A289 ==== Subject: Re: any math forum that supports math equations? >> As for banning robots, some robots are very obnoxious and need to be >> banned. I un-banned you. Your method for detecting robots being a 1x1 pixel image as the full > stop in the first sentence, that leads to a ban page? Eww... No. If you click on that comma -- not a pixel, you go to a page that tells you not to click on anything or else you would be banned. Then there is an INVISIBLE one pixel picture that is clickable. Clicking on that (pretty hard to do for a human) is what leads to banning. i -- ==== Subject: Re: any math forum that supports math equations? > No. If you click on that comma -- not a pixel, you go to a page that > tells you not to click on anything or else you would be banned. Didn't say anything like that in Lynx. - Tim ==== Subject: Want a copy of Vajda's Fibonacci and Lucas Numbers, and The Golden section I am looking for a copy of Steven Vajda's Fibonacci and Lucas Numbers, and The Golden section. Has somebody this book for sale? ==== Subject: Re: Functional equations , complex and quaternions .. >May we create interesting cases with quaternions ? >Well, you can use the quaternions to create other intermediate > possibilities, but the (temporary) use of the complex numbers has > already found all real solutions (f,g), so there seems little > point to taking a more complicated route to reach the same conclusion. Complex:complicated::quaternion:? -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) ==== Subject: Re: Zero digits in powers ... > Assume for the fun of it > that the digits in the decimal representation of 2^n are independently > and uniformly distributed. > > But they are not. The probability that the first digit is k is about > log(k + 1) - log(k), and similar formula's for larger sequences. > > log base 10? Yes, when we consider decimal digits. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ ==== Subject: Re: Zero digits in powers > Assume for the fun of it that the digits in the decimal > representation of 2^n are independently and uniformly > distributed. But they are not. The probability that the first digit is k is about > log(k + 1) - log(k), and similar formula's for larger sequences. log base 10? Yes. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) ==== Subject: Re: Zero digits in powers representation of 2^n are independently and uniformly > distributed. > But they are not. The probability that the first digit is k is about > log(k + 1) - log(k), and similar formula's for larger sequences. > log base 10? Yes. > I vaguely recall a story that in the 1960s some Russian programmers were using middle digits from products of two big numbers as a random number generator. ==== Subject: Re: Zero digits in powers Le 17/06/2005 03:35, dans .82ævkarlamov@yahoo.comæ[CapitalEG rave] a .8ecritæ: > I vaguely recall a story that in the 1960s some Russian programmers > were using middle digits from products of two big numbers as a random > number generator. Maybe you'll want to have a look at this thread Manansala Random Number generator. I believe there was a discussion on that topic, at one point. ==== Subject: Re: Zero digits in powers .82 vkarlamov@yahoo.com é a .8ecrit : I vaguely recall a story that in the 1960s some Russian programmers > were using middle digits from products of two big numbers as a random > number generator. Maybe you'll want to have a look at this thread Manansala Random Number > generator. I believe there was a discussion on that topic, at one point. > Heck, I am just trying to give productive suggestions as to how to explain the phenomenon in this thread: zeros in 2^n. ==== Subject: Re: Zero digits in powers Le 17/06/2005 03:55, dans .82ævkarlamov@yahoo.comæ[CapitalEG rave] a .8ecritæ: >> Le 17/06/2005 03:35, dans >> .82 vkarlamov@yahoo.com é a .8ecrit : >>I vaguely recall a story that in the 1960s some Russian programmers > were using middle digits from products of two big numbers as a random > number generator. >> >> Maybe you'll want to have a look at this thread Manansala Random Number >> generator. I believe there was a discussion on that topic, at one point. > Heck, I am just trying to give productive suggestions as to how to > explain the phenomenon in this thread: zeros in 2^n. > Sorry :-) It's perfectly understandable that numbers with as many as 10000 digits with no particular a priori digit distribution property, will have some 0 digits in them. But what is *very* interesting is a proof ;-) Anybody playing some time with the problem will believe the property is reasonnably true, that's another matter to find a rigorous justification. ==== Subject: Re: Zero digits in powers > Under F24 in Guy's Unsolved Problems in Number Theory, 3rd ed., > it says Dan Hoey has checked that 2^n has a zero > for 86 < n < 25000 00000. >Quite easy to beat this limit, it suffices to compute > the last few digits of 2^n, which needs only few additions > per step (on step for each n). >I remember I got 10^9 or 10^10 by leaving university > computers for some time. Well, Hoey got 2.5 x 10^9, so if what you got was 10^9, you didn't beat him. If what you got was 10^10, you should let Richard Guy (and the rest of us) know about it. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) ==== Subject: Re: Zero digits in powers Le 17/06/2005 01:25, dans gerry-A4B613.09251517062005@sunb.ocs.mq.edu.au, .82æGerry Myersonæé a .8ecritæ: > Well, Hoey got 2.5 x 10^9, so if what you got was 10^9, > you didn't beat him. If what you got was 10^10, you should let > Richard Guy (and the rest of us) know about it. Frankly, I don't consider it's computationnally difficult to obtain this. Almost anybody with a modern PC and some time (few hours, maybe few days), can obtain that, with a very easy and fast program. Nothing difficult: algorithm is almost trivial and yet probably near-optimal: Create an array T[N], whose elements represent decimal digits. Initialize with number 1. Implement multiplication by 2 - it's an addition, the most difficult part (!) is the carry :-) Multiply T[N] by 2 and repeat many times. Each time check for digits (or during computation of addition, keep trace of appearing 0 digits). If addition overflows, don't care: lost digits don't influence further computations with T[N], and if you find 0 in T[N], no need to check upper digits. If it actually happens that there is no 0 in T[N], bad luck: you must restart with a larger N. I would recommend N > 200. Not too high: not useful and computations get slower. What else ? Oh, yes: you can start from another number than 1: Just compute with BC or any bigint package, the number: (2^p) mod (10^N). [no need to say, use fast mod-power algo, but it's trivial, isn't it ?] It gives T[N] digits for 2^p, so I you are tired and want to shut down your computer, you can restart later where you stopped. Other advantage: you can run simultaneously on several machines, I used 3 machines at university, but there is absolutely no limit. You may have noticed: each step needs only N additions (plus some instructions, but no multiply here). Let's say 3*N ops for a loop. So looping thru 10^9 needs roughly 6*10^11 ops. On a 3GHz processor, it means... well, you are old enough to compute. I would not be afraid by 10^13, with enough computing power. I think it's more useful in such a situation to let people who have high computing power play this game. Maybe I had 10^10, but who cares ? It's ridiculous compared to what can be obtained. And BTW, I didn't go too far for the simple reason I believe (from intuitive statistical behaviour) all following 2^n will have a 0. I'm not going to look for a non-existent counter-example, even if I can't prove there is none. At this point, this problem needs only one thing: proof ! You can compute for eternity if you like. The problem n^40 is more tricky to program, so it would be interesting to look for a fast algorithm. Still, when I posted I was mainly interested by proof or any work on that subject. Even if numerical exploration is a work (sometimes a very patient work :-)), it's merely playing with numbers, not mathematical proof. Ok, I'm rather fussy with mathematical proofs. My feeling is: a computer is perfect to get an idea on some problem, but nothing more, pure mathematics don't like intuition. [experimental sciences, numerical analysis, etc. are another story: computers are fundamental then]. ==== Subject: Re: Newton vs. Cantor > Or maybe since the time of Newton. ahem. > > What is the this thing that draws cranks to worship Newton and despise > Cantor. I suppose it must be that in a basic calculus course someone > tells them that all these handwavy arguments that ignore technicalities > are something that Newton invented, but then these people go take > discrete math or whatnot and there they tell them about Cantor, set > theory and cardinality and require them to rigorously prove things, > which hurts their brain as it actually requires thought rather then > bulling. They like handwavy arguments, because they can follow them and are able to do the same thing themselves. Moreover, they do not understand the result of Cantor, misinterprete it, can not follow the proof, and whatever. Why is it that the Quaternions found their initial use only with Heavyside's notation (spliting the real and imaginary part)? Probably just because working in four dimensions was incomprehensible. > Why is not Cauchy so despised? He was the one most responsible (I > suppose this is a subjective claim) for making analysis rigorous. Im my opinion the most responsible are Weierstrass and Dedekind, but indeed, it is subjective. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ ==== Subject: Re: bayesian prediction using one data point? Brain Teaser X-Nntp-Posting-Host: user-48.gradstudents.utoronto.ca X-Rfc2646: Format=Flowed; Original Mark is so such to be compared with an elementary student. > what are talking about moron? is that the fake PhD title which you like > to append behind your name? i can tell by your posts that you are > actually a PhD-less idiot. > ==== Subject: Re: Multiplication formula for Bernoulli polynomials > Hi everyone >I am Atul Dixit. I am a new member of this group. >I was trying to find the proof of the following formula(due to Raabe) > regarding Bernoulli polynomials : >(1/m) *summation(Bn(x+(k/m)) = (Bn(mx))/(m^n) >where Bn(x) denotes the Bernoulli polynomial. >Will anyone help me regarding the same? >Atul Dixit > Start with the definition t*exp(xt)/(exp(t)-1) = sum(n=0, inf, B_n(x)t^n/n!. It's not too hard - I worked it out in less than 15 minutes. (Slow and careful, with a pen.) Martin Cohen ==== Subject: the mathematics of WWW Y) Since every URL starts with WWW, can somebody explain to Mark what is the value of having www. as the first part of the URL? It would save Mark from typing 3 pointless characters if the internet just dropped it, right? Z) Did anybody see the Missing on cable TV last night? In one of the early scenes, a man was murdered an hanging in a basket over a camp fire, apparently murdered. I didn't get that scene; can someone elaborate? Mark Demers, PhD EquityValue Investments ==== Subject: Re: the mathematics of WWW >I didn't get that scene YM Mark didn't get that scene. HTH. HAND. ==== Subject: Re: the mathematics of WWW >Y) Since every URL starts with WWW, can somebody explain to Mark what >is the value of having www. as the first part of the URL? It would >save Mark from typing 3 pointless characters if the internet just >dropped it, right? There is no such requirement. There are quite a few sites which do not start with www. -- 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: the mathematics of WWW On 16 Jun 2005 17:10:17 -0700, double d Y) Since every URL starts with WWW, can somebody explain to Mark what >is the value of having www. as the first part of the URL? It would >save Mark from typing 3 pointless characters if the internet just >dropped it, right? The way you exhibit ignorance of _everything_ is truly amazing. It's not true that every URL begins with www. >Z) Did anybody see the Missing on cable TV last night? In one of the early scenes, a man was murdered an hanging in a basket over a camp >fire, apparently murdered. I didn't get that scene; can someone >elaborate? Mark Demers, PhD Interesting group. I see you're the all time top poster there - congratulations. >EquityValue Investments ************************ David C. Ullrich ==== Subject: Re: the mathematics of WWW Z) Did anybody see the Missing on cable TV last night? In one > of the early scenes, a man was murdered an hanging in a basket > over a camp fire, apparently murdered. I didn't get that scene; > can someone elaborate? If that was the film about the renegade Red Indian kidnapping female settlers and selling them to a Mexican brothel keeper, the guy was the heroine's husband. Do try and keep up ;-P ==== Subject: Re: the mathematics of WWW > If that was the film about the renegade Red Indian kidnapping > female settlers and selling them to a Mexican brothel keeper, > the guy was the heroine's husband. Do try and keep up ;-P I'm afraid I'm more behind with respect to movies that Mark Demers is. All I can contribute to the subject, in a general vein, is that the movie A Beautiful Mind was nothing like the book, even though a faithful transcription of the book would have led to a much less exciting movie. Shame on me; I can't even work this group. How would I perform if I was planning to use a list of professional mathematicians for cold-calling purposes? Lousily, undoubtedly. ==== Subject: Re: the mathematics of WWW I have yet to see any mathematics of WWW discussed. ==== Subject: Re: the mathematics of WWW you won't see any. how can you when the OP of this thread is a numbskull. ==== Subject: Re: the mathematics of WWW Mark believes the addressing system on the WWW could be made much more efficient using cryptological methods. Shorter, more precise addresses would reduce typing and help everyone find Mark's web site faster. ==== Subject: Re: the mathematics of WWW What about the Missing. mark is still waiting to find out what mathematicians think about The Missing. MD ==== Subject: Re: the mathematics of WWW Sorry, I missed it... Tom Davidson Richmond, VA ==== Subject: Re: the mathematics of WWW Mark believes the addressing system on the WWW could be made much more efficient using cryptological methods. Shorter, more precise addresses would reduce typing and help everyone find the right web sites faster. For starters, they could call Mark's web address Mark. Then you visit mark automatically just by typing Mark. ==== Subject: Re: the mathematics of WWW Y) Since every URL starts with WWW, That's not true. ==== Subject: Re: the mathematics of WWW You dont have to type the entire URL for something which is of the form http://www.foo.com - just type in foo and hit Ctrl+Enter, and this will add the http://www. and .com on either side. At least this happens in Internet Explorer and (I think) Mozilla. - A C ==== Subject: Re: the mathematics of WWW > You dont have to type the entire URL for something which is of the form > http://www.foo.com - just type in foo and hit Ctrl+Enter, and this will > add the http://www. and .com on either side. >At least this happens in Internet Explorer and (I think) Mozilla. > Many browsers add the www if foo.com is not found. However, it is quite possible [in fact I have several such sites] to have separate and different web sites on foo.com and www.foo.com This breaks browsers that add www by default before attempting to contact the site because they end up at the wrong site. This is why I usually tell people that my web site is http://example.com rather than example.com -bz- -- bz please pardon my infinite ignorance, the set-of-things-I-do-not-know is an infinite set. bz+sp@ch100-5.chem.lsu.edu remove ch100-5 to avoid spam trap ==== Subject: Re: the mathematics of WWW On 16 Jun 2005 19:38:06 -0700, Ann Chance http://www.foo.com - just type in foo and hit Ctrl+Enter, and this will >add the http://www. and .com on either side. At least this happens in Internet Explorer and (I think) Mozilla. - A C And Firefox. Also, Shift+Enter -> foo.net Ctrl+Shift+Enter -> foo.org ==== Subject: Re: the mathematics of WWW X-Nntp-Posting-Host: user-48.gradstudents.utoronto.ca X-Rfc2646: Format=Flowed; Original Mark shows how ignorant he is again. For most sites, you don't need to type in www, idiot!! Y) Since every URL starts with WWW, can somebody explain to Mark what > is the value of having www. as the first part of the URL? It would > save Mark from typing 3 pointless characters if the internet just > dropped it, right? Z) Did anybody see the Missing on cable TV last night? In one of the early scenes, a man was murdered an hanging in a basket over a camp > fire, apparently murdered. I didn't get that scene; can someone > elaborate? Mark Demers, PhD > EquityValue Investments > ==== Subject: Re: the mathematics of WWW Y) Since every URL starts with WWW, can somebody explain to Mark what >is the value of having www. as the first part of the URL? It would >save Mark from typing 3 pointless characters if the internet just >dropped it, right? It doesn't. Some examples: nvl.nist.gov xxx.lanl.gov discussion.monster.com freefall.purrsia.com -- Are those morons getting dumber or just louder? -- Mayor Quimby ==== Subject: Re: the mathematics of WWW >Y) Since every URL starts with WWW, can somebody explain to Mark what > is the value of having www. as the first part of the URL? It would > save Mark from typing 3 pointless characters if the internet just > dropped it, right? False. www is just a host name within the domain specified by the url. The DNS doesn't care what you use for a host name. www is just a convention. e.g: http://groups.yahoo.com/ .com - refers the the TLD (top level domain). yahoo is a domain name either under the authority of, or delegated by .com. If you do a dig or nslookup on groups.yahoo.com - you will see that groups is actually a cname alias for something else. Try it and see. BTW a domain name can be configured to act as a host name too. e.g type yahoo.com as a url and see what happens. Information about the DNS: http://www.dns.net/dnsrd/ Mark Demers, PhD You have a counter example in your own sig LOL. Klazmon > EquityValue Investments > ==== Subject: Re: the mathematics of WWW >Y) Since every URL starts with WWW, [snmip] Dead On Arrival. http://ww1.tntvacations.com/SpecialDeals http://ww2.vet.org/ http://arXiv.org/ -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf ==== Subject: Re: the mathematics of WWW Y) Since every URL starts with WWW, can somebody explain to Mark what >is the value of having www. as the first part of the URL? It would >save Mark from typing 3 pointless characters if the internet just >dropped it, right? In order to slow down the pace of life these days, it was (officially) decided to have an abbreviation that takes longer to say than the thing being abbreviated. (Sometimes you see web.[...], which would be better. Mark should remember that when he sets up a computer network, one machine of which is a web server.) dave ==== Subject: Re: the mathematics of WWW X-RFC2646: Format=Flowed; Original >>Y) Since every URL starts with WWW, can somebody explain to Mark what >>is the value of having www. as the first part of the URL? It would >>save Mark from typing 3 pointless characters if the internet just >>dropped it, right? In order to slow down the pace of life these days, it was (officially) > decided to have an abbreviation that takes longer to say than the > thing being abbreviated. > www = world wide web > (Sometimes you see web.[...], which would be better. Mark should > remember > that when he sets up a computer network, one machine of which is a > web server.) dave ==== Subject: Re: the mathematics of WWW > Y) Since every URL starts with WWW, can somebody explain to Mark what > is the value of having www. as the first part of the URL? It would > save Mark from typing 3 pointless characters if the internet just > dropped it, right? > Unfortunately, the power of the browser is lost on most current users. Originally, it was designed to perform *all* internet functions, which at the time of its release included things like ftp, telnet, archie, and - yes - email. In fact, most browsers can *still* do all those things -- many folks are surprised that they only need a browser to do ftp transfers for example. In such cases, you replace http: with the appropriate other thing, like telnet: and then the name of the server will likely be different than the server that provides http documents. The one that http sits on is usually named 'www' by convention, but this is not at all a general rule. See my.yahoo.com. PD ==== Subject: Re: the mathematics of WWW > Y) Since every URL starts with WWW, can somebody explain to Mark what > is the value of having www. as the first part of the URL? It would > save Mark from typing 3 pointless characters if the internet just > dropped it, right? > Counting the period, that's actually _four_. Wrong for two reasons ... > Unfortunately, the power of the browser is lost on most current users. > Originally, it was designed to perform *all* internet functions, which > at the time of its release included things like ftp, telnet, archie, > and - yes - email. In fact, most browsers can *still* do all those > things -- many folks are surprised that they only need a browser to do > ftp transfers for example. In such cases, you replace http: with the > appropriate other thing, like telnet: and then the name of the server > will likely be different than the server that provides http documents. > The one that http sits on is usually named 'www' by convention, but > this is not at all a general rule. See my.yahoo.com. You can also open a file on your computer (in a Windows machine) by typing something like file:pathnamefile. --- Christopher Heckman ==== Subject: Re: the mathematics of WWW > Y) Since every URL starts with WWW, can somebody explain to Mark what > is the value of having www. as the first part of the URL? It would > save Mark from typing 3 pointless characters if the internet just > dropped it, right? Conclusion based on false premise. Every URL does NOT start with WWW. Z) Did anybody see the Missing on cable TV last night? In one of the early scenes, a man was murdered an hanging in a basket over a camp > fire, apparently murdered. I didn't get that scene; can someone > elaborate? Mark Demers, PhD > EquityValue Investments ==== Subject: Re: Solving for a Transfer Function why don't i believe you? if so, then why not just define f3 by f3(h)= (h2/h1) h, then you would have f3(h1)=h2. this would be valid since you didn't specify anything further on f3. ==== Subject: Re: So what is mass? > As many times as I've been told, I can't seem to keep it straight in my > mind. Is mass an unpecified quantity of matter; according to Newton's > bulk and density, or is it the specific inertia of a body; according to > the ratio of the magnitude of the thrust exerted on and/or by it, > divided by the acceleration caused? > Is the kilogram the unit of mass because we say it is, or is there an > irefutable scientific basis, like a mathematical ratio that makes it > so? > Don > Why don't you tell us? I thought you were on a five-year mission to educate us, the befuddled > masses? It's been more than five-years, and you're still not listening. You're > too busy telling me, and I keep forgetting. We've got to settle whether mass is an unpecified quantity of matter; > according to Newton's bulk and density, or is it the specific inertia > of a body; according to the ratio of the magnitude of the thrust > exerted on and/or by it; divided by the acceleration caused? Or is the kilogram the unit of mass because we - the people - say it > is, or is there an irrefutable scientific basis, like a mathematical > ratio that makes it so? Listen-up; I've got a lot more to teach you people: About the fictional > centrifugal force that throws water out of wet cloths, momentum, > displacement, and a host of related stuff. Don > Double-A Maybe you should tell us about those fictional forces now, otherwise you might forget. Double-A ==== Subject: Re: So what is mass? > As many times as I've been told, I can't seem to keep it straight in my > mind. Is mass an unpecified quantity of matter; according to Newton's > bulk and density, or is it the specific inertia of a body; according to > the ratio of the magnitude of the thrust exerted on and/or by it, > divided by the acceleration caused? > Is the kilogram the unit of mass because we say it is, or is there an > irefutable scientific basis, like a mathematical ratio that makes it > so? > Don > > Why don't you tell us? > I thought you were on a five-year mission to educate us, the befuddled > masses? > It's been more than five-years, and you're still not listening. You're > too busy telling me, and I keep forgetting. We've got to settle whether mass is an unpecified quantity of matter; > according to Newton's bulk and density, or is it the specific inertia > of a body; according to the ratio of the magnitude of the thrust > exerted on and/or by it; divided by the acceleration caused? Or is the kilogram the unit of mass because we - the people - say it > is, or is there an irrefutable scientific basis, like a mathematical > ratio that makes it so? Listen-up; I've got a lot more to teach you people: About the fictional > centrifugal force that throws water out of wet cloths, momentum, > displacement, and a host of related stuff. Don > Double-A > Maybe you should tell us about those fictional forces now, otherwise > you might forget. > I wouldn't forget that, we've been through this several times before; but I do forget who's so sure that there are no centrifugal forces. Who claims that centrifugal force is ficticious, but is a necessary fiction. Centrifugal force is real; it throws water out of wet cloths, and is what throws the water to the outside of a spinning bucketful, and slings rocks out from slings. Don > Double-A ==== Subject: Re: So what is mass? > As many times as I've been told, I can't seem to keep it straight in my > mind. Is mass an unpecified quantity of matter; according to Newton's > bulk and density, or is it the specific inertia of a body; according to > the ratio of the magnitude of the thrust exerted on and/or by it, > divided by the acceleration caused? > Is the kilogram the unit of mass because we say it is, or is there an > irefutable scientific basis, like a mathematical ratio that makes it > so? > Don > > Why don't you tell us? > I thought you were on a five-year mission to educate us, the befuddled > masses? > It's been more than five-years, and you're still not listening. You're > too busy telling me, and I keep forgetting. > We've got to settle whether mass is an unpecified quantity of matter; > according to Newton's bulk and density, or is it the specific inertia > of a body; according to the ratio of the magnitude of the thrust > exerted on and/or by it; divided by the acceleration caused? > Or is the kilogram the unit of mass because we - the people - say it > is, or is there an irrefutable scientific basis, like a mathematical > ratio that makes it so? > Listen-up; I've got a lot more to teach you people: About the fictional > centrifugal force that throws water out of wet cloths, momentum, > displacement, and a host of related stuff. > Don > Double-A > Maybe you should tell us about those fictional forces now, otherwise > you might forget. I wouldn't forget that, we've been through this several times before; > but I do forget who's so sure that there are no centrifugal forces. Who > claims that centrifugal force is ficticious, but is a necessary > fiction. Centrifugal force is real; it throws water out of wet cloths, > and is what throws the water to the outside of a spinning bucketful, > and slings rocks out from slings. Don Double-A I suppose that the rock feels plenty real when it hits you in the head! Double-A ==== Subject: Re: So what is mass? > As many times as I've been told, I can't seem to keep it straight in my > mind. Is mass an unpecified quantity of matter; according to Newton's > bulk and density, or is it the specific inertia of a body; according to > the ratio of the magnitude of the thrust exerted on and/or by it, > divided by the acceleration caused? > Is the kilogram the unit of mass because we say it is, or is there an > irefutable scientific basis, like a mathematical ratio that makes it > so? Because we say it is. The mathematical ratios are constructions based on the definition of mass. You know two of them. Weight, defined as mass times the local acceleration of gravity. Density, defined as the mass divided by the volume. > Don > > Why don't you tell us? > I thought you were on a five-year mission to educate us, the befuddled > masses? > It's been more than five-years, and you're still not listening. You're > too busy telling me, and I keep forgetting. > We've got to settle whether mass is an unpecified quantity of matter; > according to Newton's bulk and density, or is it the specific inertia > of a body; according to the ratio of the magnitude of the thrust > exerted on and/or by it; divided by the acceleration caused? > Or is the kilogram the unit of mass because we - the people - say it > is, or is there an irrefutable scientific basis, like a mathematical > ratio that makes it so? > Listen-up; I've got a lot more to teach you people: About the fictional > centrifugal force that throws water out of wet cloths, momentum, > displacement, and a host of related stuff. > Don > Double-A > Maybe you should tell us about those fictional forces now, otherwise > you might forget. I wouldn't forget that, we've been through this several times before; > but I do forget who's so sure that there are no centrifugal forces. Who > claims that centrifugal force is ficticious, but is a necessary > fiction. Centrifugal force is real; it throws water out of wet cloths, > and is what throws the water to the outside of a spinning bucketful, > and slings rocks out from slings. Nothing at all. The rock travels in a straight line once the sling stops pulling it in toward the center. The water, too, would like to travel in a straight line, and would too, if not for the bottom of the bucket pushing it in toward the center. The cloth cannot push the water in toward the center and so the water is left behind, to travel on in a straight line while the cloth pulls away from it toward the center. PD >Don >Double-A ==== Subject: Mathematical Model of the universe I have the following thoughts (hypotheses and corollaries) related to mathematics as a model of the universe, which I believe provide some direction to addressing fundamental inconsistencies (such as division by zero, grasping infinity, Godel's Incompleteness Theorem, Russell's Paradox). I have had some math background a long time ago, but please be warned that a lot of this is based on thinking with no recent involvement with math at a deep level. Hence, I believe there is a good chance that I am missing something critical in this analysis. I would appreciate any feedback from math experts/thinkers on these thoughts. A C Hypothesis 1: mathematical analysis is a sensory model like seeing, hearing, etc. This implies that the mind models mathematical analysis in the same way as the mind models visual images. Some characteristics of the sensory model are: a) It has a sense of distance - 1. Example: faraway objects seem closer to each other than similar objects nearby 2. Example: faraway sounds are harder to distinguish than nearby sounds b) The horizon is the limit of our sense, but there is always something beyond the horizon c) All natural surfaces in the sensory model are always curved - earth, space-time Corollary 1: The scale of the number line is not uniform in the mental model of the number line Analogous to our sense of farther things seeming closer to each other than nearby things, similarly, the farther we go, long distances seem like they are very close together till we reach a point where we cannot see any distinction between numbers. Somewhat similar to how lines that are really small get blurred in the eye tests. Corollary 2: Zero is an unperceivable entity We may have 5 apples and then eat them all. But we cannot perceive being left with nothing. There is always something left. Nothingness is a fictitious entity that is convenient from a technological perspective, but does not map to our reality or to our mental sense of math. Corollary 3: Infinity is also unperceivable This is because our mathematical model curves around or gets blurred before we can perceive infinity, just like vision. Hypothesis 2: Inconsistencies within systems of maths (such as Russell's paradox) occur only when we allow for self reference in the system. In the absence of support for self reference, mathematical systems are consistent. Corollary 4: Self recursion is also unperceivable Even though I consider myself a member of the set of all people, it is impossible for the mind (under normal circumstances) to experience the self as completely equivalent to other people. Hence, the only sets I can perceive are all other people and a set containing just me, and note that there is some similarity between the elements. Similarly, in the Russell's paradox, the catalog of books not referencing itself, cannot hold a reference to itself, if it is self aware. If it is not aware of itself as a book, then it is fully consistent without an entry for itself and all other books are covered just fine. ==== Subject: Re: Mathematical Model of the universe I have the following thoughts (hypotheses and corollaries) related to > mathematics as a model of the universe, which I believe provide some > direction to addressing fundamental inconsistencies (such as division > by zero, grasping infinity, Godel's Incompleteness Theorem, > Russell's Paradox). I have had some math background a long time ago, > but please be warned that a lot of this is based on thinking with no > recent involvement with math at a deep level. Hence, I believe there is > a good chance that I am missing something critical in this analysis. I > would appreciate any feedback from math experts/thinkers on these > thoughts. > A C Hypothesis 1: mathematical analysis is a sensory model like seeing, > hearing, etc. This implies that the mind models mathematical analysis in the same way > as the mind models visual images. Some characteristics of the sensory model are: a) It has a sense of distance - > 1. Example: faraway objects seem closer to each other than similar > objects nearby > 2. Example: faraway sounds are harder to distinguish than nearby > sounds > b) The horizon is the limit of our sense, but there is always something > beyond the horizon > c) All natural surfaces in the sensory model are always curved - > earth, space-time > Corollary 1: The scale of the number line is not uniform in the mental > model of the number line Analogous to our sense of farther things seeming closer to each other > than nearby things, similarly, the farther we go, long distances seem > like they are very close together till we reach a point where we cannot > see any distinction between numbers. Somewhat similar to how lines that > are really small get blurred in the eye tests. Corollary 2: Zero is an unperceivable entity We may have 5 apples and then eat them all. But we cannot perceive > being left with nothing. There is always something left. Yeah, but apple cores aren't apples. > Nothingness is > a fictitious entity that is convenient from a technological > perspective, but does not map to our reality or to our mental sense of > math. Corollary 3: Infinity is also unperceivable This is because our mathematical model curves around or gets blurred > before we can perceive infinity, just like vision. Hypothesis 2: Inconsistencies within systems of maths (such as > Russell's paradox) occur only when we allow for self reference in the > system. In the absence of support for self reference, mathematical > systems are consistent. Corollary 4: Self recursion is also unperceivable Even though I consider myself a member of the set of all people, it is > impossible for the mind (under normal circumstances) to experience the > self as completely equivalent to other people. Hence, the only sets I > can perceive are all other people and a set containing just me, and > note that there is some similarity between the elements. Similarly, in the Russell's paradox, the catalog of books not > referencing itself, cannot hold a reference to itself, if it is self > aware. If it is not aware of itself as a book, then it is fully > consistent without an entry for itself and all other books are covered > just fine. ==== Subject: Re: Mathematical Model of the universe 0 + 1 = 1 is the characteristic relationship that identifies our universe. If you wake up and 0 + 1 equals something else, then you must not be in our universe. MD ==== Subject: Re: Re : Manansala Random Number Generator a .8ecrit : There is no such thing as a random number generator, > by definition. >> On the contrary. Among all the number generators, >> choose one at random. How do you randomly choose which number generator to use? What's the > process? Take a dice... > If a die is a random number generator, then why do you need any other ones? ==== Subject: Re: Manansala Random Number Generator Le 17/06/2005 04:00, dans .82ævkarlamov@yahoo.comæ[CapitalEG rave] a .8ecritæ: >> Le 16/06/2005 09:20, dans >> a .8ecrit : > >> > There is no such thing as a random number generator, > by definition. >> >> On the contrary. Among all the number generators, >> choose one at random. >How do you randomly choose which number generator to use? What's the > process? >> >> Take a dice... > If a die is a random number generator, then why do you need any other > ones? > That was a joke initiated by Proginoskes: A random number generator is a random (number generator). Assume a number generator is a perfectly definde class of objects, then you can take one at random. Just take a dice for that :-) Ok, not a very good joke. Anyway, a dice IS a random number generator, actually not much better than a PRNG, for some reasons. The reason why I don't use a dice in Monte Carlo integration is I cannot throw a dice billions of times in few minutes. But to get small random data, I already used a dice, sometimes. Just for fun ;-) ==== Subject: Re: Manansala Random Number Generator .82 vkarlamov@yahoo.com é a .8ecrit : > Le 16/06/2005 09:20, dans >> a .8ecrit : > There is no such thing as a random number generator, > by definition. >> On the contrary. Among all the number generators, >> choose one at random. How do you randomly choose which number generator to use? > What's the process? >> Take a dice... Actually, that should be take a die ... If a die is a random number generator, then why do you need > any other ones? That was a joke initiated by Proginoskes: > A random number generator is a random (number generator). > Assume a number generator is a perfectly defined class of > objects, then you can take one at random. Just take a dice > for that :-) > Ok, not a very good joke. And not initiated by me, either. I parsed it as (random number) generator. > Anyway, a dice IS a random number generator, actually not much > better than a PRNG, for some reasons. The reason why I don't > use a dice in Monte Carlo integration is I cannot throw a dice > billions of times in few minutes. But to get small random data, > I already used a dice, sometimes. Just for fun ;-) There is no such thing as a (random number) generator, but there are pseudorandom number generators which can fool any pattern-searching algorithm. --- Christopher Heckman ==== Subject: Re: Manansala Random Number Generator Le 17/06/2005 07:18, dans a .8ecritæ: > Actually, that should be take a _die_ ... > [...] >And not initiated by me, either. I parsed it as (random number) > generator. > I apologize :-) >There is no such thing as a (random number) generator, but there are > pseudorandom number generators which can fool any pattern-searching > algorithm. There is a funny game: ask someone to give you some random numbers (without any computationnal or mechanical help), and try to guess. There are programs very good at such a guess (maybe one was called SAGACE ?). ==== Subject: Re: Manansala Random Number Generator > That was a joke initiated by Proginoskes: > A random number generator is a random (number generator). > Assume a number generator is a perfectly defined class of > objects, then you can take one at random. Just take a dice > for that :-) > Ok, not a very good joke. >And not initiated by me, either. I believe I deserve the credit/blame. > There is no such thing as a (random number) generator, but there are > pseudorandom number generators which can fool any pattern-searching > algorithm. Careful. For every pattern-searching algorithm (psa, for short) there is a pseudorandom number generator (prng) which can fool it. I don't think it's true that there exists a prng G such that, for every psa A, G can fool A. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) ==== Subject: Re: Manansala Random Number Generator Le 17/06/2005 08:15, dans gerry-6EF844.16150717062005@sunb.ocs.mq.edu.au, .82æGerry Myersonæé a .8ecritæ: > Careful. For every pattern-searching algorithm (psa, for short) > there is a pseudorandom number generator (prng) which can fool it. > I don't think it's true that there exists a prng G such that, for > every psa A, G can fool A. The psa would probably be quite complex for a crypto prng. But that doesn't mean it doesn't exist, you're right. ==== Subject: Re: Manansala Random Number Generator A dice is not truly like a PRNG because the result can be easily manipulated to what you want it to be. You just tilt the hand and cause a little spin with the right number on top to start with you can most of the time rig the result. Nothing really generates random numbers, least of all a computer -- which is designed to take input and produce output. Not exactly random, escpecially when it uses binary which only knows completely false (0) or completely true (1). Just food for thought... -Black Cat ==== Subject: Re: Manansala Random Number Generator > In cryptography, they say the PRNG must be cryptographically-strong. > The main one is used is known as Blum Blum Shub, but it is not good at > churning out numbers rapidly. It has to generate two long primes, the > product of which it takes one bit or maybe a few bits from. >It can't really spit out enough numbers for one-time pad encryption. A one time pad, by definition, is generated truly randomly. You're confusing a stream cipher with a one-time pad, one of the strongest signs of cryptographic snake oil. - Tim ==== Subject: Re: Manansala Random Number Generator A stream cipher uses a small random string over and over. They just continually XOR with everything in sight. A one time pad uses a random string the same length as the message. As for truly random, that is a relative term. Machines are too orderly to simulate true randomness. Even those that observe some natural phenomenon are usually constraining it in some way. Cryptographic randomness is about equiprobability and resistance to prediction. As long as you have these and can produce enough random numbers, you can one-time pad. ==== Subject: Re: Manansala Random Number Generator > A stream cipher uses a small random string over and over. They just > continually XOR with everything in sight. RSA Security - 2.1.5 What is a stream cipher? http://www.rsasecurity.com/rsalabs/node.asp?id=2174 HTH. HAND. - Tim ==== Subject: Re: Manansala Random Number Generator A one-time pad, sometimes called the Vernam cipher [Ver26], uses a string of bits that is generated completely at random. The keystream is the same length as the plaintext message and the random string is combined using bitwise XOR with the plaintext to produce the ciphertext. ...the fact that the secret key (which can be used only once) is as long as the message introduces severe key management problems. Basically, the problem has been producing strong random numbers fast enough. Most key systems use probabilities to avoid reusing keys. Otherwise there would have to be some central accounting firm recording every session key ever used. ==== Subject: Re: Manansala Random Number Generator > Basically, the problem has been producing strong random numbers fast > enough. No, that's actually not difficult with a good hardware RNG. The problem with a one time pad is getting such a huge key to the intended recipient without interception, and keeping it safe at both ends. As you ought to know. - Tim ==== Subject: Re: Manansala Random Number Generator Hardware generators aren't practical for wide usage. You don't have to send the whole key. Which isn't necessarily huge, just the size of the message. All you have to is send in the seed (another random number) that generates the key. And the random number that is produced must be not have any repeat cycles, loops, etc. MEAS http://addr.com/~apu/encrypt.pdf ==== Subject: Re: Manansala Random Number Generator > All you have to is send in the seed (another random number) that > generates the key. You're talking about a stream cipher, _again_. As I said a few messages back -- you're confusing a stream cipher with a one time pad, which is one of the surest signs of cryptographic snake oil. > And the random number that is produced must be not have any repeat ^^^^^^ > cycles, loops, etc. You misspelled pseudorandom. - Tim ==== Subject: Re: Manansala Random Number Generator I'm referring to producing one random byte for each plaintext byte. It's arguable that all one-time pads have been pseudo-random. The random bytes produced here do not have periods or loops in which sequences repeat ad infinitum, which is the main concern with all other pseudo-random numbers along with speed, and the bytes here have random distribution. But you may believe what you like. ==== Subject: Re: Manansala Random Number Generator > If you had two PRNG and ran them, put the two resulting number together to > form a string of digits, then use another PRNG to select a start point > within that string of numbers (assuming cyclic boundaries), and another to > select a random string lenght to choose from the original string, would that > be more random? Let's see ... here's one not-very-random PRNG. Does this procedure make it better? int rnd() { return 1 } First random number: 1 Second random number: 1 giving: 11 Start point: 1 Length: 1 Result: 1 Nope. - Tim ==== Subject: Re: Manansala Random Number Generator yeah, as has been said there is no such thing as completely random numbering generating. As a matter of fact, it is impossible for anything to truly be random. A dice is controlled by it weight, the angle at which it falls, at what speed, etc. So really, nothing can be random. Everything is governed by phsyical laws or another force. For every effect there is a cause. That was sort of a random post (pun intended) but I thought it needed to be said. Nothing can happen by true chance. Which would throw out at least a few branches of mathematics and science... We'll start with probability... -Black Cat ==== Subject: Re: To what purpose > The weight of the artifact at Sevres is not 9.80665 N, not unless you > happen to be at a location -- not Sevres -- where g = 9.80665 m/s/s. > In order to be ONE kilogram the weight (w) of any artifact made to > accurately represent it must be numerically equal to the acceleration > (g) at which it will free fall; so that w/g=1. > You are missing the key point that they did not have to *weigh* this > artifact (by which I mean find its weight). They established its > *mass*, not its weight. > I don't think establishing mass is possible without finding weight > first. What is a body's mass, if not weight divided by the acceleration > of free fall; or force, divided by the acceleration caused by that > force? That is incorrect. There are lots of ways of establishing mass, some of > which I've mentioned before. For example, one way is to put the mass as > the load of an oscillator. The frequency of the oscillation depends on > the mass, not the weight. > It's a subtile difference, but the frequency of the oscillation depends on the inertia - the _measure_ of the mass. > A dual-pan balance is a way of comparing *masses*, because the local > value of g cancels out the numerical equivalence -- its value is not > needed to establish the balance. > The value of any mass is it's inertia, and a balanced beam scale will balance anywhere, and/or give the same reading anywhere. > If you were right, and if weight were the primary physical quantity > upon which mass were based, then you would be absolutely right: the > value of g would be crucial for establishing the standard. But you're > not right. > Weight is not the primary physical quantity upon which mass is based: Force and weight are only _one_ of the three primary physical quantities upon which mass is based: Mass (m)=w/g=ft/s/t=ft^2/s. Weight (w)=(m)g=(w/g)g. Don > upon which mass > Mass is the primary standard. Weight is a quantity derived from mass. PD > Don > PD > > It being physically impossible to make anything that accurate, rules > out the artifact at Sevres, regardless of (g); there or anywhere. > The artifact at Sevres, or anywhere else, is approximate at best. With > the improvement of manufacturing accuracy, we might do just a little > better in the next batch. Sounds like the makings of another pork > barrel project. >Don >PD ==== Subject: Re: To what purpose > The weight of the artifact at Sevres is not 9.80665 N, not unless you > happen to be at a location -- not Sevres -- where g = 9.80665 m/s/s. > In order to be ONE kilogram the weight (w) of any artifact made to > accurately represent it must be numerically equal to the acceleration > (g) at which it will free fall; so that w/g=1. > You are missing the key point that they did not have to *weigh* this > artifact (by which I mean find its weight). They established its > *mass*, not its weight. > I don't think establishing mass is possible without finding weight > first. What is a body's mass, if not weight divided by the acceleration > of free fall; or force, divided by the acceleration caused by that > force? That is incorrect. There are lots of ways of establishing mass, some of > which I've mentioned before. For example, one way is to put the mass as > the load of an oscillator. The frequency of the oscillation depends on > the mass, not the weight. It's a subtile difference, but the frequency of the oscillation depends > on the inertia - the _measure_ of the mass. No, not the _measure_ of the mass, but the mass itself. It depends on how much stuff is there, period. I do not need to measure the mass to determine this behavior of the oscillation. I simply have to double the amount of stuff by doubling the object or taking two of them combined, and I see the period goes up by the square root of two. Since the amount of stuff is by definition the mass, the oscillation frequency depends on the mass, not the _measure_ of the mass. A dual-pan balance is a way of comparing *masses*, because the local > value of g cancels out the numerical equivalence -- its value is not > needed to establish the balance. The value of any mass is it's inertia, and a balanced beam scale will > balance anywhere, and/or give the same reading anywhere. And note that means that the value of g is irrelevant to the mass, then. If you were right, and if weight were the primary physical quantity > upon which mass were based, then you would be absolutely right: the > value of g would be crucial for establishing the standard. But you're > not right. Weight is not the primary physical quantity upon which mass is based: > Force and weight are only _one_ of the three primary physical > quantities upon which mass is based: Mass (m)=w/g=ft/s/t=ft^2/s. > Weight (w)=(m)g=(w/g)g. Weight is NONE of the primary physical quantities on which mass is based. Mass is the basis, the others are based on it. Don upon which mass > Mass is the primary standard. Weight is a quantity derived from mass. PD > Don > PD > > It being physically impossible to make anything that accurate, rules > out the artifact at Sevres, regardless of (g); there or anywhere. > The artifact at Sevres, or anywhere else, is approximate at best. With > the improvement of manufacturing accuracy, we might do just a little > better in the next batch. Sounds like the makings of another pork > barrel project. >Don >PD ==== Subject: Re: To what purpose > The weight of the artifact at Sevres is not 9.80665 N, not unless you > happen to be at a location -- not Sevres -- where g = 9.80665 m/s/s. > In order to be ONE kilogram the weight (w) of any artifact made to > accurately represent it must be numerically equal to the acceleration > (g) at which it will free fall; so that w/g=1. > You are missing the key point that they did not have to *weigh* this > artifact (by which I mean find its weight). They established its > *mass*, not its weight. > I don't think establishing mass is possible without finding weight > first. What is a body's mass, if not weight divided by the acceleration > of free fall; or force, divided by the acceleration caused by that > force? > That is incorrect. There are lots of ways of establishing mass, some of > which I've mentioned before. For example, one way is to put the mass as > the load of an oscillator. The frequency of the oscillation depends on > the mass, not the weight. > It's a subtile difference, but the frequency of the oscillation depends > on the inertia - the _measure_ of the mass. No, not the _measure_ of the mass, but the mass itself. It depends on > how much stuff is there, period. I do not need to measure the mass to > determine this behavior of the oscillation. I simply have to double the > amount of stuff by doubling the object or taking two of them combined, > and I see the period goes up by the square root of two. Since the > amount of stuff is by definition the mass, the oscillation frequency > depends on the mass, not the _measure_ of the mass. > Naive conclusion(;^) > A dual-pan balance is a way of comparing *masses*, because the local > value of g cancels out the numerical equivalence -- its value is not > needed to establish the balance. > The value of any mass is it's inertia, and a balanced beam scale will > balance anywhere, and/or give the same reading anywhere. And note that means that the value of g is irrelevant to the mass, > then. > If you were right, and if weight were the primary physical quantity > upon which mass were based, then you would be absolutely right: the > value of g would be crucial for establishing the standard. But you're > not right. > Weight is not the primary physical quantity upon which mass is based: > Force and weight are only _one_ of the three primary physical > quantities upon which mass is based: Mass (m)=w/g=ft/s/t=ft^2/s. > Weight (w)=(m)g=(w/g)g. > The value of g varies with location, and is why a body's weight varies: The ratio of a body's weight, to the acceleration at which it will free fall is a constant; equal to the ratio of the force exerted on, and/or by it, to the acceleration it causes. A body's mass (m) is a ratio equal to its weight, divided by the acceleration at which it will free fall; which is equal to the ratio of the force exerted, to the rate of displacement the force causes. > Weight is NONE of the primary physical quantities on which mass is > based. Mass is the basis, the others are based on it. > Don > upon which mass > Mass is the primary standard. Weight is a quantity derived from mass. > PD > > Don > PD > > It being physically impossible to make anything that accurate, rules > out the artifact at Sevres, regardless of (g); there or anywhere. > The artifact at Sevres, or anywhere else, is approximate at best. With > the improvement of manufacturing accuracy, we might do just a little > better in the next batch. Sounds like the makings of another pork > barrel project. >Don >PD ==== Subject: Re: Ideals and Varieties I was looking at the proof as as function from Varieties to Ideals, and the reverse, and was trying to think of the approach to proving the theorem from drawing diagrams, such as drawing a function's domain to range, and inverse image. This kind of thinking can come later, after a proof . ==== Subject: Re: mathematician salaries X-Nntp-Posting-Host: user-48.gradstudents.utoronto.ca X-Rfc2646: Format=Flowed; Original Only the idiot Mark would make such a notice. > officially closed. Nobody should post here anymore. > Marky Mark Demers PhD, AB, BS > ==== Subject: Re: mathematician salaries >officially closed. Nobody should post here anymore. >Marky Mark Demers PhD, AB, BS Whenever someone tells me that something is official, I ask what Office has the power to make that decree. The thread now officially re-opened. (Is not! Is too! Is not! ...) ==== Subject: Re: mathematician salaries Mark's power comes from the people. Mark's supporters shall ignore Dave Rusin's post. Dave will see. Time will tell. MD ==== Subject: Re: mathematician salaries On 16 Jun 2005 18:58:33 -0700, double d Dave Rusin's post. Uh, right. So far we don't have any evidence that Mark _has_ any supporters... >Dave will see. Time will tell. > MD ************************ David C. Ullrich ==== Subject: Re: mathematician salaries <97d5b1tdln9e5mdf9uhsiond3fovvv0tfl@4ax.com> Daivd & Randy can't resist the urge to have the final word in Mark's House, can they? The situation is win-win for Mark: a) If they cease posting as Mark requested, they fullfill Mark's prediction that, as Mark's supporters, Nobody should post here any more. Time will tell. b) If they continue to submit posts, they promulgate Mark's thread, consummate it with a trailer, which is fullfilling to Mark. Either way, David & Randy fullfill Mark. This is a halcyon win-win Father's Day moment for Mark. Mark needs a cigarette now. Mark Demers, PhD EquityValue Investments ==== Subject: Re: mathematician salaries On 17 Jun 2005 08:08:28 -0700, double d House, can they? >The situation is win-win for Mark: > a) If they cease posting as Mark requested, they fullfill Mark's >prediction that, as Mark's supporters, Nobody should post here any >more. Time will tell. > b) If they continue to submit posts, they promulgate Mark's thread, >consummate it with a trailer, which is fullfilling to Mark. Either way, David & Randy fullfill Mark. Given that Mark is the kind of guy who feels that having a huge number of people call him an idiot means that his thread was a big success, I doubt that David or Randy have much concern over this aspect of things. >This is a halcyon win-win >Father's Day moment for Mark. Mark needs a cigarette now. Mark Demers, PhD >EquityValue Investments ************************ David C. Ullrich ==== Subject: Re: mathematician salaries <97d5b1tdln9e5mdf9uhsiond3fovvv0tfl@4ax.com On 16 Jun 2005 18:58:33 -0700, double d Mark's power comes from the people. Mark's supporters shall ignore >Dave Rusin's post. Uh, right. So far we don't have any evidence that Mark _has_ > any supporters... Or a job. - Randy ==== Subject: Re: mathematician salaries officially closed. Nobody should post here anymore. Marky Mark Demers PhD, AB, BS ==== Subject: Re: HyperVolumes X-Rfc2646: Format=Flowed; Original > 2) However for (geometric) spheres it seems that V(n) is not monotonic >> and is in fact determined by Gamma (n) with a maximum when n is more than >> 7. For n > 7, V(Sphere) reduces with increasing n. I suspect that you mean 5, rather than 7. For example, see the first graph > at , an interesting page, mentioned in another sci.math thread recently. Some people point out, as though it were of special interest, that, for an > n-ball of unit radius, volume reaches its maximum at n = 5. But I see no > reason why that should be of special interest. The value of n at which > maximum volume is reached is _radius-dependent_. What is interesting is that, regardless of the radius of the n-ball, its > volume must _eventually_ decrease as n increases. > that covers basic hyper geometry ? ==== Subject: simple perpindicular lines in 3D I have a trick for 2D perpinduclar lines that I'm not sure extends to 3D. Perhaps you can help. If I assume that all my points represent lines from the origin (they are vectors) then to find a line perpindicular to 1,5 I can swapt the values then negate any one of them. So 1,5 is perpinduclar to 5,-1 (again all lines from the origin). But I haven't been able to extend this trick into 3D. Is this possible? For example: is 1,5,2 perp to 5,-1,2 (its not)? ==== Subject: Re: simple perpindicular lines in 3D They should be perpendicular in 3d as well : m1m2= -1 is the formula for perpendicular lines of form y=m1x+c1 and y=m2x+c2. Since in 3d, by keeping z constant, you are working on the same xy plane, 1,5,2 shd be perpendicular to 5,-1,2. - A C ==== Subject: Re: simple perpindicular lines in 3D > They should be perpendicular in 3d as well : m1m2= -1 is the formula > for perpendicular lines of form y=m1x+c1 and y=m2x+c2. Since in 3d, by > keeping z constant, you are working on the same xy plane, 1,5,2 shd be > perpendicular to 5,-1,2. This fails for lines orthogonal to the xy-plane. In fact, it is impossible to make a continuous choice of orthogonal lines that works for all possible lines through the origin. For if there were such a continuous choice of orthogonal lines then one could use this to construct a continuous nowhere vanishing tangent vector field to the unit sphere, contradicting the hairy ball theorem from topology. (The idea is to think of a given point on the unit sphere as defining a line through the origin. The continuous choice of orthogonal lines then gives us an orthogonal line, which may be identified with a unit tangent vector at the given point of the sphere.) Your method can be made to work for all lines by treating the case of lines orthogonal to the xy-plane separately. Per ==== Subject: Re: simple perpindicular lines in 3D are u certain of this? recall that the other end point is at z = 0, and so i'm not sure if this is still as though its a simple 2D problem. I could be wrong. Also, there dot product does not = 0, dot product of 1,5,2 and 5,-1,2 = 1*5 + -1*1 + 2*2 = 4. ==== Subject: Re: simple perpindicular lines in 3D > are u certain of this? recall that the other end point is at z = 0, > and so i'm not sure if this is still as though its a simple 2D problem. > I could be wrong. Also, there dot product does not = 0, dot product of 1,5,2 and 5,-1,2 = 1*5 + -1*1 + 2*2 = 4. I'm sure he meant to zero out the z component. Then it works out except in the case where x and y are both zero (i.e. the line is parallel to the z-axis or, equivalently, orthogonal to the xy-plane). Per ==== Subject: Re: simple perpindicular lines in 3D hairy ball theorem? I'm not aware of that one. That doesn't sound like a mathematical concept to me, but i'm not a mathetician :) Anyway, I guess my question is is there any simple method similar to the swap and negate method that works? ==== Subject: Re: simple perpindicular lines in 3D > hairy ball theorem? I'm not aware of that one. That doesn't sound like a mathematical > concept to me, but i'm not a mathetician :) Try looking it up. :) > Anyway, I guess my question is is there any simple method similar to > the swap and negate method that works? I already a modification of his method that will work: Given a direction vector (x, y, z), if either x != 0 or y != 0, then you may use (-y, x, 0) as an orthogonal direction vector. If x = 0 and y = 0 then z != 0 and hence you may use (0, -z, y) as an orthogonal direction vector. Per ==== Subject: Re: simple perpindicular lines in 3D Hm...that does not seem correct to me for some reason. So the lines 0,0,0 to 1,1,1 and 0,0,0 to -1,1,0 are perpinduclar? Thats odd. There dot product does equal zero, but is the dot product relationship to 0 a if AND only if relationship? ==== Subject: Re: simple perpindicular lines in 3D ==== Subject: Re: simple perpindicular lines in 3D > Hm...that does not seem correct to me for some reason. So the lines > 0,0,0 to 1,1,1 and 0,0,0 to -1,1,0 are perpinduclar? Thats odd. There > dot product does equal zero, but is the dot product relationship to 0 a > if AND only if relationship? As long as both direction vectors are nonzero then, yes, the dot product is 0 if and only if the corresponding lines are geometrically orthogonal. (A zero direction vector does not correspond to a line, of course.) In general it's true that if V and W are vectors then V.W = |V| |W| cos(angle(V,W)) where the angle is measured in the plane spanned by V and W. You can confirm this in the three-dimensional case under consideration by looking at right triangles. A perhaps better (and certainly more general) method is to reduce the problem to the two-dimensional case by a rotation of the vectors into the xy-plane. Per ==== Subject: Question about metalanguage In axiomatic set theory reference is made to the object language (the language in which we talk about sets) and the metalanguage (the language in which we talk about the object language). It is claimed that paradoxes arise from having available in the language expressions for referring to other expressions in the language. In Tarki's words, ... the semantical concepts simply have no place in the language to which they relate, that the language which contains its own semantics, and whithin the usual logical laws hold, must inevitably by inconsistent. Can someone please explain what is the metalanguage in the context of set theory? It is presumably needed to avoid paradoxes, so it would be very useful if we could have some examples of the trouble we would face if it were not available. I'm having a real hard time understanding this. ==== Subject: Re: Question about metalanguage > In axiomatic set theory reference is made to the object language (the > language in which we talk about sets) and the metalanguage (the > language in which we talk about the object language). It is claimed > that paradoxes arise from having available in the language expressions > for referring to other expressions in the language. In Tarki's words, > ... the semantical concepts simply have no place in the language to > which they relate, that the language which contains its own semantics, > and whithin the usual logical laws hold, must inevitably by > inconsistent. > For example this statement is false > Can someone please explain what is the metalanguage in the context of > set theory? It is presumably needed to avoid paradoxes, so it would be > very useful if we could have some examples of the trouble we would face > if it were not available. I'm having a real hard time understanding > this. > It's the informal language used to describe the formal language of set theory including a description of first order logic and its axiom schemata. ==== Subject: Fitting matrix of data to 2D parabola without using iterative technique I have a grid of 2D sampled data arranged in a matrix, that I have had a fair amount of success fitting to a simple (concave) 2D parabola. In either MATLAB or Excel I minimize the error of the formula: (Vi,Vj) = Extrema - R*[ (Rowi-RowExtrema)^2 + (Colj-ColExtrema)^2] to the actual samples. Since the 2D parabola is known to be concave, I'll just change the names of the variables: (Vi,Vj) = Max - R*[ (Rowi-RowMax)^2 + (Colj-ColMax)^2] where Rowi & Colj are logical (1,2,3,...) indices into my matrix, and Max, R, RowMax, and ColMax are allowed to float. So I optimize to the sum of the errors [ (Di-Vi)^2 + (Dj-Vj)^2 ] where (Di,Dj) are my samples and (Vi,Vj) come from the formula above. This works just fine, but now that I need to integrate the above into an embedded system I would very much like to avoid an iterative procedure, i.e. utilizing a general minimization routine. In a related part of the system I actually need to fit a set of 3x3 samples to a plane, which one can easily do using the cross-product. The draw-back to that method is that you don't use all of the data at your disposal; hence I set up a linear least-squares problem to directly solve for ax+by+cz+d = 0. I could of course have gone the minimization route, but a direct solution is always preferable. Is there such a way of accomplishing much the same thing with the problem I have above? Is there a nonlinear least squares solution to this problem? Should I use a nonlinear regression technique? Is it relatively simple to linearize my problem? Any pointers would be most appreciated. Shehrzad Qureshi ==== Subject: Re: Fitting matrix of data to 2D parabola without using iterative technique >I have a grid of 2D sampled data arranged in a matrix, that I have had >a fair amount of success fitting to a simple (concave) 2D parabola. In >either MATLAB or Excel I minimize the error of the formula: > >(Vi,Vj) = Extrema - R*[ (Rowi-RowExtrema)^2 + (Colj-ColExtrema)^2] > >to the actual samples. Since the 2D parabola is known to be concave, >I'll just change the names of the variables: > >(Vi,Vj) = Max - R*[ (Rowi-RowMax)^2 + (Colj-ColMax)^2] > >where Rowi & Colj are logical (1,2,3,...) indices into my matrix, and >Max, R, RowMax, and ColMax are allowed to float. So I optimize to the >sum of the errors [ (Di-Vi)^2 + (Dj-Vj)^2 ] where (Di,Dj) are my > samples and (Vi,Vj) come from the formula above. > >This works just fine, but now that I need to integrate the above into >an embedded system I would very much like to avoid an iterative >procedure, i.e. utilizing a general minimization routine. In a related >part of the system I actually need to fit a set of 3x3 samples to a >plane, which one can easily do using the cross-product. The draw-back >to that method is that you don't use all of the data at your disposal; >hence I set up a linear least-squares problem to directly solve for >ax+by+cz+d = 0. I could of course have gone the minimization route, but >a direct solution is always preferable. > >Is there such a way of accomplishing much the same thing with the >problem I have above? Is there a nonlinear least squares solution to >this problem? Should I use a nonlinear regression technique? Is it >relatively simple to linearize my problem? Any pointers would be most >appreciated. > > >Shehrzad Qureshi > for the plane fitting problem there is a simple solution, since this can be cast into a linear problem: you have 9 points and 4 unknowns clearly you may scale the unknown vector to be of length one. then the compute the matrix A=[1 x y z ] (a 9 times 4 matix) and its smallest singular value and the corresponding right singular vector. then (a,b,c,d) is this vector, you may normalize it to a^2+b^2+c^2=1. this is not exactly the orthogonal least distance plane, but usually very near to it. you may use this as input for a simple minded minimizer like a grid search (pattern search) might work here, if you want to do the best possible. the first problem is nonlinear as you formulated it. but, given Rowmax and Colmax it becomes linear in R and Max, and you can even express this dependence in rather simple closed formulae. now it remains to do a search in the rowmax colmax -plane. again a pattern search might do sufficiently good. the codes you need here are very compact, hence integrating it into an embedded system should be possible. hth peter ==== Subject: Thinning stream of water Don McDonald Nov 22 2001, 10:26 pm hide options Thinning stream of water it isn't uniform rectilinear motion. the vertical acceleration is only approx. g. parabola. so the form-shape of a stream from tap-faucet is crudely rectangular hyperbola? to narrow the stream there must also be horizontal fluid forces. 17.6.05. author Local: Thurs,Nov 22 2001 10:26 pm ==== Subject: Re: Thinning stream of water don: could be my words. ... Turn off a tap - faucet. Look at the form - shape of the fountain. Look at Nobel prize scientist - fountain of liquid Helium ** richard feynmann. I did a calculation Mensa New Zealand 1976-77. It involved 10th root. Accel due to gravity, Flow Q. Fluid rising through base of cylinder changes direction/speed and is expelled through sides. don.lo...@paradise.net.nz parabola mcdonald. - Hide quoted text - - Show quoted text - don.lotto nz 17.6.05 ==== Subject: Re: Thinning stream of water I missed the purpose of the post. What's the question? PD ==== Subject: Re: Thinning stream of water > I missed the purpose of the post. What's the question? PD I suppose that it related to the cross sectional area of a stream of water from a pipe or tap. If the discharge is horizontal the horizontal velocity decreases in relation to the resistance of the air. The vertical velocity depends on gravity and the resistance of the air. As the velocity increases the cross sectional area of the stream must decrease. R > ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! X-RFC2646: Format=Flowed; Original > In sci.math, F1refly > <42b16872$0$3073$c30e37c6@ken-reader.news.telstra.net>: > http://www.supernerd.com.au/~gray77/truman-challenge.html > This will prove I am the Truman and the Govt. spies on me and follows > me everywhere with a satellite PA system. >> How does a PA system in a satellite work? Sure they can hang dirty great >> speakers off a satellite but we won't hear anything because there's no >> air >> in space. Pedant Point: there *is* stuff in space -- the solar wind. But > the speakers still won't work as there's not enough of it. > There may be stuff in space but there's no air. ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! <42b12f0b$1_2@news.melbourne.pipenetworks.com> EMAIL : me AT contactme DOT com If you can make your intentions to fly to Townsville clear then do so. If not then stop lying that I backed out. Herc ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! > EMAIL : me AT contactme DOT com If you can make your intentions to fly to Townsville clear then do so. > If not then stop lying that I backed out. Graham, I did. You then spent a week blithering and ranting. ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! <42b12f0b$1_2@news.melbourne.pipenetworks.com> I'll fly anyone on East coast Australia to Townsville to prove I'm the Truman. [Trev] : I'll take the free plane ticket to townsville! [Herc] : Behold the 1st live witness to the Truman Show Here's my email, let me know what date this month and your address to send the ticket to. [Trev] : That doesn't reassure me if all the other witnesses are dead. [Herc] : So you're just full of BS all along, you wont take the free ticket? [Trev] : You backed out, you backed out, you backed out... ad nausiam. You're just SO FULL OF TREV I can't believe the drivel you continually spew. Really just STOP WASTING MY TIME with your lies and abuse. That's TWICE I've said OK I NEED YOUR DETAILS BEFORE I BUY THE TICKET If you expect me to buy a $300 ticket for you when you act like this and wont tell me where to send the ticket to or whos name to put it in, YOUR FREAKING STUPID. Herc ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! > [Herc] : > I'll fly anyone on East coast Australia to Townsville to prove I'm the > Truman. [Trev] : > I'll take the free plane ticket to townsville! [Herc] : > Behold the 1st live witness to the Truman Show > Here's my email, let me know what date this month and your address to > send the ticket to. [Trev] : > That doesn't reassure me if all the other witnesses are dead. [Herc] : > So you're just full of BS all along, you wont take the free ticket? Wow, selective editing there Graham. ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! <42b12f0b$1_2@news.melbourne.pipenetworks.com> <67qse.2145$Zn.98132@news.optus.net.auWow, selective editing there Graham. Really? You have a point to make then make it Herc ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! >Wow, selective editing there Graham. Really? You have a point to make then make it Yes, your selective editing ommitted the part where I replied to a thread titled from you aus.tv's first live Truman witness - I joked about you having killed all the others - then you decided to go off your trolley and use it as an excuse to not give me the plane ticket. It's all here you fruitcake. 6/9ba88b8f669a3799?q=witnesses+are+dead+aus.tv&rnum=2#9ba88b8f669a3799 ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! <42b12f0b$1_2@news.melbourne.pipenetworks.com> <67qse.2145$Zn.98132@news.optus.net.au> Gee my memory's good...... [Herc] ping Trev ----- aus.tv's first live Truman witness need your address to send the ticket. will be on Tues or Wed mid May. depart Brisbane 8:45am depart Townsville 4:45pm easy to remember, 9 to 5 Gives us a few hours to go shopping, your shout if you agree I'm the Truman! email is me AT contactme DOT com [Trev] You trying to say all the other witnesses to the Truman are dead? Doesn't inspre me with much confidence Graham. [Herc] you're gutless after all, wont meet someone at an airport. stop wasting my time. OK, who wants a free same day return flight to Townsville mid May? No time wasters like Trev the wonder loser here,I will be spending $250 on tickets going to your address so if you don't turn up I'll be mighty pissed. But if you can make it, and you're not a hopeless loser like Trev here spouting all year to take the challenge then winging his way out then the free tickets are yours. The only catch is you have to put FREE-TRUMAN in your sig till 2010 if you see the truth... Herc [Koenig] >you're gutless after all, wont meet someone at an airport. >stop wasting my time. Ah, I see yet again you are backing out of it. Typical. -- Trev [Herc] what gave it away, I need your address to send the ticket, the email me or the departure dates and times? Don't email me your particulars = no plane ticket for Trev. ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! <42B16B08.7A3240C5@tall.com> Again you're all so sure of yourselves, dozens of you all programmed by TV to think a TRUMAN is just deluded. Yet if I say, OK eveyone paypal Ghost $100, I'll buy plane tickets for 2 aus.tv subscribers in Brisbane of your choice to witness the satelite broadcasting mind probe (yes I know I wouldn't believe it either until I head it). Then, like all usenet posters who have ACTUALLY BEEN TO TOWNSVILLE ALL SAY... yes Herc is the Truman. Then I get $100 off 10 or 20 of you. I'll match the bets and paypal ghost in advance aswell. Now your LACK OF EVIDENCE, and COMPLETE IGNORANCE by NEVER BEING NEAR THE CLAIMANT will clearly show. Here's the original offer again. 121 Days have passed and no skeptic has claimed the $1000 debunkers prize. The TRUeMAN CHALLENGE Can a qualified skeptic prove the Truman is a hoax? I will pay you $1,000 AU to meet me for 30 seconds in the centre of Flinders Mall Townsville Qld. This will prove I am the Truman and the Govt. spies on me and follows me everywhere with a satellite PA system. Now if Randi can say..... PARANORMAL IS BS because nobody has won the $1,000,000. Then surely I can say.... SKITZO FREE ASSOCIATING DEFECTIVE QUACK SKEPTIC WANNABE'S are full of BS too. Really this is all you've got. HERC : IM THE TRUMAN 1,000 outspoken usenutters and 100,000 stupid onlookers : NO WAY NO WAY THE CLAIM STANDS NO DOUBT ABOUT IT Herc ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! >Again you're all so sure of yourselves, dozens of you all programmed by >TV to think a TRUMAN is just deluded. Somebody please parse that for me. >Then, like all usenet posters who have ACTUALLY BEEN TO TOWNSVILLE ALL >SAY... yes Herc is the Truman. Oh yes - there's some secret mind control or whatever thingie where one person is the most watched on earth, and they pick a guy living in a mid-sized port city on the northeast cost of Australia. This is like decideding to be a movie star, and moving to Dubuque, Iowa. * P.S. Actually, Dubuque has about 15 times the population of Townsville. -- * PV something like badgers--something like lizards--and something like corkscrews. ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! HERC777 says... > Again you're all so sure of yourselves, dozens of you all programmed by > TV to think a TRUMAN is just deluded. If I understand the movie correctly and you're the Truman, we'd all already know you were (seeing that there would be a channel dedicated to your exploits) so this whole exercise of us (the viewing public) would be pointless. I just wish someone would tell me the channel so I don't accidently stumble across it late one night after having a few too many down the pub and wonder what the hell was going on. I hate being kept out of the loop. Rod. ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! X-RFC2646: Format=Flowed; Original Then, like all usenet posters who have ACTUALLY BEEN TO TOWNSVILLE ALL > SAY... yes Herc is the Truman. Odd, there's no mention of this in the local newspaper or listed among the attractions of the town. Maybe we should all email the chamber of commerce thre and ask why they don't sell Herc tours. ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! In sci.math, HERC777 on 16 Jun 2005 17:25:09 -0700 > Again you're all so sure of yourselves, dozens of you all programmed by > TV to think a TRUMAN is just deluded. Yet if I say, OK eveyone paypal Ghost $100, I'll buy plane tickets for > 2 aus.tv subscribers in Brisbane of your choice to witness the satelite > broadcasting mind probe (yes I know I wouldn't believe it either until > I head it). How nice, I could get rich that way. There's only two eentsy teensy tiny flaws in your proposal. [1] I don't think I'd want to do that; too much hassle. [2] I don't have a Paypal, pal. :-P [rest snipped] -- #191, ewill3@earthlink.net It's still legal to go .sigless. ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! >Again you're all so sure of yourselves, dozens of you all programmed by >TV to think a TRUMAN is just deluded. Yet if I say, OK eveyone paypal Ghost $100, I'll buy plane tickets for >2 aus.tv subscribers in Brisbane of your choice to witness the satelite >broadcasting mind probe (yes I know I wouldn't believe it either until >I head it). Then, like all usenet posters who have ACTUALLY BEEN TO TOWNSVILLE ALL >SAY... yes Herc is the Truman. Not true, idiot. I've been to Townsville, and I know you are a 24 carat loon. -- Find out about Australia's most dangerous Doomsday Cult: http://users.bigpond.net.au/wanglese/pebble.htm You can't fool me, it's turtles all the way down. ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! <42B16B08.7A3240C5@tall.com> Results 1 - 10 of 1,840 for author:anglesea KOOK You were on one of your KOOK HUNTING expeditions right? Wally professionally tracks down cult leaders. Herc ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! X-RFC2646: Format=Flowed; Original Where would you get the $1000 from? You claim you're too broke to record what you hear and post it on the internet, yet you're ready to fork out $1000 for a claim you believe will be verified. -- Katharine I believe five out of four people have trouble with fractions. ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! <42B16B08.7A3240C5@tall.com> <42b220c8$0$13943$afc38c87@news.optusnet.com.au> If you totally ignore my post and reply with insignificant hand waving rubbish then I'll do the same. Herc -- The most prestigious ritual of the wealthy and elite is to take a swig from 20 wine bottles and spit! ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! X-RFC2646: Format=Flowed; Original >> The difference between what Herc believes and what most christians >> believe is that one is more likely to get you committed. Which one? It's all about context. * Herc's beliefs will gather much more attention and would be the more likely. The only time I've seen Christian beliefs cause such a problem happened when the woman. who was told by god to wait inside her apartment for a message was when the rent ran out and they tried to evict her. Just outside the front door, me on one arm and my attendant on the other, she stopped dead. She looked at me and said she was sorry, then looked up at the sky and said Strike them dead Lord. Later,on the ay to the hospital she offered me several thousand acres of land if I let her go. ==== Subject: Re: HEY MYTHBUSTERS!!!!!!!!!!!!!!!!!!! > Herc's beliefs will gather much more attention and would be the more likely. > The only time I've seen Christian beliefs cause such a problem happened when > the woman. who was told by god to wait inside her apartment for a message > was when the rent ran out and they tried to evict her. >Just outside the front door, me on one arm and my attendant on the other, > she stopped dead. > She looked at me and said she was sorry, then looked up at the sky and said > Strike them dead Lord. Later,on the ay to the hospital she offered me > several thousand acres of land if I let her go. And all the loaves and fishes you could eat? Luke ==== Subject: Vector Cross Products in 7 dimensions I have read that a vector cross product can be defined in terms of 7 dimensions as well as the usual 3, but I can't find a clear definition of the algebra. All it mentions is that Octonions are involved instead of Quaternions (neither of which I fully understand anyway). In 3 dimensions, we have A = (u1,u2,u3) and B = (v1,v2,v3), then the cross product C = A x B = ( u2.v3-u3.v2 , -u1.v3+u3.v1 , u1.v2-u2.v1 ) So when we move up to 7 dimensions, we have A = (u1,u2,u3,u4,u5,u6,u7) and B = (v1,v2,v3,v4,v5,v6,v7), the the cross product C = A x B = (???) Can someone please fill in the blanks for me ... what is ??? for the 7 dimension case. Dave P.S. Slightly off topic, but I really miss JSH ... he brightened my day with his antics ... ==== Subject: Connectedness and AC Can one prove the following without the axiom of choice? Consider a collection of connected subspaces of a topological space such that any two members of the collection have a nonempty intersection. The union of this collection must be connected. -- Stephen J. Herschkorn sjherschko@netscape.net Math Tutor in Central New Jersey and Manhattan ==== Subject: Re: Connectedness and AC > Can one prove the following without the axiom of choice? Consider a collection of connected subspaces of a topological space such > that any two members of the collection have a nonempty intersection. > The union of this collection must be connected. > Let the collection be C and the union of C, /C let f:/C -> discrete {0,1} be any continuous function. Showing f is constant, proves /C connected. Pick some x in /C some A in C with x in A Let y be any element in /C some B in C with y in B By premise some c in A / B. Thus as A,B are connected f(x) = f(A) = f(c) = f(B) = f(y) f(/C) = f(x) ==== Subject: Re: Connectedness and AC >Can one prove the following without the axiom of choice? >Consider a collection of connected subspaces of a topological space such >that any two members of the collection have a nonempty intersection. >The union of this collection must be connected. I don't see any use of AC in this proof: WLOG the space (say X) is the union of the collection. Suppose X is not connected. Then there are disjoint nonempty open sets U,V whose union contains X. Each member of the collection, being connected, must be a subset of either U or V. But then the members that are intersect U would be disjoint from the members that intersect V. Since U and V are nonempty, there is at least one member of the collection that intersects U and at least one that intersects V. This contradicts the hypothesis that the intersections are nonempty. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada ==== Subject: Re: What is This Set Called? |A = /_j f^j(S), j = 0,1,.. [...] |f(A) = f(/_j f^j(S)) subset /_j f^(j+1)(S) = S / /_j f^(j+1)(S) = A | |Why is A subset f(A) ? Is there a counter example when S is infinite? Yes. Let S={a_i : i>=0} u {b_{i,j} : i>=j>=0} for integers i,j, where the a_i and b_{i,j} are all distinct. Define the function f by f(a_i)=a_{i+1}, f(b_{m,n}) = b_{m,n-1} if n>0, and f(b_{m,0}) = a_0. The fact that a_0 = f^n(b_{n,n}) ensures that a_0 is in f^n(S) for every n. But none of the b_{i,j} is in f^n(S) for n>i, and the only solutions to a_0=f(x) are x=b_{i,0}. Keith Ramsay ==== Subject: Re: What is This Set Called? |f(A) = f(/_j f^j(S)) subset /_j f^(j+1)(S) = S / /_j f^(j+1)(S) = > A > | > |Why is A subset f(A) ? Is there a counter example when S is infinite? Yes. Let S={a_i : i>=0} u {b_{i,j} : i>=j>=0} for integers i,j, > where the a_i and b_{i,j} are all distinct. Define the function > f by f(a_i)=a_{i+1}, f(b_{m,n}) = b_{m,n-1} if n>0, and f(b_{m,0}) > = a_0. The fact that a_0 = f^n(b_{n,n}) ensures that a_0 is in > f^n(S) for every n. But none of the b_{i,j} is in f^n(S) for n>i, > and the only solutions to a_0=f(x) are x=b_{i,0}. > The great tragedy of science - the slaying of a beautiful hypothesis by an ugly fact. -- Thomas H. Huxley ==== Subject: Re: prime k-tuplets > ... > I think it is because the distances are quite arbitrary. > > They are not arbitrary the minimal distance is 26 for an octuplet starting > 3. Is it? Try 5 which has a distance of 24 for its octuplet. Or 7. > Same arguments for 5 and 7. Obviously you know, one can use info about the residues of the primes already counted, to determine which numbers in the sieve are divisible by 3, 5 and 7. E.g. four primes with unique residues mod 5 will tell us where the numbers divisible by 5 lie, > Count the number of people that have contributed to anything larger than > triplets. There is a small group of people that find it interesting enough > to spend much computer time on the topic. That is in itself not wrong (I > have devoted myself an extraordinary amount of computer time on Armstrong > numbers). But your initial complaint was: > Almost apologetic to bore you with another prime web-site, but I can never > get a response from the prime community so I have to at least mention them > here - all are verified prime. Well, I thank you for your response. It is too early to grumble about my recent batch of sextuplets, but past experience makes me nervous. I just hope lists are kept up to date. > I have no idea what the prime community is, but do not expect a large response > of mathematicians for such a site. A single acknowledgement (independent verification other than using Primo) would be nice. Richard Miller ==== Subject: Complexity of solving largest eigenvector Anyone knows some references discussing the computational complexity of finding the eigenvector corresponding to the largest eigenvalue? It must be smaller than solving all eigenvectors, which I am also interested in knowing its complexity. ==== Subject: Re: Complexity of solving largest eigenvector > Anyone knows some references discussing the computational complexity of > finding the eigenvector corresponding to the largest eigenvalue? It must be smaller than solving all eigenvectors, which I am also > interested in knowing its complexity. No. It need not. According to Pan, Chen and Zheng, the eigenproblem is O(n**3 + n log(n)**2 log(b)), where 2**-b is the allowed relative error on the eigenvalues. My recollection is the QUALEX uses their algorithm. ==== Subject: Re: Complexity of solving largest eigenvector >Anyone knows some references discussing the computational complexity of >finding the eigenvector corresponding to the largest eigenvalue? > >It must be smaller than solving all eigenvectors, which I am also >interested in knowing its complexity. > > you should be more precise: you mean complexity for approximating it to precision eps? if the eigenvalue is known and you can do linear systems exactly then the complexity is of course O(n^3). If you have to compute the corresponding eigenvalue too (or finding the eigenvector without prior finding the eigenvalue) then complexity can be something like O(log(eps)*n^2) but the constant can be quite large. practitioners would answer with O(n^3) regardless of finding one/all/eigenvalues/eigenvectors having the QR algorithm in mind. more could be said if you restrict the set of matrices you have in mind hth peter ==== Subject: Re: Complexity of solving largest eigenvector X-RFC2646: Format=Flowed; Original > Anyone knows some references discussing the computational complexity > of finding the eigenvector corresponding to the largest eigenvalue? > It must be smaller than solving all eigenvectors, which I am also > interested in knowing its complexity. Look up the power method, which would involve a bunch of matrix*vector multiplications, each of which requires n^2 operations for a full matrix. ==== Subject: Re: Complexity of solving largest eigenvector X-RFC2646: Format=Flowed; Original > Anyone knows some references discussing the computational complexity of > finding the eigenvector corresponding to the largest eigenvalue? It must be smaller than solving all eigenvectors, which I am also > interested in knowing its complexity. I don't expect the complexity of this problem is greater than that of calculating the Jordon Canonical Form for a matrix/linear transformation. -Bill ==== Subject: Re: Complexity of solving largest eigenvector X-RFC2646: Format=Flowed; Original > Anyone knows some references discussing the computational complexity of > finding the eigenvector corresponding to the largest eigenvalue? It must be smaller than solving all eigenvectors, which I am also > interested in knowing its complexity. > I assume you are concerned with a linear transformation from R^N to R^N. On what grounds do you believe that the complexity of finding the eigenvector(s) you mentioned must be smaller than the problem of finding all of the eigenvectors? --Bill ==== Subject: Re: Now how did we end up with this genius for President? > >>...I'm the Emperor of CloudCuckooLand. >With every bit as much credibility as you deserve in such capacity ... Interesting use of creative snipping. Now let me try. > I'm a ... destructive > radical ... >... while ... > pillaging and betraying -- http://hertzlinger.blogspot.com ==== Subject: Re: Now how did we end up with this genius for President? >Now let me try. Try is just the term used as an advance excuse for failure. You should post ontopic, not wallow in fallacies. The world is beginning to wonder if Americans are at all capable of using logic and dealing with reality. Perhaps it's your best excuse that you can't, so you advertise that in an attempt to gain forgiveness. >...I'm the Emperor of CloudCuckooLand. With every bit as much credibility as you deserve in such capacity ... Your utter failure to address the subject of this thread is noted, as predicted. There's a basis for certain members of the population being >One of the more amusing aspects of the left Who'd been discussing anything of the sort, and how would you be qualified to do so? >...As far as they're concerned They haven't chosen you their spokesperson. I'm a conservative Republican, so I value the Constitution, and fiscal responsibility, and the preservation of the environment. That's why I point out that the neocons are destructive radicals who aren't on the side of the USA. >...about Nazi Germany ... Are you still unaware of the close and enduring relationship of the Bush family to Nazism? Why would John Loftus consider Bush to be the Heir of the Holocaust, in your opinion? If you imagine the US could hold up for all that long while the Bush/Cheney crooks are pillaging and betraying it, you're inattentive at best. Notice how the bushkultie is too cowardly to accept valid correction. >Show us Your fleas might be able to see, but where you store your head, you don't. >where he claims to speak for God. It made the papers. You wouldn't know, being unable to read. I trust God speaks through me. Without that, I couldn.89t do my job. -- President Bush, quoted in the Lancaster New Era It's not the only time he's done that. It was also a habit of his hero Adolf Hitler. When you support Bush, you support Nazism. >...whackjob... Pleased to meet you: you'll be useful. >... my ... being a nutbag. It's your best excuse for groveling before fascists, and your posts back it up. I say go with it. >... a live nutbag right here... You even believe Bush when he claims to speak for God, don't you. >... a true kook It's your best excuse for your support of Nazism and war crimes. Your posts confirm it, too: I say go with it. Here's what scared you so much you couldn't deal with it at all: >Please tell me what is wrong with desecrating the koran? No: you are obviously too stupid to understand such things. You can't even figure out why herding Jews into concentration camps and gassing them was wrong. You reject the findings of the Nuremberg Tribunals with your support of Nazism. http://www.takebackthemedia.com/bushnonazi.html >Those ers ... Jealous? >As opposed to Dan Rather, Newsweek, NYT etc? Yup! >jt Dan Rather reported, correctly, that your vicious gay little fuhrer Bush deserted from his military obligation. Newsweek reported, correctly, that desecration of the Koran was indeed among the many vile insults Bush has caused to be heaped among the innocents in his concentration camps. He doesn't have the videos of that sent to him, though: he's into the ones with the child rapes and tortures. The NYT has had the integrity to admit and make reparations for its mistakes, which is more than your corrupt little god Bush will ever learn enough ethics to do. ==== Subject: Re: Now how did we end up with this genius for President? >Now let me try. Try is just the term used in proving that > I am a failure. So the truth finally comes out. >I should try post ontopic, not wallow in fantasies such as swallowing >Jaque Chirac's penis. Ewwwwww!!!!!!!!!! > I am also beginning to wonder if Americans are at all capable of using >condoms because I want to do the ugly with some Americans too. Ewwwwww!!!!!!!!!!! >It's the best excuse that I have, so I advertise >that in an attempt to gain forgiveness. I don't think anybody can forgive you for that. Well, Maybe Micheal Jackson.... Hell, Jesse Jackson too.... :-) -- ---------------------------------------------------------------------------- ---------------------------------------- Yomamma bin Crawdaddin www.cotse.com Brotherhood (Vice Chairman) Anti Archangel #41 The difference between John Kerry and Ted Kennedy is Stalking Filth #69.5 that Ted Kennedy has at least one confirmed kill. >--| <:((>>< >--| -- ==== Subject: Re: Now how did we end up with this genius for President? >So the truth finally comes out. It's called the Downing Street Memo. If you were literate, you could read it. >I should try post ontopic, not wallow in fantasies such as swallowing >Jaque Chirac's penis. >I don't think ... Of course you don't think: you're too cowardly and impaired for that. >Now let me try. Try is just the term used as an advance excuse for failure. You should post ontopic, not wallow in fallacies. The world is beginning to wonder if Americans are at all capable of using logic and dealing with reality. Perhaps it's your best excuse that you can't, so you advertise that in an attempt to gain forgiveness. >...I'm the Emperor of CloudCuckooLand. With every bit as much credibility as you deserve in such capacity ... Your utter failure to address the subject of this thread is noted, as predicted. There's a basis for certain members of the population being >One of the more amusing aspects of the left Who'd been discussing anything of the sort, and how would you be qualified to do so? >...As far as they're concerned They haven't chosen you their spokesperson. I'm a conservative Republican, so I value the Constitution, and fiscal responsibility, and the preservation of the environment. That's why I point out that the neocons are destructive radicals who aren't on the side of the USA. >...about Nazi Germany ... Are you still unaware of the close and enduring relationship of the Bush family to Nazism? Why would John Loftus consider Bush to be the Heir of the Holocaust, in your opinion? If you imagine the US could hold up for all that long while the Bush/Cheney crooks are pillaging and betraying it, you're inattentive at best. Notice how the bushkultie is too cowardly to accept valid correction. >Show us Your fleas might be able to see, but where you store your head, you don't. >where he claims to speak for God. It made the papers. You wouldn't know, being unable to read. I trust God speaks through me. Without that, I couldn.89t do my job. -- President Bush, quoted in the Lancaster New Era It's not the only time he's done that. It was also a habit of his hero Adolf Hitler. When you support Bush, you support Nazism. >...whackjob... Pleased to meet you: you'll be useful. >... my ... being a nutbag. It's your best excuse for groveling before fascists, and your posts back it up. I say go with it. >... a live nutbag right here... You even believe Bush when he claims to speak for God, don't you. >... a true kook It's your best excuse for your support of Nazism and war crimes. Your posts confirm it, too: I say go with it. Here's what scared you so much you couldn't deal with it at all: >Please tell me what is wrong with desecrating the koran? No: you are obviously too stupid to understand such things. You can't even figure out why herding Jews into concentration camps and gassing them was wrong. You reject the findings of the Nuremberg Tribunals with your support of Nazism. http://www.takebackthemedia.com/bushnonazi.html >Those ers ... Jealous? >As opposed to Dan Rather, Newsweek, NYT etc? Yup! >jt Dan Rather reported, correctly, that your vicious gay little fuhrer Bush deserted from his military obligation. Newsweek reported, correctly, that desecration of the Koran was indeed among the many vile insults Bush has caused to be heaped among the innocents in his concentration camps. He doesn't have the videos of that sent to him, though: he's into the ones with the child rapes and tortures. The NYT has had the integrity to admit and make reparations for its mistakes, which is more than your corrupt little god Bush will ever learn enough ethics to do. ==== Subject: Re: Now how did we end up with this genius for President? >What are you talking about Actually, I'm typing. You'll need to learn to read to figure that out. >...I never mentioned ... You've never addressed the issue because you're so inadequately > 'educated' that you wallow in your fallacies instead. I'm a lot better educated than you little kook. I guarantee that without even having to ask. Kooks tend to be poorly educated trailer trash and lash out at others because they feel threatened by their betters. Want a nice example? Visit this page: http://www.wilhelp.com/bj_faq/ You will see some striking similarities to yourself on that page. Just remember, the first step to recovery is admitting you have a problem. >That leaves you more vulnerable than you'd care to be, were > you fully sentient. > You don't know the meaning of the word. -- Now boy's don't start to ramblin' round On this road of sin are you sorrow bound Take my advice or you'll curse the day You started rollin' down that lost highway -Hank Williams ==== Subject: Re: Now how did we end up with this genius for President? >...little kook. I ... You attempt to boast of being educated, as you fail to avoid fallacy. That indicates that either you are lying about your level of education, or you're irrational and can't make valid use of any schooling you ever may have received. >... feel threatened ... You even believe the babies of Baghdad were after you with nukes they never had, don't you. >What are you talking about Actually, I'm typing. You'll need to learn to read to figure that out. >...I never mentioned ... You've never addressed the issue because you're so inadequately 'educated' that you wallow in your fallacies instead. That leaves you more vulnerable than you'd care to be, were you fully sentient. >A true kook. Not just someone being kooky. That's your best excuse. You believe the babies of Baghdad were after you with nukes they never had, too, don't you. >Show us Your fleas might be able to see, but where you store your head, you don't. >where he claims to speak for God. It made the papers. You wouldn't know, being unable to read. I trust God speaks through me. Without that, I couldn.89t do my job. -- President Bush, quoted in the Lancaster New Era It's not the only time he's done that. It was also a habit of his hero Adolf Hitler. When you support Bush, you support Nazism. >...whackjob... Pleased to meet you: you'll be useful. >... my ... being a nutbag. It's your best excuse for groveling before fascists, and your posts back it up. I say go with it. >... a live nutbag right here... You even believe Bush when he claims to speak for God, don't you. >... a true kook It's your best excuse for your support of Nazism and war crimes. Your posts confirm it, too: I say go with it. Here's what scared you so much you couldn't deal with it at all: >Please tell me what is wrong with desecrating the koran? No: you are obviously too stupid to understand such things. You can't even figure out why herding Jews into concentration camps and gassing them was wrong. You reject the findings of the Nuremberg Tribunals with your support of Nazism. http://www.takebackthemedia.com/bushnonazi.html >Those ers ... Jealous? >As opposed to Dan Rather, Newsweek, NYT etc? Yup! >jt Dan Rather reported, correctly, that your vicious gay little fuhrer Bush deserted from his military obligation. Newsweek reported, correctly, that desecration of the Koran was indeed among the many vile insults Bush has caused to be heaped among the innocents in his concentration camps. He doesn't have the videos of that sent to him, though: he's into the ones with the child rapes and tortures. The NYT has had the integrity to admit and make reparations for its mistakes, which is more than your corrupt little god Bush will ever learn enough ethics to do. ==== Subject: Re: Now how did we end up with this genius for President? Seriously >> kid, this is really not the way to troll a half dozen froups. See the >> idea is to NOT look like a stupid raving lunatic... like this? And >as long as I do my job I'm one step closer to becoming a higher >dimensional life form able to alter physical reality at will. Apparently I only needed to claim it once to get you hooked my lil Hatter addict. Tell us all, just how much of your free time do you spend slurping through Google for material to desperately try to win my attention with? -- Onideus Mad Hatter mhm Í x Í http://www.backwater-productions.net ==== Subject: Re: Now how did we end up with this genius for President? > >> Seriously > kid, this is really not the way to troll a half dozen froups. See the > idea is to NOT look like a stupid raving lunatic... >>like this? >>And >>as long as I do my job I'm one step closer to becoming a higher >>dimensional life form able to alter physical reality at will. >Apparently I only needed to claim it once to get you hooked my lil > Hatter addict. Tell us all, just how much of your free time do you > spend slurping through Google for material to desperately try to win > my attention with? > tell us all again how you dont take anything on the net personally Because I got ticked off, I took the your parents are alcoholics thing to be a REALLY mean and nasty personal remark. And even though it wasn't meant that way, that's the way I took it. I'm not going to just sit here and try to defend the fact that I'm human. I got angry, I responded heatedly, can any one else here say they didn't too? ==== Subject: Re: Now how did we end up with this genius for President? On Thu, 16 Jun 2005 18:49:56 -0700, Onideus Mad Hatter Onideus Mad Hatter That explains your obvious impairment. It is your best excuse, too. > Seriously >> kid, this is really not the way to troll a half dozen froups. See the >> idea is to NOT look like a stupid raving lunatic... like this? And >as long as I do my job I'm one step closer to becoming a higher >dimensional life form able to alter physical reality at will. Egads. Did ol' Hg-poisoned really say that? ==== Subject: Re: Now how did we end up with this genius for President? >Th If I throw a stick, will you leave? -- Onideus Mad Hatter mhm Í x Í http://www.backwater-productions.net ==== Subject: Re: Now how did we end up with this genius for President? On Thu, 16 Jun 2005 19:37:16 -0700, Onideus Mad Hatter Onideus Mad Hatter That explains your obvious impairment. It is your best excuse, too. > Seriously >> kid, this is really not the way to troll a half dozen froups. See the >> idea is to NOT look like a stupid raving lunatic... like this? And >as long as I do my job I'm one step closer to becoming a higher >dimensional life form able to alter physical reality at will. Egads. Did ol' Hg-poisoned really say that? ==== Subject: Re: Now how did we end up with this genius for President? On Thu, 16 Jun 2005 19:37:16 -0700, Onideus Mad Hatter >ThIf I throw a stick, will you leave? > Now Matthew... You know better... All he will do is bring the stick back to you. You need to take the gunny sack filled with rocks and river approach. That's the sure way to get rid of little puppies. Kittens too for that matter.... :-) -- ---------------------------------------------------------------------------- ---------------------------------------- Yomamma bin Crawdaddin www.cotse.com Brotherhood (Vice Chairman) Anti Archangel #41 The difference between John Kerry and Ted Kennedy is Stalking Filth #69.5 that Ted Kennedy has at least one confirmed kill. >--| <:((>>< >--| -- ==== Subject: Re: Now how did we end up with this genius for President? Notice that the bushworshipper isn't capable of controlling himself at all. He even attempts to blame others for his failure. Many wondered how the Germans let the first batch of Nazis get away with their crimes. We are seeing the same today in the helpless obeisance offered by the bushworshipper. On Thu, 16 Jun 2005 19:37:16 -0700, Onideus Mad Hatter Onideus Mad Hatter That explains your obvious impairment. It is your best excuse, too. > Seriously >> kid, this is really not the way to troll a half dozen froups. See the >> idea is to NOT look like a stupid raving lunatic... like this? And >as long as I do my job I'm one step closer to becoming a higher >dimensional life form able to alter physical reality at will. Egads. Did ol' Hg-poisoned really say that? ==== Subject: Re: Now how did we end up with this genius for President? >You need better medical care than Bush would ever allow you. Does it hurt to be as stupid as you? -- Onideus Mad Hatter mhm Í x Í http://www.backwater-productions.net ==== Subject: Re: Now how did we end up with this genius for President? On Thu, 16 Jun 2005 18:48:03 -0700, Onideus Mad Hatter Onideus Mad Hatter You believe the babies of Baghdad were after you with nukes they never had, don't you. On Thu, 16 Jun 2005 12:27:57 -0700, Onideus Mad Hatter ... the way to troll ... That's not appropriate use of the newsgroups. If you were aware of what they are for, you'd communicate honestly. >... look like a stupid raving lunatic... >Onideus Mad Hatter You sure do, but you're useful that way. On Wed, 15 Jun 2005 22:47:33 -0700, Onideus Mad Hatter stupidity ... It's what gets you abused as a pawn of the fascists. >... I should believe ... No: you should become informed. >... just ing around with ... If that's what you consider to be 'sex', I pity you bigtime. >... I think Mini Bush is even dumber than ... Oh, he's not really dumb. They've fooled you with that ploy. >... so angry and upset ... >Onideus Mad Hatter You really ought to calm yourself and work on your equanimity. I can lightheartedly enjoy myself even as I expose the wrongdoing of the USA's worst enemy, Bush. On Wed, 15 Jun 2005 15:17:11 -0700, Onideus Mad Hatter ... constitution [sic]... If you ever learn more about it you may be able to read it some day. It says the USA is obligated to abide by treaties to which it is signatory, and your little fuhrer Bush >environment Bush's record on that is notably worse. >...the Nazi's believed in world domination, the Bush >more of it at everyone else's expense. They're also into the torture. >... MORON... That's your best excuse for not rejecting the Bush crime family. Otherwise it's cowardice or even outright sociopathy. >... retarded kooks like ... You like watching the world unite against the USA because of Bush, or else you'd work on that. >One of the more amusing aspects of the left Who'd been discussing anything of the sort, and how would you be qualified to do so? >...As far as they're concerned They haven't chosen you their spokesperson. I'm a conservative Republican, so I value the Constitution, and fiscal responsibility, and the preservation of the environment. That's why I point out that the neocons are destructive radicals who aren't on the side of the USA. >...about Nazi Germany ... Are you still unaware of the close and enduring relationship of the Bush family to Nazism? Why would John Loftus consider Bush to be the Heir of the Holocaust, in your opinion? If you imagine the US could hold up for all that long while the Bush/Cheney crooks are pillaging and betraying it, you're inattentive at best. Notice how the bushkultie is too cowardly to accept valid correction. >Show us Your fleas might be able to see, but where you store your head, you don't. >where he claims to speak for God. It made the papers. You wouldn't know, being unable to read. I trust God speaks through me. Without that, I couldn.89t do my job. -- President Bush, quoted in the Lancaster New Era It's not the only time he's done that. It was also a habit of his hero Adolf Hitler. When you support Bush, you support Nazism. >...whackjob... Pleased to meet you: you'll be useful. >... my ... being a nutbag. It's your best excuse for groveling before fascists, and your posts back it up. I say go with it. >... a live nutbag right here... You even believe Bush when he claims to speak for God, don't you. >... a true kook It's your best excuse for your support of Nazism and war crimes. Your posts confirm it, too: I say go with it. Here's what scared you so much you couldn't deal with it at all: >Please tell me what is wrong with desecrating the koran? No: you are obviously too stupid to understand such things. You can't even figure out why herding Jews into concentration camps and gassing them was wrong. You reject the findings of the Nuremberg Tribunals with your support of Nazism. http://www.takebackthemedia.com/bushnonazi.html >Those ers ... Jealous? >As opposed to Dan Rather, Newsweek, NYT etc? Yup! >jt Dan Rather reported, correctly, that your vicious gay little fuhrer Bush deserted from his military obligation. Newsweek reported, correctly, that desecration of the Koran was indeed among the many vile insults Bush has caused to be heaped among the innocents in his concentration camps. He doesn't have the videos of that sent to him, though: he's into the ones with the child rapes and tortures. The NYT has had the integrity to admit and make reparations for its mistakes, which is more than your corrupt little god Bush will ever learn enough ethics to do. ==== Subject: Re: Now how did we end up with this genius for President? >You be Learn from your parents mistakes, use birth control! -- Onideus Mad Hatter mhm Í x Í http://www.backwater-productions.net ==== Subject: Re: Now how did we end up with this genius for President? On Thu, 16 Jun 2005 19:37:16 -0700, Onideus Mad Hatter Onideus Mad Hatter You believe the babies of Baghdad were after you with nukes they never had, don't you. On Thu, 16 Jun 2005 12:27:57 -0700, Onideus Mad Hatter ... the way to troll ... That's not appropriate use of the newsgroups. If you were aware of what they are for, you'd communicate honestly. >... look like a stupid raving lunatic... >Onideus Mad Hatter You sure do, but you're useful that way. On Wed, 15 Jun 2005 22:47:33 -0700, Onideus Mad Hatter stupidity ... It's what gets you abused as a pawn of the fascists. >... I should believe ... No: you should become informed. >... just ing around with ... If that's what you consider to be 'sex', I pity you bigtime. >... I think Mini Bush is even dumber than ... Oh, he's not really dumb. They've fooled you with that ploy. >... so angry and upset ... >Onideus Mad Hatter You really ought to calm yourself and work on your equanimity. I can lightheartedly enjoy myself even as I expose the wrongdoing of the USA's worst enemy, Bush. On Wed, 15 Jun 2005 15:17:11 -0700, Onideus Mad Hatter ... constitution [sic]... If you ever learn more about it you may be able to read it some day. It says the USA is obligated to abide by treaties to which it is signatory, and your little fuhrer Bush >environment Bush's record on that is notably worse. >...the Nazi's believed in world domination, the Bush >more of it at everyone else's expense. They're also into the torture. >... MORON... That's your best excuse for not rejecting the Bush crime family. Otherwise it's cowardice or even outright sociopathy. >... retarded kooks like ... You like watching the world unite against the USA because of Bush, or else you'd work on that. >One of the more amusing aspects of the left Who'd been discussing anything of the sort, and how would you be qualified to do so? >...As far as they're concerned They haven't chosen you their spokesperson. I'm a conservative Republican, so I value the Constitution, and fiscal responsibility, and the preservation of the environment. That's why I point out that the neocons are destructive radicals who aren't on the side of the USA. >...about Nazi Germany ... Are you still unaware of the close and enduring relationship of the Bush family to Nazism? Why would John Loftus consider Bush to be the Heir of the Holocaust, in your opinion? If you imagine the US could hold up for all that long while the Bush/Cheney crooks are pillaging and betraying it, you're inattentive at best. Notice how the bushkultie is too cowardly to accept valid correction. >Show us Your fleas might be able to see, but where you store your head, you don't. >where he claims to speak for God. It made the papers. You wouldn't know, being unable to read. I trust God speaks through me. Without that, I couldn.89t do my job. -- President Bush, quoted in the Lancaster New Era It's not the only time he's done that. It was also a habit of his hero Adolf Hitler. When you support Bush, you support Nazism. >...whackjob... Pleased to meet you: you'll be useful. >... my ... being a nutbag. It's your best excuse for groveling before fascists, and your posts back it up. I say go with it. >... a live nutbag right here... You even believe Bush when he claims to speak for God, don't you. >... a true kook It's your best excuse for your support of Nazism and war crimes. Your posts confirm it, too: I say go with it. Here's what scared you so much you couldn't deal with it at all: >Please tell me what is wrong with desecrating the koran? No: you are obviously too stupid to understand such things. You can't even figure out why herding Jews into concentration camps and gassing them was wrong. You reject the findings of the Nuremberg Tribunals with your support of Nazism. http://www.takebackthemedia.com/bushnonazi.html >Those ers ... Jealous? >As opposed to Dan Rather, Newsweek, NYT etc? Yup! >jt Dan Rather reported, correctly, that your vicious gay little fuhrer Bush deserted from his military obligation. Newsweek reported, correctly, that desecration of the Koran was indeed among the many vile insults Bush has caused to be heaped among the innocents in his concentration camps. He doesn't have the videos of that sent to him, though: he's into the ones with the child rapes and tortures. The NYT has had the integrity to admit and make reparations for its mistakes, which is more than your corrupt little god Bush will ever learn enough ethics to do. ==== Subject: Re: Now how did we end up with this genius for President? >What people should know about is the fact that the Bush >family has bitch slapped me and ed me up the ass >like a red headed step child! >>Have you considered though that maybe you deserved it? >Why haven't you? Oh I have considered it and I believe that yes, you did deserve to get ed up the ass like a red headed step child. -- Onideus Mad Hatter mhm Í x Í http://www.backwater-productions.net ==== Subject: Re: Now how did we end up with this genius for President? On Thu, 16 Jun 2005 18:46:42 -0700, Onideus Mad Hatter ed up the ass... >Onideus Mad Hatter So that's why you're bent over that way. On Thu, 16 Jun 2005 12:24:26 -0700, Onideus Mad Hatter On Wed, 15 Jun 2005 22:38:10 -0700, Onideus Mad Hatter .... ass raped ... You must like it to bend over and gape that way. >a psychotic like ... You like the way Bush is committing war crimes. >...Desperate for a lil attention? Terribly afraid >that no one cares ... You're to be pitied for that. >... trying to ATTACK the other >side. Cause really That's what war criminals like your little fuhrer do. >... lil fruit >kook ... Pleased to meet you: you'll be useful. On Tue, 14 Jun 2005 21:29:39 -0700, Onideus Mad Hatter ... been raped and tortured by George W Bush ... The policy of shock and awe is as terroristic as it gets. >sounds like ... Those voices in your head are lying to you. >What a cute little ... You support those who rape, torture, maime and murder cute little children. Your fuhrer Bush has a family tradition of pedophilia that you admire, too, no doubt. >Show us Your fleas might be able to see, but where you store your head, you don't. >where he claims to speak for God. It made the papers. You wouldn't know, being unable to read. I trust God speaks through me. Without that, I couldn.89t do my job. -- President Bush, quoted in the Lancaster New Era It's not the only time he's done that. It was also a habit of his hero Adolf Hitler. When you support Bush, you support Nazism. >...whackjob... Pleased to meet you: you'll be useful. >... my ... being a nutbag. It's your best excuse for groveling before fascists, and your posts back it up. I say go with it. >... a live nutbag right here... You even believe Bush when he claims to speak for God, don't you. >... a true kook It's your best excuse for your support of Nazism and war crimes. Your posts confirm it, too: I say go with it. Here's what scared you so much you couldn't deal with it at all: >Please tell me what is wrong with desecrating the koran? No: you are obviously too stupid to understand such things. You can't even figure out why herding Jews into concentration camps and gassing them was wrong. You reject the findings of the Nuremberg Tribunals with your support of Nazism. http://www.takebackthemedia.com/bushnonazi.html >Those ers ... Jealous? >As opposed to Dan Rather, Newsweek, NYT etc? Yup! >jt Dan Rather reported, correctly, that your vicious gay little fuhrer Bush deserted from his military obligation. Newsweek reported, correctly, that desecration of the Koran was indeed among the many vile insults Bush has caused to be heaped among the innocents in his concentration camps. He doesn't have the videos of that sent to him, though: he's into the ones with the child rapes and tortures. The NYT has had the integrity to admit and make reparations for its mistakes, which is more than your corrupt little god Bush will ever learn enough ethics to do. ==== Subject: Re: Now how did we end up with this genius for President? >So th You're so poor you can't even pay attention. -- Onideus Mad Hatter mhm Í x Í http://www.backwater-productions.net ==== Subject: Re: Now how did we end up with this genius for President? On Thu, 16 Jun 2005 19:37:15 -0700, Onideus Mad Hatter Onideus Mad Hatter If you could, you'd have noticed that it's your duty (were you competent) to supervise government officials, as opposed to worship of them. On Thu, 16 Jun 2005 18:46:42 -0700, Onideus Mad Hatter ed up the ass... >Onideus Mad Hatter So that's why you're bent over that way. On Thu, 16 Jun 2005 12:24:26 -0700, Onideus Mad Hatter On Wed, 15 Jun 2005 22:38:10 -0700, Onideus Mad Hatter .... ass raped ... You must like it to bend over and gape that way. >a psychotic like ... You like the way Bush is committing war crimes. >...Desperate for a lil attention? Terribly afraid >that no one cares ... You're to be pitied for that. >... trying to ATTACK the other >side. Cause really That's what war criminals like your little fuhrer do. >... lil fruit >kook ... Pleased to meet you: you'll be useful. On Tue, 14 Jun 2005 21:29:39 -0700, Onideus Mad Hatter ... been raped and tortured by George W Bush ... The policy of shock and awe is as terroristic as it gets. >sounds like ... Those voices in your head are lying to you. >What a cute little ... You support those who rape, torture, maime and murder cute little children. Your fuhrer Bush has a family tradition of pedophilia that you admire, too, no doubt. >Show us Your fleas might be able to see, but where you store your head, you don't. >where he claims to speak for God. It made the papers. You wouldn't know, being unable to read. I trust God speaks through me. Without that, I couldn.89t do my job. -- President Bush, quoted in the Lancaster New Era It's not the only time he's done that. It was also a habit of his hero Adolf Hitler. When you support Bush, you support Nazism. >...whackjob... Pleased to meet you: you'll be useful. >... my ... being a nutbag. It's your best excuse for groveling before fascists, and your posts back it up. I say go with it. >... a live nutbag right here... You even believe Bush when he claims to speak for God, don't you. >... a true kook It's your best excuse for your support of Nazism and war crimes. Your posts confirm it, too: I say go with it. Here's what scared you so much you couldn't deal with it at all: >Please tell me what is wrong with desecrating the koran? No: you are obviously too stupid to understand such things. You can't even figure out why herding Jews into concentration camps and gassing them was wrong. You reject the findings of the Nuremberg Tribunals with your support of Nazism. http://www.takebackthemedia.com/bushnonazi.html >Those ers ... Jealous? >As opposed to Dan Rather, Newsweek, NYT etc? Yup! >jt Dan Rather reported, correctly, that your vicious gay little fuhrer Bush deserted from his military obligation. Newsweek reported, correctly, that desecration of the Koran was indeed among the many vile insults Bush has caused to be heaped among the innocents in his concentration camps. He doesn't have the videos of that sent to him, though: he's into the ones with the child rapes and tortures. The NYT has had the integrity to admit and make reparations for its mistakes, which is more than your corrupt little god Bush will ever learn enough ethics to do. ==== Subject: Re: Now how did we end up with this genius for President? The basis of bushkultism: http://www.phule.net/mirrors/unskilled-and-unaware.html >... have a hard time using a spoon with oatmeal.. No doubt you do. You also have extreme difficulty realizing that your lame fallacies aren't ontopic here. If you cared enough about yourself, you'd be looking after your own best interests. On Thu, 16 Jun 2005 12:24:26 -0700, Onideus Mad Hatter On Wed, 15 Jun 2005 22:38:10 -0700, Onideus Mad Hatter .... ass raped ... You must like it to bend over and gape that way. >a psychotic like ... You like the way Bush is committing war crimes. >...Desperate for a lil attention? Terribly afraid >that no one cares ... You're to be pitied for that. >... trying to ATTACK the other >side. Cause really That's what war criminals like your little fuhrer do. >... lil fruit >kook ... Pleased to meet you: you'll be useful. On Tue, 14 Jun 2005 21:29:39 -0700, Onideus Mad Hatter ... been raped and tortured by George W Bush ... The policy of shock and awe is as terroristic as it gets. >sounds like ... Those voices in your head are lying to you. >What a cute little ... You support those who rape, torture, maime and murder cute little children. Your fuhrer Bush has a family tradition of pedophilia that you admire, too, no doubt. >Show us Your fleas might be able to see, but where you store your head, you don't. >where he claims to speak for God. It made the papers. You wouldn't know, being unable to read. I trust God speaks through me. Without that, I couldn.89t do my job. -- President Bush, quoted in the Lancaster New Era It's not the only time he's done that. It was also a habit of his hero Adolf Hitler. When you support Bush, you support Nazism. >...whackjob... Pleased to meet you: you'll be useful. >... my ... being a nutbag. It's your best excuse for groveling before fascists, and your posts back it up. I say go with it. >... a live nutbag right here... You even believe Bush when he claims to speak for God, don't you. >... a true kook It's your best excuse for your support of Nazism and war crimes. Your posts confirm it, too: I say go with it. Here's what scared you so much you couldn't deal with it at all: >Please tell me what is wrong with desecrating the koran? No: you are obviously too stupid to understand such things. You can't even figure out why herding Jews into concentration camps and gassing them was wrong. You reject the findings of the Nuremberg Tribunals with your support of Nazism. http://www.takebackthemedia.com/bushnonazi.html >Those ers ... Jealous? >As opposed to Dan Rather, Newsweek, NYT etc? Yup! >jt Dan Rather reported, correctly, that your vicious gay little fuhrer Bush deserted from his military obligation. Newsweek reported, correctly, that desecration of the Koran was indeed among the many vile insults Bush has caused to be heaped among the innocents in his concentration camps. He doesn't have the videos of that sent to him, though: he's into the ones with the child rapes and tortures. The NYT has had the integrity to admit and make reparations for its mistakes, which is more than your corrupt little god Bush will ever learn enough ethics to do. ==== Subject: Re: Now how did we end up with this genius for President? >The basis of bushkultism: http://www.phule.net/mirrors/unskilled-and-unaware.html >>... have a hard time using a spoon with oatmeal.. No doubt you do. You also have extreme difficulty realizing that your >lame fallacies aren't ontopic here. > I make the fukkin topic in here you little fukktard. Learn it Love it Live it. :-) -- ---------------------------------------------------------------------------- ---------------------------------------- Yomamma bin Crawdaddin www.cotse.com Brotherhood (Vice Chairman) Anti Archangel #41 The difference between John Kerry and Ted Kennedy is Stalking Filth #69.5 that Ted Kennedy has at least one confirmed kill. >--| <:((>>< >--| -- ==== Subject: Re: Now how did we end up with this genius for President? Notice that the bushworshipper definitely falls into the category of being unable to reason. It's irrationality due to hysteria. On Thu, 16 Jun 2005 19:37:16 -0700, Onideus Mad Hatter Onideus Mad Hatter If you weren't, you'd be able to do so much better. For example, you'd not bother with fallacies. One suspects you're unaware that that's all you have. On Thu, 16 Jun 2005 18:45:16 -0700, Onideus Mad Hatter Onideus Mad Hatter You envy the way James Dale Guckert got to urinate on Dubya, don'tya. The basis of bushkultism: http://www.phule.net/mirrors/unskilled-and-unaware.html >... have a hard time using a spoon with oatmeal.. No doubt you do. You also have extreme difficulty realizing that your lame fallacies aren't ontopic here. If you cared enough about yourself, you'd be looking after your own best interests. On Thu, 16 Jun 2005 12:24:26 -0700, Onideus Mad Hatter On Wed, 15 Jun 2005 22:38:10 -0700, Onideus Mad Hatter .... ass raped ... You must like it to bend over and gape that way. >a psychotic like ... You like the way Bush is committing war crimes. >...Desperate for a lil attention? Terribly afraid >that no one cares ... You're to be pitied for that. >... trying to ATTACK the other >side. Cause really That's what war criminals like your little fuhrer do. >... lil fruit >kook ... Pleased to meet you: you'll be useful. On Tue, 14 Jun 2005 21:29:39 -0700, Onideus Mad Hatter ... been raped and tortured by George W Bush ... The policy of shock and awe is as terroristic as it gets. >sounds like ... Those voices in your head are lying to you. >What a cute little ... You support those who rape, torture, maime and murder cute little children. Your fuhrer Bush has a family tradition of pedophilia that you admire, too, no doubt. >Show us Your fleas might be able to see, but where you store your head, you don't. >where he claims to speak for God. It made the papers. You wouldn't know, being unable to read. I trust God speaks through me. Without that, I couldn.89t do my job. -- President Bush, quoted in the Lancaster New Era It's not the only time he's done that. It was also a habit of his hero Adolf Hitler. When you support Bush, you support Nazism. >...whackjob... Pleased to meet you: you'll be useful. >... my ... being a nutbag. It's your best excuse for groveling before fascists, and your posts back it up. I say go with it. >... a live nutbag right here... You even believe Bush when he claims to speak for God, don't you. >... a true kook It's your best excuse for your support of Nazism and war crimes. Your posts confirm it, too: I say go with it. Here's what scared you so much you couldn't deal with it at all: >Please tell me what is wrong with desecrating the koran? No: you are obviously too stupid to understand such things. You can't even figure out why herding Jews into concentration camps and gassing them was wrong. You reject the findings of the Nuremberg Tribunals with your support of Nazism. http://www.takebackthemedia.com/bushnonazi.html >Those ers ... Jealous? >As opposed to Dan Rather, Newsweek, NYT etc? Yup! >jt Dan Rather reported, correctly, that your vicious gay little fuhrer Bush deserted from his military obligation. Newsweek reported, correctly, that desecration of the Koran was indeed among the many vile insults Bush has caused to be heaped among the innocents in his concentration camps. He doesn't have the videos of that sent to him, though: he's into the ones with the child rapes and tortures. The NYT has had the integrity to admit and make reparations for its mistakes, which is more than your corrupt little god Bush will ever learn enough ethics to do. ==== Subject: Re: Now how did we end up with this genius for President? >The bas Tell me, does it bother you that everyone thinks you're a fruit kook? -- Onideus Mad Hatter mhm Í x Í http://www.backwater-productions.net ==== Subject: Re: Now how did we end up with this genius for President? On Thu, 16 Jun 2005 18:45:16 -0700, Onideus Mad Hatter Onideus Mad Hatter You envy the way James Dale Guckert got to urinate on Dubya, don'tya. The basis of bushkultism: http://www.phule.net/mirrors/unskilled-and-unaware.html >... have a hard time using a spoon with oatmeal.. No doubt you do. You also have extreme difficulty realizing that your lame fallacies aren't ontopic here. If you cared enough about yourself, you'd be looking after your own best interests. On Thu, 16 Jun 2005 12:24:26 -0700, Onideus Mad Hatter On Wed, 15 Jun 2005 22:38:10 -0700, Onideus Mad Hatter .... ass raped ... You must like it to bend over and gape that way. >a psychotic like ... You like the way Bush is committing war crimes. >...Desperate for a lil attention? Terribly afraid >that no one cares ... You're to be pitied for that. >... trying to ATTACK the other >side. Cause really That's what war criminals like your little fuhrer do. >... lil fruit >kook ... Pleased to meet you: you'll be useful. On Tue, 14 Jun 2005 21:29:39 -0700, Onideus Mad Hatter ... been raped and tortured by George W Bush ... The policy of shock and awe is as terroristic as it gets. >sounds like ... Those voices in your head are lying to you. >What a cute little ... You support those who rape, torture, maime and murder cute little children. Your fuhrer Bush has a family tradition of pedophilia that you admire, too, no doubt. >Show us Your fleas might be able to see, but where you store your head, you don't. >where he claims to speak for God. It made the papers. You wouldn't know, being unable to read. I trust God speaks through me. Without that, I couldn.89t do my job. -- President Bush, quoted in the Lancaster New Era It's not the only time he's done that. It was also a habit of his hero Adolf Hitler. When you support Bush, you support Nazism. >...whackjob... Pleased to meet you: you'll be useful. >... my ... being a nutbag. It's your best excuse for groveling before fascists, and your posts back it up. I say go with it. >... a live nutbag right here... You even believe Bush when he claims to speak for God, don't you. >... a true kook It's your best excuse for your support of Nazism and war crimes. Your posts confirm it, too: I say go with it. Here's what scared you so much you couldn't deal with it at all: >Please tell me what is wrong with desecrating the koran? No: you are obviously too stupid to understand such things. You can't even figure out why herding Jews into concentration camps and gassing them was wrong. You reject the findings of the Nuremberg Tribunals with your support of Nazism. http://www.takebackthemedia.com/bushnonazi.html >Those ers ... Jealous? >As opposed to Dan Rather, Newsweek, NYT etc? Yup! >jt Dan Rather reported, correctly, that your vicious gay little fuhrer Bush deserted from his military obligation. Newsweek reported, correctly, that desecration of the Koran was indeed among the many vile insults Bush has caused to be heaped among the innocents in his concentration camps. He doesn't have the videos of that sent to him, though: he's into the ones with the child rapes and tortures. The NYT has had the integrity to admit and make reparations for its mistakes, which is more than your corrupt little god Bush will ever learn enough ethics to do. ==== Subject: Re: Now how did we end up with this genius for President? >You e Your village called, they're missing their idiot. -- Onideus Mad Hatter mhm Í x Í http://www.backwater-productions.net ==== Subject: Re: Now how did we end up with this genius for President? On Thu, 16 Jun 2005 19:37:16 -0700, Onideus Mad Hatter Onideus Mad Hatter If you weren't, you'd be able to do so much better. For example, you'd not bother with fallacies. One suspects you're unaware that that's all you have. On Thu, 16 Jun 2005 18:45:16 -0700, Onideus Mad Hatter Onideus Mad Hatter You envy the way James Dale Guckert got to urinate on Dubya, don'tya. The basis of bushkultism: http://www.phule.net/mirrors/unskilled-and-unaware.html >... have a hard time using a spoon with oatmeal.. No doubt you do. You also have extreme difficulty realizing that your lame fallacies aren't ontopic here. If you cared enough about yourself, you'd be looking after your own best interests. On Thu, 16 Jun 2005 12:24:26 -0700, Onideus Mad Hatter On Wed, 15 Jun 2005 22:38:10 -0700, Onideus Mad Hatter .... ass raped ... You must like it to bend over and gape that way. >a psychotic like ... You like the way Bush is committing war crimes. >...Desperate for a lil attention? Terribly afraid >that no one cares ... You're to be pitied for that. >... trying to ATTACK the other >side. Cause really That's what war criminals like your little fuhrer do. >... lil fruit >kook ... Pleased to meet you: you'll be useful. On Tue, 14 Jun 2005 21:29:39 -0700, Onideus Mad Hatter ... been raped and tortured by George W Bush ... The policy of shock and awe is as terroristic as it gets. >sounds like ... Those voices in your head are lying to you. >What a cute little ... You support those who rape, torture, maime and murder cute little children. Your fuhrer Bush has a family tradition of pedophilia that you admire, too, no doubt. >Show us Your fleas might be able to see, but where you store your head, you don't. >where he claims to speak for God. It made the papers. You wouldn't know, being unable to read. I trust God speaks through me. Without that, I couldn.89t do my job. -- President Bush, quoted in the Lancaster New Era It's not the only time he's done that. It was also a habit of his hero Adolf Hitler. When you support Bush, you support Nazism. >...whackjob... Pleased to meet you: you'll be useful. >... my ... being a nutbag. It's your best excuse for groveling before fascists, and your posts back it up. I say go with it. >... a live nutbag right here... You even believe Bush when he claims to speak for God, don't you. >... a true kook It's your best excuse for your support of Nazism and war crimes. Your posts confirm it, too: I say go with it. Here's what scared you so much you couldn't deal with it at all: >Please tell me what is wrong with desecrating the koran? No: you are obviously too stupid to understand such things. You can't even figure out why herding Jews into concentration camps and gassing them was wrong. You reject the findings of the Nuremberg Tribunals with your support of Nazism. http://www.takebackthemedia.com/bushnonazi.html >Those ers ... Jealous? >As opposed to Dan Rather, Newsweek, NYT etc? Yup! >jt Dan Rather reported, correctly, that your vicious gay little fuhrer Bush deserted from his military obligation. Newsweek reported, correctly, that desecration of the Koran was indeed among the many vile insults Bush has caused to be heaped among the innocents in his concentration camps. He doesn't have the videos of that sent to him, though: he's into the ones with the child rapes and tortures. The NYT has had the integrity to admit and make reparations for its mistakes, which is more than your corrupt little god Bush will ever learn enough ethics to do. ==== Subject: Re: Now how did we end up with this genius for President? >NoboYou killed Jesus, you pigeon molesting splatter. >Yo, Matthew.... >How do you know for sure he killed Jesus? Because Jesus told me so...that time when he and I went down to Mexico and bought fireworks. >Fukks like him have a hard time using a spoon with oatmeal.. >:-) ...you mean Jesus wasn't killed with stupidity? -- Onideus Mad Hatter mhm Í x Í http://www.backwater-productions.net ==== Subject: Re: Now how did we end up with this genius for President? On Thu, 16 Jun 2005 17:13:39 -0700, Onideus Mad Hatter >NoboYou killed Jesus, you pigeon molesting splatter. >Yo, Matthew.... >>How do you know for sure he killed Jesus? Because Jesus told me so...that time when he and I went down to Mexico >and bought fireworks. >Fukks like him have a hard time using a spoon with oatmeal.. >>:-) ...you mean Jesus wasn't killed with stupidity? That explains it.... :-) -- ---------------------------------------------------------------------------- ---------------------------------------- Yomamma bin Crawdaddin www.cotse.com Brotherhood (Vice Chairman) Anti Archangel #41 The difference between John Kerry and Ted Kennedy is Stalking Filth #69.5 that Ted Kennedy has at least one confirmed kill. >--| <:((>>< >--| -- ==== Subject: Re: Now how did we end up with this genius for President? Considering the entire scope of Bush's background and its context, can anyone name any aspect of it that would make him hesitate to commit murderous treason against the USA? On Thu, 16 Jun 2005 19:37:15 -0700, Onideus Mad Hatter Considering the entire scope of Bush's background >and its context, can anyone name any aspect of it >that would make him hesitate to commit murderous >treason against the USA? On Thu, 16 Jun 2005 19:37:15 -0700, Onideus Mad Hatter >... ammusing [sic] Nice little snip and run. Looser. LMAO :-) -- ---------------------------------------------------------------------------- ---------------------------------------- Yomamma bin Crawdaddin www.cotse.com Brotherhood (Vice Chairman) Anti Archangel #41 The difference between John Kerry and Ted Kennedy is Stalking Filth #69.5 that Ted Kennedy has at least one confirmed kill. >--| <:((>>< >--| -- ==== Subject: Re: Now how did we end up with this genius for President? >Looser. [sic] If you were any more loose, you'd be James Dale Guckert. The word you'd needed to describe yourself was loser. Considering the entire scope of Bush's background and its context, can anyone name any aspect of it that would make him hesitate to commit murderous treason against the USA? On Thu, 16 Jun 2005 19:37:15 -0700, Onideus Mad Hatter On Thu, 16 Jun 2005 19:37:15 -0700, Onideus Mad Hatter The Bu Naughty, naughty, Shortsighted! You're not to speak unless spoken to. Know your role! -- Onideus Mad Hatter mhm Í x Í http://www.backwater-productions.net ==== Subject: Re: Now how did we end up with this genius for President? On Thu, 16 Jun 2005 18:44:40 -0700, Onideus Mad Hatter Tho Rolling your head along your keyboard and hoping something ammusing or meaningful will come out isn't getting you anywhere -- Onideus Mad Hatter mhm Í x Í http://www.backwater-productions.net ==== Subject: Re: Now how did we end up with this genius for President? On Thu, 16 Jun 2005 19:37:15 -0700, Onideus Mad Hatter arguing with each other in a mad house. One of them threatened the >other one: I'll differentiate you! I'll integrate you! What did the >other one reply with complete indifference? > > I'm exponential >Yes. His reply: Go ahead. I am e^x. The way I know this joke (if it deserves that name, for as all maths it > is a bit of a groaner) goes somewhat differently, about as follows: ... > Allow me to introduce myself, he says. I'm e^x, and you've > terrorized this town for far too long. > Nice to meet you, replies the differential operator. I'm d/dy. I'm sorry to ask a totally pedestrian question, but I've seen this joke before, and can make nothing of it at all. The only way I can read 'e^x' is ee-to-the-ex, and I can't see any (other) meaning, pun, whatever. Is there some pronunciation I don't know about? Brian Chandler http://imaginatorium.org > Lasse ==== Subject: Re: Math posers. Re: An new and very interesting intellectual game! >7. There is the following educational joke: Two mathematiicans were >arguing with each other in a mad house. One of them threatened the >other one: I'll differentiate you! I'll integrate you! What did the >other one reply with complete indifference? > > I'm exponential > > Yes. His reply: Go ahead. I am e^x. The way I know this joke (if it deserves that name, for as all maths it > is a bit of a groaner) goes somewhat differently, about as follows: Allow me to introduce myself, he says. I'm e^x, and you've > terrorized this town for far too long. > Nice to meet you, replies the differential operator. I'm d/dy. > I'm sorry to ask a totally pedestrian question, but I've seen this > joke before, and can make nothing of it at all. The only way I can > read 'e^x' is ee-to-the-ex, and I can't see any (other) meaning, pun, > whatever. Is there some pronunciation I don't know about? No. Your ignorance is in mathematics. ==== Subject: Re: Math posers. Re: An new and very interesting intellectual game! > ... > Allow me to introduce myself, he says. I'm e^x, and you've > terrorized this town for far too long. > Nice to meet you, replies the differential operator. I'm d/dy. >I'm sorry to ask a totally pedestrian question, but I've seen this > joke before, and can make nothing of it at all. The only way I can > read 'e^x' is ee-to-the-ex, and I can't see any (other) meaning, pun, > whatever. Is there some pronunciation I don't know about? e^x (e to the x is the right reading, btw) is unaffected by the differential operator (d/dx (e^x) = e^x). d/dy e^x, otoh... martin ==== Subject: Re: Math posers. Re: An new and very interesting intellectual game! terrorized this town for far too long. > Nice to meet you, replies the differential operator. I'm d/dy. I'm sorry to ask a totally pedestrian question, but I've seen this > joke before, and can make nothing of it at all. The only way I can > read 'e^x' is ee-to-the-ex, and I can't see any (other) meaning, pun, > whatever. Is there some pronunciation I don't know about? e^x (e to the x is the right reading, btw) is unaffected by the > differential operator (d/dx (e^x) = e^x). d/dy e^x, otoh... Brian Chandler http://imaginatorium.org ==== Subject: Re: Re : General formula for a sequence (*) A_n= (a^n-b^n)/(a-b) . Proof [case a=/=0]: Observe that A_{k+1}=aA_k +b^k , k=1,2,... ; A_1=1 . Therefore A_{k+1}/a^{k+1} -A_k/a_k = (b/a^2)*(b/a)^{k-1} , k=1,2,...,n-1, ... By summing , using the telescoping sum SUM_{k=1 to k=n}(T_{k+1} -T_k )= T_n - T_1 , one finds (*) . In case a=0 it's nothing to prove: in that case A_n=b^{n-1} . When b=a , formula (*) reads A_n= n*a^{n-1} . Another possibility to interpret (*) may be : denote by U_0,U_1,...,U_n,... the Chebychev polynomials of the second kind. These satisfiy the three-term recurrence U_{k+1}(x)= 2x*U_{k}(x) - U_{k-1}(x) , U_0(x)=1 , U_1(x)=2x . Also, U_n is well defined on (-1,1) by U_n(x) = sin((n+1)*arccos(x) )/ sqrt(1-x^2) . It may be seen that A_n= (ab)^{(n-1)*0,5} *U_{n-1}( (a+b)/(2*sqrt(ab)) ) . ==== Subject: Re: Russell's Paradox <4ldja1990lhjqiad684gjkgpo5q2js8ebu@4ax.com> <873brknina.fsf@phiwumbda.org> <87aclrwo3b.fsf@phiwumbda.org> |I decided a few days ago that your stupidity was too extreme to be |accidental. No one says such moronic things as businessmen don't |need exponents on their calculators. Thus, you weren't really |hoaxing us so much as yanking our chains. | |You pulled one over on me. I actually felt clever for exposing your |fraud, but your posts are so ludicrous that it is more joke than |fraud. So I was suckered, not by believing your story but by thinking |you wanted us to believe it. Oh well. This is really what the term troll was coined for. People use it now like it can include spamming and so on, but it's such a convenient summary for this kind of confession. All you have to say is, I've been trolled (IBT). Keith Ramsay ==== Subject: Re: Russell's Paradox <873brknina.fsf@phiwumbda.org> <87aclrwo3b.fsf@phiwumbda.org> Discussion, linux) > This is really what the term troll was coined for. > People use it now like it can include spamming and so > on, but it's such a convenient summary for this kind > of confession. There is one disturbing difference between Mark Demers and traditional trolls. He's actually advertising non-existent jobs for recent PhDs. That disturbs me. -- Jesse F. Hughes And a journal can beg me for the right to publish it [...] because I'd rather see it in People magazine [...] --James Harris on his simple proof of Fermat's last theorem ==== Subject: Re: Russell's Paradox <873brknina.fsf@phiwumbda.org> <87aclrwo3b.fsf@phiwumbda.org> Discussion, linux) > |I decided a few days ago that your stupidity was too extreme to be > |accidental. No one says such moronic things as businessmen don't > |need exponents on their calculators. Thus, you weren't really > |hoaxing us so much as yanking our chains. > | > |You pulled one over on me. I actually felt clever for exposing your > |fraud, but your posts are so ludicrous that it is more joke than > |fraud. So I was suckered, not by believing your story but by thinking > |you wanted us to believe it. Oh well. This is really what the term troll was coined for. > People use it now like it can include spamming and so > on, but it's such a convenient summary for this kind > of confession. All you have to say is, I've been trolled (IBT). I thought the recovery procedure involved clicking the heels of your ruby red slippers. But, yes, Mark Demers is a troll in the old sense of the word. And (sob) I've been trolled. -- So now you see a math person coming out to talk about *his* program which is fast as he says it can count over 89 billions primes in less than a second. How is that objective? It's childish. -- James S. Harris, on objective facts. ==== Subject: Re: systems > Sorry if this is OT, but I'm very curios about one topic. When > computer-science people tell about something: this is a ``systems`` > As mentioned by others software people use the word system often for the underlying computer plus operating system. The other answers point you more in the mathematical direction. I would like to add one other use of the word system that computer science people also use the word for: the intangible holistic view. So even more than the sum of the components, this includes the dynamics and the interaction with the context. -- Gaudi systems architecting: ==== Subject: Re: systems computer-science people tell about something: this is a ``systems`` As mentioned by others software people use the word system often for the > underlying computer plus operating system. The other answers point you > more in the mathematical direction. I would like to add one other use > of the word system that computer science people also use the word for: > the intangible holistic view. So even more than the sum of the > components, this includes the dynamics and the interaction with the context. > -- > Gaudi systems architecting: > ==== Subject: Re: Epistemology 202: Advanced Topics <9UFre.59362$gc6.28186@okepread04> <42b04278.65127915@netnews.att.net> <42b063ae.68825158@netnews.att.net> <42b09c84.71776431@netnews.att.net> <42b1907a.77085918@netnews.att.net On 16 Jun 2005 07:02:25 -0700, Ross A. Finlayson > On 15 Jun 2005 20:26:41 +0200, Torkel Franzen in > Are there rules or assumptions anywhere which define what > mathematics is? >> No. >> Then how do you know when and whether you're doing mathematics? > If you say natural deduction can be used in mathematics, there > must be some interface between them, >> Natural deduction is just a formalization of logical inference. >> So what's the interface between logical inference and mathematics? > There can be an axiomless theory that still has rules of inference, >then. Is that agreeable? True rules of inference or only problematic rules of inference? To derive true statements from an axiom-free system, one consideration >is to derive the axioms of some other theory with applications as >theorems, thus that then all the other theorems decided by that theory >are decided by the axiomless system. Which works but only if the rules of inference are true and > exhaustive. However it may not work for axiomatic systems. The question arises then how to arrive at theorems of an axiomless >system, given the primary objects of the theory using as first >principles only those that do not contradict the rules of inference. For which contradiction is the primary object. Otherwise primary > objects cannot contradict anything. In that respect much of the groundwork for those considerations of >nullity and universality has been the domain of the modern technical >philosophers, and as well, the ancients are assumed to have kernels of >truth in their absolute reasoning. No one suggests there are no kernels of truth in most reasoning. The > problem has always been separating the wheat from the chaff and > finding the kernel of truth essential to all kernels of truth. The universe is infinite, and infinite sets are equivalent. So your idea of a primary object is infinity and lack of definition? An >axiom-free theory exclusively can be complete, and there's only one of >them, and as the theory of everything must be complete, the axiomless >theory is the theory of everything. Ok. That's what I mean by the law of contradiction or universal truth. > Hi Lester, I had not heard of that. How do you construct any contradictions from rules of inference? What do you mean, problematic. I hope that you could summarize these new phrases that you use in one to three paragraphs in less than 500 words. When you say it may not work for axiomatic systems what is it and what is your point. Universal truth seems clear enough, what do you mean when you say law of contradiction. Ross F. ==== Subject: Re: Epistemology 202: Advanced Topics On 16 Jun 2005 23:09:27 -0700, Ross A. Finlayson >> On 16 Jun 2005 07:02:25 -0700, Ross A. Finlayson > On 15 Jun 2005 20:26:41 +0200, Torkel Franzen in >> Are there rules or assumptions anywhere which define what >> mathematics is? No. Then how do you know when and whether you're doing mathematics? > If you say natural deduction can be used in mathematics, there >> must be some interface between them, Natural deduction is just a formalization of logical inference. So what's the interface between logical inference and mathematics? >There can be an axiomless theory that still has rules of inference, >>then. Is that agreeable? >> True rules of inference or only problematic rules of inference? >>To derive true statements from an axiom-free system, one consideration >>is to derive the axioms of some other theory with applications as >>theorems, thus that then all the other theorems decided by that theory >>are decided by the axiomless system. >> Which works but only if the rules of inference are true and >> exhaustive. However it may not work for axiomatic systems. >>The question arises then how to arrive at theorems of an axiomless >>system, given the primary objects of the theory using as first >>principles only those that do not contradict the rules of inference. >> For which contradiction is the primary object. Otherwise primary >> objects cannot contradict anything. >>In that respect much of the groundwork for those considerations of >>nullity and universality has been the domain of the modern technical >>philosophers, and as well, the ancients are assumed to have kernels of >>truth in their absolute reasoning. >> No one suggests there are no kernels of truth in most reasoning. The >> problem has always been separating the wheat from the chaff and >> finding the kernel of truth essential to all kernels of truth. >>The universe is infinite, and infinite sets are equivalent. >> So your idea of a primary object is infinity and lack of definition? >> An >>axiom-free theory exclusively can be complete, and there's only one of >>them, and as the theory of everything must be complete, the axiomless >>theory is the theory of everything. >> Ok. That's what I mean by the law of contradiction or universal truth. Hi Lester, I had not heard of that. How do you construct any contradictions from rules of inference? Hi Ross, Rules of inference are constructed from contradictions between contradictions not the other way around. > What >do you mean, problematic. If you're referring to my comment on your rules of inference, I was just trying to highlight the fact that there are all kinds of rules of inference possible some of which may be true and some false and without proof that various rules of inference are true we have no way to know whether they're true or false. >I hope that you could summarize these new phrases that you use in one >to three paragraphs in less than 500 words. These phrases aren't new. They appear in almost everything I've written on the subject of epistemology. >When you say it may not work for axiomatic systems what is it and >what is your point. My point is that so called rules of inference must be exhaustive and true in order for axiomatic systems to be subsumed under them. The it then are the true and exhaustive rules of inference. However this may not work for any particular axiomatic system if axioms are false. >Universal truth seems clear enough, what do you mean when you say >law of contradiction. That contradiction is true of everything. I don't know how closely you've been following these threads, Ross, but these things have been covered in considerable detail in the preceeding thread Epistemology 201: The Science of Science which I would suggest you review. ==== Subject: Re: multiple integral package > I found myself in a situation that a multiple (at least 4) integral > numerical solver is needed to support an existing Matlab program. I tried to > find some info on the web and found this package called cubpack from KUL. > Unfortunately it needs a fortran compiler and has extra problems integrating > with Matlab according to the author. Anyone knows another pack that works in the following condition 1. Freeware Sure. > 2. works in MS windows environment As long as you have the right compiler. > 3. easy integratable with Matlab (v5) Don't know about that one. Note that adaptive quadrature (or cubature) in high dimensions is very expensive. There aren't that many libraries out there that do that. One of the best known is DCUHRE[1], which is written in Fortran. The alternative is to use Monte Carlo methods. A good selection of such methods can be found in the Cuba[2] library and also the GSL[3] library, both C libraries. Note that the Cuba library contains a reimplementation of the CUHRE algorithm. [1] http://www.math.wsu.edu/faculty/genz/homepage [2] http://www.feynarts.de/cuba/ [3] www.gnu.org/software/gsl/ Hope this helps. Igor ==== Subject: Re: British English (was: Anti-humanistic mathematics <150620051040219690%edgar@math.ohio-state.edu.invalid> |Hm, that seems to imply that there is only one form of English spoken |in Britain. On the other hand, it's perfectly acceptable to refer |to American English, there being only one form of English spoken |in America (wherever that is). Nebraska, apparently, is where American English is spoken. I knew a guy from Virginia who once worked at a company somewhere in the South in the U.S., where one of his coworkers had earned the nickname the South'ner with his strong, rural accent. As he pronounced it, it was sometimes a three-syllable word. Keith Ramsay ==== Subject: Re: rational or irrational? >If you allow both 0:00 and 24:00, then you have a situation where it >is simultaneously Monday (24:00) and Tuesday (0:00) which is totally >irrational and leads to such absurdities as seen here: http://members.aol.com/rotanasnem/truth/eykw_c10.htm _All_ clock faces are wrong. -- BELANGER with apologies to Gene Ray, et al. ==== Subject: Re: rational or irrational? defaulted to noon, not midnight... > 12:00 PM is noon, although both are (technically) > misnomers. 24 hour clock here, and there is no ambiguity between 0:00 > and 24:00 - they are both simply the midnight. Or maybe > there is an ambiguity about which midnight they are. I'm trying to resist asking whether this convention is > rational or irrational. The notion of 24:00 is the product of a diseased mind. And > don't bother quoting standards, the standards were created > by people with diseased minds. Then you must not even want to hear about seven-hour delayed military time, where midnight is 24:00, 1:00 am the next day is 25:00, and so on up to 30:59, whereupon you have 7:00. (Control Data used to use this because they had contracts which went past midnight, but never any that went past 7:00 am.) --- Christopher Heckman ==== Subject: Re: rational or irrational? defaulted to noon, not midnight... > 12:00 PM is noon, although both are (technically) > misnomers. > 24 hour clock here, and there is no ambiguity between 0:00 > and 24:00 - they are both simply the midnight. Or maybe > there is an ambiguity about which midnight they are. > I'm trying to resist asking whether this convention is > rational or irrational. The notion of 24:00 is the product of a diseased mind. And > don't bother quoting standards, the standards were created > by people with diseased minds. Then you must not even want to hear about seven-hour delayed military > time, where midnight is 24:00, 1:00 am the next day is 25:00, and so > on up to 30:59, whereupon you have 7:00. (Control Data used to use this > because they had contracts which went past midnight, but never any that > went past 7:00 am.) Control Data was also a source of OEM disk drives to the company I worked for and subsequently went to their training school on disk drive maintenance. One of the maintenance proceedures was head alignment for the removable platter. This was done with a reference disk pack. Now if the customer's drive was badly out of alignment, setting it back to the standard could render all cartridges created before the re-alignment unreadable. And there was nothing that could be done because there are an infinite number of wrong settings and only one correct one. That's what standards are for, so everybody and everything is in alignment. You can arbitrarily decide to count from one to ten or from zero to nine. You CANNOT do both because that's 11 not 10. Having both 0:00 and 24:00 is irrational and stupid. > --- Christopher Heckman ==== Subject: Re: rational or irrational? > Nonvolatile memory would not help -- how would the clock know > how much time has passed? Not for the time -- just to keep the alarm setting. The marginal cost in quantity would be less than a tenth of a cent. The catch is, of course, in quantity. I agree that adding battery-backed clock circuitry would be a bit much, mainly because the cost of the battery would be more than the whole of the clock logic in these cheap things. - Tim ==== Subject: Re: Humanistic mathematics (Cantor's Theory) <42aea9f3$0$25036$8fcfb975@news.wanadoo.fr> <7eb82$42aeb170$82a1e3ad$27570@news2.tudelft.nl> |> Yes, *you* should. For instance, you would discover that constructivists |> *all* accept infinite sets and Cantor arguments... | |Brouwer certainly didn't accept them. How well informed are you, really? Brouwer commonly made use of infinite sets. He even dealt with sets of reals as subsets of the continuum, although he had a very different understanding of the continuum than Cantor. I don't remember seeing any place where he explicitly comments on either of Cantor's proofs of the uncountability of the reals, but I bet you haven't either, have you? The fact that for every sequence of reals r0,r1,... there exists a real r apart from each of the r_i is perfectly ordinary intuitionist mathematics. If by Cantor arguments one means them all, but one of the proofs of this fact about the reals was fine for intuitionists. Keith Ramsay ==== Subject: Re: Humanistic mathematics (Cantor's Theory) Keith Ramsay a .8ecrit : > [...] > |> Yes, *you* should. For instance, you would discover that > constructivists > |> *all* accept infinite sets and Cantor arguments... > | > |Brouwer certainly didn't accept them. How well informed are you, > really? >Brouwer commonly made use of infinite sets. He even dealt > with sets of reals as subsets of the continuum, although > he had a very different understanding of the continuum > than Cantor. >I don't remember seeing any place where he explicitly comments > on either of Cantor's proofs of the uncountability of the reals, > but I bet you haven't either, have you? >The fact that for every sequence of reals r0,r1,... there > exists a real r apart from each of the r_i is perfectly ordinary > intuitionist mathematics. If by Cantor arguments one means > them all, but one of the proofs of this fact about the reals > was fine for intuitionists. >Keith Ramsay > trolls, or not so obvious trolling behavior, but I had found it somewhat hard to resist here :-) ==== Subject: Re: Humanistic mathematics (Cantor's Theory) |It might be fun to see an extensive foundation of mathematics |that allowed only computable entities to exist. I'm not sure |if it's really been tried; it hardly seems worth the effort. |I think intuitionism and constructivism have tendencies in |this direction, but I don't know much about them. A lot has been done in all different directions. Most of what you would have to do at this point is just define clearly enough what kind of system you're looking for. It's possible that the effective topos does what you want, but some might find it too liberal. One issue that would need to be squared away is what exactly one means by calling something such as a set of points in the plane computable. I think getting clear on what one really means by requiring entities to be computable would be most of the trouble here. Most axiom systems designed for constructivism have some notion of type. The natural numbers would be a type. The functions from the natural numbers to the natural numbers would be a type. The functions from those functions to the natural numbers would be another one. And so on. These types are just the kind of object that illustrate the contrast between the stated goal of regarding mathematics as being about computation, and the claim that as we do so, we're going to have to dispose of noncomputable things like the real line. People who care about the relationship between mathematics and computation are almost always happy with type theories. But types are a lot like sets. The type of all functions from the natural numbers to the natural numbers is a lot like the real line (whether one makes the assumption that they are all computable or not). If I give you a Turing machine, you will not necessarily be able to tell me whether it computes a total function from the natural numbers to the natural numbers. Does that mean there's no such thing as the type, computable function from the natural numbers to the natural numbers? Surely not. Keith Ramsay ==== Subject: Possibility question I am a math idiot, so hopefully someone will be able to help me. I'm a playwright looking for an answer to a problem. Nothing major in the play, but I want it to be right. It might be easy, but I don't have a clue how to figure it out. Here's the problem: There's a lock with three (3) dials. Line them up properly and the lock opens (only one combination will work). The first lock has eight (8) stops, the second has twelve (12), and the third has twenty six (26). How many possibile combinations of these three dials are there? ==== Subject: Re: Possibility question > I am a math idiot, so hopefully someone will be able to help me. I'm a > playwright looking for an answer to a problem. Nothing major in the > play, but I want it to be right. It might be easy, but I don't have a > clue how to figure it out. Here's the problem: >There's a lock with three (3) dials. Line them up properly and the lock > opens (only one combination will work). The first lock has eight (8) > stops, the second has twelve (12), and the third has twenty six (26). > How many possibile combinations of these three dials are there? > I get 2,496 ==== Subject: Re: Possibility question <170620050738545871%anniel@nym.alias.net.invalid> The solution is 8 * 12 * 26 = 2,496. It may be more interesting (for your play and for us) if you had partial information about one or more of the locks. ==== Subject: Re: Possibility question > The solution is 8 * 12 * 26 = 2,496. It may be more interesting (for > your play and for us) if you had partial information about one or more > of the locks. > ==== Subject: Re: Possibility question > There's a lock with three (3) dials. Line them up properly and the lock > opens (only one combination will work). The first lock has eight (8) > stops, the second has twelve (12), and the third has twenty six (26). > How many possibile combinations of these three dials are there? If you had one dial with n positions, then you'd have n combinations. If you had two dials, the first with n positions and the second with one position, then you'd have n combinations. If you had two dials, the first with n positions and the second with two positions, then you'd have n combinations from the first dial when the second dial was set at position 1 and another n combinations from the first dial when the second dial was set at position 2. Thus you'll have n + n = 2n combinations. Now if the second dial had three positions, then ... If the second dial had m positions, then ... Now if you had third dial ... ==== Subject: Re: the Reals really have negative curvature built-in and negative-Reals are superfluous I find myself back playing this game of e^(i)(pi) = ....99999 in 10-adics. Now 5-adics have two i's. pi = 3.14159265....... e = 2.71828......... 5-adic i = .........303243121.2 5-adic i = .........30422141201323.3 Now, what is the very easiest way to get e,pi, i to equal ...9999. Finding the easiest way first and then supplying an explanation for why it works as a representation of (i), later. What if I use a series of 2-adics and 5-adics to alter every 4 digit in the above two 5-adics so that I subtract 1 from the 4 digit to turn it into a 3 digit. So along the 5-adic string, whenever a 4 digit appears then a subtract 1 applies. And whenever a 2 digit appears in the string then I add 1, where a 0 appears I add 3 and where a 1 appears I add 2. So in the series I have the 5-adic i and then I have a new number of a 5-adic that is 0 in every place value except where the digit is 4 and then a 1 appears in that specific place value. And so the application of this new number will be to transform every 4 digit into becoming a 3 digit. Likewise for the transforming of the 0 digit to that of 3 by adding 3, and 1 digit by adding 2 and 2 digit by adding 1. So eventually I have four new numbers, each of which alters the digits of 4,2,1,0 into becoming a 3 digit. But I need more new numbers of add and subtract to replace the digits of (pi) so that when I multiply (pi) by (i) and (e) the entire work ends up as ....999999. I want to force pi, e, i into becoming ....9999 and once I find the forcing then I want the find the least amount of forcing. Back in mid 1990s when I played this game before, I believed (i) had to be one number. Today I feel that (i) can be a plethora of numbers and each one altering a digit. I am not asking, does it work to yield ....9999. I am saying, force it to work to yield .....99999 and then examine which of these forced ways is the least or minimum of force. In mid 1990s I believed (i) like e and pi were unique numbers. Today I feel (i) is a series of operations such as adding and subtracting and even multiplying. So what I have done is the start of the search for the MINIMUM series that will transform (e) and (i) and (pi) into the desired end result of ....99999 in 10-adics. Perhaps I should bypass the 5-adic i's altogether and work with just e and pi and ask what series of numbers for i will yield .....9999. e^pi = 23.1406926... What would be the Minimum or least amount of action to make the end result ....9999 for e^(i)(pi). 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: the Reals really have negative curvature built-in and negative-Reals are superfluous The physical meaning of e^(i)(pi) = -1 It all comes out of the Atom Totality theory. Pi is the girth or circumference of the 231Pu Atom Totality where it has 22 subshells inside of 7 shells in Rational form, that is collapsed wavefunction. It has only 19 of those subshells occupied in 7 shells. Any mathematics discovered by intelligent life would find pi and e as what the same value as the Atom Totality they live in. If our Universe were a Helium Atom Totality and not a Plutonium Atom Totality then humans, if they existed and had a mathematics would find a pi and e but have a value that coincides with the characteristics of helium not plutonium. So pi represents physically the circumference of the Cosmos of the Atom Totality of 22 subshells inside of 7 shells. And e represents the fact that 19 of those subshells have grown but that 3 are ungrown or unfilled. Now what does (i) represent in the Atom Totality? We normally think of (i) as sqrt -1. So, then, applying the Atom Totality theory we see clearly what (pi) and (e) represent. We do not see what (i) represents. But we have another number to contend and deal with; that of -1. Is it really -1 or is it the Adic such as 10-adic of .....99999999. Some look at ....9999 as -1 itself, but I realize that .....9999999 is the largest number that exists in 10-adics. So the question becomes whether the equation e^(i)(pi) = -1 where -1 is .....9999 as a negative number of -1 or whether the equation should really be: e^(i)(pi) = ......9999999 where the number ....9999 is the largest number in 10-adics and is not -1. Now in physics, electrons have charge of (-1). So is the equation e^(i)(pi) = -1 saying to us that the Cosmic girth and occupied subshells of 19 ends up yielding a cosmic electron charge of -1. Or is this equation e^(i)(pi) = -1 trying to tell us that it should be e^(i)(pi) = ....999999 where the Cosmic girth and occupied subshells when multiplied in such a manner yields the entire Cosmos itself-- that is the largest number. Consider this. Consider if the Cosmos were a square and one side of the square was (e) and the other side was (pi) and so you multiply e by pi which yields the area of the Cosmos, or yields everything that is the Cosmic square and that number would be the largest number possible because the Cosmos is everything. So I have to be wary as to whether the equation e^(i)(pi) = -1 with its (-1) yield represents the physics charge of electron being -1 or whether that (-1) is really ....99999 in 10-adics which is the largest number possible. Perhaps it is both and that charge in physics is connected with the total area or total volume of space. 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: the Reals really have negative curvature built-in and negative-Reals are superfluous > I find myself back playing this game of e^(i)(pi) = ....99999 in > 10-adics. Now 5-adics have two i's. pi = 3.14159265....... e = 2.71828......... 5-adic i = .........303243121.2 5-adic i = .........30422141201323.3 Now, what is the very easiest way to get e,pi, i to equal ...9999. > Finding the easiest way first and then supplying an explanation for why > it works as a representation of (i), later. What if I use a series of 2-adics and 5-adics to alter every 4 digit in > the above two 5-adics so that I subtract 1 from the 4 digit to turn it > into a 3 digit. So along the 5-adic string, whenever a 4 digit appears > then a subtract 1 applies. And whenever a 2 digit appears in the string > then I add 1, where a 0 appears I add 3 and where a 1 appears I add 2. So in the series I have the 5-adic i and then I have a new number of a > 5-adic that is 0 in every place value except where the digit is 4 and > then a 1 appears in that specific place value. And so the application > of this new number will be to transform every 4 digit into becoming a 3 > digit. Likewise for the transforming of the 0 digit to that of 3 by > adding 3, and 1 digit by adding 2 and 2 digit by adding 1. So eventually I have four new numbers, each of which alters the digits > of 4,2,1,0 into becoming a 3 digit. But I need more new numbers of add > and subtract to replace the digits of (pi) so that when I multiply (pi) > by (i) and (e) the entire work ends up as ....999999. I want to force pi, e, i into becoming ....9999 and once I find the > forcing then I want the find the least amount of forcing. Back in mid 1990s when I played this game before, I believed (i) had to > be one number. Today I feel that (i) can be a plethora of numbers and > each one altering a digit. I am not asking, does it work to yield ....9999. I am saying, force it > to work to yield .....99999 and then examine which of these forced ways > is the least or minimum of force. In mid 1990s I believed (i) like e and pi were unique numbers. Today I > feel (i) is a series of operations such as adding and subtracting and > even multiplying. So what I have done is the start of the search for the MINIMUM series > that will transform (e) and (i) and (pi) into the desired end result of > ....99999 in 10-adics. Perhaps I should bypass the 5-adic i's altogether and work with just e > and pi and ask what series of numbers for i will yield .....9999. > e^pi = 23.1406926... What would be the Minimum or least amount of action to make the end > result ....9999 for e^(i)(pi). > Now I wonder about something which I previously deemed as fictional. I wonder about those things I called Doubly Infinites. Instead of a infinite rightward string or an infinite leftward string, i.e. Reals and Adics respectively, the Doubly Infinites would be both in one. Since I call for a forcing of e^(i)(pi) = -1 for its minimum forcing or easiest forcing, I wonder if the Doubly Infinites have a existence and have a role to play and specifically it is to provide the (i) in e^(i)(pi) = -1. Can we define Doubly Infinites such as perhaps ....33333.14159265.... or perhaps ......999999.14159265 such that it forces (pi) to conform to what we desire? Where the rightward string is pi shortened of its 3. And when we insert this Doubly Infinite into the equation e^(i)(pi) = -1, it forces the endresult of ....9999999. So that we define Doubly Infinites as the so called filler of what (i) is in this equation e^(i)(pi) = -1 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: Subgroups > S_j is a subgroup of S_k iff j <= k. Of course, fix one element. That about answers what I was after. -- Hauke Reddmann <:-EX8 fc3a501@uni-hamburg.de His-Ala-Sec-Lys-Glu Arg-Glu-Asp-Asp-Met-Ala-Asn-Asn Leonardo Da Vinci - About Aliens, Dimensions, Consciousness, Time, And Earth's Past And Future (Version 3.4.1 on 17 June 2005) (Suitable for foreign language students) ' One of the very excellent television series on Leonardo da Vinci, a three part TV series available on video disc - an epic made by Nick Rossiter, is a biographic masterpiece that covers all well-known aspects of that life time, even of Leonardo as the eminent philosopher: Leonardo was born before, indeed - as you might like to feel or see, from one of Raphael's famous paintings in the Vatican, depicting Leonardo - as the philosopher Plato, in Athens, a fact which you could assume might not have been unknown to Leonardo's friend, the painter Raphael. ' ' (*) And this is maybe the place to say, that Sigmund Freud has never said anything true about anyone, neither about others nor about himself, and the same applies to Freud's equally Criminally Minded friend, Albert Einstein, who came to a similar type of fame: The type of fame that will turn into infamy before long, as both Freud and Einstein have done more to destroy science, Freud to destroy your understanding of people, and Einstein to destroy your understanding of physics, of astronomy and of mathematics, regarded as an authority by Criminal Minds, he was even inciting another Criminal Mind into deciding to finance the physical mass destruction of man by means of an Atom bomb, building super bombs INSTEAD OF facing precisely (and making others, and people in general face precisely), the very Criminal Minds who destroy their OWN country and who try and destroy as many of their OWN people as they manage - because that is the actual purpose of Criminal Minds, what they ENJOY doing, like you know it from Mao or Stalin or Hitler or Japanese Criminal Mind Hideki - thus it is, that one might assume from a wider and more correct viewpoint, that they - the Criminal Minds Freud, and the not less known Einstein - have in the last hundred or so years, probably done more to DISABLE people's intellect, and to destroy people's understanding, managing to PREVENT people from finding correct solutions, and so causing destruction indirectly, but more lastingly and more thoroughly than anyone else, so it appears. ' ' These, and any Criminal Minds, such as also Stephen Hawking about physics, and the many 'gurus,' 'swamis' and 'pundits' of India about the spirit, and the 'buddhas' about the goals and the condition of people, ENJOY LYING, and they ENJOY doing so with the greatest force of conviction or 'certainty.' ' Those mechanisms I have explained in a way for anyone to understand, for instance already in 'Genuine Art - Producing It, Recognizing It' {HRI 20021220}. ' That will give you some understanding to begin with, of what Leonardo was opposed by, in his attempt to express his Love for Mankind, through Beauty and by means of science. ' And if you want to know more about the nature of Leonardo, then you can study of course also the nature of Plato. 'Defining Love and Hate' {HRI 20020829}, but also ' ' Should that not be enough for you to feel the soul of who was Leonardo, then you might like to know, that you may recognize the same person or soul (Leonardo, Plato) born earlier, as who became King Solomon, who, by the way, was also the king in the lives of women, as well as the writer of the 'Song of Songs,' the 'Canticle' with which to convey the height of Love between man and woman because and while the matching nature and character of their bodies' Energies make it possible, so, to make love true, of a joy that can only be tasted by those that are capable of creating and maintaining the Beauty of sexual Energies when these are created to touch and then to match the Love between a man and a woman - such as you were once capable of, to create and to feel, and may so become again if your soul is still sufficiently whole and if you wish to experience that tremendous joy - a joy which nowadays is only seldomly described or shown in public, as indeed Consciousness is pushed further down and down, not only by those 'swamis' and 'buddhas' from India who replace it with a PRETENDED Consciousness, or awareness PRETENDED, following the goals of Criminal Minds to eradicate your awareness almost complete- ly, in which effort they - starting from India indeed (after having laid some ground work in ancient Egypt) - have succeeded to quite some extent, and in which they are still going strong, down and down and down, without that you ever notice it... *(1) ' So we better find back to the Consciousness and awareness that for instance Leonardo could use, and did use to again show the Love, and with it the technical possibilities, for achieving that level of material and social freedom, in which it is possible to REGAIN, (not to evolve, but) to GET BACK some of our destroyed awareness indeed (and doing all that, DESPITE the 'pundits' and other 'Babas' and 'Anandas' and modern-day 'lamas,' 'gurus,' 'world teachers' and 'Fathers' - that is, those who like to have, and be given, the total certainty of, each of them - to the exclusion of the others too - constituting the only savior of Mankind). We get back some awareness of truth, which simply is 'that what happened' - as any normal and rather sane person can tell you and knows. And we continue to look for what actually happened: ' Further - when you study the various alphabets that have been used at times and places - you will find with King Solomon, the alphabet known as the 'Celestial Writing,' which happens to be the connection, that forms part of the true or truthful Da Vinci code. ' ' The life of Leonardo then gives you a framework from which to read the more elaborate, present day writing, from his viewpoint many centuries later: 'About Aliens, Dimensions, Consciousness, Time, And Earth's Past And Future' version when published.) ' ' The text with that title - almost 14,000 words - is dealing with the very nature of life itself, from a viewpoint so all-encompassing, so complete, so vastly educated, so truly caring and so beautifully restoring truth, that you never have even dared to imagine or hold it, but that nevertheless is also your own viewpoint, should you 'know yourself' - or gnoti seauton as Plato said in Greek. ' Koos Nolst Trenite Cause Trinity human rights philosopher and poet 'Solomon's wisdom was greater than the wisdom of all the men of the East, and greater than all the wisdom of Egypt.' 1 Kings 4:30 __________________________ Addition since version 2.0: I will give you some (very short or not so very short) definitions, ' ______ Aliens: If you consider, that there are only people existing on Earth, then you have been made and are being kept highly insane as * - (See (*) in the main body of text, above.) ' __________ Dimensions: A dimension is something that you can measure as having a distance, which of course implies a direction in which to measure. Due to the fact that an understanding of the mechanics of perception and of awareness is COMPLETELY lacking (not only in 'science,' but ALSO in psychic persons), the word 'dimension' is then used by people as 'anything that can be visible' - like in a dream, you actually do see things - or as 'anything that can be imagined in some way.' That is of course not a correct way of using the word, as it is practically undefined, then: WHILE those who use it, pretend it to be very meaningful and defined, in actual fact they do not define it at all. If you consider the amount of higher dimensions they 'throw at your senses' - in numbers well beyond those dimensions (the three dimensions that a carpenter or a mason works with), that ARE defined, and if you consider that they talk in such a way as to make you assume that THEY do know, and YOU don't know about higher dimensions, but, that they are not able to define the word dimension itself even, nor that they can define what they would like it to mean when and as they use it, much like they can not define 'Energy' or 'Frequency' or 'Wave- length' or 'Vibration' or 'Other World,' even though they throw these terms at your senses with equal conviction of knowing what they talk about, but despite all that, you could deduct, that they probably intend 'Dimension' to mean a vague where you can feel or see or imagine something to exist. ' I have never seen any of them define it, or even capable of defining it at all, because while I may understand THEM - me having studied not only physics, but also vastly more than they about the subjects they try to express and experience, and thus me having a vastly wider viewpoint and basis for evaluation of the experienced phenomena they describe - and while therefore I may understand what they are talking about, THEY themselves do not know... Which is something - the precious state of knowing what one knows and of knowing also what one does not know, (and thus being able to admit what one does NOT know and what one does NOT understand) - that is belonging to a condition or state of mind, that seems to make them feel vulnerable, and is a state of mind that even could (allow a Criminal Mind to take away the Energy with which they hold, and thus allow a Criminal Mind to) destroy what they DO know: Awareness and perception is entire- ly a matter of having (or creating or maintaining) the Life Energy to connect and so to perceive and to be aware of certain things. ' They feel, that they can not admit that they do not know (something), because (admitting) it tends to break the intention (and with that, the ability to create and direct and hold and maintain sufficient Life Energy) to feel and perceive things they do not yet know. In other words, saying that one can not perceive something, is counter to the intention to perceive, (perceiving is) to INTEND to be able to connect to something and thus to (create or use the Energy for it, and so to) perceive it, or to perceive something about it. Therefore they are reluctant to admit they do not know something, or that they can not perceive something, or that they perceive something wrongly - reluctant even to admit it to themselves, which is because of these mechanisms - and so they all, and without exception it seems, are stuck in a defense mode and an I know more than others-mode, which prevents of course a proper interaction with others - not only to verify or validate what they see, but also to increase their understanding of what they see (or rather, to determine what and whom they fail to see): They do not know and do not want to detect the fact, that it is ONLY Criminal Minds (only one percent of the population) who most vehemently try to destroy and to oppose (which is to pull or to smash away, or to contaminate the Energy for holding, and for communicating, and for feeling) any truth found out and any truth understood. They have no idea whatsoever, how tremendously evil and how fiercely driven Criminal Minds are in their joy to secretly inflict evil on anyone: Love Everyone, and that even all the time and no matter what they do to you, is how Criminal Minds do easily destroy you and easily pull away your Energy, and these INTENTIONALLY destructive ideas - ideas that Criminal Minds teach - mainly originate from the land of India. Loving everyone is the quickest way to destroy and pervert Love, and to destroy life, by empowering Criminal Minds with Energy - and it is exactly that, what they intend to bring about. The correct phrase is Do not Hate anyone - as the faithful readers know and as others are easily reminded of being the actual truth. ' _____________ Consciousness: That what you connect to with clean, clear Life Energy: You then become aware of it as it actually exists. Your consciousness is determined by how well you desire and are able to generate and use such clean, connecting Energy. The connecting IS the action of perceiving, and of being aware. However, both that ability or desire, AND the Life Energy itself necessary to connect and thus to become aware, have been very severely damaged and are very severely blocked and continuously messed up, by Criminal Minds, and they did do so not only IN the past, and they did not only distort or block perception OF the past so that you can not remember or connect to most of it now, but they also do this to you in the present, and they will of course do it in the future too, to you and others, as they have no intention to stop. In other words - and particularly in the not unlikely case, that you have or will have studied or have to listen to any of the very false concepts about consciousness, about awareness, that the 'gurus' and 'swamis' and 'buddhas' like to swamp and destroy the 'New Age' with - all the ideas of the evolution of consciousness, and of enlightenment, of life is for learning, etc., are intended ONLY to prevent you from facing Criminal Minds, and to prevent you from facing those past and present and of course future actions of Criminal Minds when they were damaging - which they do in the present also and which they intend to continue to do in the future too - which is them damaging your ability to feel and thus to enjoy life, and damaging very much your ability to defend yourself against their evil, and thus damaging your ability to stay healthy and to enjoy a life in health, and damaging your ability to perceive these Criminal Minds, when they present their 'mask' to you that hides their soul, that hides who they are and who they were, while your true perception and your detection of them, would be aided of course by an ability (by your having the Energy) to sense and to remember them as you have known them in your past, in any past. ' Our consciousness has almost completely been eradicated by Criminal Minds, and is continuously under the most severe attack by them - day and night, also during our sleep. And there is no development of Consciousness at all, as you are knocked more and more UNCONSCIOUS, and that continuously or repeatedly; but what IS there, at most, is only REGAINING some (small part of) your Consciousness and of your Abilities and of your Love and of your Beauty - regaining it for some short time at least, till these (the Energies to hold and use your abilities, your Beauty and your Love) are smashed away again; that is, unless you learn (but not from Criminal Minds, especially not from those, who claim to be and who are worshiped as spiritual teachers or want to be accepted as world teachers, not from any such who have any connection to the beliefs that are rooted in and still sprouting from India, generally, and not (PLEASE!) learning from those who are selected by aliens to spread the lies - no matter how obvious the lies are - that the chosen ones have been told indeed, and which they blindly believe because aliens said so, and are made to pass on of their own free will and judgment to keep our civilization down and confused; and more generally, not from those who will do everything to PREVENT you from being yourself and from following your ACTUAL nature, which is) that you yourself actually do want very much and have always wanted to FACE AND ALSO TO UNDERSTAND Criminal Minds, to see again who ARE Criminal Minds - instead of running away after Noble Truths, in small or even big vehicles of spiritual development trying to stop all life, and thus, by running away, betraying everyone, (really they do, that's not a joke!), while the correct thing to do, of course, is facing Criminal Minds and thus REGAINING some of your sanity and of your Love and of your Beauty, instead of convincing people, that they must do as if Criminal Minds do not exist, and that everything (that these 'non-existent' Criminal Minds do to you) is YOUR OWN fault or even for your own good, and - yes, they really say so - is necessary to develop your consciousness, claiming - wonder oh wonder - that NOT facing Criminal Minds (that BEING insane, as ALL insanity is caused by Criminal Minds and continued by not facing them) IS developing your consciousness, really now... - but that is what they, Criminal Minds indeed, love to hear (of course), and that is what they teach you in India, and beyond, to put it very mildly, as you will find from reading 'How Do You Face Evil? - A Questionnaire' {HRI 20020201} and then 'What IS Depression or Lethargy' ' ____ Time: The present is defined as what exists. It is possible to feel the past (as anyone knows) - which is called memory, or if you are connecting very strongly, it might feel like re-living it, as it is possible to feel the past so vividly, that it seems for some moment more real than the present, which many of you have experienced at some time or other, and as you know it from dreams, which are merely Life Energies that you look into and thus experience, and of course preferably those Life Energies (which contain perceptions and feelings) created by yourself, preferably those I would say, or those created together with nice people who love you, but not those of Criminal Minds who PRETEND to and want to make you feel - with such Life Energies - that they love you and that you love them. It is however not the goal of therapists to make you sane, but only to make you feel good, and so therapists even might tell you - as therapy which you even pay for - to create such extremely debilitating but temporarily happy feelings or Energies. All feelings ARE Energies, and so you can create feelings, and so others can create feelings you feel, and so Criminal Minds can make you feel very sick indeed, or even damage your body and make it sick or die - and the 'gurus' are telling you NOT to see that, but to believe it is developing your consciousness. So we now are more or less forced to give a correct definition of their Cosmic Laws: Do not ever face who does what to you or to others, and why and how - and never ever face the existence and the actual nature of any Criminal Minds. ' Energies that have been created in the past - by definition Energies intend to do something, they record something, they hold something, and when condensed very much, they can become matter - can be seen or felt now, exactly as these Energies have been created or have been shaped and formed (in the past). Light of photons has nothing whatsoever to do with time, nor with space,* because perception and feeling is done with Life Energy and not with photon's light. * - (See (*) in the main body of text, above.) And Life Energy travels instantaneously, as I have already explained to you earlier, and which you can experience yourself. ' So when you look at the past and connect very intensely with the past, you can see what has been created in the past, of course, you can remember, isn't it, how you were sitting in the class room pretending to be a moron who does not know anything and who does not sense (feel-perceive) anything and who can not see people as they are - things you pretend, to please your parents and your teachers, and to not get them upset or angry because you refrain from telling them, or even from holding (yourself aware of) the very applicable thought, that they teach you too many lies, and that they severely hinder your abilities and your use of your desire to live and be alive and be of true value for others and for the society - and you can see what of that Energy (in this case, your Energy of your agreeing to be a moron in order to please others who believe and tell you that 'they know everything and that you know nothing' how much of that feeling or compulsion still) is active in the present, which is Energy that has been created in the past, and that you might like to remove because it hinders you. In this respect, such hindering Life Energies are comparable to blocks of concrete (stone), or, to very dirty water, or, to fog in the air, or, to drugs in your body - you basically want to remove them, these Energies with those feelings and compulsions and ideas, and you can remove them too, by seeing what is actually there, existing and still intending to control you. And so it might seem to you, that you travel to the past in order to repair your present - but you are acting from the present always, LOOKING INTO the past from the present, finding what of that is IN THE PRESENT still annoying you, but that was created or put there, obviously, in the past. And unlike land mines that, for instance in Cambodia, have in the past been put in the ground, and that one has actually to physically dig out of the ground now, in the present, Life Energies are much lighter and much less dense, much finer, and they respond to your looking at it, to your sensing them, if the Life Energies that you look at are not too hard to feel and remember (to connect to and feel as they actually are). And the hard ones you can learn about, in 'Defining The Major Harmful Or Bad Energies - As They Are Created And Projected By Criminal ' _______________________ Earth's Past And Future: The past is what happened - the future is not fixed, but you can feel the Energy of what will happen, what can be expected, should you be able to feel that and be willing to 'connect that feeling to your consciousness, so as to become aware of it.' Then you could of course decide to act upon what you expect, as anyone does more or less anyway, and you can decide accordingly - that is, according to what you want life to have, or what you want life not to have, and thus you try to avoid, or you try to meet and embrace, what will probably happen. Which of course requires that you are free enough, and not dominated too much, not only to have enough data and perception to correctly predict or evaluate the future, to anticipate and to prepare, but it of course requires also that you are not dominated too much and are free enough or have enough Energy and possibilities to be able to avoid things, or on the other hand, to embrace things and people, that you will meet in the future. ' The past is what has happened - it is fixed, it can not ever be erased (even though Criminal Minds do their best to destroy or to distort your Energy for connecting to and so remembering the past) and the past is available for anyone, also for you, to remember or feel, should you have (or create or get back the Energy to connect and thus to perceive and thus to become aware of some part of the past (and that, only as long as you have and keep the Life Energy to do so). Perception of the past can of course be erroneous, because the Energy for feeling or perceiving it, has been 'booby-trapped' (severely messed up) by Criminal Minds - and Criminal Minds, as you know by now, do not want, at all, that you feel or remember the past correctly, or that you keep it in your mind and thus would remain sane and act sanely, of course: Criminal Minds want the Energy of connecting to your memories WIPED out, taken away from you. So, if someone wants that your memories are wiped out, then you are probably talking to a Criminal Mind, or to someone who wants to hide Criminal Minds because they are so very unpleasant to look at - sure they are... ' The future is not fixed, but the Energy of Life shows a prediction or expectation of how things will be. Thus you can change also a future that otherwise would indeed occur as foreseen, if you did nothing to change it. Which was the idea in the excellent TV series Early Edition, in which the main person gets tomorrow's newspaper - but he gets it today... Even when you are intensely looking at the future, or if your attention (your Energy with which you connect things to your consciousness, so that you become aware of them) if that awareness is immersed in some past, then you still are doing so from the present, and so it is recorded also in your memories (as proven by the fact, that these memories can later be contacted and have that data available to connect to). In other words, the 'now' is recorded with your looking at the past or future, and so it will later be remembered, as, for instance, 'on the first of January of the year 2005, I looked and and vividly remembered the day in the year 2000 when the new millennium started.' ' ' ________________________ (Note on teaching history) Teaching children so many lies in school about history, is of course MAKING them very unaware, and MAKING them uninterested - and making them not want to have anything to do with history, or even with any school or with studying. And then you 'have to' force them by giving them examinations, and 'terrorize them' with homework - their having to learn now at home too what they already felt they wanted to reject at school - and then you 'have to' tell them, that 'they will get bad jobs' and 'they will not be invited into certain social circles,' if they do not pass those exams. And then they have to wait thirty or forty or fifty years before their interest starts again to return, when and because they finally want to know the truth, what actually happened in the past, and not what you are told in school, that happened in the past. ' Learning is connecting with Life Energy to the things to learn about, and the connecting Life Energy is of course - it HAS of course to be - generated by the student or pupil himself: It consists of the pupil's DESIRE to connect to some subject, and his already existing connection to some subject, a connection which he may or may not be aware of, but might discover. This, any good teacher knows by intuition - and working with that knowledge makes him a good teacher, or more precisely, it makes him or her a teacher. Of course what you are told to connect to and to study, actually has also to be there, has to exist as an actuality, for you to be able to connect to it, of course. This rules out many a science, because there is nothing there to actually connect to, they do not connect to the things that ARE existing. And of course, things that you ARE NATURALLY connected to or want to be connected to BECAUSE they exist, you should be allowed to connect to and to study, rather than being most persistently taught by science, and in schools and in universities, that the very things that are most intimate to a subject do not exist or must be wholly ignored. YOU are the most important factor in studying, of course, YOUR connection to life and you ability and desire to do so. This concept still has to penetrate the subject of teaching and of learning, even of teaching private music lessons, or of taking them as a student. And you keep wondering why many children or students or adults want to have nothing at all to do with studying or learning things that they were once highly interested in and that are actually most vital for them to learn AND THAT THEY WOULD MOST EAGERLY STUDY AND LEARN IF THESE THINGS ABOUT LEARNING AND TEACHING WERE TAUGHT TO THEM FIRST.... ' ' Criminal Minds DO NOT WANT you to know, to feel or to remember or to understand the present, nor the future, nor the past. (They are Criminal Minds, remember!) So they work very hard to make you BELIEVE, that you have been taught what exists (what has happened and what was intended by whom) in the past, when in fact you are very wrongly informed indeed. This is not good for children, at all, because they are not stupid, at all, and they probably can feel better (and more) than adults can - about which highly interesting and revealing subject I intend to write for you, soon - about 'Children Wiser Than You?' ' Teaching history has of course everything to do with (and is of tremendous value for) understanding the present, and has everything to do with correctly evaluating the future, as almost all that will happen in the future, has been created, brought about, caused, in the past - often in the very distant past - of course. But Criminal Minds of course equally produce the most atrocious lies about the future, in order to make you not properly feel the future,to make you not understand the future correctly, so that you will spend your money or your time not correctly, on the wrong things, because you have been convinced (you have been and are made continuously to believe by them) that their lies are the truth about the future. ' So you have to know the basic mechanism of learning and of teaching - which very many teachers very wrongly have assumed they know or they have learned, and which they said they knew something or even all about - the principles of learning and of teaching: The desire to connect to a part of life and thus to get to understand that part, and how to go about contacting and using that desire to connect to that part of life. But they do not even know - about teaching and learning - that THAT IS LEARNING AND TEACHING. Nevertheless it can be learned correctly, also by them. ' And those who intuitively had it right, who just do it right and therefore are loved as teachers, or who therefore enjoy learning as pupils and students, will only confirm what they already felt - and acted upon - what was true. See further: 'Learning And Reading - Leonardo Da Vinci and Galileo Galilei had an excellent command of reading and writing' published). ' ' ________ Footnote: (1) 'The Become Perfect-Mind-Control of Hinduism, Buddhism and New-Age Cults' {HRI 20050514-V3.1} (14 May 2005 - Version 3.1 on 14 June 2005) __________ 'Learning And Reading - Leonardo Da Vinci and Galileo Galilei had 'Genuine Art - Producing It, Recognizing It' {HRI 20021220} (20 Dec 2002) 'The Trinity Of Science - Truth, Love and Beauty' 'About Aliens, Dimensions, Consciousness, Time, And Earth's Past 'How Do You Face Evil? - A Questionnaire' {HRI 20020201} 'Defining The Major Harmful Or Bad Energies - As They Are Created ' ____________ Verification: http://www.angelfire.com/space/platoworld ' and poet This is 'learnware' - it may not be altered, and it is free for anyone who learns from it, and (even if he can not learn from it) who passes it on unaltered, and with this message included, to others who might be able to learn from it. None of my writings may be used, ever, to support any political or religious or scientific agenda, but only to educate, and to encourage people to judge un-dominated and for themselves, about any organizations or individuals. Send free-of-Envy and free-of-Hate, Beautiful e-mails to: PlatoWorld at Lycos.com (address unreadable for Internet robots - replace ' at ' with the '@' symbol) ==== Subject: Re: Functional equation and translation . Dave Rusin a .8ecrit : We've got a functional equation like: > f( x/(x+1),y )= f(x,y + 2) + 3 1) Yes, well you appear to have an endless supply of functional equations > and I'm not entirely sure what your overall point is, but in this > case, like many, you seem to be asking for a description of all > functions f : R^2 --> R with the property that f o F = G o f > where F and G are given in (1). > (The phrase intertwining operator is sometimes used for such an f.) The domains of your functions are not entirely clear; for example, your > equation (1) makes no sense when x=-1 ; is f supposed to be defined > along that line? Also, the type of function f was not specified -- is > it supposed to come from some algebraic family (a formula)? or is it > supposed to be continuous? smooth? etc.? In this example, F(x,y) = (x/(x+1),y+2) is conjugate to a translation, > that is, F = h o T o h^{-1} where h(x,y) = (1/x, y) and > T(x,y) = (x+1, y+2). You may interpret this as being defined on the > real plane minus the vertical axis, or as being defined on the product > of two copies of the Riemann sphere, for example. (Other domains are > also possible.) So the functional equation to be solved is > f o (h o T o h^{-1}) = G o f > i.e. > (f o h) o T = G o (f o h) In other words, the function f you seek is conjugate to a function > f' = (f o h) which is to satisfy a similar functional equation > f' o T = G o f' > where G is given. This one is perhaps easier because > T is a translation and thus a bit easier to visualize than F is. So what does this functional equation say? It says f' is to be defined > on the plane, but that when you take a step from one point (x,y) to > another, (x+1, y+2), the value of the function is changed by G. > That's the only constraint. Well, then, that means you can give f' any values you like on the > strip where 0 <= x < 1, and then to define f' anywhere else, just > count the steps needed to get back to this strip; for example, > (pi, e) is three steps away (it's T^3( 0.14159..., -3.28181...) ), > so f'(pi, e) = f'( T^3( 0.14, -3.28) ) = G^3 ( f'( 0.14, -3.28 ) ) > = f'( 0.14, -3.28 ) + 9. So the value of f' is uniquely determined > by its value at the other point within the vertical strip. More generally, you could define f' arbitrarily on other regions. > The key term you need here is fundamental domain. The translation T > generates a (discrete, infinite, cyclic) group Gamma = which acts > on the plane; a fundamental domain D is a region whose translates > gamma(D) cover the plane (as gamma ranges over Gamma) and whose > intersections are contained in the boundary of D. There's no single > best choice of a fundamental domain; for example, for your T we > could choose the horizontal strip where 0 <= y < 2 instead. Likewise your G defines a map presumably from R^1 to itself, and > generates a group Delta = of self-maps of R^1. Your proposed solutions frequently mention something like fractional > iterates. There is no reason that the solutions f to your original > problem have to be consistent with any such construction. If those > are the things you are interested in, you ought to say that. More > precisely, what you are (probably) then asking for in this case is that > you want people also to find (1) an embedding of Gamma into a connected > Lie group Gamma^* acting on R^2, (2) an embedding of into a group > Delta^* acting on R^1, and (3) a function f' such that for every gamma > in Gamma^* there is a delta in Delta^* with f' o gamma = delta o f' > such that delta = G when gamma = T . The minimal Gamma^* in this > case is isomorphic to the additive group of the real numbers, but there > are many possible ways it could act on the plane. For example, the > elements of Gamma^* might be the set of motions > gamma t : (x,y) --> ( x + t, y + 2t + sin( pi t ) ). > Similarly the elements of Delta^* form a group of motions of the real > line, but could be, say, those of the form > delta t : z --> z + 3t + ( cos( 10 pi t ) - 1 ) > The role of the fundamental domain is played here by the vertical axis: > you can define f' any way you like along that axis, and then the > value of f' elsewhere will be found by following the curve gamma > back to the vertical axis and using f' o gamma = delta o f', namely > f'( x,y ) = f'( gamma x( 0, y - 2x - sin(pi x) ) ) > = delta x (f'( 0, y - 2x - sin(pi x) ) ) > = f'( 0, y - 2x - sin(pi x) ) + 3x + cos(10 pi x) - 1. Well, I'm not entirely sure where I'm going with this line of > reasoning, because I'm not entirely sure what the question is. > So let me just repeat the main points I wanted to make: You need to tell us what the expected domain and range of f are. > The geometry of those two sets is of real importance. > You need to specify what kind of function f you want (e.g. any > restrictions on continuity) > If you want f to intertwine with a continuous family of transformations > rather than just the composites of a single one, you have to tell us. Without these bits of information, the functional equations you > propose become just a sort of pointless game of moving symbols around > with no apparent goal. dave DEAR ALL, I still hope some websiter will consider my question as shown in the first thread. f is a real function R^2 ->R ,p as mentioned is R->R and we may use iterated forms like T^[a*phi(x)](y) ,T being defined .. Since Abel there are known reasons to work with iterated functions to try solving equations (lots of cases are already well known!) Alain. ==== Subject: Question about stochastic processes Hi everybody, Can anybody tell me where I can find a proof of the following fact without using martingales: If X:WxR+ ->R is random process with independent increments and continuous in probability => there exists a.s. a right continuos version of it ? ==== Subject: ISO algorithm for random derangements X-No-Confirm: yes Is there a good algorithm for sampling uniformly from the space of all derangements of an ordered list? (A derangement is a permutation in which no item remains in its original position.) The best I have found is a rejection algorithm (i.e. do Fisher-Yates shuffles until the obtained permutation proves to be a derangement). Also, is there a good algorithm for enumerating these derangments? kj -- NOTE: In my address everything before the first period is backwards; and the last period, and everything after it, should be discarded. ==== Subject: Re: ISO algorithm for random derangements >Is there a good algorithm for sampling uniformly from the space of >all derangements of an ordered list? (A derangement is a permutation >in which no item remains in its original position.) The best I >have found is a rejection algorithm (i.e. do Fisher-Yates shuffles >until the obtained permutation proves to be a derangement). >Also, is there a good algorithm for enumerating these derangments? I am not sure what you mean by Fisher-Yates shuffles; the most commonly used method to get permutations now is to exchange the element in the n-th position with a random element, the element in the n-1-st position with a random element of in the first n-1 positions, etc. This takes n steps and can be done reasonably efficiently. If one stops the procedure as soon as one finds a fixed point, this is not too bad. I will put the enumeration algorithm next, as it illustrates what needs to be done for a more direct algorithm. Any permutation is a product of cycles, and a derangement is one in which the cycles all have length at least 2. So start by enumerating all cycles with lengths not equal to 1 or n-1. This then reduces the problem to enumerating what is left over. Now to the problem of efficiently generating a random derangement. If we have a random permutation, the length of the cycle containing a given element is equally likely to be anything from 1 to n. If it is a random derangement, then it cannot be length 1, and what is left over has to be a random derangement, so the probability it is accepted is the probability that the rest is a derangement. So if one sets up a suitable sampling scheme for this, which is not too difficult, this gives a direct means to get a random derangement, which close to a minimum use of random bits. -- 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 : ISO algorithm for random derangements Le 17/06/2005 13:09, dans d8ub1d$3vc$1@reader1.panix.com, .82ækjæé a .8ecritæ: > Is there a good algorithm for sampling uniformly from the space of > all derangements of an ordered list? (A derangement is a permutation > in which no item remains in its original position.) The best I > have found is a rejection algorithm (i.e. do Fisher-Yates shuffles > until the obtained permutation proves to be a derangement). >Also, is there a good algorithm for enumerating these derangments? There are not much less derangements than permutations (proportion is roughly 1/e, if I remember well), so you could use an algo for enumerating permutation, and use a rejection approach. ==== Subject: cubic equation - is it really solvable? In some sense the cubic equation is solvable since there are explicit formulas for the solution, but in general, even for equations with rational solutions, you get answers that you can't show that it really stands for a rational number. You get the cubic root of a complex number, and you will end up with an infinite cubic-equation solving procedure if you try to find the corresponding rational number. So, is it right to say that it is theoretically solvable, but in practice, it's of minor interest unless you just want a numerical approximation of the correct value? Any important theoretical results I'm not aware of are excluded from this rant. :-) ==== Subject: Re: cubic equation - is it really solvable? >In some sense the cubic equation is solvable since there are explicit > formulas for the solution, but in general, even for equations with rational > solutions, If all the solutions are rational then the cubic can be factored. There are trial and error methods where the number of trials is happily finite. ==== Subject: Re: cubic equation - is it really solvable? > In some sense the cubic equation is solvable since there are explicit > formulas for the solution, but in general, even for equations with rational > solutions, you get answers that you can't show that it really stands for a > rational number. You get the cubic root of a complex number, and you will > end up with an infinite cubic-equation solving procedure if you try to find > the corresponding rational number. >So, is it right to say that it is theoretically solvable, but in practice, > it's of minor interest unless you just want a numerical approximation of > the correct value? >Any important theoretical results I'm not aware of are excluded from this > rant. :-) In the casus irreducibilis, the cubic equation has three real roots, but applying the Cardano formulas involves computations with non-real complex numbers. An alternative formula involves trigonometric functions, are you willing to allow that? -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ ==== Subject: Re: cubic equation - is it really solvable? > In the casus irreducibilis, the cubic equation has three real roots, > but applying the Cardano formulas involves computations with non-real > complex numbers. An alternative formula involves trigonometric > functions, are you willing to allow that? When it comes to trigonometry it's alright, as long as I get the exact rational numbers in the end. But then this isn't a possible way either, is it? ==== Subject: Re: cubic equation - is it really solvable? <170620050905237811%edgar@math.ohio-state.edu.invalid> Yes, it *is* possible. The formulae to which you refer are meant to be applied to *irreducible* cubics. You are applying them to *reducible* cubic. Irreducible cubics do not have rational roots. The way one gets *rational* roots is by factoring the cubic. This is something that should always be done first when trying to solve any polynomial. ==== Subject: Re: cubic equation - is it really solvable? > In the casus irreducibilis, the cubic equation has three real roots, > but applying the Cardano formulas involves computations with non-real > complex numbers. An alternative formula involves trigonometric > functions, are you willing to allow that? Other alternative formulas involve trigonometric or hyperbolic functions for all other cases. Trigonometric methods were of great importance at the time computers didn't exist (for they are often easy to use with logarithms). I've a Log Table from 1893 with many such formulas. ==== Subject: Re: cubic equation - is it really solvable? > complex numbers. An alternative formula involves trigonometric > functions, are you willing to allow that? What is this alternative formula? Willem ==== Subject: Re: cubic equation - is it really solvable? Le 17/06/2005 16:14, dans 9fa4b$42b2dac2$d468cfd2$28736@nf1.news-service.com, .82æWillem H. de Boeræé a .8ecritæ: >> complex numbers. An alternative formula involves trigonometric >> functions, are you willing to allow that? >What is this alternative formula? Just start with x^3+p*x+q=0 and manage to obtain an equivalent equation Of the form 4*u^3 + 3*u = A, or 4*u^3 - 3*u = A. The computation is straightforward :-) Hint: use cos(3*t) and cosh(3*t)... ==== Subject: Re: cubic equation - is it really solvable? > Just start with x^3+p*x+q=0 and manage to obtain an equivalent equation > Of the form 4*u^3 + 3*u = A, or 4*u^3 - 3*u = A. > The computation is straightforward :-) >Hint: use cos(3*t) and cosh(3*t)... And you get an exact solution without any trigonometric terms? ==== Subject: Re : cubic equation - is it really solvable? Le 17/06/2005 18:19, dans rKCse.27481$d5.179659@newsb.telia.net, .82æGunnar Gæé a .8ecritæ: >> Just start with x^3+p*x+q=0 and manage to obtain an equivalent equation >> Of the form 4*u^3 + 3*u = A, or 4*u^3 - 3*u = A. >> The computation is straightforward :-) >> >> Hint: use cos(3*t) and cosh(3*t)... > And you get an exact solution without any trigonometric terms? You get trigonometric solution, it's up to you to simplify. I don't understand what you really want: if your polynom has rationnal coefficients, I already answered you can find all rationnal roots without much computations (and only integer or rationnal +-*/). For other roots, you *need* radicals or trigonometry. ==== Subject: Re : cubic equation - is it really solvable? Le 17/06/2005 13:32, dans vxyse.27456$d5.179586@newsb.telia.net, .82æGunnar Gæé a .8ecritæ: > In some sense the cubic equation is solvable since there are explicit > formulas for the solution, but in general, even for equations with rational > solutions, you get answers that you can't show that it really stands for a > rational number. You get the cubic root of a complex number, and you will > end up with an infinite cubic-equation solving procedure if you try to find > the corresponding rational number. >So, is it right to say that it is theoretically solvable, but in practice, > it's of minor interest unless you just want a numerical approximation of > the correct value? >Any important theoretical results I'm not aware of are excluded from this > rant. :-) Given a polynom with rationnal coefficients, it is always possible (and fairly easy) to find all rationnal roots... You just need prime factorizations of first and last coefficients, and make trials. ==== Subject: Re: inner products proof help >Let T be a linear operator on an inner product space V, and suppose that >||T(x)|| = ||x|| for all x. >Prove that T is one-to-one. Suppose T(x) = T(y). Then ||T(x)|| = ||T(y)|| ==> ||x|| = ||y||. But just because the lengths are equal does not mean x = y. So what do I do >instead? You haven't used the fact that T is linear. Suppose that T(x) = T(y). Then ||x - y|| = ... = ... , so x = y. ************************ David C. Ullrich ==== Subject: question about Bezier simplices I would like to ask you a question about something that is probably taught at school .. Is it correct that *ANY* (multivariate) polynomial (in some domain simplex) p(x) can be written in form of linear combination of Bernstein polynomials where variables are barycentric corrdinates of x w.r.t the domain simplex?? In fact I would like to compute the image of a simplex by an multi-affine map, and intend to make use of the blossoming technique. Thao Dang ==== Subject: Re: question about Bezier simplices By some simple mathematical manipulation of the Bernstein polynomials, it can shown that the n-th order set of them span the space of n-th order polynomials, on some closed domain in R. This result extends easily to R^m using the tensor product. I would like to ask you a question about something that is probably > taught at school .. Is it correct that *ANY* (multivariate) polynomial (in some domain > simplex) p(x) can be written in form of linear combination of Bernstein > polynomials where variables are barycentric corrdinates of x w.r.t the > domain simplex?? In fact I would like to compute the image of a simplex by an > multi-affine map, and intend to make use of the blossoming technique. > Thao Dang > ==== Subject: Re: question about Bezier simplices polynomials, it can shown that the n-th order set of them span > the space of n-th order polynomials, on some closed domain > in R. I don't see why you think making assumptions about the domain is necessary? It is an entirely algebraic result. Let B[n,k](t) = C(n,k) t^k (1-t)^(n-k) be the family of Bernstein polynomials. The specific claim is that for any given degree n >= 1, the Bernstein polynomials B[n,0], B[n,1], ..., B[n,n] form a basis for the vector space of polynomials with real coefficients of degree less than or equal to n. Since this vector space has dimension n+1 (it has a standard basis 1, x, ..., x^n) and our list contained n+1 Bernstein polynomials, it is enough to show linear independence according to a standard theorem of linear algebra. So suppose that a_0, a_1, ..., a_n are real numbers such that sum a_k B[n,k] = 0. We want to show that this implies a_k = 0 for all k. If we regard this polynomial as a real-valued function and evaluate it at t = 0 we get a_0 = 0. Now note that B[n,k] = n/k (1-t)/t B[n-1,k-1] and thus by dividing through by (1-t)/t (which does not change the validity of the linear relation since the right-hand side is zero) we get a linear relation among the B[n-1,k-1] with coefficients b_(k-1) = n/k a_k. By induction (the basis case is trivial) this is a trivial linear relation, that is, b_k = 0 for all k and thus also a_k = 0. Is this the standard proof? I don't remember ever seeing a proof of this fact before so I'm kind of curious. Per ==== Subject: Re: An exact 1-D limit challenge - 13 <70d4d$42ad27f0$cf700aea$27013@PRIMUS.CA> Hello Jay Bryant, JB> still conferences are only conferences, Let me again point out, *International* and *Symposium* http://www.mmrc.iss.ac.cn/~issac2005/callpaper.htm ISSAC is the yearly premier international symposium in Symbolic and Algebraic Computation. It provides an opportunity to learn of new developments and to present original research results in all areas of symbolic mathematical computation. Planned activities include invited presentations, research papers, poster sessions, tutorial courses, vendor exhibits and software demonstrations. JB> and, worse still, You sound like a superciliary professor who has a dozen grad students and published a hundred of papers (to tell the truth, real professors I have happiness to know in person, http://www.cas-testing.org/index.php?list=4 http://www.cas-testing.org/SciFace.phtml So I decided to find where is your site located, and read 5-10 your papers (pubished in journals) to learn from you. However, to my utter disappointment, I found neither your site nor even a tiny home page nor a single paper. So maybe you kndly point out where to read your stuff, if any? Over 15 years I keep working in the field of computer algebra and software testing, and remember by heart many many dozens names of the researcher - but not your name. JB> papers submitted to journals are reviewed much more JB> rigorously. i guess you didn't know that. A 2 cent value trick. Failrly chintzy. I have an impression that you simply have much time and decided to chat with us. This firm impression came from the fact that upon reading almost all of about 50 your messages I, with even stronger and many of your posts are just general comments like JB> yes, that's true. i didn't go any further because i don't JB> completely understand the guy's question. JB> or pedantics who make a big deal out of small honest errors JB> to feel knowledgable. JB> indeed. silly me. JB> tell you what. a person is an expert when it is acknowledge JB> by other people Tell you what. Why don't consider reading opinions about quality & scope of my work produced by experts in the field of computer algebra systems, CAS manufacturers and top CAS folks since 1993. Find a few selected opinions from them at placed here http://www.cas-testing.org/ind?ex.php?list=7 ? which belong, respectively, to COMMENT 1 Albert D. Rich www.derive.com www.mulisp.com COMMENT 2 Prof Dr Oleg Marichev (WRI) www.functions.wolfram.com COMMENT 3 Dr Anwar Shiekh (WRI) Test Development Group Supervisor COMMENT 4 Prof Dr Walter Oevel (SciFace GmbH) http://www.math.uni-paderborn.?de/~walter/ COMMENT 5 Dr Anwar Shiekh (WRI) Test Development Group Supervisor COMMENT 6 Dr Anwar Shiekh (WRI) Test Development Group Supervisor COMMENT 7 Dr Anwar Shiekh (WRI) Test Development Group Supervisor COMMENT 8 Dr Michael Wester www.math.unm.edu/~wester COMMENT 9 Dr Anwar Shiekh (WRI) Test Development Group Supervisor COMMENT 10 Dr Anwar Shiekh (WRI) Test Development Group Supervisor COMMENT 11 Stefan Wehmeier (SciFace GmbH) http://www-math.uni-paderborn.?de/~stefanw/ COMMENT 12 Dr Anwar Shiekh (WRI) Test Development Group Supervisor COMMENT 13 Kelly Roach http://www.kellyroach.com/ COMMENT 14 Dr Anwar Shiekh (WRI) Test Development Group Supervisor Please find a recent opinion about my work made publicly by a top MuPAD developer, Herr Wehmeier Vladimir has contributed many bugs to www.mupad.de/BUGS and even got an award for being our best beta tester. Please find a last minute link to an old paper of mine here An n-Dimensional Integral Formula http://www.planetquantum.com/News/050601.html JB> i would not buy products from you because of your JB> lack of credibility. Maybe because of lack of your understanding what's going? 1) what we do for general public - the Maple Bugs Encyclopaedia - the largest world's searchable Maple bug database, calculated automatically - is *free* of charge - a string of major upgrades is coming. 2) currently, Cyber Tester, LLC offers NO services for individuals whatsoever. Our customers are companies only. 3) to call a spade a spade, in computer algebra and software testing you are a sheer ignoramus, and because of this fact, you are not in a position to judge correctly about my work and Cyber Tester. 4) graduate from kindergarten, go to school, finish grad courses, educate yourself, and maybe you see the world in brigher colors. Best wishes, Vladimir Bondarenko http://maple.bug-list.org/MapleCrisis-Review-01.pdf [16 Mb] VM and GEMM architect Co-founder, CEO, Mathematical Director Cyber Tester, LLC 13 Dekabristov Str, Simferopol Crimea 95000, Ukraine tel: +38-(0652)-447325 tel: +38-(0652)-230243 tel: +38-(0652)-523144 fax: +38-(0652)-510700 http://www.cybertester.com/ http://maple.bug-list.org/ http://www.CAS-testing.org/ > JB> only some poster papers at small conferences. Well... if you call those ISSACs (which is an acronym > for International Symposium on Symbolic and Algebraic > Computation) small conferences... No comment. > still conferences are only conferences, and, worse still, your paper > was only a poster paper. where are your journal publications? how come > an expert has none of these? anyway, standards for a good conference is > different from standards for good journals ==> papers submitted to > journals are reviewed much more rigorously. i guess you didn't know > that. JB> i don't see how identfying bugs would qualify > JB> you as a CAS expert. As Maple case shows us, streamlined CAS development > is not possible without a diagnostic toolkit which > helps identify/classify/minimize bugs - and I was > able to develop an approach to achieve this goal. > tell you what. a person is an expert when it is acknowledge by other > people not because that person calims that he is an expert. as far as i > am concerned, you have nothing to show for your expertise, so i would > not buy products from you because of your lack of credibility. ==== Subject: Re: An exact 1-D limit challenge - 13 <70d4d$42ad27f0$cf700aea$27013@PRIMUS.CA> <42B2DBC3.8020204@info.unicaen.fr> Fri, Jun 17 2005 10:18 am JK> V. Bondarenko continues to spread his hatred of any critics Of numerous systematic public intentional insults like a complete software testing ignoramus Jerzy Karczmarczuk produces, who obviously seeks promotion badly, why not? so here is his site http://users.info.unicaen.fr/~karczma/ Who of you folks is able to find *any*, even the slightest vestige of Karczmarczuk's expertise in soft testing there? ==== Subject: Numerous, systematic public intentional insults, Or, Jerzy Karczmarczuk keeps defaming the l'Universite' de Caen B asse-Normandie Alain Bretto alain.bre...@info.unicaen.fr, alain.bre...@wanadoo.fr, Patrick DUBOIS dubo...@admin.unicaen.fr, v...@cybertester.com A leading world's CAS researcher, whose services had been used by the biggest market players such as Texas Instruments, Inc, and Wolfram Research, Inc http://www.cas-testing.org/ind[CapitalEth]ex.php?list=3 the MuPAD Beta Contest First Prize winner launched by SciFace GmbH http://www.cas-testing.org/Sci[CapitalEth]Face.phtml the inventor of the LIFT and CYCLE technologies to be demonstrated in the near future, http://maple.bug-list.org/Mapl[CapitalEth]eCrisis-Review-01.pdf I must inform you sadly that, alas, a worker of l'Universite' de Caen Basse-Normandie, some Jerzy Karczmarczuk, continues defaming your organization. The day before yesterday, on Monday, 6 Jun 2005 12:19:18 I've sent you a carbon copy of a report on improper behaviour of this person. The main copy had been addressed to Professor Bretto from whom I really expected help in stopping the insulting messages the above-said Jerzy Karczmarczuk posts into Google Groups. Being too much immersed into research activity, I did not visit the Google Groups yesterday. However, today, on June 8, 2005, with much surprise, I discovered the following remark from Jerzy Karczmarczuk showing his full disrespect to me, to you, to the whole administration of your University, and thus, to the whole l'Universite' de Caen Basse-Normandie: JK> Until now I was the only one in my department who knew that JK> we have a mentally sick person in this newsgroup, now there JK> are more. Imagine the explosion of laughter when one of the JK> receivers of this text of Bondarenko: > A leading world's CAS researcher, the inventor of the LIFT and > CYCLE technologies to be demonstrated in the near future, I am > sorry to inform you [...] JK> tried, being a serious person, to verify on the Internet the JK> case of this leading world's CAS researcher, to find his JK> publications, software, or *whatever*. My detailed answer to this person you can find here: The behavior of Jerzy Karczmarczuk who even does not acquainted with me personally, and who does not have any relation to the field I am working in, automated software testing, cannot be described in other way as a wilful trespass, an wilful illegal act against my rights. Being a linguist, I hope that upon reading the statements made upon me, you certainly feel that I am right. I kindly request from you that you stop at last the described improper actions of a worker of l'Universite' de Caen Basse- Normandie, Jerzy Karczmarczuk wrt to me. Having too many a task on software testing automation, I hope that I will not be forced to get involved in further handling of this case. Just a detail, if the libel sent by Jerzy Karczmarczuk and the scandal would continue further, what would think your potential students about joining your University where their rights could be broken so easily? Best wishes, Vladimir Bondarenko v...@cybertester.com VM and GEMM architect Co-founder, CEO, Mathematical Director Cyber Tester, LLC 13 Dekabristov Str, Simferopol Crimea 95000, Ukraine tel: +38-(0652)-447325 tel: +38-(0652)-230243 tel: +38-(0652)-523144 fax: +38-(0652)-510700 http://maple.bug-list.org/Mapl[CapitalEth]eCrisis-Review-01.pdf http://www.cybertester.com/ http://maple.bug-list.org/ http://www.CAS-testing.org/ ------------------------------[CapitalEth]------------------------------[C apitalEth]----- A leading world's CAS researcher, the inventor of the LIFT and CYCLE technologies to be demonstrated in the near future, I am sorry to inform you that a worker of l'Universite' de Caen Basse- Normandie, some Jerzy Karczmarczuk, defames your organization via systematic sending publicly the insulting messages. I am too busy with research work; but now I am feeling that the time has come to stop the improper behaviour of Jerzy Karczmarczuk and ask for your resolute help in modifying the behavior of this person. Here you can find some samples of his statements about me, a person whom he never even met. JK> person, whose ego reached the stage needing a competent JK> psychiatrist. JK> the insulting slogans, as taken directly from an Ancien JK> Regime era... JK> This fellow Bondarenko visibly suffers from a heavy mental JK> disorder. JK> Insane people usually deserve some compassion JK> perhaps he will be compelled by somebody to undergo a medical JK> treatment... JK> a clinical idiot JK> V. Bondarenko is not capable of understanding the simplest JK> logic. JK> a person far from mental equilibrium and more, but I hope the quoted links will do. Also please note that, at any rate, Jerzy Karczmarczuk goes easily beyond his competence, a big defect for a research worker as well as an instructor. Had you need any kind of support to drive the nail home please don't hesitate to let me know and I guarantee you the strongest backstop imaginable to stop the above demonstrated disorderly conduct. Best wishes, Vladimir Bondarenko v...@cybertester.com VM and GEMM architect Co-founder, CEO, Mathematical Director Cyber Tester, LLC 13 Dekabristov Str, Simferopol Crimea 95000, Ukraine tel: +38-(0652)-447325 tel: +38-(0652)-230243 tel: +38-(0652)-523144 fax: +38-(0652)-510700 http://maple.bug-list.org/Mapl[CapitalEth]eCrisis-Review-01.pdf http://www.cybertester.com/ http://maple.bug-list.org/ http://www.CAS-testing.org/ ------------------------------[CapitalEth]------------------------------[C apitalEth]----- ==== Subject: Re: An exact 1-D limit challenge - 13 <70d4d$42ad27f0$cf700aea$27013@PRIMUS.CA> Let me again point out, *International* and *Symposium* > so what? having a paper in such a conference still does not qualify you as an expert. who is citing anything you have worked on, has nayone ever invited you to give a technical talk about your work. i guess the answer would be no, and no. > You sound like a superciliary professor who has a dozen > grad students and published a hundred of papers (to tell > the truth, real professors I have happiness to know in > person, http://www.cas-testing.org/index.php?list=4 > http://www.cas-testing.org/SciFace.phtml i was being polite, i didn't call you names, and i tried to remind you that maybe the way you are doing things may turn off potential customers. However, to my utter disappointment, I found neither your > site nor even a tiny home page nor a single paper. sounds like what i felt when i visited the website of a leading CAS researcher and didn't find anything of significance there. > So maybe > you kndly point out where to read your stuff, if any? > Over 15 years I keep working in the field of computer algebra > and software testing, and remember by heart many many dozens > names of the researcher - but not your name. > i don't work in CAS, i came across your email from sci.math. and it doesn't matter for me what you think, since i am not the guy making the extravagant claims. you are the one claiming yourself as a world leader in CAS. frankly that does not seem true to me, it is just a self-proclamation coming from you. This firm impression came from the fact that upon reading > almost all of about 50 your messages I, with even stronger > and many of your posts are just general comments like > no, i have never written anything to promote religion, i argued with a guy who was touting his religion and that annoyed me. yes, i give general comments sometimes and detail at others. i don't know everything, nobody does. Tell you what. Why don't consider reading opinions about quality & scope of my > work produced by experts in the field of computer algebra systems, > CAS manufacturers and top CAS folks since 1993. Find a few selected > opinions from them at placed here > tell you what. i guess what Jerzy says about you is true. that's all that i needed to know. and btw, i hardly think that the people whose name you put on your reference list will remember who you are... Please find a recent opinion about my work made publicly by > a top MuPAD developer, Herr Wehmeier > good for you then, still it's a far cry from leading CAS expert. Vladimir has contributed many bugs to www.mupad.de/BUGS and even got an award for being our best beta tester. > couldn't find any proof of this. as far as i can see it seems the mupda people prefer to keep their distance from you. Please find a last minute link to an old paper of mine here An n-Dimensional Integral Formula > http://www.planetquantum.com/News/050601.html > what credibility does this have? Maybe because of lack of your understanding what's going? > no, i understand what you are doing, i visited your shabby websites and i was none too impressed. and here i was thinking that Jerzy was being too harsh on you, sigh..... 2) currently, Cyber Tester, LLC offers NO services for individuals > whatsoever. Our customers are companies only. > yea, sure. 3) to call a spade a spade, in computer algebra and software testing > you are a sheer ignoramus, and because of this fact, you are not > in a position to judge correctly about my work and Cyber Tester. > i guess you say that to everyone. sigh. > 4) graduate from kindergarten, go to school, finish grad courses, > educate yourself, and maybe you see the world in brigher colors. > i see all the colors, do you? i think you see a shade of gray between reality and fantasy. bye. ==== Subject: An exact simplification challenge - 4 (beat all world's CASs, again) None of world's computer algebra systems can simplify this in a straightforward way, via a single command like simplify etc 4/sqrt(3)*Psi(1,1/3)-8/(3*sqrt(3))*Pi^2+12*I*polylog(2,1/2+1/6*I* 3^(1/2))-I*Pi^2+6*I*ln(6)^2-6*I*ln(6)*ln(3+I*3^(1/2))-6*I*ln(3-I* 3^(1/2))*ln(6)+6*I*ln(3-I*3^(1/2))*ln(3+I*3^(1/2)) Become a detective, use the deductive method, beat Mr Sherlock Holmes ;-) http://www.sherlock-holmes.co.uk/ http://www.sherlockian.net/ and teach us proudly how you fold up the constant! :) Again please focus on the steps and eschew using the Maple's identify feature, and please care about copying this from Google, let's hope that the grand Google Team in the (not!) long run will fix those blooming extras '-', so we need not sweat over deleting the wrong ones after pasting any longer. Best wishes, Vladimir Bondarenko http://maple.bug-list.org/MapleCrisis-Review-01.pdf [16 Mb] VM and GEMM architect Co-founder, CEO, Mathematical Director Cyber Tester, LLC 13 Dekabristov Str, Simferopol Crimea 95000, Ukraine tel: +38-(0652)-447325 tel: +38-(0652)-230243 tel: +38-(0652)-523144 fax: +38-(0652)-510700 http://www.cybertester.com/ http://maple.bug-list.org/ http://www.CAS-testing.org/ ==== Subject: Re: An exact simplification challenge - 4 (beat all world's CASs, again) X-RFC2646: Format=Flowed; Original None of world's computer algebra systems can simplify this in a > straightforward way, via a single command like simplify etc 4/sqrt(3)*Psi(1,1/3)-8/(3*sqrt(3))*Pi^2+12*I*polylog(2,1/2+1/6*I* > 3^(1/2))-I*Pi^2+6*I*ln(6)^2-6*I*ln(6)*ln(3+I*3^(1/2))-6*I*ln(3-I* > 3^(1/2))*ln(6)+6*I*ln(3-I*3^(1/2))*ln(3+I*3^(1/2)) Become a detective, use the deductive method, beat Mr Sherlock > Holmes ;-) http://www.sherlock-holmes.co.uk/ > http://www.sherlockian.net/ and teach us proudly how you fold up the constant! :) Again please focus on the steps and eschew using the Maple's > identify feature, and please care about copying this from > Google, let's hope that the grand Google Team in the (not!) > long run will fix those blooming extras '-', so we need not > sweat over deleting the wrong ones after pasting any longer. > Best wishes, Vladimir Bondarenko http://maple.bug-list.org/MapleCrisis-Review-01.pdf [16 Mb] VM and GEMM architect > Co-founder, CEO, Mathematical Director > Cyber Tester, LLC > 13 Dekabristov Str, Simferopol > Crimea 95000, Ukraine tel: +38-(0652)-447325 > tel: +38-(0652)-230243 > tel: +38-(0652)-523144 > fax: +38-(0652)-510700 http://www.cybertester.com/ > http://maple.bug-list.org/ > http://www.CAS-testing.org/ Since you are a genius at CAS, why don't you create the ultimate system? I hear your complaining loud and clear but yet I don't see you doing anything to fix the problem(if you think complaining will help then you are wrong). ==== Subject: Re: An exact simplification challenge - 4 (beat all world's CASs, again) Another funny computation I was not able to simplify with Maple, but I could by hand: The solid angle of a rectangle with vertices (0,0,0) (a,0,0) (0,b,0), seen from (0,0,c). Le 17/06/2005 16:07, dans Bondarenkoæé a .8ecritæ: >None of world's computer algebra systems can simplify this in a > straightforward way, via a single command like simplify etc >4/sqrt(3)*Psi(1,1/3)-8/(3*sqrt(3))*Pi^2+12*I*polylog(2,1/2+1/6*I* > 3^(1/2))-I*Pi^2+6*I*ln(6)^2-6*I*ln(6)*ln(3+I*3^(1/2))-6*I*ln(3-I* > 3^(1/2))*ln(6)+6*I*ln(3-I*3^(1/2))*ln(3+I*3^(1/2)) >Become a detective, use the deductive method, beat Mr Sherlock > Holmes ;-) >http://www.sherlock-holmes.co.uk/ > http://www.sherlockian.net/ >and teach us proudly how you fold up the constant! :) >Again please focus on the steps and eschew using the Maple's > identify feature, and please care about copying this from > Google, let's hope that the grand Google Team in the (not!) > long run will fix those blooming extras '-', so we need not > sweat over deleting the wrong ones after pasting any longer. Best wishes, >Vladimir Bondarenko >http://maple.bug-list.org/MapleCrisis-Review-01.pdf [16 Mb] >VM and GEMM architect > Co-founder, CEO, Mathematical Director > Cyber Tester, LLC > 13 Dekabristov Str, Simferopol > Crimea 95000, Ukraine >tel: +38-(0652)-447325 > tel: +38-(0652)-230243 > tel: +38-(0652)-523144 > fax: +38-(0652)-510700 >http://www.cybertester.com/ > http://maple.bug-list.org/ > http://www.CAS-testing.org/ > ==== Subject: Re: Seeing and feeling the third derivative Consider the vectors i=(1,0,0),j=(0,1,0) k=(0,0,1) and x,y,z in C^{3}[t_0,t_1]. Further let (C) be the traejctory having the vectorial equation r=r(t) , t in [t_0,T_0] , where r(t)=x(t)*i+y(t)*j+z(t)*k v(t)=r'(t)=x'(t)*i+y'(t)*j+z'(t)*k a(t)=v'(t)=r(t)=x(t)*i+y(t)*j+z(t)*k a'(t)=v(t)=x^{(3)}(t)*i+y^{(3)}(t)*j+z^{(3)}(t)*k . Perhaps in Mechanics a name for a'(t) may be ,,hyper-acceleration vector. Consider that P=(x(t),y(t),z(t)) is not a singular point, that is ||r'(t)|| > 0 . Further denote by {T(t),N(t),B(t)} the ,,Frenet-Serret basis applied in P, that is T(t)=r'(t)/||r'(t)|=the unit tangent vector, N(t)= T'(t)/||T'(t)||= the unit principal normal vector B(t)=T(t) x N(t)= the binormal vector. The positions (locations) of the vectors v(t) and a(t), with respect to {T(t),N(T),B(t)} are well-known. For instance v(t) is applied in P having the same direction as T(t) a(t) is situated in the (osculator) plane determined by T,N . Questions: 1) where is a'(t) ?? 2) It's not hard to find the scalar functions u,v,w from the equality a'(t)=u(t)*T(t)+v(t)*N(t)+w(t)*B(t) . Which is the (mechanical) meaning of these u(t),v(t),w(t) ? Perhaps in Mechanichs there is a significance (as in case of a(t) ). 3) Which are the trajectories for which a'(t) lies (if possible ) in plane (T,N) ? (or (N,B) , or (B,T) ?) I remember a nice monograph published between 1965-1975 , by ? Harris (?) with approx. title ,,Shocks and Vibrations(?). It's said that ||v'(t)|| has an influence on the human body (by a violent shock ?), By collision of two jet-planes ? Perhaps this is a reason why a'(t) is difficult to be put in evidence. ==== Subject: Re: Seeing and feeling the third derivative >Hi! >It's easy to see the effect of the first and the > second derivatives on a function's graph. Also, > the first and second derivatives have physical > meaning: velocity and accelaration. >What about the third derivative? Has it a physical > meaning? >I've heard the small corrections that a person (inconsciently) > does when he/she drivers a car is related with the third > derivative. > Hi Of course it has meaning. It means the acceleration is changing over time. As an example drop an item from high up say at the distance of the moon(no lateral motion allowed). The acceleration is a = G*M_earth/r^2, where G is gravitational constant. As the item approaches the earth the acceleration will increase until it is 32 ft/sec/sec at the surface. The third derivative will not be a constant in such a case and its effects can be seen on the graph of the velocity. ==== Subject: Re: Seeing and feeling the third derivative [references to physics deleted] >> It's easy to see the effect of the first and the >> second derivatives on a function's graph. ... >> What about the third derivative? ... >The third derivative will not be a constant >in such a case and its effects can be seen on the graph of the >velocity. Certainly the third derivative (or its effects) are *recorded* on the graph. That doesn't mean they can be *seen* there. The topologist and differential geometer the graphs of some simple functions from R^1 to R^2'' that ``If the function is not too complicated, then one can tell visually whether it is continuous at a point, whether it is differentiable there...even whether the derivative is continuous. Beyond that...existence of second derivatives, class C^2, and so forth...visual examination loses its power.'' (His ellipses.) This claim (about human vision) is very credible, and has been confirmed (somewhat) by experiments (and in any case, never experimentally disconfirmed, as far as I have been able to discover). As a simple illustration, ask yourself whether you can honestly say you're able to look at an arc of a conic section--say, near a vertex--and decide *without measuring the graph* (and doing calculations with the measurements) whether you are seeing a piece of an ellipse or a piece of a hyperbola. Lee Rudolph ==== Subject: Re: Seeing and feeling the third derivative As one can see, the physical meaning and use of high order derivatives are not very known in calculus classes. physical meaning of high order derivatives (MAA Monthly, Springer Mathematical Intelligencer, Revista Cubo)? ==== Subject: Re: martingale betting system question Many years ago, I was simulating such a Martingale betting system (on a Commodore 128!). After several hours, I checked and discovered that the computer had made a HUGE amount of money off the casino! When I checked the program, I discoverd that I had stumbled into a cycle of pseudo-random numbers that repeated after SIX numbers. Since these all happened to be winners in my betting system and since I only reseeded the RNG after a loss, ... ==== Subject: Re: martingale betting system question Le 17/06/2005 16:26, dans .82æjmorriss@idirect.comæ[CapitalE Grave] a .8ecritæ: > Many years ago, I was simulating such a Martingale betting system (on a > Commodore 128!). After several hours, I checked and discovered that > the computer had made a HUGE amount of money off the casino! >When I checked the program, I discoverd that I had stumbled into a > cycle of pseudo-random numbers that repeated after SIX numbers. Since > these all happened to be winners in my betting system and since I only > reseeded the RNG after a loss, ... > Bad luck :-) ==== Subject: Re: martingale betting system question On Thu, 16 Jun 2005 19:01:26 +0200, Jean-Claude Arbaut Le 16/06/2005 19:04, dans s4c3b1h0o01rko4gq8f9l1jnbjko791jq3@4ax.com, >.82æDavid C. Ullrichæé a .8ecritæ: > On Thu, 16 Jun 2005 17:11:29 +0200, Jean-Claude Arbaut > > Le 16/06/2005 17:03, dans 6153b1lonhrc6n4hrrau92avivhjd8f8pv@4ax.com, > .82æDavid C. Ullrichæé a .8ecritæ: > >> On Thu, 16 Jun 2005 15:19:32 +0200, Jean-Claude Arbaut >> > > > > Le 16/06/2005 15:12, dans d8rtr0$qut$1@mailhub227.itcs.purdue.edu, .82æDave > Seamanæé a .8ecritæ: > >> > Le 16/06/2005 15:13, dans llu2b1ddnfgoi4ppd5par45kfe1ahfm2si@4ax.com, > .82æDavid C. Ullrichæé a .8ecritæ: >> > > Well, you could just *borrow* an infinite amount of money. >> >> Ooh, I can? Where? (Ya think they'd notice if I borrowed an >> infinite amount of money and then only paid half of it back?) >> > That would mean ruin for casinos :-) Every guy would win > with the 2^n martingale. Too easy. >> >> What difference would it make whether you pay back twice infinity or only >> half of infinity? >> >> > Oh, sorry, I answered the previous question :-) > Yeah, you're right, no difference. But, you can give infinite > money to everybody on earth, there is still no difference. >> >> You still need to read more carefully. Yes of course if >> everyone had infinitely much money then money would be >> worthless. But Richard (Tobin - you should be more careful >> about attributions) didn't say anything about everyone >> having infinitely much money, he said that _I_ could >> borrow infinitely much money. >You don't understand: if you borrow infinitely much money, > then you can give infinitely much money to infinitely many > people (also to finitely many, obviously), and you still > have infinitely much money. Am I wrong ? >> >> Sigh. Yes, of course I _can_ do that. But why _would_ I? >> As you point out, after I do that my money will have >> no value. >> >> Nope, not me. I'm gonna borrow my infinitely much money, >> give half back, and keep the rest. >> KAPITALIST ! You're not very generous :-) Now, is that a nice thing to say? I might agree that I'm not _infinitely_ generous... >But of course, if the world was generous, >There would be no such thing as a Third World... And besides, would it really be a generous thing for me to give everyone infinitely much money? If I did that then _everyone's_ money would become worthless! Which would you rather have, a small amount of useful money or infinitely much useless money? > That's a question of bijection of N on N^2. > > Infinite money leads to end of money :-) I mean, an infinite > quantity of money would have an infinitely small value. >> >> >> ************************ >> >> David C. Ullrich >> >> >> ************************ >> >> David C. Ullrich ************************ David C. Ullrich ==== Subject: Re: martingale betting system question Le 17/06/2005 14:10, dans t9f5b1lpisb69aklleh5hn7kritetkhdtb@4ax.com, .82æDavid C. Ullrichæé a .8ecritæ: >> >> KAPITALIST ! >> >> You're not very generous :-) >Now, is that a nice thing to say? I might agree that I'm > not _infinitely_ generous... I didn't want to hurt, you know... May I recall you all this thread has drifted to a joke for some time ? >> But of course, if the world was generous, >> There would be no such thing as a Third World... >And besides, would it really be a generous thing for > me to give everyone infinitely much money? Depends on your philosophy :-) > If I did > that then _everyone's_ money would become worthless! > Which would you rather have, a small amount of useful > money or infinitely much useless money? Do you really want to know ? ;-) ==== Subject: Re: martingale betting system question On Fri, 17 Jun 2005 14:10:39 +0200, Jean-Claude Arbaut Le 17/06/2005 14:10, dans t9f5b1lpisb69aklleh5hn7kritetkhdtb@4ax.com, >.82æDavid C. Ullrichæé a .8ecritæ: > KAPITALIST ! >You're not very generous :-) >> >> Now, is that a nice thing to say? I might agree that I'm >> not _infinitely_ generous... I didn't want to hurt, you know... >May I recall you all this thread has drifted to a joke >for some time ? concern (seriously). > But of course, if the world was generous, > There would be no such thing as a Third World... >> >> And besides, would it really be a generous thing for >> me to give everyone infinitely much money? Depends on your philosophy :-) > If I did >> that then _everyone's_ money would become worthless! > Which would you rather have, a small amount of useful >> money or infinitely much useless money? Do you really want to know ? ;-) ************************ David C. Ullrich ==== Subject: Re: Uses of a very good bidimensional nonlinear equation solver >Hi! > >Suppose you have a very good bidimensional numerical >nonlinear equation solver, that is, suppose you have >a very good numerical routine that computes efficiently >F^(-1)(c) (including degenerated cases), where F is a >(nonlinear) function from the plane to the plane. > >I=B4m looking for pratical uses of such routine, that is, >are there particular problems in optics, mechanics, >biology, etc that would go to benefit of such numerical >bidimensional inversor? > >Any pointers are welcome! > > any fitting problem involving two nonlinear parameters (there are many such) would be a good test case. but two variables is indeed a bit special. hth peter ==== Subject: Can any one help? Can any one help me with these two questions? 1. Let K be a field, a is in K and p is a prime number, show that: x^p-a in K[x] over K is irreducible <=> in K has no root 2. F is a finite field and Char(F)=p. If N:F->F , N(a)=a^p is a Frobenius automorphism, show that Aut(F) is a cyclic group and Aut(F) = ==== Subject: best mathematician movie of all time Mark loves movies about mathematicians, theoretical physicists, and writers. They remind Mark about his halcyon days in graduate school. What are people's Top 5 favorite movies about mathematicians and theoretical physicists? Here are some of Mark's nominations, not in any particular order: 1) Beautiful Mind 2) the movie about Einstein and Meg Ryan 3) Pi 4) the movie about space travel and Jodie Foster Mark Demers, PhD EquityValue Investments ==== Subject: Re: best mathematician movie of all time > Mark loves movies about mathematicians, theoretical physicists, and > writers. They remind Mark about his halcyon days in graduate school. > What are people's Top 5 favorite movies about mathematicians and > theoretical physicists? Here are some of Mark's nominations, not in > any particular order: > 1) Beautiful Mind > 2) the movie about Einstein and Meg Ryan > 3) Pi > 4) the movie about space travel and Jodie Foster You obviously missed Good Will Hunting. ==== Subject: Re: best mathematician movie of all time How about Wall Street? I'm sure more than a few mathematicians would find/have found the process of second-guessing the algorithms used by the Securities and Exchange Commission to spot trading patterns indicative of a sequence of trades contrary to SEC regulations to be quite fascinating. ==== Subject: Re: best mathematician movie of all time Mark can think of other mathematicians in the movies: 1) The nerdy monkey in Planet of the Apes. 2) The looney Mad Scientist in Back to the Future. 3) The geeky control room guys wearing short sleeve shirts in Apollo 13. ==== Subject: Re: best mathematician movie of all time >Mark loves movies about mathematicians, theoretical physicists, and > writers. They remind Mark about his halcyon days in graduate school. > What are people's Top 5 favorite movies about mathematicians and > theoretical physicists? Here are some of Mark's nominations, not in > any particular order: > 1) Beautiful Mind > 2) the movie about Einstein and Meg Ryan > 3) Pi > 4) the movie about space travel and Jodie Foster Mark has the brain of a hamster. Hey dude - how 'bout the movie with the, you know, and like it all happens but the problem, uh, and that is wonderfully solved with the math and his horniness in the broken-down car? That one. With the guy who played an angel and shot everybody except the gal who didn't say bless you. And he assigned NMR lines to the molecule on a napkin and everything. In the first movie not the second one where he is stuck in Wisconsin with the other angel who as a guy s a fat-assed Puerto Rican from the Bronx. But not in the movies, except for Gigli that nobody saw. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf ==== Subject: Re: best mathematician movie of all time X-RFC2646: Format=Flowed; Original > Mark loves movies about mathematicians, theoretical physicists, and > writers. They remind Mark about his halcyon days in graduate school. > What are people's Top 5 favorite movies about mathematicians and > theoretical physicists? Here are some of Mark's nominations, not in > any particular order: > 1) Beautiful Mind > 2) the movie about Einstein and Meg Ryan > 3) Pi > 4) the movie about space travel and Jodie Foster Mark Demers, PhD > EquityValue Investments > hmm... none of these movies are about mathematics ;/ In these movies mathematics plays no essential role. The closest you will get are documentaries or tutorials/lessons. ==== Subject: Re: best mathematician movie of all time X-RFC2646: Format=Flowed; Original > Mark loves movies about mathematicians, theoretical physicists, and > writers. They remind Mark about his halcyon days in graduate school. > What are people's Top 5 favorite movies about mathematicians and > theoretical physicists? Here are some of Mark's nominations, not in > any particular order: > 1) Beautiful Mind > 2) the movie about Einstein and Meg Ryan > 3) Pi > 4) the movie about space travel and Jodie Foster > Really, well 1, 3, and 4 are themes that difficult endeavor by the individual destroys the individual. So I like HGW's Time Machine where a garden society of the future had become helpless but content... ==== Subject: Re: best mathematician movie of all time > Mark's question, as posed in his Subject, is silly. All time includes the future and the the future is unpredictable. ==== Subject: Re: best mathematician movie of all time X-RFC2646: Format=Flowed; Original Mark's question, as posed in his Subject, is silly. All time includes > the future and the the future is unpredictable. Depends if future time is real or imaginary. How do we know time exists in the future? (and don't say something stupid like because if it didn't then we couldn't experience it in the present(because this assumes that time is simple and linear)). ==== Subject: Re: best mathematician movie of all time > Mark's question, as posed in his Subject, is silly. All time includes > the future and the the future is unpredictable. >Depends if future time is real or imaginary. How do we know time exists in > the future? The answer may be we don't. But you probably need to rephrase your question: if time just tops, what do you mean by the future? ==== Subject: Re: best mathematician movie of all time X-RFC2646: Format=Flowed; Original >> message >> Mark's question, as posed in his Subject, is silly. All time >> includes >> the future and the the future is unpredictable. >> Depends if future time is real or imaginary. How do we know time exists >> in >> the future? The answer may be we don't. But you probably need to rephrase your > question: if time just tops, what do you mean by the future? I can rephrase it however you want but we will probably never get anywhere useful. ==== Subject: Pure Mathematics in Hardy's day. I've long been puzzled by the title of G H Hardy's book A Course of Pure Mathematics. What the book really is, is a course of real and complex analysis. In Hardy's day _was_ pure mathematics all analysis? Surely not. DoeS aNyBody know what part one of the Maths Tripos consisted of then? ==== Subject: Re: Pure Mathematics in Hardy's day. > I've long been puzzled by the title of G H Hardy's book A Course of Pure > Mathematics. It's not like the book is titled A course covering everything in pure mathematics. My guess is that the book was intended to be the first real mathematics book its target audience would encounter, and I think the title makes a lot of sense in light of that. Per ==== Subject: Re: Pure Mathematics in Hardy's day. >I've long been puzzled by the title of G H Hardy's book A Course of Pure >Mathematics. What the book really is, is a course of real and complex >analysis. In Hardy's day _was_ pure mathematics all analysis? Surely >not. DoeS aNyBody know what part one of the Maths Tripos consisted of >then? Hardy does include number theory. There is even an interaction between number theory and analysis. However, there was quite a bit of group theory and matrix theory around then. I do not know where you would put combinatorics. Topology was not well developed, but many things were there, including Tykhonov's example of a completely regular space with is not normal, and unknown in his time, and the same is true with respect to logic. There were few mathematicians in his day who did not know a fair amount of real and complex analysis, while knowledge of the other branches was far from universal. One could get a PhD then and not have the slightest idea of what constitutes a group. -- 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: help on simulating correlated random variables Is there any particular text you would recommend for generating multivariate distributions... the problem i am working on has around 10-20 dimensions..each dimension is a normal/lognormal/poisson distribution, their means are known..i also have the correlation matrix(pearsons) for all the dimensions..i was able to simulate the normal and the lognormal distributions..but i dont know how to simulate the poisson distribution.... any help/references on this will be appreciated FIGARO ==== Subject: -> A worker for l'Universite' de Caen Basse-Normandie Jerzy Karczmarczuk: a progress from systematic wilful libel to pestering my acquaintances Jerzy Karczmarczuk VB> Why don't consider reading opinions about quality & scope VB> of my work produced by experts in the field of computer VB> algebra systems, CAS manufacturers and top CAS folks since VB> 1993. Find a few selected opinions from them at placed here VB> COMMENT 2 Prof Dr Oleg Marichev (WRI) VB> www.functions.wolfram.com VB> COMMENT 4 Prof Dr Walter Oevel (SciFace GmbH) VB> http://www.math.uni-paderborn.[CapitalEth][CapitalEth]de/~walter/ VB> COMMENT 8 Dr Michael Wester www.math.unm.edu/~wester VB> COMMENT 11 Stefan Wehmeier (SciFace GmbH) VB> http://www-math.uni-paderborn.[CapitalEth][CapitalEth]de/~stefanw JK> Thus, I send them a copy of this posting. I was wondering do you realize that by your new actions you - wilfully - attempt to make a piece of damage to the reputation of the organization which provides you with living, l'Universite' de Caen Basse-Normandie? How a student willing to enter l'Universite' de Caen Basse- Normandie will feel about learning - maybe even at the computer/informatics department where you teach - from a person who systematically both shows his sheer computer incompetence in the field of software testing and throws in packs variegated insults - to a person you even NEVER met before these weeks? Zero cool, yes? Do you also realize that the way of actions you proceed - *after* me contacting your superiors on account of your slanderous behaviour - characterizes you as a wilful tresspasser? Last but not least. How you make researches if you are obviously cannot foresee even the nearest impact of your actions - the impact of your wilful libel and scandalous character on your further career? Do you really expect from me that I'd sit and wait? JK> Thus, I send them a copy of this posting. This beats all and I must inform, in particular, Mme Le Querler and Professor Bretto http://users.info.unicaen.fr/~bretto/ and do this the very moment. We the Russians are a peculiar nation, we are humorous, much forgiving but... you have decided to wage a war against a Russian? Forgot 1945? My grandfather, Miron Dmitrievich Bondarenko, who was decorated with several orders for his exceptional courage, who went to war a private and returned a captain of artillery, took Berlin. http://www.nevsky-prospekt.com/alexander.html Whoever will come to us with sword, from sword will perish. -- Alexander Nevsky x: +38-(0652)-510700 http://maple.bug-list.org/MapleCrisis-Review-01.pdf http://www.cybertester.com/ http://maple.bug-list.org/ http://www.CAS-testing.org/ ==== Subject: The Hypergeometric Hypothesis http://www.mindpixel.com/chris/2005/06/hypergeometric-hypothesis.html The Hypergeometric Hypothesis (Specific): Evolution maximized hypersurface in the seven-layer mammalian thalamocortical loop [I am implicitly defining the thalamus as the seventh layer of the neocortex.] Immediate memories are points on the maximum hypersurface of a Milnor-sphere and complex cognition is a trajectory on the same hypersurface. Falsification of the specific hypothesis would involve the discovery of an animal with an eight-layer thalamocortical loop. [Note: I consider the amygdala and hippocampus to be Hopf fibrations of the thalamocortical Milnor-sphere, but as of yet this is not formally part of the specific hypothesis as I can think of no way to falsify the conjecture.] IBM's Custom 7 Qubit Molecule - 8 anyone? The Hypergeometric Hypothesis (General): Omniconnected systems are sensitive to hypersurface area. Falsification of the general hypothesis could be achieved by the creation of a single molecule eight qubit NMR quantum computer. The current state-of-the-art is IBM's seven qubit system. [Note: IBM says While NMR will continue to provide a testbed for developing quantum computing tools and techniques, it will be very difficult to develop and synthesize molecules with many more than seven qubits. - I think it might be much more difficult than the IBM team realizes for fundamental geometric reasons.] ==== Subject: Re: Orlow cardinality question stephen@nomail.com said: > So you do not think there is anything inconsistent in saying > that size is a universal measure of sets and at the same > time admitting that our notion of size does not apply to > ^^^^ > your > all sets? >Oops. Leave of one letter, and the whole meaning changes. > It is a shame English is not a little more fault tolerant. :) >Stephen > I don't think one measure can accurately be applied to all possible infinite sets, since one relies on the properties of the set members in such cases. -- Smiles, Tony ==== Subject: Re: Orlow cardinality question > stephen@nomail.com said: >> So you do not think there is anything inconsistent in saying >> that size is a universal measure of sets and at the same >> time admitting that our notion of size does not apply to >> ^^^^ >> your >> all sets? >> >> Oops. Leave of one letter, and the whole meaning changes. >> It is a shame English is not a little more fault tolerant. :) >> >> Stephen >>I don't think one measure can accurately be applied to all possible infinite > sets, since one relies on the properties of the set members in such cases. Cardinality applies to all possible infinite sets. A bijection either exists between two sets, or it does not. It does not matter if one set contains elephants, and the other set contains sets of matrices. A bijection exists or it does not exist. Stephen ==== Subject: Re: Orlow cardinality question Virgil said: >Virgil said: If an infinite set doesn't have an infinite size, then what makes > it infinite? >A set is infinite (not finite) by definition when there is an > injection from the set to some proper subset. >If the set is infintie by that definition, then its size, by any > reasonable measure is also infinite. >So TO has things backwards as usual. >Not really. You are using the word infinite, not proper > subset-bijectable. the infinite part is the number of elements. >There is no such thing as a finite set or an infinite set until they are > defined. And the definition only says they differ by whether one can > inject them into proper subsets or not, and says nothing about number. That is one definition. Unending is another, which is more egenral and can be applied to sets, or values, or patience. >So any connection between number of elements and finiteness of a set > is irrelevant until number of elements is also defined. Is number defined? Is element defined? >If every set doesn't have a size, then what measure IS common to > all sets? >Unless one uses cardinality, there is no measure which is both > consistent AND common to all sets (with AC allows any two sets to > be compared for relative size). >So, cardinality IS supposed to address the question of set size > measure, and yet fails to distinguish between some sets that have > clearly different sizes intuitively. This is a situation that can be > improved. >TO's intuition is badly in need of service. It purrs like a kitten, Baby, and roars like a lion. > -- Smiles, Tony ==== Subject: Re: Orlow cardinality question Virgil said: Who says that number of elements is the one universal measure of > sets? That is something you just made up. You have to define > number of elements before the question even makes sense. >Which term do you not understand, number or element? >How do you, TO, define number of elements of a set? > It is not that we do not understand in general, it is that we do not > know what your understanding about that phrase is. How about the integral of the density over the domain? Does that satisfy your need for mathematical definition? There are several ways to state this, but number of elements is the most basic, and the way we intuitively think about sets. A set is a number of elements, members, units, or whatever. You can use induction to prove that all finite sets have a certain > property. You cannot use it to prove that an all infinite sets > have a certain property. >Induction is supposed to prove something true for all members of the > infinite set of naturals. >Only those members that can be generated by adding one once to some > other member. There is no provision in induction for anything other than > one-at-a-time. Yeah like the entire set of naturals. Adding one an infinite number of times is the same as adding infinity once, even if done one-at-a-time. There is not time involved That is a figure of speech. > -- Smiles, Tony ==== Subject: Re: Orlow cardinality question > Virgil said: >> >> >> Who says that number of elements is the one universal measure of >> sets? That is something you just made up. You have to define >> number of elements before the question even makes sense. >> >> Which term do you not understand, number or element? >> >> How do you, TO, define number of elements of a set? >> It is not that we do not understand in general, it is that we do not >> know what your understanding about that phrase is. > How about the integral of the density over the domain? Does that satisfy your > need for mathematical definition? Not even close. Consider the set of regular languages over the alphabet {a,b}. What is the integral of the density over the domain of this set? > There are several ways to state this, but > number of elements is the most basic, and the way we intuitively think about > sets. A set is a number of elements, members, units, or whatever. I do not see how number of elements is in general related to integral of the density over the domain. When I think of sets, I do not think of integrals or density. Stephen ==== Subject: Re: Orlow cardinality question Virgil said: >Virgil said: >The difficulty with subset ordering is that it is only a partial > order leaving lots of sets unable to be compared. Even {1,2} and > {3} cannot be compared by subset ordering. Cardinality certainly > works perfectly for finite sets, I never claimed that all comparisons can be handled with subset > relations. being a proper subset SHOULD make one set smaller than the > other, however. Of course, the mere fact that one set is a proper > subset of the other doesn't tell us much more than that, but that > fact at least should be preserved, and not discarded. >Then it is incomplete, which cardinality is not. >In finite sets of naturals, you freely admit that the set size > can't be larger than the maximum element value, but somehow this > flies out the window at infinity. >That only holds when we define the number of an initial set of > 1-origin-naturals to be its largest, so is circular. We don't define that relation to hold. It follows from the definition > of the set, and is proven through induction, which means it holds for > the infinite set of natural numbers and the sets they each define. >What does the natural number '3' mean? One completely accurate > definition is that it is the natural nuber that comes immediately after > '2'. That definition in no way requires any number properties. All > those number properties are acquired through deduction. >A path is representable by a set of branches, not all such sets > representing paths. So it is not surprising that there are more > such sets of branches than branches when the set of branches is > infinite in a a maximal binary tree. That TO finds it disturbing is > his problem, not ours. > What's disturbing is that you can't see that it's incorrect. I am not > disturbed by false facts. I am disturbed by trying to imagine the > mechanics of a mind that accepts them, and fights to defend them. >I have exactly that problem with WM and TO. They do not even make the > same mistakes, but each of them fights to defend his own mistakes. >Now, you just said something interesting. IF a path were simply ANY > set of branches in a tree, THEN the set of paths WOULD be the > powerset of the set of branches. HOWEVER, most sets of branches in > the tree are NOT paths, but only a very small fraction of them, that > represent SEQUENCES of branches from the root and through each level > of the tree. THEREFORE, it is IMPOSSIBLE that the set of paths is > equivalent to the power set of the branches. >TO has conceded that the set of paths is countable, i.e., can be > bijected with the naturals. Conceded? You were the one claimingthe set of paths was UNcountable, while the set of branches was countable. I always disagreed with that. >I have shown that the set of paths is bijectable with P(N): > For each path construct the set which contains n if and only if the nth > branch of the path is a right branch. That is a different type of tree than the one where the branches are countable. In the tree where each branch is a digit in a digital number, each path is a digital number. In the tree you are describing, each path defines a set of numbers, and each level in the tree corresponds to a number than can be in the set. So, while you have digits and sets of digits that correspond to numbers, in the second you have numbers, and sets of numbers. The first tree is the set of all numbers, and the second is the set of all sets of numbers. By changing the meaning of the nodes, you derive either countability or uncountability, but rather than concentrating on the properties of the meanings you assign to the parts of thetree, you should be concentrating on the properties of trees themselves, as WM has done. Then you will get solid answers, instead of convoluted conclusions. >Each branch in this way creates a unique subset of N and every subset of > N determines a unique path in this way. >So the allegedly impossible bijection obviously exists. I never said the bijection doesn't exist. All sorts of nonsense can be accomplished with bijections. >And what TO has declared impossible had now been done. That is not what I declared impossible, but it is what I see as just another Cantorian feint. If each branch denotes the membership or lack thereof for a given number in any given set, then for each path you will have two branches, one that includes the next number and one that won't. it's ultimately the same thing. Two branches for every infinite path. The only way to get another result is to change trees midstream. It is a MUCH smaller > set. In fact, the set is SMALLER than the set of individual branches, > by HALF, as I have shown numerous times. I offered a system for sets defined by mapping functions that > works precisely, both for finite and infinite sets. It wasn't > welcome. >It wasn't consistent and it wasn't complete. > For sets defined by mapping functions it was both, plus intuitively > satisfying in every respect, but i doubt you paid any attention > anyway. >You'd rather have your kludge of inconsistencies that violate > information theory and infinite series >Those alleged violations of information theory and infinite series > only betray TO's ignorance of both. They are both irrelevant to the > issue of consistency of cardinality, at least as TO has cited them. > That is false, but I am not surprised by such a typical spewage on > Virgil's part. ... The size of the set is the number of elements in the set. It > doesn't get much simpler than that. If that doesn't make sense to > you, then I don't know what you think we're talking about. A set > is a unit that consists of a number of units. The size of that > set is the number of units of which it consists. If nothing is > know about the units themselves, then this is all we know about > the set, and is really the only pure measure of a set. >And how does one determine the number of elements in an infinite > set? One way is by considering injections, surjections and > bijections with other sets, i.e., cardinalities. All the alternate > methods suggested by TO have been found even less satisfactory that > cardinalities. > Oh, because they correctly conclude that there are hald as many evens > as naturals, infinitely more rationals than naturals, infinitely > fewer squares than rationals, etc? Yeah. Whatever. Cling to your > flotsam. >Note that TO's example of the even naturals being half of all > naturals relies on structural properties of those sets and their > members other than mere set and member properties, so it is > measuring structural relationships other than mere membership. > And your conclusion that they are equivalent in size depends on using > mathematical mapping formulas that make use of their properties as > numbers as well, to establish tyour sorrespondences and bijections, > except that you conveniently forget about that in the last stage of > your bijection, and incorrectly declare them equal. >Since as mere sets, the naturals and the even naturals are in > simple on-to-one correspondence, it must be the additional > not-purely-set structure that leads TO to say that the even > naturals are half of the naturals. > It is the nature of numbers in the context of the real line that > leads me to conclusions about sets of numbers. If you can create your > correspondence between the elements of the two sets without reference > to their proeprties as numbers, I'd love to see it. >A: Start with {}, > and for each x create (x union {x}) >B: Start with {{}}, > and for each x create (x union {x}) union {x union {x}} >Done! What does this have to do with the naturals vs. evens? >There is nothing wrong with such a measure as long as one is aware > of what it is measuring, which TO seems not to be > . > By TO, I take it you mean Virgil. >TO takes it erroneously. > -- Smiles, Tony ==== Subject: Re: Orlow cardinality question Jiri Lebl said: > Sets have one universal measure: number of elements. If this is not what > cardinality is measuring, then what is it measuring? If number of elements is defined by cardinality then number of > elements in a set is its cardinality, but TO wants number of elements > to be something else, but can't quite say what. >Of course he did say what number of elements means, it means the > size of the set, and size of the set is defined as the number of > elements. To Tony, this seems entierly logical and unambiguous. It > is as obvious as saying that frmgtmfut means biglybigly foo, and if > you ask what biglybigly foo means, well then obviously I say: > frmgtmfut and that should of course, completely define what > biglybigly foo means and you can now go and prove theorems about it. >Jiri > So, you claim to have no idea what number, element, size or set mean? I can't help you then. If you don't know what a number is then don't do math, and if you don't know what an element is, then don't do sets. -- Smiles, Tony ==== Subject: Re: Orlow cardinality question can't help you then. If you don't know what a number is then don't do math, and > if you don't know what an element is, then don't do sets. Oh poor tony, still totally confused as to what it means to define something in mathematics. But of course you know that you are talking nonsense. You do it to get a rise out of others, who happily oblige you. Were your parents not attentive enough that you want to get attention of others like this? I am still trying to guess what age are you. I'm thinking between 16-19 (yes I know you've been thinking about this for 25 years, we've heard that, but we all know we shouldn't trust usenet postings with such information). You must have definatley heard about all this, so you are probably in high school or perhaps (at most) a freshman in college. On the other hand you must be immature enough to be doing this, thus my dilema. Jiri ==== Subject: Re: Orlow cardinality question Virgil said: I never claimed there was a largest integer. Infinite integers? Yes, > I claim there are such things. >Where? Not in any standard version of arithmetic. And in some > non-standard versions, every natural is infintie. They all have an infinite number of digits, but when they are all leading zeroes, we ignore them. Do you claim there is an infinite set of distinct finite naturals? >I do not have to claim anything like that, as there is no definition of > finiteness for naturals by which one can separate finite naturals from > infinite naturals. That's gobbledegook talk. >In the natural definition of naturals, each natural is the set of all > previous naturals, but no such natural can be injected into any previous > natural. Such an injection only becomes possible by a non-succesor > operatin of taking the union of all naturals, so that what is created is > not any longer a natural, as it was acheived unnaturally. Sure. Whatever you say. > > Well, according to both information theory and infinite series that > is impossible. >The TO must be misunderstanding both information theory and infinite > series, since according to all other interpreters of either, no such > impossibility is implied by either. COmment specifically on the proofs. I am entitled to my objections, when Cantorians tell > me my understanding of set size is wrong and theirs is right. If you > want a contest, you lose. >Fortunately for the future of mathematics, it will not be TO who > ultimately decides who is right. I will put forth the correct notion until the incorrect one yields. >Cardinality is woefully inconsistent with > the rest of mathematics when it comes to infinite sets, because many > of its assumptions and axioms are unfounded. >Axioms are unfounded. That is the nature of axioms. Not good ones. Axioms should be well-considered, and not generated willy-nilly. >There may be reasons for choosing a particular set of axioms, but, once > chosen, they are all that one is allowed to consider in deciding what > follows from them. Allowed? Tie your own hands, not mine. In my world, any axiom which is assumed true may be used in any argument. > -- Smiles, Tony ==== Subject: Re: Orlow cardinality question > Virgil said: >> >> Axioms are unfounded. That is the nature of axioms. > Not good ones. Axioms should be well-considered, and not generated willy-nilly. So which of the axioms of set theory do you object to. Here is a list. http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html >> >> There may be reasons for choosing a particular set of axioms, but, once >> chosen, they are all that one is allowed to consider in deciding what >> follows from them. > Allowed? Tie your own hands, not mine. In my world, any axiom which is assumed > true may be used in any argument. So when someone is discussing Spherical Geometry, you think it is perfectly valid to make arguments using Euclids Fifth Postulate? Stephen ==== Subject: Re: Orlow cardinality question Virgil said: >Sets have one universal measure: number of elements. If this is not what > cardinality is measuring, then what is it measuring? >If number of elements is defined by cardinality then number of > elements in a set is its cardinality, but TO wants number of elements > to be something else, but can't quite say what. > I want number of elements to be measured in a way that actually makes different size sets have a different measure, and works the same way for finite sets as infinite sets whenever possible. You have already backed away from the notion that cardinality gives anything like an exact set measure for infinite sets. That's a good first step. -- Smiles, Tony ==== Subject: Re: Orlow cardinality question Jiri Lebl said: > Because you are ignoring the range of values. When you take the infinite sets > of naturals vs even naturals, you are looking at the same infinite range, over > which the evens have half the density, and therefore are half as large a set. > In each of your finite examples, you have the same number of elements in each > pair of sets, but the second has HALF the density over TWICE the range. Unless > you want to claim that the largest even naturals is TWICE as large as the > largest natural (which makes absolutely no sense), then you have to concede > that in the infinite case you are entirely ignoring the set density difference > over an identical range, and therefore getting an incorrect equivalence between > the sizes of the sets. >But I wasn't interested in the DENSITY, but in the SIZE of the set. > You are then generalizing a DIFFERENT concept then SIZE. Of course > size is rather vague for infinite sets. Furthermore set size > however you want to define it should be SET THEORETIC and thus not > dependent on the set of natural numbers. The set size of {1,2,3} and > {mouse, elephant, dog} should be the same, and yet you notice that what > the hell do you mean by range on the second set? What is the > density of mouse, elephant and dog in what range? Finite sets are easy and straightforward. You really can't compare a generic infinite set of elephants with a generic infinite set o lollipops. The only way to determine sizes of infiite sets is by using some properties of the members to form correspondences between them. Do you know what density IS? Density is a measure of units of one kind per unit in some domain. When we talk about set density over a given domain, we are talking about how many members there are in the set for each unit of the domain. So, if you have a domain measure in units, and a set density in terms of members/unit, the product of these two measures, domain and density, IS the total number of members. >DENSITY can only be applied if you have some FIXED set of which all > your sets are subsets of. Such as, you could attempt to measure the > density of subsets of the natural numbers, altough you are going to run > into problems with limits not existing as someone has already pointed > out to you. Further you will run into counter intuitive things such as > the density of primes in N is 0, thus if density measured set size then > it would be an empty set. And if I take a different FIXED set, then I > get different densities, totally screwing up any INTRINSIC definition > of SIZE as you claim to have defined. I have already been through all this. Set density only works for linear mapping functions. In order to handle all functions, we generalize this method to use the inverse of the mapping function over the domain of the set, as a measure of the set size. This leads to descriptions that go beyond N/2, and include functions such as N^2 (for square roots of the naturals), or log2(N) (for the integral powers of 2). These functions may not equate to identifiable numbers, but being defined on the same unit infinity, N, they provide a means of precisely comparing the sizes of these infinite sets. Similar mapping comparisons can be done on sets of reals, if desired. Now, the primes are another matter, but since we know that the primes less than or equal to n is asymptotic to n/log(n), we can conclude that over N, there are N/log(N) primes. >You are a TOTALLY lost case for logic, trust me, go do something else > then math. There must be something else you're not totally horrible > at, but math is definately not it. Jiri - Go learn some manners, and patience, and don't be so full of yourself. Bad professor! No cookie for you! >Jiri > -- Smiles, Tony ==== Subject: Re: Orlow cardinality question Virgil said: >I think this is at the heart of the problem. You think you are > investigating a fact about the universe; mathematicians aren't. (Or at > least haven't been since the time of Euclid) Brian Chandler > http://imaginatorium.org Or maybe since the time of Newton. ahem. > -- > Smiles, >Tony >Euclid! > Oh, Newton didn't develop calculus to describe the motion of physical bodies, which is a fact about the universe? I see. -- Smiles, Tony ==== Subject: Re: Orlow cardinality question Virgil said: >That rests on the nonsensical notion that subtracting froma > value doesn't always make that value smaller. Conveniently non-functional. >Wrong again. Subtraction is only defined for finite cardinals. In your world. I have shown how subtraction works for infinite numbers as well, but you reject that. Too bad for you. >Does TO wish to require that removing one member from a set which has an > injection into a proper subset (is infinite) should prevent any > injection of that proper subset into any of its own proper subsets (make > it finite)? > -- Smiles, Tony ==== Subject: Re: Orlow cardinality question Virgil said: >Jiri Lebl said: > I believe you have missed much of this discussion. My Theory of > Bigulosity exactly calculates what out intuitions ACTUALLY tell > us: that adding an element increases the size of the set by one, > that the even integers are exactly HALF of the integers, etc. > This is not beyond reach, and should be regarded as progress, not > rebellion. The goal is consistnecy, which is sorely lacking in > cardinality. >You have not answered Jan's primary complaint about what you said. > Let's give it in finite terms first. Does multiplying every > element by 2 give a smaller or larger set? Let's see: >{1,2,3} {2,4,6} >So far so good >{1,2,3,4,5,6} {2,4,6,8,10,12} >Hmm. It seems that I don't get a set that's half the size, why > would then I intuitively get half the set when I multiply > {1,2,3,4,...} by 2? > I certainly have not added nor taken away any elements, I've just > relabeled them. Do I get a different set when I multiply every > element by 2 and yet a different one when I pick out just the even > integers? If so, I would like to know what do you mean by an even > number since it obviously can't be a number with a divisor of 2. > If this intuition is not supposed to carry over to infinite sets, > then why does your bigulosity intuition carry over and not this > one? >Jiri Because you are ignoring the range of values. When you take the > infinite sets of naturals vs even naturals, you are looking at the > same infinite range, over which the evens have half the density >How does one define the relative densities of evens versus all naturals > when both have essentially zero density, at least in the reals, or even > in the rationals. So density depends on what environment one is > working in, and is, therefore, not a property of the sets themselves but > of their environment. That's right. The naturals have a density of 1 in the naturals, and the evens have a density of 1/2 in the naturals, and they both have densities of 0 in the reals. > -- Smiles, Tony ==== Subject: Re: Orlow cardinality question >> How does one define the relative densities of evens versus all naturals >> when both have essentially zero density, at least in the reals, or even >> in the rationals. So density depends on what environment one is >> working in, and is, therefore, not a property of the sets themselves but >> of their environment. > That's right. The naturals have a density of 1 in the naturals, and the evens > have a density of 1/2 in the naturals, and they both have densities of 0 in the > reals. Oh Tony, You're losing it. You should have said that densities of both the naturals and the evens are /infinitesimals/, but not the same ones: the infinitesimal density of the evens in the reals is still twice as small as the density of the naturals in the reals. Since obviously, according to all acceptable intuition, the density of some set in the set of reals should be inversely related to their sizes. It would be very nice if you could write down your theories and ideas on a nice website, together with all the precise intuitions that you wish to capture. That would make this discussion much easier. Jan ==== Subject: Re: Orlow cardinality question stephen@nomail.com said: >> To me this is an internal inconsistency that leads away from >> intuitive results. >It's not inconsistent, but it certainly may lead to unintuitive > results. Which is the mark of _any_ serious science. A science that > can't pass naive intuition is not progress. >unintuitive is a mark of quality. unapplicable is, in contrast, a > slight shortcoming, but still does not affect validity. > incomprehensible can be a shortcoming of a treatise. It applies to > a manner of reasoning instead of unintuitive which usually applies > to results. >Tony is one of those people who would have agreed with the > New York Times when they said: > That Professor Goddard, with his chair in Clark College and the > countenancing of the Smithsonian Institution, does not know the > relation of action to reaction, and of the need to have something better > than a vacuum against which to react--to say that would be absurd. > Of course he only seems to lack the knowledge ladled out daily in > high schools. > It is afterall highly unintuitive that you can accelerate if you have > nothing to push against, so therefore it must be wrong. :) Yeah, sure, unless you're falling in a gravitational field. What are you talking about? >Stephen > -- Smiles, Tony ==== Subject: Re: Orlow cardinality question > stephen@nomail.com said: > To me this is an internal inconsistency that leads away from > intuitive results. >> >> It's not inconsistent, but it certainly may lead to unintuitive >> results. Which is the mark of _any_ serious science. A science that >> can't pass naive intuition is not progress. >> >> unintuitive is a mark of quality. unapplicable is, in contrast, a >> slight shortcoming, but still does not affect validity. >> incomprehensible can be a shortcoming of a treatise. It applies to >> a manner of reasoning instead of unintuitive which usually applies >> to results. >> >> Tony is one of those people who would have agreed with the >> New York Times when they said: >> That Professor Goddard, with his chair in Clark College and the >> countenancing of the Smithsonian Institution, does not know the >> relation of action to reaction, and of the need to have something better >> than a vacuum against which to react--to say that would be absurd. >> Of course he only seems to lack the knowledge ladled out daily in >> high schools. >> It is afterall highly unintuitive that you can accelerate if you have >> nothing to push against, so therefore it must be wrong. :) > Yeah, sure, unless you're falling in a gravitational field. What are you > talking about? I am talking about the fact that Newtonian physics is highly unintuitive, and therefore must be wrong according to you. To quote you: A science that can't pass naive intuition is not progress. Newtonian physics cannot pass naive intuition. Plenty of surveys have shown that it does not match most peoples intuitions at all. When Goddard proposed using rockets to travel to the moon, not possible work because in the vacuum of space there is nothing to push against. That was their naive intuition in 1920, and is still a common naive intuition. Stephen ==== Subject: Re: Orlow cardinality question stephen@nomail.com said: > stephen@nomail.com said: >> stephen@nomail.com said: > stephen@nomail.com said: >> stephen@nomail.com said: > stephen@nomail.com said: > Cardinality is not a theory. It is a definition. Two > sets have the same cardinality if there exists a bijection between them. > I am not sure what you mean by purpose, or what you would > accept as a valid answer. What is the purpose of the size of a set? > > Stephen > >> Size is one measure of a set. The purpose of a set is to act as a collection. >> That collection may have many attributes, but as a set, one attribute it always >> has is its size, or the number of elements it includes. >> >> That really does not answer what the purpose of the size of a set is. >> It applies equally well to any measure of a set, such as cardinality. > The size of a set is the one measure which applies to sets in general. The > purpose of cardinality is supposed to be to provide that measure in as general > a way as possible, otherwise, I don't know what the purpose of it is. When I > speak of the evens as being half as big a set as all integers, Cantorians tell > me that I am wrong because of cardinality, so obviously cardinality is thought > of as being a means of measuring set sizes that applies to infinite sets as > well as finite sets. Certainly, for finite sets, it is precisely the size of > the set. Is it something different for infinite sets? If so, has it missed its > mark? >> >> The problem that is >> supposedly addressed by cardinality is the measure of set size, for both finite >> and infinite sets, hopefully addressed in some consistent manner. >> >> What if they cannot be both addressed in a consistent manner? >> I put consistent in quotes, because I am not really sure what >> you mean. There is nothing inconsistent about cardinality. >> It upsets your sensibilities and intuitions, but your sensibilites >> and intuitions are not the standard of consistent. >There has certainly been admission here that a proper subset can always be > thought of as somehow smaller than its superset, but cardinality ignores this > in most cases. >That is not an inconsistency. As has been repeatedly pointed out > to you and others, size is not a well defined term, nor > is smaller. Two things can have the same volume but different > weights. In one sense they are the same size, in another they > are different sizes. Yes a subset is somehow smaller than > its superset, but it can also be somehow the same size. >> Sets have one universal measure: number of elements. If this is not what >> cardinality is measuring, then what is it measuring? >> >> Who says that number of elements is the one universal measure of sets? >> That is something you just made up. You have to define number of elements >> before the question even makes sense. > Which term do you not understand, number or element? What other universal > measure of sets is there, if size is not the only one? What, exactly, is your > objection? >My objection is that it is not defined. You have to define > what you mean by number of elements. There is no preexisting > definition of the term. Cardinality is defined. It is one interpretation > of number of elements. If you mean something other than cardinality, > you have to define what you mean. > > In finite sets of naturals, you freely admit that the set size > can't be larger than the maximum element value, but somehow this flies out the > window at infinity. >In an infinite set of naturals there is no maximum element. > Obviously the set size cannot be defined in terms of something > that does not exist. But of course you seem to think there > is a largest finite integer, or some strange gobbledygook like that. >> No, I seem to think that this relationship is provable using induction, which >> proof does not suffer from the same flaw as your proof that all naturals are >> finite, since the property being proven is one of constant equality between two >> measures of the set, the universal measure of size, and the element measure of >> maximum value. >> >> There is no maximum element in an infinite set of natural numbers. >> That is a simple result. You cannot use something that does >> not exist as your basis for size of a set. >> >> You can use induction to prove that all finite sets have >> a certain property. You cannot use it to prove that an all >> infinite sets have a certain property. > Induction is supposed to prove something true for all members of the infinite > set of naturals. If that property is that a set defined a certain wy by that > natural number has a certain constant property, then that property is proven > for all values of n in N. >Yes, it can prove something that is true for all members of > the infinite set of naturals. It cannot prove something about sets > of naturals. You are trying to prove something about sets, not > naturals. You are trying to prove that for all sets, the > size of the set is not larger than the maximum element in the > set. You cannot prove this using induction. It is not a statement > about natural numbers. It is a statement about sets of natural numbers. What I proved is that for all n in N, the set defined as the whole numbers from 1 to n has the property that its maximal element and its size are equal to n. This is a property of n, since the set is defined by n, according to a simple rule. There is absolutely nothing wrong with the way I have applied induction in this case. > I offered a system for sets defined by mapping functions that works precisely, > both for finite and infinite sets. It wasn't welcome. >For one reason, it only applied to some sets. >> Yes, sets defined by mapping functions, as I have said repeatedly. Other >> approaches are necessary for other types of sets. >> >> Sets are not defined by mapping functions. That phrase does not mean anything. >> The set of even numbers is the set of all numbers divisible by 2. >> Is that defining it by a mapping function? > You map the naturals to the evens using E=2*N, do you not? How else do you draw > your bijection and declare equal cardinality, based on correspondence between > elements? >What does that have to do with sets defined by mapping functions. > E is not defined by a mapping function. There exists a function > that maps each element of N to each element of E and vice versa. > There actually exist an endless number of functions. But > E is not defined by a mapping function. The mapping is perfomed using a function. Show me a bijection between these two sets without it. You're avoiding the issue. You know exactly what role mapping functions play in cardinality. > >> >> Cardinality applies to all sets. If your idea does not apply >> to all sets, then it clearly cannot be a measure of size of >> sets, especially a universal measure of sets as you claim >> size must be. Do you not notice these inconsistencies in your >> posts. > No, I notice that you also cannot say anything about the relative sizes of > infinite sets without resorting to some properties of the members of those > sets, but that you then deny that, since you ignore it, after having done it. > That is inconsistency for you. >So you do not think there is anything inconsistent in saying > that size is a universal measure of sets and at the same > time admitting that our notion of size does not apply to > all sets? I don't think there is anything inconsistent in saying that every set has a size, but that we can only determine the relative sizes of infinite sets based on properties of their members. Finite sizes we can count. Infinite sizes we have to calculate, so we need some data to work with, something with which to compare the set elements. >There is nothing inconsistent about finding a mapping between > two sets. There are many ways to do it. When describing > such a mapping I may make use of some properties of the elements, > but I can describe other mappings that make use of other > properties. It does not matter, and will not change the > fact of whether a bijection exists or not. You can define a mapping between two sets that uses properties other than those of the elements? That sounds interesting, and probably failure-prone. > >>You could > not explain what the size of a set of Turing Machines was, or > how it related to the size of a set of functions. Are there > more functions than Turing Machines according to your system? >> You cannot distinguish between any of these, claiming they are all simply the >> same uncountable infinity. Big result! I wasn't interested in your multilayered >> proofs where you introduce all sorts of different kinds of elements and misuse >> the properties of them to prove your points. Maybe I'll look at Turing machines >> at some point in this context, but if I can't get across some simple ideas >> about simple element types, then I am not going into a complex discussion like >> that with you fellows at this point. >> >> So your idea cannot be used when talking about Turing Machines, >> or sets of sets, or sets of strings. That does not seem like >> a very universal measure of sets. > Actually I already addressed sets of strings rather explicitly, but that > explanation doesn't go anywhere with you, so there is no point getting into > more complex ideas where you are bound to get even more lost. If you have sets > of sets that have similar properties, then they can be compared as well. >I want to compare sets of sets with sets of integers. Can you do that? What kinds of sets? This might be interesting..... >It is far more useful than that. Again, note your phrase with the most > precision possible. I have yet to see a way of ordering all sets > (not just sets of numbers) more precisely. >> Listen, if you want to talk about infinite sets and draw ANY conclusions, then >> you have to work with some examples, which means sets with elements that have >> properties of their own that can be used to confirm the conclusions we are >> drawign about sets in general. The peoperties of those elements depend on what >> kind of elements we are using. Quantitative elements (numbers) are different >> from symbolic representations of those numbers as strings. Different type of >> numbers have different properties and different type of string representations >> have different properties. Certainly, you can't argue that Bigulosity doesn't >> do a far better job, at least where you have unvertible mapping functions? >> Alas, you probably do, as you won't budge an inch from your ivory tower. >> >> I do not care about your Bigulosity. It has nothing to do with >> cardinality, and changes nothing about cardinality. There are >> no inconsistencies with cardinality and transfinite cardinals. > Sure, and they have nothing to do with set size, so I am free to devise a set > size theory that works. yay! >You are free to define a theory. However you keep claiming that > cardinality is inconsistent. You are not free to claim that, > and as long as you do, people will object. I am free to claim whatever I want, especially if I can prove it. >And you still have not defined set size. Why do you think > such a thing even exists if you cannot even define it? It's the number of elements in the set. The count of the units in the whole. These terms are simple enough that they shouldn't need explanation, and your insistence that they do is just an attempt to derail the point. > >> >> What does size of a set signify? Number of elements is >> not a satisfactory answer because the two are apparently >> synonymous. You seem to be assuming that size of a set >> is some fundamental concept that needs no explanation. >> Given that it is not a well defined term in general, that >> seems strange. >That's exactly what it is. Synonymous words or phrases are what definitions > ARE. The size of the set is the number of elements in the set. It doesn't get > much simpler than that. If that doesn't make sense to you, then I don't know > what you think we're talking about. >So you have a circular justification for size of a set. > You cannot say what it signifies other than it signifies itself. > Why then does cardinality have to signify something other than itself? > Your question what does cardinality signify seems to be meaningless. >> A circular justification? That's like justifying the weight of an elephant. >> >> So why does cardinality need a justification? Cardinality measures >> cardinality. > If it doesn't answer a question, then it is a statement and a system with no > purpose. >What question does size of a set answer? Why do you think > that answers a question, but cardinality does not? Again, you > refuse to look at your own assumptions. You are assuming that > size is some real thing that exists independent of our > definitions. It does not. It has no more meaning than cardinality. > In fact, given that it does not have a definition for infinite sets, > it is currently meaningless. It is certainly well understood for finite sets. The question is how to apply the concept to infinite sets. > >> >> It's a measure of the set, and the only one that can be discussed when dealing >> with a set of generic units. A set is just a number of units taken as a unit. >> The number of units in the set IS its size. It's a definition, not a >> justification. >> >> But you cannot answer number of units until you define some >> numbers that are applicable. > Come again? What does this mean? >The answer to the question what is the number of units should > be a number, don't you agree? However, if you have no numbers > that are applicable, then there is no answer to the question. > There is no answer to the number of natural numbers if you > restruct number to the natural numbers. That is true, if you restict natural numbers to finite values, but that is entirely unnecessary. > >> > A set is a unit that consists of a number > of units. The size of that set is the number of units of which it consists. If > nothing is know about the units themselves, then this is all we know about the > set, and is really the only pure measure of a set. >But number of elements is meaningless for an infinite set until > you define some infinite numbers. There are no infinite natural > numbers, despite your confused ramblings on the subject, and > there is no reason that infinite cardinals need to behave exactly > like finite cardinals. >> The ARE infinite numbers, and transfinite numbers are some of them. Unless >> you allow partial members, all cardinalities are whole numbers of elements, and >> some cardinalities are infinite. Before you jump to conclusions about the >> differences in behavior between finite and infinite set sizes, you should do >> some exploration and see what makes sense intuitively, to you. >> >> Cardinality makes sense intuitively to me. I have studied >> this stuff for a long time in far more depth than you likely have. >Yes, I have not wasted too much time on cardinality, since it seemed obviously > flawed since the day I learned it. >That is a nice approach to learning. If something does not seem > correct at first glance, ignore it. If one thing seems wrong and useless, and something else seems fascinating and pertinent, which do YOU spend your time on? If the conclusions of a system are at odds with everything else you know, do you invest a lot of time unlearning what you know in order to learn something that doesn't make sense? > >> >> Before Cantor, there were no infinite numbers. He was the >> first to define such numbers, and he was about to answer >> questions about the number of elements using these numbers. >> You have not defined the infinite numbers you keep talking >> about, but just throw around alot of hand wavy statements. >> In any case, any definition you come up with has no >> affect on cardinality. > As you wish, but be aware that Cantor did not invent infinity any more than he > invented zero. The Indians did both of those, as well as inventing the first > modern religions, which is no coincidence. Cantor may be the first western > mathematician to approach the topic with an axiomatic approach, but if so, the > first try is rarely perfect, and it's not surprising if it later needs > refinement >Can you cite an example of the Indians using infinity as a number? > Did they define addition and subtraction for infinity? How was > it used? Just having a concept of size without bound is not > the same thing has the concept of an infinite number. No, they did not develop a real transfinite arithmetic that I know of, but discovered zero and the digital number systems and regarded infinity as the inverse and complement of zero. They also invented negative numbers. Cantor didn't invent infinity. He invented set theory. >Stephen > -- Smiles, Tony ==== Subject: Re: Orlow cardinality question > stephen@nomail.com said: >> Yes, it can prove something that is true for all members of >> the infinite set of naturals. It cannot prove something about sets >> of naturals. You are trying to prove something about sets, not >> naturals. You are trying to prove that for all sets, the >> size of the set is not larger than the maximum element in the >> set. You cannot prove this using induction. It is not a statement >> about natural numbers. It is a statement about sets of natural numbers. > What I proved is that for all n in N, the set defined as the whole numbers from > 1 to n has the property that its maximal element and its size are equal to n. > This is a property of n, since the set is defined by n, according to a simple > rule. There is absolutely nothing wrong with the way I have applied induction > in this case. But you have not proven anything about all sets. There are sets that are not defined as the whole numbers from 1 to n. In particular, the set of natural numbers is not defined as the whole numbers from 1 to n. There is no n such that 1 to n is all the natural numbers. Therefore your proof says nothing about the set of all natural numbers. >> I offered a system for sets defined by mapping functions that works precisely, >> both for finite and infinite sets. It wasn't welcome. >> >> For one reason, it only applied to some sets. > Yes, sets defined by mapping functions, as I have said repeatedly. Other > approaches are necessary for other types of sets. >Sets are not defined by mapping functions. That phrase does not mean anything. > The set of even numbers is the set of all numbers divisible by 2. > Is that defining it by a mapping function? >> You map the naturals to the evens using E=2*N, do you not? How else do you draw >> your bijection and declare equal cardinality, based on correspondence between >> elements? >> >> What does that have to do with sets defined by mapping functions. >> E is not defined by a mapping function. There exists a function >> that maps each element of N to each element of E and vice versa. >> There actually exist an endless number of functions. But >> E is not defined by a mapping function. > The mapping is perfomed using a function. Show me a bijection between these two > sets without it. You're avoiding the issue. You know exactly what role mapping > functions play in cardinality. I do not know what sets defined by mapping functions mean. Given two sets I can find a bijection betweeen them if they have the same cardinality. There are untold number of such mappings. They need not be functions in the sense of being algebraic functions. They are of course all functions, because that is essentially the definition of a function. Here is nonstandard mapping function for you. For an element of N, consider its binary representation. Invert each of the digits (1 to 0, 0 to 1) except for the first 1. Add a 0 to the end. This is now the binary representation of an even number. This is a bijection between the positive integers and the positive even integers. So you do not think there is anything inconsistent in saying >> that size is a universal measure of sets and at the same >> time admitting that our notion of size does not apply to >> all sets? > I don't think there is anything inconsistent in saying that every set has a > size, but that we can only determine the relative sizes of infinite sets based > on properties of their members. Finite sizes we can count. Infinite sizes we > have to calculate, so we need some data to work with, something with which to > compare the set elements. That does not sound very universal to me. It would be nice to compare any two sets independent of how we interpret the elements in the set. or sets of sets, or sets of strings. That does not seem like > a very universal measure of sets. >> Actually I already addressed sets of strings rather explicitly, but that >> explanation doesn't go anywhere with you, so there is no point getting into >> more complex ideas where you are bound to get even more lost. If you have sets >> of sets that have similar properties, then they can be compared as well. >> >> I want to compare sets of sets with sets of integers. Can you do that? > What kinds of sets? This might be interesting..... How about sets of strings over the alphabet {a,b}? Or finite sets of real numbers? cardinality, and changes nothing about cardinality. There are > no inconsistencies with cardinality and transfinite cardinals. >> Sure, and they have nothing to do with set size, so I am free to devise a set >> size theory that works. yay! >> >> You are free to define a theory. However you keep claiming that >> cardinality is inconsistent. You are not free to claim that, >> and as long as you do, people will object. > I am free to claim whatever I want, especially if I can prove it. You have yet to prove any of your claims. >> >> And you still have not defined set size. Why do you think >> such a thing even exists if you cannot even define it? > It's the number of elements in the set. The count of the units in the whole. > These terms are simple enough that they shouldn't need explanation, and your > insistence that they do is just an attempt to derail the point. It does need explanation. That is the whole point. >> What question does size of a set answer? Why do you think >> that answers a question, but cardinality does not? Again, you >> refuse to look at your own assumptions. You are assuming that >> size is some real thing that exists independent of our >> definitions. It does not. It has no more meaning than cardinality. >> In fact, given that it does not have a definition for infinite sets, >> it is currently meaningless. > It is certainly well understood for finite sets. The question is how to apply > the concept to infinite sets. Yes. That is the question. One answer is to not use size when describing infinite sets. People have come up with many different measures of size for infinite sets, all useful in different contexts. All these measures have different names, and none claim to be *the* size of an infinite set. > It's a measure of the set, and the only one that can be discussed when dealing > with a set of generic units. A set is just a number of units taken as a unit. > The number of units in the set IS its size. It's a definition, not a > justification. >But you cannot answer number of units until you define some > numbers that are applicable. >> Come again? What does this mean? >> >> The answer to the question what is the number of units should >> be a number, don't you agree? However, if you have no numbers >> that are applicable, then there is no answer to the question. >> There is no answer to the number of natural numbers if you >> restruct number to the natural numbers. > That is true, if you restict natural numbers to finite values, but that is > entirely unnecessary. By definition natural numbers are all finite. I know you cannot follow such a simple inductive proof, but it is a fact. 0 is finite. if n is finite, n+1 is finite therefore all n are finite There are no infinite natural numbers. Before Cantor's time there were not non-infinite numbers at all in the West. An infinite number would be an actual infinity which was severely frowned upon. first to define such numbers, and he was about to answer > questions about the number of elements using these numbers. > You have not defined the infinite numbers you keep talking > about, but just throw around alot of hand wavy statements. > In any case, any definition you come up with has no > affect on cardinality. >> As you wish, but be aware that Cantor did not invent infinity any more than he >> invented zero. The Indians did both of those, as well as inventing the first >> modern religions, which is no coincidence. Cantor may be the first western >> mathematician to approach the topic with an axiomatic approach, but if so, the >> first try is rarely perfect, and it's not surprising if it later needs >> refinement >> >> Can you cite an example of the Indians using infinity as a number? >> Did they define addition and subtraction for infinity? How was >> it used? Just having a concept of size without bound is not >> the same thing has the concept of an infinite number. > No, they did not develop a real transfinite arithmetic that I know of, but > discovered zero and the digital number systems and regarded infinity as the > inverse and complement of zero. They also invented negative numbers. Cantor > didn't invent infinity. He invented set theory. And he invented infinite numbers. The Indians had a single infinity, assuming your understanding of the matter is correct. Something was either infinite or not, and I do not know if they worried about potential or what is the number of naturals, or what is the number of reals, the Indians would have only had one possible answer: infinity. So your example reinforces my point: before you can talk about number of elements of an infinite set, you need some numbers which make the question meaningful. Stephen ==== Subject: Re: Orlow cardinality question Jan de Vos said: > When you declare both the naturals and the even naturals as infinite > sets, do you imagine that the infinite limit on the values of those > two sets is the same omega? >I do not imagine any limit. If you look at these two series (looking > at them as series, because a set, like a bag, does not have an > inherent order on the elements), they both go on 'forever', at each > point, there is a further point. >But I take it your intuition tells you that the limit of such a > sequence should be related to the cardinality of the set. >Or is the even omega twice the natural omega, and therefore able to > contain the same number of elements, even though its elements are > half as dense in the reals as the naturals? >Well, Tony, what do /you/ think? For example, take these two sets: >N' is gotten from N by removing all odd elements, and > N is gotten from N by multiplying all elements by 2. > (where N is the set of all finite integers) >Do you think these are different sets? According to your logic, the > first should have the same 'range' as N, while the second set would > have twice the range (or limit, as you would say). Sure, the first would be half the second, because they both have a constant density of 1/2, but first has half the elements removed and the range preserved, which the second doubles the range while halving the density, thus preserving the overall set size. >So my question is: how do the sizes of N, N' and N relate? Is any of > the sets bigger than any of the other two? |N|=|N|=2*|N'| >On the one hand, cardinality asserts there are different infinities, > but on the other hand, it declares them all the same implicitly > during the course of its bijections. >Well, no, for instance, N and R have different cardinalities (because > one cannot bijectively map N to R (and vice-versa). Yes I know, but the value range between N and R only differ by 1, even though the set sizes are incomparable. When you apply your bijections, you should make sure you are using the same value range for two sets you are comparing. >To me this is an internal inconsistency that leads away from > intuitive results. >Again, clearly your intuition tells you different things than mine > tells me :-) Well, yes, I guess so. Jan > -- Smiles, Tony ==== Subject: Re: Orlow cardinality question imaginatorium@despammed.com said: imaginatorium@despammed.com said: > Jiri Lebl said: > You have not answered Jan's primary complaint about what you said. > Let's give it in finite terms first. Does multiplying every element by > 2 give a smaller or larger set? Let's see: > {1,2,3} > {2,4,6} > So far so good > {1,2,3,4,5,6} > {2,4,6,8,10,12} > Hmm. It seems that I don't get a set that's half the size, why would > then I intuitively get half the set when I multiply {1,2,3,4,...} by 2? > I certainly have not added nor taken away any elements, I've just > relabeled them. Do I get a different set when I multiply every element > by 2 and yet a different one when I pick out just the even integers? > If so, I would like to know what do you mean by an even number since > it obviously can't be a number with a divisor of 2. If this > intuition is not supposed to carry over to infinite sets, then why does > your bigulosity intuition carry over and not this one? > Jiri > (My *emphasis*...) > Because you are ignoring the *range* of values. > Range? What is this range? Doesn't a range normally have two ends? > I mean isn't a range from A to B? In this case, if you are talking > about the pofnats, I know what A is: 1 (or possibly 0, depending on > your definition). But B doesn't exist. If you would only, for once > accept that when a mathematician says endless P, she means there is > no end to P... > Brian Chandler > http://imaginatorium.org > (sigh) In which case it has an infinite range. The infinite range of values for > naturals is no different than the infinite range of even values, except maybe > by a difference of 1. >What exactly is an infinite range? Suppose that in comparing the > bigulosity of the pofnats and the even pofnats, one starts from 0 on > the left and sets off towards infinity, with one's left hand touching > each pofnat, and one's right hand skipping over the evens (pofeven! > gap! pofeven! gap! pofeven! OK?) then plainly in normal mathematics > this journey never ends, and one can't say much in the way of > comparing ranges since, well, the journey is unending. In Orlowmaths, > does this journey stop at infinity? Or do the two hands not just not > stop, but somehow not stop simultaneously (That's not the absence of > simultaneous stopping, but rather the simultaneity of not stopping...) >Supposing the mathematician on this journey suddenly notices that each > pofnat on his left side is actually printed on one side of a card which > had been used for some mathematical teaching purposes, and on the > reverse side of every card is printed twice the number on the front > (could this ever be impossible? a pofnat that can't be doubled?). Since > you seem to think there's a place called Infinity where this process > ends, what has happened to the number on the back of the cards with the > pofnats on the front? Is it somehow twice the last pofnat? >Here's a diagram: The top row is what's printed on the *back* of the > cards. 2 4 6 8 10 12 14 16 18 ... ?? bigulosity = infinity? X? > 1 2 3 4 5 6 7 8 9 ... bigulosity = infinity >walk - > _ 2 _ 4 _ 6 _ 8 _ ... bigulosity = infinity / 2 So what *is* the bigulosity of the numbers on the back of the cards? > What's the bigulosity of the set of cards? Does the bigulosity change > when you turn the cards over? Do the numbers on the back of the cards > somehow include an extra helping of evens? Is this a way to count and > reach twice infinity? >Anyway, no inconsistency here, eh? We're all enjoying watching > bigulosity working perfectly... >Brian Chandler > http://imaginatorium.org > You have some number aleph_0 which you have assigned as the number of all naturals. Consider this the limit of all natural numbers, odd, even or otherwise. This is the value range that applies to them all. When you get to your last natural, what is on the back of the card? Certainly, others have noted that the evens are clearly half as numerous as the naturals, and come up with set density measures to address this, but it doesn't seem to be well integrated with the rest of set theory. By just saying it goes on forever, you ignore this aspect of set size, and sweep it under the rug. I am not sure how people can be satisfied with this. -- Smiles, Tony ==== Subject: Re: Orlow cardinality question > imaginatorium@despammed.com said: >> >> Anyway, no inconsistency here, eh? We're all enjoying watching >> bigulosity working perfectly... >> >> Brian Chandler >> http://imaginatorium.org >> >>You have some number aleph_0 which you have assigned as the number of all > naturals. Consider this the limit of all natural numbers, odd, even or > otherwise. This is the value range that applies to them all. When you get to > your last natural, what is on the back of the card? No one here has a last natural other than you. Only you can answer that question. Unending means undending. There is no last element. Stephen ==== Subject: Re: Orlow cardinality question stephen@nomail.com said: > Virgil said: >> Given the axiom of choice, there are no exceptions and dismissals to >> cardinality as a measure of set size. And two sets may be compared and >> the relative sizes of their cardinalities determined. > Yeah, sure. They're either equal or incomparable. Fine distinctions! >Can you read? Any two sets can be compared. There are no > incomparable sets with respect to cardinality. Given two sets A and B, > either |A| > |B|, or |A| < |B| or |A| = |B|. It does not matter > if A is a set of reals, or B is a set of regular expressions. > All sets are comparable using cardinality. >Stephen > By incomparable I meant so infinitely different that they can't even be thought of as functions of each other. You have two basic infinities: N, the discrete infinity, and R, the continuous infinity. Then cardinality adds other alephs on top of that to add extra dimensionality to the continuum. But, it can't say one plane of twice the size has twice the infinity of lines or points. There isn't any fine distinction. The alephs are only broad categorizations of infinity, and not quantifications. I knew you'd jump on that. Hope you had fun. -- Smiles, Tony ==== Subject: Re: Orlow cardinality question >stephen@nomail.com said: >> Virgil said: > Given the axiom of choice, there are no exceptions and dismissals to > cardinality as a measure of set size. And two sets may be compared and > the relative sizes of their cardinalities determined. >> Yeah, sure. They're either equal or incomparable. Fine distinctions! >> >> Can you read? Any two sets can be compared. There are no >> incomparable sets with respect to cardinality. Given two sets A and B, >> either |A| > |B|, or |A| < |B| or |A| = |B|. It does not matter >> if A is a set of reals, or B is a set of regular expressions. >> All sets are comparable using cardinality. >> >> Stephen >> >By incomparable I meant so infinitely different that they can't even be thought >of as functions of each other. That's not what incomparable means. Stephen gave exactly the correct definition when it comes to comparability and incomparability of cardinalities. In ANY partially ordered set (with order <), two elements x and y are said to be comparable if x < y or y < x or x = y, and two elements are said to be incomparable if they are not comparable. Under the Axiom of Choice, if m and n are cardinalities of sets, then m < n or m > n or m = n. It follows that all cardinalities are mutually comparable, according to the standard mathematical definition of the word. If you are going to use a word that is used in mathematics, but not with the meaning that is used in mathematics, then it is YOUR responsibility to point out that you are using a meaning distinct from the usual meaning. As far as two sets being functions of each other, or not being functions of each other, that is not standard terminology in any way. What exactly does the statement that a set is a function of another mean, anyway? Do you mean that there exists a bijection between the sets? Do you mean that there is a function from the first set ONTO the other set (i.e. there exists a function from the first set to the other set such that the second set is the range of the function)? Your vague terminology tells us absolutely nothing about what you want to say. > You have two basic infinities: N, the discrete >infinity, and R, the continuous infinity. Then cardinality adds other alephs on >top of that to add extra dimensionality to the continuum. But, it can't say one >plane of twice the size has twice the infinity of lines or points. There isn't >any fine distinction. The alephs are only broad categorizations of infinity, >and not quantifications. I knew you'd jump on that. Hope you had fun. This is garbage. The alephs are of distinct cardinality. Distinct alephs are not mutually bijective. The cardinalities give an exact quantification to the size of an infinite set (subject to the Axiom of Choice). There are so many alephs that no set is large enough to contain all of them. Given any aleph, there exist sets of alephs whose cardinality is the given aleph, and no such set can contain all the alephs. ----- ==== Subject: Re: Cantor and the binary tree Randy Poe said: Randy Poe said: >For some reason you seem to get confused between things > you say and things we say. > Cardinality arguments do not require a numerical mapping > function of the type you describe. They require only > that you can establish properties of the abstract > labeling, as Jiri says. The one who introduces > mapping functions is you. > That is a pile of crap. Don't tell me that Cantorians haven't used mapping > functions to draw bijections. (sigh) >They're convenient. They're neither unique nor necessary. > You've made the statement that E is mapped from N > with 2*N. That's nonsense, or in your inimitable words, > a pile of crap. There are infinitely many maps from > E onto N, and from N onto E, and any such bijective map > is suitable for establishing equal cardinality. And they are all linear relations that provide the same answer when domain and density are properly accounted for. >When dealing with numbers, sometimes it's convenient > to use an order-preserving map expressible in a few > lines of arithmetic, and sometimes it isn't. Sometimes you have to rearrange one of the sets out of quantitative order for your bijections, but this is an indication that the infinities are NOT the same, as is the case with the naturals vs. the rationals. >When using more general kinds of mappings such as in > the general proof that P(S) has larger cardinality than > S, there is absolutely nothing equivalent to your > f(x) = 2*x. I agree that the power set of any set is clearly larger than the original set, being 2^x, if the original set had x elements. It's the same size as the set mapped by f(x)=log2(x). > Fine, try giving a proof that the integers and the even integers have the same > cardinality, WITHOUT using any mapping function. >I have to use some MAPPING. I have to establish that it > is bijective. But you have a narrow meaning for mapping > function which restricts it to things which can be written > down simply in a line of algebra. >I don't have to use f(x) = 2*x. Whatever you use, it will boil down to that linear mapping function, in this case. > - Randy > -- Smiles, Tony ==== Subject: Re: Cantor and the binary tree David Kastrup said: >That is a pile of crap. Don't tell me that Cantorians haven't used > mapping functions to draw bijections. (sigh) Fine, try giving a proof that the integers and the even integers > have the same cardinality, WITHOUT using any mapping function. >A bijection is _defined_ as a mapping. >You can show the existence of a mapping without giving it in explicit > form. >For example, like the following: >The natural 0 can be mapped to the even number 0. >If natural n is mapped to even k, one can map n+1 to k+2. >By using the axioms of the natural numbers, you can then show that > this mapping exhausts both the natural as well as the even numbers. > You may not have put it in formulaic format, but this is a linear mapping function nonetheless. -- Smiles, Tony ==== Subject: Re: Cantor and the binary tree for my mapping f is the set [-oo,1]? If Mueck actually tried to read and follow my example, > perhaps even he would have spotted the flaw. Let's see > if he comments on the fixed version. > Not so much time to read all contributions. Of course, I agree. In http://www.fh-augsburg.de/~mueckenh/Infinity/MA6. I say that the set {m, M, f} is an impossible set. This has nothing to do with cardinality, as can be shown by the following bijection from N on the union of the set of even numbers and the set of nongenerators under the mapping. f: N--> E u {non-generators under the actual mapping}. You may try to construct any bijection. It will fail, but not because there are too less elements in N. ==== Subject: Re: Cantor and the binary tree Two paths in a maximal binary tree are distinct if and only if there is > a node at which one branches left and the other branches right. If this does not happen there is no them to distinguish, only an it > which cannot be distinguished from itself. You insist that some numbers do exist though you know that they don't. Therefore I spoke of them. Nevertheless. The nodes are the only chances for paths to separate / distinguish themselves from others. Therefore there are only countably many fifferent paths. ==== Subject: Re: Cantor and the binary tree <0pudndyo75_okDrfRVn-hw@comcast.com> the whole tree) accompanied by infinitely many paths which are due to > terminating rational numbers. These form a bunch which does never > separate. The due numbers are one and the same number. ==> Irrationals > do not exist. Insanity to claim that what is non-existent has a path. Never heard of a proof by contradiction? And what does WM mean by accompanied. Every path is accompanied by > the entire tree, as without the tree there are no paths. Accompanied of course means sharing the same edges. If WM is trying to describe something like a filter or a net, he is > failing miserably. A node is the only chance for a (bunch of) path(s) to distinguish itself from others. These chances are countable. Therefore, the binary representations of numbers which are distinguishable from others are countable. It is very simple. ==== Subject: Re: Cantor and the binary tree that any set has a smallest element. But it is defined which element comes first, which comes second and so wohlgeordneten Menge ist jede wohldefinierte Menge zu verstehen, bei welcher die Elemente durch eine bestimmt vorgegebene Sukzession miteinander verbunden sind, welcher gem.8a€ es ein erstes Element der Menge gibt und sowohl auf jedes einzelne Element (falls es nicht das letzte in der Sukzession ist) ein bestimmtes anderes folgt, wie auch zu jeder beliebigen endlichen oder unendlichen Menge von Elementen ein bestimmtes Element geh.9art, welches das ihnen allen n.8achstfolgende Element in der Sukzession ist ( es sei denn, da€ es ein ihnen allen in der Sukzession folgendes .9fberhaupt nicht gibt). > It doesn't mean that you can make > it into a list. Suppose we take an inductive set like in peano's > axioms. That is a set where each element has a successor. That does > not imply that each element (except one) has a predecessor for one, > which would be necessary (but not sufficient) to make it into a list. > For example reorder the naturals as such: {1,3,5,7,...,2,4,6,8,...}, > this is a well ordering of the naturals, but 2 has no predecessor. If transfinite numbers are called whole numbers, then a well ordering may be called a list or a sequence, although there is an element, like 2 in your example, which is the next one to all the odd n e N. You must not forget that *all* are existing. ==== Subject: Re: Cantor and the binary tree An old defence: The tree cannot be infinite! If arguments are lacking. > > You misread. When counting you will not get to either infinitely many nodes > or infinitely many paths... The tree can however be infinite. > > Well, but the whole infinite tree consists of a countable set of edges. That is just a statement. > In the infinite tree there is the complete path representing 1/3. There > is no edge by which 1/3 separates from all other reals. ==> There are > reals the paths of which do never separate from that of 1/3. They make > up a bunch of paths. The bunches which separate at some edge are > countable. The paths of a bunch which do never separate may be > uncountable. But they do not represent different numbers. Eh? Numbers which do not differ at any finite bit are not different. Paths which do not differ in the tree by at least one node do not differ at all. Bunches of paths which have at least one node of their own indicate by this fact that they belong to a countable set. At most a countable set of bunches can differ by a node. At most a countable set of numbers has a binary representation which differes by at least one bit. > I see you have dropped the N -> P(N) argument... > > That argument stands as given in > http://www.fh-augsburg.de/~mueckenh/Infinity/MA6. > Cantor's theorem does not prove the uncountability of P(N), but the > impossibility of finding a set which contains the element x if it does > not contain the element x. Yes? So what? For surjectivity there is a requirement that such a set > exists. I see you write: We will see now, that the impossible set does > not exist and that the paradox-generating requirement cannot be > satisfied, even if the mapping is defined between equivalent set. > However, in the example you give there is no such paradox-generating > requirement. You apparently still do not get it. In a mapping > N -> P(N), if it is surjective, there *must* be an m such that f(m) = M. > In the mapping {1, a} -> {{}, {1}}, there is *no* such requirement. > The requirement here is that either f(1) = M or f(a) = M. And that > requirement is satisfied. No, the requirement is to map a natural number on the set of non-generators with respect to natural numbers. This has nothing to do with cardinality, as can be shown by the following bijection from N on the union of the set of even numbers and the set of nongenerators under the mapping. f: N--> E u {non-generators under the actual mapping}. You may try to construct any bijection. It will fail, but not because there are too less elements in N. > Try the well-ordered set of real numbers to construct it by the > diagonal argument. If you well-order the reals it is not a list. Not every well-ordered > set is a list. > But it is defined which element comes first, which comes second and so wohlgeordneten Menge ist jede wohldefinierte Menge zu verstehen, bei welcher die Elemente durch eine bestimmt vorgegebene Sukzession miteinander verbunden sind, welcher gem.8a€ es ein erstes Element der Menge gibt und sowohl auf jedes einzelne Element (falls es nicht das letzte in der Sukzession ist) ein bestimmtes anderes folgt, wie auch zu jeder beliebigen endlichen oder unendlichen Menge von Elementen ein bestimmtes Element geh.9art, welches das ihnen allen n.8achstfolgende Element in der Sukzession ist ( es sei denn, da€ es ein ihnen allen in der Sukzession folgendes .9fberhaupt nicht gibt). So, if transfinite numbers are called whole numbers, then a well ordering may be called a sequence or a list, although there is an element, like omega with respect to N, which is the next one to all the finite elements n e N. ==== Subject: Re: Cantor and the binary tree imaginatorium@despammed.com said: Martin Shobe said: > On Wed, 15 Jun 2005 10:12:55 -0400, Tony Orlow (aeo6) >Martin Shobe said: >> On Mon, 13 Jun 2005 12:43:17 -0600, Virgil >There is a path P (for instance 1/3 = 0.010101... = P) This path has >got a node (a node is mapped on it). In the same edges there are many >other paths, but that does not bother us. They will get their nodes >in the next node. Among them is the path P'. The node, where this >happens, is mapped on P'. Its companions remain nodeless nude. >So we have two nodes mapped on two paths, P and P'. The next time when >a bunch of paths separates from P, *one* of those gets the node where >that happens. (Same for separation of a bunch from P' and that bunch >remaining with P'.) The others do not yet get nodes but will have to >wait until their turn will have come. So every path is either equipped >with a node or it has not yet been separaed from other paths or it has >alreay its node but is not yet separated from all others. In any case >we make sure that an individual path cannot exist separated from all >others without carrying a node. Whether individual paths separated from >all others do exist at all, that is another question. > You still do not have a bijection, as this will not assign a node to > every path. > Proof. > Let N be the set of nodes, and P be the set of Paths. > Let f:N->P be a function described above. For all n in N, n is on > f(n). (I.e. the path f(n) goes through the node it is assigned to). > Construct a path p as follows. Start at the root. If the node > assigned to the root goes to the left, got to the right. After this, > as you visit each node, go the way that the path assigned to that node > does not go. Because the tree is maximal, we can always go the other > way. Therefore, this path exists. >Yes. If the tree corresponds to the reals in [0,1), then the complement is 1-n, >where the original value was n. If the tree corresponds to the integers in >[1,oo), then the complement is oo-n. What does it prove if a complement of an >infinite binary string exists? > You're the one bringing this up, why don't you tell me? I beg your pardon? This is the situation you are describing, inverting all the > digits, and claiming the inversion isn't associated with any node. It is indeed > associated with a value, even if that value doesn't diverge from all others > until infinity. >Ah, there's a lot of talk (on the crank side) about paths diverging off > - something I find hard to understand, since no path can ever > separate from all others, since the first thing any path does is to > split again at the next node. But you have the answer, I see! It may > not diverge from all others until infinity. What is it like, this > place infinity? Seems to be where all impossible things happen. I > wonder if there is an integer between 2 and 3 once you get to > infinity? Or perhaps a four-sided triangle? > (And if not, why not?) >Brian Chandler > http://imaginatorium.org > You seem to have failed to understand my point about the child branches vs. the sibling branches. The child branches continue a path of constant value, while the sibling branches initiate a new path with a new value. A value like 1/3 in binary is an infinitely repeating string of digits, so it does not have a distinct sibling node in any finite number of branches, but only a conceptual last node at infinity. Your other spewages are not worth responding to. -- Smiles, Tony ==== Subject: Re: Cantor and the binary tree <41m1b1dgopivid6ttjha3355dunvk1a713@4ax.com> Ah, there's a lot of talk (on the crank side) about paths diverging off > - something I find hard to understand, since no path can ever > separate from all others, since the first thing any path does is to > split again at the next node. But you have the answer, I see! It may > not diverge from all others until infinity. What is it like, this > place infinity? Seems to be where all impossible things happen. I > wonder if there is an integer between 2 and 3 once you get to > infinity? Or perhaps a four-sided triangle? > (And if not, why not?) You seem to have failed to understand my point about the child branches vs. the > sibling branches. Quite possibly. Let me guess: at each branch point (node), you draw the left branch straight down, and the right branch sort of hooked to the right? Then from the right (hooked) branch you can select the straight-down path to be associated with this node? Yes, this is a 1-1 mapping of the straight-down paths onto the nodes. Of course it is, because the straight-down paths correspond to binary fractions that terminate, with an unending sequence of zeros, and these correspond to (some of) the rationals. They're a countable set. OK, I've guessed a bit what you were getting at - please correct any major misapprehensions. > ... The child branches continue a path of constant value, while > the sibling branches initiate a new path with a new value. A value like 1/3 in > binary is an infinitely repeating string of digits, so it does not have a > distinct sibling node in any finite number of branches, but only a conceptual > last node at infinity. Ah! The conceptual last node at infinity. As I understand an infinite tree (which incidentally I think is quite a strange thing, certainly not to be considered by anyone who still hasn't sorted out the pofnats), it means that every node is non-terminal; there are no end nodes; every node is followed by a split into two branches. Whether you draw one side straight-down, or symmetrically makes little difference. But here _you_ have a conceptual last node at infinity; how can a tree with no terminal nodes have a last node anywhere, unless infinity is just where impossible things happen. Almost all of your proofs can be transformed to the same essential mistake: considering the end of an unending sequence. You dress this in various bits of linguistic tinsel like conceptual, but conceptual comes from the verb conceive, and I can't conceive of the end of something with no end. Can you? Brian Chandler http://imaginatorium.org ==== Subject: Re: Cantor and the binary tree > Don't tell me that Cantorians haven't used mapping > functions to draw bijections. (sigh) In sets of more than a very few members, drawing is much too inefficient. >Fine, try giving a proof that the integers and the even integers have > the same cardinality, WITHOUT using any mapping function. A is the smallest set containing all of (starting with {}, for any x let the next one be (x union {x}) ). B is the smallest set containing all of (starting with {{}, for any x let the next be (x union {x}) union {x union {x}) ) ==== Subject: Re: Cantor and the binary tree > Virgil said: >On Tue, 14 Jun 2005 16:47:59 -0400, Tony Orlow (aeo6) > >it would look like: >.____._____.____.____.________.... >| | | | | | >._. ._. ._. ._. ._.... ._.... >| | | | | | | | | | | | >. . >. . >. . >Now, clearly, every vertical path of branches represents a series of >insignificant zeroes and an unchanging value, and every sideways >sibling >branch represents a change in value, and the beginning of a new infinite >vertical path of unchanging value. When viewed this way, it becomes >clear >that, >if each branch is taken to represent a binary digit, with a child branch >being >a 0 and a sibling branch being a 1, each unique value in the number >system >has >a 1-1 correspondence with a unique infinite path starting at its last >sibling >branch, and a 1-1 correspondence with the pair of branches that >distinguish >the >beginning of that new path from the continuation of the old path from >which >it >diverges. Perhaps viewing things this way will help those who haven't >understood WM that there is indeed a direct correspondence between >paths, >branches and nodes, and perhaps it can help WM see that the >correspondence >is >one of one path per every TWO branches or nodes. Please also note that >the >nodes themselves do not really represent anything. They are the spaces >between >digits, which are represented by the branches. >What about the numbers represented by paths that hove no last sibling > branch? >Martin >I fail to see that sibling/child branchings are any different that > left-child.right/child branchings, so long as there are exactly two > branches beginning at each node and one node to end each branch for the > entire maximal binary tree (maximal in the sense that there is no place > left to add another branch or node without destroying its binary > property of exactly two branches beginning at each node and one node at > the end of each branch). > Virgil fails to open his eyes, and wonders why he cannot see. Perhaps > Virgil doesn't understand what was explained, that every terminating > vertical run of child branches represents an unchanging value and a > unique number, If vertical runs terminate it must either be because the paths in which they lie are not infinite paths as required. If the vertical runs mentioned do not terminate but run verticaly forever, then they only represent those rationals whose denominators are powers of two, and they omit most reals. > It remains the case that there are easy bijectins between the set of > naturals and either the set of nodes or the set of branches, but at best > an injection which is not a bijection from the set of naturals to the > set of paths. > That is absolutely not true. It absolutely is true! Each infinite path corresponds to one number > with > infinite digits. Each infinite path maps onto a real number, but in countably many instances two paths map onto the same binary rational. > If you restrict the naturals to finite values, That is not a restriction. At least not in any standard mathematics. What happens in TO's version of mathematics only TO can say. ==== Subject: Re: Cantor and the binary tree > Martin Shobe said: > On Tue, 14 Jun 2005 16:47:59 -0400, Tony Orlow (aeo6) > >it would look like: >.____._____.____.____.________.... >| | | | | | >._. ._. ._. ._. ._.... ._.... >| | | | | | | | | | | | >. . >. . >. . >Now, clearly, every vertical path of branches represents a series of >insignificant zeroes and an unchanging value, and every sideways sibling >branch represents a change in value, and the beginning of a new infinite >vertical path of unchanging value. When viewed this way, it becomes clear >that, >if each branch is taken to represent a binary digit, with a child branch >being >a 0 and a sibling branch being a 1, each unique value in the number system >has >a 1-1 correspondence with a unique infinite path starting at its last >sibling >branch, and a 1-1 correspondence with the pair of branches that >distinguish the >beginning of that new path from the continuation of the old path from >which it >diverges. Perhaps viewing things this way will help those who haven't >understood WM that there is indeed a direct correspondence between paths, >branches and nodes, and perhaps it can help WM see that the correspondence >is >one of one path per every TWO branches or nodes. Please also note that the >nodes themselves do not really represent anything. They are the spaces >between >digits, which are represented by the branches. >What about the numbers represented by paths that hove no last sibling > branch? >Martin There are alternating such sequences, such as 0.0101010... for 1/3. The > inverse > is also alternating, as one should expect. 0.101010101.... is 2/3. > Interesting. >The inverses of numbers which end in infinite series of child branches, or > 0's, > end in infinite series of siblings, or 1's. As I pointed out in another post, > this infinite series of 1's is equivalent to an addition of 1 in the digit to > the left of them, and their inversion back to 0's. It was at that point that > I > had an epiphany about why 2's complement notaton works so well in binary. > Maybe > you haven't gotten to that post yet. It was a fine moment. But it ignores what happens in those uncountably many paths which never become all 0's or all 1's from some node onward. They represent all but countably many of the real numbers. ==== Subject: Re: Cantor and the binary tree On Tue, 07 Jun 2005 19:22:21 -0400, Robert Kolker In mathematics, arguments unsupportted by proof mean nothing. There is > no proof possible without assumptions not valid in standard mathematics. The argument in supporting an assertion is the proof. A proof is an > argument. Mere unsupported assertion is... > ...M.9fckenheim!!! :-) A. ==== Subject: Re: Cantor and the binary tree > Virgil said: >If TO wants to relabel one of them vertical and the other > horizontal, then I suppose he might call a path of all verticals > a vertical path. > Yes, and since all the vertical child branches correspond to 0, each > of these infinite paths starting at a sibling node corresponds to a > single value, not a set of values. There are infinitely many paths that eventually become and remain vertical and represent terminating binaries, but there are as many which eventually become and remain horizontal, and more than both of these together which never do either. ==== Subject: Re: ed Topics On 16 Jun 2005 22:35:41 +0200, Torkel Franzen in > It goes considerably further back than all that. All the way to >> Aristotle in formal logic who regressed syllogistic inference to his >> canons of logic. Actually, Aristotle was merely echoing the mystic doctrines of >Xonthes, whose basic act of regression was the foundation of the >whole school of Regressionism, pre-dating Aristotle by four or five >centuries. Aristotle may indeed been echoing someone but I rather doubt it was your cousin.