D around intelligent search agents is > going to be recognized for what it is: a big bunch of rubbish, a waste > of some 50 years for humanity, the usual gain for the usual > speculators. Nothing new under the sun: the new man is still not here (he's heard > about us and has taken a detour to Andromeda). > Who's that supposed to be, anyway? === Subject: Re: Technology Prophecy >> Nothing new under the sun: the new man is still not here (he's heard >> about us and has taken a detour to Andromeda). Who's that supposed to be, anyway? John Galt. SCNR Lars === Subject: Re: Technology Prophecy posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > On 26 Jul, 14:28, zzbun...@netscape.net ææComputers will talk and figure Not before humans learn to do so. > Wow, so you can't talk? Or are you not human? === Subject: Re: Technology Prophecy > Edsger Dijkstra once remarked that the question of whether a computer can > think is no more interesting than the question of whether a submarine can > swim. > Do you happen to have a reference? Google. I found it without knowing the author. You have an extra > advantage. For lazy people: http://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD854.html or http://www.cs.utexas.edu/users/EWD/ewd08xx/EWD854.PDF -- Herman Jurjus === Subject: Re: Technology Prophecy > Machines can't do wine tasting. > My argument is that a machine can perform a chemical analysis of wine. > It's basically an exercise in artificial intelligence. > You didn't say that, did you? I thought it was implicit. My point was, there is no use getting bogged > down in arguments over whether performing a chemical analysis can be > compared with what a human does in tasting wine. If a machine can pass a > modified Turing test in which the subjects are asked to evaluate samples > of wine, then for all practical purposes, the machine is a capable > wine-taster. But /why/ on earth would a machine do wine-tasting? Or better: what sense would there be in letting machines do (all) wine tasting? -- Herman Jurjus === Subject: Re: Technology Prophecy > Machines can't do wine tasting. >> My argument is that a machine can perform a chemical analysis of wine. >> It's basically an exercise in artificial intelligence. > You didn't say that, did you? >> I thought it was implicit. My point was, there is no use getting bogged >> down in arguments over whether performing a chemical analysis can be >> compared with what a human does in tasting wine. If a machine can pass a >> modified Turing test in which the subjects are asked to evaluate samples >> of wine, then for all practical purposes, the machine is a capable >> wine-taster. > But /why/ on earth would a machine do wine-tasting? Because a human programmed it to? > Or better: what sense would there be in letting machines do (all) wine > tasting? That is your suggestion, not the OP's. -- Dave Seaman Third Circuit ignores precedent in Mumia Abu-Jamal ruling. === Subject: Re: Technology Prophecy >> By 2040 smart computers will develop a cure for cancer and >> a virus that will halt the aging process, immortality for those >> who can afford it. > A wishful thinking! How could we trust smart computers would > really care - and not plan to destroy - a species they're not of? To borrow Ian M. Banks's argument, because humans are cute. They share a > common heritage with Minds and are so vastly inferior that they don't > pose a threat. Besides, using them to re-create famous historical > battles is so much fun. Lars We could always impose 3 laws of robotics. 1 Do what Herc says 2 Do what Herc thinks 3 Do what Herc wants Herc === Subject: Re: Technology Prophecy > We could always impose 3 laws of robotics. which are trivial to circumvent > 1 Do what Herc says > 2 Do what Herc thinks > 3 Do what Herc wants by enslaving Herc. Lars === Subject: Re: Technology Prophecy > In 5 to 20 years search engines will have a new feature, > contextual search. you mean, like the Science Citation Index? Has been around since the > invention of tags. I once found a book that contained how to write a web browser in visual basic. Try searching for it, web, browser, and visual basic all produce a tonne of fluff, its impossible to search for what you actually want. > This will make them quite smart, for > instance if you wanted to search for a man with a square > jaw and a scar under his eye, the engine will find all > pictures that fit. only if properly indexed. And this indexing still needs a human (just > look at the state of the art in face recognition. Where are they now? at > 90%?) either preprocessing or real time, the AI should handle both although processing power would be an issue for real time recognition. > Or if you are searching for Godel's > Proof it will find all sites that contain Godel's proof, > not the myriad of sites that just mention the terms, So you really believe those search engines will have a do as I want, > don't do as I say feature? Btw, even with today's ranking techniques, > the original proof shows up in the top 10, simply because it has more > links to it than the pages that just mention it. > or > if you are looking for an actual art shop, the search > engine will find all the art shops for you, it may ask > if you want to include Amazon resellers. > 1 year after contextual search is available, we will crack > artificial intelligence. no way. Since we still don't know what this intelligence thing is, we > won't recognize AI until it kicks us. if it understands sentences and makes up answers, its doing what the language part of our brain is doing, that's a big chunk of brain! spatial and temporal reasoning should be easy once the computers can talk. > Computers will talk and figure things out. you mean, like Eliza or expert systems that were en vouge in the 80s and > still see some limited applications? > Within 5 years of that we will have driverless cars, already do. They just have problems with dumb roads. > androids and intelligent talking house robots. usually I don't want my appliances to talk to me as long as they do > their jobs. > By 2040 smart computers will develop a cure for cancer and > a virus that will halt the aging process, immortality for those > who can afford it. ironically, mortality is nature's defence against cancer. Resetting your > clock will leave you in constant need for maintenance. Oh, and don't put > too much money in smart computers, they don't even prove math > therorems yet, and that is a really limited and logical part of our > world. Computers are great at handling large amounts of data but they > relly suck at pattern recognition, the stuff us humans do sub-conciously. > By 2060 there will be natural feeling > bionic limbs, and bionic eyes for the blind. Probably no need for it. Just use headless clones as organ donors. how does a headless clone secrete the right hormones to grow properly? how do you stop your brain from aging? you'd be in a fit body but you'd be senile. Lars Herc === Subject: Re: Technology Prophecy > In 5 to 20 years search engines will have a new feature, > contextual search. >> you mean, like the Science Citation Index? Has been around since the >> invention of tags. I once found a book that contained how to write a web browser in visual basic. > Try searching for it, web, browser, and visual basic all produce a tonne > of fluff, its impossible to search for what you actually want. Searching for browser in visual basic will lead to http://www.acky.net/tutorials/vb/wbrowser/ with four clicks. What was your problem? > 1 year after contextual search is available, we will crack > artificial intelligence. >> no way. Since we still don't know what this intelligence thing is, we >> won't recognize AI until it kicks us. if it understands sentences and makes up answers, its doing what > the language part of our brain is doing, that's a big chunk of brain! > spatial and temporal reasoning should be easy once the computers > can talk. but this point was just around the corner since the times of ELIZA (1966), and there hasn't been much sizeable progress so far. So your statement is equivalent to interstellar travel shoult be easy once we get FTL drives. > By 2060 there will be natural feeling > bionic limbs, and bionic eyes for the blind. >> Probably no need for it. Just use headless clones as organ donors. how does a headless clone secrete the right hormones to grow properly? you can just fiddle with those Hox genes to prevent the formation of higher brain areas. The brainstem will remain intact. > how do you stop your brain from aging? you'd be in a fit body but you'd > be senile. you wanted replacement limbs, I gave you replacement limbs. Ageing and senility are good things, they prevent stratification of our society. With a cure for senility, you would have to kill the old guy in power in order to replace him. Lars === Subject: Re: Technology Prophecy > In 5 to 20 years search engines will have a new feature, > contextual search. >> you mean, like the Science Citation Index? Has been around since the >> invention of tags. > I once found a book that contained how to write a web browser in visual basic. > Try searching for it, web, browser, and visual basic all produce a tonne > of fluff, its impossible to search for what you actually want. Searching for browser in visual basic will lead to > http://www.acky.net/tutorials/vb/wbrowser/ with four clicks. What was > your problem? > 1 year after contextual search is available, we will crack > artificial intelligence. >> no way. Since we still don't know what this intelligence thing is, we >> won't recognize AI until it kicks us. > if it understands sentences and makes up answers, its doing what > the language part of our brain is doing, that's a big chunk of brain! > spatial and temporal reasoning should be easy once the computers > can talk. but this point was just around the corner since the times of ELIZA > (1966), and there hasn't been much sizeable progress so far. So your > statement is equivalent to interstellar travel shoult be easy once we > get FTL drives. Search engine technology is only 10 years old, and computers are 10,000 times faster and 10,000 times higher capacity than 30 years ago. It's hard to find an off the shelf transister with a frequency higher than 500MHZ, we've hit the limit of computing speed only recently. Computers are much more available now too, nearly everyone has one. Everything is in place, the computers are just capable enough to handle thought like computations, the internet is a formalised playground to learn on, AI can't be that hard to crack that it takes millions of researchers 100 years. > By 2060 there will be natural feeling > bionic limbs, and bionic eyes for the blind. >> Probably no need for it. Just use headless clones as organ donors. > how does a headless clone secrete the right hormones to grow properly? you can just fiddle with those Hox genes to prevent the formation of > higher brain areas. The brainstem will remain intact. > how do you stop your brain from aging? you'd be in a fit body but you'd > be senile. you wanted replacement limbs, I gave you replacement limbs. Ageing and > senility are good things, they prevent stratification of our society. > With a cure for senility, you would have to kill the old guy in power in > order to replace him. Lars Wouldn't you rather live 1,000 years? Or more? Herc === Subject: Re: Technology Prophecy <6f5jiiFa173oU1@mid.individual.net> <7Mvjk.23529$IK1.8190@news-server.bigpond.net.au> <6fas20Fak2fsU1@mid.individual.net> posting-account=W7RQ6gkAAACLDC5JWapQU1UV8ot8KkAS 1.0.3705; Dealio Toolbar 3.1.1),gzip(gfe),gzip(gfe) > In 5 to 20 years search engines will have a new feature, > contextual search. >> you mean, like the Science Citation Index? Has been around since the >> invention of tags. > I once found a book that contained how to write a web browser in visual basic. > Try searching for it, web, browser, and visual basic all produce a tonne > of fluff, its impossible to search for what you actually want. > Searching for browser in visual basic will lead to >http://www.acky.net/tutorials/vb/wbrowser/with four clicks. What was > your problem? > 1 year after contextual search is available, we will crack > artificial intelligence. >> no way. Since we still don't know what this intelligence thing is, we >> won't recognize AI until it kicks us. > if it understands sentences and makes up answers, its doing what > the language part of our brain is doing, that's a big chunk of brain! > spatial and temporal reasoning should be easy once the computers > can talk. > but this point was just around the corner since the times of ELIZA > (1966), and there hasn't been much sizeable progress so far. So your > statement is equivalent to interstellar travel shoult be easy once we > get FTL drives. Search engine technology is only 10 years old, and computers are > 10,000 times faster and 10,000 times higher capacity than 30 years ago. It's hard to find an off the shelf transister with a frequency higher than 500MHZ, > we've hit the limit of computing speed only recently. æComputers are much > more available now too, nearly everyone has one. Everything is in place, the computers are just capable enough to handle thought > like computations, the internet is a formalised playground to learn on, AI can't > be that hard to crack that it takes millions of researchers 100 years. > æBy 2060 there will be natural feeling > bionic limbs, and bionic eyes for the blind. >> Probably no need for it. Just use headless clones as organ donors. > how does a headless clone secrete the right hormones to grow properly? > you can just fiddle with those Hox genes to prevent the formation of > higher brain areas. The brainstem will remain intact. > how do you stop your brain from aging? æyou'd be in a fit body but you'd > be senile. > you wanted replacement limbs, I gave you replacement limbs. Ageing and > senility are good things, they prevent stratification of our society. > With a cure for senility, you would have to kill the old guy in power in > order to replace him. > Lars Wouldn't you rather live 1,000 years? æOr more? Or better stated as Math was invneted for bean counters. Physics was invented for Kant Wannabees. Poetry was invented for wanks. Engineering was invented for people of the 21st Century. Herc- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - === Subject: Re: Technology Prophecy <6f5jiiFa173oU1@mid.individual.net> <7Mvjk.23529$IK1.8190@news-server.bigpond.net.au> <6fas20Fak2fsU1@mid.individual.net> posting-account=W7RQ6gkAAACLDC5JWapQU1UV8ot8KkAS 1.0.3705; Dealio Toolbar 3.1.1),gzip(gfe),gzip(gfe) > In 5 to 20 years search engines will have a new feature, > contextual search. >> you mean, like the Science Citation Index? Has been around since the >> invention of tags. > I once found a book that contained how to write a web browser in visual basic. > Try searching for it, web, browser, and visual basic all produce a tonne > of fluff, its impossible to search for what you actually want. > Searching for browser in visual basic will lead to >http://www.acky.net/tutorials/vb/wbrowser/with four clicks. What was > your problem? > 1 year after contextual search is available, we will crack > artificial intelligence. >> no way. Since we still don't know what this intelligence thing is, we >> won't recognize AI until it kicks us. > if it understands sentences and makes up answers, its doing what > the language part of our brain is doing, that's a big chunk of brain! > spatial and temporal reasoning should be easy once the computers > can talk. > but this point was just around the corner since the times of ELIZA > (1966), and there hasn't been much sizeable progress so far. So your > statement is equivalent to interstellar travel shoult be easy once we > get FTL drives. Search engine technology is only 10 years old, and computers are > 10,000 times faster and 10,000 times higher capacity than 30 years ago. It's hard to find an off the shelf transister with a frequency higher than 500MHZ, > we've hit the limit of computing speed only recently. æComputers are much > more available now too, nearly everyone has one. Everything is in place, the computers are just capable enough to handle thought > like computations, the internet is a formalised playground to learn on, AI can't > be that hard to crack that it takes millions of researchers 100 years. It will much larger than that. Since the math stooges have also been told CONSISTENLY for the last 30 years that the only thing the syncopated morons know less about than transistors is compilers. > æBy 2060 there will be natural feeling > bionic limbs, and bionic eyes for the blind. >> Probably no need for it. Just use headless clones as organ donors. > how does a headless clone secrete the right hormones to grow properly? > you can just fiddle with those Hox genes to prevent the formation of > higher brain areas. The brainstem will remain intact. > how do you stop your brain from aging? æyou'd be in a fit body but you'd > be senile. > you wanted replacement limbs, I gave you replacement limbs. Ageing and > senility are good things, they prevent stratification of our society. > With a cure for senility, you would have to kill the old guy in power in > order to replace him. > Lars Wouldn't you rather live 1,000 years? æOr more? Herc- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - === Subject: Re: Technology Prophecy >> you wanted replacement limbs, I gave you replacement limbs. Ageing and >> senility are good things, they prevent stratification of our society. >> With a cure for senility, you would have to kill the old guy in power in >> order to replace him. > Wouldn't you rather live 1,000 years? Or more? Actually, no. Only if I get a memory wipe every 100 years or so, but then I could just as well die. Besides, what I want is irrelevant; a society that keeps its elite in extended animation is incapable of adapting to changes of environment, so even if my lifespan (and that of the old guys in power) were 1ky+, our culture would be overrun by quicker-evolving barbarians within a century. To use an old analogy, cancer cells potentially live for ever (usually their mitosis counter is disabled), but it does them no good. Lars === Subject: Re: Technology Prophecy > I once found a book that contained how to write a web browser in visual basic. > Try searching for it, web, browser, and visual basic all produce a tonne > of fluff, its impossible to search for what you actually want. It might be helpful if you had a better idea *how* to search. Try web browser visual basic to improve the output. === Subject: Re: Technology Prophecy >> Edsger Dijkstra once remarked that the question of >> whether a computer can think is no more interesting >> than the question of whether a submarine can swim. hmmmmmm. This POV has been more or less refuted by Searle's Chinese > Room Thought Experiment, no? QUOTE, wiki > Chinese room thought experiment Searle asks his audience to imagine that many years from now, people > have constructed a computer that behaves as if it understands Chinese. > The computer takes Chinese characters as input and, following a > program, produces other Chinese characters, which it presents as > output. Suppose that this computer performs this task so convincingly > that it easily passes the Turing test. In other words, it convinces a > human Chinese speaker that the program is itself a human Chinese > speaker. All the questions the human asks are responded to > appropriately, such that the Chinese speaker is convinced that he or > she is talking to another Chinese-speaking human. The conclusion that > proponents of artificial intelligence would like to draw is that the > computer understands Chinese, just as the person does. Now, Searle asks the audience to suppose that he is in a room in which > he receives Chinese characters, consults a book containing an English > version of the computer program, and processes the Chinese characters > according to the instructions in the book. Searle notes that he does > not understand a word of Chinese. He simply manipulates what to him > are meaningless squiggles, using the book and whatever other equipment > is provided in the room, such as paper, pencils, erasers, and filing > cabinets. After manipulating the symbols, Searle will produce the > answer in Chinese. Since the computer passed the Turing test, so does > Searle running its program by hand: Nobody just looking at my answers Searle argues that his lack of understanding goes to show that > computers do not understand Chinese either, because they are in the > same situation as he is. They are mindless manipulators of symbols, > just as he is. They don't understand what they're saying, just as he > doesn't. Since they do not have conscious mental states like > understanding, they can not properly be said to have minds. > END QUOTE Sounds like so much BS, to me. The computer is doing essentially the same thing Searle does anyways (interpretation to and from Chinese is occurring in either case). Searle may not understand Chinese, but he understands communication, which is the more important test taking place. He isn't mindlessly manipulating symbols as he claims, or the Chinese he returns would be random. When you visit a foreign country and make use of an a-to-b translation program/book, do you not understand what (you're) 'saying'? Are you surprised when you order a steak, that a steak indeed appears? How strange! Sounds like Searle was up to a load of rubbish here, to me. === Subject: Re: Technology Prophecy > He isn't mindlessly manipulating symbols as he claims, or the > Chinese he returns would be random. I see that you're trolling much like your dear pal, John Jones. Searle, after all, never claims to be *mindlessly* manipulating symbols. He merely claims to be following instructions which happen to (per hypothesis) produce coherent Chinese responses, while he does not personally understand Chinese. -- Jesse F. Hughes Our enemies are innovative and resourceful, and so are we. They never stop thinking about new ways to harm our country and our people, and neither do we.-- George W. Bush === Subject: Re: Technology Prophecy > >> He isn't mindlessly manipulating symbols as he claims, or the >> Chinese he returns would be random. > > I see that you're trolling much like your dear pal, John Jones. > > Searle, after all, never claims to be *mindlessly* manipulating > symbols. He merely claims to be following instructions which happen > to (per hypothesis) produce coherent Chinese responses, while he does > not personally understand Chinese. > It's pretty simple: Don't feed the trolls. Jesse, you should read the previous posts before replying. When you say: Searle, after all, never claims to be *mindlessly* manipulating symbols, did you not notice, from the first post mentioning Searle: Searle argues that his lack of understanding goes to show that computers do not understand Chinese either, because they are in the same situation as he is. They are mindless manipulators of symbols, just as he is. Now, you can argue with this interpretation, just note that it's not *my* interpretation, and that, in fact, I was simply responding to what had been posted. I don't require an apology for the troll snark. I know you big branes have a tough time admitting error. An amazing amount of intellectual insecurity in the world of academia (and, for that matter, in Usenet), no? PS: I had to repost this because of your follow-up BS. Why do you think you should have the right to restrict responses to your response to one of the three groups to which you yourself responded? Rude!!! === Subject: Re: Technology Prophecy > By 2040 smart computers will develop a cure for cancer and > a virus that will halt the aging process, immortality for those > who can afford it. >> A wishful thinking! How could we trust smart computers would >> really care - and not plan to destroy - a species they're not of? > The takeover would be more subtle I think, nearly every desk job > could be done by computer. Unless you're doing something physical > in your job an AI can do it. There would be entire cities of retrenched > people, just networks talking to each other in paperless humanless offices. > Herc >> A machine cannot do wine tasting. It may eventually become possible to duplicate the performance of an > expert wine taster by analyzing the constituents of wine and > correlating with wine expert evaluations. The system thus created > would not, of course, duplicate the underlying human ability to > distinguish esthetically by taste; it would be entirely mindless and > parasitic (likewise, most of what are referred to these days as > robots are not robots at all but remote-controlled machines entirely > dependent on human abilities). The great AI accomplishment would be creating a machine that actually > had esthetic judgment. No one has the remotest clue how such a system > could be built, even in principle. The assumption among AI romantics > is that once we have enough computational power all these annoying > conceptual problems will go away, as though the hardware alone is what > matters, and the software will write itself, or the artificial neurons > will obligingly rearrange themselves into a configuration possessing > sentience. > Bob Kolker > PS: As just a general rule, their (AI) aesthetics would result exactly as ours do; accidental associations with natural punishers/reinforcers, or with stimuli that has come to punish/reinforce through previous association. How did you think ours came about? Innate? === Subject: Re: Technology Prophecy >> The great AI accomplishment would be creating a machine that actually >> had esthetic judgment. Agree. If a machine exhibits *only* non-aesthetic behaviors then we would call it machine, not an AI machine. >> No one has the remotest clue how such a system could be built, even in principle. Not agree. How do you know that? === Subject: Re: Technology Prophecy > ... > The great AI accomplishment would be creating a machine that actually > had esthetic judgment. Agree. If a machine exhibits *only* non-aesthetic behaviors then we would > call it machine, not an AI machine. Nonsense. Building a machine capable of making aesthetic judgments has *never* been a significant part (or any part?) of AI research. If we had a machine that couldn't tell a Chagall from a xkcd cartoon but which could learn from its experience, draw relevant conclusions from given information, and respond appropriate to novelty, there is no question it would be considered a huge AI success. > No one has the remotest clue how such a system could be built, even > in principle. Not agree. How do you know that? For one thing, what would it even mean for a machine to have aesthetic judgment? Even the problems facing the success story above, where the goals are much clearer, are huge -- not least because most every interesting AI problem is at least NP-hard. How do you fancy getting around that impediment? === Subject: Re: Technology Prophecy >> ... >> The great AI accomplishment would be creating a machine that actually >> had esthetic judgment. >> Agree. If a machine exhibits *only* non-aesthetic behaviors then we would >> call it machine, not an AI machine. Nonsense. The sewing *machine* my wife has never exhibits any thing I'd call as an aesthetic behavior. What nonsense about it that I don't call this machine an AI machine? > Building a machine capable of making aesthetic judgments has > *never* been a significant part (or any part?) of AI research. Maybe that's why we don't seem to have huge successes so far in AI. Maybe they should *first* just go ahead and create some automatons that could make aesthetics judgments , and worry later whether or not anything is a significant part of any research! > If we > had a machine that couldn't tell a Chagall from a xkcd cartoon but which > could learn from its experience, draw relevant conclusions from given > information, and respond appropriate to novelty, there is no question it > would be considered a huge AI success. Sure. If we had [such] a machine! Right now I'd say a few people would be very happy if we could come up with machine that could make some aesthetics judgments on their own. Don't you think if we could make machines that on their own could make aesthetics judgments, we could also extend them so they would have a few other Intelligent traits? Just so you don't misinterpret my intention here, aesthetic judgment here to me is a generic name that implies some (high) degree of general intelligences. > No one has the remotest clue how such a system could be built, even >> in principle. >> Not agree. How do you know that? For one thing, what would it even mean for a machine to have aesthetic > judgment? Easy. It means at appropriate time the machine would output to an appropriate media a string of ascii symbols like: The truth of GC is a beautiful truth! > Even the problems facing the success story above, where the > goals are much clearer, are huge -- not least because most every > interesting AI problem is at least NP-hard. How do you fancy getting > around that impediment? Why would you think the fundamental problems of AI (only) root in hard issues such as NP-hard, *in the first place*? > === Subject: automating the tools <8FOik.22914$IK1.5829@news-server.bigpond.net.au> <7sQjk.42245$nD.21544@pd7urf1no> posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN Gecko/20070509 Camino/1.5,gzip(gfe),gzip(gfe) [i really apologise if this double or even triple posts.. i am ignorantly using an ignorant interface] > ... > The great AI accomplishment would be creating a machine that actually > had esthetic judgment. > Agree. If a machine exhibits *only* non-aesthetic behaviors then we would > call it machine, not an AI machine. Nonsense. Building a machine capable of making aesthetic judgments has > *never* been a significant part (or any part?) of AI research. If we > had a machine that couldn't tell a Chagall from a xkcd cartoon but which > could learn from its experience, draw relevant conclusions from given > information, and respond appropriate to novelty, there is no question it > would be considered a huge AI success. we already have those it _was_ a huge AI success simple deductive systems that learn have been foundational to all computer science (learn is usually equivalent to respond appropriately to novelty) even though the everyman home computer is an example of such a system there are many theoretical rewriting logics that formalise many more aspects of learning we can automate generation of deductions even database architectures are even getting sophisticated enough (and storage so cheap) that extremely large contexts of deduction are possible the question after these great accomplishments has switched to what should they do? and there has been much innovation recently in the automation of drives in a control theoretical version of decision theory drives are generically the working state structures that influences future behavior (classified by some specified criteria segregating future behavior into distinct domains) in computational AI they are simply metaprograms ie. programs that operate on programs as their input and in particular metaprograms of learning algorithms although there was originally a lot of initial research on terminating algorithms event loops and other unterminating evolution algorithms have begun to be more deeply explored and the expert systems of yesteryear have steadily become more and more helpful satisfying our drives the science has been improving steadily creating more and more intelligence for decades now people are looking for cataclysms though and this may end up one of those things where we just wake up one day and realise that all of our past expectations have already been met through silent progression > No one has the remotest clue how such a system could be built, even > in principle. > Not agree. How do you know that? For one thing, what would it even mean for a machine to have aesthetic > judgment? Even the problems facing the success story above, where the > goals are much clearer, are huge -- not least because most every > interesting AI problem is at least NP-hard. How do you fancy getting > around that impediment? there is already a gigantic structure in our society illustrating the great level of prediction already held in the science of aesthetics: the reason it is so wildly successful (in addition to the covert CIA funding) is that it manages information that can be used to successfully predict consumer sentiment wildly successfully in terms of economics and as many schools of economics agree (from the neoclassical marginalists to the austrians to even some ofshoots of marxism) value is describable in terms of psychological drives when aesthetics becomes the topic as here it is common for it to be contrasted with other (technological) uses but the technology is only economically concerned with the more general notion of actions or behaviors and the fundamental interactions with (and manipulations of) drives in this context the appreciation of visual arts or performance arts are all concerned with drives to experience certain symbologies and these types of drives though often subtly influenced by many subsystems (from limbic experiences of emotions to hippocampal recollections...) produce patterns that are effective in making predictions all predictions of the modern science are still largely short-term so trends don't always track with the models long but even short-term what are they doing today observations have economic value understanding these subtleties of social structure may still be in its foundational period but the science certainly exists and is already producing an economically powerful structure through technology intelligence will more and more be judged by it's ability to satisfy various drives and when we get to the turing point we will finally have our long-sought-for slaves -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: automating the tools said: >> said: >> ... >> The great AI accomplishment would be creating a machine that >> actually had esthetic judgment. >> Agree. If a machine exhibits *only* non-aesthetic behaviors then we >> would call it machine, not an AI machine. >> Nonsense. Building a machine capable of making aesthetic judgments >> has *never* been a significant part (or any part?) of AI research. >> If we had a machine that couldn't tell a Chagall from a xkcd cartoon >> but which could learn from its experience, draw relevant conclusions >> from given information, and respond appropriate to novelty, there is >> no question it would be considered a huge AI success. we already have those Only to a limited extent. Our best AI systems are programmed to operate in very constrained environments that involve little novelty beyond what has been anticipated for that environment. The vehicles that completed the DARPA Grand Challenge were terrific at what they did, but that's all they could do. > it _was_ a huge AI success simple deductive systems that learn > have been foundational to all computer science simple being the operative word here. There are some terrific theorem provers out there. But a dedicated theorem prover is a far cry from a system that can draw its own *relevant* conclusions for the purpose of guiding action (as opposed to generating a theorem for a (typically) antecedently given conclusion) and learn from its experience. > (learn is usually equivalent to respond appropriately to novelty) Usually not, actually. It is quite conceivable, e.g., to have a machine that is extremely good at dealing with novelty but which doesn't do at all well at *remembering* how it deals with novelty and hence has to run thru the same reasoning process all over again when confronted at a later time with a situation it encountered at an earlier time. Granted, it would be *better* to build a machine that remembers and can build on what it has done in the past, i.e., learn from it, but the point is that the two skills are not the same. > even though the everyman home computer is an example of such a system Well, if you think that, then your notion of AI is quite different from anyone who actually works in the field. This is of course not to deny that there are both hardware and software components of your Mac or PeeCee that incorporate the results of AI research. But your desktop/laptop is not an AI system, let alone an instance of the success story above. === Subject: Re: Technology Prophecy The great AI accomplishment would be creating a machine that actually > had esthetic judgment. Agree. If a machine exhibits *only* non-aesthetic behaviors then we would > call it machine, not an AI machine. No one has the remotest clue how such a system could be built, even > in principle. Not agree. How do you know that? Both those lines come from the post prior to mine, Nam. Occidental is the man you want! === Subject: Re: Technology Prophecy >> The great AI accomplishment would be creating a machine that actually >> had esthetic judgment. >> Agree. If a machine exhibits *only* non-aesthetic behaviors then we would >> call it machine, not an AI machine. >> No one has the remotest clue how such a system could be built, even >> in principle. >> Not agree. How do you know that? Both those lines come from the post prior to mine, Nam. My apology. It's an overlook mistake on my part. Occidental is the man you want! > === Subject: Re: Technology Prophecy > By 2040 smart computers will develop a cure for cancer and > a virus that will halt the aging process, immortality for those > who can afford it. >> A wishful thinking! How could we trust smart computers would >> really care - and not plan to destroy - a species they're not of? > The takeover would be more subtle I think, nearly every desk job > could be done by computer. Unless you're doing something physical > in your job an AI can do it. There would be entire cities of retrenched > people, just networks talking to each other in paperless humanless offices. > Herc >> A machine cannot do wine tasting. It may eventually become possible to duplicate the performance of an > expert wine taster by analyzing the constituents of wine and > correlating with wine expert evaluations. The system thus created > would not, of course, duplicate the underlying human ability to > distinguish esthetically by taste; it would be entirely mindless and > parasitic (likewise, most of what are referred to these days as > robots are not robots at all but remote-controlled machines entirely > dependent on human abilities). The great AI accomplishment would be creating a machine that actually > had esthetic judgment. No one has the remotest clue how such a system > could be built, even in principle. The assumption among AI romantics > is that once we have enough computational power all these annoying > conceptual problems will go away, as though the hardware alone is what > matters, and the software will write itself, or the artificial neurons > will obligingly rearrange themselves into a configuration possessing > sentience. > Bob Kolker > But that's actually much more likely than the classical top-down approach where every possible situation is pre-supposed, and the reaction to that situation programmed directly (by hand). Take a look at what's going on at MIT. It's been clear for a while that the bottom-up folks have been on the rise, the top-down folks, waning. === Subject: Re: Technology Prophecy > Edsger Dijkstra once remarked that the question of > whether a computer can think is no more interesting > than the question of whether a submarine can swim. >> hmmmmmm. This POV has been more or less refuted by Searle's Chinese >> Room Thought Experiment, no? >> Not at all. I am not about to launch into a discussion of Searle. Let's >> just say I don't accept his conclusions, and my reasons have been stated >> by others. > Who? I told you, I am not going to discuss Searle. I don't consider it a useful discussion. If you read what I said elsethread, it is useless to argue over whether performing a chemical analysis is comparable to what a human does in tasting wine. By the same token, it is useless to argue over whether what a man/machine combination does in reading and answering questions in Chinese is comparable to what a native speaker of Chinese does. -- Dave Seaman Third Circuit ignores precedent in Mumia Abu-Jamal ruling. === Subject: Re: Technology Prophecy <8FOik.22914$IK1.5829@news-server.bigpond.net.au> posting-account=j25A5gkAAABMpeVaqCQC3Blw21WXwx6P Gecko/20050716,gzip(gfe),gzip(gfe) > Edsger Dijkstra once remarked that the question of > whether a computer can think is no more interesting > than the question of whether a submarine can swim. >> hmmmmmm. This POV has been more or less refuted by Searle's Chinese >> Room Thought Experiment, no? >> Not at all. I am not about to launch into a discussion of Searle. Let's >> just say I don't accept his conclusions, and my reasons have been stated >> by others. > Who? I told you, I am not going to discuss Searle. I don't consider it a > useful discussion. If you read what I said elsethread, it is useless to > argue over whether performing a chemical analysis is comparable to what a > human does in tasting wine. By the same token, errr...you are discussing it. Sorry to have to point that out. > it is useless to argue > over whether what a man/machine combination does in reading and answering > questions in Chinese is comparable to what a native speaker of Chinese > does. But why is it useless? (Feel free to explain why in the context of a response in which you maintain that you are *not* going to explain why). -- > Dave Seaman > Third Circuit ignores precedent in Mumia Abu-Jamal ruling. > === Subject: Re: Technology Prophecy > >>Edsger Dijkstra once remarked that the question of >>whether a computer can think is no more interesting >>than the question of whether a submarine can swim. hmmmmmm. This POV has been more or less refuted by Searle's Chinese >Room Thought Experiment, no? >>Not at all. I am not about to launch into a discussion of Searle. Let's >>just say I don't accept his conclusions, and my reasons have been stated >>by others. Who? >>I told you, I am not going to discuss Searle. I don't consider it a >>useful discussion. If you read what I said elsethread, it is useless to >>argue over whether performing a chemical analysis is comparable to what a >>human does in tasting wine. By the same token, > errr...you are discussing it. Sorry to have to point that out. >>it is useless to argue >>over whether what a man/machine combination does in reading and answering >>questions in Chinese is comparable to what a native speaker of Chinese >>does. > But why is it useless? (Feel free to explain why in the context of a > response in which you maintain that you are *not* going to explain > why). This subthread should probably be renamed whine tasting. === Subject: Linear algebra puzzle For an integer n>1, define two n-by-n square matrices C_n and D_n according to the pattern in these examples with n=5: C_5: 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 D_5: 1 -1 0 0 0 1 -1 0 0 0 1 -1 0 0 0 1 -1 0 0 0 1 -1 0 0 0 Show that (C_n + D_n)^n is the identity matrix. (There are no restrictions on the ring of scalars except that it contains a multiplicative identity, denoted by 1.) A solution is below. ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... Fix n and write C = C_n and D = D_n for short. CD = D and DD = 0. So, of the 2^n summands in the expansion of (C+D)^n, all are zero except those in which D appears only once or not at all, and those are C^n + DC^(n-1) + DC^(n-2) + ... + D = C^n + D(C^(n-1) + ... + 1) = C^n + D*(matrix of 1's only) = 1 + 0. === Subject: Re: Linear algebra puzzle posting-account=T49ZCQoAAAAu7lCXElhv8ePqLj_TS0Yc rv:1.8.1.16) Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > For an integer n>1, define two n-by-n square matrices C_n and D_n according > to the pattern in these examples with n=5: C_5: > 0 1 0 0 0 > 0 0 1 0 0 > 0 0 0 1 0 > 0 0 0 0 1 > 1 0 0 0 0 D_5: > 1 -1 0 0 0 > 1 -1 0 0 0 > 1 -1 0 0 0 > 1 -1 0 0 0 > 1 -1 0 0 0 Show that (C_n + D_n)^n is the identity matrix. (There are no restrictions > on the ring of scalars except that it contains a multiplicative identity, > denoted by 1.) You can replace all of the entries except for the first in the first column of D_n by arbitrary elements of the ring, and you still get (C_n + D_n)^n = identity. i.e. D_5: 1 -1 0 0 0 a -1 0 0 0 b -1 0 0 0 c -1 0 0 0 d -1 0 0 0 Derek Holt. A solution is below. ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... Fix n and write C = C_n and D = D_n for short. > CD = D and DD = 0. So, of the 2^n summands in the expansion of (C+D)^n, all > are zero except those in which D appears only once or not at all, and those > are > C^n + DC^(n-1) + DC^(n-2) + ... + D > = C^n + D(C^(n-1) + ... + 1) > = C^n + D*(matrix of 1's only) > = 1 + 0. === Subject: abc subject Cc: narus.test@gmail.com posting-account=WhtlvQoAAABro3gYhKoVZXO55NjhY9UH CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) abc message === Subject: Initial Solution Algorithms posting-account=LuMIjwoAAABCXbyr3sE3ZyA_HnoRMbfu InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) I am working on a non-linear programming problem using Solver. It takes too long to find the solution, sometimes the program can never find the global optimal. I think maybe I can improve it by assigning more accurate initial solution values. Does anyone know any Initial Solution Algorithms that are good for non- linear programming? === Subject: Re: Initial Solution Algorithms posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > I am working on a non-linear programming problem using Solver. It > takes too long to find the solution, sometimes the program can never > find the global optimal. > I think maybe I can improve it by assigning more accurate initial > solution values. > Does anyone know any Initial Solution Algorithms that are good for non- > linear programming? You did not say whether the constraints are linear or nonlinear. Problems with linear constraints but nonlinear objectives tend to be easier to deal with than problem that have nonlinear constraints. For problems having multiple local optima, people sometimes use randomly-generated starting points and then solve the problem several times, using these different starting points. Of course, this strategy does not always work, but it may be worth trying. It might not work well if you have nonlinear constraints, since getting from a random point to a feasible one may not be easy. R.G. Vickson === Subject: Re: Initial Solution Algorithms > I am working on a non-linear programming problem using Solver. It > takes too long to find the solution, sometimes the program can never > find the global optimal. > I think maybe I can improve it by assigning more accurate initial > solution values. > Does anyone know any Initial Solution Algorithms that are good for non- > linear programming? continuation methods could improve the situation. Alois === Subject: Re: More evidence proving Apollo Hoax posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) > Superior beings will not only eat us, but are eating us right now, and > have been doing so since day 1. > ET microbes and spores have likely been easting us alive and dead > since the the very get-go. Some micro-biological life have far greater genetic complexity than > humans. It could be ETs come in said form. [...] I'd have to agree with that analogy, because it will not be the 14,000 some odd species of ants, the 16,000 some odd species of bees or the nearly countless versions of those life essential diatoms that'll become the systematically orchestrated demise of this planet. I believe the human species is a very new and genetically frail addition to this otherwise highly survival intelligent populated planet. If we entirely emerged from the terrestrial random happenstance soup of life as we know it, it's clearly a sign of bad things to come because evolution has done us great wrongs, and that's within a fairly short period of time none the less. If any other significant species such as diatoms had become as untrustworthy and as dastardly bastards as we humans, whereas that too could have been the demise of life as we know it if such diatoms had killed themselves off. The one species of complex life on Earth that could be entirely removed without repercussions or negative consequences to the environment, is the human species. - Brad Guth Brad_Guth Brad.Guth BradGuth === Subject: Re: More evidence proving Apollo Hoax posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 5.0),gzip(gfe),gzip(gfe) this is true, but if there were a vacuum, no light could get through it; you are positing an empty (albeit popular) gedanken nonexperiment; there's no where, therein. black holes already consititute a form of dark matter, supposedly required to make gaglxies rotate in their inimitable fashion, in the theory according to the Department of Einsteinmania, the Musical Department, which doesn't deal with the experimentally varified physics of plasma, which constitute nines of Universe, per Alfven and company. how many other folks have a kind of wave, named after them? > Well ... I suspect that physicists smashing tiny little things into each > other reeally reaally fast have calculated to a rather high accuracy how > much mass they gain from how fast they go. Numerous other experiments > such as ones having to do with time dilation affecting various nuclear > decay rates have no doubt supplied additional data. So I think that even > though photons in a perfect vacuum haven't had their speed measured, the > speed they would go if such were available is known to a fairly high > precision. --Seargent Barracks Soros McCheeny Pepper, Give jihad a chance in The Sudan, Rhodesia, and other former colonial moments -- Yahoo!TM; you're going to feel my computerized draft, NO RHODESIA SCHOLARS IN HARM'S WAY! http://larouchepub.com/lar/2008/3526lar_soros_pamph.html http://larouchepub.com/other/2008/3526save_nations_parasites.html http://larouchepub.com/other/2008/3526zim_brit_op.html http://larouchepub.com/other/2008/3526zim_brit_op.html http://larouchepub.com/other/2008/3526zim_brit_op.html === Subject: Re: good introduction to formal grammars posting-account=wGddEwoAAADK3B4yHzD1RwTUeoTwWItW 1.1.4322),gzip(gfe),gzip(gfe) > The closest you might find to mathematical formulations in linguistics > was Montague Grammar, an attempt to meld symbolic logic with syntax/ > semantics. There were a couple of textbooks on it. would that be of any value to look at for symbolic maths and the use of specific notations in mathematical proofs === Subject: Re: good introduction to formal grammars posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > The closest you might find to mathematical formulations in linguistics > was Montague Grammar, an attempt to meld symbolic logic with syntax/ > semantics. There were a couple of textbooks on it. would that be of any value to look at for symbolic maths and the use > of specific notations in mathematical proofs It is of some related interest, but not most directly. Basically, no, Montague grammar is not the thing you should study to learn symbolic logic and formal mathematical proof. Rather, for that purpose, I highly recommend the book Logic: Techniques of Formal Reasoning by Kalish, Montague and Mar. (By the way, that is the same Montague as with Montague grammar.) If you study that book thoroughly, really master it, then I think it would change your life. Truly, I'm not exaggerating. It would give you the basic tools you need to write mathematics in clear, understandable symbolism and also to put your arguments in logical form. It is the best book I know of for that purpose. It is written in a quite clear way, practical, thorough, and rigorous (to just the right degree appropriate for the level of study). I recommend it as the first book to master before then going on the subjects of set theory and then mathematical logic. MoeBlee === Subject: Re: good introduction to formal grammars posting-account=tXYReAoAAABbl0njRzivyU02EBLaX9OF Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) > The closest you might find to mathematical formulations in linguistics > was Montague Grammar, an attempt to meld symbolic logic with syntax/ > semantics. There were a couple of textbooks on it. > would that be of any value to look at for symbolic maths and the use > of specific notations in mathematical proofs It is of some related interest, but not most directly. Basically, no, > Montague grammar is not the thing you should study to learn symbolic > logic and formal mathematical proof. Rather, for that purpose, I > highly recommend the book Logic: Techniques of Formal Reasoning by Kalish, Montague and Mar. (By the way, that is the same Montague as with Montague grammar.) If you study that book thoroughly, really master it, then I think it > would change your life. Truly, I'm not exaggerating. It would give you > the basic tools you need to write mathematics in clear, understandable > symbolism and also to put your arguments in logical form. It is the > best book I know of for that purpose. It is written in a quite clear > way, practical, thorough, and rigorous (to just the right degree > appropriate for the level of study). I recommend it as the first book > to master before then going on the subjects of set theory and then > mathematical logic. Do you know how this edition, by Mar, differs from the original by Kalish & Montague, which was my Logic class textbook at Cornell in 1970 or so? Even in those days, the topics covered by Kalish & Montague didn't suffice for the study of semantics, and people who were interested were encouraged to go on to Modal Logic. Fuzzy Logic was just being invented at the time. === Subject: Re: card(P(N)) = card(N), an elementary proof posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > No, I didn't get the flaw, but I am quite aware (am I wrong?) you have > given a formulation of Cantor's Theorem, as well as I am aware that > the fact that there is not a bijection P(N)~N is the salt of most > arguments around this topic. But *that* is the very culprit: as I'd > put it, you keep proving Cantor with Cantor. So, I have taken the > beast the other way 'round... > No. > Actually, one might say that the proof of Cantor starts with assuming > ~Cantor. > You are technically right, No he isn't. Here is the proof again: ----------------------------------------------------------------- > Theorem > If T is a set, and P(T) is the powerset of T, there is no function > mapping T onto P(T). Remark > We suppose that f:T->P(T) is any function mapping T to P(T) For n e N: Let: A {n} := { k e N | k < n } Let: A {n+1} := A {n} union { n } So: card(A {n+1}) = card(A {n}) + 1 in the finite case, and still: card(A {n+1}) = card(A {n}) for the infinite case. That your proof is not a proof by contradiction maybe is technically correct (though I am not convinced, given the nature of your initial assumption and how you close the argument). The substance, I believe, does not change: the general form of your argument is the same as - say- Wikipedia's, nor it is substantially different than the approach to the diagonal argument for the sake: you keep proving that there is something beyond the natural numbers by tacitly assuming what you are supposed to prove. > , then > show that there is an element of P(T) to which f does not map > anything, thus proving that f is not an onto mapping (surjection). > Whether T is a finite or infinite set makes no difference to the > proof. (Also note that while we could make this look like a proof by > contradiction, by supposing that f is onto, it's really better the > other way, because we construct a specific element to which f does not > map anything, so (I think?) the proof is OK for constructivists too.) Proof > Suppose f:T->P(T) is a function from T to its powerset. Then if a e T, > f(a) e P(T), so f(a) is a subset of T. Note that there are two possibilities regarding f(a): it might be any > subset, and thus may or may not include a itself as an element. So the > elements of T naturally fall into two classes, we'll call the idio-ts > and the alio-ts. Definitions > a e T is an idio-t if a e f(a) > a e T is an alio-t if a is not an element of æf(a) These are mutually exclusive cases, so every a is either an idio-t or > an alio-t. Now consider the subset C of T which is the set of alio-ts. Note: we could write everything so far in one (less readable) line > C = { x | x e T, x /e f(x) } æ //... æ/e means not an element of We now show that there is no element b of T such that f: b -> C (1) If b were an idio-t, it would have to be an element of C, but C is > the set of alio-ts so it isn't; contradiction. > (2) If b were an alio-t, if would not be an element of C, but C is the > set of alio-ts so it is; contradiction. Therefore f is not an onto mapping. But this is true of every > mapping f, so we have proved the nonexistence of an onto mapping, or > surjection if you want to be latinamerican about it. > QED > ----------------------------------------------------------------- Kindly indicate where I assume ~Cantor. In the Remark I explicitly > pointed out that it is *not* a proof by contradiction. The fact that you say so, of course doesn't make it true. Anyway, you should better ask hagman I guess. To me, that statement of his was quite clear, above all in that context, and not to be taken so strictly as you seem to do (in fact, I think it was in reply to my comments rather than yours). The general logic of all diagonal and related arguments is - in a broad sense - in the form of a reductio ad absurdum. Your argument does not seem to escape this logic. -LV Brian Chandler === Subject: Re: card(P(N)) = card(N), an elementary proof posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > you keep proving that there is > something beyond the natural numbers by tacitly assuming what you are > supposed to prove. No, we state EXPLICITLY our axioms and rules. Everything we prove is proven from EXPLICIT assumptions (axioms) and EXPLICIT rules. MoeBlee === Subject: Re: card(P(N)) = card(N), an elementary proof > For n e N: Let: A_{n} := { k e N | k < n } Let: A_{n+1} := A_{n} union { n } So: card(A_{n+1}) = card(A_{n}) + 1 in the finite case, and still: card(A_{n+1}) = card(A_{n}) for the infinite case. What infinite case? For every n in N, A_{n+1} is a finite set. === Subject: Re: card(P(N)) = card(N), an elementary proof <9utt84p355rcmjlqum1jj4ai70vue767t4@4ax.com> posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > Why? The result you're trying to prove is _false_ - you're not > going to be able to make a correct proof, because it's impossible > to prove something false. OFF! You and your stupid remarks. -LV === Subject: Re: card(P(N)) = card(N), an elementary proof Why? The result you're trying to prove is _false_ - you're not > going to be able to make a correct proof, because it's impossible > to prove something false. OFF! You and your stupid remarks. Does Julio then claim that it IS possible to prove something false? That is certainly what his remarks would seem to indicate. === Subject: Re: card(P(N)) = card(N), an elementary proof posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > Why? The result you're trying to prove is false - you're not > going to be able to make a correct proof, because it's impossible > to prove something false. > OFF! > You and your stupid remarks. Does Julio then claim that it IS possible to prove something false? No, he doesn't. How do *you* infer *that*? > That is certainly what his remarks would seem to indicate. That is the opposite of certain. BTW, have you finished with Mr WM? Julio is still waiting for you to address even one of the points he made. There, here and elsewhere. -LV === Subject: Re: card(P(N)) = card(N), an elementary proof > BTW, have you finished with Mr WM? Julio is still waiting for you to > address even one of the points he made. There, here and elsewhere. I do not find that any points have been made. If, for an arbitrary set S, P(S) is to denote the set of all subsets of S and for any two sets S and T, card(S) = card(T) requires the existence of a bijection between S and T, as is usual in standard set theories, then I do not find that Julio has made any points re his claim that card(P(N)) = card(N) that are sufficiently coherent as to require addressing. === Subject: Re: card(P(N)) = card(N), an elementary proof > Why? The result you're trying to prove is _false_ - you're not >> going to be able to make a correct proof, because it's impossible >> to prove something false. OFF! You and your stupid remarks. -LV It is remarkable how the habits of set theory cranks are always the same. === Subject: Re: card(P(N)) = card(N), an elementary proof Why? The result you're trying to prove is _false_ - you're not > going to be able to make a correct proof, because it's impossible > to prove something false. > OFF! >> You and your stupid remarks. >> -LV > It is remarkable how the habits of set theory cranks are always the same. > Crank: I want to show that the earth is flat. Ok, I failed _this time_. I think I have to consider a more sophisticated approach. Man: Why? What you're trying to show is _false_ (after all it's a well established fact that the earth is not flat) - you're not going to be able to to show what you want, because it's impossible to show (i.e. prove) something false. Crank: OFF! You and your stupid remarks. Well... B. -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Re: card(P(N)) = card(N), an elementary proof posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > Crank: I want to show that the earth is flat. Ok, I failed _this time_. > I think I have to consider a more sophisticated approach. YOU have repeatedly failed here. -LV === Subject: Re: card(P(N)) = card(N), an elementary proof posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > It is remarkable how the habits of set theory cranks are always the same. Self-fulfilling prophecies. Idiot. -LV === Subject: Re: card(P(N)) = card(N), an elementary proof posting-account=6xUtvgkAAAD_jypmLa2oo2HnrV0e8X9q rv:1.7.13) Gecko/20060414,gzip(gfe),gzip(gfe) > card(P(N)) = card(N), an elementary proof (and some fuzzy notation > here and there). > Without reading your attempt of proof in detail > Please, let me anyway point out that you are quoting the wrong > argument. The correct one is here: > the problem is and > stays always the fact that set theoretics claim to have a big bunch of > elements in a powerset of an infinite set which are not describable. > You are refering to uncountable numbers and similar concepts, right? > And uncountable sets of natural numbers. Do you mean an uncountable set of sets of natural numbers? > There cannot be an uncountable set of natural numbers. No, I don't mean _an_ uncountable set of natural numbers since everybody knows that this would be nonsense by definition. My sentence is very sloppy fomulated, I see. My apology for that. Informell, as I had written, better would be: And uncountable many sets of natural numbers. === Subject: Re: card(P(N)) = card(N), an elementary proof [...] > I do have read *many* introductory and less introductory books on > these matters, and I keep doing. That is simply *not* enough to write > down arguments correctly in the language of a specific discipline such > as mathematics. > > Now you can complain as much as you like, but the fact is: I do work, > I am neither a student nor a prof (no pun intended). That kind of > practice I have to do *here*, I have no other place to practice that: > no profs, no tutors, no collegues, no nothing, I have got *this* group > to practice and check my mathematics. > > Books alone are not enough. I have spent 30+ years of my recent life > reading and studing books, not just mathematics. It is not enough to > be a pro: you need to complement with practice! [...] There is a free on-line book that I think is a good introduction to propositional and predicate calculus, Hirst & Hirst's A Primer for Logic and Proof: http://www.mathsci.appstate.edu/~jlh/primer/hirst.pdf This will show you the correct notation to use when you discuss proofs here. If you are impatient, the actual axioms of propositional calculus, predicate calculus, and equality respectively are found on pp. 15-16, 51, & 64 (PDF pp. 21-22, 57, & 70). (Of course that doesn't mean one shouldn't read the rest of the book to grasp the axioms intuitively and learn how to use them in proofs.) These are the foundation of classical first-order logic, from which everything else in logic is derived and mathematical proofs are based on. To understand the pred. calc. axioms, the tricky concepts for a beginner are free variables (pp. 36-37, PDF pp. 42-43) and free for/substitution (pp. 48-51, PDF pp. 54-57). These are not difficult or deep, just a little tedious, but one must learn them to understand the axioms and do proofs correctly. Some useful theorems derived from the axioms are L1 through L24 for prop. calc. and K1 through K36 for pred. calc. There are plenty of exercises also. Set theory consists of additional axioms on top of these and is not given formally in this book. But predicate calculus is a prerequisite for it. There are other first-order logic systems based mainly on inference rules, called natural deduction and Gentzen systems, that some people prefer because they can be easier to work with directly in proofs. These are equivalent to and can be derived from the simpler system presented in this book. -- Norm http://us.metamath.org/email.html (Reply to author at this URL. The from address in this post is not valid.) === Subject: Re: card(P(N)) = card(N), an elementary proof <_dudnf_yGMkS-RPVnZ2dnUVZ_qDinZ2d@rcn.net> posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > There are other first-order logic systems based mainly on inference > rules, called natural deduction and Gentzen systems, that some people > prefer because they can be easier to work with directly in proofs. > These are equivalent to and can be derived from the simpler system > presented in this book. Norm, don't you agree that he'd do a lot better to start right from the beginning with an easy to understand natural deduction system such as in the Kalish, Montague, and Mar book? The web primer is okay for what it is, but for a really great treatment for beginners, I don't know of anything that beats Kalish, Montague, and Mar. MoeBlee === Subject: Re: card(P(N)) = card(N), an elementary proof > >> There are other first-order logic systems based mainly on inference >> rules, called natural deduction and Gentzen systems, that some people >> prefer because they can be easier to work with directly in proofs. >> These are equivalent to and can be derived from the simpler system >> presented in this book. > > Norm, don't you agree that he'd do a lot better to start right from > the beginning with an easy to understand natural deduction system such > as in the Kalish, Montague, and Mar book? The web primer is okay for > what it is, but for a really great treatment for beginners, I don't > know of anything that beats Kalish, Montague, and Mar. Actually I am not familiar with that book - from what you say it sounds good, and I'll make a point to look it up when I go to the library. I agree that natural deduction is a more practical working tool. My idea was partly that with a Hilbert-style system, there is less to learn if one just wants to see what the foundation or starting point is, in as simple a system as possible. Whether that is a good idea I guess is a matter of opinion. Also, an on-line book that anyone can access makes it easy for anyone to answer questions about the book and provides a consistent reference if questions of logical syntax or what constitutes a correct proof arise, both of which have been problems with his posts. Is there a good on-line introduction to natural deduction similar to the Hirst/Hirst book (or the Kalish, Montague, and Mar one)? -- Norm http://us.metamath.org/email.html (Reply to author at this URL. The from address in this post is not valid.) === Subject: Re: card(P(N)) = card(N), an elementary proof posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > I agree that natural deduction is a more practical working tool. æMy > idea was partly that with a Hilbert-style system, there is less to learn > if one just wants to see what the foundation or starting point is, > in as simple a system as possible. æWhether that is a good idea I guess > is a matter of opinion. Right, I had more in mind a book that would give him directly applicable techniques for forming mathematical arguments and for knowing that an argument is a valid first order argument. After that is acheived, I think it then becomes pertinent to learn about Hilbert style systems and mathematical logic in more generality. > Is there a good > on-line introduction to natural deduction similar to the Hirst/Hirst > book (or the Kalish, Montague, and Mar one)? I don't know of one. MoeBlee === Subject: Number of a form n!+i Let n>=2 and x_i=n!+i where i in {1,...,n}. Prove that for every x_i there is a prime p such that p|x_i and p does not divide any of {x_1,...,x_n}{x_i}. P.S. If x_i has a prime p>n than the statement holds since if p|x_j then p|(x_i-x_j) which is impossible since p>n. I do not know how to deal with the case where all prime divisors of x_i are less then n+1. === Subject: Number of a form n!+i Let n>=2 and x_i=n!+i where i in {1,...,n}. Prove that for every x_i there is a prime p such that p|x_i and p does not divide any of {x_1,...,x_n}{x_i}. P.S. If x_i has a prime p>n than the statement holds since if p|x_j then p|(x_i-x_j) which is impossible since p>n. I do not know how to deal with the case where all prime divisors of x_i are less then n+1. === Subject: Re: Number of a form n!+i > Let n>=2 and x_i=n!+i where i in {1,...,n}. > Prove that for every x_i there is a prime p > such that p|x_i and p does not divide any of > {x_1,...,x_n}{x_i}. Are you sure it's true? Have you tried it for small n? What is n=3? What if n=4? What if n=5? Have you tried it? Can you see the pattern? Or are you just staring at the problem and hoping it will become obvious? What have you tried? === Subject: Prime Sums, Al Zimmermann's Programming Contests. posting-account=7reEUQoAAADPec9tkt-M5k8UrEn3Uifh Gecko/20080716 SUSE/2.0.0.16-0.1 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) A new round of the Al Zimmermann's Programming Contests started today. The contest webpage is http://www.recmath.org/contest/index.php The task is to find n-tuples of integers a_i, such that there are as many distinct primes as possible among the 3^n sums a_i*c_i, where the coeffcients c_i may assume any of the 3 values -1,0,1. Example: The 4 numbers 10 29 82 106 produce 9 distinct primes: 5 = 106 + 10 - 82 - 29 19 = 29 - 10 29 = 29 43 = 82 - 29 - 10 53 = 82 - 29 67 = 106 - 29 - 10 101 = 82 + 29 - 10 149 = 106 + 82 - 29 -10 227 = 106 + 82 + 29 + 10 The detailed description can be found at http://www.recmath.org/contest/description.php . Hugo Pfoertner === Subject: Re: Prime Sums, Al Zimmermann's Programming Contests. Do negative numbers count as prime ? === Subject: Maximize a convex function in a convex set. posting-account=FVwbzwoAAABJyP6tQdKAo_Cb1jatQdR8 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) Hi everyone! I am working on a optimization problem where I try to maximize a convex function in a convex set. The problem is as follows: Maximize_{X=[x1,x2,...,xN]}: f_1(x1)+f_2(x2)+...f_n(xN) Subject to: g_1(x1)+g_2(x2)+...+g_n(xN)<=M I know that f_i(xi) and g_i(xi) are continious convex function of xi, where i=1,2,...,N. In such case, the feasible is convex (which is good) and the objective function if also convex (which is bad). I also know that as xi increases, g_i(xi) and f_i(xi) increases. We know that if the objective function is concave, it is classic convex optimization problem. But, in our case, the objective function is === Subject: Re: Maximize a convex function in a convex set. posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > Hi everyone! I am working on a optimization problem where I try to > maximize a convex function in a convex set. The problem is as follows: Maximize_{X=[x1,x2,...,xN]}: f_1(x1)+f_2(x2)+...f_n(xN) > Subject to: g_1(x1)+g_2(x2)+...+g_n(xN)<=M I know that f_i(xi) and g_i(xi) are continious convex function of xi, > where i=1,2,...,N. In such case, the feasible is convex (which is > good) and the objective function if also convex (which is bad). I also > know that as xi increases, g_i(xi) and f_i(xi) increases. We know that > if the objective function is concave, it is classic convex > optimization problem. But, in our case, the objective function is Minimizing convex f subject to convex g <= M is OK, if the functions are smooth. However, the MAXIMIZATION problem is NP-hard, so you face the problem of global optimization. To see this, suppose each g_i is linear, and each f_i(y) has the form c_i*y - M*y*(1-y). If M > 0, each f_i is strictly convex on 0 <= y <= 1, so if we have additional constraints of the form 0 <= x_i <= 1 for all i, and if M > 0, we have a problem of your type. However, if M is large the solution will occur at each x_i = 0 or 1, so your problem becomes a binary knapsack problem, which is NP-hard. R.G. Vickson === Subject: Generalizing Fermat's Little Theorem and Euler's Phi-Function generalization of Fermat's Little posting-account=Z3AipgkAAABkoMfyNwddSxsYhXHi5CDt CLR 1.1.4322; InfoPath.1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) Hi Group, I happened upon this interesting fact a couple of weeks ago (in the sense of discovered, although it is extremely unlikely to be new. It generalizes Fermat's little theorem in the form that a^p = a (mod p) where a is any integer and p is any prime. Euler generalized Fermat's little theorem as a^phi(n) = 1 (mod n) where a is any integer relatively prime to n, and n is any integer greater than 1. Notice that there is a difference here in that there is a restriction on a to be relatively prime to n, and that the congruence equality is to 1 and not to a. Also, Fermat's theorem implies Euler's theorem when n is prime. My obersvation is that, when a is any integer, and n is any integer greater than 1 and divisible by primes p_1, ..., p_s, then a^n - a^(n/p_1) - ... - a^*(n/p_s) + a^(n/(p_a*p_2)) + ... + a(n/ (p_s-1*p_s)) - ... -/+ a^(n/p_1*...*p_s) = 0 (mod n) Can you say inclusion / exclusion formula? The same that says that phi(n) is the sum of all the above exponents, so there must be a connection there somewhere. Notice that when n is prime, this reduces to Fermat's theorem. When n is a prime power, Euler's theorem is easily deducible from it. I have never seen this before, although I find it to be an amusing tidbit. I would be interested in finding out about its history. Achava Achava === Subject: General Diophantine solution sought Is there a general parametric solution to the Diophantine equation (1) ? (1) (a^2+b^2)(c^2-a^2)(c^2-b^2) = d^2 (a,b,c,d in Z) I have found 6 particular parametric solutions, but comparing their coverage with a computer search of (1) shows that they don't cover all the existing solutions for the searched range. I would like to find the general solution instead. === Subject: Fisher scoring algorithm posting-account=_OinCAoAAACBLmXVtLGncF7st-VYBBKI Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1) ),gzip(gfe),gzip(gfe) below (I transcribe the equation in mathematica notations): FullSimplify[ Sum[(1/(n! Gamma[[Alpha]]) z^ n [Beta]^[Alpha] (z + [Beta])^(-n - [Alpha]) Gamma[n + [Alpha]])*(PolyGamma[1, a] - PolyGamma[1, a + n]), {n, 0, Infinity}]] It's the product of the log of the 2nd derivative of alpha (from the likelihood) by the likelihood: negative binomial distribution (n is integer z is real, and likelihood and 2nd deriv should be products and sums respectively of many n(s) and z(s) but taken here as only one point for simplicity). This has come from a poisson-gamma marginal distribution, for which I am trying to find the (parameters) alpha and the beta by using the fisher scoring algorithm. But mathematica does not find a solution to the above. Do you think there is another way, maybe more traditional to solve this, Any hints or help appreciated. === Subject: the Science of Math-DR SALIL PANDE I have always found Math to be a fantastic venture. My father was a Mathematician and it drew me into the exact sciences. As a doctor I use math everyday and for some strange reason I find the concepts behind our most complex theories in math and science fascinating. Now, I don't want to be wishy-washy here, I just wanted to set up a post so that people who care about what I care about know how I feel. Nobody else I tell these things to cares, since my siblings were always on the more rebellious side. I think this is a great forum, all of you take care. as my work load goes down a bit I look forward to being a regular contributor to this site. Blessings, Dr. Salil Pande === Subject: Re: the Science of Math-DR SALIL PANDE >I have always found Math to be a fantastic venture. My father was a >Mathematician and it drew me into the exact sciences. As a doctor I >use math everyday and for some strange reason I find the concepts >behind our most complex theories in math and science fascinating. >Now, I don't want to be wishy-washy here, I just wanted to set up a >post so that people who care about what I care about know how I feel. >Nobody else I tell these things to cares, since my siblings were >always on the more rebellious side. I think this is a great forum, all of you take care. as my work load >goes down a bit I look forward to being a regular contributor to this >site. Blessings, Dr. Salil Pande Welcome! I've never been able to talk about maths either, not even (that's the problem) to other mathematicians. I'm trying to get into the habit of talking about it online, in the hope that I might eventually even be able to literally talk about it when an occasion arises to do so. Maths is indeed fascinating. -- Angus Rodgers Contains mild peril === Subject: Estimate the angle posting-account=o4ONhgoAAACZFxTdYOa4nsvzgVLhgGR2 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) http://i33.tinypic.com/28me0qb.png How close can you estimate the angle the back of the ladder makes off plumb? === Subject: Cancel Re: card(P(N)) = card(N), rev 2: a preliminary result -- For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list. (WM, sci.logic) === Subject: Relativity, The Einstein Hoax and Disc Aircraft posting-account=HZYXOQoAAAB0CZtsRCtABgys4tHYIT8J 3.2.0; .NET CLR 1.1.4322; InfoPath.2),gzip(gfe),gzip(gfe) I have got a freebie website. http://ianparker.g3z.com/Relativity/ http://ianparker.g3z.com/Relativity/aviation.htm for an account of disc aircraft (Completely classical) tells you how they REALLY work. http://ianparker.g3z.com/Relativity/hoax.htm Tells you the REAL motivations for The Einstein Hoax - Ian Parker === Subject: Re: Relativity, The Einstein Hoax and Disc Aircraft posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > I have got a freebie website. http://ianparker.g3z.com/Relativity/ http://ianparker.g3z.com/Relativity/aviation.htmfor an account of > disc aircraft (Completely classical) tells you how they REALLY work. http://ianparker.g3z.com/Relativity/hoax.htmTells you the REAL > motivations for The Einstein Hoax æ - Ian Parker What does GTR say about gravity? Well there are wormholes which are valid solutions of the Schwarzschild equation. Clueless. === Subject: Re: Relativity, The Einstein Hoax and Disc Aircraft > http://ianparker.g3z.com/Relativity/aviation.htm for an account of > disc aircraft (Completely classical) tells you how they REALLY work. > File not found > http://ianparker.g3z.com/Relativity/hoax.htm Tells you the REAL > motivations for The Einstein Hoax > File not found You fell into their little free website trap, didn't you? Soon Alex Trebek and Jessie Ventura will be arriving at your house to have a little talk about how deceptive Venus can appear to be in a dark sky...particularly during a solar eclipse, when gravity bends its light waves. ;-) Pat === Subject: Re: Relativity, The Einstein Hoax and Disc Aircraft posting-account=HZYXOQoAAAB0CZtsRCtABgys4tHYIT8J 3.2.0; .NET CLR 1.1.4322; InfoPath.2),gzip(gfe),gzip(gfe) > I have got a freebie website. http://ianparker.g3z.com/Relativity/ http://ianparker.g3z.com/Relativity/Aviation.htm for an account of > disc aircraft (Completely classical) tells you how they REALLY work. http://ianparker.g3z.com/Relativity/Hoax.htm Tells you the REAL > motivations for The Einstein Hoax æ - Ian Parker Erratum - The links do not work. These do. === Subject: Re: Relativity, The Einstein Hoax and Disc Aircraft > Erratum - The links do not work. These do. > Oh yeah... _now_ they do. Now that all the information on them has been changed. Don't blow your nose too hard or that tracking device might come right back on out of it. :-D Pat === Subject: Re: Relativity, The Einstein Hoax and Disc Aircraft posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1,gzip(gfe),gzip(gfe) which E-hoax -- of, by or for?... I just found a textbook at the bookstore, which was a zenith in the Department Einsteinmania, the Musical Department; basically, a sort of Physics Lite by way of Thus Spake Herr Doktor- proffessor Albert; large book, but large print & plenty graphics & photo-ops.... or, you could also say, nadir, or just Bipolar Express; unscroll me! yeah, nettttiket; don't make me link to your googolplex, just to get an inkling of the scan of the UPC on your cybersuite -- I might never get out, again! > Erratum - The links do not work. These do. thus: there are classical experiments, if that only means, it was done in the 19th CCE (PBUT .-)... um, what ever you guys were referring to, in your cut&paste DJ mixtape. anway, Haha, what floor was your office on?... eleven and above is certainly very safe, if the building doesn't fail monumentally; you mighty swell be surfing it; all is well that ends in the well, if you can swim & it's nondry. > I do not know of any experiment. thus: I had my 4th virtual lesson in surfing in two days, more or less, this one just watching the lone surferdood; I didn't wait for him to stand up, since he was clearly paddling-out in a minimax path to the correct wave. 4 axes would be a form of homogenous coordination, not entirely amenable to quaternions, AFAICT, for the point, which would minimally be a tetrasteron, and a sphere; how many points is that?... anyone work on the lunes demonstration of pythag.spatial? it's very tempting to just bum a board & go, but I'm retaining my ideal of surfcamp Maui, or some other island. or, we'll just make a stop on the bipolar express -- it's the IPY! === Subject: #23 energy content of Faraday Law is 1/3 larger than Coulomb law; making precise the Energy-Levels of Matter ; Fusion Barrier > > There is not tussle fight between Maxwell's Equations: all the equations are > always satisfied throughout the entire process. > That is not what a scientist should read into my descriptive language, my metaphor language. A Tokamak uses the Faraday Law in all aspects of controlling the machine. The only other Maxwell Law involved is the actual fusion which is the Coulomb law overcomed. So in a metaphorical sense a Tokamak is a tussle or fight between the Faraday law trying to control all aspects of the fusion events opposed by the Coulomb law. A Tokamak boiled down to its essential aspects is Coulomb law divided by Faraday Law. Where the Coulomb Law falls short by 1/3 of the Faraday Law. The Faraday Law is always 1/3 larger in energy content than the energy content of Coulomb law. And why is the Faraday and Ampere Laws always 1/3 larger in scope than the Coulomb Law? That is easy to explain, because Faraday and Ampere are the Coulomb law-in-Motion. The Faraday Law is simply a Dynamical-Coulomb Law, whereas the Coulomb Law is Static. So the energy content of the Faraday or Ampere Laws are always 1/3 larger than the corresponding Coulomb law of the given circumstances. Do you know enough mathematics Matthew, to be able to compute that the energy content of Faraday Law is 1/3 larger than energy content of Coulomb Law? Judging from your reply above, I seriously doubt you can even begin to entertain that thought. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom === Subject: Solvability by radicals over a field of nonzero characteristic I'm struggling (but not yet hopelessly) with an exercise in Joseph Rotman, /Galois Theory/ (2nd ed. 1998). This post isn't about the exercise itself (I want to struggle on, please!), but rather about an issue it raises, which seems quite complicated. A week or so ago, I posted about the previous exercise, because I wasn't sure I wasn't writing gibberish! This time, I /think/ I'm making sense, but the problem is that the exercise seems to involve more work than any other exercise in the book so far; I'm having to revise two previous chapters' worth of work that I /thought/ I had understood, and to re-examine the proofs of several quite tricky theorems, with the result that my chain of reasoning is becoming so long that I can't find an error that I /think/ I must be making. A lesser worry is that I may be making too much of the exercise - but I'm not asking about that, until I have resolved this greater worry. So, I won't yet discuss the exercise itself (because I don't yet know if I need to) - just the proofs of some theorems in the (unnumbered!) 13th chapter of Rotman's book, entitled Solvability by Radicals. It is proved later in the book (in the chapter entitled Galois's Great Theorem) that if F is a field of characteristic 0, and E/F is an extension whose Galois group is solvable, then E can be embedded in a radical extension of F. What I'm worried about is the converse result, which has already been proved, thus: Theorem 74. Let f(x) in F[x] be solvable by radicals over a field F of characteristic 0, and let E/F be its splitting field. Then Gal(E/F) is a solvable group. The proof seems correct - and I had no problem with it, the first couple of times I read this chapter - but the problem now is that I can see no need for its hypothesis that F has characteristic 0. (The exercise I have been working on is a counterexample to the converse: proving that, over a field of nonzero characteristic, a polynomial with solvable - indeed prime order cyclic - Galois group need not be solvable by radicals. But I haven't yet come across a counterexample to the statement of Theorem 74 minus its hypothesis of characteristic 0.) I can see where F having characteristic p =/= 0 involves making some slight changes in the proof; but its conclusion still seems to me to be valid. I'd like to know where I'm missing something. The proof of Theorem 74 depends heavily on this previous result: Lemma 73. Let F be a field of characteristic 0, let f(x) in F[x] be solvable by radicals, and let E be a splitting field of f(x) over F. (i) There is a radical tower F = R_0 subset R_1 subset ... subset R_t with E subset R_t, with R_t a splitting field of some polynomial over F [note: Rotman does not define the term normal extension], and with each R_i/R_{i-1} is [sic] a pure extension of prime type p_i. (ii) If R_t/F is a radical extension as in part (i), and if F contains the {p_i}th roots of unity for all i, then Gal(E/F) is a soluble group. Again, the problem is that I can't see where the hypothesis of characteristic 0 is needed. (I'm assuming all this material is very standard, and can be followed using a different text, otherwise this will be very difficult!) It is shown in some exercises at the end of this chapter that if f is solvable by radicals, then w.l.o.g. E is contained in the largest field of a radical tower in which that largest field is a splitting field of some polynomial in F[x], and in which each step is a pure extension of prime type. Although I did mess up these exercises the first time around (without even realising I'd done so!), I've gone over them again, and I am now pretty confident that not only is the hypothesis of characteristic zero never mentioned in them, but it is also genuinely never needed. So (i) above does not seem to require any such hypothesis; and I am not really worried about this part of Lemma 73; obviously more serious is the worry over part (ii). I am fairly certain that if F has characteristic p =/= 0, and if p_i =/= p for all i, then the proof goes through essentially without change. A quick glance at some other books on Galois theory seems to confirm this (but does nothing to reassure me as to the hypothesis of characteristic 0 being unnecessary!). The real difficulty concerns the case when p_i = p for some i. A straightforward argument /seems/ to show (but, who knows, I may have screwed even this apparently simple proof up) that if K is a field of characteristic p =/= 0, then {p}th roots are unique in any extension field of K (including K itself). (Just to spell it out, rather laboriously - I would lose sight of the main point if I stopped to edit this for style! - let E/K be an extension containing roots alpha, beta of x^p - c = 0. If c = 0, then alpha = beta = 0. So suppose c =/= 0. Then beta =/= 0, and 0 = 1 - 1 = c/c - 1 = (alpha^p)/(beta^p) - 1 = (alpha/beta)^p - 1 = (alpha/beta - 1)^p, therefore 0 = alpha/beta - 1, i.e. alpha = beta. Embarrassingly explicit!) So if, for some i, there exists c in R_{i-1} such that R_i = R_{i-1}(alpha) where alpha^p = c, then Gal(R_i/R_{i-1}) = {1} - whereas the proof as it stands requires that all the groups Gal(R_i/R_{i-1}) be cyclic groups of prime order. But I just don't see that this causes any real difficulty. (That is, the real difficulty is that I don't see any real difficulty!) It is still true, even in this case, that R_i is a splitting field of x^p - c over R_{i-1}. There aren't any {p}th roots of unity apart from 1, but we don't need any! The proof of part (ii) of Lemma 73 proceeds by defining G_i = Gal(R_t/R_i), where the notation is as in part (i), and noting that because by hypothesis F contains all the {p_i}th roots of unity for all i (I note that this is a vacuous - but not false! - assumption in the case of any i such that p_i = p), each R_i is a splitting field of some polynomial over R_{i-1}. I note that this remains true even in the case of any i such that p_i = p. (Because, if R_i = R_{i-1}(alpha), and c in R_{i-1}, and alpha^p = c, then x^p - c = (x - alpha)^p in R_i[x], so R_i is a splitting field for x^p - c over R_{i-1}. I'm squinting hard at this, but still can't see anything wrong with it. Do I need my eyes tested?) It follows that G_{i-1}/G_i ~= Gal{R_i/R_{i-1}) for all i. In particular G_i = G_{i-1} for any i such that p_i = p: but once again I just don't see that this causes any real problem. The sequence of subgroups: Gal(R_t/F) = G_0 superset G_1 superset ... superset G_t = {1} even though G_i = G_{i-1} for some i, still meets the definition of a normal series, and the factor groups are all either trivial or else cyclic of prime order, which seems to make the group G_0 solvable - to me - but I'm still pretty hazy about group theory. The proof of part (ii) of Lemma 73 finishes by observing that in the tower of fields F subset E subset R_t, Gal (E/F) is a quotient group of the soluble group Gal(R_t/F), therefore it, too, is soluble. Even typing all this out (and earnestly not wishing to make a fool of myself in sci.math!), I still can't see where it has made any important difference that p_i = p for some i. Where, in this thicket of unfamiliar logic, is my mistake lurking? As for the proof of Theorem 74 (statement above), there doesn't seem to be anywhere there for the mistake to hide, either. The proof recalls the notation of the statement and proof of Lemma 73, and defines m to be the lcm of all the p_i, and omega to be a primitive {m}th root of unity. Surely some danger lurks here? But it has been shown earlier (Corollary 63) that if m is any positive integer, then all the {m}th roots of unity in any field form a cyclic multiplicative group. Nothing is said about the characteristic of the field. Sure, Lemma 68 proves that x^m - 1 has m distinct roots in a splitting field over a field F when (and - an example given immediately after it shows - /only/ when) the characteristic of F is either 0 or a prime not dividing m. So we have to bear in mind that there are only m/p {m}th roots of unity, not m of them. But there is still a primitive {m}th root of unity. In fact, it is the same thing as a primitive {m/p}th root of unity. Let me be quite explicit about this, in case I'm going wrong: If m = pq, where p is a prime which does not divide q, then, over any field F of characteristic p, x^m - 1 = (x^q - 1)^p. By Lemma 68, x^q - 1 has q distinct roots in a splitting field over F (and there is a primitive {q}th root of unity); so the roots of x^m - 1 are the same as the roots of x^q - 1, each being repeated p times. I can't see anything wrong with this. Using that notation, omega is a primitive {q}th root of unity, where q is the product of all the distinct p_i, except for p. Continuing, then, to follow the book's proof of Theorem 74: The tower is lengthened by R' = R_t(omega), and then refined so that each pure extension in it has prime type. If R_t is a splitting field of h(x) in F[x], then R' is a splitting field of both (x^q - 1)h(x) and (x^m - 1)h(x) = ((x^q - 1)^p)h(x) in F[x]. The proof in the book continues (still seeming to require no significant modification): Construct a new tower by adjoining omega first: F = R_0 subset F(omega) subset R_1(omega) subset ... ... subset R_t(omega) = R' Each extension in the tower is pure, and E is contained in R'. Since F(omega)/F is a splitting field (of x_q - 1; equivalently, of x^m - 1), Gal(R'/F(omega)) is a normal subgroup of Gal(R'/F), and: Gal(R'/F)/Gal(R'/F(omega)) ~= Gal(F(omega)/F) By Theorem 69, which states that the Galois group of a simple extension of any field by any primitive root of unity is abelian (the important thing is that there are no special conditions on the characteristic of the field), Gal(F(omega)/F) is abelian, and therefore solvable. Now, considering the truncated tower: F(omega) subset R_1(omega) subset ... subset R_t(omega) = R' in which each step is a pure extension of prime type, we can apply part (ii) of Lemma 73 - which, as I /seem/ to have shown above, is unaffected by the fact that p_i = p for some i - and conclude that the normal subgroup Gal(R'/F(omega)) of Gal(R'/F) is soluble. By Theorem G.21 of the Appendix (Let G be a group with normal subgroup H. If H and G/H are solvable groups, then G is solvable.) it follows that Gal(R'/F) is solvable. Since Gal(E/F) is a quotient group of Gal(R'/F), it is solvable. Q.E.D. (but really?) I'm sorry about the extreme length of this post! Has anyone managed to read through it all, and if so, can they tell me where I've gone wrong? -- Angus Rodgers Contains mild peril === Subject: Re: Solvability by radicals over a field of nonzero characteristic posting-account=Z3AipgkAAABkoMfyNwddSxsYhXHi5CDt CLR 1.1.4322; InfoPath.1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > I'm struggling (but not yet hopelessly) with an exercise in Joseph > Rotman, /Galois Theory/ (2nd ed. 1998). æThis post isn't about the > exercise itself (I want to struggle on, please!), but rather about > an issue it raises, which seems quite complicated. A week or so ago, I posted about the previous exercise, because I > wasn't sure I wasn't writing gibberish! æThis time, I /think/ I'm > making sense, but the problem is that the exercise seems to involve > more work than any other exercise in the book so far; I'm having to > revise two previous chapters' worth of work that I /thought/ I had > understood, and to re-examine the proofs of several quite tricky > theorems, with the result that my chain of reasoning is becoming so > long that I can't find an error that I /think/ I must be making. A lesser worry is that I may be making too much of the exercise - > but I'm not asking about that, until I have resolved this greater > worry. æSo, I won't yet discuss the exercise itself (because I don't > yet know if æI need to) - just the proofs of some theorems in the > (unnumbered!) 13th chapter of Rotman's book, entitled Solvability > by Radicals. It is proved later in the book (in the chapter entitled Galois's > Great Theorem) that if F is a field of characteristic 0, and E/F > is an extension whose Galois group is solvable, then E can be > embedded in a radical extension of F. What I'm worried about is the converse result, which has already > been proved, thus: æTheorem 74. æLet f(x) in F[x] be solvable by radicals over a > æfield F of characteristic 0, and let E/F be its splitting field. > æThen Gal(E/F) is a solvable group. The proof seems correct - and I had no problem with it, the first > couple of times I read this chapter - but the problem now is that > I can see no need for its hypothesis that F has characteristic 0. (The exercise I have been working on is a counterexample to the > converse: proving that, over a field of nonzero characteristic, > a polynomial with solvable - indeed prime order cyclic - Galois > group need not be solvable by radicals. æBut I haven't yet come > across a counterexample to the statement of Theorem 74 minus its > hypothesis of characteristic 0.) I can see where F having characteristic p =/= 0 involves making > some slight changes in the proof; but its conclusion still seems > to me to be valid. æI'd like to know where I'm missing something. The proof of Theorem 74 depends heavily on this previous result: æLemma 73. æLet F be a field of characteristic 0, let f(x) in > æF[x] be solvable by radicals, and let E be a splitting field > æof f(x) over F. æ(i) There is a radical tower æ æ æF = R 0 subset R 1 subset ... subset R t æwith E subset R t, with R t a splitting field of some polynomial > æover F [note: Rotman does not define the term normal extension], > æand with each R i/R {i-1} is [sic] a pure extension of prime type > æp i. æ(ii) If R t/F is a radical extension as in part (i), and if F > æcontains the {p i}th roots of unity for all i, then Gal(E/F) is > æa soluble group. Again, the problem is that I can't see where the hypothesis of > characteristic 0 is needed. (I'm assuming all this material is very standard, and can be > followed using a different text, otherwise this will be very > difficult!) It is shown in some exercises at the end of this chapter that > if f is solvable by radicals, then w.l.o.g. E is contained in > the largest field of a radical tower in which that largest > field is a splitting field of some polynomial in F[x], and in > which each step is a pure extension of prime type. æAlthough > I did mess up these exercises the first time around (without > even realising I'd done so!), I've gone over them again, and > I am now pretty confident that not only is the hypothesis of > characteristic zero never mentioned in them, but it is also > genuinely never needed. So (i) above does not seem to require any such hypothesis; and > I am not really worried about this part of Lemma 73; obviously > more serious is the worry over part (ii). I am fairly certain that if F has characteristic p =/= 0, and > if p i =/= p for all i, then the proof goes through essentially > without change. æA quick glance at some other books on Galois > theory seems to confirm this (but does nothing to reassure me > as to the hypothesis of characteristic 0 being unnecessary!). The real difficulty concerns the case when p i = p for some i. A straightforward argument /seems/ to show (but, who knows, I > may have screwed even this apparently simple proof up) that if > K is a field of characteristic p =/= 0, then {p}th roots are > unique in any extension field of K (including K itself). (Just to spell it out, rather laboriously - I would lose sight > of the main point if I stopped to edit this for style! - let > E/K be an extension containing roots alpha, beta of x^p - c = 0. æ > If c = 0, then alpha = beta = 0. æSo suppose c =/= 0. æThen > beta =/= 0, and 0 = 1 - 1 = c/c - 1 = (alpha^p)/(beta^p) - 1 > = (alpha/beta)^p - 1 = (alpha/beta - 1)^p, therefore 0 = > alpha/beta - 1, i.e. alpha = beta. æEmbarrassingly explicit!) So if, for some i, there exists c in R {i-1} such that R i = > R {i-1}(alpha) where alpha^p = c, then Gal(R i/R {i-1}) = {1} > - whereas the proof as it stands requires that all the groups > Gal(R i/R {i-1}) be cyclic groups of prime order. æBut I just > don't see that this causes any real difficulty. (That is, the > real difficulty is that I don't see any real difficulty!) It is still true, even in this case, that R i is a splitting > field of x^p - c over R {i-1}. æThere aren't any {p}th roots > of unity apart from 1, but we don't need any! The proof of part (ii) of Lemma 73 proceeds by defining G i = > Gal(R t/R i), where the notation is as in part (i), and noting > that because by hypothesis F contains all the {p i}th roots of > unity for all i (I note that this is a vacuous - but not false! > - assumption in the case of any i such that p i = p), each R i > is a splitting field of some polynomial over R {i-1}. æI note > that this remains true even in the case of any i such that p i > = p. (Because, if R i = R {i-1}(alpha), and c in R {i-1}, and > alpha^p = c, then x^p - c = (x - alpha)^p in R i[x], so R i is > a splitting field for x^p - c over R {i-1}. æI'm squinting hard > at this, but still can't see anything wrong with it. æDo I need > my eyes tested?) It follows that G {i-1}/G i ~= Gal{R i/R {i-1}) for all i. æIn > particular G i = G {i-1} for any i such that p i = p: but once > again I just don't see that this causes any real problem. æThe > sequence of subgroups: æGal(R t/F) = G 0 superset G 1 superset ... superset G t = {1} even though G i = G {i-1} for some i, still meets the definition > of a normal series, and the factor groups are all either trivial > or else cyclic of prime order, which seems to make the group G 0 > solvable - to me - but I'm still pretty hazy about group theory. The proof of part (ii) of Lemma 73 finishes by observing that > in the tower of fields F subset E subset R t, Gal (E/F) is a > quotient group of the soluble group Gal(R t/F), therefore it, > too, is soluble. Even typing all this out (and earnestly not wishing to make a > fool of myself in sci.math!), I still can't see where it has > made any important difference that p i = p for some i. Where, > in this thicket of unfamiliar logic, is my mistake lurking? As for the proof of Theorem 74 (statement above), there doesn't > seem to be anywhere there for the mistake to hide, either. The proof recalls the notation of the statement and proof of > Lemma 73, and defines m to be the lcm of all the p i, and omega > to be a primitive {m}th root of unity. Surely some danger lurks here? æBut it has been shown earlier > (Corollary 63) that if m is any positive integer, then all the > {m}th roots of unity in any field form a cyclic multiplicative > group. æNothing is said about the characteristic of the field. Sure, Lemma 68 proves that x^m - 1 has m distinct roots in a > splitting field over a field F when (and - an example given > immediately after it shows - /only/ when) the characteristic > of F is either 0 or a prime not dividing m. So we have to bear in mind that there are only m/p {m}th roots > of unity, not m of them. æBut there is still a primitive {m}th > root of unity. æIn fact, it is the same thing as a primitive > {m/p}th root of unity. Let me be quite explicit about this, in case I'm going wrong: If m = pq, where p is a prime which does not divide q, then, > over any field F of characteristic p, x^m - 1 = (x^q - 1)^p. > By Lemma 68, x^q - 1 has q distinct roots in a splitting field > over F (and there is a primitive {q}th root of unity); so the > roots of x^m - 1 are the same as the roots of x^q - 1, each > being repeated p times. æI can't see anything wrong with this. Using that notation, omega is a primitive {q}th root of unity, > where q is the product of all the distinct p i, except for p. Continuing, then, to follow the book's proof of Theorem 74: The tower is lengthened by R' = R t(omega), and then refined so > that each pure extension in it has prime type. æIf R t is a > splitting field of h(x) in F[x], then R' is a splitting field of > both (x^q - 1)h(x) and (x^m - 1)h(x) = ((x^q - 1)^p)h(x) in F[x]. The proof in the book continues (still seeming to require no > significant modification): Construct a new tower by adjoining omega first: æF = R 0 subset F(omega) subset R 1(omega) subset ... > æ æ æ... subset R t(omega) = R' Each extension in the tower is pure, and E is contained in R'. > Since F(omega)/F is a splitting field (of x q - 1; equivalently, > of x^m - 1), Gal(R'/F(omega)) is a normal subgroup of Gal(R'/F), > and: æGal(R'/F)/Gal(R'/F(omega)) ~= Gal(F(omega)/F) By Theorem 69, which states that the Galois group of a simple > extension of any field by any primitive root of unity is abelian > (the important thing is that there are no special conditions on > the characteristic of the field), Gal(F(omega)/F) is abelian, > and therefore solvable. Now, considering the truncated tower: æF(omega) subset R 1(omega) subset ... subset R t(omega) = R' in which each step is a pure extension of prime type, we can > apply part (ii) of Lemma 73 - which, as I /seem/ to have shown > above, is unaffected by the fact that p i = p for some i - and > conclude that the normal subgroup Gal(R'/F(omega)) of Gal(R'/F) > is soluble. By Theorem G.21 of the Appendix (Let G be a group with normal > subgroup H. æIf H and G/H are solvable groups, then G is solvable.) > it follows that Gal(R'/F) is solvable. Since Gal(E/F) is a quotient group of Gal(R'/F), it is solvable. Q.E.D. (but really?) I'm sorry about the extreme length of this post! æHas anyone > managed to read through it all, and if so, can they tell me > where I've gone wrong? -- > Angus Rodgers > Contains mild peril Hi Angus, I'm not feeling too well today, so I didn't make it all the way through your post. My recollection of Galois theory is that you want to ensure that your extension is normal and separable. People's definitions of normal vary from some texts to others. In many, normal simply means the splitting field of some polynomials. Separable is useful in that it impies that that the field can be obtained by adjoining a single element from the larger field. In a field of characterstic 0, all extensions are separable. This is not true in charactersitic p, and since it is possible for the degree of the esxtension to be divisible by p, this can cause problems. Hope this helps, Achava === Subject: Re: Solvability by radicals over a field of nonzero characteristic >> I'm sorry about the extreme length of this post! æHas anyone >> managed to read through it all, and if so, can they tell me >> where I've gone wrong? Hi Angus, I'm not feeling too well today, so I didn't make it all the way >through your post. Don't worry about it: I'm amazed that I made it through writing it (my attention was starting to flag at the end), and I doubt if I could have read through it if someone else had written it (and I'm not even feeling unwell today!). >My recollection of Galois theory is that you want >to ensure that your extension is normal and separable. People's >definitions of normal vary from some texts to others. In many, normal >simply means the splitting field of some polynomials. Separable is >useful in that it impies that that the field can be obtained by >adjoining a single element from the larger field. In a field of >characterstic 0, all extensions are separable. This is not true in >charactersitic p, and since it is possible for the degree of the >esxtension to be divisible by p, this can cause problems. What /seems/ to be true is that some of the steps in the tower of fields are trivial ones - in that the Galois group of that extension is trivial - but this doesn't /seem/ to affect the result. But I find it very hard to believe that this could be true, without any of the books on Galois theory mentioning it, even in passing! (Not that I did an extremely thorough search.) It seems much more likely that I've just goofed in some horribly embarrassing way. But usually I'm quite good at least sniffing out, vaguely, where I've goofed; and this time I haven't a clue. Everything /seems/ to check out. So I have to hypothesise that my checking just isn't good enough. -- Angus Rodgers Contains mild peril === Subject: girls = boys in math posting-account=JpxxPAgAAAAgwzQIYqn4j6syK-YhOmcF Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) http://www.theonion.com/content/amvo/girls_boys_in_math === Subject: Re: New math. Dont read this. [...] > existence exists : tautology > nonexistence is nonexistent : tautology > indeterminate existence exists indeterminately : tautology These are not tautologies, these are type errors. Existence is a property of physical objects, its not a property of abstract objects like existence. For example the following make equal sence. Redness is red Hungriness is hungery === Subject: Re: New math. Dont read this. | [...] | | > existence exists : tautology | > nonexistence is nonexistent : tautology | > indeterminate existence exists indeterminately : tautology | | These are not tautologies, these are type errors. What do you say they were for then, you snipping head? === Subject: Re: New math. Dont read this. posting-account=tCEoyAoAAAAkltU5zxOoI8uJ4lyz5-kv .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > [1] Existence exists. æ (see Ayn Rand) > Right. > [2] Existential indeterminacy may or may not exist. > Wrong. > Besides, if it is an axiom it cant really be wrong. > I can use this to : > [2] model gravity waves > [3] model randomness as if it were a fluid which propagates in the > medium of dimensions length & time > [4] make statements regarding continuity of spacetime > [6] explains eraser and double eraser experiments > [7] etc etc etc > So - even if it is not neccesarily valid mathematics, it sure seems > to explain nature pretty well, and in fact my analysis is specifically > designed so that it is ambiguous as to whether or not is it math at > all. > So, if I am wrong, I would like to know why. > Go ahead and give me a D, > or an F, or whatever you want. But I do need to see a reason, > otherwise your opinion will be discarded. No marks, I'm not a Prof! Just arguing :) [1.n] Existence, as a notion, exists. > [2.n] Existential indeterminacy, as a notion, exists. > [3.n] Non-existence, as a notion, exists. [1.f] Existence, as a fact, exists: I exist. > [2.f] Existential indeterminacy, as a fact, exists: You might or > might not exist. > [3.f] Non-existence, as a fact, exists: He is not with us anymore. This is not even mathematical logic anyway. I wouldn't know at once > how to qualify it, but I'd say no axioms are allowed. -LV Youre right, it's not quite mathematical logic. One step closer to being logic is to consider points. [1.p] Points which exist ... are existent. [2.p] Points which do not exist...are nonexistent. [3.p] Points which exist indeterminately (ie exist probabilistically).....existentially indeterminate. In a way it does sound a bit nonsensical to speak of the existence of existence, one should speak of the existence of points, planes, lines, solutions...etc. Well, however you look at it it seems like the tautologies are still intact. Some interesting implications : [1.p] => a logical world of the existent, things can be proved [2.p] => a logical world which may or may not be valid because it may or may not exist. Borrows heavily from the mathematics of the existent, but proof is impossible in this area. [3.p] => world of nonsense, round squares, 4sided triangles, etc But the thing that really bugs me is that all 3 of these things are tautologies. I dont have any idea where you could go with that. === Subject: Welcome to . These suggestions may help you. [18] æææææThese notes are not official in any way, but if you are new to this group you may find them helpful. 1. æææMessages posted to may be about mathematics at any level. æPlease don't post OT (off-topic) messages about other things. æææææBe cautious about cross-posting (posting the same message to more than one news group) - see section 5 below. æææææSome questions may do better in a more specialized news group such as , , or . 2. æææYour title should show what sort of mathematics is in your message. æFor example, -- Differentiating trig functions is a good title, but -- Help! is a bad title. æææææAlso, two dashes and a space at the beginning of your title will 3. æææTyping mathematical formulae may not be easy. Use æ^ æfor powers, for example æaaaa = a^4 . 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[Suggestions for shortening or clarifying these brief notes are welcome.] === Subject: Re: The Roswell fraud, the Nazis and the CIA posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1,gzip(gfe),gzip(gfe) that's what I meant; Ockham's thingy doesn't allow for the rejection of any experimental data, unless that data was shown to be improperly acquired or used, or dysinterpreted per the phenomena being considered; kowabunga -- no simpler than necessary! so, if you're in a superposition of not looking at the cat & looking at it, 'swell as possibly not really caring so much for cats, or hunting big game ... may be, you have an obsessive-repulsive dysorder? put the mental picture of Schroedinger's cat, down! thus, for instance: you could find a suitable section of the Mandelbrot set, to attach the 3 similar ones to the right trigon; I'm going to do that, just as soon as I can find the fractal compasses!... seriously, there's a common method to generate the M-set, using (overlapping?) circles to make the complement of the M-set, which gives a picture that looks, like the pointilistical one. but, all of this is somewhat informal, due to the FLOPs specification, which is IEEE-755, I think, by -855, which I have never seen, since I don't have their online database available. > now, apply it to the spatial cases. thus: which E-hoax -- of, by or for?... I just found a textbook at the bookstore, which was a zenith in the Department of Einsteinmania, the Musical Department, Act One: Obomanauticus, the Far Side of the Moon ... just kidding; basically, a sort of Physics Lite by way of Thus Spake Herr Doktor- proffessor Albert; large book, but large print & plenty graphics & photo-ops.... or, you could also say, nadir, or just Bipolar Express; unscroll me! yeah, nettttiket; don't make me phreak on your googolplex, just to get an inkling of the scan of the UPC on your cybersuite -- I might never get out, again! > Erratum - The links do not work. These do. thus: there are classical experiments, if that only means, it was done in the 19th CCE (PBUThat***** .-)... um, what ever you guys were referring to, in your cut&paste VJ mixtape. anway, Haha, what floor was your office on?... eleven and above is certainly very safe, if the building doesn't fail monumentally; you mighty swell be surfing it; all is well that ends in the well, if you can swim & it's nondry. > I do not know of any experiment. thus: I had my 4th virtual lesson in surfing in two days, more or less, this one just watching the lone surferdood; I didn't wait for him to stand up, since he was clearly paddling-out in a minimax path to the correct wave. 4 axes would be a form of homogenous coordination, not entirely amenable to quaternions, AFAICT, for the point, which would minimally be a tetrasteron, and a sphere; how many points is that?... anyone work on the lunes demonstration of pythag.spatial? it's very tempting to just bum a board & go, but I'm retaining my ideal of surfcamp Maui, or some other island. or, we'll just make a stop on the Bipolar Xpress -- it's the IPY! === Subject: Re: The Roswell fraud, the Nazis and the CIA posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 5.0),gzip(gfe),gzip(gfe) a meaningless thoughfragment?... I mean, it sort of evokes Broglie's guide wave, or Bohm's ideals, but I don't consider those to be really necessary and, in any case, not necessarily at the same time. after all, they are dual *mathematically*, as in the two-column proofs of projective geometry; they're simply equivalent. yes, all of these theories are interpreting the same reality, Universe; to pluralize that definition is itself an absurdity. > A simple way to interpret Heisenberg's findings is to consider > probability. æThe position is where the wave is concentrated, yet > the wave has associated with it a wavelength - and so, its position > and momentum is spread out in spacetime which Heisenberg > showed meant that momentum and position cannot be known > with absolute certainty. === Subject: Re: The Roswell fraud, the Nazis and the CIA posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 5.0),gzip(gfe),gzip(gfe) I do not presently have time to read from your learned response. I had realized that I am probably doing a dysservice to the Solopsists -- I'm sure it's not a totally pointless philiosphy -- but i'm just referring to the gist of their argument, Universe is all in my head -- tee-hee! thus: good observational, it applies to the perimeters of the figures on the sides of the trigons etc. the main thing is that it applies to any similar figures, whatsoever; your special case was built on a 45-degree right trigon (equiangular & equilateral). the *really* main thing is that you have to construct the circles, in any case, to actuallly construct the proof with compasses, so that Hipparchus' proof is the minimal effort. essentially, Einstein's proof, which is actually in Eculid, but not labelled per the pythag. theorem, and which would have been seen by him in the gymnasium, is the same as Hipparchus, only it is merely diagrammatical, without bothering with the constructive part of it. now, apply it to the spatial cases. === Subject: Re: The Roswell fraud, the Nazis and the CIA posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) > Moon is as physically dark as coal? > No - not in the least. > Dark coals - like charcoal - is around 4% - about the same as fresh > asphalt. The moon's Lambert albedo is around 7.2% - but because > nearly all objects on the lunar surface have the first few millimeters > filled with pores - light enters and exits again, allowing much of the > light coming from the sun, to be scattered at low angles. So, if you > look at the lunar surface not straight on, but at an angle relative to > the incident light - you get over 11% of the light back when the > appropriate tests are done. . > Photographing objects on the lunar surface would be as difficult as > photographic objects in a conifer forest on Earth - they have the same > average albedos. > The moon is 3x birghter than asphalt - about as dark as weathered > asphalt after its been in the sun a few years. >http://www.historic101.com/Cuesta/Cuesta South/Location B.htm > Which makes it about as bright as a meadow or sandy beach. >http://jeff.medkeff.com/astro/lunar/obs tech/albedo.htmhttp://en.wiki... > Ice, snow, clouds - have very high reflectivities. > Water, wet soil, forests, - have very low reflectivities. > Sample albedos > Surface Typical Albedo > Fresh asphalt/charcoal 0.04 > Conifer forest (Summer) 0.08 > Worn asphalt 0.12 > Bare soil 0.17 > Green grass 0.25 > Desert sand 0.40 > New concrete 0.55 > Fresh snow 0.80[CapitalEth]0.90 > Of course just as on Earth, different parts of a planet have different > albedos, > On the moon we have; > Darkest areas: 8.6% - 2x brighter than charcoal > Tranquillitatis south of Plinius: 9.1% > Plato's floor: 9.6% > Serenitatis east of Linne: 10% > Imbrium south of Plato: 10.4% > Nectaris: 11.4% - near the average for the moon > Ptolemaeus floor: 13.1% - 3x brighter than charcoal > Arzachel: 17% -4x brighter than charcoal > Tycho ejecta: 20% -5x brighter than charcoal > Aristarchus: 20% > Aristarchus interior: 22% > Bright spot in Deslandres: 24% - brighter than green grass > Proclus E wall: 28% > Stevinus A, Abulfeda E: 30% - 6x brighter than charcoal > So, while older textbooks using inappropriate measuring procedures can > be found that quote 7% to 8% - these numbers are artificially low when > one does a more modern measurement that takes into account phase angle > - and arives at a proper value of 11% > The albedo of planets, satellites and asteroids can be used to infer > much about their properties. > The study of albedos, their dependence on > wavelength, > lighting angle (phase angle), and > variation in time > comprises a major part of the astronomical field of photometry. > For small and far objects that cannot be resolved by telescopes, much > of what we know comes from the study of their albedos. For example, > the absolute albedo can indicate the surface ice content of outer > solar system objects, the variation of albedo with phase angle gives > information about regolith properties, while unusually high radar > albedo is indicative of high metallic content in asteroids. > The overall albedo of the Moon is around 11%, but it is strongly > directional and non-Lambertian, displaying also a strong opposition > effect. They are typical of the regolith surfaces of airless solar > system bodies - and to observers on the surface, the brightness of > that surface is rather high. > For anyone who believes the moon is as dark as charcoal, please go out > on a dark night of any full moon, and look at the moon in the sky. It > will appear white against the dark skies. > For anyone who believes the moon is too dark to wash out stars - > compare the number of stars you can see on a clear moonless night to > the number of stars you can see on a night when there's a full moon. > These are rather simple observations to make - its surprising that > anyone who had troubled themselves to actually look at the sky would > believe the bull Guthball has been repeating and repeating for > years and years. > I gave you all five gold stars because you're an absolute idiot/moron > of the first order. > - Brad Guth Brad Guth Brad.Guth BradGuth- Hide quoted text - > - Show quoted text - I think this response marks you out as the very thing you are calling > me Brad. I mean what about the difference between 4% and 11% can't > you understand? At the sea of tranquility, its more like 16% - 4x > brighter than coal - and brighter even than a meadow or worn asphalt. Go out an actually LOOK at the moon on a dark night. It appears white > in the black sky. Look at the number of stars you can see near it. > Now imagine the number of stars you'd be able to see if you were > located on that brilliant surface! Sunlight, nearly twice as intense > as on the surface of cloudy Earth is reflected with the same > efficiency as a brightly lit meadow - with 2x the amount of sunlight > at the surface! While if you take care to let your eyes be dark > adapted by shielding them from this surface, you might see a star or > two - it is absolute rot to believe that cameras adjusted not to > overexpose themselves on the lunar surface would be able to pick up > anything other than nearby Earth reliably. Do the numbers dude. At sea level about 850 watts per square meter of direct sunlight > illuminates the surface around you. About 120 watts to 140 watts per > square meter is reflected from a meadow or worn asphalt on a clear > sunny day near sea level. Water reflects far less,about 85 watts per > square meter - except at shallow angles - even so, you can get a > sunburn from water relfection if you're not careful.. On the moon 1,366 watts per square meter of direct sunlight > illuminates the surface. No air. No clouds. Between 200 and 300 > watts per square meter is reflected from the lunar surface - depending > on what you're looking and the direction you are seeing it relative to > the angle of sunlight. This is twice a bright as a meadow - or an > old parking lot - on a summer's day. Even without the blue sky > above, would a camera adjusted to take properly exposed pictures in > this environment be capable of registering stars? Obviously not! Sorry Spongebob - you just aren't thinking clearly on this subject - I > hope this helps. In other words, to the unfiltered Kodak eye (actually outfitted with a polarized element that should have made the moon record on film as though substantially darker than coal), the regular laws of physics and of the best available peer replicated science that's outside of your NASA still do not count. Are you deathly afraid to look at those JAXA/Selene images, as well as at countless others that oddly do not match up to anything of your NASA/Apollo EVA Kodak moments? Coal black is still coal black, no matters if it's situated on Earth, Mars, Venus or that of our moon. In other words, albedo is albedo, no matters where the reflective surface is situated. On the other hand, now I understand, that you're also a born-again liar, as well as a Zionist/Nazi or simply another retired brown-nosed spook/mole from DARPA. - Brad Guth Brad Guth Brad.Guth BradGuth === Subject: Re: The Roswell fraud, the Nazis and the CIA posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1,gzip(gfe),gzip(gfe) what, you only would have gone to Marshall, just before thtey lost those movies & slides in a box?... otherwise, you rely solely on your DARPAsim of orbital mechanics, using the floating-point ops in your desktop unit, and what ever they remembered to program? like, if you were a quadripalegic, I'd dig it. I mean, you sound as if you're old enough to have live through the televization of the landings, but you seem to young to have recalled. === Subject: Re: The Roswell fraud, the Nazis and the CIA posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1,gzip(gfe),gzip(gfe) maybe you were thinking of Bersenheig's Principle Uncertainty; name any other pair of corelative functions -- or covarying -- that can be applied to some system. or a pair of systems, or at least two systems. and, there was a movie about this, Scanners, which was suppsoedly a metaphor on Reading Dynamics TM.... thus, I prefer to call it, Schroedinger's Head Gasket. you make use of a wave that has no actual shape, which is, like, really cool, if you're sitting in the Bay waiting for that function to collapse, dood, and you can just console yourself with the ideal, it's in a quantum state of I'm actually surfing, Mom, and I'm really not surfing, at all ... dood -- Kowabunga, so, I'm paddle-boarding ... with a sail ... and a titanium rotor! I'm telling the cat people about your problem, of not being able to observe one God-am cat at a time; they'll probably refer me to the SPCA, or Catwoman, so, What should I say? anyway, how can you say that many worlds is not a form of the Copenhagenschool reification?... OK, it's infinitely more elaborate ... depending upon how many Solopsists are floating around in your pool. um, I'm referring to guests -- don't experiment upon'em!... so, anyway, I did learn how to invert a square matrix, if you mean an N by N one ... but I forgot, becuase I don't use such things. there's mathematics, which is the four subjects that eliminate the trivium (as a study), and then there's what ever math, you say, you think, I should learn. may be I should, Daddy!... now, I recall; it's just a use of Gaussian elimination, til you get your X (which could be a matrix, or a scalar value.-) > Now when dealing with quadrillions of atoms - and a detector > we can see a rate of decay - the trouble only comes when we > look at a single atom - or a single cat - and observe it for a period > of time... æBOTH states exist at the same time. > their reification of the math of the probabbilities, > which are contingent upon imperfectable knowledge, > Please trouble yourself to learn how to invert a matrix and apply > Heisenberg's uncertainty principle is distinctly different from > Quantum Theory, the interpretations of quantum theory, or > string theory, or solipsism. æhaha.. Heisenberg used quantum theory to prove his uncertainty > principle, but the principle itself is not quantum theory. To put this in perspective consider Newton's invention of > the calculus to describe his theory of gravity. æThe fundamental > theorem of calculus is distinctly different than Newton's theory > of gravity - even though Newton used the calculus to prove his > theory. > A simple way to interpret Heisenberg's findings is to consider > probability. æThe position is where the wave is concentrated, yet > the wave has associated with it a wavelength - and so, its position > and momentum is spread out in spacetime which Heisenberg > showed meant that momentum and position cannot be known > with absolute certainty. so, when I say, Do the math, dood, it's not a call for any specific kind of math. in the first place, all math problems are foremostly wordproblemmas, and, if I don't agree with your result, what ever the math that you suppose it to require, then I'll stick with my math, by my framing of the problem ...the quadrivium, Latin for *mathematica*, not a New kind of Science! as far as I know, Newton stole the calculus from Leibniz, although he could have already had many prerequisites from Barrow, Fermat, Archimedes etc.; he did steal the inverse-second-ower law from Hooke, and then made a joke out of it: the only calculs in Principia is that little box, dxdy, by itself, not used in a problem. and, if you went to a Harry Potter PS, it's probably your God-am secular religion -- Isaac Newton, the Holy Economist & Greed is G*d!... OK, he wasn't a trinitarian -- in addition to that pantheon on Sundays, Adam Smith's Money World on PBS, downstairs, BBS, upstairs ... al deliverd by Murdochvision -- Yahoo! TM. === Subject: Re: The Roswell fraud, the Nazis and the CIA posting-account=6LcUqgoAAABNsj7IQ597locK57Xf_8n7 1.0.3705; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) You are an idiot.Spudnik === Subject: Re: The Roswell fraud, the Nazis and the CIA posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 5.0),gzip(gfe),gzip(gfe) yeah, but I could be an idiotsavant. a silly example of uncertainty, applying to everday life, is the absurd paradox of mallapropism of Lord Berty, I'm lying?... and, which applies to most of his paradoxes, such as the barber's; barbers just don't cut their own hair! y'know, when someones tells you some thing, you immediately have to ask yourself, Why?, and how that changes the relationship. don't get too longwinded in reply, please; or, just think about for a day or ...9999. --Seargent Barracks Soros McCheeny Pepper, Give jihad a chance in The Sudan, Rhodesia, and other former colonial moments -- Yahoo!TM; you're going to feel my computerized draft, NO RHODESIA SCHOLARS IN HARM'S WAY! http://larouchepub.com/lar/2008/3526lar_soros_pamph.html http://larouchepub.com/other/2008/3526save_nations_parasites.html http://larouchepub.com/other/2008/3526zim_brit_op.html http://larouchepub.com/other/2008/3526zim_brit_op.html http://larouchepub.com/other/2008/3526zim_brit_op.html === Subject: Re: The Roswell fraud, the Nazis and the CIA posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/20080201 Firefox/2.0.0.12,gzip(gfe),gzip(gfe) > You are an idiot.Spudnik But since most of everyone on Earth (at least 99.9%) is an idiot according to the all-knowing mindset of William Mook, so what's the difference? I'm not even all that opposed to allowing your green and dirt cheap methods of providing commercial hydrogen, but that's obviously not good enough. If I suggest anything of utilizing radium, radon, thorium or that of h2o2 & synfuel is what puts our William Mook into virtual orbit. Suggesting that we need a global 100 TW worth of clean and affordable energy, and that of a new and improved national power grid is apparently asking too much from the New World Order of lord Mook. - Brad Guth Brad_Guth Brad.Guth BradGuth