16511 === Subject: Re: Proof of property of naturals posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) >ÊI do have the Schaum's. ÊI have the Suppes > Axiomatic Set Theory book. ÊIs that the one you refer to? Right. Those are the ones. You can breeze through the Suppes (it's easy and, unfortunately, there are only a few difficult exercises), but it will be helpful for you to fill in several details not mentioned in Halmos. (Just remember, if you like, to drop the business about urelements: Just take the axiom of extensionality as \Axy(Az(zex <-> zey) -> x=y)\; and take '0' as defined (not primitive) as justfied by the existence proof from the axiom schema of separation; then you can ignore all his qualifications about set vs. urelement in the rest of the book.) The Lipschutz book is good for having some alternative proofs, especially of the equivalences of certain choice principles without using the axiom schema of replacement. But I wouldn't get bogged down in the too many exercises that are not of the form of proving a theorem. MoeBlee === Subject: Re: Simple inequality posting-account=zurtQQoAAADN1H6R1Sixkz7BkxevAolj Gecko/2009042316 Firefox/3.0.10 (.NET CLR \ 3.5.30729),gzip(gfe),gzip(gfe) correctly (this is more difficult): Let x be a real number in [0,1] and y>=0. Can we show that: (1-a)/(xa) <= (1-b)/b, where a=exp(-yx), b=exp(-y). === Subject: Re: Simple inequality > correctly (this is more difficult): > > Let x be a real number in [0,1] and y>=0. Can we show that: > (1-a)/(xa) <= (1-b)/b, > where a=exp(-yx), b=exp(-y). > Fix y > 0. Note a = b^x. Multiply top and bottom on the left by b^(-x) = (1/b)^x. Set c = 1/b. The inequality then looks like (c^x - 1)/x <= c - 1 or c^x <= 1 + (c - 1)x. Is this true? Sure, c^x is convex on [0, 1], hence stays below its secant line through (0, 1) and (1, c) on that interval. === Subject: Re: Ordinal numbers - some doubts posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > In message > > >> In message > > >> >> Once again, the question is, does Z prove the existence of the > >> >> least wellordered cardinal greater than omega? > > >> >(1) ALL cardinals are well ordered by the epsilon relation on that > >> >cardinal. (2) Z does not even prove that w+w \properly refers\ (i.e. \ is > >> >not just 0 by Fregean default), let alone proving that there is an > >> >ordinal that DOMINATES w. Put another way, Z does not even prove the > >> >existence of a limit ordinal other than w. Indeed, any limit ordinal > >> >other than w is a universe of a MODEL of Z. > > >> I know very little about Z, but from the Wikipedia entry, it's V a \ which > >> is a model of Z, for any limit ordinal a other than omega, not a \ itself. > > >You're correct. Yes, I meant V k, not the ordinal k itself. > > >> This apparently shows that aleph omega need not exist, but suggests > >> smaller alephs do (although defined differently). > > >If I'm not mistaken V w exists (as described) in Z set theory > >(right?); It's V k for any limit ordinal k above w that we can't prove > >to exist (as described) in Z set theory. > > >> \In the usual cumulative hierarchy V a of ZFC set theory (for \ ordinals > >> a), any one of the sets V a for a a limit ordinal larger than the \ first > >> infinite ordinal omega (such as V omegaá2) forms a model of \ Zermelo set > >> theory. So the consistency of Zermelo set theory is a theorem of ZFC \ set > >> theory. Zermelo's axioms do not imply the existence of aleph omega or > >> larger infinite cardinals, as the model omegaá2 does not \ contain such > >> cardinals. > > >Okay, that's in accord with what I've said. > > >> (Cardinals have to be defined differently in Zermelo set > >> theory, as the usual definition of cardinals and ordinals does not \ work > >> very well: with the usual definition it is not even possible to prove > >> the existence of the ordinal omegaá2.)\ (Wikipedia) > > >I agree with the essence of that as to cardinals, but I would put it > >differently. As to ordinals, there's no problem with definining > >'ordinal' in Z set theory. > > >> The usual proof of Hartog's theorem uses Replacement, but if we modify > >> it to produce the set of equivalence classes of well-orderings of > >> subsets of the original set, > > >Equivalent in terms of isomorphic you mean? > > Yes. > > >> rather than of the ordinal types of such > >> well-orderings, as far as I can see that still holds in Z (without C). > > >What still holds? You mean the existence of the set of equivalence > >classes? > > Yes. > > >> So we have a well-ordered set which cannot be mapped into the original > >> set. In particular, from any well-ordered set we can produce one of > >> greater cardinality. > > >I'd have to give that some thought more quiet than I can afford at > >this moment. But what is the more basic point you are arguing for? Are > >you arguing that Hartogs's theorem is provable in Z? So then are you > >arguing that Z set theory proves that there exist ordinals that are > >uncountable? (If you are, and if you are correct, then I'm confused, > >since Z doesn't prove that w+w exists (as desribed, i.e., other than > >as Fregean default 0), so surely Z doesn't prove the existence of an > >uncountable ordinal). > > Ê I avoided ordinals since I'm not sure what they are in Z. That shouldn't be at issue. x is an ordinal <-> x is well ordered by the membership relation on x & Az(zex -> z subset of x) > I'm > suggesting that what can be saved of Hartog's theorem is that for any > set there is a well-orderable set which cannot be mapped 1-1 into it. Okay. I like that as a theorem to note. But I don't think it addresses the earlier question that arose. That is, your theorem does not entail that Z set theory proves that there exists an uncountable ordinal. Rather, it seems safe to continue to say that Z does not prove that there exists an uncountable ordinal. > The quotation said that w+w *with the usual definition* cannot be proved > to exist. I assume you can still have orderings of that type. V (w+w) > may not contain w+w, but it contains isomorphic well-orderings, and also > uncountable ones. Same reply. > >But wait, when you say \for every well-ordered set there is a well > >ordered set of greater cardinality\ I wonder whether you are taking > >\strictly dominates\ and \of greater cardinality\ as equivalent (in > >*Z*). I think this might be the subtle point (and perhaps just a > >matter of terminological difference between us) that is at the crux > >here. > > >When I say \x is of greater cardinality than y\ I don't JUST mean that > >x strictly dominates y. Rather, I mean that there DOES EXIST an > >ORDINAL s (in fact, the least such ordinal) that is equinumerous with > >x and an ordinal t (in fact, the least such ordinal) that is > >equinumerous with y, thus s and t are cardinals, and s is cardinal- > >greater than t. > > I was taking 'same cardinality' to mean there's a bijection, and 'of > greater cardinality' to mean one set can be injected into the other, and > not vice versa. That's fine in ZFC, since the theory supports it with the relevant theorems: card(x)=card(y) <-> Ef(f is a bijection from x onto y) card(x) card < card(y) <-> Ef(f is a bijection from x into y) And it's okay, but only INFORMALLY, in Z, and only to an extent. For the precise technical question as to what Z proves about the existence of ordinals and cardinals having certain properties, we can't conflate \same cardinality\ with \have a bijection\, etc. As to defininig 'card' in Z, we may do so as follows (using the Fregean method): card(x) = the least ordinal equinumerous with x, if there is an ordinal equinumerous with x 0, if there is no ordinal equinumerous with x > >So even if we grant that for every well ordered set Y there is a well > >ordered set X that strictly dominates X, without the numeration > >theorem, we're not ensured that there is an ORDINAL to serve as the > >ordinal for that well ordered set X. So, I think, my point stands: We > >still have not produced an ORDINAL that strictly dominates w. > > Lwalke asked for a least well-ordered cardinal greater than omega, in Z. > Since we don't have the usual von Neumann cardinals and ordinals I don't > know exactly what he means by that. Sure we have von Neumann ordinals and cardinals in Z. It's just that we can't prove that there is a limit ordinal greater than w. > My construction, if valid - and I > would not be very surprised if it isn't - is a well-ordered set which is > of greater cardinality than omega. Granting that it is, still, the question is as to ORDINALS, not just well-ordered sets. > Its least initial sub-ordering which > is still greater than omega has smaller or equal cardinality to any > other such well-ordered set. That may be the nearest we can get. And it's a welcome theorem to know, and indeed the nearest we may get, but what was at stake is not something near, but rather, indeed, exactly some ordinal. In that sense my original point stands, while your result is good to know too, but does not contradict my original point. MoeBlee === Subject: Re: Ordinal numbers - some doubts posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR \ 3.0.04506),gzip(gfe),gzip(gfe) > > Its least initial sub-ordering which > > is still greater than omega has smaller or equal cardinality to any > > other such well-ordered set. That may be the nearest we can get. > And it's a welcome theorem to know, and indeed the nearest we may get, > but what was at stake is not something near, but rather, indeed, > exactly some ordinal. In that sense my original point stands, while > your result is good to know too, but does not contradict my original > point. OK then. So let me combine Hartley's and MoeBlee's comments and see how I can apply this to Z and the proposed theory TST. We begin with Hartley's construction and let x be a wellordered cardinal that is greater than omega. Now according to MoeBlee, \aleph 1\ is just a term , and we can define the term \aleph 1\ in Z anyway we wish -- so let us define \aleph 1\ to be the set that we obtained by applying Hartley's construction! Or of course, if one feels that the name \aleph 1\ is misleading since we can't actually prove in Z that this is the standard aleph 1, then maybe we can call it \a 1\ instead (but once we reach the theory TST, we'll go back to calling it \aleph 1\ again). So we have a definition of the set a 1. Notice that every model of ZF is a model of Z, and in those models of Z that are also models of ZF, a 1 is provably equal to aleph 1. In the other models, a 1 isn't necessarily equal to aleph 1. At this point, I wonder whether someone will object that what I gave isn't really a definition of a 1, since we can't tell whether it's equal to aleph 1 or not. But then again, Hartley's process was described as a construction , and I would think that we can give an object that is constructed as a valid definition, so there ought to be nothing wrong with defining a 1 to be the set constructed by Hartley. Now that we have a 1, can we constuct and define a 2? What if we try to repeat Hartley's construction, so that we obtain a wellordered cardinal that is greater than a 1? Then we can define that set to be a 2, and then repeat the construction again and define the constructed set to be a 3, and so on. Of course, we can't reach a omega or beyond without Replacement Schema (and if we had that schema, then all the a's are really alephs all along). Still, the a n for natural n might have all the properties that tommy1729 desires in his cardinals. === Subject: Re: Ordinal numbers - some doubts posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > > > > Its least initial sub-ordering which > > > is still greater than omega has smaller or equal cardinality to any > > > other such well-ordered set. That may be the nearest we can get. > > And it's a welcome theorem to know, and indeed the nearest we may get, > > but what was at stake is not something near, but rather, indeed, > > exactly some ordinal. In that sense my original point stands, while > > your result is good to know too, but does not contradict my original > > point. > > OK then. So let me combine Hartley's and MoeBlee's comments and > see how I can apply this to Z and the proposed theory TST. > > We begin with Hartley's construction and let x be a wellordered > cardinal that is greater than omega. In WHAT theory? In Z we haven't proven that there exists a cardinal greater than w. Also, as I said before, 'well ordered cardinal' is redundant. Every cardinal is an ordinal, thus well ordered. > Now according to MoeBlee, \aleph 1\ is just a term , and we can > define the term \aleph 1\ in Z anyway we wish -- so let us > define \aleph 1\ to be the set that we obtained by applying > Hartley's construction! No, that is NOT AT ALL implied by my remarks. Of course, definitions are stipulative. But that is not what I was even talking about. My point is that we define 'aleph 1' so that aleph 1 is the least ordinal that strictly dominates aleph 0 IF there is an ordinal that strictly dominates and aleph 0 and aleph 1 is 0 (or whatever Fregean escape-object we choose) otherwise. Second point, I need to go over Hartley's proof carefully, but in the meantime, are you sure that it produces a PARTICULAR well ordered set? That is, a well ordered set that can be defined as THE well ordered set that strictly dominates w and such that [fill in unique distinguishing property here]? > Or of course, if one feels that the name > \aleph 1\ is misleading since we can't actually prove in Z that > this is the standard aleph 1, then maybe we can call it \a 1\ > instead (but once we reach the theory TST, we'll go back to > calling it \aleph 1\ again). > > So we have a definition of the set a 1. Notice that every model > of ZF is a model of Z, and in those models of Z that are also > models of ZF, a 1 is provably equal to aleph 1. What do you even mean by that equality assertion, let alone how do you prove it? Do you mean that the object that the model maps from the term 'a 1' is the same object that the model maps from the term 'aleph 1'? MoeBlee P.S. I'm not responding to your comments that you made in another thread recently, since, at this time at least, I wish not to post in the context of the racist cesspool (not your posts, though I found your response to be, as usual for you, utterly daft) that is filling up there. === Subject: Re: Ordinal numbers - some doubts In message .... >My point is that we define 'aleph_1' so that aleph_1 is the least >ordinal that strictly dominates aleph_0 IF there is an ordinal that >strictly dominates and aleph_0 and aleph_1 is 0 (or whatever Fregean >escape-object we choose) otherwise. It seems rather pointless to define cardinals as initial ordinals in this context. We cannot prove any uncountable ones exist, but all cardinalities aleph_n for finite n do. Certainly Kuratowski in the original post cannot have been using that definition. Similarly, von Neumann ordinals are useless as canonical representatives of order-types. omega + omega may not exist, but well-orderings with cardinality aleph_n exist for each finite n. >Second point, I need to go over Hartley's proof carefully, but in the >meantime, are you sure that it produces a PARTICULAR well ordered set? >That is, a well ordered set that can be defined as THE well ordered set >that strictly dominates w and such that [fill in unique distinguishing >property here]? The dominating set produced is determined by the set we start with. So starting with w we can produce a sequence of (well-ordered) sets with increasing cardinality. I suppose these could be defined to be the cardinals aleph_n. They would not have many of the useful properties that the von Neumann cardinals do in ZF. >> Or of course, if one feels that the name >> \aleph_1\ is misleading since we can't actually prove in Z that >> this is the standard aleph_1, then maybe we can call it \a_1\ >> instead (but once we reach the theory TST, we'll go back to >> calling it \aleph_1\ again). >> >> So we have a definition of the set a_1. Notice that every model >> of ZF is a model of Z, and in those models of Z that are also >> models of ZF, a_1 is provably equal to aleph_1. No, it will never be equal to the usual aleph_1. It doesn't even contain omega (as a subset or an element). It will have the same cardinality as the usual aleph_1, if that exists. (Or , if using MoeBlee's style of definition, if it's not 0.) -- David Hartley === Subject: Re: all matrices whose image contains a given vector posting-account=a6woBRAAAADpNFZJBA7ZBx35zXaKmaP4 Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > > > > > Hi everyone, > > I have a general linear algebra question. ÊAre there any \ results that > > characterize all matrices whose image contains a certain vector or set > > of vectors? ÊFor example, I'd like to find some way to \ characterize > > all matrices whose image contains e 1 through e k, where e i denotes a > > vector of 0's with a 1 in the ith position (and k is just some > > number). ÊI suspect I'm not going to have much success, but \ I figured > > I'd give it a shot here. > > > (In the long run, I'm trying to characterize all matrices of the form > > > Ê+-------------------+-----+ > > Ê| Ê Ê Ê \ Ê Ê Ê Ê Ê \ Ê | Ê Ê | > > Ê| Ê Ê Ê A \ Ê Ê Ê Ê Ê | \ ÊB Ê| > > Ê...... .............|...... > > Ê| Ê Ê | Ê \ Ê Ê Ê Ê Ê \ Ê Ê Ê | > > Ê| ÊC Ê| Ê \ Ê Ê ÊA Ê Ê \ Ê Ê Ê| > > Ê+-----+-------------------+ > > > that contain e 1 through e k in their image, but I think that's a > > problem that requires substantially more thought than a sci.math post > > should be allowed =) ) > > > I'm not sure what is meant by the \image\ > of a matrix. ÊIt's rowspace? Or simply > the set of rows? ÊThe set of columns? > If Peter's interpretation (but not his conclusion) is correct, what you mean by the \image\ of a matrix is its columnspace. I can't think of a way to reframe the question of whether certain vectors are contained in the columnspace so that it will further your goal of characterizing the indicated block structured matrices which have this property. === Subject: Expanding space and The Universe's age posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) How long did it take expanding space of the universe to carry objects out to the 13.7 billion light years in distance? It took 22 billion since expansion is lower than light speed. How long did it take for the light then to return to us now? Mitch Raemsch === Subject: Re: Expanding space and The Universe's age > How long did it take expanding space of the universe to carry objects > out to the 13.7 billion light years in distance? > > It took 22 billion since expansion is lower than light speed. > > How long did it take for the light then to return to us now? > > Mitch Raemsch Read up on how an inflationary universe may work. if you can use Google, it should be an easy task to look up such terms as \Big bang\ and \inflation cosmology\ etc. In a few years when you get done reading, come back for more questions rather than posting assertions. === Subject: Re: Expanding space and The Universe's age posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > > How long did it take expanding space of the universe to carry objects > > out to the 13.7 billion light years in distance? > > > It took 22 billion since expansion is lower than light speed. > > > How long did it take for the light then to return to us now? > > > Mitch Raemsch > > Read up on how an inflationary universe may work. > if you can use Google, it should be an easy task to look up such terms > as \Big bang\ and \inflation cosmology\ etc. > In a few years when you get done reading, come back for more questions > rather than posting assertions. The age of the universe is not based on light years distance since expansion happened below light speed. Inflation only applies to the beginnning. I am talking the expansion we see now which goes back to near beginning. Mitch Raemsch === Subject: Re: Expanding space and The Universe's age \ What happens first is not necessarily the beginning. \ -- Henning Mankell -- Ahmed Ouahi, Architect \BURT\ kirjoitti > > How long did it take expanding space of the universe to carry objects > > out to the 13.7 billion light years in distance? > > > It took 22 billion since expansion is lower than light speed. > > > How long did it take for the light then to return to us now? > > > Mitch Raemsch > > Read up on how an inflationary universe may work. > if you can use Google, it should be an easy task to look up such terms > as \Big bang\ and \inflation cosmology\ etc. > In a few years when you get done reading, come back for more questions > rather than posting assertions. The age of the universe is not based on light years distance since expansion happened below light speed. Inflation only applies to the beginnning. I am talking the expansion we see now which goes back to near beginning. Mitch Raemsch === Subject: Re: Expanding space and The Universe's age posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) On May 9, 11:26Êam, \Ahmed Ouahi, Architect\ \ > \ What happens first is not necessarily the beginning. \ There is nothing before the beginning of time. > > -- Henning Mankell > > -- > Ahmed Ouahi, Architect > > \BURT\ kirjoitti > > > > How long did it take expanding space of the universe to carry objects > > > out to the 13.7 billion light years in distance? > > > > It took 22 billion since expansion is lower than light speed. > > > > How long did it take for the light then to return to us now? > > > > Mitch Raemsch > > > Read up on how an inflationary universe may work. > > if you can use Google, it should be an easy task to look up such terms > > as \Big bang\ and \inflation cosmology\ etc. > > In a few years when you get done reading, come back for more questions > > rather than posting assertions. > > The age of the universe is not based on light years distance since > expansion happened below light speed. Inflation only applies to the > beginnning. I am talking the expansion we see now which goes back to > near beginning. > > Mitch Raemsch === Subject: Re: Expanding space and The Universe's age > On May 9, 11:26 am, \Ahmed Ouahi, Architect\ > >>\ What happens first is not necessarily the beginning. \ > > > There is nothing before the beginning of time. So when did it begin? How long ago? === Subject: Re: Expanding space and The Universe's age posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > > On May 9, 11:26 am, \Ahmed Ouahi, ÊArchitect\ \ > > >>\ What happens first is not necessarily the beginning. \ > > > There is nothing before the beginning of time. > > So when did it begin? How long ago? If I told you how would you know it was right? Mitch Raemsch === Subject: Re: Expanding space and The Universe's age > >> >>>On May 9, 11:26 am, \Ahmed Ouahi, Architect\ >> >>>>\ What happens first is not necessarily the beginning. \ >> >>>There is nothing before the beginning of time. >> >>So when did it begin? How long ago? > > > If I told you how would you know it was right? The real point of the question was \how do you know there was a beginning?\ Since you cannot identify \when\ you also cannot reasonably infer there was a beginning. But you can infer that time has existed in the past because it exists now. Anything past the next tick is up for grabs. === Subject: Re: Expanding space and The Universe's age <7332c$4a05e708$cdd08502$8421@DIALUPUSA.NET> posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > > > >>>On May 9, 11:26 am, \Ahmed Ouahi, ÊArchitect\ \ > > >>>>\ What happens first is not necessarily the beginning. \ > > >>>There is nothing before the beginning of time. > > >>So when did it begin? How long ago? > > > If I told you how would you know it was right? > > The real point of the question was \how do you know > there was a beginning?\ Since you cannot identify > \when\ you also cannot reasonably infer there was > a beginning. But you can infer that time has existed > in the past because it exists now. Anything past the > next tick is up for grabs.- Hide quoted text - > > - Show quoted text - Why do you question it? Space-time shrinks back to zero. Mitch Raemsch === Subject: Re: Expanding space and The Universe's age > >> >> >> >>>>>On May 9, 11:26 am, \Ahmed Ouahi, Architect\ \ >> >>>>>>\ What happens first is not necessarily the beginning. \ >> >>>>>There is nothing before the beginning of time. >> >>>>So when did it begin? How long ago? >> >>>If I told you how would you know it was right? >> >>The real point of the question was \how do you know >>there was a beginning?\ Since you cannot identify >>\when\ you also cannot reasonably infer there was >>a beginning. But you can infer that time has existed >>in the past because it exists now. Anything past the >>next tick is up for grabs.- Hide quoted text - >> >>- Show quoted text - > > > Why do you question it? > > Space-time shrinks back to zero. It appears to you to do so. That is a very poor foundation for your pronouncement. === Subject: Re: Expanding space and The Universe's age For the time being, it depends, on the way and how you do see the time, as if is it along a bureauctrical matter... However, or a simply as a cycles, as in an either case, you would be along an interval, which would make all the difference, all along... -- Ahmed Ouahi, Architect \BURT\ kirjoitti On May 9, 11:26 am, \Ahmed Ouahi, Architect\ > \ What happens first is not necessarily the beginning. \ There is nothing before the beginning of time. > > -- Henning Mankell > > -- > Ahmed Ouahi, Architect > > \BURT\ kirjoitti > > > > How long did it take expanding space of the universe to carry objects > > > out to the 13.7 billion light years in distance? > > > > It took 22 billion since expansion is lower than light speed. > > > > How long did it take for the light then to return to us now? > > > > Mitch Raemsch > > > Read up on how an inflationary universe may work. > > if you can use Google, it should be an easy task to look up such terms > > as \Big bang\ and \inflation cosmology\ etc. > > In a few years when you get done reading, come back for more questions > > rather than posting assertions. > > The age of the universe is not based on light years distance since > expansion happened below light speed. Inflation only applies to the > beginnning. I am talking the expansion we see now which goes back to > near beginning. > > Mitch Raemsch === Subject: Re: Expanding space and The Universe's age posting-account=TbPjIQkAAACzP8U_C0Zcf8kprNJ34-sk AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.64 \ Safari/525.19,gzip(gfe),gzip(gfe) > How long did it take expanding space of the universe to carry objects > out to the 13.7 billion light years in distance? > > It took 22 billion since expansion is lower than light speed. > > How long did it take for the light then to return to us now? Expansion is an illusion that occurs when light comes to the end of its range. === Subject: Re: Expanding space and The Universe's age >> How long did it take expanding space of the universe to carry objects >> out to the 13.7 billion light years in distance? >> >> It took 22 billion since expansion is lower than light speed. >> >> How long did it take for the light then to return to us now? > > > Expansion is an illusion that occurs when light comes to the end of > its range. *blink* Wow, I forgot just how vapid the assertions of some of the clowns on this group really are. === Subject: Re: Expanding space and The Universe's age <%AhNl.246311$Za7.1971@en-nntp-08.dc1.easynews.com> posting-account=TbPjIQkAAACzP8U_C0Zcf8kprNJ34-sk AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.64 \ Safari/525.19,gzip(gfe),gzip(gfe) > >> How long did it take expanding space of the universe to carry objects > >> out to the 13.7 billion light years in distance? > > >> It took 22 billion since expansion is lower than light speed. > > >> How long did it take for the light then to return to us now? > > > Expansion is an illusion that occurs when light comes to the end of > > its range. > > *blink* > > Wow, I forgot just how vapid the assertions of some of the clowns on > this group really are. You believe light travels infinite distances in a finite Universe? It occurs to me that if light did have a finite range, the Universe itself would appear finite. But that's all just an illusion based on old Dogma: Light is absolutely perfect. I disagree, but everyone needs some kind of absolute in their life. === Subject: Re: Expanding space and The Universe's age >>>> How long did it take expanding space of the universe to carry objects >>>> out to the 13.7 billion light years in distance? >>>> It took 22 billion since expansion is lower than light speed. >>>> How long did it take for the light then to return to us now? >>> Expansion is an illusion that occurs when light comes to the end of >>> its range. >> *blink* >> >> Wow, I forgot just how vapid the assertions of some of the clowns on >> this group really are. > > > You believe light travels infinite distances in a finite Universe? > > It occurs to me that if light did have a finite range, the Universe > itself would appear finite. > > But that's all just an illusion based on old Dogma: Light is > absolutely perfect. > > I disagree, but everyone needs some kind of absolute in their life. Tell me, is the universe infinite and unbounded, finite and bounded, infinite and bounded or finite and bounded. Can you even tell me what consequences each of these postulates have for any model of the universe? Oh wait... why am I even bothering to ask you, as you have no clue. === Subject: Re: Expanding space and The Universe's age posting-account=TbPjIQkAAACzP8U_C0Zcf8kprNJ34-sk AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.64 \ Safari/525.19,gzip(gfe),gzip(gfe) > >>>> How long did it take expanding space of the universe to carry \ objects > >>>> out to the 13.7 billion light years in distance? > >>>> It took 22 billion since expansion is lower than light speed. > >>>> How long did it take for the light then to return to us now? > >>> Expansion is an illusion that occurs when light comes to the end of > >>> its range. > >> *blink* > > >> Wow, I forgot just how vapid the assertions of some of the clowns on > >> this group really are. > > > You believe light travels infinite distances in a finite Universe? > > > It occurs to me that if light did have a finite range, the Universe > > itself would appear finite. > > > But that's all just an illusion based on old Dogma: Light is > > absolutely perfect. > > > I disagree, Êbut everyone needs some kind of absolute in \ their life. > > Tell me, is the universe infinite and unbounded, finite and bounded, > infinite and bounded or finite and bounded. Can you even tell me what > consequences each of these postulates have for any model of the > universe? Oh wait... why am I even bothering to ask you, as you have no > clue. If we're talking about size, then that means we are talking about measurements of length, relative space. Relative space certainly doesn't appear to be infinite. Obler's Paradox sort of neatly decides that issue. I think asking about the size of the Universe is a ridiculous question. === Subject: Re: Expanding space and The Universe's age > >> >>> >>>> >>>>> >>>>>>How long did it take expanding space of the universe to carry objects >>>>>>out to the 13.7 billion light years in distance? >>>>>>It took 22 billion since expansion is lower than light speed. >>>>>>How long did it take for the light then to return to us now? >>>>> >>>>>Expansion is an illusion that occurs when light comes to the end of >>>>>its range. >>>> >>>>*blink* >> >>>>Wow, I forgot just how vapid the assertions of some of the clowns on >>>>this group really are. >> >>>You believe light travels infinite distances in a finite Universe? >> >>>It occurs to me that if light did have a finite range, the Universe >>>itself would appear finite. >> >>>But that's all just an illusion based on old Dogma: Light is >>>absolutely perfect. >> >>>I disagree, but everyone needs some kind of absolute in their life. >> >>Tell me, is the universe infinite and unbounded, finite and bounded, >>infinite and bounded or finite and bounded. Can you even tell me what >>consequences each of these postulates have for any model of the >>universe? Oh wait... why am I even bothering to ask you, as you have no >>clue. > > > > If we're talking about size, then that means we are talking about > measurements of length, relative space. > > Relative space certainly doesn't appear to be infinite. > > Obler's Paradox sort of neatly decides that issue. > > I think asking about the size of the Universe is a ridiculous question. How about a question regarding the physical boundary limits? === Subject: Re: Expanding space and The Universe's age posting-account=TbPjIQkAAACzP8U_C0Zcf8kprNJ34-sk AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.64 \ Safari/525.19,gzip(gfe),gzip(gfe) > > > > > > >>>>>>How long did it take expanding space of the universe to carry \ objects > >>>>>>out to the 13.7 billion light years in distance? > >>>>>>It took 22 billion since expansion is lower than light speed. > >>>>>>How long did it take for the light then to return to us now? > > >>>>>Expansion is an illusion that occurs when light comes to the end of > >>>>>its range. > > >>>>*blink* > > >>>>Wow, I forgot just how vapid the assertions of some of the clowns on > >>>>this group really are. > > >>>You believe light travels infinite distances in a finite Universe? > > >>>It occurs to me that if light did have a finite range, the Universe > >>>itself would appear finite. > > >>>But that's all just an illusion based on old Dogma: Light is > >>>absolutely perfect. > > >>>I disagree, Êbut everyone needs some kind of absolute in \ their life. > > >>Tell me, is the universe infinite and unbounded, finite and bounded, > >>infinite and bounded or finite and bounded. Can you even tell me what > >>consequences each of these postulates have for any model of the > >>universe? Oh wait... why am I even bothering to ask you, as you have no > >>clue. > > > If we're talking about size, then that means we are talking about > > measurements of length, relative space. > > > Relative space certainly doesn't appear to be infinite. > > > Obler's Paradox sort of neatly decides that issue. > > > I think asking about the size of the Universe is a ridiculous question. > > How about a question regarding the physical boundary limits? Isn't that Hubble's Limit? Basically, space is as big as our measurements may reveal it. If our measurements are based on light, and light is overtaken by the expansion of space (big bang) or light turns out to have a finite range (my cosmology), then that is the boundary limit to physical space. You can calculate the Hubble Limit in my cosmology by finding when v = 0, where v = c - Hd === Subject: Re: Expanding space and The Universe's age It is a simply, a conventional matter! -- Ahmed Ouahi, Architect \Jack Sprat\ kirjoitti viestiss\.8a:bc2d7$4a05e78b$cdd08502$8575@DIALUPUSA.NET... > >> >>> >>>> >>>>> >>>>>> >>>>>>>How long did it take expanding space of the universe to carry \ objects >>>>>>>out to the 13.7 billion light years in distance? >>>>>>>It took 22 billion since expansion is lower than light speed. >>>>>>>How long did it take for the light then to return to us now? >>>>>> >>>>>>Expansion is an illusion that occurs when light comes to the end of >>>>>>its range. >>>>> >>>>>*blink* >>> >>>>>Wow, I forgot just how vapid the assertions of some of the clowns on >>>>>this group really are. >>> >>>>You believe light travels infinite distances in a finite Universe? >>> >>>>It occurs to me that if light did have a finite range, the Universe >>>>itself would appear finite. >>> >>>>But that's all just an illusion based on old Dogma: Light is >>>>absolutely perfect. >>> >>>>I disagree, but everyone needs some kind of absolute in their life. >>> >>>Tell me, is the universe infinite and unbounded, finite and bounded, >>>infinite and bounded or finite and bounded. Can you even tell me what >>>consequences each of these postulates have for any model of the >>>universe? Oh wait... why am I even bothering to ask you, as you have no >>>clue. >> >> >> >> If we're talking about size, then that means we are talking about >> measurements of length, relative space. >> >> Relative space certainly doesn't appear to be infinite. >> >> Obler's Paradox sort of neatly decides that issue. >> >> I think asking about the size of the Universe is a ridiculous question. > > How about a question regarding the physical boundary limits? === Subject: Re: Expanding space and The Universe's age 1Ó=1 11Ó=121 111Ó=12321 1111Ó=1234321 11111Ó=123454321 111111Ó=12345654321 1111111Ó=1234567654321 11111111Ó=123456787654321 The question is Who would be having Any ability pretending To end this -- Ahmed Ouahi, Architect \Michael Helland\ kirjoitti > >>>> How long did it take expanding space of the universe to carry \ objects > >>>> out to the 13.7 billion light years in distance? > >>>> It took 22 billion since expansion is lower than light speed. > >>>> How long did it take for the light then to return to us now? > >>> Expansion is an illusion that occurs when light comes to the end of > >>> its range. > >> *blink* > > >> Wow, I forgot just how vapid the assertions of some of the clowns on > >> this group really are. > > > You believe light travels infinite distances in a finite Universe? > > > It occurs to me that if light did have a finite range, the Universe > > itself would appear finite. > > > But that's all just an illusion based on old Dogma: Light is > > absolutely perfect. > > > I disagree, but everyone needs some kind of absolute in their life. > > Tell me, is the universe infinite and unbounded, finite and bounded, > infinite and bounded or finite and bounded. Can you even tell me what > consequences each of these postulates have for any model of the > universe? Oh wait... why am I even bothering to ask you, as you have no > clue. If we're talking about size, then that means we are talking about measurements of length, relative space. Relative space certainly doesn't appear to be infinite. Obler's Paradox sort of neatly decides that issue. I think asking about the size of the Universe is a ridiculous question. === Subject: Re: Expanding space and The Universe's age posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > > > > > > > >>>> How long did it take expanding space of the universe to carry \ objects > > >>>> out to the 13.7 billion light years in distance? > > >>>> It took 22 billion since expansion is lower than light speed. > > >>>> How long did it take for the light then to return to us now? > > >>> Expansion is an illusion that occurs when light comes to the end of > > >>> its range. > > >> *blink* > > > >> Wow, I forgot just how vapid the assertions of some of the clowns on > > >> this group really are. > > > > You believe light travels infinite distances in a finite Universe? > > > > It occurs to me that if light did have a finite range, the Universe > > > itself would appear finite. > > > > But that's all just an illusion based on old Dogma: Light is > > > absolutely perfect. > > > > I disagree, Êbut everyone needs some kind of absolute in \ their life. > > > Tell me, is the universe infinite and unbounded, finite and bounded, > > infinite and bounded or finite and bounded. Can you even tell me what > > consequences each of these postulates have for any model of the > > universe? Oh wait... why am I even bothering to ask you, as you have no > > clue. > > If we're talking about size, then that means we are talking about > measurements of length, relative space. > > Relative space certainly doesn't appear to be infinite. > > Obler's Paradox sort of neatly decides that issue. > > I think asking about the size of the Universe is a ridiculous question.- \ Hide quoted text - > > - Show quoted text - Wanting to know the age is an important question. If it expanded slower than light it is older than the light year distance of 13.7 billion. Mitch Raemsch === Subject: Re: Expanding space and The Universe's age posting-account=TbPjIQkAAACzP8U_C0Zcf8kprNJ34-sk AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.64 \ Safari/525.19,gzip(gfe),gzip(gfe) > > > > > > > >>>> How long did it take expanding space of the universe to carry \ objects > > > >>>> out to the 13.7 billion light years in distance? > > > >>>> It took 22 billion since expansion is lower than light speed. > > > >>>> How long did it take for the light then to return to us now? > > > >>> Expansion is an illusion that occurs when light comes to the end \ of > > > >>> its range. > > > >> *blink* > > > > >> Wow, I forgot just how vapid the assertions of some of the clowns \ on > > > >> this group really are. > > > > > You believe light travels infinite distances in a finite Universe? > > > > > It occurs to me that if light did have a finite range, the Universe > > > > itself would appear finite. > > > > > But that's all just an illusion based on old Dogma: Light is > > > > absolutely perfect. > > > > > I disagree, Êbut everyone needs some kind of absolute \ in their life. > > > > Tell me, is the universe infinite and unbounded, finite and bounded, > > > infinite and bounded or finite and bounded. Can you even tell me what > > > consequences each of these postulates have for any model of the > > > universe? Oh wait... why am I even bothering to ask you, as you have \ no > > > clue. > > > If we're talking about size, then that means we are talking about > > measurements of length, relative space. > > > Relative space certainly doesn't appear to be infinite. > > > Obler's Paradox sort of neatly decides that issue. > > > I think asking about the size of the Universe is a ridiculous question.- \ Hide quoted text - > > > - Show quoted text - > > Wanting to know the age is an important question. If it expanded > slower than light it is older than the light year distance of 13.7 > billion. First of all, if expansion were real, it would be the expansion of space, not the Universe. The Universe is timeless and sizeless. Physical reality is a different matter. Physical reality is as old and large as we measure it to be. === Subject: Re: Expanding space and The Universe's age posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/20090501 Gentoo Firefox/3.5b4,gzip(gfe),gzip(gfe) > > > How long did it take expanding space of the universe to carry objects > > out to the 13.7 billion light years in distance? > > > It took 22 billion since expansion is lower than light speed. > > > How long did it take for the light then to return to us now? > > Expansion is an illusion that occurs when light comes to the end of > its range. Except expansion has been verified by observation, including the correct falloff in luminosity. I seem to recall having a discussion with you about this, Mike. Guess you didn't learn. === Subject: Re: Expanding space and The Universe's age posting-account=TbPjIQkAAACzP8U_C0Zcf8kprNJ34-sk AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.64 \ Safari/525.19,gzip(gfe),gzip(gfe) > > > > > How long did it take expanding space of the universe to carry objects > > > out to the 13.7 billion light years in distance? > > > > It took 22 billion since expansion is lower than light speed. > > > > How long did it take for the light then to return to us now? > > > Expansion is an illusion that occurs when light comes to the end of > > its range. > > Except expansion has been verified by observation, including the > correct falloff in luminosity. Luminosity falls off. But light goes for infinity. So there must be extra space. But light would never slow down and die out. That would mean we'd have to change our views of the Universe. So extra space it is. === Subject: Re: Expanding space and The Universe's age >> >>>> How long did it take expanding space of the universe to carry objects >>>> out to the 13.7 billion light years in distance? >>>> It took 22 billion since expansion is lower than light speed. >>>> How long did it take for the light then to return to us now? >>> Expansion is an illusion that occurs when light comes to the end of >>> its range. >> Except expansion has been verified by observation, including the >> correct falloff in luminosity. > > Luminosity falls off. > > But light goes for infinity. > > So there must be extra space. > > But light would never slow down and die out. > > That would mean we'd have to change our views of the Universe. > > So extra space it is. Like all the extra space in your brain case? === Subject: Re: Expanding space and The Universe's age posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/20090501 Gentoo Firefox/3.5b4,gzip(gfe),gzip(gfe) > > > > > > > > > How long did it take expanding space of the universe to carry \ objects > > > > out to the 13.7 billion light years in distance? > > > > > It took 22 billion since expansion is lower than light speed. > > > > > How long did it take for the light then to return to us now? > > > > Expansion is an illusion that occurs when light comes to the end of > > > its range. > > > Except expansion has been verified by observation, including the > > correct falloff in luminosity. > > Luminosity falls off. > > But light goes for infinity. > > So there must be extra space. > > But light would never slow down and die out. > > That would mean we'd have to change our views of the Universe. Current theory works fine. Find a new hobby. > > So extra space it is. === Subject: Re: Expanding space and The Universe's age posting-account=TbPjIQkAAACzP8U_C0Zcf8kprNJ34-sk AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.64 \ Safari/525.19,gzip(gfe),gzip(gfe) > > > > > > > > > > > How long did it take expanding space of the universe to carry \ objects > > > > > out to the 13.7 billion light years in distance? > > > > > > It took 22 billion since expansion is lower than light speed. > > > > > > How long did it take for the light then to return to us now? > > > > > Expansion is an illusion that occurs when light comes to the end of > > > > its range. > > > > Except expansion has been verified by observation, including the > > > correct falloff in luminosity. > > > Luminosity falls off. > > > But light goes for infinity. > > > So there must be extra space. > > > But light would never slow down and die out. > > > That would mean we'd have to change our views of the Universe. > > Current theory works fine. I doubt you'll reach your full potential with that attitude. > Find a new hobby. > > > > > So extra space it is. === Subject: Re: Expanding space and The Universe's age posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/20090501 Gentoo Firefox/3.5b4,gzip(gfe),gzip(gfe) [...] > I doubt you'll reach your full potential with that attitude. > > > Find a new hobby. > > > > So extra space it is. I'm pretty sure I could program cash registers. === Subject: Re: Expanding space and The Universe's age posting-account=TbPjIQkAAACzP8U_C0Zcf8kprNJ34-sk AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.64 \ Safari/525.19,gzip(gfe),gzip(gfe) > > [...] > > > I doubt you'll reach your full potential with that attitude. > > > > Find a new hobby. > > > > > So extra space it is. > > I'm pretty sure I could program cash registers. Most academics are pretty sure they'd survive in the real world. I think there's a name for that, when you're too incompetent to know what your limitations are. ;-) === Subject: Re: Expanding space and The Universe's age >> >> [...] >> >>> I doubt you'll reach your full potential with that attitude. >>>> Find a new hobby. >>>>> So extra space it is. >> I'm pretty sure I could program cash registers. > > > Most academics are pretty sure they'd survive in the real world. > > I think there's a name for that, when you're too incompetent to know > what your limitations are. ;-) Please tell us the name... is it by any chance Michael Helland? === Subject: Re: Expanding space and The Universe's age posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > > > > > > > > > > > > > How long did it take expanding space of the universe to carry \ objects > > > > > out to the 13.7 billion light years in distance? > > > > > > It took 22 billion since expansion is lower than light speed. > > > > > > How long did it take for the light then to return to us now? > > > > > Expansion is an illusion that occurs when light comes to the end of > > > > its range. > > > > Except expansion has been verified by observation, including the > > > correct falloff in luminosity. > > > Luminosity falls off. > > > But light goes for infinity. > > > So there must be extra space. > > > But light would never slow down and die out. > > > That would mean we'd have to change our views of the Universe. > > Current theory works fine. > > Find a new hobby. > > > > > > > So extra space it is.- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text - Current theories are completely incomplete. When Einstein said Quantum Mechanics was incomlpete he needed to point out it is true of all science. Mitch Raemsch === Subject: Re: Expanding space and The Universe's age > > Luminosity falls off. > > But light goes for infinity. > > So there must be extra space. > by Phil Schewe and Ben Stein Our Universe Has a Topology Scale of at least 24 GPC Our universe has a topology scale of at least 24 Gpc, or about 75 billion light years, according to a new analysis of data from the Wilkinson Microwave Anisotropy Probe (WMAP). What does this mean? Well, because of conceivable hall-of-mirrors effects of spacetime, the universe might be finite in size but give us mortals the illusion that it is infinite. For example, the cosmos might be tiled with some repeating shape, around which light rays might wrap themselves over and over (\wrap\ in the sense that, as in video games, something might disappear off the left side of the screen and reappear on the right side). A new study by scientists from Princeton, Montana State, and Case Western looks for signs of such \wrapped \ light in the form of pairs of circles, in opposite directions in the sky, with similar patterns in the temperature of the cosmic microwave background. If the universe were finite and actually smaller than the distance to the \surface of last scattering\ (a distance that essentially constitutes the edge of the \visible universe,\ and the place in deep space whence comes the cosmic microwaves), then multiple imaging should show up in the microwave background. But no such correspondences appeared in the analysis. The researchers are able to turn the lack of recurring patterns into the form of a lower limit on the scale of cosmic topology, equal to 24 billion parsecs, a factor of 10 larger than previous observational bounds. (Cornish, Spergel, Starkman, Komatsu, Physical Review Letters, corn...@physics.montana.edu.) === Subject: Re: Expanding space and The Universe's age >> How long did it take expanding space of the universe to carry objects >> out to the 13.7 billion light years in distance? >> >> It took 22 billion since expansion is lower than light speed. >> >> How long did it take for the light then to return to us now? > > > Expansion is an illusion that occurs when light comes to the end of > its range. === Subject: Re: Expanding space and The Universe's age posting-account=TbPjIQkAAACzP8U_C0Zcf8kprNJ34-sk AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.64 \ Safari/525.19,gzip(gfe),gzip(gfe) > >> How long did it take expanding space of the universe to carry objects > >> out to the 13.7 billion light years in distance? > > >> It took 22 billion since expansion is lower than light speed. > > >> How long did it take for the light then to return to us now? > > > Expansion is an illusion that occurs when light comes to the end of > > its range. > > Ê Ê The alternative is that light has an infinite range in a finite Universe. You'd laugh at that, if it weren't for your beliefs. === Subject: Re: Expanding space and The Universe's age > > The alternative is that light has an infinite range in a finite > Universe. > > You'd laugh at that, if it weren't for your beliefs. The observational evidence fits the model o EM radiation has infinite range o the observable universe is finite and unbounded No Center http://www.astro.ucla.edu/~wright/nocenter.html http://www.astro.ucla.edu/~wright/infpoint.html Also see Ned Wright's Cosmology Tutorial http://www.astro.ucla.edu/~wright/cosmolog.htm http://www.astro.ucla.edu/~wright/cosmology_faq.html http://www.astro.ucla.edu/~wright/CosmoCalc.html WMAP: Foundations of the Big Bang theory http://map.gsfc.nasa.gov/m_uni.html WMAP: Tests of Big Bang Cosmology http://map.gsfc.nasa.gov/m_uni/uni_101bbtest.html === Subject: Re: Expanding space and The Universe's age posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/20090501 Gentoo Firefox/3.5b4,gzip(gfe),gzip(gfe) > > > >> How long did it take expanding space of the universe to carry \ objects > > >> out to the 13.7 billion light years in distance? > > > >> It took 22 billion since expansion is lower than light speed. > > > >> How long did it take for the light then to return to us now? > > > > Expansion is an illusion that occurs when light comes to the end of > > > its range. > > > Ê Ê > > The alternative is that light has an infinite range in a finite > Universe. > > You'd laugh at that, if it weren't for your beliefs. Since you think it is silly, it obviously can't happen eh Mike? Nothing preps you for studying physics than programming cash registers! === Subject: Re: Point charges inside a sphere I find the results truly beautiful. The fact that even though the charge density on the sphere (or circle) continues to climb as new charges are added - there is never a time when it's better to place one of the charges internally is very nice. I was hoping to get some hint as to the field of mathematics involved in deriving which configurations are optimal - in practice numerical optimization will give the results & a bit of work will show that they are locally stable. Is there a neater way? >A question I need some guidance in answering (relevant math skills in need \ >of a dust off). > > n like charges are confined to the inside of a sphere. My intuition says \ > that the relevant electric potential is minimised by the following charge \ > configurations: > > n=2 two charges diametrically opposit (though the diameter might > obviously be moving) > n=3 tree charges coplanar and at the vertices of an equilateral triangle > (again possibly in motion) > n=4 four charges at the verices of a tetrahedron (also possibly in \ motion) > n=6 six charges at the vertices of an octohedron (ditto) > n=8 eight charges at the verices of a cube (ditto). > > 1) How to prove this short of brute force algebra? > 2) What are the configurations that minimise the electric potential when n \ > = 5, or 7 (or 9, 10,11, ...)? > === Subject: Larry Sarner, Mathematics, and Pseudoscience? posting-account=j5NBmQoAAAC2KcZXmk-MDrfAdD3wqIwW Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) Very interesting storiesÉ http://larrysarnerpseudoscience.wordpress.com/ === Subject: Re: Hitting a spec of debris at .97*c might kill you. Would some knowledgeable person address the issue of mass energy and maybe, just maybe suggest that neither the spec of debris nor the craft is privileged and therefore the effect would be nil? As objects approach c relative to each other, they each enter into the dimension of the creation of space in which there are no privileged masses. === Subject: Re: A Short and Plain Proof of Fermat`s Last Theorem about Pythagorean triples Please, modify A=X-Y to A=Z-Y. --------------------------------------------------- You must not calculated like these: A=2^(2k+1)a^2 , B=b^2. A=X-Y and B=Z-X was defined at first. And A=c^2 and B=2d^2 was defined. Please, read appendix pdf file paper. And understand our short and perfect FLT proof. ---------------------------------------------------- === Subject: Re: update on why pi is a constant in Eucl and why it is imaginary, \ not transcendental #491 new book 2nd edition: New True Mathematics I sense I am getting close to home on this. you lost in woods w no flashlight. > > Archimedes Plutonium > www.iw.net/~a_plutonium > whole entire Universe is just one big atom > where dots of the electron-dot-cloud are galaxies === Subject: Re: Mental Event & Mental Object: Is there a Difference? >>>> Yes, a 'mental state' is an object. >>> It is not an object. Mr. Jones, anything one observes of a state is a >>> tentative declaration of something within its moment. It is not that >>> moment, nor what it was (to you or any observer) at that moment. >>> Jones - your object is DEAD. >> A mental state is an object, and because it is an object it is an >> example of bad grammar. So your position is the same as mine. > > A mental state is only an object to a machine or to another person. > Your own mental state is a subject. Your statement is an abuse of > language. > What's a 'mental state'? What's 'my own mental state'? Why give this mental term a false credence by treating it as a physical object? === Subject: Re: Mental Event & Mental Object: Is there a Difference? \ posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > > What's a 'mental state'? What's 'my own mental state'? Narcissism. Marshall === Subject: Applying the inclusion-exclusion principle posting-account=4W9t0woAAAB3dq7-fhllNhT3_mnzEKiC Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) How many numbers between 100 and 500 (inclusive) are divisible by either 4 or 5? |4| = 101 |5| =81 |4 intersect 5| = 21 |4| - |4 intersect 5| + |5| - |4 intersect 5| = 140 Right? === Subject: Re: Applying the inclusion-exclusion principle > How many numbers between 100 and 500 (inclusive) are divisible by > either 4 or 5? > >> 4| = 101 >> 5| =81 >> 4 intersect 5| = 21 > >> 4| - |4 intersect 5| + |5| - |4 intersect 5| = 140 > > Right? You only want to subtract the intersection once, or you remove ALL counted instances of divisibility of 4 and 5. === Subject: Re: Applying the inclusion-exclusion principle >> How many numbers between 100 and 500 (inclusive) are divisible by >> either 4 or 5? >> >>> 4| = 101 >>> 5| =81 >>> 4 intersect 5| = 21 >> >>> 4| - |4 intersect 5| + |5| - |4 intersect 5| = 140 >> >> Right? > > You only want to subtract the intersection once, or you remove ALL > counted instances of divisibility of 4 and 5. Never mind. You are correct. === Subject: Re: Applying the inclusion-exclusion principle \ posting-account=3WPJYgoAAAA55VjhzK9i07RN8h8u8eEs Gecko/2008092417 Firefox/3.0.3,gzip(gfe),gzip(gfe) > >> How many numbers between 100 and 500 (inclusive) are divisible by > >> either 4 or 5? > > >>> 4| = 101 > >>> 5| =81 > >>> 4 intersect 5| = 21 > > >>> 4| - |4 intersect 5| + |5| - |4 intersect 5| = 140 > > >> Right? > > > You only want to subtract the intersection once, or you remove ALL > > counted instances of divisibility of 4 and 5. > > Never mind. ÊYou are correct. I think you had it correct the first time: the answer should be 161. You can check it numerically, although the logic you gave in your first reply suffices to prove this assertion. The answer the original poster obtains is the case when you want to find the number of elements that are divisible by 4 or 5, but not both (i.e. the exclusive \OR\ or \NOR\, if you wish). However, he did not specify that the OR in his problem was exclusive, so we assume under this convention it is the normal usage of \OR\, which means the set of numbers he is interested can be divisible by 4,5 or both 4 and 5. M === Subject: Re: Applying the inclusion-exclusion principle >>>> How many numbers between 100 and 500 (inclusive) are divisible by >>>> either 4 or 5? >> >>>>> 4| = 101 >>>>> 5| =81 >>>>> 4 intersect 5| = 21 >> >>>>> 4| - |4 intersect 5| + |5| - |4 intersect 5| = 140 >> >>>> Right? >> >>> You only want to subtract the intersection once, or you remove ALL >>> counted instances of divisibility of 4 and 5. >> >> Never mind. You are correct. > > I think you had it correct the first time: the answer should be 161. > You can check it numerically, although the logic you gave in your > first reply suffices to prove this assertion. > The answer the original poster obtains is the case when you want to > find the number of elements that are divisible by 4 or 5, but not both > (i.e. the exclusive \OR\ or \NOR\, if you wish). However, he did not > specify that the OR in his problem was exclusive, so we assume under > this convention it is the normal usage of \OR\, which means the set of > numbers he is interested can be divisible by 4,5 or both 4 and 5. > > M I think I agree with you now; I have been debating precisely the proper mathematical interpretation of the OP's statement since I posted my retraction. Perharps the OP can rephrase the problem in a purely mathematical context. === Subject: Re: Looking for info on very symmetric 4x4 matrix posting-account=H1y7YgoAAADzGQwbcYaL9UvwttgsjOjp AppleWebKit/525.27.1 (KHTML, like Gecko) Version/3.2.1 \ Safari/525.27.1,gzip(gfe),gzip(gfe) > What I really have is 4 sets of simultaneous linear equations. I think you mean one set of 4 simultaneous linear equations. > Specifically, > > Y = M * X > > where M is the matrix I described. > > What I want to do is invert these equations, so that I have X in terms > of Y. You can't. For some Y there are (infinitely) many X, for other Y there are none. -- GN === Subject: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO SV1),gzip(gfe),gzip(gfe) An informal and highly experimental, unorthadox proof P=NP has been published on CERN preprints. http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-1939656818Hw\ f-1468147288IdV-15212827115758210PDF_HI0001.pdf It is mine, and no it is not published anywhere else. My purpose in posting it here is for feedback and suggestions on how to strengthen it. I would specifically, as was my intention with this experiment, like feedback from anyone interested in the methodology I used and suggestion as to how I might go about pursuing a more broadly accepted peer-reviewed published proof building on this basic result. Martin Musatov m[dot]mm[at]vzw[dot]blackberry[dot]net. === Subject: Re: P=NP Proof Published at CERN posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > An informal and highly experimental, unorthadox proof P=NP has been > published on CERN preprints. > > http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... > > It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. > > I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. A two-page, literally unreadable text with nothing in it (at least that did not get mangled) even remotely similar to anything related to computational complexity theory is not something you can get feedback on. It is actually even impossible to see *what* it is you want feedback on. -- m === Subject: Re: P=NP Proof Published at CERN > An informal and highly experimental, unorthadox proof P=NP has been > published on CERN preprints. > > > \ http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-1939656818Hwf\ - > 1468147288IdV-15212827115758210PDF_HI0001.pdf > > It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. > > I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. > > > Martin Musatov > m[dot]mm[at]vzw[dot]blackberry[dot]net. The mathematics formulas in that PDF are unintelligible. Was that done === Subject: Re: P=NP Proof Published at CERN <090520090900584812%anniel@nym.alias.net.invalid> posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/20090423 Firefox/3.5b4,gzip(gfe),gzip(gfe) > > > > > An informal and highly experimental, unorthadox proof P=NP has been > > published on CERN preprints. > > >http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... > > 1468147288IdV-15212827115758210PDF_HI0001.pdf > > > It is mine, and no it is not published anywhere else. My purpose in > > posting it here is for feedback and suggestions on how to strengthen > > it. > > > I would specifically, as was my intention with this experiment, like > > feedback from anyone interested in the methodology I used and > > suggestion as to how I might go about pursuing a more broadly accepted > > peer-reviewed published proof building on this basic result. > > > > Martin Musatov > > m[dot]mm[at]vzw[dot]blackberry[dot]net. > > The mathematics formulas in that PDF are unintelligible. Was that done Sorry for the report: *A N Niel: the actual culprit believe it or not was Google docs uploading a .txt file converting to .pdf which created the in and out character/equations on the left side of the page. The vertical numbering appeared when I attempted to upload a proof a manuscript system. It looked very sturdy and well-enforced so I tried to throw it up against the CERN server and see if it woulds stick and it did. I then began to experiment with other \geometric\ databases: A first example of which can be found here: *http://cdsweb.cern.ch/record/1164207/export/xm note: no missing \L\ there... and: *http://documents.cern.ch/photo/photo-tsic/icon-dfbx-2009-001.gif a neat picture I used in developing my theory. My interests began in geometry and then shifted into numerical analysis and prime numbers so P==NP was my way to reconcile all of this. When I saw the error Google Docs generated I began to wonder if we could define functions pertaining to numerical analysis not by their presence but by their absence, and more specifically the geometry of the space that makes up that absence. After all as complicated as numbers can be we only have 10 plus a zero. In the end this was the shape, or an example of it in binary to which I was able to parse two sets of data readable and absent from one document: ****************************************************************************\ **************** NOTE: The Google Docs parsing began generating content vertically as it ran the equations I had prepared in a Microsoft Word file, then ctl +c, ctl+v into .txt file. IT RAN RIGHT THROUGH THE REFERENCES BEFORE SEALING OFF THE SOLUTION JUST THIS SIDE OF INFINITY it was pretty neat: ****************************************************************************\ ***************** So indeed my proof stands correct and I hope it makes its way over to Mr. Cook for his comments;! ****************************************************************************\ ***************** ----------Here is a sample parsing from a \Polynomial Time Algorithm\------------------------- MARTIN M. MUSATOV: m[dot]mm[at]vzw[dot]blackberry[dot]net An Open Address to Mr. Stephen A. Cook: sacook [at] cs [dot] toronto [dot] edu STATEMENT OF THE SOLUTION This solution to P versus NP explains how every language accepted by some non deterministic algorithm in polynomial time can be accepted by some (deterministic) algorithm in polynomial time. To define the solution it is formally it is necessary to observe the model of a computer, or Turing machine and process information in real-time as it is received as a computable function or linear stream. By this declaration, formally, the class P contains the indecision problems P = . ... . N. ... . P The area of a circle [2]: . ..=....2 The binomial theorem [3]: ..+.. ..= .. .. ........-.. .. ..=0 Expansion of a sum (Taylor Series) [4];. 1+.. ..=1+ .... 1! + .. ..-1 ..22! +. Followed by the Fourier Series [5]:. .. .. =..0+ ....cos ...... .. +....sin ...... .. 8 ..=1 The Pythagorean Formula [6]:. ..2+..2=..2 1 Arfken, G. \Special Coordinate Systems--Rectangular Cartesian Coordinates.\ \.81\.982.3 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 94-95, 1985. 2 Richmond, Bettina (1999-01-12). \Area of a Circle\. Western Kentucky University. Retrieved on 2007-11-04. 3Amulya Kumar Bag. Binomial Theorem in Ancient India. Indian J.History Sci.,1:68-74,1966. 4 \Neither Newton nor Leibniz - The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala\. MAT 314. Canisius College. Retrieved on 2006-07-09. 5William E. Boyce and Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Eighth edition. John Wiley & Sons, Inc., New Jersey, 2005. ISBN 0-471-43338-1 6Bell, John L., The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development, Kluwer, 1999. ISBN 0-7923-5972- 0. 7Heaton, H. (1896) A Method of Solving Quadratic Equations, American Mathematical Monthly 3(10), 236-237. Through the Quadratic Equation [7]:. ..= -..\.81} ..2-4.... 2.. Page 2 of 3 http://mc.manuscriptcentral.com/imamat Manuscripts submitted to (i)The IMA Journal of Applied Mathematics(/i) To be succeed by a modified Taylor Series Expansion [8];. ....=1+ .. 1! + ..22! + ..33! +.,-8<..<8 \.81\.87 m [dot] mm [at] vzw [dot] blackberry [dot] net === Subject: Re: P=NP Proof Published at CERN posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) > An informal and highly experimental, unorthadox proof Does that mean \bogus\? > P=NP has been > published on CERN preprints. === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/20090423 Firefox/3.5b4,gzip(gfe),gzip(gfe) On May 9, 2:46Êam, \victor meldrew ...@yahoo.co.uk\ > > > An informal and highly experimental, unorthodox proof > > Does that mean \bogus\? No. informal==English== * {{rhymes|?¢°(r)m?l}} {{en-adj}} # Not [[formal]] or [[ceremonious]]; [[casual]]. #: ''an '''informal''' get-together'' # Not in [[accord]] with the [[usual]] [[regulation]]s; [[unofficial]]. #: ''an '''informal''' agreement'' # [[suit|Suited]] for [[everyday]] use. #: '''''informal''' clothes'' # {{context|of language}} Reflecting [[everyday]], non-ceremonious [[usage]]. {{trans-top|not formal or ceremonious; casual}} * Czech: {{t-|cs|neform\.87ln\.92}} * Polish: {{t+|pl|potoczny}} {{trans-mid}} * Spanish: {{t-|es|informal}} {{trans-bottom}} * [[colloquial]] * [[slang]] ---- ==Spanish== {{es-adj|pl=informales}} # [[#English|informal]] # [[unreliable]] {{gloss|person}} [[fa:informal]] [[fr:informal]] [[io:informal]] [[hu:informal]] [[pl:informal]] [[pt:informal]] [[ru:informal]] [[simple:informal]] [[fi:informal]] [[ta:informal]] [[te:informal]] [[tr:informal]] [[vi:informal]] [[zh:informal]] * {{audio|en-us-highly.ogg|Audio (US)}} {{infl|en|adverb}} # In a [[high]] or [[esteem]]ed manner. # [[extremely]]; [[greatly]]; [[awfully]] * The adverb '''highly''' and the adverb '''[[high]]''' shouldn't be mistaken. *: ''This is certainly '''highly''' recommended.'' *: '''''High''' above us the stars were shining.'' {{trans-top|in a high or esteemed manner}} * Czech: {{t-|cs|vysoko}} * [[Scots]]: {{t¿|sco|heichly|xs=Scots}} {{trans-mid}} * [[Scottish Gaelic]]: {{t-|gd|gu h-\.88rd|xs=Scottish Gaelic}} {{trans-bottom}} {{trans-top|extremely, greatly, awfully}} * Czech: {{t-|cs|vysoko}} * [[Scots]]: {{t¿|sco|heichly|xs=Scots}} {{trans-mid}} * [[Scottish Gaelic]]: {{t-|gd|gu h-\.88rd|xs=Scottish Gaelic}} {{trans-bottom}} {{checktrans-top}} * Dutch: [[zeer]], [[hoog]] * Swedish: [[h\.9agt]] {{trans-bottom}} [[et:highly]] [[es:highly]] [[fr:highly]] [[io:highly]] [[it:highly]] [[hu:highly]] [[ja:highly]] [[pl:highly]] [[fi:highly]] [[sv:highly]] [[te:highly]] [[vi:highly]] [[zh:highly]] *: {{rhymes|?nt?l}} {{en-adj}} # of or pertaining to an [[experiment]] * [[pokusnù]] {{m}}, [[experiment\.87ln\.92]] {{m}} * Finnish: [[kokeellinen]] * German: [[experimentell]] * Spanish: [[experimental]] * [[experimentally]] ---- ==Spanish== {{es-adj|pl=experimentales}} # [[#English|experimental]] * [[experimento]] [[ar:experimental]] [[el:experimental]] [[fr:experimental]] [[ko:experimental]] [[io:experimental]] [[hu:experimental]] [[ja:experimental]] [[pl:experimental]] [[ru:experimental]] [[fi:experimental]] [[ta:experimental]] [[vi:experimental]] [[tr:experimental]] [[zh:experimental]] > > > P=NP has been > > published on CERN preprints. > > h-a-d-o-x\) and that could have somehow let this comment stick in there to help me prove my P Versus NP? re: victor meldrew ...@yahoo.co.uk: > Does that mean \bogus\? No. unorthodox==English== {{en-adj-more}} #[[unusual]], [[unconventional]], or [[idiosyncratic]] *[[heretical]] *[[heterodox]] *[[orthodox]] *Swedish: [[oortodox]] *German: [[unorthodox]] *Norwegian: [[uortodoks]] [[ru:unorthodox]] [[fi:unorthodox]] [[vi:unorthodox]] [[zh:unorthodox]] So to answer your question clearly and definitively: No.~~~~ Got most of this from this great site I just used for the honestly first time: it's called http://www.wiktionary.com. I have used WikiPedia before (http://www.wikipedia.org) but never witkionary. I a section on NPComplete at: http://meami.org/wiki/?NPcomplete you dearly for the interaction. --Martin Musatov m [ dot ] m m [ at ] v z w [ dot] b l a c k b e r r y [ dot ] net. p.s. Completely, please someone tell me if I am doing the email bracket thing wrong. I saw the way Mr. Cook did his and he had more spaces than mine. Is his way best? === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/20090423 Firefox/3.5b4,gzip(gfe),gzip(gfe) Also here are some additional related results: 1) Access to Photograph: \ http://documents.cern.ch/cgi-bin/setlink?base=PHO&categ=photo-tsic&id=dfbx-20\ 09-001 2)Conversions Information: Portable Document Format:http:// documents.cern.ch/archive/electronic/hep-lat/9612/9612008.pdf re:L****victor meldrew ...@yahoo.co.uk: I like a fool misspelled \orthodox\. While you share the same first name with my father I can only pray the reason the \666\ is there because 2/3 didn't fit. Re: \Does that mean it's bogus?\ ***You tell me: ***If you have feedback, I very much encourage, welcome, thank and appreciate. ***If anyone is attempting to disprove undecidability of P==NP please email me. On May 9, 2:46Êam, \victor meldrew ...@yahoo.co.uk\ > > > An informal and highly experimental, *unorthodox* proof > > Does that mean \bogus\?. No, you are welcome to try to disprove it. > > > P=NP has been > > published on CERN preprints. > > === Subject: Re: P=NP Proof Published at CERN Martin Musatov a \.8ecrit : > An informal and highly experimental, unorthadox proof P=NP has been > published on CERN preprints. > > \ http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-1939656818Hwf\ -1468147288IdV-15212827115758210PDF_HI0001.pdf > > It is mine, and no it is not published anywhere else. My purpose in > posting it here is for feedback and suggestions on how to strengthen > it. > > I would specifically, as was my intention with this experiment, like > feedback from anyone interested in the methodology I used and > suggestion as to how I might go about pursuing a more broadly accepted > peer-reviewed published proof building on this basic result. Dont worry : if you have really proved P=NP, any working program solving any NP-complete problem in polynomial time will be enough to bring you fame, the Clay prize money, and perhaps even chicks... > > > Martin Musatov > m[dot]mm[at]vzw[dot]blackberry[dot]net. === Subject: Re: P=NP Proof Published at CERN <4a054d67$0$296$7a628cd7@news.club-internet.fr> posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/20090423 Firefox/3.5b4,gzip(gfe),gzip(gfe) On May 9, 2:31Êam, Denis Feldmann \ > Martin Musatov a \.8ecrit : > > > An informal and highly experimental, unorthodox proof P=NP has been > > published on CERN preprints. > > >http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... > > > It is mine, and no it is not published anywhere else. My purpose in > > posting it here is for feedback and suggestions on how to strengthen > > it. > > > I would specifically, as was my intention with this experiment, like > > feedback from anyone interested in the methodology I used and > > suggestion as to how I might go about pursuing a more broadly accepted I am just going to answer all up here to make it easy: ****Denis: I understand the effort required to keep a nice garden, so I apologize if I trampled your shrubs. Re: \ http://www.ietf.org/html.charters/ecrit-charter.html, though I hope you're right re: neat results, Millenium Prize money, and the ladies! (though my heart is really with only one) ****victor meldrew 666@yahoo.co.uk: I like a fool misspelled \orthodox\. While you share the same first name with my father I can only pray the reason the \666\ is there because 2/3 didn't fit. Re: \Does that mean it's bogus?\ ***You tell me: ***If you have feedback, I very much encourage, welcome, thank and appreciate. ***If anyone is attempting to disprove undecidability of P==NP please email me. *A N Niel: the actual culprit believe it or not was Google docs uploading a .txt file converting to .pdf which created the in and out character/equations on the left side of the page. The vertical numbering appeared when I attempted to upload a proof a manuscript system. It looked very sturdy and well-enforced so I tried to throw it up against the CERN server and see if it woulds stick and it did. I then began to experiment with other \geometric\ databases: A first example of which can be found here: *http://cdsweb.cern.ch/record/1164207/export/xm note: no missing \L\ there... and: *http://documents.cern.ch/photo/photo-tsic/icon-dfbx-2009-001.gif a neat picture I used in developing my theory. My interests began in geometry and then shifted into numerical analysis and prime numbers so P==NP was my way to reconcile all of this. When I saw the error Google Docs generated I began to wonder if we could define functions pertaining to numerical analysis not by their presence but by their absence, and more specifically the geometry of the space that makes up that absence. After all as complicated as numbers can be we only have 10 plus a zero. In the end this was the shape, or an example of it in binary to which I was able to parse two sets of data readable and absent from one document: ****************************************************************************\ **************** NOTE: The Google Docs parsing began generating content vertically as it ran the equations I had prepared in a Microsoft Word file, then ctl +c, ctl+v into .txt file. IT RAN RIGHT THROUGH THE REFERENCES BEFORE SEALING OFF THE SOLUTION JUST THIS SIDE OF INFINITY it was pretty neat: ****************************************************************************\ ***************** So indeed my proof stands correct and I hope it makes its way over to Mr. Cook for his comments;! ****************************************************************************\ ***************** ----------Here is a sample parsing from a \Polynomial Time Algorithm\------------------------- MARTIN M. MUSATOV: m[dot]mm[at]vzw[dot]blackberry[dot]net An Open Address to Mr. Stephen A. Cook: sacook [at] cs [dot] toronto [dot] edu STATEMENT OF THE SOLUTION This solution to P versus NP explains how every language accepted by some non deterministic algorithm in polynomial time can be accepted by some (deterministic) algorithm in polynomial time. To define the solution it is formally it is necessary to observe the model of a computer, or Turing machine and process information in real-time as it is received as a computable function or linear stream. By this declaration, formally, the class P contains the indecision problems P = . ... . N. ... . P The area of a circle [2]: . ..=....2 The binomial theorem [3]: ..+.. ..= .. .. ........-.. .. ..=0 Expansion of a sum (Taylor Series) [4];. 1+.. ..=1+ .... 1! + .. ..-1 ..22! +. Followed by the Fourier Series [5]:. .. .. =..0+ ....cos ...... .. +....sin ...... .. 8 ..=1 The Pythagorean Formula [6]:. ..2+..2=..2 1 Arfken, G. \Special Coordinate Systems--Rectangular Cartesian Coordinates.\ ¤2.3 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 94-95, 1985. 2 Richmond, Bettina (1999-01-12). \Area of a Circle\. Western Kentucky University. Retrieved on 2007-11-04. 3Amulya Kumar Bag. Binomial Theorem in Ancient India. Indian J.History Sci.,1:68-74,1966. 4 \Neither Newton nor Leibniz - The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala\. MAT 314. Canisius College. Retrieved on 2006-07-09. 5William E. Boyce and Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Eighth edition. John Wiley & Sons, Inc., New Jersey, 2005. ISBN 0-471-43338-1 6Bell, John L., The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development, Kluwer, 1999. ISBN 0-7923-5972- 0. 7Heaton, H. (1896) A Method of Solving Quadratic Equations, American Mathematical Monthly 3(10), 236\[CapitalEth]237. Through the Quadratic Equation [7]:. ..= -..± ..2-4.... 2.. Page 2 of 3 http://mc.manuscriptcentral.com/imamat Manuscripts submitted to (i)The IMA Journal of Applied Mathematics(/i) To be succeed by a modified Taylor Series Expansion [8];. ....=1+ .. 1! + ..22! + ..33! +.,-8<..<8 ° > > peer-reviewed published proof building on this basic result. > > Dont worry : if you have really proved P=NP, any working program solving > any NP-complete problem in polynomial time will be enough to bring you > fame, the Clay prize money, and perhaps even chicks... > > > > > > Martin Musatov > > m[dot]mm[at]vzw[dot]blackberry[dot]net. > > === Subject: Re: P=NP Proof Published at CERN posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/20090423 Firefox/3.5b4,gzip(gfe),gzip(gfe) > On May 9, 2:31Êam, Denis Feldmann \ > > > > An informal and highly experimental, unorthodox proof P=NP has been > > > published on CERN preprints. > > > \ >http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-19396... > > > > It is mine, and no it is not published anywhere else. My purpose in > > > posting it here is for feedback and suggestions on how to strengthen > > > it. > > > > I would specifically, as was my intention with this experiment, like > > > feedback from anyone interested in the methodology I used and > > > suggestion as to how I might go about pursuing a more broadly \ accepted > > I am just going to answer all up here to make it easy: > ****Denis: I understand the effort required to keep a nice garden, so > I apologize if I trampled your shrubs. \ Re:http://www.ietf.org/html.charters/ecrit-charter.html, > though I hope you're right re: neat results, Millenium Prize money, > and the ladies! (though my heart is really with only one) > ****victor meldrew ...@yahoo.co.uk: I like a fool misspelled > \orthodox\. While you share the same first name with my father I can > only pray the reason the \666\ is there because 2/3 didn't fit. > Re: \Does that mean it's bogus?\ ***You tell me: > ***If you have feedback, I very much encourage, welcome, thank and > appreciate. > ***If anyone is attempting to disprove undecidability of P==NP please > email me. > *A N Niel: the actual culprit believe it or not was Google docs > uploading a .txt file converting to .pdf which created the in and out > character/equations on the left side of the page. The vertical > numbering appeared when I attempted to upload a proof a manuscript > system. It looked very sturdy and well-enforced so I tried to throw it > up against the CERN server and see if it woulds stick and it did. I > then began to experiment with other \geometric\ databases: > A first example of which can be found here: > *http://cdsweb.cern.ch/record/1164207/export/xm > note: no missing \L\ there... > and: > *http://documents.cern.ch/photo/photo-tsic/icon-dfbx-2009-001.gif > a neat picture I used in developing my theory. My interests began in > geometry and then shifted into numerical analysis and prime numbers so > P==NP was my way to reconcile all of this. When I saw the error Google > Docs generated I began to wonder if we could define functions > pertaining to numerical analysis not by their presence but by their > absence, and more specifically the geometry of the space that makes up > that absence. After all as complicated as numbers can be we only have > 10 plus a zero. In the end this was the shape, or an example of it in > binary to which I was able to parse two sets of data readable and > absent from one document: > \ *****************************************************************************\ *************** > NOTE: The Google Docs parsing began generating content vertically as > it ran the equations I had prepared in a Microsoft Word file, then ctl > +c, ctl+v into .txt file. IT RAN RIGHT THROUGH THE REFERENCES BEFORE > SEALING OFF THE SOLUTION JUST THIS SIDE OF INFINITY it was pretty > neat: > \ *****************************************************************************\ **************** > So indeed my proof stands correct and I hope it makes its way over to > Mr. Cook for his comments;! > \ *****************************************************************************\ **************** > ----------Here is a sample parsing from a \Polynomial Time > Algorithm\------------------------- > MARTIN M. MUSATOV: m[dot]mm[at]vzw[dot]blackberry[dot]net > An Open Address to Mr. Stephen A. Cook: sacook [at] cs [dot] toronto > [dot] edu > Ê Ê Ê Ê \ ÊSTATEMENT OF THE SOLUTION > This solution to P versus NP explains how every language accepted by > some non deterministic algorithm in polynomial time can be accepted by > some (deterministic) algorithm in polynomial time. ÊTo define \ the > solution it is formally it is necessary to observe the model of a > computer, or Turing machine and process information in real-time as it > is received as a computable function or linear stream. > By this declaration, formally, the class P contains the indecision > problems > P = > . > ... > . > N. > ... > . > P > The area of a circle [2]: . ..=....2 > The binomial theorem [3]: ..+.. ..= .. > .. > ........-.. > .. > ..=0 > Expansion of a sum (Taylor Series) [4];. > 1+.. ..=1+ > .... > 1! > + > .. ..-1 ..22! > +. > Followed by the Fourier Series [5]:. > .. .. =..0+ ....cos > ...... > .. > +....sin > ...... > .. > 8 > ..=1 > The Pythagorean Formula [6]:. ..2+..2=..2 > 1 Arfken, G. \Special Coordinate Systems--Rectangular Cartesian > Coordinates.\ ¤2.3 in > Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic > Press, pp. 94-95, 1985. > 2 Richmond, Bettina (1999-01-12). \Area of a Circle\. Western Kentucky > University. > Retrieved on 2007-11-04. > 3Amulya Kumar Bag. Binomial Theorem in Ancient India. Indian J.History > Sci.,1:68-74,1966. > 4 \Neither Newton nor Leibniz - The Pre-History of Calculus and > Celestial Mechanics in > Medieval Kerala\. MAT 314. Canisius College. Retrieved on > 2006-07-09. > 5William E. Boyce and Richard C. DiPrima, Elementary Differential > Equations and Boundary > Value Problems, Eighth edition. John Wiley & Sons, > Inc., New Jersey, 2005. ISBN 0-471-43338-1 > 6Bell, John L., The Art of the Intelligible: An Elementary Survey of > Mathematics in its > Conceptual Development, Kluwer, 1999. ISBN 0-7923-5972- > 0. > 7Heaton, H. (1896) A Method of Solving Quadratic Equations, American > Mathematical > Monthly 3(10), 236\[CapitalEth]237. > Through the Quadratic Equation [7]:. > ..= > -..± ..2-4.... > 2.. > Page 2 of 3http://mc.manuscriptcentral.com/imamat > Manuscripts submitted to (i)The IMA Journal of Applied Mathematics(/i) > To be succeed by a modified Taylor Series Expansion [8];. > ....=1+ > .. > 1! > + > ..22! > + > ..33! > +.,-8<..<8 ° > > > > peer-reviewed published proof building on this basic result. > > > Dont worry : if you have really proved P=NP, any working program \ solving > > any NP-complete problem in polynomial time will be enough to bring you > > fame, the Clay prize money, and perhaps even chicks... > > > > > Martin Musatov > > > m[dot]mm[at]vzw[dot]blackberry[dot]net. > > I have apparently been reviewed again as he page parsed at CERN and gave a new URL: Here it is: http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-1939656818Hw\ f-1468147288IdV-15212827115758210PDF HI0001.pdf?version=1 Version1, cool! > > > Martin Musatov > > > m[dot]mm[at]vzw[dot]blackberry[dot]net. === Subject: Re: a.s. question In seems that your reasoning works even when the random sequence has \ exponential distribution... or not? Laurence === Subject: Re: a.s. question > If X_1, X_2,... is a i.i.d. sequence of rv's with Cauchy distribution > what's the sequence b_n such that limsup X_n/b_n = c a.s. with 0 < c < \ +oo? > There is no such sequence. Suppose b_n is such a sequence. This means that for any epsilon > 0, almost surely there are infinitely many X_n with X_n > (c - epsilon) b_n, and almost surely only finitely many with X_n < (c + epsilon) b_n. In particular, almost surely there are infinitely many X_n with (c + epsilon) b_n > X_n > (c - epsilon) b_n. Now if epsilon is small enough, for sufficiently large t we have P{X > (c + epsilon) t} > P{(c+epsilon) t > X > (c-epsilon) t} so if a.s. there are infinitely many X_n with (c+epsilon) t > X_n > (c-epsilon) t, there will also a.s. be infinitely many with X_n > (c+epsilon) t. -- 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 ravages of the New Math > > > > [...] It is especially difficult for the integers; > to paraphrase > > Dirichlet in his famous paper, \What are and what > should > > be the `numbers'\, the essential conclusion is that > if it > > behaves like the numbers, it is a version of them. > There > > are two totally different basic concepts, and then > other > > concepts derived from extensions. > > Said famous paper \Was sind und was sollen die > Zahlen?\ > is by Dedekind, not Dirichlet. > > > One does not get a good understanding of a concept > from generalization > > I strongly disagree. One often gains great insight > via generalizations. > Indeed, much of abstract algebra evolved from the > interplay between > concrete and general manifestations of the intuitive > concept of number. > I interpreted Rubin as saying that utility is not equivalent to understanding. I think Dedekind would agree. Tom > --Bill Dubuque === Subject: Re: The ravages of the New Math >>> >>> [...] It is especially difficult for the integers; to paraphrase >>> Dirichlet in his famous paper, \What are and what should >>> be the `numbers'\, the essential conclusion is that if it >>> behaves like the numbers, it is a version of them. There >>> are two totally different basic concepts, and then other >>> concepts derived from extensions. >> >> Said famous paper \Was sind und was sollen die Zahlen?\ >> is by Dedekind, not Dirichlet. >>> >>> One does not get a good understanding of a concept from generalization >> >> I strongly disagree. One often gains great insight via generalizations. >> Indeed, much of abstract algebra evolved from the interplay between >> concrete and general manifestations of the intuitive concept of number. > > I interpreted Rubin as saying that utility is not equivalent > to understanding. My reply concerns only his above quoted remark on generalization. --Bill Dubuque === Subject: Re: The ravages of the New Math > >>> > >>> [...] It is especially difficult for the > integers; to paraphrase > >>> Dirichlet in his famous paper, \What are and what > should > >>> be the `numbers'\, the essential conclusion is > that if it > >>> behaves like the numbers, it is a version of > them. There > >>> are two totally different basic concepts, and > then other > >>> concepts derived from extensions. > >> > >> Said famous paper \Was sind und was sollen die > Zahlen?\ > >> is by Dedekind, not Dirichlet. > >>> > >>> One does not get a good understanding of a > concept from generalization > >> > >> I strongly disagree. One often gains great insight > via generalizations. > >> Indeed, much of abstract algebra evolved from the > interplay between > >> concrete and general manifestations of the > intuitive concept of number. > > > > I interpreted Rubin as saying that utility is not > equivalent > > to understanding. > > My reply concerns only his above quoted remark on > generalization. > Right. That one finds a generalization useful does not imply that one understands its root. For example, the field of complex numbers as a generalization of points in the Cartesian plane follows explicit rules for manipulating the algebra that solves equations requiring the imaginary number--does knowing the generalization and the rules, however, lend insight to complex analysis? Suppose, though, as Rubin suggests, that one begin with variables. Then how does substituting a complex variable affect the calculus,and why? To get there, one would need to understand the complex plane and the effect of rotations therein. Actually, I think Herman Rubin's pedagogy is the most intuitive. Tom > --Bill Dubuque === Subject: Discount wholesaler Air max shoes (paypal payment) www.guoshitrade.com posting-account=MBg39QoAAAAYL0CiYyBFqCxoPZc-xY64 TencentTraveler 4.0; CIBA),gzip(gfe),gzip(gfe) discount wholesaler Air max 95 shoes (paypal payment) ( www.guoshitrade.com ) wholesale Air Max 87 shoes discount wholesaler Air MAX LTD shoes sell Air max 90 shoes discount wholesaler Air Max 88 shoes (paypal payment) ( www.guoshitrade.com ) discount wholesaler Air MAX 89 shoes discount wholesaler Air max tn shoes discount wholesaler Air Max tn8 shoes discount wholesaler Air MAX tn9 shoes (paypal payment) ( www.guoshitrade.com ) discount wholesaler MEN'S WOMEN'S Shox R5 R4 trainers discount wholesaler Men's women's shocks OZ NZ TL trainers For more products pls visit: (paypal payment)( www.guoshitrade.com ) discount wholesaler Air max 95 shoes (paypal payment) ( www.guoshitrade.com ) wholesale Air Max 87 shoes discount wholesaler Air MAX LTD shoes sell Air max 90 shoes discount wholesaler Air Max 88 shoes (paypal payment) ( www.guoshitrade.com ) discount wholesaler Air MAX 89 shoes discount wholesaler Air max tn shoes discount wholesaler Air Max tn8 shoes discount wholesaler Air MAX tn9 shoes (paypal payment) ( www.guoshitrade.com ) discount wholesaler MEN'S WOMEN'S Shox R5 R4 trainers discount wholesaler Men's women's shocks OZ NZ TL trainers For more products pls visit: (paypal payment)( www.guoshitrade.com ) discount wholesaler Air max 95 shoes www.guoshitrade.com wholesale Air Max 87 shoes discount wholesaler Air MAX LTD shoes sell Air max 90 shoes discount wholesaler Air Max 88 shoes www.guoshitrade.com discount wholesaler Air MAX 89 shoes discount wholesaler Air max tn shoes discount wholesaler Air Max tn8 shoes discount wholesaler Air MAX tn9 shoes www.guoshitrade.com discount wholesaler MEN'S WOMEN'S Shox R5 R4 trainers discount wholesaler Men's women's shocks OZ NZ TL trainers For more products pls visit: www.guoshitrade.com discount wholesaler Air max 95 shoes www.guoshitrade.com wholesale Air Max 87 shoes discount wholesaler Air MAX LTD shoes sell Air max 90 shoes discount wholesaler Air Max 88 shoes www.guoshitrade.com discount wholesaler Air MAX 89 shoes discount wholesaler Air max tn shoes discount wholesaler Air Max tn8 shoes discount wholesaler Air MAX tn9 shoes www.guoshitrade.com discount wholesaler MEN'S WOMEN'S Shox R5 R4 trainers discount wholesaler Men's women's shocks OZ NZ TL trainers For more products pls visit: www.guoshitrade.com === Subject: wavelength/Diameter question posting-account=4bJiBwoAAABx6ELU3eKqFPIAOGmQlYVP Trident/4.0; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET \ CLR 3.0.30618; .NET CLR 3.5.30729; InfoPath.2; \ yie8),gzip(gfe),gzip(gfe) Resolving power is equal to theta = wavelength (of light) / diameter (of aperture) of a telescope. How is the relationship acquired? I know there is a sine involved.. as in sine theta = wavelength / diameter but what has the wavelength (of light) got to do with the diameter (of the aperture) geometrically? For example, wavelength at green light is 0.00055 micron Aperture is say 100mm. Resolving power is theta = 0.00055/100 = 0.0000055 radian or 1.34 arcsecond How does wavelength, diameter relate geometrically? Why? Pete === Subject: Re: wavelength/Diameter question posting-account=33KaEgkAAAA9tz8WICNABjrkyMKXFbGS AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.65 \ Safari/525.19,gzip(gfe),gzip(gfe) > > Resolving power is equal to theta = wavelength (of light) / diameter > (of aperture) of a telescope. How is the relationship acquired? > > I know there is a sine involved.. as in > > sine theta = wavelength / diameter > > but what has the wavelength (of light) got to do with the > diameter (of the aperture) geometrically? > > For example, wavelength at green light is 0.00055 micron > Aperture is say 100mm. > > Resolving power is theta = 0.00055/100 = 0.0000055 radian > or 1.34 arcsecond > > How does wavelength, diameter relate geometrically? ÊWhy? > > > Pete sin( theta ) ~ theta for small theta, = lambda/D. So it does not matter for paraxial rays. === Subject: Re: Calendar versus pyramidal numbers posting-account=lREQ0goAAABJGVkI7Y-7onQ9_lq1aWhl .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET \ CLR 3.0.30618),gzip(gfe),gzip(gfe) > > > > > > > > > Refound in another context are thereby the main figures from that \ Old- > > > Cretan \ inscription:http://www.youtube.com/watch?v=CKw4hP3fNvkhttp://web.gvdnet.dk/GV\ D002... > > > Ole > > > To have solved thisdiscis of course a faithful matter, at the age of > > 32 . > > I must ask you full of sadness: What is the matter with you? > > DonÕt you understand that I am in need of just a handfull \ of > > followers > > not to have my life ruined by them Õ grey \ dogsÕ. > > The hollow pyramid is the long awaited key, as you ought to know; The > > equivalence to thePhaistosdisc. > > Ole \ Hagenhttp://web.gvdnet.dk/GVD002393/chain3.htmhttp://www.youtube.com/watch...\ > > My urge did fail, or what? Are you seeking cannibalistic advantages , > by keeping mute? (hopefully beeing members of the club;-) > Let me tell you this: Under the parallel world of depression in the > thirties, people in Europe with dislexia was sterialized; > excalating... > For God sake(and the equality of men) let this never be again! > Chain smoker > Ole Hagenhttp://www.youtube.com/watch?v=CKw4hP3fNvk- Skjul tekst i \ anf¿rselstegn - > > - Vis tekst i anf¿rselstegn - Another demonstration: http://www.youtube.com/watch?v=Lwnc3Y1M sE http://web.gvdnet.dk/GVD002393/FIG05C.htm === Subject: Re: The complete infinite binary tree has only countably many posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > ... > Ê> > Ê> Less than omega is not enough to evade \ the case that the diagonal of > Ê> > Ê> the list > Ê> > Ê> > Ê> > Ê> 0.0 > Ê> > Ê> 0.1 > Ê> > Ê> 0.11 > Ê> > Ê> 0.111 > Ê> > Ê> ... > Ê> > Ê> is not distinct from every line. > Ê> > > Ê> > Pray tell to which line it is equal. > Ê> > Ê> If all lines exist, then N is in a line. > > By which rule? Ê(And we were talking about the diagonal...) By the rule that the diagonal cannot exist without lines. The diagonal is made from the last digits of the lines. If the diagonal were longer than every line, then it could not exist. The diagonal has more digits than every line. Hence there must be a line that has more digits than every line. Or actual infinity is wrong a concept. === Subject: Re: The complete infinite binary tree has only countably many > > not enough to evade the case that the diagonal of Ê> > \ Ê> the list > > Ê> > Ê> Ê> > Ê> 0.0 \ Ê> > Ê> 0.1 Ê> > Ê> 0.11 \ Ê> > Ê> 0.111 Ê> > Ê> > > ... Ê> > Ê> is not distinct from every line. \ Ê> > Ê> > Pray tell to > > which line it is equal. Ê> Ê> If all lines \ exist, then N is in a > > line. > > > > By which rule? Ê(And we were talking about the \ diagonal...) > > By the rule that the diagonal cannot exist without lines. Non sequitur. > The diagonal is made from the last digits of the lines. > If the diagonal were longer than every line, then it could not exist. If the \diagonal\ is NOT longer than every line, it cannot exist (unless there is a longest line, which there isn't). WM, as usual, has things backwards. > The diagonal has more digits than every line. Which immediately requires it to be longer than every line! > Hence there must be a line > that has more digits than every line. Only in the warped mathUnrealistic world of WM. >Or actual infinity is wrong a concept. 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halloween joke photos of halloween funny halloween costume photos adult nightclub photos halloween michael myers halloween photos halloween movie photos leandra halloween photos bootlegged rob zombie halloween photos halloween face painting photos mickeys not so scary halloween photos halloween wallpaper photos brazilian halloween mission rock photos halloween food photos photos of athens ohio halloween party calente resort halloween photos photos halloween costumes halloween photos halloween parade photos halloween photos at night time photos of halloween h20 halloween party photos hot halloween recipes photos halloween panic photos photos halloween === Subject: Re: Why physicists never say: =?windows-1252?Q?=91potential_ma?= =?windows-1252?Q?ss/energy_E=3DMc=5E2=92_=3F?= > On 7 Maj, 15:15, \Paul B. Andersen\ >>> On 7 maijs, 08:21, \Paul B. Andersen\ >>>>> While Strich was arguing about the failings of relativity he stated: >>>>> \TRILLIONS and trillions of neutrinos, and not one of a right-handed >>>>> helicity\ >>>> Quote from the above: >>>> << >>>> In summary, here is what we have established: >>>> 1) Helicity is frame-dependent. >>>> 2) Neutrino helicity is frame dependent. >>>> 3) We expect both left and right handed neutrinos. >>>> According to relativity, a non-massless neutrino would have frame- >>>> dependent helicity. According to relativity, we would expect to \ find >>>> left-handed and right-handed neutrinos. What does experiment find? >>>> 4) Experiment only finds left-handed neutrinos. >>>> The Helicities of neutrinos are never measured. >>>> The helicity is measured in a frame of reference where the decaying \ metal >>>> are found. >>>> all neutrinos are left handed. >>>> Logic isn't Strich's strong side, so he makes the rather naive >>>> error that this implies that the helicity of neutrinos is invariant. \ :-) >>>> Would you please repeat the hilarious reasoning that leads >>>> to this conclusion, Strich? :-) >>>> -- >>>> Paul >>>> http://home.c2i.net/pb_andersen/ >> Strich using his 200 IQ BRAIN: >> >>> Here is perenial idiot Paul trying to argue that Beowulf, unicorns and >>> right-handed neutrinos exist in some fantasyland. >>> The temperature in Paul's homeland was so low that his brain has been >>> frozen at the infant level :-) >> Since you find it too embarrassing to repeat the reasoning that lead >> to the conclusion that always the same in one particular frame imply >> invariance, I will do it for you: >> >> >> << >> A child would indeed think the metal is solid. A physicist would >> know the atoms are vibrating, in all directions. Sometimes, this >> velocity can be faster than the neutrino. Remember, we are now in \ the >> quantum world. The uncertainty principle certainly grants me a few >> atoms with velocity much faster than the neutrino. >> >> >> >> What's makes this even more hilarious is that if the decaying atom \ really >> did move faster than a neutrino, we would in Goldhabers experiment have: >> >> c <-gamma v <-neutrino >> >> The gamma is measured to be left handed. >> Which means that the neutrino is right handed. >> >> But Strich is too dumb and ignorant to understand this, logic >> is - as so frequently demonstrated - not his strong side, so what >> else can he do than responding with the following ad hominems? > Paul the perenial idiot is still confused about the Goldhaber > experiment, and insists that all the right-handed neutrinos are hiding > somewhere, most likely in the hair of Goldilocks or the armor of > Beowulf. See? :-) > Worse, he thinks that a metal is solid despite the century old proof > by Rutherford that an atom is mostly space. > > And as expected, he is totally ignorant of the Heisenberg Uncertainty > Principle and its numerous implications... -- Paul http://home.c2i.net/pb_andersen/ === Subject: Re: Why physicists never say: =?windows-1252?Q?=91potential_ma?= =?windows-1252?Q?ss/energy_E=3DMc=5E2=92_=3F?= > > Brad, luckily for me, I said trillions and trillions, for this merely > implied addition, as opposed to trillions upon trillions, which > implies multiplication. The former is at least 4E12 while the latter > is at least 4E24. Yeah, lucky! And stoooopid! === Subject: Dorn Strich, P.D. is at: TheDraperFamily @ gMail .COM DornÊStrich, P.D. is at: TheDraperFamily @ gMail .COM By the way, unlike Google Groups, NNTP servers don't block this eMail address \.81\\ eMail harvesters already have it. Better to use an eMail addess like mine: _@Paul_Draper.Austin.inValid ScreenShot of me googling \.81g \paul draper\, \Cedar Park\, Texas \ \.81h: www.JeffRelf.F-M.FM/Paul-Draper.PNG Cedar Park [ near Austin ] High School Band Booster Director Digital Marketing Strategy @ Houghton Mifflin Harcourt Indiana University Bloomington B.A., M.S., Physics, Philosophy, 1974 \.81\\ 1980, University of Kansas Lawrence ( Kansas ) High School 1974 born September 14th, 1956 I'm not the only who can find this informatin, so please don't blame me. === Subject: Solution Manual to Accounting Information Systems posting-account=_ObeYAoAAABc8H8zknYzs3d0mwhkVSTP CLR 2.0.50727; CIBA),gzip(gfe),gzip(gfe) I have the following solutions manual. To get the solution manual you want, just contact me. My email address is hotsolution@hotmail.com, hotsolution(at) hotmail.com, please replace (at) to @ , just send email to me. Note: All solutions manual in soft copy that mean in PDF format or doc format. 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Any idea is welcome, Alain === Subject: Re: The complete infinite binary tree has only countably many infinite paths. posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG Gecko/20080829 Firefox/2.0.0.17,gzip(gfe),gzip(gfe) >> 0.333... is an abbreviation of 1/3 or one third, exactly. >> But \0.333...\ is only a name consisting of eight symbols. >> By means of digits it seems impossible to get more than the sequence >> (a_n) = SUM [n in N] 3*10^-n >> 0.3 >> 0.33 >> 0.333 >> ... >> which does not include a representation of 1/3 with an infinite number >> of digits. I conclude that it is not possible to obtain such a >> representation. Do you know a tool how to accomplish it? > >> Perhaps something other than a list of finite-length digit strings? > > Namely? Um, something that produces infinite-length digit strings? 0.333... is a digit string of infinite length. Your attempt to construct it using a sequence of finite-length digit strings is obviously the wrong approach. It's like trying to find an odd number by listing all the even numbers. It simply, and obviously, does not work. Perhaps you should consider a method that produces strings of infinite length in order to derive the particular string you're looking for. === Subject: Re: The complete infinite binary tree has only countably many infinite paths. posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > >> 0.333... is an abbreviation of 1/3 or one third, exactly. > >> But \0.333...\ is only a name consisting of eight symbols. > >> By means of digits it seems impossible to get more than the sequence > >> (a_n) = SUM [n in N] 3*10^-n > >> 0.3 > >> 0.33 > >> 0.333 > >> ... > >> which does not include a representation of 1/3 with an infinite number > >> of digits. I conclude that it is not possible to obtain such a > >> representation. Do you know a tool how to accomplish it? > > >> Perhaps something other than a list of finite-length digit strings? > > > Namely? > > Um, something that produces infinite-length digit strings? > > 0.333... is a digit string of infinite length. Your attempt > to construct it using a sequence of finite-length digit > strings is obviously the wrong approach. It's like trying > to find an odd number by listing all the even numbers. > It simply, and obviously, does not work. > > Perhaps you should consider a method that produces > strings of infinite length in order to derive the particular > string you're looking for Such a method does not exist. At least it does not appear in any Cantor list. If it would exist, then the binary tree would show that the number of reals is limited by a countable set. === Subject: Re: The complete infinite binary tree has only countably many infinite paths. <2009050717325250073-angrybaldguy@gmailcom> posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > >> However, for every natural number, there is a line that contains it. > > > That's what I meant. All natural numbers are elements of the union of > > all lines. > > This is true. This is not true, but merely a meaningless sentence. But it would be true if all natural numbers and all lines existed. > > But the union of all lines in your list is an infinite set, and no line > in your list is an infinite set. That is a contradiction. > Furthermore, you need to perform > infinitely many unions to obtain it, so I don't think the union of all > lines in your list is constructable in the sense you use the term. Every line is constructable. Everything that does exist is constructable. An infinite set is not constructable, although every element is constructable. Doesn't this shed some light on this kind of mathematics? At least it proves that what you call the infinite set is different from all its elements, because they are constructable --- every element and all smaller elements (if we consider an ordered set like N). Your kind of maths requires that you deny the basic equality every element and all smaller elements = all elements. That is a contradiction. > > But if looked at closely enough we see: ZFC does claim: There exists > > an infinity set, implying that its elements are fixed. Therefore there > > are all numbers in the list. There are all lines existing > > simultaneously. > > Yes. > > > But it is forbidden to consider all lines as existing simultaneously. > > No. All of the lines in the list exist if the list exists. They do not > pop in and out of existence. You (and I) must consider all lines as > existing, simultaneously, at every point in any discussion about the > list. Therefore also the elements do not pop in and out. Unless there is some non-linearity, there is no chance for the lines to get rid off all smaller numbers. Every line contains all smaller numbers. Every and all smaller = all. > > We may identify the lines by their properties, and no line has the > property that it contains every natural number (trivially, for each > line L, the natural number max(L) + 1 is not in that line). We can only > identify for every natural number a line that contains that natural > number. That is potential infinity. No line in Cantor's list has the property to be the last and final one. Therefore its contents is unknown and remains so. > > > Only some line B may be considered behind which another line B' may > > appear, if necessary. > > No. If you have line B, then you NECESSARILY have line B' (the > successor to B). That's the very reason your assertion that there is a > line containing every natural number is so much garbage: See Weyl. Line B' necessarily contains what all its predecessors contain. This fact can be predicted with mathematical precision for every successor. > if there were > a line B that contained every number that is an element of any line, > then you would NECESSARILY have line B', which contained an element not > in B. You are the one chosing to argue that there is some line B with > no line B'. No. I only know that there is no finished infinity which is tantamount to an infinite finite line, i.e., an infinite line in a set of finite lines. > > The list can simultaneously be considered as a set of numbers as as a > > set of lines. > > Why not? > > If you consider each element of the list as a number, then you must > also adjust the entire rest of your argument to match the change of > conventions: > > Every element of the list > > Ê1 (from {1}), > Ê2 (from {2, 1}), > Ê3 (from {3, 2, 1}), > Ê... > > is a natural number. There is no element e of this list such that for > every element f of the list, e >= f. > > This is EXACTLY the same argument as presented about your list of > finite sets of natural numbers. You cannot escape from the argument by > changing the premise to an isomorphic one, because for every list > isomorphic to the natural numbers, there will be an argument that the > number of elements of that list is greater than any natural number. And in any case it will be wrong and refurable by the same basic axiom: > > >>> All are in one line or not all are in one line. > > >> For every natural number, there is a line in the list that contains it > > > and *all* preceding numbers. > > Red herring. For me it is an undisputable truth and not subject to negotiations: And I know that many sober minds support my position. Of course in order to do exercises in matheology, this premise may be dropped. > > >> For every line L, every element of L is an element of L's successor. > > >> For every line L, L's successor contains an element that L does not. > > > For every L's successor there is a line that contains it and L. > > For every L's successor L' there is a line L'' that contains L' and L. > > But L'' has a successor that contains an element not in L''. And there is no successor that is not contained in some line, together with all its predecessors. (Finite logic is not suitable for infinite sets, cp. Weyl.) > > >> None of these facts imply that there is a line that contains every > >> natural number, and the third one directly implies that there is no > >> line that contains every element. > > > And the fact that \every number and all preceding numbers\ is the \ same > > as \all numbers\ shows that your logic is inconclusive and not > > convincing. By no means it is justified to apply it in this one-way- > > road-manner. > > I am doing no such thing. At every point in my argument, I attempt to > assume both that there is a line that contains every element of every > line, and that every line has a successor that's distinct from it. > Provably, both of those *cannot* be true of the same list. So which > statement do you wish to discard? Both. Infinity is potential. There is no finished infinite set. Elements are not existing somewhere but are created. That's the only possible escape from the trap of infinity. === Subject: Re: The complete infinite binary tree has only countably many \ infinite paths. > > > >> However, for every natural number, there is a line that contains it. > > > > > That's what I meant. All natural numbers are elements of the union of > > > all lines. > > > > This is true. > > This is not true, but merely a meaningless sentence. Then in the weird world of WM, all sentences are equally maeaningless. > But it would be > true if all natural numbers and all lines existed. In order to prove they do not one must a priori assume they do not. And WM always denies assuming his assumptions. > > > > But the union of all lines in your list is an infinite set, and no line > > in your list is an infinite set. > > That is a contradiction. Not unless one requires that union to be one of its members, which is unsound mathematics. > > > Furthermore, you need to perform > > infinitely many unions to obtain it, so I don't think the union of all > > lines in your list is constructable in the sense you use the term. > > Every line is constructable. > Everything that does exist is constructable. Even in strict constructivism that is not claimed. The most that is claimed is that unless a thing can be constructed it cannot be KNOWN to exist. > An infinite set is not constructable, although every element is > constructable. Which only restricts constructivists to saying that infinite sets cannot be proved to exist. But, equally for constructionists, they cannot be proved not to. > Doesn't this shed some light on this kind of mathematics? It sheds a lot more light on the anti-mathematics of WM. > > At least it proves that what you call the infinite set is different > from all its elements, because they are constructable. Perhaps different from each of its elements, but not necessarily different from \all\ of them. In ZFC, and I suspect any decent set theory, if there are to be any unconstructable-because-infinite sets, there are also sets whose members are not constructible. > > Your kind of maths requires that you deny the basic equality > every element and all smaller elements = all elements. Is that one of the axioms of WM's anti-set theory? It is certainly not true for \elements\ which are not ordered. And the mention of elements presumes a set to which they belong > > That is a contradiction. It is nonsense as stated. > > > > But if looked at closely enough we see: ZFC does claim: There exists > > > an infinity set, implying that its elements are fixed. Therefore \ there > > > are all numbers in the list. There are all lines existing > > > simultaneously. > > > > Yes. > > > > > But it is forbidden to consider all lines as existing simultaneously. > > > > No. All of the lines in the list exist if the list exists. They do not > > pop in and out of existence. You (and I) must consider all lines as > > existing, simultaneously, at every point in any discussion about the > > list. > > Therefore also the elements do not pop in and out. Unless there is > some non-linearity, there is no chance for the lines to get rid off > all smaller numbers. While true, it is totally irrelevant. Another attempt by WM to introduce red herrings. > > Every line contains all smaller numbers. Not unless every line IS a number. > > > > > We may identify the lines by their properties, and no line has the > > property that it contains every natural number (trivially, for each > > line L, the natural number max(L) + 1 is not in that line). We can only > > identify for every natural number a line that contains that natural > > number. > > That is potential infinity. That is an actual infinity of lines, since lines are or are not but do not flicker into and out of existence like fireflies lights. > No line in Cantor's list has the property to be the last and final > one. > Therefore its contents is unknown and remains so. When sets are defined by properties, as N is in ZFC, then satisfying the appropriate properties is the only condition for membership. WM seems to have some other criterion for set membership, which is irrelevant in all standard set theories. > > > > > Only some line B may be considered behind which another line B' may > > > appear, if necessary. > > > > No. If you have line B, then you NECESSARILY have line B' (the > > successor to B). That's the very reason your assertion that there is a > > line containing every natural number is so much garbage: > > See Weyl. > Line B' necessarily contains what all its predecessors contain. This > fact can be predicted with mathematical precision for every successor. When WM can produce a line that contains all of its SUCCESSORS, only then will he have anything but garbage as his own set theory. > > > > if there were > > a line B that contained every number that is an element of any line, > > then you would NECESSARILY have line B', which contained an element not > > in B. You are the one chosing to argue that there is some line B with > > no line B'. > > No. Yes! > I only know that there is no finished infinity which is tantamount > to an infinite finite line, i.e., an infinite line in a set of finite > lines. It ain't what you don't know that hurts you, it's what you know for sure that just ain't so. And WM is hurting. > > > > The list can simultaneously be considered as a set of numbers as as a > > > set of lines. > > > Why not? > > > > If you consider each element of the list as a number, then you must > > also adjust the entire rest of your argument to match the change of > > conventions: > > > > Every element of the list > > > > Ê1 (from {1}), > > Ê2 (from {2, 1}), > > Ê3 (from {3, 2, 1}), > > Ê... > > > > is a natural number. There is no element e of this list such that for > > every element f of the list, e >= f. > > > > This is EXACTLY the same argument as presented about your list of > > finite sets of natural numbers. You cannot escape from the argument by > > changing the premise to an isomorphic one, because for every list > > isomorphic to the natural numbers, there will be an argument that the > > number of elements of that list is greater than any natural number. > > And in any case it will be wrong and refurable by the same basic > axiom: > Equally axiomatic is \Every and all smaller\ == \Every and all larger\. Consider how it applies to, for example, the set of negative integers. > > > > >>> All are in one line or not all are in one line. > > > > >> For every natural number, there is a line in the list that contains \ it > > > > > and *all* preceding numbers. > > > > Red herring. > > For me it is an undisputable truth and not subject to negotiations: Is it equally true that for every line there is a successor line? If so then \Every and all smaller\ == \Every and all larger\. > \Every and all smaller\ == \Every and all larger\. > > And I know that many sober minds support my position. Of course in > order to do exercises in matheology, this premise may be dropped. And to do much of mathematics WM-ology must be dropped. > > > > At every point in my argument, I attempt to > > assume both that there is a line that contains every element of every > > line, and that every line has a successor that's distinct from it. > > Provably, both of those *cannot* be true of the same list. So which > > statement do you wish to discard? > > Both. Infinity is potential. There is no finished infinite set. One and only one of the following can hold: There is a last line. There is no last line. WM rejects tertium non datur. > Elements are not existing somewhere but are created. That's the only > possible escape from the trap of infinity. I prefer escape from WM's illogical, unproven and unprovable assumptions. === Subject: Re: The complete infinite binary tree has only countably many infinite paths. posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > > Every line is constructable. > > Everything that does exist is constructable. > > Even in strict constructivism that is not claimed. The most that is > claimed is that unless a thing can be constructed it cannot be KNOWN to > exist. If these things are nothing but thoughts, then \cannot be known to exist\ is tantamount to \exist\. > > Your kind of maths requires that you deny the basic equality > > every element and all smaller elements = all elements. > > Is that one of the axioms of WM's anti-set theory? > It is certainly not true for \elements\ which are not ordered. > And the mention of elements presumes a set to which they belong \every element and all smaller elements\ = \all elements\ This is an axiom that holds for all sequences, for instance the sequence of natural numbers. If you find a theory which does not accept this axiom, then better forget it. === Subject: Re: The complete infinite binary tree has only countably many infinite paths. posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > > > >> However, for every natural number, there is a line that contains it. > > > > That's what I meant. All natural numbers are elements of the union of > > > all lines. > > > This is true. > > This is not true, but merely a meaningless sentence. But it would be > true if all natural numbers and all lines existed. So we have WM: if all natural numbers and all lines exist then all natural numbers are elements of the union of all lines. from which immediately follows i: if all natural numbers and all lines exist then no line contains all natural numbers This is the first half of the putative contradiction. To finish this contradicton we need ii: if all natural numbers and all lines exist then there exists a line that contains all natural numbers However, if all natural numbers exist and all lines exist, then neither the set of natuaral numbers nor the set of lines has a last element. To finsh the contradiction, we need a proof of ii that does not assume a last element. WM has not provided such a proof. - William Hughes === Subject: Re: The complete infinite binary tree has only countably many infinite paths. posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR \ 3.5.30729),gzip(gfe),gzip(gfe) > If all numbers are in the list but not in any single line, then there > must be at least two lines A and B such that there are two numbers a > and b with > (a e A & b !e A) & (b e B & a !e B). Wrong. This is a list of ALL the numbers in increasing order, so, since for all distinct a and b, either a Can you supply a natural number n, that the program won't print? No. Can you understand that at *any* step there are infinitely many numbers remaining that have not been printed and will never be printed, because they belong to the set that is remaining after any step? This is a contradiction contradicting the axiom of infinity. \... classical logic was abstracted from the mathematics of finite sets and their subsets .... Forgetful of this limited origin, one afterwards mistook that logic for something above and prior to all mathematics, and finally applied it, without justification, to the mathematics of infinite sets. ... As Brouwer pointed out this is a fallacy, the Fall and Original sin of set theory even if no paradoxes result from it.\ (Hermann Weyl) === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > > > Can you supply a natural number n, that the program won't print? > > No. Can you understand that at *any* step there are infinitely many > numbers remaining that have not been printed and will never be > printed, because they belong to the set that is remaining after any > step? that \1\ has not and never will be printed because it belongs to the set that is remaining. That's a lame argument even for you. Oh, and limit one crank per thread, pally. You're already consuming most of the attention on sci.math, and have been for many, many, years. THIS thread is the one where we make fun of LudicoVan, not the thread where we make fun of you. Aren't you satisfied with getting the vast majority of the attention? You have to inject your sense of humor in here as well? I see we can add greediness to your list of vices. Marshall === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > > > Can you supply a natural number n, that the program won't print? > > No. Wolenmuekenheim logic There are infinitely many natural numbers that will never be printed. It is impossible to supply one of them. - William Hughes === Subject: Re: Diagonal wanderings (incongruent by construction) >> >>> >>> Can you supply a natural number n, that the program won't print? >>> >> No. >> > Wolenmuekenheim logic[:] > > There are infinitely many natural numbers that will never be \ printed. > > It is impossible [for him] to supply one of them. > Oh, c'mon. That's easy: There are SO MANY of them, that he simply does not know where to start! :-) Herb === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Right now, the only mathematician of whom I am aware is making > an attempt at an inconsistency proof is Ed Nelson. He believes > that he can proof PA to be inconsistent -- and since ZFC proves > that PA is consistent, if PA is proved to be inconsistent, then > ZFC would also be proved inconsistent. Here is another proof: http://www.hs-augsburg.de/~mueckenh/GU/GU12.PPT#361,25,Folie 25 === Subject: Re: Diagonal wanderings (incongruent by construction) > >> Right now, the only mathematician of whom I am aware is making >> an attempt at an inconsistency proof is Ed Nelson. He believes >> that he can proof PA to be inconsistent -- and since ZFC proves >> that PA is consistent, if PA is proved to be inconsistent, then >> ZFC would also be proved inconsistent. > > Here is another proof: > http://www.hs-augsburg.de/~mueckenh/GU/GU12.PPT#361,25,Folie 25 > Yes, that is a proof. It proves that you are even too stupid to provide a working link. === Subject: Re: Diagonal wanderings (incongruent by construction) <20090506222934.N59609@agora.rdrop.com> \ posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > > ... you need not search the whole universe in order to find a second one \ if > > you have got the first. > > But, yes, in order to be sure that 1 (or any other number) does not > > appear in a sequence you must know the whole sequence. > > Or perhaps you need to only know a property shared by every > element in the sequence. For example, every element in the > sequence of even integers is even. This is true regardless > of how many elements have been \searched\ or how many > remain to be \searched\. One such property is that every set of natural numbers has even or odd cardinality. If you know this, you can exclude that there is a set of natural numbers with cardinal number aleph_0 (because aleph_0 + 1 = aleph_0). Yes, such conjectures could be done, if infinity would follow the same logic as finity. But it seems it doesn't. So why do you believe it does in case of Cantor's simple idea? === Subject: Re: Diagonal wanderings (incongruent by construction) <20090506222934.N59609@agora.rdrop.com> \ posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I WM continues to deliberately confuse elements and sets of elements. One such property is that every natural number has even or odd cardinality. Look! Over There! A Pink Elephant! > One such property is that every set of natural numbers has even or odd > cardinality. - William Hughes === Subject: Re: Diagonal wanderings (incongruent by construction) <20090506222934.N59609@agora.rdrop.com> \ posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > >> The computed number differs from every entry > >> checked up to the n-th line. > >> It does not differ from all lines, given that > >> there are more than n + 1 for every n. > >> It does not differ from all lines unless the > >> list can be checked completely. > > >> Another consequence of your rule is > >> One (1) does not differ from all even integers unless the > >> list (of even integers) can be checked completely. > > > No. If you know that an element exists only once in the world, ... > > And how do you know that? I don't know that. But I know that 1 is unique in N. > > > ... you need not search the whole universe in order to find a second one \ if > > you have got the first. > > But, yes, in order to be sure that 1 (or any other number) does not > > appear in a sequence you must know the whole sequence. > > Or perhaps you need to only know a property shared by every > element in the sequence. For example, every element in the > sequence of even integers is even. This is true regardless > of how many elements have been \searched\ or how many > remain to be \searched\. This is true if it is possible that a meaning can be given to the word \every\. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media \ Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR \ 3.0.30618),gzip(gfe),gzip(gfe) > > > So what are *you* asking for when you ask whether the program can \ *output* > > > its anti-diagonal? > > > That's the key issue here: what's this anti-diagonal at all. Note that > > the OP is about falsifying the diagonalisation procedure: by showing > > that the anti-diagonal is not a valid construct. I have put this in > > terms of an incongruency: an incomplete list by a complete anti- > > diagonal. > > you need to say more about what you are getting at here. \ ÊThere are > too many terms (like \complete\, \incongruency\) where I don't know > what of several possible sense you intend. Ê(\falsifying a \ procedure\ > is already problematic, since procedures don't normally have truth \ values) > > Maybe you can clarify. I'afraid, not more than I have already tried. For instance you might see my reply to Mr Chow: [quote] Not that part, it's the conclusion that is \problematic\. We have a construction of the list (our 'f'), then we define the construction of an item ('d') so that it differs in each place for each item in the list given by 'f'. If we now run this game of 'f' against 'd', there is no winner, yet Cantor's conclusion is that the anti-diagonal wins. [/quote] -LV === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media \ Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR \ 3.0.30618),gzip(gfe),gzip(gfe) > > > > > > Face facts: Cantor's diagonal proof that |R| > |N| is SIMPLE. \ ÊIt has > > > > > even been CHECKED BY COMPUTERS. > > > > > Formal proofs are irrelevant to the diagonal argument: they have it > > > > embedded, as an informing principle, into their axioms and > > > > definitions. > > > > Why should we believe this assertion of yours? > > > You have made it several times, and not yet given the slightest > > > reason for anyone to believe it. > > > There has been a discussion specifically on this in the thread \Levy > > proof that R is uncountable\: > > > I have been following the thread. > > You have rightly said that logical priority is different from historical > priority. At no point Êhave you or anyone else given us any \ reason > to suppose that the diagonal argument is embedded into the axioms > and definitions of either classical or constructive theories > of the real numbers. You can say that nobody has explicitly acknowledged it, but this point is clear enough. I just won't go back collecting links on this too, I can't take the burden of what is rather a problem of \generalised denial\. -LV === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > > > > > > > > As others have noted, if you are serious about constructivism, so \ that > > > not only the decimal expansions of the reals is taken to be > > > constructive, but also an enumeration of such reals is itself given > > > constructively, then lo and behold it is possible to construct \ effectively > > > a real not in the given list. > > > > This argument is given eg by Bishop in his book \Constructive \ Analysis\. > > > It might help such as LV to note that Bishop does not state the claim \ in > > > the form that one set is larger than another, but in the form that \ says > > > that for any effectively given enumeration, a missing real can be > > > constructed. > > > That is only true if the reals are given as infinite sequences of > > digits (which is in principle impossible). If they are given in the > > form of finite words, the argument fails because the lis of all finite > > words does not allow a diagonal: > > If a real is defined well enough in words to be constructively > distinguished from any other equally well defined real, that is possible, > its decimal > expansion to any desired finite extent should be finitely constructible, Nevertheless this expansion does not help anything at all because it is not the expansion that distinguishes the real from all others but the finite definition. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media \ Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR \ 3.0.30618),gzip(gfe),gzip(gfe) > > > > Whether an intuitionist accepts the axioms used in the diagonal > > > argument is one matter. But ASIDE from the axioms, the LOGIC used in > > > the diagonal argument IS intuitionistic. > > > The diagonal argument is impredicative. > > So, where does impredicativity play a role in the argument? There is a lot of literature on this even available on the web. There are indeed subtler distinctions than I am making here. Here are few links I have collected: http://www.cs.nyu.edu/pipermail/fom/2001-February/004737.html http://www.tc.umn.edu/~hellm001/PredImp.pdf -LV === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > > > So I suppose the next question is, does Cantor's argument work in > > > intuitionist mathematics? I'm afraid I don't know the answer to that > > > one > > > It is asserted, erroneously, that it does. > > Which is WM's own erroneous assertion. > > There is a sense in which Cantor's argument does work, i.e., for any > constructible binary list, No. That is possible only for lists with entries of infinite length. However, it is impossible to construct any sequence of bits which can be identified with certainty as a certain irrational number. Therefore the constructibility argument is wrong. > one can show by constructible methods that > there is a constructible non-member Neither any member nor the non-member can be identified. Therefore that is not mathematics but at most matheology. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media \ Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR \ 3.0.30618),gzip(gfe),gzip(gfe) > > > > Let's look at total functions taking two natural numbers and \ returning > > > either 0 or 1, eg f(n,m). ÊIf we leave out the question \ of > > > multiple representations, let's suppose you have implemented > > > such a total function. > > > Great. > > > > So, the anti-diagonal is itself something given algorithmically, > > > and you can easily write the procedure to return its nth digit, > > > provided that the given listing of reals itself is a total > > > function -- this does not mean that all the digits involved must > > > be computed, of course! > > > My point (my take) is that this simply does not solve our issue: the > > fact that the anti-diagonal does not belong to the list cannot be > > proven from the algorithmic definition alone. The key issue is what > > happens at infinity, and my thesis, to report it here in short, is > > that the anti-diagonal, as any other computable string, is simply > > there, in the range of a putative function 'f' like you describe > > above: there is no member missing. > > All that is claimed by the diagonal argument in this context is > that for every *natural number* n, the anti-diagonal > differs from sequence f(n,0), f(n,1), f(n,2), ... > And that we can show fairly easily -- it looks from your post > here that you accept that. > > So the conclusion is that the anti-diagonal does not appear > as a row in the *given* listing -- nothing more than that. The conclusion is still unwarranted: \the fact that the anti-diagonal does not belong to the list cannot be proven from the algorithmic definition alone\. -LV === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR \ 3.5.30729),gzip(gfe),gzip(gfe) > The conclusion is still unwarranted: \the fact that the anti-diagonal > does not belong to the list cannot be proven from the algorithmic > definition alone\. So who needs an algorithmic definition? Are you trying to say that only algorithmic definitions are legitimate? In the case of the axioms from which it IS proved, the anti-diagonal is DEFINED as differing from every element on the list (it differs from the nth element in its nth position). In that case, there is nothing (more) TO prove! === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media \ Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR \ 3.0.30618),gzip(gfe),gzip(gfe) > > > The conclusion is still unwarranted: \the fact that the anti-diagonal > > does not belong to the list cannot be proven from the algorithmic > > definition alone\. > > So who needs an algorithmic definition? > Are you trying to say that only algorithmic definitions are > legitimate? You don't even know what we are talking about. -LV === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media \ Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR \ 3.0.30618),gzip(gfe),gzip(gfe) > > As I have already noted in this thread, the formal, axiomatic proofs > > presuppose what here is in question, mainly a decision about > > \infinities\. > > And I already responded to that claim. You just skipped dealing with > my response. Please, if there is to be any dialogoue, it is not > practical if you are going to just pretend that my responses don't > exist. It's you who are pretending my responses do not exist. > So would you please address that question: What axiomatization do you > propose instead? I have already answered this question of yours many times now. Maybe I was not clear, so I'll try again: we are investigating foundational issues here, the diagonal argument specifically; it is improper, if not a basic misunderstanding, to ask for axiomatisations in this context. -LV === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media \ Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR \ 3.0.30618),gzip(gfe),gzip(gfe) > > > > Whether an intuitionist accepts the axioms used in the diagonal > > > argument is one matter. But ASIDE from the axioms, the LOGIC used in > > > the diagonal argument IS intuitionistic. > > > The diagonal argument is impredicative. > > If you are the same poster about a year ago under a different name > whom I'm thinking of, then it was *I* who first told you about > impredicativity. I'm not, though I am glad to admit that I am learning a lot from the group. How to fight in the crowd, above all. -LV === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media \ Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR \ 3.0.30618),gzip(gfe),gzip(gfe) > >> You can't do the same for the reals. That's because the reals > >> aren't countable and the naturals are. > > >That ultimately depends on your stance on the diagonal argument. > > No. The reals _are_ uncountable. This has nothing to do with > one's \stance\ on the diagonal argument - the argument is > correct, regardless of anyone's \stance\ on it. Apart from the apparent dogmatism, what you state is incorrect and, strictly speaking, false. Whether the diagonal argument or the arguments for uncontability are acceptable or not properly depends on one's stance on some key foundational issues. -LV === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > > (Incidentally, what's an i***?) http://www.urbandictionary.com/define.php?term=ijit Marshall === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR \ 3.0.04506),gzip(gfe),gzip(gfe) > > And their programmers want them to formulate proofs > > in the dominant theory, not in alternate theories. > Prover9 takes your first order theory as input. > It doesn't have any way to tell if the input you gave > it is \dominant\ or not. What I'd love to see is someone enter a \crank\ theory (or a rigorous version thereof) into Prover9 and prove theorems whose negations are theorems of ZFC (assuming ZFC and the \crank\ theory to be consistent). But no one is going to enter a \crank\ theory into Prover9 (not even a rigorous version of the theory). Surely the standard set theorists won't do it. > > On the other hand, computers can't completely do what their > > programmers want. Surely typing in the Riemann Hypothesis or > > Goldbach's Conjecture and clicking \Prove\ isn't going to > > result in a proof of either conjecture -- at least not during > > any of our lifetimes. > A few years back you could have said the same thing > about the Robbins Conjecture. It had survived many > decades without anyone coming up with a proof or > a counterexample, and it had been worked on by the > likes of Huntington, Tarski, and of course Robbins. > Then one day Bill McCune typed the Robbins conjecture > into EQP, hit \Prove\ and got out a proof. (EQP is a > precursor to Otter which is a precursor to Prover9.) Wow! Interesting. > (I'm not a number theorist, but couldn't Goldbach's > conjecture be expressed as a first order sentence, within > some appropriate axiomatization of the naturals? If so, > it is entirely possible that someone will one day type > it in a hit \prove\ and get a proof, if it is actually true.) Actually, my comment was that if someone could enter Goldbach (or its negation) into Prover9 (and let's say that PA is this \appropriate axiomatization of the naturals), it might take years , or even centuries , from the time the input is first entered to the time the proof is output. Similarly, one might enter an RSA number into a factoring program and the computer might find the factors, but only after many years of calculation. (This is the problem with most JSH algorithms, of course.) No one will consider a computer that factors RSA only after centuries of calculation to be a threat to RSA security. === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > > > And their programmers want them to formulate proofs > > > in the dominant theory, not in alternate theories. > > Prover9 takes your first order theory as input. > > It doesn't have any way to tell if the input you gave > > it is \dominant\ or not. > > What I'd love to see is someone enter a \crank\ theory > (or a rigorous version thereof) into Prover9 and prove > theorems whose negations are theorems of ZFC (assuming > ZFC and the \crank\ theory to be consistent). But no > one is going to enter a \crank\ theory into Prover9 > (not even a rigorous version of the theory). Surely > the standard set theorists won't do it. What you're asking is pretty easy, actually, at least in the degenerate case. Type in the negation of the axiom of infinity and viola! The problem of course isn't doing proofs from a formal theory, whether \crank\ or no; the problem is in trying to formalize a crank \theory.\ Formalization proceeds from clarity, and clarity can be hard to come by sometimes. > > > On the other hand, computers can't completely do what their > > > programmers want. Surely typing in the Riemann Hypothesis or > > > Goldbach's Conjecture and clicking \Prove\ isn't going to > > > result in a proof of either conjecture -- at least not during > > > any of our lifetimes. > > A few years back you could have said the same thing > > about the Robbins Conjecture. It had survived many > > decades without anyone coming up with a proof or > > a counterexample, and it had been worked on by the > > likes of Huntington, Tarski, and of course Robbins. > > Then one day Bill McCune typed the Robbins conjecture > > into EQP, hit \Prove\ and got out a proof. (EQP is a > > precursor to Otter which is a precursor to Prover9.) > > Wow! Interesting. Yeah, crazy cool. I love Prover9. Mace4, which didn't attract me as much at first, is comparably cool. The original paper on how they implemented it was a fun read for me. A math teacher of mine years ago was asked by a fellow student what he meant by \elegant.\ He said a proof is elegant if, when you see it, you wish you had thought of it. I consider Mace4 elegant. > > (I'm not a number theorist, but couldn't Goldbach's > > conjecture be expressed as a first order sentence, within > > some appropriate axiomatization of the naturals? If so, > > it is entirely possible that someone will one day type > > it in a hit \prove\ and get a proof, if it is actually true.) > > Actually, my comment was that if someone could enter > Goldbach (or its negation) into Prover9 (and let's > say that PA is this \appropriate axiomatization of > the naturals), it might take years , or even > centuries , from the time the input is first entered > to the time the proof is output. Oh. Yeah, that's certainly possible. Marshall === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR \ 3.0.04506),gzip(gfe),gzip(gfe) On May 8, 10:36Êam, Mariano Su\.87rez-Alvarez > > And their programmers want them to formulate proofs in the > > dominant theory, not in alternate theories. > Programmers are mostly theory-agnostic when they are > programming provers. What on earth suggests to you > that, say, Prover9 is restricted to (whatever it is > that you consider) dominant set theory? By \dominant set theory\ I usually mean ZFC, i.e. the set theory that most set theorists use. Well, I suppose that Prover9 isn't limited to ZFC, since Marshall says that he was able to use it to prove theorems in a theory whose lone axiom is \Ax (Ay (x=y)),\ which is hardly equivalent to ZFC. But what I've never seen is a theory that is proposed by a so-called \crank\ entered into Prover9, despite my attempts to make the \crank\ theories rigorous. Indeed, what I would love to see is a rigorous version of a \crank\ theory entered into Prover9 -- and I'll consider my attempts to make \crank\ theories to be successful if my version of the theory can be entered into Prover9 to prove theorems, especially if those theorems are negations of those that are provable in ZFC (assuming both ZFC and my proposed theory to be consistent). > That you seem to think there is such a restriction There is a restriction -- Prover9 can only give proofs in theories that someone types into the prover. If no one enters a rigorous version of a \crank\ theory, then Prover9 won't prove anything in that theory. This is probably what WM means when he says that computers do only what their programmers program them to do. > is a clear sign that you have absolutely no idea what > an automatic prover is. I'd like to know more about how Prover9 works. I've tried asking Prover9 users how it works, but answers have not been forthcoming. If I don't know how something works, I'd much rather be told how it does work, not simply \you don't know how (whatever) works.\ But standard theorists on sci.math are far more likely to say the latter than the former. > > The more time passes, the more likely we'll see a proof of, > > say, the Riemann Hypothesis or Goldbach's Conjecture. > > The more time passes, the less likely we'll see a proof that > > ZFC is inconsistent. > What possible basis do you have for the two claims you make? Mathematicians all over the world are searching for proofs of Riemann and Goldbach. As more and more time passes, it becomes more and more likely that someone will discover a proof of one of these conjectures. It's more likely that a proof of RH will be discovered by 2020 than by 2010, and it's still more likely that a proof of RH will be found by 2100 than by 2020. Therefore, the more time passes, the more likely that we'll see a proof of Riemann or Goldbach. Mathematicians all over the world are also searching for proofs that ZFC is inconsistent. But, as Knox points out, if there really is a proof of ~Con(ZFC), we most likely would have found it by now. For many inconsistent theories it's easy to find a proof of its inconsistency. It took only a few years to find a contradiction in Cantor's naive set theory, and those \cranks\ who propose theories on sci.math, that turn out to be inconsistent, it often takes mere hours to find the inconsistency. But ZFC has withstood the test of time. It seems hard to believe that mathematicians would have overlooked an inconsistency for so long -- well over a century. Since we haven't found a contradiction by now, it's unlikely that we'll see one by 2010 or 2020. And if we haven't found one by 2100, we may as well consider ZFC to be consistent -- since we'll likely never find a proof of ~Con(ZFC). This seems to be Since Mariano asked me, I ask the same of Mariano, and I wonder what his opinion of the likelihood that we'll ever see a proof of Riemann, Goldbach, or ~Con(ZFC). > > If there were a > > rigorous theory in which more of their intutions are provable > > than in ZFC, then maybe LV and the other opponents of the > > dominant set theory would have less reason to start these > > threads and complain about set theory all the time. > Can you please point to *someone* who *does* see > a reason why opponents of ZFC can't have an alternate > theory? Here are some reasons given for why opponents of ZFC can't have an alternate theory: The alternate theories (i.e., the particular alternate theory proposed by the particular opponent of ZFC) aren't rigorous enough. The alternate theories aren't coherent enough. The alternate theories can't prove anything that is useful to applied science. The alternate theories are inconsistent (which even I consider to be a valid reason). And so on. I'll leave it to Mariano to find the posters who gave these as reasons that opponents of ZFC can't have their alternate theories. === Subject: Re: Diagonal wanderings (incongruent by construction) sha1:lxnsVnPeZKuy7ex+DKbkzlJLTAk= > There _is_ a restriction -- Prover9 can only give proofs > in theories that someone types into the prover. Oh my! How unfair! Why won't someone drop whatever they're doing and start working on your formalization of crank theories? It's just not fair that they don't. This is just as tragic as the fact that books cost money and you have to travel to libraries. -- Jesse F. Hughes \Of course, I don't need any more education.\ -- Quincy P. Hughes (age 7) === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > Mathematicians all over the world are also searching for > proofs that ZFC is inconsistent. They are? Would you please name several countries and a mathematician from each of those countries who is searching for a contradiction in ZFC? Or in the rubric of 'mathematician', do you include cranks? MoeBlee === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR \ 3.0.04506),gzip(gfe),gzip(gfe) > > Mathematicians all over the world are also searching for > > proofs that ZFC is inconsistent. > They are? Would you please name several countries and a mathematician > from each of those countries who is searching for a contradiction in > ZFC? Or in the rubric of 'mathematician', do you include cranks? In this particular post, I'm not including so-called \cranks\ but only standard set theorists. Well probably at first , right after ZFC was formulated, likely as many mathematicians sought a proof that ZFC was inconsistent as sought a proof that the naive set theory of Cantor and Frege was inconsistent. Fields medal. It's not unreasonable to guess that many mathematicians around the world would do research that would earn them a Fields medal, the most prestigious prize in all of mathematics. So if, as MoeBlee might be implying here, very few mathematicians seek a proof of ~Con(ZFC), then they likely believe that no proof is possible. And if this is really the case, then this would actually prove the point that I was making to Mariano -- that the more time passes, the less likely a proof of ~Con(ZFC) will be found, and the fewer mathematicians will even search for a proof! AFAIK, there is only one mathematician seeking a proof that PA and ZFC are inconsistent -- Ed Nelson. Mariano here! === Subject: Re: Diagonal wanderings (incongruent by construction) lwalke3@lausd.net a \.8ecrit : >>> Mathematicians all over the world are also searching for >>> proofs that ZFC is inconsistent. >> They are? Would you please name several countries and a mathematician >> from each of those countries who is searching for a contradiction in >> ZFC? Or in the rubric of 'mathematician', do you include cranks? > > In this particular post, I'm not including so-called \cranks\ > but only standard set theorists. So, can you answer his question? > > Well probably at _first_, right after ZFC was formulated, > likely as many mathematicians sought a proof that ZFC was > inconsistent as sought a proof that the naive set theory > of Cantor and Frege was inconsistent. > > Fields medal. It's not unreasonable to guess that many > mathematicians around the world would do research that > would earn them a Fields medal, the most prestigious prize > in all of mathematics. > Is it concievable that you will stop trolling someday? Cannot you recognize a joke here? Dont you understand taht a contradiction in ZFC would be almost as unplausible that a contradiction inPA (which, of course, would win you a Fields medal too)? > So if, as MoeBlee might be implying here, very _few_ > mathematicians seek a proof of ~Con(ZFC), then they likely > believe that no proof is possible. Indeed And if this is really > the case, then this would actually _prove_ the point that > I was making to _Mariano_ -- that the more time passes, > the less likely a proof of ~Con(ZFC) will be found, and > the fewer mathematicians will even search for a proof! > > AFAIK, there is only one mathematician seeking a proof > that PA and ZFC are inconsistent -- Ed Nelson. > > Mariano here! No, just helping to prove you speak (as always) out of your hat === Subject: Re: Diagonal wanderings (incongruent by construction) In Dread Ink, the Grave Hand of Denis Feldmann Did Inscribe: > lwalke3@lausd.net a \.8ecrit : >>>> Mathematicians all over the world are also searching for >>>> proofs that ZFC is inconsistent. >>> They are? Would you please name several countries and a mathematician >>> from each of those countries who is searching for a contradiction in >>> ZFC? Or in the rubric of 'mathematician', do you include cranks? >> >> In this particular post, I'm not including so-called \cranks\ >> but only standard set theorists. > > So, can you answer his question? >> >> Well probably at _first_, right after ZFC was formulated, >> likely as many mathematicians sought a proof that ZFC was >> inconsistent as sought a proof that the naive set theory >> of Cantor and Frege was inconsistent. >> >> Fields medal. It's not unreasonable to guess that many >> mathematicians around the world would do research that >> would earn them a Fields medal, the most prestigious prize >> in all of mathematics. >> > > > Is it concievable that you will stop trolling someday? Cannot you > recognize a joke here? Dont you understand taht a contradiction in ZFC > would be almost as unplausible that a contradiction inPA (which, of > course, would win you a Fields medal too)? > >> So if, as MoeBlee might be implying here, very _few_ >> mathematicians seek a proof of ~Con(ZFC), then they likely >> believe that no proof is possible. > > > > Indeed > And if this is really >> the case, then this would actually _prove_ the point that >> I was making to _Mariano_ -- that the more time passes, >> the less likely a proof of ~Con(ZFC) will be found, and >> the fewer mathematicians will even search for a proof! >> >> AFAIK, there is only one mathematician seeking a proof >> that PA and ZFC are inconsistent -- Ed Nelson. >> >> Mariano here! > No, just helping to prove you speak (as always) out of your hat I think the punchline of ZFC is Johnny von Neumann, who advises: don't engage in bad logic games. -- Frank Drug war, well, as Rush Limbaugh said, anyone who uses drugs illegally should be prosecuted and put away. I don't agree with him; I think they should be treated, but that's what Rush believes and so, you know, we're praying for Rush because he's in recovery and you take responsibilities for your actions so I'm sure any day now Rush will demand to be put away for the maximum sentence and ask for the most dangerous prison and we'll be praying for maybe an African American cellmate who saw the Donovan McNabb comments on ESPN. So we're prayin'. ~~ Al Franken, Book TV, on Rush Limbaugh's illegal drug arrest and racist remarks === Subject: Re: Diagonal wanderings (incongruent by construction) posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR \ 3.5.30729),gzip(gfe),gzip(gfe) > Cantor claims: \whichever list of infinite (binary) strings you can > come up with, I will (anti-)diagonalise it.\ True. > It is (AFAIK) easy enough to come up with a production This is UTTER bullshit. You CANNOT EVEN DEFINE \production\! ONE thing is for sure: IF this thing SOMEhow \deals with\ ALL binary strings, REGARDLESS of whether it is or isn't the product of anything LEGITIMATELY referrable to as a strings!! === Subject: Re: Diagonal wanderings (incongruent by construction) > If PA is inconsistent but > ZFC proves PA consistent, then all we can infer from those mere facts > is that ZFC proves false arithmetical statements, not necessarily that > ZFC is inconsistent. The actual reasoning for the inconsistency of ZFC > given the inconsistency of PA is that PA is embedded in ZFC. So this > is not a matter of whether ZFC proves PA consistent. Rather, if PA is > inconsistent then ZFC is inconsistent, since ZFC embeds PA. Is \embeds\ a standard term? I think in terms of \emulation\: ZFC can emulate PA (like one computer can emulate another). I also wonder if it would be too far from standard usage to say that ZFC \models\ PA, not in the sense of there being sets that are models of PA, but in the sense of one formalism embedding (or emulating) another formalism. This doesn't seem too distant to me; we have models of non-Euclidean plane geometry in Euclidean solid geometry -- I don't think anyone would be seriously misled if one asserted that Euclidean geometry models non-Euclidean geometry. I guess it is more common to say that there is an interpretation of one in the other. But what I'm really curious about is whether ZFC can be embedded in PA; I don't see why not, offhand. PA can \model\ itself via the standard Godelian encoding -- I don't see any reason offhand why ZFC cannot be similarly encoded within the formalism of PA. It is, after all, just a r.e. set of symbols and a r.e. set of finite strings of those symbols. (We could get by with a finite number of symbols: for variables write x, x', x'', ... so we just need a code number for \x\ and a code number for \'\). -- hz === Subject: Re: Diagonal wanderings (incongruent by construction) <4A04C230.3373A9F6@gmail.com> posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > > If PA is inconsistent but > > ZFC proves PA consistent, then all we can infer from those mere facts > > is that ZFC proves false arithmetical statements, not necessarily that > > ZFC is inconsistent. The actual reasoning for the inconsistency of ZFC > > given the inconsistency of PA is that PA is embedded in ZFC. So this > > is not a matter of whether ZFC proves PA consistent. Rather, if PA is > > inconsistent then ZFC is inconsistent, since ZFC embeds PA. > > Is \embeds\ a standard term? ÊI think in terms of \ \emulation\: > ZFC can emulate PA (like one computer can emulate another). Actually, I think \can be interepreted in\ is a pretty common way of putting it. Though informally, in context, 'embeds' (better, \embeds\) should convey the idea and, in context, be understood as distinct from 'embeds' in the sense of an embedding function. Though, I imagine we could describe a certain embedding function from the fact that one theory is interpreted in another - which would be literally an embedding of the set of formulas of the language of theory T into the set of formulas of the language of theory T*, with the isomorphism appropriately defined by the property of theoremhood). But I don't want to commit to working all of that out just to justify my informal sense of 'embed' in this context. > I also wonder if it would be too far from standard usage to say > that ZFC \models\ PA, not in the sense of there being sets that > are models of PA, but in the sense of one formalism embedding > (or emulating) another formalism. The structure in Z models first order PA. >ÊI guess it is more common to say > that there is an interpretation of one in the other. Right. > But what I'm really curious about is whether ZFC can be > embedded in PA; Ê Not first order PA. I think we can prove that by the second incompleteness theorem, if I'm not mistaken (?). > PA can > \model\ itself via the standard Godelian encoding Then I think you're indulging some slippage in the notion of 'models'. Godel encoding onto itself is not a provision for a model of first order PA (in the ordinary sense in mathematical logic of 'model') nor is Godel encoding onto itself a theory in which first order PA is interpreted. (Maybe there's some other sense in which Godel encoding can be utlitized to perform certain other notions of 'model' and 'theory interpreted in theory', but I don't see how in the exact senses of those in mathematical logic.) > - I don't > see any reason offhand why ZFC cannot be similarly encoded > within the formalism of PA. ÊIt is, after all, just a r.e. > set of symbols and a r.e. set of finite strings of those > symbols. Well, there's a lot more to interpreting one theory in another. Roughly put, to interpret theory T in theory S, you have to extend S by definitions to a theory S* and then show that every theorem of T is a theorem of S* (or, for any axiomatization of T, that every axiom of T is a theorem of S*). That's easy to do for interpreting first order PA in Z set theory. But to interpret Z set theory in first order PA you'd have have to extend first order PA by definitions to a theory PA*, which would be to add 'e' as a symbol and define it from PA, and then show that every theorem (or just every axiom) of Z is a theorem of PA*. (I hope I've stated that fairly accurately. But you can also check a textbook in mathematical logic under the subject of interpreting one theory in another, however it is actually worded in the book.) MoeBlee === Subject: Re: Diagonal wanderings (incongruent by construction) Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) >> > Whether an intuitionist accepts the axioms used in the diagonal >> > argument is one matter. But ASIDE from the axioms, the LOGIC used in >> > the diagonal argument IS intuitionistic. >> >> The diagonal argument is impredicative. > >So, where does impredicativity play a role in the argument? Formation of power sets is impredicative, so if you conceive of \the \ diagonal argument\ as beginning by saying, \Let R be the power set of N...\ then \ you could argue that it is impredicative. However, I think it is more plausible to say that \the diagonal argument\ is just the part of the argument that takes a given list and constructs a diagonal element. This part isn't impredicative. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Diagonal wanderings (incongruent by construction) \ <4a04aa1e$0$315$b45e6eb0@senator-bedfellow.mit.edu> posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media \ Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR \ 3.0.30618),gzip(gfe),gzip(gfe) > > >> > Whether an intuitionist accepts the axioms used in the diagonal > >> > argument is one matter. But ASIDE from the axioms, the LOGIC used in > >> > the diagonal argument IS intuitionistic. > > >> The diagonal argument is impredicative. > > >So, where does impredicativity play a role in the argument? > > Formation of power sets is impredicative, so if you conceive of \the \ diagonal > argument\ as beginning by saying, \Let R be the power set of N...\ then \ you > could argue that it is impredicative. > > However, I think it is more plausible to say that \the diagonal \ argument\ > is just the part of the argument that takes a given list and constructs a > diagonal element. ÊThis part isn't impredicative. Not that part, it's the conclusion that is \problematic\. We have a construction of the list (our 'f'), then we define the construction of an item ('d') so that it differs in each place for each item in the list given by 'f'. If we now run this game of 'f' against 'd', there is no winner, yet Cantor's conclusion is that the anti-diagonal wins. -LV === Subject: Re: Diagonal wanderings (incongruent by construction) \ <4a04aa1e$0$315$b45e6eb0@senator-bedfellow.mit.edu> posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR \ 3.5.30729),gzip(gfe),gzip(gfe) > > However, I think it is more plausible to say that \the diagonal \ argument\ > > is just the part of the argument that takes a given list and constructs \ a > > diagonal element. ÊThis part isn't impredicative. > > Not that part, it's the conclusion that is \problematic\. It's really a shame you don't know how this works. IT'S A PROOF. IN A LOGIC. If the rules and their application are sound then it IS NOT POSSIBLE for the conclusion to be \problematic\! > We have a construction of the list (our 'f'), NO, WE DON'T! f DOES NOT need to be \constructed\ or \constructible\ IN ANY sense! This works for ALL lists, constructible OR NOT!! The inference rule being used is universal generalization. What part of UNIVERSAL don't you understand?!? f IS AN *ARBITRARY* name/symbol in this proof!! We know ABSOLUTELY NOTHING about f, because absolutely nothing about f EVEN MATTERS in this proof, beyond that it defines a list!! > then we define the construction of > an item ('d') so that it differs in each place for each item in the > list given by 'f'. If we now run this game of 'f' against 'd', You CAN'T run this game. There ARE NO games in this paradigm. In what you call a game, people TAKE TURNS and TIME progesses. That IS NOT HAPPENING here. We are using universal generalization AGAIN both in the definition of the (anti)- diagonal and over the places of the numbers (horizontally) in the list: the anti-diagonal differs from EVERY row it, that the anti-diagonal differs from it. There is no d VERSUS f here! d is constructed FROM f !! === Subject: Re: Diagonal wanderings (incongruent by construction) \ <4a04aa1e$0$315$b45e6eb0@senator-bedfellow.mit.edu> posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media \ Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR \ 3.0.30618),gzip(gfe),gzip(gfe) > > then we define the construction of > > an item ('d') so that it differs in each place for each item in the > > list given by 'f'. If we now run this game of 'f' against 'd', > > You CAN'T run this game. > There ARE NO games in this paradigm. There are no games in your paradigm maybe. You don't even know what we are talking about. -LV === Subject: Re: Diagonal wanderings (incongruent by construction) >>>> Whether an intuitionist accepts the axioms used in the diagonal >>>> argument is one matter. But ASIDE from the axioms, the LOGIC used in >>>> the diagonal argument IS intuitionistic. >>> The diagonal argument is impredicative. >> So, where does impredicativity play a role in the argument? > > Formation of power sets is impredicative, so if you conceive of \the \ diagonal > argument\ as beginning by saying, \Let R be the power set of N...\ then \ you > could argue that it is impredicative. > > However, I think it is more plausible to say that \the diagonal \ argument\ > is just the part of the argument that takes a given list and constructs a > diagonal element. This part isn't impredicative. Very true indeed. But that part of the argument does not prove the existence of uncountable sets... -- Herman Jurjus === Subject: Re: Diagonal wanderings (incongruent by construction) \ <4a04aa1e$0$315$b45e6eb0@senator-bedfellow.mit.edu> posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > > >> > Whether an intuitionist accepts the axioms used in the diagonal > >> > argument is one matter. But ASIDE from the axioms, the LOGIC used in > >> > the diagonal argument IS intuitionistic. > > >> The diagonal argument is impredicative. > > >So, where does impredicativity play a role in the argument? > > Formation of power sets is impredicative, so if you conceive of \the \ diagonal > argument\ as beginning by saying, \Let R be the power set of N...\ then \ you > could argue that it is impredicative. Or we can cast the argument in the hypothetical: IF there is a set N whose members are all and only the natural numbers and IF there is a set PN whose members are all and only the subsets of N, then there is no function from N onto PN. And, it seems to me, that the heart of diagonal argument doesn't even require more than that hypothetical context, since if the hypotheses fail, then the matter is trivial anyway. > However, I think it is more plausible to say that \the diagonal \ argument\ > is just the part of the argument that takes a given list and constructs a > diagonal element. ÊThis part isn't impredicative. That seems right to me, as long as the instance of axiom schema of separation used to carve out the contradicting function is not impredicative (Aatu had a convincing argument about that, but, alas, I forgot his conclusion). MoeBlee === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=hbYmMgkAAADthgUY8i5E5MN4qZlh2_fb InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > > >Real scientists do not do, nor report, their research on this forums. > >They study the subjects, they make measurements and simulations and, > >finally, report their findings in conferences and journals (that is at > >least what I do). > > >Talking of real people doing science, and working in real problems, > >here are some references to read: > > >1) 10 General Relativistic Models for Space-time Coordinates and > >XXVIIA Reports on Astronomy 2006-2009, pp55-59. > >Tou Ni, Michael C.W. Sandford, Christian Veillet, An-Ming Wu, Patricia > >Fridelance, Etienne > >Samain, George Spalding and Xiaohui Xu, ÊAdv. Space Res. \ Vol. 32, No. > >4) Relativistic Corrections to Lunar Occultations, Costantino > >Sigismondi, Tenth Italian-Korean Meeting on Relativistic Astrophysics > >Pescara, June 25-30, 2007. > >5) Deep-space laser-ranging missions ASTROD and ASTROD I for > >astrodynamics and astrometry, W. T. Ni and the ASTROD I ESA COSMIC > >Astrometry Proceedings IAU Symposium No. 248, 2007. > > >Miguel Rios > > I was not \Talking of real people doing science\, > I was \Talking of real people doing\ REALITY. > > As can be seen from your reference > \10 General Relativistic Models for Space-time..\ > and Ashby's paper that uses 13 Classical Physics hacks > of GPS data to fit it to General Relativity, > > unlike DNA scientists, computer scientists, electronics scientists, etc. > all of the General Relativity Gurus seem to be guys on the Public Dole, > who have never made Êa real world contribution to mankind. > > One would think that if General Relativity Gurus > possessed such powerful, esoteric knowledge, > they would use it to make a few bucks in the free market, > > rather than being a burden to hardworking taxpayers, > and wasting the minds and time of young folks > on issues such as time travel, worm holes, > the beginning and end of the universe, > and the mind of God. > > A mind is a terrible thing to waste. > > -- > Tom Well Mr. potter, regarding the chicken situation, I'm quite sure you do not need Galileo, Newton, nor Einstein theories to find your way to your bathroom at night. That is how reality works!!. Science, on the other hand, has always worked differently to that. You observe Nature and wonder how and why it works like like you see it. Then you build a model that may, or may not, be useful to predict the results of observations. Many advances on physics or mathematics take several years to understand, and then more years to get into real useful applications of those new advances. One example: in the early 60's, Dr. Robert Gallager, on his Ph.D. thesis, found a mathematical method that could be used in coding systems. The method is called Low Density Parity Check (LDPC). For over 30 years nothing happened with his development (even him had forgotten it), until somebody found the method could be applied to the 3G and 4G cellular systems. So now, almost all cellular systems are using these LDPC codes to improve the quality of communications. Furthermore, History has shown that nobody has ever developed a new and useful theory without being familiar with the then-current theories and experiments. That's why the idiots and crackpots around here are so pathetic: if they truly wanted to make a contribution, they would be seriously STUDYING the current theories and experimental record, and trying to extend one or the other. Miguel Rios === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole > > PD makes a good point when he points out that > > \Physics a *quantitative* science. > If you do not do calculations, then you are not doing physics.\ > > Hopefully, rather than make unsubstantiated claims, > and attack posters who oppose Relativity, > > the General Relativity Cultists will begin to post calculations > rather than useless references that may or may not > support their positions. > > One would think that if the General Relativity Gurus > and Cultists were privy to such powerful, esoteric knowledge, > that they would use their powerful knowledge > to make a few bucks in the free market. > > The best I can determine is that the > General Relativity Gurus and Cultists > are either phones, bullshippers, brainwashed students, > or on the public dole. > My, my Potter, you do try to disparage things you have FAILED to understand, such as General Relativity and it's applications! Hey, Potter, GTR has directly contributed to a $30B+ GPS industry, benefiting people all over the world. Aviation, shipping, asset management, survey, mining, agriculture, time dissemination, communications networks... and on and on! Bluster on, Potter, bluster some more! Froth at the mouth! Whatever! === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole > > As can be seen from your reference > \10 General Relativistic Models for Space-time..\ > and Ashby's paper that uses 13 Classical Physics hacks > of GPS data to fit it to General Relativity, > > unlike DNA scientists, computer scientists, electronics scientists, etc. > all of the General Relativity Gurus seem to be guys on the Public Dole, > who have never made a real world contribution to mankind. > > One would think that if General Relativity Gurus > possessed such powerful, esoteric knowledge, > they would use it to make a few bucks in the free market, > > rather than being a burden to hardworking taxpayers, > and wasting the minds and time of young folks > on issues such as time travel, worm holes, > the beginning and end of the universe, > and the mind of God. > > A mind is a terrible thing to waste. > My, my Potter, you do try to disparage things you have FAILED to understand, such as General Relativity and it's applications! Hey, Potter, GTR has directly contributed to a $30B+ GPS industry, benefiting people all over the world. Aviation, shipping, asset management, survey, mining, agriculture, time dissemination, communications networks... and on and on! Bluster on, Potter, bluster some more! Froth at the mouth! Whatever! === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole > > As I asked: > \What point do \all inertial observers\ reference the acceleration of \ an \Observed acceleration\ to\ > Potter, did you ever learn calculus or take a calculus based physics course? === Subject: combinations and cutting stock problem My question is basically, is there standard code routines to assemble all combinations of a list of unique numbers where the list of numbers have different quantities. This would be a flat list similar to: 1 1 1 2 2 4 4 4 8 8 8 8 8 9 14 15 15 etc. I am doing a 'cutting stock problem' scenerio. The combination code for I arrived at seemed a little linear and since it's rather new to me maybe there's better solutions. This works nice but doesn't scale too well in my opinion. It eventually will go into a database and I'd like to use database scalability. with an array or list of 'finish' lengths in ascending order. add to the first finish, check total length and if less than 'stock' length record the qnt of finish lengths needed for each iteration when it exceeds the stock length return to 0 qnt and do a carry carry is function that: advances to next finish length and increments it. If no more finish lengths signal done. check total length and if less than stock do like above if over then mark as zero qnt and recurse into another carry. check total is a routine that: loops through all the finish qnts to calculate the total being used. -- Phil === Subject: Re: Is this a bad assumption on my part-- that of \ Continued-Fractions Matrix?? #494 new book 2nd edition: New True Mathematics posting-account=qKxGxgkAAADAPfYVCc-ZQkIzl0senr2M .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET \ CLR 1.1.4322; Zune 2.5),gzip(gfe),gzip(gfe) > Now there is a assumption I am leaning on, but need to prove it. > > Notice the Continued-Fractions of \pi and e\ > > pi = 3 + 1/(7 +1)/(15 + 1)/(1 + 1)/292 +... You notation is a little confusing. I would write: pi = 3 + 1/(7 + 1/(15 + 1/(1 + 1/(292 + ... for pi = 3 + 1 7 + 1 1 + 1 15 + 1 292 + ... > > e = 2 + 1/(1 +1)/(2 + 1)/(1 + 1)/(1 + 1)/4 +... > > Those use all integer values. It is easily provable that all real number, whether rational or irrational, can be expressed as continued fractions using only integers. Rational numbers, when expressed as continued fractions, will have a finite number of terms. Irrational numbers will have an infinite number of terms. As a side note, the square roots of rational numbers will be either rational or will be irrational with a continued fraction in whcih the integers in the denominators will repeat cyclically. > But in the construction of AP-Reals-Rationals-Irrationals > > where we start with the AP-Reals as a starting set, and > construct AP-Reals-Rationals as a larger set and a huge > matrix of every AP-Real possible combinations as numerators > and denominators. So the Rationals in AP-Reals-Rationals are > a larger set than the AP-Reals themselves. Continued fractions require integer division. The operation of division is not defined for matrices. > So, if you are math savvy, you can anticipate my next question. > Is the matrix of AP-Reals-Rationals-Irrationals a larger set than > that of Continued Fractions that use only integers? Non. Every real number can be expressed as a continued fraction. Think of the proof as an exercise in converting from decimal representation into continued fraction representation. > You see, I was assuming that using fractions themselves is > superfluous as the numbers in the Continued-Fractions. ??? > If my assumption is wrong and that there are \more numbers\ > than using only integers in Continued-Fractions, then I have > to reconsider the idea of \transcendental numbers\. No. Long a go I constructed a spreadsheet (originally in Lotus 1-2-3, now in Excel) that will calculate the continued fraction representation of any number input to the limit of the precision of the computer. As a side exercise, I was able to simultaneously calculate the precision of the representation and the equivalent ratio of integers. For example, the continued fraction approximation of pi given above can also be represented as a sequence of integer ratios: pi: 3, 22/7, 25/8, 355/113, ... Interestingly, the precision is related to the integers A and B in the rational representation x ~= A/B in that the error e <= 1/(A*B) so the fractional error of representing pi as 355/113 is less than 1/ (355/113) > Already, I know that the AP-Reals-Rationals-Irrationals have > numbers such as 0d000...0001/0d000...0002 which is not an > Old Real, not an Old Rational of Old Reals. I have never seena definition of \AP-Reals-Rationals-Irrationals\. I know that the set of all real numbers is the union of the set of all rational numbers and the set of all irrational numbers, but the AP confuses me. Is this some sort of vanity label, Archie? > So if I use that number in a Continued-Fraction such as this: > > 2 + 1/(0d000...0001/0d000...0002 +1)/(0d000...0001/0d000...0002 + > 1)/... First you must define \AP-Reals-Rationals-Irrationals\. Then you must defin *division* by \AP-Reals-Rationals-Irrationals\. Tom Davidson Richmond, VA === Subject: Re: Is this a bad assumption on my part-- that of \ Continued-Fractions Matrix?? posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG Gecko/20080829 Firefox/2.0.0.17,gzip(gfe),gzip(gfe) > Already, I know that the AP-Reals-Rationals-Irrationals have > numbers such as 0d000...0001/0d000...0002 which is not an > Old Real, not an Old Rational of Old Reals. Wouldn't 0d000...001/0d000...002 just be the same as 1/2, which is 0.5? If not, why not? === Subject: Re: Is this a bad assumption on my part-- that of \ Continued-Fractions Matrix?? #494 new book 2nd edition: New True Mathematics > Now there is a assumption I am leaning on, but need to prove it. > > Notice the Continued-Fractions of \pi and e\ > > pi = 3 + 1/(7 +1)/(15 + 1)/(1 + 1)/292 +... > > e = 2 + 1/(1 +1)/(2 + 1)/(1 + 1)/(1 + 1)/4 +... > > Those use all integer values. > equations are still wrong what you want is high rate of convergance, try another series good book out on pi and lists all the series. > Archimedes Plutonium > www.iw.net/~a_plutonium > whole entire Universe is just one big atom > where dots of the electron-dot-cloud are galaxies === Subject: >>>>>> NUDE TITS <<<<<< posting-account=gpeakwoAAAC4rsr-Gh4QDGE-xHmY9_hC SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; \ .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) ******************************************************************* 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nude tits sex video brooke langton nude tits beautiful tits nude free meg white fake nude tits yovo free nude big tits fuckingpics nude thailand women tits young nudes small tits porno jill nude tits heidi honey nude tits nude big japaneses tits nude preeten tits nude women tits and ass nude women and large tits naked sexy nude pussy ass tits nude asian tits and ass non nude bit tits nude tits wet pussy free nude big tits housewife pics kimberly kupps nude pierced tits pics free nude tits senior nude grannies tits free hardcore nude tits 101 nude teen tits ashlee simpson naked nude tits nude big tits round asses nude women with big tits elizabeth starr big tits nude nude pussy big tits nude teen big tits small tiny nude tits nude little tits red head bbw milky tits nude nudes group with big tits free nude big tits milfs nude tits free personal webcam nude tits long hanging nude big natural tits tinyest tits nude pics nude woman tits nude celeb tits nude black girl with big tits nudes a popping tits nude teen with big tits nude natural tits nude tits clits skiny girls nude with big tits nude dancing tits tits ass nude fucking nude tied to bed tiny tits nude asian women tits grils with nude tits jayden jaymes nude tits === Subject: Re: JSH: EMIS has my old paper back up? > Looks like EMIS has my paper back: > > > I find that curious enough that I will read replies in this thread. I > haven't been reading replies to my previous postings, as, what's the > point? Then what's the point of posting? > Crazed and obsessive people \Crazed and obsessive\ It looks as if you are talking about yourself. > I at times call the \angry idiots\ Yes. I was right. > dominate those threads and don't say anything new. > > Here I'm curious as to whether or not anyone knows why it'd be back up > now. > > Oh yeah, those wondering how crappy this paper really is given the > drama around it can now see it for themselves, if that link works. > (It worked just now when I noticed it.) It's still crappy. > Some sci.math'ers thought it worth upending the journal system to > attack that paper with an email assault. The editors pulled it from > the journal after publication and managed just one more edition before > folding, shutting down. > > The American journal had its archives kept up by EMIS, a European > agency. Europeans saving the records of an American journal. But > maybe they care about knowledge in a way people in this country > demonstrably don't. That's why no European journal will ever publish your crap. Jose Carlos Santos === Subject: Re: Cantor's argument is erroneous >>>> So, for the millionth time, MoeBlee, I'm not talking about defining >>>> languages! What I simply stated is basically you can't validly apply >>>> rules of inference to a formula that's not expressed in the L(T) >>>> whose signatures are in the axioms of T. >> [...] >> >>> But also we can stipulate a language irrespective of having first >>> stipulated a set of non-logical axioms (as I understand, you say now >>> that you agree with this). And in THAT situation - say, in which we >>> stipulate '+' and '0' as non-logical symbols at the appropriate >>> arities - we can go on to stiplulate \Axy x=y\ as a sole non-logical >>> axiom and then prove \Axy x+y=0\. And THAT is the situation I said my >>> proof pertained to, from the very first proof in which I gave my proof >>> and I as I reiterated that over and over in subsequent posts. >> Careful! I don't think he agrees. >> >> I think he's saying that we can define millions of different languages >> for T, but rules of inference must only apply to the minimal language > > But I didn't opine as to his view of rules of inference. I meant only > that he seems to agree that a language can be defined before > specifiying any particular theory that uses that language. (And IFhe > says that is not something he agrees with, then I leave for him to say > for himself what EXACTLY he means). Correct. Naturally, a FOL language *can be* defined well in advanced of any theory - theory which may or may *not* use any non-logical symbol at all in that language! > > As to rules of inference, that matter is subsumed in other of my > remarks. It's my \right\ as a poster that I stay confined within the context of syntactical/symbolical proof in axiom-set systems of FOL=, when talking about valid application of rules of inference. (Recall that very early in the debate, I mentioned *to you*: > Of course. (And I usually assume FOL=). and, iirc, you acknowledged that. So, MoeBlee, for what it's worth, I'm carrying my defending in this debate in the manner of one-issue-one-logic-framework-at-a-time. Any thing else like \proof-in-a-language\ or \equational logic\ is irrelevant and I'd only engage in a new thread (or sub-thread), if I have time or interest. > But to put the matter directly here: In ordinary context of > mathematical logic, If by \ordinary context of mathematical logic\ you mean the context of FOL= syntactical proofs *in formal systems*, then I already gave examples explaining what you said below is invalid. > the rules of inference generalize over formulas of > the language - and it is my very point that where '+' and '0' are in > the language, the rules of inference allow instantiations to formulas > that have those symbols EVEN THOUGH those symbols do not occur in any > of the non-logical axioms for some particular axiomatization of some > particular theory. Again, as far as FOL= syntactical proofs *in a formal system* T is \ concerned, Rules of inference can *not* allow such generalization (\instantiation\, \expansion\, or the like) without committing to the error of \ over-generalization, from specific hypothesis/information to general conclusion, as I gave in \ one example before. > > As we surely agree, there is no ordinary convention that the rules of > inference pertain only to formulas with only symbols mentioned in some > non-logical set of axioms. If Nam disputes that, then he's just wrong. In so far as you and others have not been able to refute my specific \ examples at all (other than saying something like \Shoenfield, Roger, etc... didn't say that\, or invoking off-the-topic non-FOL= logic frameworks) then I'm correct and you and other opponents of mine are *not*. -- \To discover the proper approach to mathematical logic, we must therefore examine the methods of the mathematician.\ (Shoenfield, \Mathematical Logic\) === Subject: Re: Cantor's argument is erroneous >> >> As we surely agree, there is no ordinary convention that the rules of >> inference pertain only to formulas with only symbols mentioned in some >> non-logical set of axioms. If Nam disputes that, then he's just wrong. > > In so far as you and others have not been able to refute my specific > examples > at all (other than saying something like \Shoenfield, Roger, etc... \ didn't > say that\, or invoking off-the-topic non-FOL= logic frameworks) then > I'm correct and you and other opponents of mine are *not*. Also you (MoeBlee) should have realized that as far as FOL= *proof in a \ theory* is concerned, *rules of inference don't \pertain\ to just _any_ formula*! Specifically, rules of inference pertain *only* to formulas that are *theorems*. But since theorems are defined from axioms, it isn't much an exaggeration to say rules of inference pertains to *axioms*. [And that's not just (in your words) \ordinary convention\ but it's the very heart of \ the definition of proofs - in FOL=]. So you and others are not *just* disputing with me: you're disputing the very fundamental notion of syntactical proofs in FOL=. -- \To discover the proper approach to mathematical logic, we must therefore examine the methods of the mathematician.\ (Shoenfield, \Mathematical Logic\) === Subject: Re: Cantor's argument is erroneous > >> Moreover, the raw notion of a language stipulated by >> giving a signature would seem to need to be already >> in place before one could THEN speak about some set >> of formulas from which to extract a signature for a >> language, since the notion of 'formula' itself is in >> language which in turn reverts to the notion of >> symbols of certain kinds and arities. > > > I have a question about this \axioms first, language after\ > procedure. If one defines one's system in this fashion, > how would one go about showing that the axioms and other > formulas can be unambiguously parsed? > > If one defines one's system \language first, axioms after\ > then, of course, one has a clear description of the > syntax to work with. The other way, I suppose you > have to draw analogies with well-known systems. This > is why we assumed '0' was a constant (or 0-ary function?) > and '+' was a 2-ary function. > > However, if I recall correctly, Nam claimed at one point > that \x + y = 0\ was not well formed in his system, > to the surprise, it seemed, of everyone except Nam. If by \system\ you meant a logic framework system, then that's not what I had meant. (I always talk in the context of FOL= system). Otoh, if you meant \formal system\ then of course \x+y=0\ is not well-formed in the L(T) that has zero nonlogical symbol (where T = {Axy[x=y]}. I think in fact this L(T) is call the language of FOL; and \x+y=0\ isn't a wff in this language. Hence it's not provable in this T. > It probably wasn't Nam's intent there, It's my intent all right to say to MoeBlee, Jesse, and others that \x+y=0\ is simply *not provable in this T*, in accordance to *syntactical* provability *in FOL=*. > but his rejoinder > served as perfect illustration of why, for reasons > of clarity and unambiguity, one might avoid defining > a system \axioms first, language after\. Two issues. First, it's far from being a \perfect illustration of why, for reasons of clarity and unambiguity\. Many times people do think of operations, models first before even specifying any (non-logical) symbol at all, to *symbolize* the operations, models. The more complex a targeted domain of abstraction is, the more difficult one would find to come up with a balanced number of nonlogical symbols, representing the concepts in the domain. For instance, we might know well enough many biological processes and relations such as DNA replication, heredity, protein \ synthesis, ... But that doesn't mean it's that readily available to our mind what kind of nonlogical symbols or how many of them we must have to cohesively formalize/symbolize these biological concepts. Secondly, all this \axioms first, language after\ that I'm purported to try to \enforce\ in FOL reasoning is a) untrue and b) quite \ irrelevant. My opponent just exaggerated it to the point of ridiculousness (such as \backassward\!). It's untrue because *many times* in the thread I already said one is *free to stipulate* as many languages as one could, meaning that even one doesn't contemplate on creating any formal system at all (hence no axioms would ever need to be written) one could perfectly stipulate a million language if one would like. I don't understand why people couldn't come to grasp such a simple and repeatedly-said notion! It's irrelevant because the central issue here is actually not about whether or not any human stipulate language or axioms - first or last! The is issue here is whether or not certain \peculiar\ Rules, such as A-Instantiation or Expansion, would *permit* an *introduction* of nonlogical symbols - beyond those found in the axioms of a theory (i.e. beyond the minimum set of nonlogical symbols for this axiom-set theory). If those rules permit that (which I've been defending that they don't!), then not only the language that we all would agree to stipulate, but countably infinite nonlogical symbols would be *validly* _introduced_ into a language - whether or not we'd care to desire or stipulate. Otoh, if those rules don't permit (which my opponents have been defending that they do!), then it's immaterial whether or not any stipulate anything language first or last, the Rules would tersely look at the *underlying* axioms to discern the minimal language from there and any symbol appearing in the hypothesis or conclusion would be in that language L(T= {axioms}). No \foreign\ symbols would be \ permitted. Period. All of course within the context of formal (i.e. syntactical or symbolical) proofs in good old FOL=, which doesn't require a new concept such as proof *in a language\ as the other poster has tried to introduced into the \ debate. -- \To discover the proper approach to mathematical logic, we must therefore examine the methods of the mathematician.\ (Shoenfield, \Mathematical Logic\) === Subject: Re: Cantor's argument is erroneous >> >>> Moreover, the raw notion of a language stipulated by >>> giving a signature would seem to need to be already >>> in place before one could THEN speak about some set >>> of formulas from which to extract a signature for a >>> language, since the notion of 'formula' itself is in >>> language which in turn reverts to the notion of >>> symbols of certain kinds and arities. >> >> >> I have a question about this \axioms first, language after\ >> procedure. If one defines one's system in this fashion, >> how would one go about showing that the axioms and other >> formulas can be unambiguously parsed? >> >> If one defines one's system \language first, axioms after\ >> then, of course, one has a clear description of the >> syntax to work with. The other way, I suppose you >> have to draw analogies with well-known systems. This >> is why we assumed '0' was a constant (or 0-ary function?) >> and '+' was a 2-ary function. >> >> However, if I recall correctly, Nam claimed at one point >> that \x + y = 0\ was not well formed in his system, >> to the surprise, it seemed, of everyone except Nam. > > If by \system\ you meant a logic framework system, then > that's not what I had meant. (I always talk in the context > of FOL= system). Otoh, if you meant \formal system\ then > of course \x+y=0\ is not well-formed in the L(T) that > has zero nonlogical symbol (where T = {Axy[x=y]}. > I think in fact this L(T) is call the language of FOL; > and \x+y=0\ isn't a wff in this language. Hence it's > not provable in this T. > >> It probably wasn't Nam's intent there, > > It's my intent all right to say to MoeBlee, Jesse, and others > that \x+y=0\ is simply *not provable in this T*, in accordance > to *syntactical* provability *in FOL=*. > >> but his rejoinder >> served as perfect illustration of why, for reasons >> of clarity and unambiguity, one might avoid defining >> a system \axioms first, language after\. > > Two issues. > First, it's far from being a \perfect illustration of why, for reasons > of clarity and unambiguity\. Many times people do think of operations, > models first before even specifying any (non-logical) symbol at all, > to *symbolize* the operations, models. The more complex a targeted > domain of abstraction is, the more difficult one would find to come up > with a balanced number of nonlogical symbols, representing the concepts > in the domain. For instance, we might know well enough many biological > processes and relations such as DNA replication, heredity, protein > synthesis, > ... But that doesn't mean it's that readily available to our mind what \ kind > of nonlogical symbols or how many of them we must have to cohesively > formalize/symbolize these biological concepts. > > Secondly, all this \axioms first, language after\ that I'm purported > to try to \enforce\ in FOL reasoning is a) untrue and b) quite \ irrelevant. > My opponent just exaggerated it to the point of ridiculousness (such > as \backassward\!). > > It's untrue because *many times* in the thread I already said one is > *free to stipulate* as many languages as one could, meaning that even one > doesn't contemplate on creating any formal system at all (hence no axioms > would ever need to be written) one could perfectly stipulate a million > language if one would like. I don't understand why people couldn't come > to grasp such a simple and repeatedly-said notion! > > It's irrelevant because the central issue here is actually not about > whether or not any human stipulate language or axioms - first or last! > > The is issue here is whether or not certain \peculiar\ Rules, such as > A-Instantiation or Expansion, would *permit* an *introduction* of > nonlogical symbols - beyond those found in the axioms of a theory > (i.e. beyond the minimum set of nonlogical symbols for this axiom-set > theory). If those rules permit that (which I've been defending that > they don't!), then not only the language that we all would agree to > stipulate, but countably infinite nonlogical symbols would be *validly* I meant \*uncountably* infinite\ > _introduced_ into a language - whether or not we'd care to desire or > stipulate. Otoh, if those rules don't permit (which my opponents have > been defending that they do!), then it's immaterial whether or not > any stipulate anything language first or last, the Rules would tersely > look at the *underlying* axioms to discern the minimal language from > there and any symbol appearing in the hypothesis or conclusion would > be in that language L(T= {axioms}). No \foreign\ symbols would be > permitted. > Period. > > All of course within the context of formal (i.e. syntactical or \ symbolical) > proofs in good old FOL=, which doesn't require a new concept such as \ proof > *in a language\ as the other poster has tried to introduced into the > debate. > > -- \To discover the proper approach to mathematical logic, we must therefore examine the methods of the mathematician.\ (Shoenfield, \Mathematical Logic\) === Subject: Re: K-12 Calculator Woes >They unanimously put forward the existence of >calculators to do the calculations, and calculators use decimals There are calculators that *do* other fractions. When I was teaching the lower math classes in high school, these were often used so the kids never had to do any fractions at all aside from entering them into calculators. http://wize.com/calculators/t61953-fractions -- Dorothy There is no sound, no cry in all the world that can be heard unless someone listens .. The Outer Limits === Subject: Re: K-12 Calculator Woes > >> >> No amount of facility at arithmetic yields an understanding >> of numbers. ÊA serious question is whether it interferes >> with the subsequent gaining such an understanding. \ ÊFamiliarity >> with arguments by induction is important, and few have it. > >This maybe is true for someone who is a number wizard, but I >understand better consepts than do calculations, because my working >memory is very low. It is good to do different kinds of calculations >in school, so that you became familiar with them. But you always have >to understand what you are doing, so you have to be able to guess or >know by experiance what kind of answer the calculations probably >yield. The problem with calculators in the schools is that they are used as a crutch instead of being used to teach concepts. They *can* be used to teach, but this has to be consciously done. As with any other tool, calculators can be used in a good or a bad way. Everything depends on the teacher's approach. Using calculators as an exploration tool can be valuable. For example, let preschoolers explore what happens when you add 0 to any number. Let them start with a number and subtract 1 repeatedly and observe their reactions when they hit negative numbers. Do pattern puzzles on the calculator with children in elementary school. See what patterns emerge by adding 2, 5 or 10 repeatedly. Have them make their own pattern puzzles. There are lots of things that can be done using calculators in a shorter lesson time than can be done by hand and which allow students to explore and build concepts. Using calculators to *get the answer* to problems is not always the way to go. Using computers in the classroom is similar. It's a tool, not an end. -- Dorothy There is no sound, no cry in all the world that can be heard unless someone listens .. The Outer Limits === Subject: Re: K-12 Calculator Woes On 6 May 2009 15:02:53 -0400, hrubin@odds.stat.purdue.edu (Herman >What mathematics do non-mathematicians need? They need >to understand the mathematical concepts which will be >used in their work, and for most this will need an >understanding of the real numbers and limits. They >need to be able to use \mathematical notation\ to >translate their real-world problems into mathematical >representations which then can be solved by mathematical >methods. What they will not be able to do, except in >very simple situations, is carry out the solution. Herman, most non-mathematicians in non-technical fields do NOT use these concepts at all. -- Dorothy There is no sound, no cry in all the world that can be heard unless someone listens .. The Outer Limits === Subject: Re: K-12 Calculator Woes ................ >>>>>>>>>> Knowing how to do arithmetic is useful, but not >>>>>>>>>> essential. Understanding the numbers, and I do not >>>>>>>>>> mean strings of numerals, is essential, and most of >>>>>>>>>> our high school teachers of mathematics do not have >>>>>>>>>> any of that. >>>>>>>>> Using calculators removes students from the numbers, hindering >>>>>>>>> understanding. >>>>>>>> No, it does some removing students from operators >>>>>>>> with sequences of numerals. The understanding does >>>>>>>> not at all come from familiarity with arithmetic, >>>>>>>> but in understanding numbers as such. >>>>>>> And calculators remove the need to understand numbers, replacing \ that >>>>>>> understanding with an understanding of programming calculators. >>>>>> Understanding numbers is NOT understanding strings of >>>>>> decimal digits. There are two main concepts for the >>>>>> integers, and neither of them has anything to do with >>>>>> the decimal representation. >>>>>> The decimal representation is only ONE way of representing >>>>>> numbers; it is sometimes not even useful. >>>>> For 99% of he population it is the only way of representing and >>>>> manipulating numbers. Even rational fractions disappear from their >>>>> lexicon for most, unless they user a tool like a tape measure. Heck, >>>>> even fractions have virtually disappeared from he stock market. There are other means as well. Those in the sciences, and in many other fields as well, misuse mathematics because they have learned procedures which require assumptions to be met to be valid. >> They have NOT. The string 6.43 means 6 plus 43/100. If they >> do not understand the decimal fractions are fractions, they do >> not understand decimal fractions. >I said the rational representation of fractions. I agree that not enough is done with this, and that computers have a lot to do with the problem. It is easy to get computers to run in base 2 arithmetic, including for \real\ numbers, and even the important fixed-point arithmetic is difficult on them. The representation of fractions is, for a machine, much harder than floats or decimals, and is more complicated to work with. However, the teaching of fractions leaves even more to be desired. In can be made both rigorous and more simple. Of course, anything is simpler if one has \algebraic notation\, by which I mean that a variable is a symbolic expression which can stand for anything. So we have, for h not 0, a/b = ah/bh, and if the idea of fractions is presented with a modicum of intelligence, it is obvious that a/b + c/b = (a+c)/b. >Because of calculators people do not use that form, and they cannot >manipulate them, and often cannot understand them. My concern is that they understand them, and hence can properly use them. >>>> That 99% thinks that the decimal representations ARE the >>>> numbers, and have no ideas of the properties of numbers. >>> They have no need to know more. They certainly do; that is the problem. Once they get that attitude, it becomes very difficult to teach them the concepts. >> If they think a representation is the thing represented, at >> best they are confused. It is like the following non-paradox: >> One cat has one more tail than no cat. >> No cat has eight tails. >> Therefore, one cat has nine tails. >> How can you be so confident? We are turning out far too >> many people who do not understand what they are doing, using >> routine procedures which have assumptions which are not stated >> and which are usually not correct. >You totally misunderstand me. >I am not confident, I am appalled. As am I. >But I think your position is far too much of a swing of the pendulum Concepts and even proofs are easy if properly done. I have seen another with the same idea of an introductory approach to the integers, namely, use a notation which is clumsy for computation, but excellent for understanding, which is 0 followed by a string of tick marks. With this, one can introduce from the Peano Postulates addition as a moving of tick marks, etc. The associative law of addition is a simple example of the use of the axioms. Also, one can introduce the cardinal concept as moving the whole bunch of tick marks at the same time. >I have repeatedly stated that math skills for students need to be >improved, and that the very first step in that improvement is the >removal of calculators from the classroom. I agree that the skills are USEFUL, and should not be discouraged. I practice my computational skills. >Calculators, and computers, have changed attitudes int he public away >from the need to understand basic mathematical concepts, and the >rational representation of fractions is a perfect example. Some calculators have rational capabilities, somewhat limited. If we insist on more, it can be provided. Some of the present ones will attempt to figure out which fraction corresponds to a decimal representation of a number. >When teaching I was repeatedly confronted by angry parents whose >children could not manipulate what I will call fractions (as opposed to >decimal fractions). They unanimously put forward the existence of >calculators to do the calculations, and calculators use decimals. Wall >Street now uses decimals. Banks no longer give 5 1/4%, but 5.25% I have seen Federal Reserve rates given in quarters. But with the requirement of an APR, and with rates being compounded at least monthly, if not daily, one almost has to use rounded decimals. >Outside of a few trades like construction, where the English measuring >system still rules, fractions are disappearing from our society. We still use ounces and inches. There is also the use of minutes and seconds, which corresponds to the ancient base 60 notation. But I have seen few cookbooks which point out that 1/3 of an ounce (liquid) is two teaspoons. >And people do not understand the tragedy of this. As I have related int >he past, I have seen errors made because of a reliance on rote button >pushing caused by an undeserved faith in calculators. Adults do not >realize that 20% = 2/10, so they cannot calculate tips. They think that >a .300 wrench is huge, not being able to recognize it is 3/10. And on >and on and on. >Too many parents already teach their kids that \math is hard\. And now >htey put the calculator up as a method for making math easy. And if it >cannot be done on a calculator then it is too hard. This view comes from the emphasis on memorization and computation the \old-fashioned\ way. >This goes beyond mere arithmetic. Graphing calculators are hurting >students' understanding. It takes very little to graph a line, with >understanding. I am not sure what you mean. It is easy with a ruler and two points on the line, but I do not do a good job freehand. But still students push buttons, and have an undeserved >faith in the calculator. This is correct, but will the average student be able to do any better? Calculators are super-fast sub-imbeciles, and will do exactly what they have been told, no matter how stupid it is. The tiny screen limits what can be displayed, >and important behavior beyond the display go unrevealed because students >think that what was displayed was *the* answer because they do not have >hte experience from manually graphing to know otherwise. How many points to graph? Also, while I do some manual graphing, I prefer to put it on the computer, because I do not do a good job. Understanding how is not adequate without sufficient drawing skills. >i see students in other subjects that lose understanding because of >calculators. Finance majors do not understand the effects of changes in >period on interest because all the do is push buttons. Chemistry >students do not understand the gas laws because they program formulas >into a calculator and push buttons based on which variables are provided >in the question. >You put the rote calculations down, pushing instead for theory. We have seen what learning rote calculations does. We have not seen, at the lower levels, what learning concepts, not theory, can do, nor the advantages of learning theory. Students who learned Euclid geometry do not seem to do any worse than those learning geometry by calculation. >But most of us need the chance to explore and build relationships that >doing those calculations provides. Does doing the calculations achieve this? Or is it knowing what things mean, and trying them out? Algebraic notation, which is trivial, is what is needed. Yes, in the first grade doing rote >additon may sem barren, but it isn;t It develops skills, attitudes, and >expectations critical for success in many, many subjects in the future. But producing the addition tables by using successor, and the multiplication tables by addition, will do a better job of this. >> One cannot know that one can use something unless one knows >> of its existence and its basic concepts. >Not true. >Many , many people, for example, use a pc without the slightest >understanding of how it works. In the extreme, they know to click on >this and their e-mail is displayed, and they are happy with this. They know the computer exists, and they know the concept of email. >> A scientist who understands the mathematical concepts needed >> for his part of science can formulate his problems in such a >> way that mathematicians not knowing his field of science can >> come up with an answer, if it is known how to do so, or if one >> can be deduced. Knowing a few procedures does not achieve >> this result, and may achieve badly incorrect results. >Often the math concepts exceed the ability of the scientist,a nd rightly \ so. >For example, a professor friend did her dissertation on a graphing >technique that mapped amino acids in a large protein. The biologist >who wanted the info had a theory, but the need for PhD level math was >too much, so they formed a partnership. He provided the data, she >manipulated it. The biologist knew the concepts and could translate them into mathematical terminology, so the mathematician could use the power of mathematics. Alas, these days the emphasis is on combining the two, and the resulting biomathematician will not have either the understanding or the ability. >>> And they do have ideas about the properties of number, they just don;t >>> have the \official\ names. In fact, the way I have taught math teaches \ >>> group and field theory, without using all of the formal names. >>> They know additive and multiplicative inverses, identities, closure. >>> They no symmetry, distance, and maybe even isomorphisms. They just do;t \ >>> know the vocabulary. >>>> They also think that there is a great difference between >>>> using \Arabic\ numerals and Roman numerals. There is no >>>> such difference, except some need to memorize. >>> The differences are significant. Roman numerals have no additive inverse \ >>> or identity, no multiplicative inverse, no placeholder. >> These are numerals, not numbers. Arabic numerals have no >> inverses, etc. It is the numbers which do, and their >> inverses do not depend on the representation. The >> have the traces of that in minutes and seconds. >There is no zero in Roman numerals, a significant difference. There are >no negative roman numerals,nor fractions. Are there negative Arabic numerals? The use of negative numbers was later. Zero as a digit was older, and used by the Sumerians for their base 60 arithmetic more than 4000 years ago. The Egyptians had fractions, as did the Greeks and Romans. The notation is not the concepts. >Roman numerals do not form a group. >They are not isomorphic with arabic numerals. It is only by using strings of Arabic numerals to form representations of numbers, and the use of the minus sign, that one can get the Arabic numerals to form a group. The same could be done with the Roman or Greek numerals, by adding bars for thousand times. >>>>> It should help >>>>>> in understanding if students produce the addition and >>>>>> multiplication tables to more than one base from first >>>>>> ordinal principles, but memorizing them, no. >>>>> Yes, memorization of base 7 is worthless, and for all but computer \ nerds >>>>> any base except 10 is not needed. >> But is the memorization of the table needed? At most, it >> is the ability to use the table. The Chisenbop method of >> multiplication, which has been touted, only has products >> by 1, 2, 5, and 10 learned; it uses the distributive law >> for the rest. >Yes, the memorizations is vital. People cannot carry around a paper copy >if the table, so they carry a calculator. Then they rely on the >calculator for this operation, and eventually all operations. There is too much emphasis on memorization. >Why do the work when the calculator can do it? And the knee-jerk jump to >use the calculator eliminates the possibility of actually exploring the >situation. One can explore the situation by putting other entries into the calculator, or by programming the computer to investigate far more situations than can be done by hand. >Again, yes \learning\ the tables is rote, drudge work, and maybe byt he >time you turn 60 you can start relying on machines to do the work. >But good habits start young, and bad habits start younger. In my state >calculators can be used as early as the 6th grade, and parents often let >their kids use them for homework even earlier. >And people wonder why kids cannot understand that 6 - 3 is really 6 + >(-)3 .The calculator uses the first expression., and that is all kids see. The Sumerians, Babylonians, Egyptians, Greeks, Romans, and many more only used the first expression. They did not know about negative numbers, and this applied to the Arabs who took the Hindu numerals west. Do elementary school students learn the second? >>>> No, it is needed to know that the base of the representation >>>> is immaterial. Also, producing the tables from first principles >>>> makes them meaningful, and not \something to remember\. It even >>>> enables one to get by with forgetting some of it. >>> Bases are no more than a teaching tool for exponents and modulus. The >>> properties of the different bases are identical, and beyond showing they \ >>> are the sam as the decimal system bases are a curiosity for most. >>> Converting from decimal to base 8, for ex., is rote calculation at its >>> worst. >>>>> That said, an understanding of bases and modulus can be useful, in >>>>> particular as I noted in division. >>>> You are using modulus in a non-mathematical sense here. >>> No >>>>>>>> It turns them into programmers, not mathematicians. >>>>>>>> What does knowing how to do arithmetic do? It turns >>>>>>>> them into the equivalent of the machine doing the >>>>>>>> result of the programming. >>>>>>> But that requires an understanding of numbers, while the use of >>>>>>> calculators does not. >>>>>> No amount of facility at arithmetic yields an understanding >>>>>> of numbers. >>>>> I disagree, and we will have to agree to disagree. >>>>> I suspect you are approaching this from a far higher theoretical level \ >>>>> than most people reach. >>>> I want first graders to reach this level, and I believe >>>> most can do it with ease if the ordinal approach is the >>>> first used. It is SIMPLE. But trying to teach it to >>>> high school and college students is very difficult; they >>>> \know\ the numbers, and are unwilling to learn the basics >>>> which they do not know at all. >>> Most first graders are incapable of doing what you want. Getting them to \ >>> even learn the basics of the integers is a full time job. But the basics of the integers from the Peano Postulates and the \base 1\ notation are easy. It is using base 10 from the beginning which makes it harder. >> Do YOU know the basics of the integers? Knowing them does not >> require being able to count above 3, although I may be somewhat >> wrong on just how high. I am not even sure if Landau's book >> even gets to 2, except for the numbering of statements, etc. >Yes, I do. >You are oversimplifying and isolating the concepts. I am pointing out that the concepts are simple. >>> Teaching math to older students is difficult not because they think they \ >>> know it all, but because by the time they reach that age society has >>> taught them that math is irrelevant. >> How about teachers who are going to teach math? >I saw it in my classes to the point that students changed their majors, >even elementary ed majors. They could not do the work even inthe math >for middle school courses. >Getting >> non-computational concepts to them is almost a lost cause; >> many never get it. >Because they have never been exposed to them, usually because technology >has taken the lead. >And how about the 80% of prospective >> high school teachers of math who could not set up a problem >> using calculus, in a course which had the full calculus >> prerequisite, on a take-home final? >I need more info on this. This was in a probability course. The problems were quite similar to those done in class. >For ex., my college strongly suggested that prospective teachers take >the certification exams early and often even before the preparation >courses had been taught. >Certification standards are also changin; now most states require at >least a BA in math to teach HS math, and no one can get that degree and >not set up a calculus equation. Unfortunately, this is false. They can calculate derivatives and anti-derivatives, but the rest is forgotten. Heck, many states and national >certification now even require formal proofs to teach HS math Do they require them to pass an examination? Having taken courses which taught this is not sufficient. > The math professors >> who taught them were not surprised; they are quite aware >> that the bulk of calculus students can only memorize formulas >> and their use. They are not even at the level of programmers; >> they are at the level of the computer hardware. >That is the fault of the professors, not the students. My professors >would not pass a student wh could not explain what they were doing, and >absolutely refused to allow the use of technology. If the professors did not do this, the enrollment in calculus courses would drop drastically. Engineers and physicists do not care, as far as their courses are concerned, whether there is understanding, and would teach the students themselves. Using technology is another matter. How do you expect students to get the square root of 1.37 on an exam? Technology was used for such even BC (before computers); slide rules were used. And slide rules were used for multiplying back then. >Larry -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: K-12 Calculator Woes > > The representation of fractions is, for a machine, much > harder than floats or decimals, and is more complicated > to work with. Why do you believe that is true? === Subject: Re: NY Times math problem >> riverman said: >> >> >> >> > What about just >> > saying 'the agent moves to minimize the distance between himself >> > and the rabbit'? >> >> Splash! >> > >LOL. Within, of course, the constraints of the stated problem. >\...a rabbit in the middle of a pond, an agent who can run >around the shore four times as fast as the rabbit can swim.\ > >Let's not let all this precision affect our accuracy, shall we? >:-) > >--riverman No. What he said is 100% true. Also, the rabbit is doing the exact opposite. i.e Trying to maximize the distance between himself and the agent. The rabbit will win eventually, and he only needs to wait until the agent is *near* the 180 degree point. He doesn't have to get him there exactly. === Subject: Re: NY Times math problem >> then if the agent always runs toward the aim point then the rabbit >> can escape (even if the agent is very fast). But this assumes a >> stupid agent > >Yes it does, which is exactly why I was arguing that it was a poor >strategy for the agent to employ. > > >- Tim The rabbit will ALWAYS use his peripheral vision to determine the agent's position, and will always swim away from that attempt at capture. They have over 270 degrees of vision without even turning their head. === Subject: Re: NY Times math problem >> >>>>>> DId anyone here see the problem presented in >> >>>>>> the Science section of NY Times last week? >> >>>>>> Quite startling, to see something so sophisticated >> >>>>>> in a 'general readership' publication. >> >>>>>> Is it solvable without a calculus of variations approach? >> >>>>>> -- >> >>>>>> Mark >> >>>>> Yes. >> >>>>> Spoiler below 13 >> >>>>> 0 >> >>>>> 1 >> >>>>> 2 >> >>>>> 3 >> >>>>> 4 >> >>>>> 5 >> >>>>> 6 >> >>>>> 7 >> >>>>> 9 >> >>>>> 10 >> >>>>> 11 >> >>>>> 12 >> >>>>> 13 >> >>>>> Since the agent can run four times as fast as the rabbit can swim, \ no >> >>>>> matter what the agent does, the rabbit can swim away from the \ centre, >> >>>>> and keep the agent on the far side as long as the rabbit is no more \ than >> >>>>> 1/4 of the radius from the centre. So the rabbit can reach a point \ 3/4 >> >>>>> of a radius from the edge while the agent is still on the opposite \ side. >> >>>> Only if the agent stands still until the last possible moment. I \ think >> >>>> the agent will move continuously, and as soon as the rabbit starts >> >>>> moving in any direction, the agent will move toward the point that \ is >> >>>> the closest to the rabbit at that moment. Let's call the agent \ 'Xeno'. >> >>> No - until the rabbit is 1/4 of the radius away from the centre, he >> >>> can swim fast enough, in a suitable direction, to keep the agent >> >>> exactly opposite. So it doesn't matter if the agent moves. >> >> Which shows, I think (to return to the very original question about >> >> whether this needs horrible maths to solve) that there is a simple \ proof >> >> that pretty-well anyone can follow that shows the rabbit can escape \ in >> >> the specific case (it goes to where it can just swim faster than the >> >> agent, swims round in a circle until it gets to 180 degrees away from >> >> the agent, and can then make it to the shore faster than the agent \ can >> >> run round), but that the optimum strategy, and hence the answer to \ the >> >> unasked question about which size of ponds or relative speeds allow \ the >> >> rabbit to escape do require the horrid maths. >> >> -- >> >> Online waterways route planner:http://canalplan.org.uk >> >> development version:http://canalplan.eu-Hide quoted text - >> >> >> - Show quoted text - >> >> > I'm not convinced about the 'keep the agent on the opposite side' >> > logic. Lets expand the problem to their being TWO agents, already on >> > opposite sides. If the rabbit swims in any direction, off-center, then >> > both agents will move together to be at the point the rabbit is >> > apparently aiming for, then the rabbit moves slowly back towards >> > center and the problem is reduced to the original one. So the rabbit >> > can escape with TWO agents around the pool...or even an INFINITE >> > number of them? (well, slightly less than infinite, in this case....) >> >> When the rabbit moved back towards the centre of the pool, the agents >> would move back to positions oppoisite each other. > >They may not have time. They would eventually end up together as was originally claimed. Just like a spinning cylinder in space will eventually develop a wobble, and will eventually end up spinning end over end. >> It appears that the rabbit cannot escape if there are two agents. > >Assume that the two agents are unaware of each other's existence and >choose the optimal strategy for a lone agent (always move so as >to decrease the angular difference). The rabbit must very slightly >modify his strategy, keep almost but not quite 180 degrees from the >agents >(otherwise they might split up). In this case the rabbit escapes. > >However, assume that the two agents are aware of each other's >existence >but cannot communicate. They can stop the rabbit escaping. They >divide the >circle in two halves. Each agent adopts the strategy, move toward the >point >in my half that is closest to the rabbit. > > - William Hughes > Not if the rabbit determines where their parting line is located. === Subject: Re: NY Times math problem <003549bc$0$25289$c3e8da3@news.astraweb.com> <00447442$0$2469$c3e8da3@news.astraweb.com> <87hc012hno.fsf@temporary-address.org.uk> >> >>> It seems obvious to me that the rabbit will end up describing >>> a spiral path, as it will constantly be trying to stay 180 >>> degrees away from the agent. >> >> Nope, when the rabbit is close enough to a point on shore >> that he can reach it before the agent, the rabbit will >> take a straight line path. It no longer matters if it >> is 180 degrees from the agent. > > yes, this straight line may not be a radius, but it is unlikely > to differ greatly from a radius. It will never be a radius. If it were, he would get eaten. It will be along a radial line. -- [mail]: Chuck F (cbfalconer at maineline dot net) [page]: Try the download section. === Subject: Re: NY Times math problem posting-account=O9zR9AkAAACmp918j6u5m5plppeILcze Filter 1.2.0.72; GTB6; .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; \ .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Dave: > > I made a small spreadsheet to use your rabbit's strategy. Correct me > if I am wrong, but isn't it true that after the agent has gone about > 295 degrees around the pond, he is approximately on the radius > containing the rabbit? If, at that point, he keeps running at full > speed, as in your program, he will be running away from the rabbit. > This is hardly an optimal strategy for the agent. In fact, once the > agent gets on the rabbit's radius, he should stop. The rabbit will > swim back through the center and the cycle will repeat. By your > strategy, the rabbit never will reach the shore even at a speed ratio > of only 4, assuming that the agent uses his best strategy. > > > It's a systematic method only... > > But we now know what happens if the rabbit takes one straight line to \ shore > and we know what happens if the agent only loops around the circle in one > direction...with the rabbit correcting direction with each movement of \ the > agent. In one case the rabbit has the wrong strategy and in the other \ case > the agent has the wrong strategy. In the second case, both the agent and the rabbit have the wrong strategy. Dave === Subject: Re: NY Times math problem > Dave: > > I made a small spreadsheet to use your rabbit's strategy. Correct me > if I am wrong, but isn't it true that after the agent has gone about > 295 degrees around the pond, he is approximately on the radius > containing the rabbit? If, at that point, he keeps running at full > speed, as in your program, he will be running away from the rabbit. > This is hardly an optimal strategy for the agent. In fact, once the > agent gets on the rabbit's radius, he should stop. The rabbit will > swim back through the center and the cycle will repeat. By your > strategy, the rabbit never will reach the shore even at a speed ratio > of only 4, assuming that the agent uses his best strategy. > > > It's a systematic method only... > > But we now know what happens if the rabbit takes one straight line to > shore > and we know what happens if the agent only loops around the circle in one > direction...with the rabbit correcting direction with each movement of \ the > agent. In one case the rabbit has the wrong strategy and in the other \ case > the agent has the wrong strategy. In the second case, both the agent and the rabbit have the wrong strategy. No...in the second case if the agent is dumb enough to just systematically run clockwise around the circle...then the rabbit's strategy in response is \ good enough. === Subject: Re: NY Times math problem > > > > I made a small spreadsheet to use your rabbit's strategy. Correct me > > if I am wrong, but isn't it true that after the agent has gone about > > 295 degrees around the pond, he is approximately on the radius > > containing the rabbit? If, at that point, he keeps running at full > > speed, as in your program, he will be running away from the rabbit. > > This is hardly an optimal strategy for the agent. In fact, once the > > agent gets on the rabbit's radius, he should stop. The rabbit will > > swim back through the center and the cycle will repeat. By your > > strategy, the rabbit never will reach the shore even at a speed ratio > > of only 4, assuming that the agent uses his best strategy. > > > > > > > > It's a systematic method only... > > > > But we now know what happens if the rabbit takes one straight line to > > shore and we know what happens if the agent only loops around the circle \ > > in one direction...with the rabbit correcting direction with each \ movement > > of the agent. In one case the rabbit has the wrong strategy and in the > > other case the agent has the wrong strategy. > > > > Really I was interested in the rabbit path plot with the agent looping > > around the circle in one direction...and with the rabbit correcting > > direction with each movement of the agent. > > So the rabbit...and it should be a duck...is never caught if he keeps > turning away from the agent with each movement of the agent. Then assuming \ a > strategy of reversing direction by the agent...the rabbit can only get out \ > by picking some point where he breaks for shore. But the agent can't be \ sure > of where the rabbit curves are going to carry and the rabbit can't be sure \ > of his break point. It's merely possible for the rabbit to get out... The rabbit can always move to the center of the pond. same diameter as the agent at least until the rabbit's angular velocity about the pond center equals the agents angular velocity about the pond center at full speed, i,e, to 1/4 of a radius from the center in the direction opposite to the agent but on the same diameter. The rabbit is now 3/4 of a radius from the nearest point on the circumference and the agent must travel pi times that radius along the edge of the pond to get to that same point. === Subject: Re: NY Times math problem >> > >> > It's a systematic method only... >> > >> > But we now know what happens if the rabbit takes one straight line to >> > shore and we know what happens if the agent only loops around the >> > circle >> > in one direction...with the rabbit correcting direction with each >> > movement >> > of the agent. In one case the rabbit has the wrong strategy and in the >> > other case the agent has the wrong strategy. >> > >> > Really I was interested in the rabbit path plot with the agent looping >> > around the circle in one direction...and with the rabbit correcting >> > direction with each movement of the agent. >> >> So the rabbit...and it should be a duck...is never caught if he keeps >> turning away from the agent with each movement of the agent. Then >> assuming a >> strategy of reversing direction by the agent...the rabbit can only get >> out >> by picking some point where he breaks for shore. But the agent can't be >> sure >> of where the rabbit curves are going to carry and the rabbit can't be >> sure >> of his break point. It's merely possible for the rabbit to get out... > > The rabbit can always move to the center of the pond. > > same diameter as the agent at least until the rabbit's angular velocity > about the pond center equals the agents angular velocity about the pond > center at full speed, i,e, to 1/4 of a radius from the center in the > direction opposite to the agent but on the same diameter. > > The rabbit is now 3/4 of a radius from the nearest point on the > circumference and the agent must travel pi times that radius along the > edge of the pond to get to that same point. while the agent is moving. So I suppose the rabbit rotates with the moving agent...from a postion on the far side of the radius point...while spiraling \ outward. It's intricate... Well...consider the graphics plot that I made. As the agent moves the rabbit \ turns away from the agent and the rabbit carries the rabbit's distance of movement. Now from any agent point on the circle a line can be scaled from the agent point to a tangent point on the rabbit path and that by knowing that the rabbit path direction...and the fact that the rabbit is moving away \ from the agent. And from that strategies can be developed... code can be modified so that the agent systematically runs clockwise to a point but then changes to counterclockwise movement. I don't have time to work with it but that's interesting. For instance the agent can run clockwise for 360 degrees and then run counterclockwise 90 degrees or so to \ run the rabbit back toward the center. === Subject: Re: NY Times math problem > >> > > >> > It's a systematic method only... > >> > > >> > But we now know what happens if the rabbit takes one straight line \ to > >> > shore and we know what happens if the agent only loops around the > >> > circle > >> > in one direction...with the rabbit correcting direction with each > >> > movement > >> > of the agent. In one case the rabbit has the wrong strategy and in \ the > >> > other case the agent has the wrong strategy. > >> > > >> > Really I was interested in the rabbit path plot with the agent \ looping > >> > around the circle in one direction...and with the rabbit correcting > >> > direction with each movement of the agent. > >> > >> So the rabbit...and it should be a duck...is never caught if he keeps > >> turning away from the agent with each movement of the agent. Then > >> assuming a > >> strategy of reversing direction by the agent...the rabbit can only get \ > >> out > >> by picking some point where he breaks for shore. But the agent can't be \ > >> sure > >> of where the rabbit curves are going to carry and the rabbit can't be > >> sure > >> of his break point. It's merely possible for the rabbit to get out... > > > > > > The rabbit can always move to the center of the pond. > > > > same diameter as the agent at least until the rabbit's angular velocity > > about the pond center equals the agents angular velocity about the pond > > center at full speed, i,e, to 1/4 of a radius from the center in the > > direction opposite to the agent but on the same diameter. > > > > The rabbit is now 3/4 of a radius from the nearest point on the > > circumference and the agent must travel pi times that radius along the > > edge of the pond to get to that same point. > > > while the agent is moving. So I suppose the rabbit rotates with the moving \ > agent...from a postion on the far side of the radius point...while \ spiraling > outward. It's intricate... But so long as the rabbit is less than 1/4 of a radius from center, it can continue to move outward and simultaneously maintain its position on the opposite side of same diameter that the agent is on. > > Well...consider the graphics plot that I made. As the agent moves the \ rabbit > turns away from the agent and the rabbit carries the rabbit's distance of \ > movement. Now from any agent point on the circle a line can be scaled from \ > the agent point to a tangent point on the rabbit path and that by knowing \ > that the rabbit path direction...and the fact that the rabbit is moving \ away > from the agent. And from that strategies can be developed... Unnecessarily complicated. All the rabbit has to do is stay on the diameter thru the agent's position until it is 3/4 of a diameter from the point opposite the agent, then run straight for that point. What the agent does cannot prevent the rabbit from ding exactly that, but if the agent at any time is not going around the pond at top speed one way or the other, it helps the rabbit. > > code can be modified so that the agent systematically runs clockwise to a \ > point but then changes to counterclockwise movement. > I don't have time to > work with it but that's interesting. For instance the agent can run > clockwise for 360 degrees and then run counterclockwise 90 degrees or so \ to > run the rabbit back toward the center. Agent strategy: 1. While the rabbit is not on the same diameter as the agent, the agent runs as fast as possible along the boundary of the pond towards the boundary point nearest to the rabbit. 2. While the rabbit is on the same radius as the agent, stay still. 3. While the rabbit is on the opposite half of the diameter through the agent, go as fast as possible in either direction, switching directions at random. Rabbit strategy: 1. Move as fast as possible to center of pond, then. 2. Move as fast as possible away from the agent while keeping on the same diameter as the agent until the rabbits time to the nearest point on the boundary is noticeably less than the agent's time to that point, if possible, or until it takes all the rabbits speed to maintain that distance. 3. If the rabbits time to the nearest boundary point is now less than the agent's time, run for that point, otherwise tread water. === Subject: Re: NY Times math problem > Unnecessarily complicated. All the rabbit has to do is stay on the > diameter thru the agent's position until it is 3/4 of a diameter from > the point opposite the agent, then run straight for that point. > The rabbit does not know anything except whether or not it is rotating with \ a radial to the agent...and if it is on the other side of the radius. > Agent strategy: > 1. While the rabbit is not on the same diameter as the agent, the > agent runs as fast as possible along the boundary of the pond > towards the boundary point nearest to the rabbit. > 2. While the rabbit is on the same radius as the agent, stay still. > 3. While the rabbit is on the opposite half of the diameter through > the agent, go as fast as possible in either direction, switching > directions at random. > > Rabbit strategy: > 1. Move as fast as possible to center of pond, then. > 2. Move as fast as possible away from the agent while keeping on the > same diameter as the agent until the rabbits time to the nearest > point on the boundary is noticeably less than the agent's time to > that point, if possible, or until it takes all the rabbits speed > to maintain that distance. > 3. If the rabbits time to the nearest boundary point is now less than > the agent's time, run for that point, otherwise tread water. === Subject: Re: NY Times math problem \ \ <3A3Nl.39172$qa.25218@bignews4.bellsouth.net> \ posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > > Unnecessarily complicated. All the rabbit has to do is stay on the > > diameter thru the agent's position until it is 3/4 of a diameter from > > the point opposite the agent, then run straight for that point. > > > The rabbit does not know anything except whether or not it is rotating \ with > a radial to the agent...and if it is on the other side of the radius. If the rabbit also knows the direction to the nearest shore. adopt the following strategy (which does not involve calculation): Step 1. a: Keep \rotating with a radial to the agent\ b: if not using maximum speed for a: turn toward the nearest shore until using maximum speed. c: continue until not approaching the nearest shore Step 2. a: Swim directly toward the nearest shore at maximum speed. This will allow the rabbit to escape given any agent strategy if the agent's top speed is less than (pi+1) times the rabbit's (a slightly more complex strategy for step 2, also involving no calculation, can improve this a little). - William Hughes === Subject: Re: NY Times math problem >> >> The rabbit does not know anything except whether or not it is rotating >> with >> a radial to the agent...and if it is on the other side of the radius. > > > If the rabbit also knows the direction to the nearest shore. > adopt the following strategy (which does not involve > calculation): > > > Step 1. > > a: Keep \rotating with a radial to the agent\ > b: if not using maximum speed for a: > turn toward the nearest shore until > using maximum speed. > c: continue until not approaching the nearest > shore > > Step 2. > > a: Swim directly toward the nearest shore > at maximum speed. > > This will allow the rabbit to escape given any > agent strategy if the agent's top > speed is less than (pi+1) times the rabbit's > (a slightly more complex strategy for step 2, also > involving no calculation, can improve this a > little). > Okay the rabbit's name is Duck... The speeds are fixed but since the agent can stop maybe I should allow Duck \ to slow down. But when they sprint just say that both increase speed at the \ same percentage so that it's not necessary to allow for increased speed of a \ sprint...over their given rates. But I'm not allowing Duck to know where 1/4 radius distance is as some point \ in the water. I'm only allowing Duck to know whether or not he is rotating with the agent...and that finds the break point. === Subject: Re: NY Times math problem >>> >>> The rabbit does not know anything except whether or not it is rotating >>> with >>> a radial to the agent...and if it is on the other side of the radius. >> > > >> >> If the rabbit also knows the direction to the nearest shore. >> adopt the following strategy (which does not involve >> calculation): >> >> >> Step 1. >> >> a: Keep \rotating with a radial to the agent\ >> b: if not using maximum speed for a: >> turn toward the nearest shore until >> using maximum speed. >> c: continue until not approaching the nearest >> shore >> >> Step 2. >> >> a: Swim directly toward the nearest shore >> at maximum speed. >> >> This will allow the rabbit to escape given any >> agent strategy if the agent's top >> speed is less than (pi+1) times the rabbit's >> (a slightly more complex strategy for step 2, also >> involving no calculation, can improve this a >> little). >> > > > Okay the rabbit's name is Duck... > > The speeds are fixed but since the agent can stop maybe I should allow > Duck to slow down. But when they sprint just say that both increase speed \ > at the same percentage so that it's not necessary to allow for increased > speed of a sprint...over their given rates. > > But I'm not allowing Duck to know where 1/4 radius distance is as some > point in the water. I'm only allowing Duck to know whether or not he is > rotating with the agent...and that finds the break point. I think we should stay with the fixed speeds... We just find them in motion. The agent can't stop but can reverse direction. \ And don't worry about sprint speeds as both speeds could increase at the same rate... === Subject: Re: NY Times math problem > >>>> >>>> The rabbit does not know anything except whether or not it is rotating \ >>>> with >>>> a radial to the agent...and if it is on the other side of the radius. >>> >> >> >>> >>> If the rabbit also knows the direction to the nearest shore. >>> adopt the following strategy (which does not involve >>> calculation): >>> >>> >>> Step 1. >>> >>> a: Keep \rotating with a radial to the agent\ >>> b: if not using maximum speed for a: >>> turn toward the nearest shore until >>> using maximum speed. >>> c: continue until not approaching the nearest >>> shore >>> >>> Step 2. >>> >>> a: Swim directly toward the nearest shore >>> at maximum speed. >>> >>> This will allow the rabbit to escape given any >>> agent strategy if the agent's top >>> speed is less than (pi+1) times the rabbit's >>> (a slightly more complex strategy for step 2, also >>> involving no calculation, can improve this a >>> little). >>> >> >> >> Okay the rabbit's name is Duck... >> >> The speeds are fixed but since the agent can stop maybe I should allow >> Duck to slow down. But when they sprint just say that both increase speed \ >> at the same percentage so that it's not necessary to allow for increased \ >> speed of a sprint...over their given rates. >> >> But I'm not allowing Duck to know where 1/4 radius distance is as some >> point in the water. I'm only allowing Duck to know whether or not he is >> rotating with the agent...and that finds the break point. > > I think we should stay with the fixed speeds... > > We just find them in motion. The agent can't stop but can reverse > direction. And don't worry about sprint speeds as both speeds could > increase at the same rate... We just find them in motion... And allowing the agent to reverse direction is just to eliminate the with the agent by spiraling outward but must also maneuver to be on the point on the other side of the radius from the agent. === Subject: Re: NY Times math problem > >> > >> The rabbit does not know anything except whether or not it is rotating \ > >> with > >> a radial to the agent...and if it is on the other side of the radius. > > > > > > > > If the rabbit also knows the direction to the nearest shore. > > adopt the following strategy (which does not involve > > calculation): > > > > > > Step 1. > > > > a: Keep \rotating with a radial to the agent\ > > b: if not using maximum speed for a: > > turn toward the nearest shore until > > using maximum speed. > > c: continue until not approaching the nearest > > shore > > > > Step 2. > > > > a: Swim directly toward the nearest shore > > at maximum speed. > > > > This will allow the rabbit to escape given any > > agent strategy if the agent's top > > speed is less than (pi+1) times the rabbit's > > (a slightly more complex strategy for step 2, also > > involving no calculation, can improve this a > > little). > > > > > Okay the rabbit's name is Duck... > > The speeds are fixed but since the agent can stop maybe I should allow \ Duck > to slow down. But when they sprint just say that both increase speed at \ the > same percentage so that it's not necessary to allow for increased speed of \ a > sprint...over their given rates. > > But I'm not allowing Duck to know where 1/4 radius distance is as some \ point > in the water. I'm only allowing Duck to know whether or not he is rotating \ > with the agent...and that finds the break point. If you mean that Duck can tell when it cannot get any farther from the agent and still stay on the same diameter I concur. === Subject: Re: NY Times math problem > > > Unnecessarily complicated. All the rabbit has to do is stay on the > > diameter thru the agent's position until it is 3/4 of a diameter from > > the point opposite the agent, then run straight for that point. > > > > > The rabbit does not know anything except whether or not it is rotating \ with > a radial to the agent...and if it is on the other side of the radius. The issue is not whether the rabbit knows how to escape but whether it can escape if it acts correctly. And the following shows it can. > > > > Agent strategy: > > 1. While the rabbit is not on the same diameter as the agent, the > > agent runs as fast as possible along the boundary of the pond > > towards the boundary point nearest to the rabbit. > > 2. While the rabbit is on the same radius as the agent, stay still. > > 3. While the rabbit is on the opposite half of the diameter through > > the agent, go as fast as possible in either direction, switching > > directions at random. > > > > Rabbit strategy: > > 1. Move as fast as possible to center of pond, then. > > 2. Move as fast as possible away from the agent while keeping on the > > same diameter as the agent until the rabbits time to the nearest > > point on the boundary is noticeably less than the agent's time to > > that point, if possible, or until it takes all the rabbits speed > > to maintain that distance. > > 3. If the rabbits time to the nearest boundary point is now less than > > the agent's time, run for that point, otherwise tread water. === Subject: Re: NY Times math problem > >> The rabbit can always move to the center of the pond. >> >> same diameter as the agent at least until the rabbit's angular velocity >> about the pond center equals the agents angular velocity about the pond >> center at full speed, i,e, to 1/4 of a radius from the center in the >> direction opposite to the agent but on the same diameter. >> >> The rabbit is now 3/4 of a radius from the nearest point on the >> circumference and the agent must travel pi times that radius along the >> edge of the pond to get to that same point. > > > while the agent is moving. So I suppose the rabbit rotates with the moving \ > agent...from a postion on the far side of the radius point...while > spiraling outward. It's intricate... > Well...the rabbit must spiral out from the radius point as he works to get on the same radial rotation with the agent but also position on the opposite \ side of the radius point. If the rabbit is rotating too fast then he would just keep working outward until the rotation is correct. But if the rotation \ is correct but the positon is wrong then the rabbit would have to zig-zag to \ work into position. When in correct position on the opposite side of the radius point and on the same radial rotation with the agent...then break for \ the opposite shore. But break for shore hoping that it will work because the \ rabbit is not calculating... > Well...consider the graphics plot that I made. As the agent moves the > rabbit turns away from the agent and the rabbit carries the rabbit's > distance of movement. Now from any agent point on the circle a line can be \ > scaled from the agent point to a tangent point on the rabbit path and that \ > by knowing that the rabbit path direction...and the fact that the rabbit > is moving away from the agent. And from that strategies can be > developed... > > code can be modified so that the agent systematically runs clockwise to a \ > point but then changes to counterclockwise movement. I don't have time to \ > work with it but that's interesting. For instance the agent can run > clockwise for 360 degrees and then run counterclockwise 90 degrees or so > to run the rabbit back toward the center. > === Subject: Re: NY Times math problem > > > >> The rabbit can always move to the center of the pond. > >> > >> same diameter as the agent at least until the rabbit's angular \ velocity > >> about the pond center equals the agents angular velocity about the \ pond > >> center at full speed, i,e, to 1/4 of a radius from the center in the > >> direction opposite to the agent but on the same diameter. > >> > >> The rabbit is now 3/4 of a radius from the nearest point on the > >> circumference and the agent must travel pi times that radius along the > >> edge of the pond to get to that same point. > > > > > > while the agent is moving. So I suppose the rabbit rotates with the \ moving > > agent...from a postion on the far side of the radius point...while > > spiraling outward. It's intricate... > > > > Well...the rabbit must spiral out from the radius point as he works to get \ > on the same radial rotation with the agent but also position on the \ opposite > side of the radius point. If the rabbit is rotating too fast then he would \ > just keep working outward until the rotation is correct. But if the \ rotation > is correct but the positon is wrong then the rabbit would have to zig-zag \ to > work into position. Unless the agent is continually switching directions, the rabbit never need zig nor zag until it is ready to run for the edge. > When in correct position on the opposite side of the > radius point and on the same radial rotation with the agent...then break \ for > the opposite shore. But break for shore hoping that it will work because \ the > rabbit is not calculating... If the speeds are correct the rabbit has .75 radii to cover but the agent has pi radii ( half a circumference) to cover, and the ratio of those distances is less that the ratio of speeds, 1 to 4 ( or about 0.2387 ) so the rabbit has a bit of a cushion. Relative distance ratio of .75/pi is roughly 5/21 to the relative speeds 5/20, so the rabbit has a bit of a cushion. === Subject: Re: NY Times math problem > >> > >> >> The rabbit can always move to the center of the pond. >> >> >> >> the >> >> same diameter as the agent at least until the rabbit's angular >> >> velocity >> >> about the pond center equals the agents angular velocity about the >> >> pond >> >> center at full speed, i,e, to 1/4 of a radius from the center in the >> >> direction opposite to the agent but on the same diameter. >> >> >> >> The rabbit is now 3/4 of a radius from the nearest point on the >> >> circumference and the agent must travel pi times that radius along \ the >> >> edge of the pond to get to that same point. >> > >> > >> > while the agent is moving. So I suppose the rabbit rotates with the >> > moving >> > agent...from a postion on the far side of the radius point...while >> > spiraling outward. It's intricate... >> > >> >> Well...the rabbit must spiral out from the radius point as he works to >> get >> on the same radial rotation with the agent but also position on the >> opposite >> side of the radius point. If the rabbit is rotating too fast then he >> would >> just keep working outward until the rotation is correct. But if the >> rotation >> is correct but the positon is wrong then the rabbit would have to zig-zag \ >> to >> work into position. > > Unless the agent is continually switching directions, the rabbit never > need zig nor zag until it is ready to run for the edge. > Well the speeds are fixed and the rabbit needs a particular postion on its circle...as it hunts for that circle which rotates with the agent movement. > >> When in correct position on the opposite side of the >> radius point and on the same radial rotation with the agent...then break \ >> for >> the opposite shore. But break for shore hoping that it will work because \ >> the >> rabbit is not calculating... > > If the speeds are correct the rabbit has .75 radii to cover but the > agent has pi radii ( half a circumference) to cover, and the ratio of > those distances is less that the ratio of speeds, 1 to 4 ( or about > 0.2387 ) so the rabbit has a bit of a cushion. > > Relative distance ratio of .75/pi is roughly 5/21 to the relative speeds > 5/20, so the rabbit has a bit of a cushion. The rabbit...and it's really a duck...can't calculate anything. The rabbit does not know how far to be on the other side of the radius. The rabbit only \ knows if it is rotating with a radial to the agent and if it is on the other \ side of the radius...but when so then break for it. === Subject: Re: NY Times math problem > > > >> > > >> >> The rabbit can always move to the center of the pond. > >> >> > >> >> the > >> >> same diameter as the agent at least until the rabbit's angular > >> >> velocity > >> >> about the pond center equals the agents angular velocity about the > >> >> pond > >> >> center at full speed, i,e, to 1/4 of a radius from the center in \ the > >> >> direction opposite to the agent but on the same diameter. > >> >> > >> >> The rabbit is now 3/4 of a radius from the nearest point on the > >> >> circumference and the agent must travel pi times that radius along \ the > >> >> edge of the pond to get to that same point. > >> > > >> > > >> > while the agent is moving. So I suppose the rabbit rotates with the > >> > moving > >> > agent...from a postion on the far side of the radius point...while > >> > spiraling outward. It's intricate... > >> > > >> > >> Well...the rabbit must spiral out from the radius point as he works to \ > >> get > >> on the same radial rotation with the agent but also position on the > >> opposite > >> side of the radius point. If the rabbit is rotating too fast then he > >> would > >> just keep working outward until the rotation is correct. But if the > >> rotation > >> is correct but the positon is wrong then the rabbit would have to \ zig-zag > >> to > >> work into position. > > > > > > Unless the agent is continually switching directions, the rabbit never > > need zig nor zag until it is ready to run for the edge. > > > > > Well the speeds are fixed and the rabbit needs a particular postion on its \ > circle...as it hunts for that circle which rotates with the agent \ movement. Since the rabbit only needs to keep rack of that diameter of the pond passing through the Agent, and the pond itself does not rotate, I have no idea what rotating circle you are talking about. > > > > >> When in correct position on the opposite side of the > >> radius point and on the same radial rotation with the agent...then \ break > >> for > >> the opposite shore. But break for shore hoping that it will work \ because > >> the > >> rabbit is not calculating... > > > > > If the speeds are correct the rabbit has .75 radii to cover but the > > agent has pi radii ( half a circumference) to cover, and the ratio of > > those distances is less that the ratio of speeds, 1 to 4 ( or about > > 0.2387 ) so the rabbit has a bit of a cushion. > > > > Relative distance ratio of .75/pi is roughly 5/21 to the relative \ speeds > > 5/20, so the rabbit has a bit of a cushion. > > > The rabbit...and it's really a duck...can't calculate anything. The rabbit \ > does not know how far to be on the other side of the radius. The rabbit \ only > knows if it is rotating with a radial to the agent and if it is on the \ other > side of the radius...but when so then break for it. Whether a rabbit or a duck, the issue is not whether it knows how to escape but whether it can escape under the given conditions. And my analysis shows that it can. But if it were a wise duck it could merely float at the center of the pond forever, whereas a rabbit would have to keep swimming to keep its head above water. === Subject: Re: NY Times math problem \ posting-account=O9zR9AkAAACmp918j6u5m5plppeILcze Filter 1.2.0.72; GTB6; .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; \ .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > > > > > > > > > I made a small spreadsheet to use your rabbit's strategy. Correct me > > > if I am wrong, but isn't it true that after the agent has gone about > > > 295 degrees around the pond, he is approximately on the radius > > > containing the rabbit? If, at that point, he keeps running at full > > > speed, as in your program, he will be running away from the rabbit. > > > This is hardly an optimal strategy for the agent. In fact, once the > > > agent gets on the rabbit's radius, he should stop. The rabbit will > > > swim back through the center and the cycle will repeat. By your > > > strategy, the rabbit never will reach the shore even at a speed ratio > > > of only 4, assuming that the agent uses his best strategy. > > > > > It's a systematic method only... > > > > But we now know what happens if the rabbit takes one straight line to > > > shore and we know what happens if the agent only loops around the \ circle > > > in one direction...with the rabbit correcting direction with each \ movement > > > of the agent. In one case the rabbit has the wrong strategy and in \ the > > > other case the agent has the wrong strategy. > > > > Really I was interested in the rabbit path plot with the agent \ looping > > > around the circle in one direction...and with the rabbit correcting > > > direction with each movement of the agent. > > > So the rabbit...and it should be a duck...is never caught if he keeps > > turning away from the agent with each movement of the agent. Then \ assuming a > > strategy of reversing direction by the agent...the rabbit can only get \ out > > by picking some point where he breaks for shore. But the agent can't be \ sure > > of where the rabbit curves are going to carry and the rabbit can't be \ sure > > of his break point. It's merely possible for the rabbit to get out... > > The rabbit can always move to the center of the pond. > > same diameter as the agent at least until the rabbit's angular velocity > about the pond center equals the agents angular velocity about the pond > center at full speed, i,e, to 1/4 of a radius from the center in the > direction opposite to the agent but on the same diameter. > > The rabbit is now 3/4 of a radius from the nearest point on the > circumference and the agent must travel pi times that radius along the > edge of the pond to get to that same point. This has been stated numerous times. Now, we're fighting down those who have suboptimal strategies for either the rabbit or the agent, especially when determining the answer to the second part of the puzzle, the fastest speed of the agent that still allows the rabbit to escape. Dave === Subject: Re: Alan Schwartz Jewish science in full-bloom >> On May 7, 11:18 am, plutonium.archime...@gmail.com, you titled your >> post as \Alan Schwartz Jewish science in full-bloom\: >> > A mind is a terrible thing to waste. I detect a longing in your tone Pothead... a regret at having wasted what little mind you had. === Subject: Re: Alan Schwartz Jewish science in full-bloom posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR \ 3.0.04506),gzip(gfe),gzip(gfe) > On May 7, 11:18Êam, plutonium.archime...@gmail.com, you \ titled your > post as \Alan Schwartz Jewish science in full-bloom\: > What is \Jewish science\? And who is Alan Schwartz in this connection > or does it matter? AP is referring to Alan Schwartz, who is the second poster in this thread. On Usenet Schwartz goes by the username \Uncle Al,\ but anyone can click on the second link in Uncle Al's sig and learn that Uncle Al's real name is Alan Schwartz. Uncle Al's political views are controversial, to say the least (which explains the warning \Toxic URL! Unsafe for children and most mammals\ in his sig). It appears that Uncle Al is a Jew by birth, but not by faith, since many of his posts espouse some form of atheism. Many of Uncle Al's posts have negative views of blacks, Latinos, and Muslims, possibly because these groups score lower on IQ tests than whites and Jews. On Usenet, Uncle Al's posts often resemble those of standard set theorists and analysts. Most of his posts on sci.math belittle AP and JSH, and on sci.physics he also argues against those who are considered \cranks,\ as well as those who espouse some form of theism. Further discussion of Uncle Al's political views are probably off-topic for sci.math, but if MoeBlee is going to point out AP's anti-Semitism, then let me point out Uncle Al's possible prejudice against blacks, Latinos, and theists. On the other hand, I don't consider Uncle Al's extreme views on race or religion to be representative of the standard theorists (fortunately for the standard theorists). Even though AP and Uncle Al have views similar to those on their own side of the \crank\ debate (many opponents of Cantor are anti-Semitic since Cantor was a Jew, while both Uncle Al and Virgil argue against theists), I will only judge both sides' posts based on math , not the poster's opinion of Jews or Muslims. And so I'll continue to consider whether AP's theory can be rigorous, while regarding Uncle Alan Schwartz as a standard theorist \bully.\ === Subject: Re: Alan Schwartz Jewish science in full-bloom sha1:+EwapXhX8/zmref/K3yiOnXgzd0= > Further discussion of Uncle Al's political views are probably > off-topic for sci.math, but if MoeBlee is going to point out > AP's anti-Semitism, then let me point out Uncle Al's possible > prejudice against blacks, Latinos, and theists. Okay! So there are two assholes, not one! That's much better. In any case, I have known for quite some time that Uncle Al is an asshole. I bet that Moe has noticed this fact too. But I must say that AP's anti-Semitism is something new for me. And pointing out his anti-Semitism is not a defense of Uncle Al. -- \The Hammer is not force. It is absolute power. The Hammer is from Idea \ Space. That's the real world. Here is the magical realm. You are creatures in that realm, who do not quite understand. But it doesn't matter. There is a story to be told...\ James S. Harris, \ poet. === Subject: Re: Alan Schwartz Jewish science in full-bloom posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > > On May 7, 11:18 am, plutonium.archime...@gmail.com, you titled your > > post as \Alan Schwartz Jewish science in full-bloom\: > > > What is \Jewish science\? And who is Alan Schwartz in this connection > > or does it matter? > oh, stop your laughing I'm not laughing. Believe me, I'm not laughing. Since you won't give me a plain answer, I'm taking it that not only are spewing crackpot mathematics, but also you're posting anti-Semitic garbage. MoeBlee === Subject: Re: Jewish community last hope for their lost son Alan Schwartz sha1:XSYqRgNF4ZSU58SOoHsjgniXdXo= > Jack Markan, try helping Alan Schwartz from making himself and the > Jewish community from looking so bad-- as a stalking hatemongering > bully on Usenet. > > The Jewish community is the last hope of reeling in this ugly bully. And, I suppose, the Periodic Table is the last hope of talking sense to Archimedes Plutonium? -- Jesse F. Hughes \Well, I'm a pragmatist. I've been wrong MANY TIMES and it seems to me that it would be simpler to be wrong with this paper.\ --James S. Harris explains his latest paper === Subject: Re: Ooops... An Inertial Motion Detector posting-account=XbpThQoAAACtPo22j_KAb5B7K8_euNJy Gecko/20081217 Firefox/2.0.0.20,gzip(gfe),gzip(gfe) > > > > > > > > > > > > > > > [...] > > > > > > > > > Lavatrice''inwww.bbamateur.blogspot.com.. \.8f in grado di \ risolvere alcuni > > > > > > > > Problemi .. e poi si pu\.98 parlare ... > > > > > > > >http://www.bbamateur.blogspot.com/ > > > > > > > > N\.8e orologi, n\.8e le ciliegie sono molto dolci nel loro > > > > > > > forma naturale. Di conseguenza, alcuni specifici di selezione \ per > > > > > > > scopo \.8f di uso comune. > > > > > > > >http://en.wikipedia.org/wiki/Cherry picking > > > > > > > > E 'anche utile per sapere quali sono i criteri di selezione. > > > > > > > >http://farside.ph.utexas.edu/teaching/em/lectures/node108.html > > > > > > > > Sue ... > > > > > > > story of cherries .... i read also the other things , but the \ cherries > > > > > > pickup by me , are intouched ... inside a rocket started at \ 200.000 > > > > > > km.s.from your garden , do you think possible send a bullet in \ the > > > > > > same direction at 200.000 km.s.? > > > > > > Of course it is. > > > > > > are p + p, d + Au, Cu + Cu and Au + Au. The projectiles > > > > > typically travel at a speed of 99.995% of the speed of > > > > > light in vacuum. For Au + Au collision, the center-of-mass > > > > > energy \\sqrt{s {NN}} is typically 200 GeV (or 100 GeV per \ nucleus); >> > > http://en.wikipedia.org/wiki/Relativistic Heavy Ion Collider > > > > > > > > > > > smiles and frish cherries.. > > > > > > :-) > > > > > > Sue... > > > > > ...and from the window of rocket ,somebody could see inside 1)a > > > > bullet going at 400.000 km.s. or 2)a bullet with very high > > > > energy ? ..you can choose and confront with the consequences \ ...note > > > > that my dog , inside the rocket , think rightly to be in \ aninertial > > > > frame ( sistem ).. > > > > What people see is not the result of Newton's > > > of the gravito-inertialfield so it bears little > > > consideration. > > > > A very massive bullet, passing would be necessary > > > to get your dog scratching his head about anomalous > > > results. > > http://www.bestweekever.tv/bwe/images/2007/12/9%20dog%20professor.JPG > > > > > > << Einstein's relativity principle states that: > > > > Allinertialframes are totally equivalent > > > for the performance of all physical experiments.>> > > http://farside.ph.utexas.edu/teaching/em/lectures/node108.html > > > > > > Sue... > > > itself too much ..one easier example(another!) : i convinced my dog to > > start with a rocket at 200.000km.s. and i too start with same speed in > > opposite direction ...: after 10 sec. , which distance it is between > > me and my dog ? > > For modern time dependent Maxwell's equations and > no Cherenkov radiation: > > 200.000km/s x 10sec x 2paths = 4.000.000km > > http://whyslopes.com/etc/fractions/fractions18a constant speed and ve... > > http://espg.sr.unh.edu/ism/what1.htmlhttp://en.wikipedia.org/wiki/Free \ space > > :-) > > To assume Newton's light-corpuscle moving under the > influence of inertia, some problems are attendant > that can be approximately resolved with some > smearing and curve-fitting: > > << Can we construct a new transformation which makes > the velocity of light invariant between differentinertialframes, in \ accordance with the relativity > principle, but reduces to the Galilean transformation > at low velocities, in accordance with our everyday > experience? \ >>http://farside.ph.utexas.edu/teaching/em/lectures/node110.html > > You should note that *light* in that page assumes > equations used. > > < or with modern terminology, photons, were > explicitly mentioned in the reports on which > the prize decision rested only in connection > with emission and absorption processes. The > Committee says that the most important application > of Einstein's photoelectric law and also its most > convincing confirmation has come from the use > Bohr made of it in his theory of atoms, which > > Sue... ...so i am departing from my dog at 400.000 km.s . . . . ( perheps you can say that in some different way ..) Suddenly i remember that my dog started without foods and immediately i shoot a flesh' torpedo in direction of my dog at 500.000km.s.....: i am sure that my dog shall not die famished ! ( Einstein permitting ?) and Sue ... permitting ? === Subject: Re: Levy proof that R is uncountable. > > > > > > > > > > > Several other \cranks\ has proposed new illfounded > > > > > definitions of the natural numbers, such as: > > > > > > > 1 = {1} > > > > > 2 = {1,2} > > > > > 3 = {1,2,3} > > > > > etc. > > > > > > Those aren't DEFINITIONS! > > > > > > What the blazes is wrong with you that you can't recognize > > > > circularity?! > > > > > FWIW, the above would constitute definitions in ZFA (though it \ happens > > > that they all define the same set). > > > > Are you sure you don't mean that they are THEOREMS of ZFA. That they > > are theorems of some theory is not problematic. But they can't be > > DEFINITIONS (at least not definitions in the sense of providing for > > the eliminability of the defined term), since they are circular. > > equations like the above (for some precise definition of \like the > above\) has a unique solution. So people working in ZFA do define sets > by writing down such systems of equations. That is the Anti-Foundation Axiom. A flat system of equations has a defintition, which I will not write here. This is flat system of equations: x = {x,y} y = {p,q,y,z} z = {p,x,y} AFA states that each flat system of equations has a unique solution. -- Michael Press === Subject: Re: Levy proof that R is uncountable. > > > Those equations serve as definitions in the following sense: there is > > a unique solution for this family of equations. > > > > In ZFA, it is common to say that an equation like > > > > Ê x = {17,x} > > > > is a *definition* for a particular set, since there is provably only > > one solution for that equation. > > Question: How are you using 'x'? As an actual variable? If so, what > symbol is being defined? 'x' is not being defined, since it is a > variable. > > On the other hand, along the lines you've drawn, I see no problem with > this as a definition [where 't' is a 0-place function symbol]: > > That's fine, since this definition can be cast as: > > t = the_unique x such that x = {17 x} > > which is a perfectly acceptable definition. Conceptually is not much different from the following situation. Pick numbers from a uniform distribution on [0, 1) until the sum of the numbers exceeds t. Let E(t) denote the expected count necessary to exceed t. Then E(t) = int_t^1 dx + int_0^t (1 + E(t - x)) dx = 1 + int_0^t E(u) du. The fascinating thing is that AFA does not lead to immediate contradictions. -- Michael Press === Subject: Re: Levy proof that R is uncountable. <27p8v4tivdguvifhf5fk4hsf1p0oqnl87a@4ax.com> \ <49f46eb5$0$293$7a628cd7@news.club-internet.fr> \ posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > > 1 = {1} > > 2 = {1,2} > > 3 = {1,2,3} > > etc. > > Those aren't DEFINITIONS! > > What the blazes is wrong with you that you can't recognize > circularity?! I'm retracting that comment. In view of my discussion with Jesse and Rotwang, it seems that lwal is using a presentation that informally appears circular but that can be justified by a formal version that is not circular. MoeBlee === Subject: Re: Levy proof that R is uncountable. posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > > > > > It's a theorem of ZFA that every system of > > > equations like the above (for some precise definition of \like the > > > above\) has a unique solution. > > > As I mentioned in my post just now to Jesse, I understand what it > > means for an equation with free variable 'x' (or even a set of > > equations) to have a unique solution and then to define 't' as 'the > > unique x such that [fill in set of equations here]'. > > > But I don't understand how that would apply to the equations you > > mentioned, since they have no free variables: > > > 1 = {1} > > 2 = {1,2} > > 3 = {1,2,3} > > You could define 1, 2, 3 etc. by writing down the system of equations > > x = {x} > y = {x,y} > z = {x,y,z}, > > denoting the solution by s, and then letting > > 1 = s(x) > 2 = s(y) > 3 = s(z). That is essentially the proposal I also made this morning. It seems to me that Jesse, you, and I are together now. > However, assuming that you have some familiarity with how flat systems > of equations work in ZFA, you lose nothing but wear and tear on your > fingers by simply writing > > 1 = {1} > 2 = {1,2} > 3 = {1,2,3} > > in the first place. You may think that this is sloppy, but consider > that mathematicians routinely write equally sloppy things e.g. when > defining functions recursively - for example, one will often write > something like \let f: N -> N be given by > > f(0) = 0 > f(n + 1) = f(n) + n\ > > rather than \by the recursion theorem, there is a unique function F: N > -> N such that > > F(0) = 0 > F(n + 1) = F(n) + n. > > Let f = F\. EXACTLY. I'm in perfect agreement. I don't consider it sloppy; but rather just routine working informality. And I had myself suggested the analogy with recursive functions. But one point: Notice that in the recursion example, the result is, in its FORMAL version, a THEOREM and not an actual FORMAL definition. And that is what I meant previously about such cases as \1={1}\. The actual formal definition is not circular, but we get a result \1= {1}\, and THEN we allow ourselves to the informality of taking \1={1}\ as if it's a definition even though the actual formal definition that justifies the equation \1={1}\ is not circular. > A quote from /Vicious Circles/: > > \When defining functions by recursion, once one understands the basic > process, one rarely if ever goes back and explicitly puts a recursive > definition in the form required by some particular theorem justifying > definitions by recursion. So too with definitions by corecursion. Once > we understand the basic process, it is seldom necessary to resort to > the Corecursion Theorem for justification\. Yes, and that is exactly the point I made myself earlier when I mentioned recursively defined function. > > Now it is not clear to me whether the above is meant to imply that > > circular definitions in non-wellfounded set theory are to be > > \straightened out\ just as in standard set theory or whether actual > > circular definitions are somehow allowed for. > > Definitions like the example above may be straightened out by > referring to the flat system of equations whose solution (and the > uniqueness thereof) guarantees the existence of something satisfying > the definition. Yep, exactly. > But this is such a trivial application of the Solution > Lemma that there's really no need to do so. Sure, no need to do so for working purposes. But that is acceptable only because we know that the circular appearing informal version does have a non-circular formal justification, even though, for working purposes, we don't have to mention that each time. > \Define rb: A^{trees} -> A^{oo} by > > rb(t) = <1^{st}(t),rb(3^{rd}(t))>\ > > As it happens, the existence and uniqueness of such an rb is a > consequence of a very non-trivial theorem, unlike the existence and > uniqueness of the set 1 = {1} in ZFA. But the authors nonetheless > define things in this way without comment. I have no argument against any of that, since, again, it's in perfect accord with what I've been saying all along. MoeBlee === Subject: Re: Looking for info on very symmetric 4x4 matrix; the 69 matrix > I'm trying to solve a simple set of homogeneous linear equations, and > the problem I run into is that the resulting matrix is singular. But > the matrix has such an odd symmetry that I'm sure someone knows > something about this. The specific matrix is as follows. > > 1 0 1 0 > 0 1 0 1 > 1 0 0 1 > 0 1 1 0 > > Is there really no solution? Any pointers as to how I can solve this > would be greatly appreciated. > This particular matrix has so to say the symmetry of complementarity: columns 1 and 2 fit together like pegs and holes; so do columns 3 and 4. Said more formally, add columns 1 and 2 to obtain (1, 1, 1, 1)^T and add \ columns 3 and 4 to obtain the same sum. Its determinant is not changed by replacing columns 1 and 4 by the sums of \ columns 1 and 2 and of columns 3 and 4, respectively (a general property of matrices and \ determinants). Columns 1 and 4 are now equal, from which it follows that the matrix is \ singular. Previous repliers to your post already gave solutions to the set of \ equations. This kind of symmetry has AFAIK no generally accepted name. But the columns 3 and 4 remind me of a very common and frequent and very \ well-known activity of humankind. You do know the expression \sixty-nine\? Look at the binary representations below of the numbers 6 and 9: 0 1 or =O <= 1 0 or => O= 1 0 or => O= 0 1 or =O <= Very complementary and satisfying indeed! I do not yet have real-life \ pictures of this. The outcome is unsure, so there is no determinant. Have a greeat and happy night again - cheers: Johan E. Mebius === Subject: Re: Why absurd theories are formed by Physics posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > Our Theories are based on Maths. > > And Maths is based on simple principles of addition/ subtractions. > > Say we talk about Integration it assumes the curve is smooth. But in > reality the world is not smooth. Everything is made of Proton/ Nutron/ > Electron etc. So when we create theories using Integration/ > Differentiation we apply Maths which assume world is continious. But > world is made of moving electrons & protonsd not a smooth material. > > But reality is that world is discrite with mountains. And not smooth. > That is why all theories fail when applied universally. > > We use Theories to predict Volcanic Eruption. But why we fail because > the Maths we use is incorrect. > > Theory of Relativity uses Integration/ Differentiation which assumes a > smooth world. But reality is not like that. > > Further Maths has no definition for what is 5/0 and 3/0 When in your > calculator we get 5/0 it shows \E\ meaning error. > > But when in nature 5/0 is to be done it cannot ourput \E\ So it > creates funny principles like Quantum Mechanics and Uncertainity > principles. Dual nature of Light and other absurd things. > > When the Maths understands what is 5/0 and 3/0 It will be able to > descrive these complex phenomena.of Universe. > > These days not much research is being done in Mathematics as Maths > does not pays as much as other sciences.. > > Bye > Sanny > > Enjoy & Chat:http://www.GetClub.com If the science isn't sufficiently Zionist Nazi approved, it doesn't hardly matter anyway. ~ BG === Subject: Re: Why absurd theories are formed by Physics posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > > > > > > > > > Êan atom. > > > > > > Enumerate the reasons. > > > > > > john- Hide quoted text - > > > > > > - Show quoted text - > > > > > When you try to use the inverse square law to calculate orbits, the > > > > model fails. I think that this model was either the Rutherford or \ the > > > > Bohr model of the atom. Bohr improved on Rutherford. But Newtonian > > > > mechanics does not work in these models. > > > > >http://en.wikipedia.org/wiki/History of quantum mechanics > > > > > I will tell you something radical, John, that Newtonian mechanics \ can > > > > probably be made to work if you bend space just the right way. And > > > > that is why I dont criticize your galaxy model. Please note however > > > > that I cannot put that down on paper and actually make the \ argument. > > > > I've got too much on my plate just devising the tools to make it > > > > possible to even make the argument. > > > > -------------------- > > > Newtons fist law of movement of mass > > > *must be expanded *!! > > > > there is an exception to it > > > it is the > > > Circlon Ê !! movement Êthat moves > > > naturally in a closed circle > > > or curved path!! > > > > it can explain very nicely > > > the 1/R^2 Êlaw as well Ê!!! > > > actually it can do it much better than any other theory !!! > > > > ATB > > > Y.Porat > > > ----------------------------- Hide quoted text - > > > > - Show quoted text - > > > Newtons fist law of movement of mass > > > *must be expanded *!! > > > I dont see why it shouldnt. > > > ( Newtonian Mechanics ) + ( a trivial component ) = ( Newtonian > > Mechanics ) > > > Makes perfect sense to me, and when you start talking about about > > Quantum scale physics then the (trivial component) becomes a more > > prominent feature. That is how I understand emergence, the only way I > > can imagine that order and disorder are emergent from each other. > > > If you use these methods, I would not be surprised one bit to find > > that the Rutherford Atom could be resurrected, and STILL make perfect > > sense with respect to the rest of QM. How does that grab ya ? Am I a > > quack now ? > > The Rutherford model had electrons going around > in circles, with > the circles being distributed in different planes. > Not surprisingly, it becomes way too complex. > > The Galaxy Model has the electrons in concentric coplanar rings > with up to 16 electrons sharing the same ring.The rings > are turning, so the electrons still travel in circles, > but the plane of the disc is precessing in lock-step with that > rotation, Êso all the electrons come back to where they > started every rotation but do not travel circles. > Rather they travel Great Circles. > > john > galaxy model for the atom Perhaps the three of you should get a room, and have yourselves a quicky before this topic turns real ugly. Why not run this interesting interpretation of yours through a public funded supercomputer? (there are lots of public owned supercomputers to pick from). ~ BG === Subject: Re: Why absurd theories are formed by Physics posting-account=5GUrzQkAAADun29oaK3p_W_saUVxxHUF Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > > > > > > > > > Êan atom. > > > > > > Enumerate the reasons. > > > > > > john- Hide quoted text - > > > > > > - Show quoted text - > > > > > When you try to use the inverse square law to calculate orbits, the > > > > model fails. I think that this model was either the Rutherford or \ the > > > > Bohr model of the atom. Bohr improved on Rutherford. But Newtonian > > > > mechanics does not work in these models. > > > > >http://en.wikipedia.org/wiki/History of quantum mechanics > > > > > I will tell you something radical, John, that Newtonian mechanics \ can > > > > probably be made to work if you bend space just the right way. And > > > > that is why I dont criticize your galaxy model. Please note however > > > > that I cannot put that down on paper and actually make the \ argument. > > > > I've got too much on my plate just devising the tools to make it > > > > possible to even make the argument. > > > > -------------------- > > > Newtons fist law of movement of mass > > > *must be expanded *!! > > > > there is an exception to it > > > it is the > > > Circlon Ê !! movement Êthat moves > > > naturally in a closed circle > > > or curved path!! > > > > it can explain very nicely > > > the 1/R^2 Êlaw as well Ê!!! > > > actually it can do it much better than any other theory !!! > > > > ATB > > > Y.Porat > > > ----------------------------- Hide quoted text - > > > > - Show quoted text - > > > Newtons fist law of movement of mass > > > *must be expanded *!! > > > I dont see why it shouldnt. > > > ( Newtonian Mechanics ) + ( a trivial component ) = ( Newtonian > > Mechanics ) > > > Makes perfect sense to me, and when you start talking about about > > Quantum scale physics then the (trivial component) becomes a more > > prominent feature. That is how I understand emergence, the only way I > > can imagine that order and disorder are emergent from each other. > > > If you use these methods, I would not be surprised one bit to find > > that the Rutherford Atom could be resurrected, and STILL make perfect > > sense with respect to the rest of QM. How does that grab ya ? Am I a > > quack now ? > > The Rutherford model had electrons going around > in circles, with > the circles being distributed in different planes. > Not surprisingly, it becomes way too complex. > > The Galaxy Model has the electrons in concentric coplanar rings > with up to 16 electrons sharing the same ring.The rings > are turning, so the electrons still travel in circles, > but the plane of the disc is precessing in lock-step with that > rotation, Êso all the electrons come back to where they > started every rotation but do not travel circles. > Rather they travel Great Circles. > > john > galaxy model for the atom ------------------ have you ever heared about the 'chain of orbitals idea ?? if not have a look at just at the beginning and if you like it is hidden all laong the modfel btw chemistry is full of that system of 'CHAIN OF ORBITALS' !! without calling it by that name ..... TIA Y.Porat ---------------------- === Subject: Re: Why absurd theories are formed by Physics posting-account=5GUrzQkAAADun29oaK3p_W_saUVxxHUF Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > > > > > > > Êan atom. > > > > > Enumerate the reasons. > > > > > john- Hide quoted text - > > > > > - Show quoted text - > > > > When you try to use the inverse square law to calculate orbits, the > > > model fails. I think that this model was either the Rutherford or the > > > Bohr model of the atom. Bohr improved on Rutherford. But Newtonian > > > mechanics does not work in these models. > > > >http://en.wikipedia.org/wiki/History of quantum mechanics > > > > I will tell you something radical, John, that Newtonian mechanics can > > > probably be made to work if you bend space just the right way. And > > > that is why I dont criticize your galaxy model. Please note however > > > that I cannot put that down on paper and actually make the argument. > > > I've got too much on my plate just devising the tools to make it > > > possible to even make the argument. > > > -------------------- > > Newtons fist law of movement of mass > > *must be expanded *!! > > > there is an exception to it > > it is the > > Circlon Ê !! movement Êthat moves > > naturally in a closed circle > > or curved path!! > > > it can explain very nicely > > the 1/R^2 Êlaw as well Ê!!! > > actually it can do it much better than any other theory !!! > > > ATB > > Y.Porat > > ----------------------------- Hide quoted text - > > > - Show quoted text - > > Newtons fist law of movement of mass > > *must be expanded *!! > > I dont see why it shouldnt. > > ( Newtonian Mechanics ) + ( a trivial component ) = ( Newtonian > Mechanics ) > > Makes perfect sense to me, and when you start talking about about > Quantum scale physics then the (trivial component) becomes a more > prominent feature. That is how I understand emergence, the only way I > can imagine that order and disorder are emergent from each other. > > If you use these methods, I would not be surprised one bit to find > that the Rutherford Atom could be resurrected, and STILL make perfect > sense with respect to the rest of QM. How does that grab ya ? Am I a > quack now ? ----------------- 1 the Newtonian mechanism doe snot work for cases of very hight speed Newton could not know at his time that it becomes more and more difficult to add velocity to very hight ones so SR is rigth (GR is nonsense one of the big skills in life is to be able to take each item and judge it for itself and not jump to conclusions by sweeping conclusions ie if Einstein was rigth about SR he will be right i anything other that he will suggest ) 2 imho the Newton first law of movement **has to be expanded** for as basic aprticle that **moves naturally in a curved path** see the 'Circlon' ATB Y.Porat -------------------- === Subject: Re: K-12 Calculator Woes >On 6 May 2009 15:02:53 -0400, hrubin@odds.stat.purdue.edu (Herman >>What mathematics do non-mathematicians need? They need >>to understand the mathematical concepts which will be >>used in their work, and for most this will need an >>understanding of the real numbers and limits. They >>need to be able to use \mathematical notation\ to >>translate their real-world problems into mathematical >>representations which then can be solved by mathematical >>methods. What they will not be able to do, except in >>very simple situations, is carry out the solution. >Herman, most non-mathematicians in non-technical fields do NOT use >these concepts at all. The use of technical fields is expanding, and even those in non-technical fields could make good use of the concepts to simplify their calculations. Furthermore, if they have not seen the concepts, and have even moderate difficulty with the manipulations, they may well not enter a technical field. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: K-12 Calculator Woes >> The representation of fractions is, for a machine, much >> harder than floats or decimals, and is more complicated >> to work with. >Why do you believe that is true? Fractions, unless their size is limited, will require at least two words, and their operations are more complex. Machines rarely do exact arithmetic, as would be required with fractions to give the answers desired. Avoiding computer roundoff would be expensive. I am reasonably familiar with computer architecture, and I can see no way around it. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: K-12 Calculator Woes posting-account=9tP_uwoAAAD1vfWhLdsNH4ImDfm7cP1K 4337.29; Windows NT 5.1; GTB6; .NET CLR 1.1.4322; .NET CLR \ 2.0.50727; InfoPath.1; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; .NET CLR \ 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) spider-mtc-ta01.proxy.aol.com[400C7001] (Prism/1.2.1), HTTP/1.1 cache-mtc-ae12.proxy.aol.com[400C7510] (Traffic-Server/6.1.5 \ [uScM]) > > >piece by Frank Quinn, \K-12 Calculator Woes,\ at: > >http://www.ams.org/notices/200905/rtx090500559p.pdf > > The real problem is that learning arithmetic from rules > is the same as learning reading without phonics. ?A > mathematician does not have to be adept at arithmetic; > how many are we losing this way? > > We CAN teach the structure and conceptS; yes, there is > more than one concept of the integers. ?The two major > ones are the cardinal and the ordinal, and the original > new math people seemed stuck on the cardinal, which looks > easy, but that is deceptive. ?The ordinal one can be > understood by children quite easily, and one can build > from it, including putting in the cardinal one. > > Children should not memorize addition and multiplication > tables, but should build them themselves. ?The teaching > of anything by memorization and routine hinders and even > may destroy understanding. > > There is no sour grapes in this; I probably use mental > arithmetic too much. ?Not only here but elsewhere I > have found concepts to be hard to get at given computation > or weaker concepts, but easy to understand once found, > and even easy to teach to those not prejudiced. > > -- > This address is for information only. ?I do not claim that these views > are those of the Statistics Department or of Purdue University. > Herman Rubin, Department of Statistics, Purdue University > hru...@stat.purdue.edu ? ? ? ? Phone: (765)494-6054 ? FAX: (765)494-0558 Herman; As I recall, Purdue has a selective enrollment. I teach at an open enrollment state university. In the past (say 10-15 years ago), incoming freshmen engineers knew a reasonable amount of arithmetic, algebra and trigonometry, so that we could at least get them to learn the rote calculations in calculus, and sometimes learn how to actually formulate and use the same ideas. Now, they stumble over simplifying 2 (3x), let alone 3(3^n) or sqrt(9). In terms of your idea of teaching the background, how would it be to teach english without any spelling or grammar, except that provided by Word (TM)? Do you realize how slow everyone would be? === Subject: Re: K-12 Calculator Woes >: >.com>, >> >piece by Frank Quinn, \K-12 Calculator Woes,\ at: >> >http://www.ams.org/notices/200905/rtx090500559p.pdf >Herman; >As I recall, Purdue has a selective enrollment. I teach at an open >enrollment state university. In the past (say 10-15 years ago), >incoming freshmen engineers knew a reasonable amount of arithmetic, >algebra and trigonometry, so that we could at least get them to learn >the rote calculations in calculus, and sometimes learn how to actually >formulate and use the same ideas. Now, they stumble over simplifying 2 >(3x), let alone 3(3^n) or sqrt(9). The Purdue enrollment is not that selective, and this is still likely to arise. Do you think the Indiana high schools teach any better than yours? One of my colleagues told me about a minority student having difficulties; nobody had ever indicated to him that HE could formulate word problems. >In terms of your idea of teaching the background, how would it be to >teach english without any spelling or grammar, except that provided by >Word (TM)? Do you realize how slow everyone would be? I do not know how badly it is done now, but the linguists' idea of teaching a foreign language is to do it orally, with minimal emphasis on the written language. American school children are not held to much spelling, and in some places, grammar is absent. I would teach the principles of the language, which definitely include the grammar, or enough of it to logically develop the rest, and similarly for spelling, although here there are lots of exceptions. I would not do it word by word, as is commonly done. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: K-12 Calculator Woes > >> They unanimously put forward the existence of >> calculators to do the calculations, and calculators use decimals > > There are calculators that *do* other fractions. When I was teaching > the lower math classes in high school, these were often used so the > kids never had to do any fractions at all aside from entering them > into calculators. > > http://wize.com/calculators/t61953-fractions > > When I taught these were too expensive. We had to standardize models --- imagine having to support 5 different types! It was a poor community and the school had to supply many devices for the poorest,and keep prices down for the rest. Besides, manipulating rationals on a calculator only requires pushing a couple more buttons. Larry === Subject: Re: K-12 Calculator Woes >>> They unanimously put forward the existence of >>> calculators to do the calculations, and calculators use decimals >> There are calculators that *do* other fractions. When I was teaching >> the lower math classes in high school, these were often used so the >> kids never had to do any fractions at all aside from entering them >> into calculators. >> http://wize.com/calculators/t61953-fractions >When I taught these were too expensive. We had to standardize models --- >imagine having to support 5 different types! I know of several $5 calculators which have fractions. >It was a poor community and the school had to supply many devices for >the poorest,and keep prices down for the rest. >Besides, manipulating rationals on a calculator only requires pushing a >couple more buttons. >Larry -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: K-12 Calculator Woes > > ................ > >>>>>>>>>>> Knowing how to do arithmetic is useful, but not >>>>>>>>>>> essential. Understanding the numbers, and I do not >>>>>>>>>>> mean strings of numerals, is essential, and most of >>>>>>>>>>> our high school teachers of mathematics do not have >>>>>>>>>>> any of that. > > >>>>>>>>>> Using calculators removes students from the numbers, hindering >>>>>>>>>> understanding. > >>>>>>>>> No, it does some removing students from operators >>>>>>>>> with sequences of numerals. The understanding does >>>>>>>>> not at all come from familiarity with arithmetic, >>>>>>>>> but in understanding numbers as such. > > >>>>>>>> And calculators remove the need to understand numbers, replacing \ that >>>>>>>> understanding with an understanding of programming calculators. > >>>>>>> Understanding numbers is NOT understanding strings of >>>>>>> decimal digits. There are two main concepts for the >>>>>>> integers, and neither of them has anything to do with >>>>>>> the decimal representation. > >>>>>>> The decimal representation is only ONE way of representing >>>>>>> numbers; it is sometimes not even useful. > >>>>>> For 99% of he population it is the only way of representing and >>>>>> manipulating numbers. Even rational fractions disappear from their >>>>>> lexicon for most, unless they user a tool like a tape measure. Heck, \ >>>>>> even fractions have virtually disappeared from he stock market. > > There are other means as well. Those in the sciences, and > in many other fields as well, misuse mathematics because > they have learned procedures which require assumptions to > be met to be valid. > You continue to miss the point. Yes, there are other methods, like base 16 for carpentry using caricatures of tools instead of letters and numerals because studs are 16 inches on center. But for those out there in the real world other methods do not exist, either because they are unaware of them, because their technology cannot handle them, or they just plain flat out refuse to acknowledge their existence. Why us a base 16 measuring system when the base 10 is perceived to be better, the technology is designed around that system and they already know it? Does any other system work better. Absolutely no!. Talk a bout wasting time and effort! >>> They have NOT. The string 6.43 means 6 plus 43/100. If they >>> do not understand the decimal fractions are fractions, they do >>> not understand decimal fractions. > > >> I said the rational representation of fractions. > > I agree that not enough is done with this, and that > computers have a lot to do with the problem. It is > easy to get computers to run in base 2 arithmetic, > including for \real\ numbers, and even the important > fixed-point arithmetic is difficult on them. The > representation of fractions is, for a machine, much > harder than floats or decimals, and is more complicated > to work with. > > However, the teaching of fractions leaves even more > to be desired. In can be made both rigorous and > more simple. Of course, anything is simpler if one > has \algebraic notation\, by which I mean that a > variable is a symbolic expression which can stand > for anything. So we have, for h not 0, > > a/b = ah/bh, > > and if the idea of fractions is presented with a > modicum of intelligence, it is obvious that > > a/b + c/b = (a+c)/b. > I don;t know about your school district, but that is part of my districts middle school curriculum. You suggest that 6 yr olds can handle this. I disagree, and most other s do, too, because most 6 yr old have not reached the mental stage to understand representation. They are still in a concrete world. I also agree with you that too many early ed teachers lack the math understanding to teach this. But that is slowly changing as a ndew crop of teachers enters the schools. I, for ex, was he first math certified teacher in my middle school, the others were gen ed. 4 years later all 4 8th grade math teachers are math certified (i'm gone). >> Because of calculators people do not use that form, and they cannot >> manipulate them, and often cannot understand them. > > My concern is that they understand them, and hence > can properly use them. > My experience is they have no idea how hey work, they are magic black boxes. Even worse, they have no interest in understanding how they work, even to the point that they refuse to even try. Starting in the 4th grade. Why bother to understand how a tv works? Push certain buttons and good things happen. Or a pc, microwave, elevator, or cell pone. Most don;t care until they break, then they go to an expert to fix it, or even worse, throw the broken one away and get a new one. >>>>> That 99% thinks that the decimal representations ARE the >>>>> numbers, and have no ideas of the properties of numbers. > > >>>> They have no need to know more. > > They certainly do; that is the problem. Once they > get that attitude, it becomes very difficult to > teach them the concepts. > That attitude develops i elementary school usually through parental adn peer input. And for most of wht they do, it is enough. I agree, more is needed, at the very least a grounding in logic that induction can give. When when technology can do it , why bother? >>> If they think a representa tion is the thing represented, at >>> best they are confused. It is like the following non-paradox: > >>> One cat has one more tail than no cat. >>> No cat has eight tails. >>> Therefore, one cat has nine tails. > >>> How can you be so confident? We are turning out far too >>> many people who do not understand what they are doing, using >>> routine procedures which have assumptions which are not stated >>> and which are usually not correct. > > >> You totally misunderstand me. > >> I am not confident, I am appalled. > > As am I. > >> But I think your position is far too much of a swing of the pendulum > > Concepts and even proofs are easy if properly done. I'd love to see this. I never have. I have had claases taught by or attended by geniuses who get it. But I and others, including some of my professors, had to work hard to get many concepts. For most many concepts are beyond their early understanding. New math, for ex., code for set theory, make s little sense in the early years as concepts of members, union, intersection, subsets, complement,and such are taught. Bt those concepts, as you well know, are critical for an understanding of continuity, I doubt 9th grade algebra class could grasp continuity even in a semi-formal manner, but hey cn grasp \new math\. But, as seen in this forum, society hates new math,and they, who pay the bills, are trying to get rid of it. They do this in part because they see no use for it. Absolute value is a fairly easy concept to grasp, but until ut is expanded to a neighborhood and used to prove a set is closed, etc., it has little real world connection Systems of linear equations mean little at the 2x2 or 3x3 level taught in schools. But when you get to optimization and solve a system of 22 equations in 31 variables (and yes, at first we did the simplex tables by hand) , you can relate to the concept. > I have seen another with the same idea of an introductory > approach to the integers, namely, use a notation which > is clumsy for computation, but excellent for understanding, > which is 0 followed by a string of tick marks. With this, > one can introduce from the Peano Postulates addition as a > moving of tick marks, etc. The associative law of addition > is a simple example of the use of the axioms. Also, one > can introduce the cardinal concept as moving the whole > bunch of tick marks at the same time. And the same thing can be, and is taught with arabic numerals. The reflexive, symmetric, and transitive properties are taught at early levels. All the texts I've seen also use alternative symbols like fruit, geometric shapes, and animals to reinforce the concepts. > >> I have repeatedly stated that math skills for students need to be >> improved, and that the very first step in that improvement is the >> removal of calculators from the classroom. > > I agree that the skills are USEFUL, and should not be > discouraged. I practice my computational skills. > >> Calculators, and computers, have changed attitudes int he public away >>from the need to understand basic mathematical concepts, and the >> rational representation of fractions is a perfect example. > > Some calculators have rational capabilities, somewhat limited. > If we insist on more, it can be provided. Some of the present > ones will attempt to figure out which fraction corresponds > to a decimal representation of a number. > Most don't, and few care to ask for more, let alone pay for it. As I noted, outside of a few areas rational representation no longer exists. >> When teaching I was repeatedly confronted by angry parents whose >> children could not manipulate what I will call fractions (as opposed to \ >> decimal fractions). They unanimously put forward the existence of >> calculators to do the calculations, and calculators use decimals. Wall >> Street now uses decimals. Banks no longer give 5 1/4%, but 5.25% > > I have seen Federal Reserve rates given in quarters. But > with the requirement of an APR, and with rates being > compounded at least monthly, if not daily, one almost > has to use rounded decimals. > One of the benefits of technology. Or is it just the fact that because it can be done it is done? 5% compounded daily is danged close to 5 1/4% compounded quarterly --- about 0.2% of principal. >> Outside of a few trades like construction, where the English measuring >> system still rules, fractions are disappearing from our society. > > We still use ounces and inches. There is also the use > of minutes and seconds, which corresponds to the ancient > base 60 notation. But I have seen few cookbooks which > point out that 1/3 of an ounce (liquid) is two teaspoons. > But we rarely do calculations on them. >> And people do not understand the tragedy of this. As I have related int >> he past, I have seen errors made because of a reliance on rote button >> pushing caused by an undeserved faith in calculators. Adults do not >> realize that 20% = 2/10, so they cannot calculate tips. They think that >> a .300 wrench is huge, not being able to recognize it is 3/10. And on >> and on and on. > >> Too many parents already teach their kids that \math is hard\. And now \ >> htey put the calculator up as a method for making math easy. And if it >> cannot be done on a calculator then it is too hard. > > This view comes from the emphasis on memorization and > computation the \old-fashioned\ way. > No. This view comes from a history of not using math and parents that never took math classes in their schooling. 40% of the adults in my state did not graduate high school, and probably never took even an algebra I class. My mother dropped out (from anther state) at 14, which was routine. Only the 2 youngest of her 10 siblings graduated HS. It worked well for decades --- get out of school as early as 14, get a job in a textile mill or a factory, and earn enough to buy a house, 2 cars, and a big screen tv. They did not have to understand credit cards, income taxes, investments, etc. But the world changed, and they didn;t, so here we are. Larry > >> This goes beyond mere arithmetic. Graphing calculators are hurting >> students' understanding. It takes very little to graph a line, with >> understanding. > > I am not sure what you mean. It is easy with a ruler and > two points on the line, but I do not do a good job freehand. > > But still students push buttons, and have an undeserved >> faith in the calculator. > > This is correct, but will the average student be able to > do any better? Calculators are super-fast sub-imbeciles, > and will do exactly what they have been told, no matter > how stupid it is. > > The tiny screen limits what can be displayed, >> and important behavior beyond the display go unrevealed because students \ >> think that what was displayed was *the* answer because they do not have >> hte experience from manually graphing to know otherwise. > > How many points to graph? Also, while I do some manual > graphing, I prefer to put it on the computer, because I > do not do a good job. Understanding how is not adequate > without sufficient drawing skills. > > >> i see students in other subjects that lose understanding because of >> calculators. Finance majors do not understand the effects of changes in >> period on interest because all the do is push buttons. Chemistry >> students do not understand the gas laws because they program formulas >> into a calculator and push buttons based on which variables are provided \ >> in the question. > >> You put the rote calculations down, pushing instead for theory. > > We have seen what learning rote calculations does. We > have not seen, at the lower levels, what learning concepts, > not theory, can do, nor the advantages of learning theory. > Students who learned Euclid geometry do not seem to do any > worse than those learning geometry by calculation. > >> But most of us need the chance to explore and build relationships that >> doing those calculations provides. > > Does doing the calculations achieve this? Or is it knowing > what things mean, and trying them out? Algebraic notation, > which is trivial, is what is needed. > > Yes, in the first grade doing rote >> additon may sem barren, but it isn;t It develops skills, attitudes, and >> expectations critical for success in many, many subjects in the future. > > But producing the addition tables by using successor, > and the multiplication tables by addition, will do a > better job of this. > >>> One cannot know that one can use something unless one knows >>> of its existence and its basic concepts. > > >> Not true. > >> Many , many people, for example, use a pc without the slightest >> understanding of how it works. In the extreme, they know to click on >> this and their e-mail is displayed, and they are happy with this. > > They know the computer exists, and they know the concept > of email. > > >>> A scientist who understands the mathematical concepts needed >>> for his part of science can formulate his problems in such a >>> way that mathematicians not knowing his field of science can >>> come up with an answer, if it is known how to do so, or if one >>> can be deduced. Knowing a few procedures does not achieve >>> this result, and may achieve badly incorrect results. > > >> Often the math concepts exceed the ability of the scientist,a nd rightly \ so. > >> For example, a professor friend did her dissertation on a graphing >> technique that mapped amino acids in a large protein. The biologist >> who wanted the info had a theory, but the need for PhD level math was >> too much, so they formed a partnership. He provided the data, she >> manipulated it. > > The biologist knew the concepts and could translate them into > mathematical terminology, so the mathematician could use the > power of mathematics. Alas, these days the emphasis is on > combining the two, and the resulting biomathematician will not > have either the understanding or the ability. > >>>> And they do have ideas about the properties of number, they just don;t \ >>>> have the \official\ names. In fact, the way I have taught math \ teaches >>>> group and field theory, without using all of the formal names. > >>>> They know additive and multiplicative inverses, identities, closure. >>>> They no symmetry, distance, and maybe even isomorphisms. They just do;t \ >>>> know the vocabulary. > > >>>>> They also think that there is a great difference between >>>>> using \Arabic\ numerals and Roman numerals. There is no >>>>> such difference, except some need to memorize. > > >>>> The differences are significant. Roman numerals have no additive \ inverse >>>> or identity, no multiplicative inverse, no placeholder. > >>> These are numerals, not numbers. Arabic numerals have no >>> inverses, etc. It is the numbers which do, and their >>> inverses do not depend on the representation. The >>> have the traces of that in minutes and seconds. > > > >> There is no zero in Roman numerals, a significant difference. There are >> no negative roman numerals,nor fractions. > > Are there negative Arabic numerals? The use of negative numbers > was later. Zero as a digit was older, and used by the Sumerians > for their base 60 arithmetic more than 4000 years ago. > > The Egyptians had fractions, as did the Greeks and Romans. > The notation is not the concepts. > >> Roman numerals do not form a group. > >> They are not isomorphic with arabic numerals. > > It is only by using strings of Arabic numerals to > form representations of numbers, and the use of the > minus sign, that one can get the Arabic numerals to > form a group. The same could be done with the Roman > or Greek numerals, by adding bars for thousand times. > >>>>>> It should help >>>>>>> in understanding if students produce the addition and >>>>>>> multiplication tables to more than one base from first >>>>>>> ordinal principles, but memorizing them, no. > > >>>>>> Yes, memorization of base 7 is worthless, and for all but computer \ nerds >>>>>> any base except 10 is not needed. > >>> But is the memorization of the table needed? At most, it >>> is the ability to use the table. The Chisenbop method of >>> multiplication, which has been touted, only has products >>> by 1, 2, 5, and 10 learned; it uses the distributive law >>> for the rest. > > >> Yes, the memorizations is vital. People cannot carry around a paper copy \ >> if the table, so they carry a calculator. Then they rely on the >> calculator for this operation, and eventually all operations. > > There is too much emphasis on memorization. > >> Why do the work when the calculator can do it? And the knee-jerk jump to \ >> use the calculator eliminates the possibility of actually exploring the >> situation. > > One can explore the situation by putting other entries into > the calculator, or by programming the computer to investigate > far more situations than can be done by hand. > >> Again, yes \learning\ the tables is rote, drudge work, and maybe byt he \ >> time you turn 60 you can start relying on machines to do the work. > >> But good habits start young, and bad habits start younger. In my state >> calculators can be used as early as the 6th grade, and parents often let \ >> their kids use them for homework even earlier. > >> And people wonder why kids cannot understand that 6 - 3 is really 6 + >> (-)3 .The calculator uses the first expression., and that is all kids \ see. > > The Sumerians, Babylonians, Egyptians, Greeks, Romans, > and many more only used the first expression. They > did not know about negative numbers, and this applied > to the Arabs who took the Hindu numerals west. > > Do elementary school students learn the second? > > >>>>> No, it is needed to know that the base of the representation >>>>> is immaterial. Also, producing the tables from first principles >>>>> makes them meaningful, and not \something to remember\. It even >>>>> enables one to get by with forgetting some of it. > > >>>> Bases are no more than a teaching tool for exponents and modulus. The >>>> properties of the different bases are identical, and beyond showing \ they >>>> are the sam as the decimal system bases are a curiosity for most. >>>> Converting from decimal to base 8, for ex., is rote calculation at its \ >>>> worst. > >>>>>> That said, an understanding of bases and modulus can be useful, in >>>>>> particular as I noted in division. > >>>>> You are using modulus in a non-mathematical sense here. > > >>>> No > >>>>>>>>> It turns them into programmers, not mathematicians. > >>>>>>>>> What does knowing how to do arithmetic do? It turns >>>>>>>>> them into the equivalent of the machine doing the >>>>>>>>> result of the programming. > > >>>>>>>> But that requires an understanding of numbers, while the use of >>>>>>>> calculators does not. > >>>>>>> No amount of facility at arithmetic yields an understanding >>>>>>> of numbers. > >>>>>> I disagree, and we will have to agree to disagree. > >>>>>> I suspect you are approaching this from a far higher theoretical \ level >>>>>> than most people reach. > >>>>> I want first graders to reach this level, and I believe >>>>> most can do it with ease if the ordinal approach is the >>>>> first used. It is SIMPLE. But trying to teach it to >>>>> high school and college students is very difficult; they >>>>> \know\ the numbers, and are unwilling to learn the basics >>>>> which they do not know at all. > > >>>> Most first graders are incapable of doing what you want. Getting them \ to >>>> even learn the basics of the integers is a full time job. > > But the basics of the integers from the Peano Postulates and > the \base 1\ notation are easy. It is using base 10 from the > beginning which makes it harder. > >>> Do YOU know the basics of the integers? Knowing them does not >>> require being able to count above 3, although I may be somewhat >>> wrong on just how high. I am not even sure if Landau's book >>> even gets to 2, except for the numbering of statements, etc. > > >> Yes, I do. > >> You are oversimplifying and isolating the concepts. > > I am pointing out that the concepts are simple. > >>>> Teaching math to older students is difficult not because they think \ they >>>> know it all, but because by the time they reach that age society has >>>> taught them that math is irrelevant. > >>> How about teachers who are going to teach math? > >> I saw it in my classes to the point that students changed their majors, >> even elementary ed majors. They could not do the work even inthe math >> for middle school courses. > >> Getting >>> non-computational concepts to them is almost a lost cause; >>> many never get it. > >> Because they have never been exposed to them, usually because technology \ >> has taken the lead. > > >> And how about the 80% of prospective >>> high school teachers of math who could not set up a problem >>> using calculus, in a course which had the full calculus >>> prerequisite, on a take-home final? > >> I need more info on this. > > This was in a probability course. The problems were quite > similar to those done in class. > >> For ex., my college strongly suggested that prospective teachers take >> the certification exams early and often even before the preparation >> courses had been taught. > >> Certification standards are also changin; now most states require at >> least a BA in math to teach HS math, and no one can get that degree and >> not set up a calculus equation. > > Unfortunately, this is false. They can calculate derivatives > and anti-derivatives, but the rest is forgotten. > > > Heck, many states and national >> certification now even require formal proofs to teach HS math > > Do they require them to pass an examination? Having taken > courses which taught this is not sufficient. > >> The math professors >>> who taught them were not surprised; they are quite aware >>> that the bulk of calculus students can only memorize formulas >>> and their use. They are not even at the level of programmers; >>> they are at the level of the computer hardware. > > >> That is the fault of the professors, not the students. My professors >> would not pass a student wh could not explain what they were doing, and >> absolutely refused to allow the use of technology. > > If the professors did not do this, the enrollment in calculus > courses would drop drastically. Engineers and physicists do > not care, as far as their courses are concerned, whether there > is understanding, and would teach the students themselves. > > Using technology is another matter. How do you expect students > to get the square root of 1.37 on an exam? Technology was used > for such even BC (before computers); slide rules were used. And > slide rules were used for multiplying back then. > > >> Larry > === Subject: Re: K-12 Calculator Woes ................ >>>>>>>>>>>> Knowing how to do arithmetic is useful, but not >>>>>>>>>>>> essential. Understanding the numbers, and I do not >>>>>>>>>>>> mean strings of numerals, is essential, and most of >>>>>>>>>>>> our high school teachers of mathematics do not have >>>>>>>>>>>> any of that. >>>>>>>>>>> Using calculators removes students from the numbers, hindering >>>>>>>>>>> understanding. >>>>>>>>>> No, it does some removing students from operators >>>>>>>>>> with sequences of numerals. The understanding does >>>>>>>>>> not at all come from familiarity with arithmetic, >>>>>>>>>> but in understanding numbers as such. >>>>>>>>> And calculators remove the need to understand numbers, replacing \ that >>>>>>>>> understanding with an understanding of programming calculators. >>>>>>>> Understanding numbers is NOT understanding strings of >>>>>>>> decimal digits. There are two main concepts for the >>>>>>>> integers, and neither of them has anything to do with >>>>>>>> the decimal representation. >>>>>>>> The decimal representation is only ONE way of representing >>>>>>>> numbers; it is sometimes not even useful. >>>>>>> For 99% of he population it is the only way of representing and >>>>>>> manipulating numbers. Even rational fractions disappear from their >>>>>>> lexicon for most, unless they user a tool like a tape measure. Heck, \ >>>>>>> even fractions have virtually disappeared from he stock market. >> There are other means as well. Those in the sciences, and >> in many other fields as well, misuse mathematics because >> they have learned procedures which require assumptions to >> be met to be valid. >You continue to miss the point. >Yes, there are other methods, like base 16 for carpentry using >caricatures of tools instead of letters and numerals because studs are >16 inches on center. If one understands the numbers, integer, fractional, real, and if need be complex (try handling AC circuits without it), the representation becomes of little importance. Being able to make limited use of a particular representation does NOT convey understanding. No matter how well one does base 10 arithmetic, this conveys no more than having the mechanical processes in ones memory banks. There is not even understanding of the processes. >But for those out there in the real world other methods do not exist, >either because they are unaware of them, because their technology cannot >handle them, or they just plain flat out refuse to acknowledge their >existence. If they are unaware of them, how can they know if they can make use of them? If they refuse to acknowledge their existence, can they be said to be educated about the numbers? >Why us a base 16 measuring system when the base 10 is perceived to be >better, the technology is designed around that system and they already >know it? Computer technology is NOT designed about base 10, and will not be in the future. It is really base 2, but 16 is used as a convenient version so that expressions will not be too long. >Does any other system work better. Absolutely no!. Talk a bout wasting >time and effort! See the above. There are other places where these come in. >>>> They have NOT. The string 6.43 means 6 plus 43/100. If they >>>> do not understand the decimal fractions are fractions, they do >>>> not understand decimal fractions. >>> I said the rational representation of fractions. >> I agree that not enough is done with this, and that >> computers have a lot to do with the problem. It is >> easy to get computers to run in base 2 arithmetic, >> including for \real\ numbers, and even the important >> fixed-point arithmetic is difficult on them. The >> representation of fractions is, for a machine, much >> harder than floats or decimals, and is more complicated >> to work with. >> However, the teaching of fractions leaves even more >> to be desired. In can be made both rigorous and >> more simple. Of course, anything is simpler if one >> has \algebraic notation\, by which I mean that a >> variable is a symbolic expression which can stand >> for anything. So we have, for h not 0, >> a/b = ah/bh, >> and if the idea of fractions is presented with a >> modicum of intelligence, it is obvious that >> a/b + c/b = (a+c)/b. >I don;t know about your school district, but that is part of my >districts middle school curriculum. Do they use algebraic notation? Do they still ask students to use the least common denominator? >You suggest that 6 yr olds can handle this. I disagree, and most other s >do, too, because most 6 yr old have not reached the mental stage to >understand representation. They are still in a concrete world. I have never suggested that 6 year olds have the understanding of integers needed to start on fractions. I do not know how fast one can do the work, nor do I have any objection to them learning arithmetic operations to base 10 before doing much, or even starting, with fractions. Children are capable of understanding abstract ideas, NOT as abstractions. It is this confusion that too many are making; an abstract idea may have come about as the result of a process of abstraction, but it is more than that, and easier to understand if taught directly. >I also agree with you that too many early ed teachers lack the math >understanding to teach this. But that is slowly changing as a ndew crop >of teachers enters the schools. I, for ex, was he first math certified >teacher in my middle school, the others were gen ed. 4 years later all 4 >8th grade math teachers are math certified (i'm gone). >>> Because of calculators people do not use that form, and they cannot >>> manipulate them, and often cannot understand them. >> My concern is that they understand them, and hence >> can properly use them. >My experience is they have no idea how hey work, they are magic black >boxes. Even worse, they have no interest in understanding how they work, >even to the point that they refuse to even try. Starting in the 4th grade. Whether they know exactly how the black box works is not a problem; they need to know how the numbers work. Teach concepts, and these problems might well not even arise. >Why bother to understand how a tv works? Push certain buttons and good >things happen. Or a pc, microwave, elevator, or cell pone. >Most don;t care until they break, then they go to an expert to fix it, >or even worse, throw the broken one away and get a new one. This is not the problem. \They need to understand the concepts involved in viewing a TV. These are only optical. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: K-12 Calculator Woes \ \ posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009042708 Fedora/3.0.10-1.fc9 \ Firefox/3.0.10,gzip(gfe),gzip(gfe) > > > Ê Ê Ê Ê \ Ê Ê Ê Ê Ê \ Ê Ê Ê Ê \ Ê................ > > >>>>>>>>>>> Knowing how to do arithmetic is useful, but not > >>>>>>>>>>> essential. ÊUnderstanding the numbers, and I do \ not > >>>>>>>>>>> mean strings of numerals, is essential, and most of > >>>>>>>>>>> our high school teachers of mathematics do not have > >>>>>>>>>>> any of that. > > >>>>>>>>>> Using calculators removes students from the numbers, hindering > >>>>>>>>>> understanding. > > >>>>>>>>> No, it does some removing students from operators > >>>>>>>>> with sequences of numerals. ÊThe understanding \ does > >>>>>>>>> not at all come from familiarity with arithmetic, > >>>>>>>>> but in understanding numbers as such. > > >>>>>>>> And calculators remove the need to understand numbers, replacing \ that > >>>>>>>> understanding with an understanding of programming calculators. > > >>>>>>> Understanding numbers is NOT understanding strings of > >>>>>>> decimal digits. ÊThere are two main concepts for the > >>>>>>> integers, and neither of them has anything to do with > >>>>>>> the decimal representation. > > >>>>>>> The decimal representation is only ONE way of representing > >>>>>>> numbers; it is sometimes not even useful. Ê > > >>>>>> For 99% of he population it is the only way of representing and > >>>>>> manipulating numbers. Even rational fractions disappear from their > >>>>>> lexicon for most, unless they user a tool like a tape measure. \ Heck, > >>>>>> even fractions have virtually disappeared from he stock market. > > > There are other means as well. ÊThose in the sciences, and > > in many other fields as well, misuse mathematics because > > they have learned procedures which require assumptions to > > be met to be valid. Ê > > You continue to miss the point. I think the problem is you two are talking about two different points. IMO the purpose of a math class is not to teach maths but to teach a mode of knowing---of course, the only way available to do that is to teach some mathematics, so the teaching of maths in a good math class is unavoidable. But as soon as we lose sight of the fact that the real purpose is not to have students know facts about, say, numbers but to know them in a specific way, chaos (in various manifestations) follows. It is my conclusion after having participated in way too many discussions about math education (at the college level but, really, mutatis mutandi, the issues are exactly the same as in any other level) that essentially all disagreements are due to the opposing parties having a different opinion on this. Moreover, in the enormous majority of cases none of the parties recognize that the matter of contention is not material (*what* subjects to teach?, for example) but epistemiological---and this results in countless hours/emails of argumentation for and against the teaching of various subjects and other trivia, discussion which will never ever help in getting close to an agreement for it is a discussion on something rather irrelevant to the disagreement. This is entirely similar to the \debates\ between the right and the left when it turns to the minutiae of the management and implementation of policies, while leaving aside the ideological and programmatic side of things---side which, nowadays, has really bad press, for we are, as we all know, living in post-ideological times... -- m === Subject: Re: K-12 Calculator Woes .................... <> >>>>>>>>>>> Knowing how to do arithmetic is useful, but not <> >>>>>>>>>>> essential. =A0Understanding the numbers, and I do not <> >>>>>>>>>>> mean strings of numerals, is essential, and most of <> >>>>>>>>>>> our high school teachers of mathematics do not have <> >>>>>>>>>>> any of that. <> >>>>>>>>>> Using calculators removes students from the numbers, \ hindering <> >>>>>>>>>> understanding. <> >>>>>>>>> No, it does some removing students from operators <> >>>>>>>>> with sequences of numerals. =A0The understanding does <> >>>>>>>>> not at all come from familiarity with arithmetic, <> >>>>>>>>> but in understanding numbers as such. <> >>>>>>>> And calculators remove the need to understand numbers, \ replacing= > that <> >>>>>>>> understanding with an understanding of programming calculators. <> >>>>>>> Understanding numbers is NOT understanding strings of <> >>>>>>> decimal digits. =A0There are two main concepts for the <> >>>>>>> integers, and neither of them has anything to do with <> >>>>>>> the decimal representation. <> >>>>>>> The decimal representation is only ONE way of representing <> >>>>>>> numbers; it is sometimes not even useful. =A0 <> >>>>>> For 99% of he population it is the only way of representing and <> >>>>>> manipulating numbers. Even rational fractions disappear from \ their <> >>>>>> lexicon for most, unless they user a tool like a tape measure. \ Hec= >k, <> >>>>>> even fractions have virtually disappeared from he stock market. <> > There are other means as well. =A0Those in the sciences, and <> > in many other fields as well, misuse mathematics because <> > they have learned procedures which require assumptions to <> > be met to be valid. =A0 >> You continue to miss the point. >I think the problem is you two are talking about two >different points. >IMO the purpose of a math class is not to teach maths >but to teach a mode of knowing---of course, the only >way available to do that is to teach some mathematics, >so the teaching of maths in a good math class is unavoidable. Knowing WHAT? >But as soon as we lose sight of the fact that the real purpose >is not to have students know facts about, say, numbers but to >know them in a specific way, chaos (in various manifestations) >follows. It is NOT important to know facts, other than a few, but to UNDERSTAND. The present methods of teaching teach lots of facts, but little or even NO understanding. As of this time, the students coming out of a calculus class may know many facts and methods, but few of them will have an understanding of derivative or integral. Concepts are not taught by teaching the words, but by getting the student to internalize the ideas. >It is my conclusion after having participated in way too >many discussions about math education (at the college level >but, really, mutatis mutandi, the issues are exactly the same >as in any other level) that essentially all disagreements >are due to the opposing parties having a different opinion >on this. Moreover, in the enormous majority of cases none >of the parties recognize that the matter of contention is >not material (*what* subjects to teach?, for example) but >epistemiological---and this results in countless hours/emails >of argumentation for and against the teaching of various >subjects and other trivia, discussion which will never ever >help in getting close to an agreement for it is a discussion on >something rather irrelevant to the disagreement. No, you do not get it. I would require much of a good course on \real variables\ before calculus. Solving problems is not the goal, except for adepts; knowing the concepts well enough to set up the problem and communicate with the specialist is primary. Only then does one become a specialist. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: solve an integration equation > Hi .My problem is this. > > I have integral > > \\!\\( > \\*SubsuperscriptBox[\\(\\[Integral]\\), \\(a\\), \\(b\\)]\\( > SqrtBox[ > FractionBox[\\(1 + c\\ > \\*SuperscriptBox[\\(x\\), \\(2\\)]\\), \\(1 + d\\ > \\*SuperscriptBox[\\(x\\), \\(2\\)]\\)]] \\[DifferentialD]x\\)\\) = e > > I know a,b,d &e but need to find c > how can i find c .Please help me try finding exact integral of lhs part === Subject: Re: issues with GraphPlot Thought I replied to this, but it doesn't appear. So, here it goes again: GraphPlot[ {{\B\ -> \A\, \BA\}, {\A\ -> \B\, \AB\}, {\A\ -> \C\, \AC\}, {\C\ -> \A\, \CA\}, {\C\ -> \B\, \CB\}, {\B\ -> \ \C\, \BC\}}, DirectedEdges -> True, VertexLabeling -> True, VertexRenderingFunction -> ({White, EdgeForm[Black], Disk[#, .05], Black, Text[#2, #1]} &), EdgeLabeling -> True, EdgeRenderingFunction -> ( If[First[#1][[1]] - Last[#1][[1]] > 0, {Inset[Text[Style[#3, 16]], Mean[#1], Scaled[{0.5, 1.2}], Automatic, First[#1] - Last[#1]], Arrowheads[Medium], Arrow[#1, 0.07]}, {Inset[Text[Style[#3, 16]], Mean[#1], Scaled[{0.5, -0.2}], Automatic, Last[#1] - First[#1]], Arrowheads[Medium], Arrow[#1, 0.07]}] &), PlotStyle -> Thickness[0.005]] > On my version (7.0 for Microsoft Windows (32-bit) (February 18, > 2009)), the code proposed by Sjoerd produces an upside-down upper > label. This can be better seen with: > > GraphPlot[{{\B\ -> \A\, \BA\}, {\A\ -> \B\, \AB\}}, > DirectedEdges -> True, > VertexLabeling -> True, > VertexRenderingFunction -> ({White, EdgeForm[Black], Disk[#, .05], > Black, Text[#2, #1]} &), > EdgeLabeling -> True, > EdgeRenderingFunction -> ( > {Inset[ > Text[Style[#3, 18]], > Mean[#1], > Center, > Automatic, > First[#1] - Last[#1] > ], > Arrowheads[Large], > Arrow[#1, 0.07] > } &), > PlotStyle -> Thickness[0.005] > ] > > In this way, it is may be useful only with mirror-invariant labels, > like (+), (-), etc. > > I do not know how to adjust this. > > ADL > > On Apr 30, 12:19 pm, \Sjoerd C. de Vries\ > > > Hi Sean, > > > below is the complete code for the label. Read the Inset doc page for > > more details on the parameters I used. > > > > GraphPlot[{{\B\ -> \A\, \+\}, {\A\ -> \B\, \+\}}, > > DirectedEdges -> True, VertexLabeling -> True, > > VertexRenderingFunction -> ({White, EdgeForm[Black], Disk[#, .05], > > Black, Text[#2, #1]} &), EdgeLabeling -> True, > > EdgeRenderingFunction -> ({Inset[Text[Style[#3, 16]], Mean[#1], Top, > > Automatic, First[#1] - Last[#1]], Arrowheads[Medium], > > Arrow[#1, 0.07]} &), PlotStyle -> Thickness[0.005]] === Subject: Re: RegionPlot3d under sampling plot points? Hi Bob, but I reckon that should do it gramathon > > FullSimplify[Reduce[ > {2 x (y - 1) <= 5/2 z + 2 (y - 1) z, z <= x, x >= 1, y >= 2, > z >= 1}], > {z <= x, x >= 1, y >= 2, z >= 1}] > > x == z || (z < x < (9*z)/4 && (5*x)/(z - x) + 4*y + 1 <= 0) || (4*x == > 9*z && y == 2) > > Show[ > Plot3D[x, {x, 1, 864000}, {y, 2, 500}, > PlotStyle -> LightBlue], > RegionPlot3D[(z < x < (9*z)/4 && > (5*x)/(z - x) + 4*y + 1 <= 0), > {x, 1, 864000}, {y, 2, 500}, {z, 1, 864000}, > PlotStyle -> Lighter[Green]], > ParametricPlot3D[{x, 2, 4 x/9}, {x, 1, 864000}, > PlotStyle -> {AbsoluteThickness[3], Red}]] > > > Bob Hanlon > > > Hi All, > I am new to Mathematica, so apologies ahead of time if this is a silly > problem. I am trying to use RegionPlot3D to plot the following, > RegionPlot3D[ > 2 x(y - 1) <= 2.5 z+ 2 (y - 1) z&& z<= x, {x, 1, > 864000}, {y, 2, 500}, {z, 1, 864000}, PlotStyle -> Orange,PlotPoints- > >100] > > The problem is I end up getting gaps in regions where I expect none to > exist. > - I tried increasing the PlotPoints.Though that reduces the number of > gaps at first (partly removes the gaps for the higher values of NA and > NP but gaps remain, in the lower values of the two axises) after a > certain number of point >= PlotPoints -> 150the graph ends up looking > completely different with Spikes everywhere and still has gaps which > does not make sense....(I am not sure if this could be due to the > graphics card because the above code is relatively smoother on my less > powerful machine but still has gaps) > - I tried providing different plotpoints to different axises E.g. > PlotPoints-> {111,100,111}... but that did not seem to help either. > - I tried MaxRecursion as well but that does not seem to help in this > case either... > I am completely lost, and have been spending quite a bit of time > trying to search for an answer...WOULD REALLY APPRECIATE it if anyone > could Help > Version 7 of Mathematica > > > === Subject: Re: Solving the system with inexact coefficients Semenov's method, which is implemented in my demonstrations http://demonstrations.wolfram.com/SemenovsAlgorithmForSolvingSystemsOfNonlin\ earEquations/ and http://demonstrations.wolfram.com/SolvingSystemsOfTranscendentalEquations/ can find (with provable certainty) all the solutions of a system of n- equations in n-variables that line in an n-dimensional arbitrary rectangular box. It is only required that the functions defining these equations have continuous second derivatives - they need not be analytic. My implementation only deals with the case n=2 or the complex one dimensional case, but this restriction is only due to the need of graphical interpretation in a demonstration. The method is thus considerably more general that Mathematica's Root function. Like the Root function it can't definitely determine the presence of multiple roots. It is of course much slower than the built in Root function, but that's normal for user defined functions. Andrzej Kozlowski > A few people replied to a problem on how to find trancedental roots > of a > function in one dimension, and recommended my RootSearch package. > > However, based on > \ http://blog.wolfram.com/2008/12/18/mathematica-7-johannes-kepler-and-transcen\ dental-roots/#more-880 > > The built-in Root function is the prefeered approach in Mathematica 7 > (provided Root can handle the problem). > What trancedental roots can the Root function handle? > Well the above blog seems to indicate Root can find roots of a > holomorphic function of a single variable. > The blog says a holomorphic function is essentially polynomials of > infinite degree. > > I say the built-in Root function is prefeered over RootSearch because > the Root objects are tightly integrates into Mathematica. Also I > believe > the algorithms used by the Root function are gaurenteed to work > (neglecting the effect of bugs). On the other hand my RootSearch > package > relies on taking a finite number of samples. RootSeach has been > shown to > be relaible, but it can be tricked by a pathological problem. > > Notice the built-in Root function has been able to find the roots of a > polynomial of any finite degree for a long time (those roots are > algebraic numbers). More about the built-in Root function can be found > at > http://reference.wolfram.com/mathematica/ref/Root.html > > My RootSeach function is still the method of choice for finding > roots in > one dimension when Root in Mathematica 7 can't be used. > > > Ted Ersek > > -------------------------------------------------------------- > > === Subject: Linux Mathematica Ubuntu 9.04 Jaunty 64 bit Mathematica 7.0.0 64 bit I see high cpu usage, causing my laptop to get extremely hot. I would like to resolve the issue, so that I can get more Mathematica work done. It seems that Java may be part of the cause; can that be disabled? Also, I work on a campus with a Mathematica 6.00 network license. Can I setup my 7.0.0 frontend to utilize their 6.0 kernels over the network, freeing my machine of the cpu-hogging kernel? === Subject: Re: Remove quotes from Cell Expression > Can someone show me how to write the list m1 to a notebook without the \ quotes showing? > > m1 = {{\a\,b},{c,d}}; > nb = CreateDocument[]; > NotebookWrite[nb, Cell[ToBoxes@Grid[m1],\Text\]] > > The expression below gives the right result so there is something missing \ in my limited understanding of Cell expressions. > > Grid@m1 That has nothing to do with the convertion to boxes but is controlled by Cell properties. There are two ways to achieve what you want: 1) use cells of style \Output\, which will by default not show the string characters (which is why you don't see them with Grid@m1): NotebookWrite[nb, Cell[BoxData[ToBoxes@Grid[m1]], \Output\]] 2) stay with the \Text\ style cells, but change the settings for ShowStringCharacters: NotebookWrite[nb, Cell[BoxData[ToBoxes@Grid[m1]], \Text\, ShowStringCharacters -> False]] Note that I have wrapped the box expression with BoxData, which was necessary in my version to avoid an error indication for the created \ cell... hth, albert === Subject: Re: Remove quotes from Cell Expression If you are wanting to suppress the showing of explicit quotation marks use the option ShowStringCharacters->False as an option to the Cell expression. --David On May 6, 5:25 am, robert prince-wright > Can someone show me how to write the list m1 to a notebook without the \ qu= otes showing? > > m1 = {{\a\,b},{c,d}}; > nb = CreateDocument[]; > NotebookWrite[nb, Cell[ToBoxes@Grid[m1],\Text\]] > > The expression below gives the right result so there is something \ missing= in my limited understanding of Cell expressions. > > Grid@m1 > > Robert === Subject: Re: Picking Off Lists That Have No Numbers ?Number Number represents an exact integer or an approximate real number in Read. >> ?NumberQ NumberQ[expr] gives True if expr is a number, and False otherwise. >> ?NumericQ NumericQ[expr] gives True if expr is a numeric quantity, and False \ otherwise. >> NumberQ /@ {Pi, E, 2, 3/2, 5.7} {False,False,True,True,True} NumericQ /@ {Pi, E, 2, 3/2, 5.7} {True,True,True,True,True} Consequently you never would use Number to test for a number and almost \ always use NumericQ. FreeQ[#, _?NumericQ] & /@ {{\NA\, 2.3, 3/8}, {\NA\, \NA\, \NA\}} {False,True} MemberQ[#, _?NumericQ] & /@ {{\NA\, 2.3, 3/8}, {\NA\, \NA\, \NA\}} {True,False} Bob Hanlon Hi everyone, In a previous thread, \Select and Cases Give Different Answers,\ I discussed a bug, confirmed by others on the list and which Daniel Lichtblau of Wolfram said has been fixed in the development kernel, and I wonder whether we have the same problem here. I want to know if a list has no numbers in it. Here I get the wrong answer for the first list. FreeQ[#, _Number] & /@ {{\NA\, 2.3, 3/8}, {\NA\, \NA\, \NA\}} yields {True, True} And same here. MemberQ[#, _Number] & /@ {{\NA\, 2.3, 3/8}, {\NA\, \NA\, \NA\}} {False, False} If I use Real or Rational for the criterion, I get the right answers, but that's no good if you have some lists that are mixtures of strings and reals and others that are mixtures of strings and rationals. FreeQ[#, _Real] && FreeQ[#, _Rational] & /@ {{\NA\, 2.3, 3/8}, {\NA\, \NA\, \NA\}, {\NA\, 2.3, \NA\}, \ {\NA\, 2.3, 9.4}} Now this works. Count[#, _String] == Length[#] & /@ {{\NA\, 2.3, 3/8}, {\NA\, \NA\, \NA\}} {False, True} But this does not! Count[#, _Number] == 0 & /@ {{\NA\, 2.3, 3/8}, {\NA\, \NA\, \NA\}} {True, True} I don't mean to be a pain, but it is important in my sample selection procedures to be able to make the distinction between strings and numbers, so I'd be interested in knowing whether I'm misunderstanding properties such as Number or Numeric (don't really know the difference) or this is a bug. =09Gregory === Subject: Re: Given a matrix, find position of first non-zero A = {{0, 0, 5}, {50, 0, 100}, {0, 75, 100}, {75, 100, 0}, {0, 75, 100}, {0, 75, 100}}; Union[Position[A, _?(# != 0 &)], SameTest -> (#1[[1]] == #2[[1]] &)] {{1, 3}, {2, 1}, {3, 2}, {4, 1}, {5, 2}, {6, 2}} Bob Hanlon This is a little problem I saw in another forum, and I am trying to also solve it in Mathematica. Given a Matrix, I need to find the position of the first occurance of a value which is not zero in each row. The position found will be the position in the orginal matrix ofcourse. So, given this matrix, A = { {0, 0, 5}, {50, 0, 100}, {0, 75, 100}, {75, 100, 0}, {0, 75, 100}, {0, 75, 100} }; The result should be {{1, 3}, {2, 1}, {3, 2}, {4, 1}, {5, 2}, {6, 2}} This is how I solved this problem and after a bit of struggle. I wanted to \ see if I could avoid using a Table, and solve it just using Patterns and Position and Select, but could not so far. Table[Flatten[{i, Flatten[Position[A[[i,All]], _?(#1 != 0 & ), 1, 1]]}], {i, \ 1, 6}] Out[174]= {{1, 3}, {2, 1}, {3, 2}, {4, 1}, {5, 2}, {6, 2}} I am not happy with the above solution. I am sure there is a better one (the \ above also do not work well when one row has all zeros). Do you see a better and more elegant way to do this? --Nasser === Subject: Re: Function parameter passing? Figured it out. a = 3; b = 2; cutoff = a b; g = b; data = {0, {10, 15}, 1, 20, 7, 55}; gen[a_, b___, c___] := Flatten[Table[ Partition[Union[Flatten[Range[i, cutoff + i, {a, b, c}]]], 2, 1], {i, 0, cutoff - 1, cutoff}], 1]; width[gen_, width_] := {#1, #2 + (2 Mean[{#1, #2} - #1]*width/100)} & @@@ gen hight[gen_, highLow_] := If[Mod[#[[1]], g] == 0, highLow[[1]], highLow[[2]]] & /@ gen; datacut[data_] := Flatten[Table[data, {cutoff/Length[data] + 1}], 1]; output[gen_, hight_, data_] := Table[{data[[i]], gen[[i]], hight[[i]]}, {i, 1, Length[gen]}]; final[gen_, w_: 0, highLow_: {100, 50}, data_] := output[width[gen, w], hight[gen, highLow], datacut[data]]; out1 = gen[a, b]; out2 = gen[a]; final[out1, data] final[out2, -50, {40, 30}, data] And it does defaults too. However, can I avoid the extra step from the output to the final function? === Subject: Re: Introducing the Wolfram Mathematica Tutorial Collection Bob F (author of the original post appended below) and I are evidently very much in agreement about the value of PDF documentation. Let me just add one note. Split windows are certainly good, particularly if you have either large (or multiple) monitors and/or excellent eyesight. An equally good, maybe even better, alternative is to be able to jump back and forth (preferably with a single keystroke or mouseclick) between two different full-screen \environments\ or \views\, with Mathematica open and running in one of these and the PDF documentation open and viewable in some reader-friendly application in the other. The \Spaces\ capability in Apple's Leopard OS provides a sophisticated way to do this; the Cmd-Tab application switching capability in earlier Mac operating systems is almost equally handy. I'd assume there are equivalent capabilities on most other platforms. A non-trivial side benefit is that in this situation you know where you are at all times; and some accidental or mistaken keystroke in one space can't mess up what you're doing in the other space. > I think people are missing the value and use of these PDF documents. > Yes, Mathematica currently does have the same content (and more as the > \Tutorial Collection\ does not seem to have the \How To\ examples and > perhaps more, but so far that is all I have noticed as missing in the > new PDF files), but to get to it you might have to click many, many, > mnay links to get to it. Surely people don't enjoy having to do all > the clicking of links and going back and forth between windows that > the DC user interface forces one to do? > > In these new PDF versions, the entire topic is within one single > document. You can now do a search in the PDF file for some string and > get ALL the occurences. In my use of the DC, the search mechanism > within the Documentation Center gets extraneous content and also > misses some important content IMO. But, now that you have the PDF > file, you get a summary of all the occurances of what you are looking > for visible alongside of the content (in Acrobat Pro anyway - not sure > about other PDF viewers), so you don't spend so much time going back > and forth looking for things the way you do in the DC - just another > click in the search window which is adjacent to the main PDF window. > > IMO a better documentation interface is a combination of what both the > PDF and the DC interface has plus the ability to \split\ a window > (either horizontally or vertically as the need arose) so that you can > scroll in both halves and read two different parts at the same time, > or even more than two if you want (plus the ability to go decrease the > number of splits back to just one if you want). Something like what > vim or emacs or many other editor programs do that people use and have > been using for many many years. The DC user interface is good, but it > could be better. > > In fact this divided screen ability would be so very handy for > notebook windows as well. Would save a LOT of time in scrolling around > to find something that happened before and that you would dearly love > to have visible on the screen at the same time as you are typing > something many many lines below it that used some part of what was > screens above or below the current position. > > Another user interface issue I would like to see -- it would be so > nice to have some sort of \auto completion\ mode your could turn on or > off as you needed -- perhaps a template of the command as you type. > Something that would supply the complete command and you simply change > it as you go to fit your needs, plus once you have the basic command, > there should be some way to modify it by perhaps right-clicking and > have all the optional parameters displayed and you pick and choose > which are needed. This would be so much more productive than looking > up the command in the DC, reading thru pages and pages of options > sometimes and finally finding the one that is needed, and then back to > the notebook and type in the just found optional parameter. > > -Bob === Subject: Re: programmatically rotating a function plot This doesn't work on my version $Version 7.0 for Mac OS X x86 (64-bit) (February 19, 2009) Bob Hanlon plot4[p_] := Module[{R, p1, p2, p3}, R[q_] := Show[q /. {x_, y_} :> {-y, x}]; p1 = R[p]; p2 = R[p1]; p3 = R[p2]; Show[p, p1, p2, p3, PlotRange -> All]]; ?? Jens > This (from some book) worked in Mathematica 4, but not now: > > - - - - - - - - - - - - > pic1 = Plot[8 Sin[Pi t] Exp[-t], {t, 0, 4}] > > plot4[p_] := Module[{R, p1, p2, p3}, > R[q_] := Show[q/.{x_, y_}:> {-y,x}]; > p1 = R[p]; p2 = R[p1]; p3 = R[p2]; > Show[p,p1,p2,p3] > ]; > > plot4[pic1] > > - - - - - - - - - - - - - > > > -- Bob Hanlon === Subject: Re: solve an integration equation With[{a = 1, b = 2, d = 4, e = 7}, FindRoot[ Integrate[ Sqrt[(1 + c*x^2)/(1 + d*x^2)], {x, a, b}, GenerateConditions -> False] == e, {c, 2}]] // Chop {c -> 219.67294373109104} Quiet[With[{a = 1, b = 2, d = 4, e = 7}, FindRoot[ NIntegrate[ Sqrt[(1 + c*x^2)/(1 + d*x^2)], {x, a, b}] == e, {c, 2}]] // Chop] {c -> 219.67294373109013} Bob Hanlon Hi .My problem is this. I have integral \\!\\( \\*SubsuperscriptBox[\\(\\[Integral]\\), \\(a\\), \\(b\\)]\\( SqrtBox[ FractionBox[\\(1 + c\\ \\*SuperscriptBox[\\(x\\), \\(2\\)]\\), \\(1 + d\\ \\*SuperscriptBox[\\(x\\), \\(2\\)]\\)]] \\[DifferentialD]x\\)\\) = e I know a,b,d &e but need to find c how can i find c .Please help me === Subject: Re: Functions in partial differential equations with different \ number would like to clarify my question a bit more: Consider the following set of equations of motion: {-I*v_g*D[R[x,t],x] + V*DiracDelta[x]*F[t] ==I*D[R[x,t],t], \\Omega*F[t] + V*R[0,t]== I*D[F[t],t]}, which describes the one-dimensional wave in a one-way waveguide (i.e., no reflection) incident upon an excitable localized target at x=0. v_g is the wave velocity; V is the coupling constant, while \\Omega is the resonance frequency of the localized target (in the following, v_g = 1, V=1, and \\Omega = 2). Also, R[0, t] is taken as (R[0^+, t] + R[0^-, t])/2, for all \ t. This set of equations has analytic solution for constant frequency e (take v_g=1): R_E =( UnitStep[-x] + UnitStep [x] t_e ) Exp[I* e*x - I*e*t] , where t_e = (e-\\Omega - I* V^2/2)/(e-\\Omega +I* V^2/2), F_E = V/(e-\\Omega+ I*V^2/2) Exp[-I*e*t]. I was wondering if it's possible to simulate the original set of equations of motions numerically (with DiracDelta approximated by some regularized functions, of course). Dave > s=0.01; > NDSolve[{-I*D[R[x,t],x] + (s/(Pi (x^2+ s^2)))*F[t] ==I*D[R[x,t],t], 2 \ F[t] > + R[0,t]== I*D[F[t],t], R[-20, t]==R[20,t], R[x,0]==Exp[-(x+5)^2], > F[0]==0},{R, F}, {x,-20, 20}, {t, 0,10}] > > where I is the imaginary number Sqrt[-1]. > > However, Mathematica gave an error message saying that R and F have > different number of dependent variables: > \NDSolve::\dvlen\ : \The function F[t] does not have the same number \ of > arguments as independent variables (2).\ > > This set of equations simulate a one-dimensional wave hits a localized > target at x=0 (approximates using a Lorentzian). Initial wave form at t=0 \ is > given by R[x, 0]. The computation domain in x is assumed to be periodic. > > > Dave > === Subject: Re: Making a user interface Hi Jason: Here's one example... Module[{Entry1 = \\, Entry2 = \\, Answer = \\}, Panel[Column[{Row[{\Entry 1: \, InputField[Dynamic[Entry1], String, Background -> LightCyan]}], Row[{\Entry 2: \, InputField[Dynamic[Entry2], String, Background -> LightYellow]}], Dynamic@Row[{\Answer: \, Answer}], Row[{Button[\Clear\, Entry1 = \\; Entry2 = \\; Answer = \\], Button[\Calculate\, Answer = ToExpression[Entry1] ToExpression[Entry2]]}]}], Style[\Enter and Calculate_Multiplication\, 16, Bold, Italic]]]; Framed[%, Background -> LightOrange] Hth, Bill PS. I used Mathematica 6.0.1 with Win XP on a PC. === Subject: Help with an error with NonlinearModelFit, Mathematica 7.0 I'm trying to find a fit to a large set of data. Here are In[1], In[2]. In[1] := {{421.1, 6591.10}, ...}; (there are way more points, in fact there are 35 in total, but I don't want to list them. All are real numbers.) In[2] := nlm = NonlinearModelFit[data, Log[ak^2 + bk + c], {a,b,c}, k] Then mathematica gives an error that basically says that the function \is not a list of real numbers\ Of course it is, so how do I fix this? === Subject: Re: Mathematica 7 power consumption on Linux Similarly, my Mathematica 7 (64) on Jaunty 64, while not pegging my processors, causes them to remain highly active around 40% each. This in turn makes my hardware get hot very fast. I can't use Mathematica 7 for more than 15-20 minutes at a time without having to close everything so that I can let my processor cores cool down. > > Recently I was playing around with Intel's powertop utility and noticed \ that > Mathematica causes a significant number of CPU wakeups from idle. For > example, a completely idle Linux Gnome desktop without any additional > applications running causes ~ 15 wakeups from idle per second. When > Mathematica is running, powertop reports ~ 14.000 wakeups! > > Thus, when Mathematica is running the CPU remains in the C2 power saving > state for a considerable time, instead of switching to the C4 or C6 power \ > saving modes. > > These are the results reported by Intel's powertop: > > Mathematica running, on AC power: > http://omploader.org/vMWsxZw > > Mathematica running, on battery: > http://omploader.org/vMWsxaA > > No Mathematica running, on battery: > http://omploader.org/vMWsxaQ > > As you can image, failure to switch to C6 power state significantly \ reduces > battery runtime. > > I tested this on my ThinkPad X200 with Linux x86_64 and Kernel 2.6.29 > (wireless turned off, screen brightness at 50%, no screen dimming, blank > screens, screen savers, etc.): > > Idle desktop, no applications running: ~ 5h 15min > Idle desktop, Mathematica 7.0.1 running (one empty notebook): ~ 3h 20min > > Has anyone else noticed this behavior? So far Mathematica is the only > application I've encountered which keeps the CPU in C2 state for a > considerable time, and I don't understand why this is the case. > > Is there anything I can do about this (such as modifying the kernel > configuration)? > > Richard > > > > > === Subject: Odd ordering of results? I'm evaluating an optical interferometer problem in which an input wave e1 produces internal, reflected and transmitted waves e2 thru e7 that are connected by the linear equations waveEqns = {e1 == 1, e2 == rho12 e1 + t42 e4, e3 == rho43 e4 + t13 e1, e4 == gL e6, e5 == gL e3, e6 == rho56 e5, e7 == t57 e5}; where the rho_nm and t_nm are reflection and transmission coefficients and the input wave amplitude is arbitrarily set to e1==1; and then solving these using waveSolns = Solve[waveEqns, {e2, e3, e4, e5, e6, e7}] and getting a set of rules en-> for e2 thru e7 which are ordered in the sequence Out[] = {{e2 e7 e3 e6 e5 e4 }} with the \stuff\ stripped out for brevity. What puzzles me -- not a problem, just curious -- is the _order_ in which these rules appear. Even more puzzling: If I take out the leading \e1==1,\ statement in waveEqns I get the same results, except each \stuff\ becomes \e1*same_stuff\ -- and the set of rules produced by waveSolns is now in the different order Out[] = {{e2 e7 e3 e4 e5 e6 }} Odd . . . (seems like the natural thing would be to order the list on the left side of the en-> terms, getting e2 to e7 in either case) === Subject: Re: derivative of a well-behaved function > > the following ZS function is an analytical description of the \ transmittance > of a laser beam through an Iris after propagating inside a nonlinear \ sample > (Z-Scan curve): > > \\[Gamma][z_, z0_] := 1/2 (I/z0 (z + (z^2 + z0^2)/(DD - z)) + 1); > > ZS[z_, z0_, \\[Phi]_] := > Abs[\\[Gamma][z, z0] Gamma[\\[Gamma][z, z0], 0, > I \\[Phi]/(1 + (z/z0)^2)] /(I \\[Phi]/(1 + (z/z0)^2))^\\[Gamma][z, > z0]]^2; > > Altough the function has imaginary arguments and is defined in terms of \ the > incomplete Gamma function, it is well-behaved and Mathematica calculates \ an= > d > plots it without problems: > > DD = 300; > Plot[ZS[z, 1, 0.5], {z, -4, 4}] > > The problem is that when I calculate its derivative in z, the result is > given in terms of infinite quantities and DirectInfinity functions, and \ it > is not possible to get numerical values of it neither plot its graph: > > dZS = D[ZS[z, 1, 0.5], z]; > dZS /. z -> 1 > N[%] > Plot[dZS[z, 1, 0.5], {z, -4, 4}] > > Since the ZS function is well-behaved and has no discontinuities, its > derivative should be easily evaluated to numerical values and also \ plotted. > Does anybody has any idea on how to obtain the values? (I could easily \ writ= > e > a function to numerically calculate the derivative, but that=B4s not \ really > what I want). > > > Ricardo > > -- > ____________________________________ > Ricardo Elgul Samad > [...] Derivative (and D) really require analytic finctions in complex variables to do their work. In your example I think D gets thwarted by presence of Abs. One way around this would be to take explicit numeric differences, as below. eps = 10^(-6); dZS[z_Real] := Re[(ZS[z + eps, 1, 1/2] - ZS[z - eps, 1, 1/2])/(2*eps)] Plot[dZS[z], {z, -4., 4.}] Alternatively, you could load the numerical calc package: Needs[\NumericalCalculus`\] and then use ND. Daniel Lichtblau Wolfram Research === Subject: Re: derivative of a well-behaved function Hi Ricardo, I can not tell what is going wrong. But you could calcu\.9alate an approximate function and get the derivative of it. Herei is your example: fun = FunctionInterpolation[ZS[z, 1, 0.5], {z, -4, 4}]; Plot[{fun[z], ZS[z, 1, 0.5]}, {z, -4, 4}] Plot[fun'[z], {z, -4, 4}] Daniel > > the following ZS function is an analytical description of the \ transmittance > of a laser beam through an Iris after propagating inside a nonlinear \ sample > (Z-Scan curve): > > \\[Gamma][z_, z0_] := 1/2 (I/z0 (z + (z^2 + z0^2)/(DD - z)) + 1); > > ZS[z_, z0_, \\[Phi]_] := > Abs[\\[Gamma][z, z0] Gamma[\\[Gamma][z, z0], 0, > I \\[Phi]/(1 + (z/z0)^2)] /(I \\[Phi]/(1 + (z/z0)^2))^\\[Gamma][z, > z0]]^2; > > Altough the function has imaginary arguments and is defined in terms of \ the > incomplete Gamma function, it is well-behaved and Mathematica calculates \ an= > d > plots it without problems: > > DD = 300; > Plot[ZS[z, 1, 0.5], {z, -4, 4}] > > The problem is that when I calculate its derivative in z, the result is > given in terms of infinite quantities and DirectInfinity functions, and \ it > is not possible to get numerical values of it neither plot its graph: > > dZS = D[ZS[z, 1, 0.5], z]; > dZS /. z -> 1 > N[%] > Plot[dZS[z, 1, 0.5], {z, -4, 4}] > > Since the ZS function is well-behaved and has no discontinuities, its > derivative should be easily evaluated to numerical values and also \ plotted. > Does anybody has any idea on how to obtain the values? (I could easily \ writ= > e > a function to numerically calculate the derivative, but that=B4s not \ really > what I want). > > > Ricardo > > > -- > ____________________________________ > Ricardo Elgul Samad > > tel: (+55 11) 3133-9372 > fax: (+55 11) 3133-9374 > > Centro de Lasers e Aplica=E7=F5es > IPEN/CNEN-SP > AV. Prof. Lineu Prestes 2242 > Cidade Universit=E1ria > 05508-000 > S=E3o Paulo - SP > Brazil > ____________________________________ > > === Subject: Re: Remove quotes from Cell Expression > > > Can someone show me how to write the list m1 to a notebook without the > quotes showing? > > m1 = {{\a\,b},{c,d}}; > nb = CreateDocument[]; > NotebookWrite[nb, Cell[ToBoxes@Grid[m1],\Text\]] > > The expression below gives the right result so there is something missing > in my limited understanding of Cell expressions. > > Grid@m1 > > > Robert Actually, Grid@m1 *does* create something with quotes. They're just hidden \ by virtue of the fact that the \Output\ style has ShowStringCharacters->False \ set. To see this, evaluate Grid@m1, then click in the cell and type a character. \ This auto-converts the cell into an Input cell, and the quotes will pop \ back into existence. If this kind of solution is satisfactory to you, then the only thing you \ have to change is... NotebookWrite[nb, Cell[ToBoxes@Grid[m1],\Text\, \ ShowStringCharacters->False]] However, if there are quotes you did want to see, and they don't show up \ inside of a string (e.g. \a quote -> \\\ <-\), then this will cause problems. John Fultz jfultz@wolfram.com User Interface Group Wolfram Research, Inc. === Subject: Re: GRAPHICS IN A DO LOOP DOES NOTHING > Hi > > I tried to produce several circles using : > > Do[Graphics[Circle[{x[[k]], x[[k]]}, 0.5]], {k, 4}]] > > even \wrapping\ with Print as explained in post mg78335 > > > The command works for an individual set of data and can be superposed > with Show > , but how to do with a \large\ number. > > Graphics[Circle[{x[[1]], x[[1]]}, 0.5] > > > x1= {36.827, 36.5061, 36.1605, 35.8261} > > > y1= {-3.8282, -3.84959, -3.82263, -3.82826} > > Wrapping with Print is the appropriate solution if you need to create a series of distinct plots - but I think you want to place a series of circles on one plot: x1= {36.827, 36.5061, 36.1605, 35.8261}; y1= {-3.8282, -3.84959, -3.82263, -3.82826}; Graphics[Table[Circle[{x1[[k]], y1[[k]]}, 0.5], {k, 1, 4}]] To see more clearly how this works, you might wish to evaluate the Table command on its own: In[8]:= Table[Circle[{x1[[k]], y1[[k]]}, 0.5], {k, 1, 4}] Out[8]= {Circle[{36.827, -3.8282}, 0.5], Circle[{36.5061, -3.84959}, 0.5], Circle[{36.1605, -3.82263}, 0.5], Circle[{35.8261, -3.82826}, 0.5]} David Bailey http://www.dbaileyconsultancy.co.uk === Subject: Re: problems with DSolve steps further with mathematica to check whether it will be suitable for solving some overparametrized systems describing biological systems (kinetics of gene cascades). i will try to inform people here what was the result (if i would manage to finish). It is interesting, new perspective for me, since previously i was using numerical approach and tools like c/python. > Let's see what happens when the Plot statement tries to get its first \ poi= nt, > say at t = 0 (although it probably doesn't actually start there.) Then = you > get > > Plot[(x[0] /. DSolve[{x'[0] == y[0], y'[0] == -x[0], x[0] == = 1, y[0] > == 2}, {x, y}, 0]), at t = 0] > > and your Dsolve equations and statement are shot to pieces because t has > been everywhere replaced by 0. > > Whenever you are plotting it is better to calculate the plotting \ function= s > FIRST instead of trying to cram all calculations into the plot statement. > > In your example the equations can be solved for the generic case of \ initi= al > values so: > > Clear[x, y]; sols = > First@DSolve[{x'[t] == y[t], y'[t] == -x[t], x[0] == x0, > y[0] == y0}, {x, y}, t]; > x[x0_, y0_][t_] = x[t] /. sols > y[x0_, y0_][t_] = y[t] /. sols > > Giving > > x0 Cos[t] + y0 Sin[t] > y0 Cos[t] - x0 Sin[t] > > Then, the Manipulate statement would be: > > Manipulate[ > Plot[{x[x0, y0][t], y[x0, y0][t]}, {t, 0, 2 \\[Pi]}, > PlotRange -> {{0, 2 \\[Pi]}, {-6, 6}}, > Frame -> True], > {{x0, 0}, -5, 5, .1, Appearance -> \Labeled\}, > {{y0, 0}, -5, 5, .1, Appearance -> \Labeled\}] > > In a case like this you should always specify a PlotRange so the scale \ wo= n't > be jumping around as you vary the conditions, \The Manipulation \ Jitters\. > > If your differential equations are such that you can't obtain a generic > solution with DSolve, but have to use NDSolve on each set of initial > conditions, then you can use the following custom dynamic presentation. \ A= t > first, it looks more difficult than Manipulate because it is longer. But \ = it > is actually easier because you have complete control of the layout and \ th= e > calculation of intermediate results - in this case the solutions to the > differential equations. The main trick here is the use of the second > argument in Dynamic that appears in the controls. For example, the second > argument, (x0 = #; calcsolution[x0, y0]) &, says to set x0 to the curre= nt > value of the slider and then calculate the solutions to the differential > equations using the current values of x0 and y0. > > Module[ > {x0 = -5, y0 = -5, > x, y, calcsolution}, > > (* Routine to calculate the x and y solutions *) > calcsolution[xi_, yi_] := > Module[{sols}, > Clear[x, y]; > sols = First@ > NDSolve[{x'[t] == y[t], y'[t] == -x[t], x[0] == xi= , > y[0] == yi}, {x, y}, {t, 0, 2 \\[Pi]}]; > x[t_] = x[t] /. sols; > y[t_] = y[t] /. sols; > ]; > (* Initialize the solutions *) > calcsolution[x0, y0]; > > (* Set up the display and controls *) > Panel[ > Column[ > {(* x0 Slider and InputField *) > Row[{\x0: \, > Slider[Dynamic[x0, (x0 = #; calcsolution[x0, y0]) &], {-5, > 5, .1}], Spacer[10], > InputField[Dynamic[x0, (x0 = #; calcsolution[x0, y0]) &], > FieldSize -> {5, 1}]}], > (* y0 Slider and InputField *) > Row[{\y0: \, > Slider[Dynamic[y0, (y0 = #; calcsolution[x0, y0]) &], {-5, > 5, .1}], Spacer[10], > InputField[Dynamic[y0, (y0 = #; calcsolution[x0, y0]) &], > FieldSize -> {5, 1}]}], > (* Plot *) > Dynamic@ > Plot[{x[t], y[t]}, {t, 0, 2 \\[Pi]}, > PlotRange -> {{0, 2 \\[Pi]}, {-8, 8}}, > Frame -> True, > ImageSize -> 400] > }](* Column *), > Style[\Differential Equations with Dynamic Initial Conditions\, 16] > ](* Panel *) > ] > > David Park > djmp...@comcast.nethttp://home.comcast.net/~djmpark/ > > > hello, > > i am new to mathematica, therefore sorry if my question is trivial. I > would like to understand why the following line does not work: > > Plot[(x[t] /. DSolve[{x'[t] == y[t], y'[t] == -x[t], x[0] == = 1, y[0] > == 2}, {x, y}, t]), {t, 0, 5}] > > whereas after splitting into two lines it works: > sol = DSolve[{x'[t] == y[t], y'[t] == -x[t], x[0] == 1, y[0= ] == 2}, > {x, y}, t] > Plot[(x[t] /. sol), {t, 0, 5}] > > i would like to use Manipulate to play with boundary conditions, so > the first notation would be highly useful. > === Subject: Re: Reading csv with ; A better way to read in text data is to use ReadList[] instead of Import[]. It is better documented as well. I made a test file: 1;2;3;4;5;6 7;8;9;10;11;12 FilePrint[\tempList.txt\] 1;2;3;4;5;6 7;8;9;10;11;12 The lines are terminated with carriage returns, and there is an extra carriage return at the end. Here is what happens with Import[]: In[33]:= Import[\tempList.txt\, \Table\, \FieldSeparators\ -> \ \;\] Out[33]= {{1, 2, 3, 4, 5, 6}, {7, 8, 9, 10, 11, 12}, {}} Here is what happens with ReadList[]: In[24]:= ReadList[\tempList.txt\, Word, WordSeparators -> \;\] Out[24]= {\1\, \2\, \3\, \4\, \5\, \6\, \7\, \8\, \9\, \ \10\, \11\, \12\} You can preserve the records like this: In[38]:= ReadList[\tempList.txt\, {Word, Word, Word, Word, Word, Word}, WordSeparators -> \;\] Out[38]= {{\1\, \2\, \3\, \4\, \5\, \6\}, {\7\, \8\, \9\, \ \10\, \11\, \12\}} You can convert the strings to numbers by wrapping ToExpression[] around it. In[39]:= ToExpression[ ReadList[\tempList.txt\, {Word, Word, Word, Word, Word, Word}, WordSeparators -> \;\]] Out[39]= {{1, 2, 3, 4, 5, 6}, {7, 8, 9, 10, 11, 12}} Note that in the last three examples, the extra carriage return is lost. Here is a final way to do it: In[52]:= Partition[ToExpression[StringSplit[Import[\tempList.txt\], {\;\, \\\n\}]], 6] Out[52]= {{1, 2, 3, 4, 5, 6}, {7, 8, 9, 10, 11, 12}} Using Import[] is more elegant here. It is too bad that \FieldSeparators\ is so poorly documented. As a final note, just incase someone from Wolfram is paying attention: ? *Separator* System` NumberSeparator VerticalSeparator $PathnameSeparator RecordSeparators WordSeparators=09 I think that this command should at least list FieldSeparators. It does not. george woodrow > > > Hi Dennis, > > assume we have a file: > > 1;2 > > 3;4 > > we can read this by e.g.: > > > > Import[\d:/tmp/t.txt\, \Table\, \FieldSeparators\ -> {\;\}] > > > > The magic word is \FieldSeparators\. > > Daniel > > > > >> I'm trying to read a csv with mathematica > >> > >> Now the problem is that my system settings are at \;\ as seperator >> instead of more traditional \,\. So the it effectively looks like >> 1;1;1;1 instead of 1,1,1,1 > >> > >> Normally this makes not difference as in most software you can >> choose the delimiter/seperator before reading a file, so you pick >> =93separator = ;=94 or whatever. > >> > >> With mathematica however I have so far been unable to do this. Now >> the question of course: how so I change the seperator with >> mathematica? > >> > >> Because quite a few files have a =93;=94 separator I would like to find >> a solution within mathematica instead of changing the system >> settings. > >> > > >> > >> Dennis > >> > > > === Subject: Re: Reading csv with ; \magic word is right\. I knew that there was an option for field separators, and it took me a while to track it down. In version 5.2, the option WAS \FieldSeparator\ (no final 's'), but the option was listed on the documentation page for Export, so someone might have a chance to find it if they didn't already know about it. (It might have been good to have the option listed on the Import doc page, but I don't think it is there in 5.2.) In version 7, the option appears only on the page for Table, and then only in the examples. At least that is what a search in the Documentation Center gives. Also it is the only place that a Google search gives for the on-line version of the Version 7 documentation. Spotlight does not find anything in Mathematica -- perhaps the plug-in is broken. This is another example of the problem with Mathematica Documentation. It's not going to be fixed with PDFs or even a physical book. It's too hard to find things without knowing about them in the first place. The information (most of it, anyway) is there, but it is not arranged to be accessible by non-experts quickly. george woodrow > > > Hi Dennis, > > assume we have a file: > > 1;2 > > 3;4 > > we can read this by e.g.: > > > > Import[\d:/tmp/t.txt\, \Table\, \FieldSeparators\ -> {\;\}] > > > > The magic word is \FieldSeparators\. > > Daniel > > > > >> I'm trying to read a csv with mathematica > >> > >> Now the problem is that my system settings are at \;\ as seperator >> instead of more traditional \,\. So the it effectively looks like >> 1;1;1;1 instead of 1,1,1,1 > >> > >> Normally this makes not difference as in most software you can >> choose the delimiter/seperator before reading a file, so you pick >> =93separator = ;=94 or whatever. > >> > >> With mathematica however I have so far been unable to do this. Now = >> the question of course: how so I change the seperator with >> mathematica? > >> > >> Because quite a few files have a =93;=94 separator I would like to = find >> a solution within mathematica instead of changing the system >> settings. > >> > > >> > >> Dennis > >> > > > === Subject: Re: Reading csv with ; Look at the documentation page for Table (ref/format/Table). There is a description for an option, \FieldSeparators\ , that will work. The example uses spaces and '|' as separators, but you could specify the semi-colon and it will work. In earlier versions of Mathematica, this option was not quite as buried as it is now. george >> I'm trying to read a csv with mathematica=85 >> >> Now the problem is that my system settings are at \;\ as seperator >> instead of more traditional \,\. So the it effectively looks like >> 1;1;1;1 instead of 1,1,1,1 >> >> Normally this makes not difference as in most software you can >> choose the delimiter/seperator before reading a file, so you pick >> =93separator = ; or whatever. >> >> With mathematica however I have so far been unable to do this. Now >> the question of course: how so I change the seperator with >> mathematica? >> >> Because quite a few files have a =93;=94 separator I would like to >> find a solution within mathematica instead of changing the system >> settings. >> >> >> Dennis > > Good day, > > My DIY way to do it: > > In[1]:= test=Import[\test.csv\] > Out[1]= {{1.0;2.0;3.0;4.0},{5.0;6.0;7.0;8.0},{9.0;10.0;11.0;12.0}} > > In[2]:= %//FullForm > Out[2]//FullForm= List[List[\1.0;2.0;3.0;4.0\],List > [\5.0;6.0;7.0;8.0\],List[\9.0;10.0;11.0;12.0\]] > > In[3]:= test/.str_String:> > Sequence@@ToExpression@(\{\<>StringReplace[str,\;\->\,\]<>\}\) > Out[3]= {{1.,2.,3.,4.},{5.,6.,7.,8.},{9.,10.,11.,12.}} > > In[4]:= %//FullForm > Out[4]//FullForm= List[List[1.`,2.`,3.`,4.`],List[5.`,6.`,7.`, > 8.`],List > [9.`,10.`,11.`,12.`]] > > === Subject: two graph problems in Adjacency types I have two graph handling problems: 1) ToAdjacencyMatrix g below works with: << DiscreteMath`GraphPlot`; g = { 1 -> 2, 1 -> 4, 1 -> 5, 1 -> 9, 2 -> 1, 2 -> 3, 2 -> 6, 2 -> 10, 3 -> 2, 3 -> 4, 3 -> 7, 3 -> 10, 4 -> 1, 4 -> 3, 4 -> 8, 4 -> 12, 5 -> 1, 5 -> 6, 5 -> 8, 5 -> 9, 6 -> 2, 6 -> 5, 6 -> 7, 6 -> 10, 7 -> 3, 7 -> 6, 7 -> 8, 7 -> 11, 8 -> 4, 8 -> 5, 8 -> 7, 8 -> 12, 9 -> 1, 9 -> 5, 9 -> 10, 9 -> 12, 10 -> 2, 10 -> 6, 10 -> 9, 10 -> 11, 11 -> 3, 11 -> 7, 11 -> 10, 11 -> 12, 12 -> 4, 12 -> 8, 12 -> 9, 12 -> 11}; GraphPlot[g, \EdgeStyleFunction\ -> (Arrow[{#1, #2}] &)]; g2 below works with: << DiscreteMath`ComputationalGeometry` PlanarGraphPlot[g2, TextStyle -> {\FontSize\ -> 8}] DiagramPlot[g2] 1) Mathematica: << DiscreteMath`ComputationalGeometry` << DiscreteMath`Combinatorica` g = { 1 -> 2, 1 -> 4, 1 -> 5, 1 -> 9, 2 -> 1, 2 -> 3, 2 -> 6, 2 -> 10, 3 -> 2, 3 -> 4, 3 -> 7, 3 -> 10, 4 -> 1, 4 -> 3, 4 -> 8, 4 -> 12, 5 -> 1, 5 -> 6, 5 -> 8, 5 -> 9, 6 -> 2, 6 -> 5, 6 -> 7, 6 -> 10, 7 -> 3, 7 -> 6, 7 -> 8, 7 -> 11, 8 -> 4, 8 -> 5, 8 -> 7, 8 -> 12, 9 -> 1, 9 -> 5, 9 -> 10, 9 -> 12, 10 -> 2, 10 -> 6, 10 -> 9, 10 -> 11, 11 -> 3, 11 -> 7, 11 -> 10, 11 -> 12, 12 -> 4, 12 -> 8, 12 -> 9, 12 -> 11}; ShowGraph[g] ToAdjacencyMatrix[g] 2) Mathematica: Needs[\Combinatorica`\] g2 = {{-0.9280755637296179`, -0.19419929835443286`}, {-0.9280755637296179`, \\ 0.19419929835443286`}, {-0.6501667625820613`, -0.2919430658415227`}, \\ {-0.6501667625820613`, 0.2919430658415227`}, {-0.48283076848225387`, \\ -0.11693236237728927`}, {-0.48283076848225387`, 0.11693236237728927`}, \\ {-1.1392923850800492`, -0.46926092334332986`}, {-1.1392923850800492`, \\ 0.46926092334332986`}, {-1.4197713561114567`, 0}, {-0.4785669339713638`, \\ -0.5281299674972387`}, {-0.4785669339713638`, 0.5281299674972387`}, {-0.2866442761736428`, -0.20825925704946527`}, \\ {-0.2866442761736428`, 0.20825925704946527`}, {-0.7983543675400564`, \\ -0.9385218466866597`}, {-0.7983543675400564`, 0.9385218466866597`}, \\ {-0.4714856294164916`, -0.8226414290121405`}, {-0.4714856294164916`, \\ 0.8226414290121405`}, {-0.2604121980728394`, -0.423065261465852`}, \\ {-0.2604121980728394`, 0.423065261465852`}, {-1.2647924812445637`, 0}, \\ {-0.129178585243926`, -0.093853735887278`}, {-0.129178585243926`, 0.093853735887278`}, {-0.43873347716520544`, -1.350282799879008`}, \\ {-0.43873347716520544`, 1.350282799879008`}, {-0.1020966130966314`, \\ -0.9426631959865617`}, {-0.3908423710622271`, -1.2028891310487582`}, \\ {-0.3908423710622271`, 1.2028891310487582`}, {-0.1020966130966314`, \\ 0.9426631959865617`}, {-0.03799362766342498`, -0.49533343579983613`}, \\ {-0.03799362766342498`, 0.49533343579983613`}, {0.09423295043665249`, \\ -1.2285410469049964`}, {0.09423295043665249`, 1.2285410469049964`}, \\ {0.07674177634016656`, -0.7085607049671481`}, {0.04934182894455409`, \\ -0.15185853463677154`}, {0.04934182894455409`, 0.15185853463677154`}, \\ {0.07674177634016656`, 0.7085607049671481`}, {0.10948837081771987`, \\ -0.3369705563778359`}, {0.10948837081771987`, 0.3369705563778359`}, \\ {1.0232386116845091`, -0.743426367685959`}, {1.0232386116845091`, \\ 0.743426367685959`}, {0.15967351259874374`, 0}, {0.6458822508733686`, \\ -1.0492993237800035`}, {0.6458822508733686`, 1.0492993237800035`}, \\ {0.3543961314959318`, -0.6183453362321933`}, {0.3543961314959318`, \\ 0.6183453362321933`}, {0.32188717898816915`, -0.3784010734225469`}, \\ {0.32188717898816915`, 0.3784010734225469`}, {1.148619155220934`, \\ -0.8345206647495994`}, {1.148619155220934`, 0.8345206647495994`}, \\ {0.6366814195430888`, -0.7026196620377195`}, {0.6366814195430888`, \\ 0.7026196620377195`}, {0.35431181071184575`, 0}, {0.4593494152303489`, \\ -0.18920053671127346`}, {0.4593494152303489`, 0.18920053671127346`}, \\ {1.1975315513100848`, -0.2900192002183368`}, {1.1975315513100848`, \\ 0.2900192002183368`}, {0.8649763866996519`, -0.38839859670886573`}, \\ {0.8649763866996519`, 0.38839859670886573`}, {0.6975957887173267`, \\ -0.14597153292076134`}, {0.6975957887173267`, 0.14597153292076134`}}; === Subject: copy and paste to other programs before Mathematica 7 it was a pleasure to use Mathematica in the preparation of Powerpoint presentations or Word documents: Do the calculations and generate the plots and tables in Mathematica, then copy as Metafile invoking the right mouse context menu and paste to the other program. The copy and paste takes 2 seconds. Copy as Metafile disappeared in Mathematica 7. Just copy and paste produces crazy fonts when the Powerpoint file is opened on a computer without Mathematica. My current workaround is to print the Mathematica notebook to a file using a Postscript printer, then to convert the printer file to PDF with Acrobat Distiller and to copy what is needed from the PDF. This works reliable whereas saving as PDF from the Mathematica file menu produces sometimes strange PDF output. The workaround takes perhaps 10 x 2 = 20 seconds and creates intermediate files which clutter your directories. Doing this once is not a problem but preparing a presentation with 30 slides or just doing a quick change on an existing presentation is now a pain. Did I oversee something in the new interface of Mathematica 7? Are there quicker ways? By the way, I am not really a fan of Powerpoint or Word, but as a matter of fact are these programs de-facto standards to exchange information with colleges in some non-academic areas. Hannes Kessler === Subject: BinaryReadList before Mathematica 7 the following command could be used to return the contents of a binary file as a list of records, each record being a nested list of a certain structure, for example BinaryReadList[file,{\Integer32\, {\Real64\, \Real64\}, \ \Integer32\}] Mathematica 7 complains: BinaryReadList::format {\Integer32\, {\Real64\, \Real64\}, \Integer32\} is not a recognized binary format. I know there are other ways (see below one suggestion). But what is the purpose to eliminate useful existing functionality in new Mathematica revisions? Here is my workaround: format = {\Integer32\, {\Real64\, \Real64\}, \Integer32\}; data = BinaryReadList[file, Flatten @ format]; formats = ConstantArray[format, Length[data]]; positions = Position[formats, _String]; rules = Inner[Rule, positions, Flatten[data], List]; ReplacePart[formats, rules] Hannes Kessler === Subject: Re: Some function like Position[] but uses criteria, not pattern? Hi. Same solution as others, just displayed differently for small arrays. m = RandomInteger[{9}, {10, 10}]; sol = Position[m, _?(# > 3 &)]; MatrixForm[SplitBy[sol, First]] = = = HTH Dana DeLouis > V 7.0 > > Position[] works by returning position of elements which matches a pattern. > This is all good and well. > > But sometimes, I need to find the positions (i.e index) of elements that > matches a criteria, not a pattern. > > For example, using pattern > > a = {1, 0, 4, -5, 8} > Position[a, 0] > Out[15]= {{2}} > > But what if I wanted the position of the elements which, say, are larger > than 3? this is not a pttern, but a criteria. Which in this example should > find elements which are in position 3 and 5 in list 'a' above. > > I can't type > Position[a, #1 > 3 & ] > > Now, Select[] does take a criteria, good, so I could type > > Select[a, #1 > 3 & ] > {4, 8} > > But I wanted the positions of the elements, not the elements themselves. > > I could use Select to find the elements, then use Position to find the > position of these elements as follows > > c = Select[a, #1 > 3 & ]; > Flatten[(Position[a, #1] & ) /@ c] > > Out[65]= {3, 5} > > But I think this is bit messy. I think Position[] or new function similar, > should have an option to return position of elements based on criteria, not > just pattern. The above gets more messy for me, when I wanted to find > position of elements in a matrix based on some criteria. > > For example, find the position (i.e. row and column) index in a matrix (list > of lists) of those elements which matches some criteria. Say >3. > > --Nasser > > > > === Subject: Re: Bug with Hypergeometric2F1? > >>If you want to use machine precision numbers you should be using >>NSum rather than Sum. That is: >>In[4]:= f[n_, k_] := NSum[Binomial[n, i], {i, 0, k}] >>In[5]:= f[1000, 1.] >>Out[5]= 1001. >The supposed advantage of NSUm over Sum in this particular case is a >mere illusion. >g[n_, k_] := Sum[Binomial[n, i], {i, 0, k}] >g[1000, 1.] >1001 >Note that you are using SetDelayed while the original post has Set; >hence the difference. I don't believe your interpretation of what occurs is correct. I am reasonably certain when you use Sum with machine precision numbers a numerical estimate is made using the same code used by NSum. That is, I believe the effect of using machine precision numbers is to call NSum. I used SetDelayed since Set cannot be used with NSum in this example. With Set, Mathematica tries to evaluate the right hand side which cannot be done since n and k are not defined at this point. === Subject: Re: Picking Off Lists That Have No Numbers >In a previous thread, \Select and Cases Give Different Answers,\ I >discussed a bug, confirmed by others on the list and which Daniel >Lichtblau of Wolfram said has been fixed in the development kernel, >and I wonder whether we have the same problem here. >I want to know if a list has no numbers in it. Here I get the wrong >answer for the first list. >FreeQ[#, _Number] & /@ {{\NA\, 2.3, 3/8}, {\NA\, \NA\, \NA\}} >yields {True, True} And same here. >MemberQ[#, _Number] & /@ {{\NA\, 2.3, 3/8}, {\NA\, \NA\, \NA\}} >{False, False} Both FreeQ and MemberQ are operating as documented in these examples. If you do In[18]:= Union@ Flatten@Map[Head, {{\NA\, 2.3, 3/8}, {\NA\, \NA\, \NA\}}, {2}] Out[18]= {Rational,Real,String} you see that none of the elements in either list have the head Number. So, FreeQ correctly reports both list have nothing matching the specified pattern. Similarly, MemberQ reports anything matching this pattern is not a member of either list. >If I use Real or Rational for the criterion, I get the right >answers, Which of course works because there are elements with head Real and Rational in these lists. The basic problem is there is nothing built-in to Mathematica with the he