mm-20 James Harris The majority of the links on that page that work seem to lead to FLTproofs, and their discrediting. So one presumes you arent claiming thattheyre still true.As for the crank label. Surely that depends on what an individualsde?ition of a crank is? The website seems to present evidence, from which the reader should drawshould be clear: the ?crank ones tend to be anti-establishment pieces,where the author somehow presumes to know the ?truth, and is often notpersuaded by cogent arguments that they are talking cods-wallop. You perhaps should read the anti-cantor ones and decide if you think thearguments are sound (I dont think they are). Draw your own conclusions asto whether or not the author is misguided, mistaken, or something else.Can we get back to maths now? Ive had plenty of ideas about the primecounting one. Including youll be delighted to know, realizing some of myearlier criticisms were inaccurate. I would still like it if you were to rewrite your arguments in clearEnglish. I mean, you at one point say dS(x,y) is a ?count of the composites, so whatis S then? I mean, seriously, what does it do? I can guess but Id likeyou to make it clear. Why is p_y(x,y) = p_x(y,y) or similar; that directional derivative bit? I mean asimple counter example shows it isnt. Perhaps we should read thedifferentials differently?p_y(y,y) = partial d by du of p(u,v) evaluated at u=v=y? Im trying to solve the complex equation z^(2i) + z^i + 1 = 0 for z.First I substitute y = z^i to get:y^2 + y + 1 = 0y = (1/2)(+/-Sqrt(3)i - 1)So we have:z^i = (1/2)(+/-Sqrt(3)i - 1)z^i = e^(i*(+/-2pi/3 + 2pi*n)) for all integers n.e^(i*ln(z)) = e^(i*(+/-2pi/3 + 2pi*n))At this stage I get a bit confused. I think the right hand side shouldreally be e^(i*(ln(z) + 2pi*m)) for all integers m, however thesolutions I have do not do this. The solutions I have then 2pi*n)ln(z) = +/-2pi/3 + 2pi*nz = e^(+/-2pi/3 + 2pi*n) = e^(2pi(+/-(1/3) + n)However, I cant see how for two complex numbers a and b, e^a = e^b<=> a = b is necessarily true. What about the followingcounter-example:e^(i*2pi) = e^(i*4pi) <=> 2i*pi = 4i*piWhich is clearly incorrect. Surely this renders the above solution tothe aforementioned equation incorrect? Have I missed something?Richard Hayden. > However, I cant see how for two complex numbers a and b, e^a = e^b> <=> a = b is necessarily true. Since e^(0*i) = e^(2*pi*i), your <=> is false.It is true is that if a = b then e^a = e^b, but given e^a = e^b, the best you can say is that a = b + n*pi*i for some integer n. Has anyone any ideas how to obtain an identity of the followingform, with x, y real, valid in the critical strip 0 <= x <= 1 : zeta (x + i.y) = 1/t + e^(i.f_0(x, y)) + t.e^(i.f_1(x,y)) + .. + t^n.e^(i.f_n(x,y)) + ..where: t := SQRT(x.(1 - x))and the f_i are real-valued functions of x, y.As this would be a pretty easy way of earning $1M, I presumethe answer is no. All the same it looks tantalizingly simple,and analogous to Fourier series if you could ?d some factorthat would ?orthogonalize the terms on the right when bothsides were multiplied by this factor and integrated.John Ramsden > Has anyone any ideas how to obtain an identity of the following> form, with x, y real, valid in the critical strip 0 <= x <= 1 :> zeta (x + i.y) = 1/t + e^(i.f_0(x, y)) +> t.e^(i.f_1(x,y)) + .. + t^n.e^(i.f_n(x,y)) + ..>where:> t := SQRT(x.(1 - x))>and the f_i are real-valued functions of x, y.The LHS has a simple pole at z = 1 and a ?ite value at z = 0. It seems to me that the RHS has a pole of order 1/2 at both places.-- I need to ?d a closed-form integral (if one exists!) for a functionof this form:exp{(a*x)+[b*exp(c*x)]}or, alternatively,[exp(a*x)]*[exp(b*exp(c*x)]Any help would be much appreciated. I know the exponential of anexponential yields the exponential integral, but this is at least one >I need to ?d a closed-form integral (if one exists!) for a function>of this form:>exp{(a*x)+[b*exp(c*x)]}>or, alternatively,>[exp(a*x)]*[exp(b*exp(c*x)]>Any help would be much appreciated. I know the exponential of an>exponential yields the exponential integral, but this is at least oneThis is possible if and only if a is a positive integer multipleof c (or b or c is 0). Set u = exp(c*x); then du = u*c*dx. So the integral of the given function with respect to xbecomes that of u^(a/c - 1)*exp(b*u)/c with respect to u.As a/c - 1 must be a non-negative integer for this to beintegrable in closed form, that gives the answer.-- This address is for information only. I do not claim that these viewsare those of the Statistics Department or of Purdue University.Herman Rubin, Department of Statistics, Purdue University >> Oh - I wasnt paying attention, sorry. If were talking about>> sequences of integers then of course its true that an in?ite>> random sequence (with a suitable distribution) contains every>> ?ite sequence (with probability one.)>> >> Of course calling this the Shoenfeld theorem is a little silly,>> since its well-known and also easy to prove...>> >>in which case your argument falls down>>because there are only countably many such sequences.>Can you please point me to resources that cover this subject? I have>never seen any such material concerning random sequences and their>containing subsequences.Its an immediate consequence of various well-known facts. Finda book on probability theory that contains a thing called theLaw of large numbers, for example. Or a discussion ofnormal numbers...The Law of large numbers says that if you have a random sequenceof integers between 0 and N-1 then (with probability 1) each integerappears in 1/N of the places; in particular it appears at least once.Thats exactly your theorem for subsequences of length 1. The generalization to subsequences of length greater than 1 isimmediate:For example say we have a sequence of integers between 0 and 9and we want to talk about subsequences of length 3. Take theoriginal sequence, consider the terms in groups of 3 and youget a sequence of numbers between 0 and 999 (for exampleif the original sequence was 0,1,2,3,0,1,2,3,0,1,2,3,... thenthe new sequence is 12,301,239,123,...). The law of largenumbers says that every number between 0 and 999 appearsin the new sequence, which says that every 3-digit sequenceappears in the original sequence.>JS************************David C. Ullrich >The Law of large numbers says that if you have a random sequence> of integers between 0 and N-1 then (with probability 1) each integer> appears in 1/N of the places; in particular it appears at least once.> Thats exactly your theorem for subsequences of length 1.> The generalization to subsequences of length greater than 1 is> immediate:Hey! The Law of Large Numbers is much stronger than SchoenfeldsTheorem!!!-- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the last laugh. Alan Partridge, _Bouncing Back_ (14 times) An in?ite bounded sequence of random numbers contains all ?ite>>sequences of bounded numbers.>> At the very least you should phrase your theorem carefully. There is>> no such thing as a random number. I think what you mean is something>> like a random number generator, where random modi?s generator,>> not number. Better: A randomly selected bounded sequence of numbers...Your arguments are of little value.Why not counter them, then? All you have to do is to de?e what you mean by sequence of random numbers.>Whether or not I chose to disguise>simple concepts with excessive academic pedantryIn mathematics, thats usually phrased rigorous proof. Do it, and youre unassailable. Dont, and youre open to onslaught by a host of academic pedants. And one or two people who wonder what you think a random number might be.>is irrespective of>the validity of the Schoenfeld Theorem.That much is true. Your simple concepts say nothing about its validity.> But then of course the result is nonsense: if you select a bounded>> sequence at random, you might very well select (0,0,0,0,0,...).If the in?ite random sequence R contains all 0s, then it is boundBounded.>by [0,0], and the Schoenfeld Theorem remains true.Also, the Schoenfeld Theorem says sequence of random numbers not>random sequence of numbers.Thats worse, until you de?e random numbers..> See how clear things become when you try to state things with precision?> (As you try to do so, you will eventually ?d that the word random>> almost never belongs in a carefully-worded mathematical sentence!>> For all... There exists... ...measure... -- thoses are the phrases>> you probably want to use instead.)Your disproof of the Schoenfeld Theorem [Copyright(c) John>Schoenfeld] amounts to a set of befuddled attacks on my mathematical>ettiquette. Try again, champ.-- Richard Herring >SCHOENFELD THEOREM:>>An in?ite bounded sequence of random numbers contains all ?ite>>sequences of bounded numbers.At the very least you should phrase your theorem carefully. There is>no such thing as a random number. I think what you mean is something>like a random number generator, where random modi?s generator,>not number. Better: A randomly selected bounded sequence of numbers...I understand random number is sometimes taken to mean a uniformlydistributed random variable.>(As you try to do so, you will eventually ?d that the word random>almost never belongs in a carefully-worded mathematical sentence!Really? Not even in probability texts? Or number theory? > >Youre the best troll in the history of the Internet. >Hardly. Hes not even the best troll in the history of sci.math/physics.Shhhhhh! Youll give somebody the idea its a competition.Socks > all of you if you think Ill let you control my speech on Usenet> with insults!!! you losers who give away rights of others for no good reason!!! you if you think you can insult me into silence!!!> James HarrisNo no no no no James.... YOUing nut-job extordanirre....K. Jones > I understand your point of view, but I dont agree with it. Journal> and formalism. It forces you to review the literature in order to make> it clear how your work ?s into (and differs from) previous work.Now what if some person says they found a brilliant gem, should theygo through college courses, and learn a lot of techniques in theanalysis of gems?Or cant they just holler out that they found something?Mathematicians have created an environment hostile to outsiders on thepresumption that theyve found everything simple enough for anon-mathematician to ?d. So then if you claim youve foundsomething, they try to force you to learn everything necessary toeither be or come off as a mathematician i.e. a math expert.Thats wrong because it takes away the miracle of discovery assomething that just sometimes happens to surprising people.Mathematicians are saying, no, only by their rules can importantdiscoveries in mathematics be made, so by their rules must they beknown.> have done and how it is new, and this, in turn, helps protect your> intellectual property. The Usenet news groups are OK for tossing ideas> around and getting some feedback, but they are not the best way to> ---- it takes a lot of time; you have to use conventional terminology> and formalism; you have to typeset equations; you have to learn a> particular journals convention for bibliographic references; you have> to respond to referee reports; etc. In spite of these drawbacks, there> are still good reasons for such a system. It has clear advantages over> posting to usenet or sending incomplete summaries to random faculty.Its a demanding process that requires a lot of skills speci? tothat process alone, so if a person whos not a mathematician ?dssomething, theyre tasked with learning a lot speci? to writingability to write them over a lifetime.Besides, Ive contacted math professors and graduate studentsspeci?ally noting that Im NOT a mathematician, and asking for helpand advice with that process.The search for knowledge is hard enough without a discoverer having toface an antagonistic process, where *style* is used to block outsubstance. > I know in physics, there are sites where you can post un-refereed> papers (e.g. http://arxiv.org/) I see that this site also has an> archive for math. You could post a paper there. In the end, I> recommend that you produce a report which is more formal than a usenet> post and then put it on one of the archive sites, or turn it into aThey dont accept papers unless youre properly af?iated, as itchecks your gateway and bounces messages not from certain ones, likeuniversities.I know because I tried to post a math paper there.James Harris >> I understand your point of view, but I dont agree with it. Journal>> and formalism. It forces you to review the literature in order to make>> it clear how your work ?s into (and differs from) previous work.>Now what if some person says they found a brilliant gem, should they> go through college courses, and learn a lot of techniques in the> analysis of gems?>Or cant they just holler out that they found something?And when those college-trained geologists look at it and see that itsa piece of common quartz crystal, and isnt worth anything no matterhow shiny it happens to be, what should your amateur rockhound do then?Insist its the biggest ?d since the Hope diamond? That seems to beyour approach.> Mathematicians have created an environment hostile to outsiders on the> presumption that theyve found everything simple enough for a> non-mathematician to ?d. So then if you claim youve found> something, they try to force you to learn everything necessary to> either be or come off as a mathematician i.e. a math expert. Thats wrong because it takes away the miracle of discovery as> something that just sometimes happens to surprising people.>Mathematicians are saying, no, only by their rules can important> discoveries in mathematics be made, so by their rules must they be> known.Oh yes, and if one of the experts dares to suggest that your rockhoundshould read a book on geology and gemstones, he should declare that hedoesnt want to pollute his mind with false teachings because hes taughthimself everything he needs to know about gems. He also should take itas evidence that theres a world-wide conspiracy to suppress gems foundby non-professionals.-- Wayne Brown (HPCC #1104) | When your tails in a crack, you improvisefwbrown@bellsouth.net | if youre good enough. Otherwise you give | your pelt to the trapper.e^(i*pi) = -1 -- Euler | -- John Myers Myers, Silverlock > Now what if some person says they found a brilliant gem, should they> go through college courses, and learn a lot of techniques in the> analysis of gems?>Or cant they just holler out that they found something?Bad analogy.Someone says theyve found a gem. Lots of people look at it. Everyone who knows about gems says, Thats just a lump of coal.Would that mean that it really was just a lump of coal, or does it mean that the discoverer can carry on shouting that hes being ignored?-- Attention: Spam block in use! > Now what if some person says they found a brilliant gem, should they> go through college courses, and learn a lot of techniques in the> analysis of gems?>Or cant they just holler out that they found something?>Bad analogy.>Someone says theyve found a gem. Lots of people look at it. Everyone > who knows about gems says, Thats just a lump of coal.>Would that mean that it really was just a lump of coal, or does it mean > that the discoverer can carry on shouting that hes being ignored?Yeah, but here I can show the ?d:dS(x,y) = [p(x/y, y-1) - p(y-1, sqrt(y-1))][ p(y, sqrt(y)) - p(y-1,sqrt(y-1))],S(x,1) = 0, p(x, y) = ?) - S(x, y) - 1, and S(x,y) is the sum of dS from dS(x,2) to dS(x,y).Reference: http://mathforpro?.blogspot.com/Where p(x,sqrt(x)) is the count of primes, for instance, p(100,10) =25, which is the number of primes up to 100 or p(10,3) = 4, and thoseprimes are 2, 3, 5 and 7.So its more like someone ?ding a gem, and having experts claim itsglass, only to then have that person cut glass with it.I want critical thinkers to search on prime counting function andsee the methods that mathematicians have on record for counting primenumbers to compare with what I just gave and see for yourselves howobvious it is that what I have isnt just junk.Remember, mathematicians are ?hting to totally dismiss my result asunimportant to justify not putting it in math references.James HarrisMy math discoveries, found for pro?http://mathforpro?.blogspot.com/ > So its more like someone ?ding a gem, and having experts claim its> glass, only to then have that person cut glass with it.FWIW, glass cuts glass. So, good analogy. As can be seen by the number of posts in this thread,and the references to his web site in thousands of other posts,a computer programmer, who took some data processing classesat a third rate California college, has become a highly regarded expertin math, physics, and other science disciplines, andmany people, who pretend to be rational, intelligent, open-mindedscientists (Or at least, pretend to have a scienti? mind.),frequently use this programmer as a major reference.I assert that this indicates that science,is pretty much like show business and politics,and that the ideas that get elevated to high statusare those that are promoted best.I suggest that those folks,who feel passionate about their ideas, and want to promote them,should ?st set up a web site much like the highly regarded crank.net,and after they become recognized as a highly regarded expert,to slowly incorporate their ideas into the web site,and take sly shots at competing ideas.As it would be helpful to new readers to knowwho the sociopaths are in the newsgroups,another web site that would be popularwould be one that puts the internet ? in the spotlight,by posting some of their posts, and their backgrounds.--Tom Potter http://tompotter.us > As can be seen by the number of posts in this thread,> and the references to his web site in thousands of other posts,> a computer programmer, who took some data processing classes> at a third rate California college, has become a highly regarded expert> in math, physics, and other science disciplines, and> many people, who pretend to be rational, intelligent, open-minded> scientists (Or at least, pretend to have a scienti? mind.),> frequently use this programmer as a major reference.> What third rate California college? Who rated it? What criteria?>Hey Wormley,as you use this programmers web site as your primary rederence,it seems to me that you should know what college your resident expertattended.If you want to know how this college rates,I suggest that you learn how to use Google.Ill give you some hints.Caltech and Stanford and ?st rate California colleges.The college that Baez teaches at is a second rate college.Your expert took some data processing classes at a third rate college.> Most scientist are computer programmers... are you knocking us Potter?Wormley,why do you always try to identify yourself with some group?Does identifying yourself with a group make you feel more secure,or do you think [sic] that it lends strength to your position?Do you have the courage to express any independent ideas you have(Assuming that you have an independent idea.),or the knowledge to address the point of a dichotomy,rather than try to position an opponents pointagainst some group that you identify with?In other words Wormley,are you a man or a mouse?--Tom Potter http://tompotter.us instigates con?nd war for power and wealth?WHO instigated the class wars of the 1900s?WHO is instigating the religious wars of the 2000s?WHO has a well organized propaganda machine?WHO gang attacks all who expose their agenda and methods?Visit my web site, and download the worlds best physics tutorial! number of posts in this thread,> and the references to his web site in thousands of other posts,> a computer programmer, who took some data processing classes> at a third rate California college, has become a highly regarded expert> in math, physics, and other science disciplines, and> many people, who pretend to be rational, intelligent, open-minded> scientists (Or at least, pretend to have a scienti? mind.),> frequently use this programmer as a major reference.>>What third rate California college? Who rated it? What criteria?>Most scientist are computer programmers... are you knocking us Potter?professional.Are you arguing Sam Wormley that Francis has other credentials, likephysics credentials, beyond just being a computer programmer?James Harris > As can be seen by the number of posts in this thread,> and the references to his web site in thousands of other posts,> a computer programmer, who took some data processing classes> at a third rate California college, has become a highly regarded expert> in math, physics, and other science disciplines, and> many people, who pretend to be rational, intelligent, open-minded> scientists (Or at least, pretend to have a scienti? mind.),> frequently use this programmer as a major reference.>I assert that this indicates that science,> is pretty much like show business and politics,> and that the ideas that get elevated to high status> are those that are promoted best.>I suggest that those folks,> who feel passionate about their ideas, and want to promote them,> should ?st set up a web site much like the highly regarded crank.net,> and after they become recognized as a highly regarded expert,> to slowly incorporate their ideas into the web site,> and take sly shots at competing ideas. Well, thats really, since Inter-Web-Ware trash was invented in Switzerland its just a matter of time before it collapses just like Texass Statewide Accelerator sort of took the turn south to France. Or as the Inter-Sci UN Anthem is now composed: O Say Does That Redneck Banner Yet Wave, in the Land of the Early Aussies, and >As it would be helpful to new readers to know> who the sociopaths are in the newsgroups,> another web site that would be popular> would be one that puts the internet ? in the spotlight,> by posting some of their posts, and their backgrounds. > I understand your point of view, but I dont agree with it. Journal> and formalism. It forces you to review the literature in order to make> it clear how your work ?s into (and differs from) previous work.> have done and how it is new, and this, in turn, helps protect your> intellectual property. The Usenet news groups are OK for tossing ideas> around and getting some feedback, but they are not the best way to> ---- it takes a lot of time; you have to use conventional terminology> and formalism; you have to typeset equations; you have to learn a> particular journals convention for bibliographic references; you have> to respond to referee reports; etc. In spite of these drawbacks, there> are still good reasons for such a system. It has clear advantages over> posting to usenet or sending incomplete summaries to random faculty. I know in physics, there are sites where you can post un-refereed> papers (e.g. http://arxiv.org/) I see that this site also has an> archive for math. You could post a paper there. In the end, I> recommend that you produce a report which is more formal than a usenet> post and then put it on one of the archive sites, or turn it into aJames, this I think is the best advice you can take, if you are trulyinterested in learning math and having your ideas accepted if they are ofvalue. But, youve heard it before and ignored it, right? > I understand your point of view, but I dont agree with it. Journal> and formalism. It forces you to review the literature in order to make> it clear how your work ?s into (and differs from) previous work.> have done and how it is new, and this, in turn, helps protect your> intellectual property. The Usenet news groups are OK for tossing ideas> around and getting some feedback, but they are not the best way to> ---- it takes a lot of time; you have to use conventional terminology> and formalism; you have to typeset equations; you have to learn a> particular journals convention for bibliographic references; you have> to respond to referee reports; etc. In spite of these drawbacks, there> are still good reasons for such a system. It has clear advantages over> posting to usenet or sending incomplete summaries to random faculty.> I know in physics, there are sites where you can post un-refereed> papers (e.g. http://arxiv.org/) I see that this site also has an> archive for math. You could post a paper there. In the end, I> recommend that you produce a report which is more formal than a usenet> post and then put it on one of the archive sites, or turn it into a>James, this I think is the best advice you can take, if you are truly> interested in learning math and having your ideas accepted if they are of> value. But, youve heard it before and ignored it, right?No. I ?d your post strange, as you seem to be assuming that I amindeed some kind of crank, so I wonder what evidence you have.Can you tell me why you assume that Ive ignored good advice before?James Harris [snip suggestion to James]> No. I ?d your post strange, as you seem to be assuming that I am> indeed some kind of crank, so I wonder what evidence you have.Thats a *conclusion*, not an *assumption. Your posting record reveals your crankhood clearly, consistently and repeatedly.*You* have provided suf?ient evidence for an unambiguous conclusion that you are, indeed, a crank -- in particular, yourrepeated passionate defense of your own blatant errors, which constantly drives you to attack those who point them out toyou.> Can you tell me why you assume that Ive ignored good advice before?*Conlude*, James, conclude. Because you have a long track record of ignoring good advice -- especially about learning themathematics which is still over your head.> James HarrisJames, you are in such a serious and extreme (possibly terminal) state of denial over your own posting behavior that no one inthis newsgroup is likely to be of any help. You need professional assistance, and not just from some world-class psychiatristat Johns Hopkins or NIMH. You need a team of specialists, preferably from Vienna. Even then you wont get good odds from yourreaders that a recovery is likely. Possibly the best solution for you is an exorcist.--There are two things you must never attempt to prove: the unprovable -- and the obvious.--Democracy: The triumph of popularity over principle.--http://www.crbond.com >No. I ?d your post strange, as you seem to be assuming that I am> indeed some kind of crank, so I wonder what evidence you have.>Can you tell me why you assume that Ive ignored good advice before?>> James HarrisDo you still claim that youve found some hundred year old mistake inalgebra? Are you claiming to have taken all the comments made there intoaccount? Because they unequivocally showed you were mistaken. Yet you still decided to have it published in that unrefereed journal. Ithink that is ignoring good advice. You have stopped claiming FLT proofs it appears. However you assertedWiles was wrong. Indeed there were some errors in its original form, but they were tidied up. Im amazed, though, and would like to know where you learned enough modular form stuff to have read Wiless paper and understood it enough to have spotted them. There are many comments on your ?prime counting function. I cant believeyou ?d them all too far beneath you to comment on. I put the quotationmarks as an indicator that youve swapped from prime counting to compositecounting.The best advice youve received, practically, is to write more clearly.That you have repeatedly ignored. > I keep seeing people posting about how bad I am and questioning my> sanity, when everyone seems to be ignoring a simple fact--posters> verbally abuse me in threads I create, which has been going on for> YEARS. I dont know from crank but when great breakthroughs and advances are onlyposted on> usenet one has to draw some obvious conclusions.What conclusions do you draw? > Someone who wasnt already familiar with you might be taken in by mostof> the pack of lies you posted. But your last three sentences demonstrate> clearly why nothing you say deserves to be taken seriously.> (Has anyone else noticed that James tends to post his mostobscenity-laden> diatribes on Sunday afternoons? My theory is that Sunday is hisfavorite> drinking-day. I suggest he try church instead; it would be a much less> self-destructive use of his time.) I did not notice that, but let me guess as to the motivation.> Possibly JSH can chime in if he spots any errors in my reasoning. The few people remaining who can tolerate JSH in person have jobs to> Monday through Friday, those who are not sick of James are unable to> listen to his diatribes against the sci.math machine. He knows he> will be all alone for the upcoming week. He becomes disconsolate on> Sunday after fully realizing both this and the fact that he struck out> bigtime with the ladies on Friday and Saturday night. He may have noticed (or may not, it is JSH after all) that he holds> court for a smaller and smaller group of regulars -- some of them may> not reappear the next weekend. If he does notice, he will, of course,> attribute that to something other than his asinine personality.> Rather than reassess his [lack of] social standing or scour the want> ads for a job, James hits the bottle. Suf?iently looped, James lashes out at David Ullrich. :):):) David> and the rest (myself a willing specator/occasional participant in this> trainwreck) then have a weekly party at James expense. What amazes me is that anybody responds to the mathematics in his> posts. IMO, JSH deserves *only* the ridicule he gets, and none of the> help/corrections. Bye,> Jay of your responses to me earlier, I should have realized what the> quotes signify. So, with your instructions in mind, I retract calling> you a tool in favor of calling you a tool. I know you may disagree,> but to me you are a total loser. Keep up the good work. Idiot P.P.S. JSH, no hard feelings. Please let me state that this is a> psychological experiment I am performing on you. It is part of entertainment and experimentation as well. At least youveprogressed to psychological experiments on other people now your a grownup. > Someone who wasnt already familiar with you might be taken in by most> of> > the pack of lies you posted. But your last three sentences demonstrate> > clearly why nothing you say deserves to be taken seriously.> (Has anyone else noticed that James tends to post his most> obscenity-laden> > diatribes on Sunday afternoons? My theory is that Sunday is his> favorite> > drinking-day. I suggest he try church instead; it would be a much less> > self-destructive use of his time.)> I did not notice that, but let me guess as to the motivation.> Possibly JSH can chime in if he spots any errors in my reasoning.> The few people remaining who can tolerate JSH in person have jobs to> Monday through Friday, those who are not sick of James are unable to> listen to his diatribes against the sci.math machine. He knows he> will be all alone for the upcoming week. He becomes disconsolate on> Sunday after fully realizing both this and the fact that he struck out> bigtime with the ladies on Friday and Saturday night.> He may have noticed (or may not, it is JSH after all) that he holds> court for a smaller and smaller group of regulars -- some of them may> not reappear the next weekend. If he does notice, he will, of course,> attribute that to something other than his asinine personality.> Rather than reassess his [lack of] social standing or scour the want> ads for a job, James hits the bottle.> Suf?iently looped, James lashes out at David Ullrich. :):):) David> and the rest (myself a willing specator/occasional participant in this> trainwreck) then have a weekly party at James expense.> What amazes me is that anybody responds to the mathematics in his> posts. IMO, JSH deserves *only* the ridicule he gets, and none of the> help/corrections.> Bye,> Jay> of your responses to me earlier, I should have realized what the> quotes signify. So, with your instructions in mind, I retract calling> you a tool in favor of calling you a tool. I know you may disagree,> but to me you are a total loser. Keep up the good work. Idiot> P.P.S. JSH, no hard feelings. Please let me state that this is a> psychological experiment I am performing on marketing class.>kid for entertainment and experimentation as well. At least youve> progressed to psychological experiments on other people now your a grown> up.You are kidding, right? Jim was correct in my intentions.James self-diagnosed narcisstic personality disorder.James has repeatedly stated that he is testing the group, orperforming an experiment on it (sociological or psychological, orwhatever he thinks at the moment).James took pride in the crank label, and now he wants everubody torevisit it in numerous curent posts. He disowns that pride now anddismisses it because he used quotes around the term. Hence, I did thesame, albeit with some sarcasm.James has repeatedly requested that others refrain from posting tohis threads, as if he owned them. David Ullrich, in particular,receives this request.James posted one un?ished short story and posted to alt.writing,requesting help. Immediately, *he* starting attacking the critics,who were there for the sole purpose to critique his writing style. Immediately, he came across as the arrogant expert (in his own mind). One un?ished story and he alienated many within days.James read *one* marketing book. If it were a textbook, I amreasonably sure he didnt *read* the whole book. Rather, he justskimmed a bit. In any case, it called for a few posts from theforemost marketer of all time.James saw (or read)A Beautiful Mind and next thing you know,similarities to John Nash appear in a JSH post. JSH then becomes theformost expert games, much like his own version of mathematics, and demanded thatothers heed his every word. He couldnt get the terms and de?itionsright, though (again, like his mathematics).think???) had an impromptu contest to test some prime counters. JSHwas nowhere near the fastest, yet still he posts on its worth as ifnothing else has ever been so brilliant.Usenet is too small for James as well. He has contacted some topmathematicians, and when they cannot be bothered with him, he insultsand heaps scorn on them. As if they owe him something.Incredible arrogance coupled with a total unwillingness to learn or totake *any* form of criticism. Instead, JSH starts the attacks andbrings on the deserved replies.James is not innocent in this at all. You say it is obvious that hehas some mental problems. James has claimed that there is mentalillness in his family, I think. But, why should anyone believe him? many topics is nil, so why believe him when he speaks of his mentalhealth problems? Possibly that is a self-serving statement. Ifanother stated that s/he has mental health problems, I would supporthim/her 100%. I just dont believe James.I neither know nor care how his mind works, but I see two primary waysto ignore the trolls: ignore them or insult them. Most of the time Ichoose to ignore. On this occasion, I just wanted to illustrate theJSH hypocrisy.James is a crank because he produces oodles of erroneous math and doesnot correct any mistakes when they are repeatedly shown to him. Hecontinues to wail about the injustice and the conspiracies againsthim.James is clearly a troll, too. He baits others and then does it somemore when they respond. Again, I am amazed at the help that hismathematics receives. He doesnt deserve any help. Yet, in directrefutation of his claims that mathematicians are out to get him, hedoes receive help on the occasional post that contains mathematics. It *should* indicate that the math community -- David Ullrich is thespokesperson :):) -- is not out to get him, but it doesnt register.Does his behavior on usenet, sci.math in particular, justify theinsults he receives? I say yes.Who knows what he does outside of usenet? Who cares? That part of mypost was just some ribbing using some of his previous claims (usingmath to score with women was one of my JSH favorites). I only see hisusenet personality and respond as I see ?. For all anybody knows,James could be a nice guy. I think he is a tool.Jay > > > > Someone who wasnt already familiar with you might be taken in bymost> of> > the pack of lies you posted. But your last three sentencesdemonstrate> > clearly why nothing you say deserves to be taken seriously.> > > (Has anyone else noticed that James tends to post his most> obscenity-laden> > diatribes on Sunday afternoons? My theory is that Sunday is his> favorite> > drinking-day. I suggest he try church instead; it would be a muchless> > self-destructive use of his time.)> I did not notice that, but let me guess as to the motivation.> > Possibly JSH can chime in if he spots any errors in my reasoning.> The few people remaining who can tolerate JSH in person have jobs to> > Monday through Friday, those who are not sick of James are unable to> > listen to his diatribes against the sci.math machine. He knows he> > will be all alone for the upcoming week. He becomes disconsolate on> > Sunday after fully realizing both this and the fact that he struck out> > bigtime with the ladies on Friday and Saturday night.> He may have noticed (or may not, it is JSH after all) that he holds> > court for a smaller and smaller group of regulars -- some of them may> > not reappear the next weekend. If he does notice, he will, of course,> > attribute that to something other than his asinine personality.> > Rather than reassess his [lack of] social standing or scour the want> > ads for a job, James hits the bottle.> Suf?iently looped, James lashes out at David Ullrich. :):):) David> > and the rest (myself a willing specator/occasional participant in this> > trainwreck) then have a weekly party at James expense.> What amazes me is that anybody responds to the mathematics in his> > posts. IMO, JSH deserves *only* the ridicule he gets, and none of the> > help/corrections.> Bye, Jay> of your responses to me earlier, I should have realized what the> > quotes signify. So, with your instructions in mind, I retract calling> > you a tool in favor of calling you a tool. I know you may disagree,> > but to me you are a total loser. Keep up the good work. Idiot> P.P.S. JSH, no hard feelings. Please let me state that this is a> > psychological experiment I am performing on you. It is part of for entertainment and experimentation as well. At least youve> progressed to psychological experiments on other people now your agrown> up.> You are kidding, right? Jim was correct in my intentions. James self-diagnosed narcisstic personality disorder. James has repeatedly stated that he is testing the group, or> performing an experiment on it (sociological or psychological, or> whatever he thinks at the moment). James took pride in the crank label, and now he wants everubody to> revisit it in numerous curent posts. He disowns that pride now and> dismisses it because he used quotes around the term. Hence, I did the> same, albeit with some sarcasm. James has repeatedly requested that others refrain from posting to> his threads, as if he owned them. David Ullrich, in particular,> receives this request. James posted one un?ished short story and posted to alt.writing,> requesting help. Immediately, *he* starting attacking the critics,> who were there for the sole purpose to critique his writing style.> Immediately, he came across as the arrogant expert (in his own mind).> One un?ished story and he alienated many within days. James read *one* marketing book. If it were a textbook, I am> reasonably sure he didnt *read* the whole book. Rather, he just> skimmed a bit. In any case, it called for a few posts from the> foremost marketer of all time. James saw (or read)A Beautiful Mind and next thing you know,> similarities to John Nash appear in a JSH post. JSH then version of the theory> of games, much like his own version of mathematics, and demanded that> others heed his every word. He couldnt get the terms and de?itions> right, though (again, like his mathematics). think???) had an impromptu contest to test some prime counters. JSH> was nowhere near the fastest, yet still he posts on its worth as if> nothing else has ever been so brilliant. Usenet is too small for James as well. He has contacted some top> mathematicians, and when they cannot be bothered with him, he insults> and heaps scorn on them. As if they owe him something. Incredible arrogance coupled with a total unwillingness to learn or to> take *any* form of criticism. Instead, JSH starts the attacks and> brings on the deserved replies. James is not innocent in this at all. You say it is obvious that he> has some mental problems. James has claimed that there is mental> illness in his family, I think. But, why should anyone believe him?> many topics is nil, so why believe him when he speaks of his mental> health problems? Possibly that is a self-serving statement. If> another stated that s/he has mental health problems, I would support> him/her 100%. I just dont believe James. I neither know nor care how his mind works, but I see two primary ways> to ignore the trolls: ignore them or insult them. Most of the time I> choose to ignore. On this occasion, I just wanted to illustrate the> JSH hypocrisy. James is a crank because he produces oodles of erroneous math and does> not correct any mistakes when they are repeatedly shown to him. He> continues to wail about the injustice and the conspiracies against> him. James is clearly a troll, too. He baits others and then does it some> more when they respond. Again, I am amazed at the help that his> mathematics receives. He doesnt deserve any help. Yet, in direct> refutation of his claims that mathematicians are out to get him, he> does receive help on the occasional post that contains mathematics.> It *should* indicate that the math community -- David Ullrich is the> spokesperson :):) -- is not out to get him, but it doesnt register. Does his behavior on usenet, sci.math in particular, justify the> insults he receives? I say yes. Who knows what he does outside of usenet? Who cares? That part of my> post was just some ribbing using some of his previous claims (using> math to score with women was one of my JSH favorites). I only see his> usenet personality and respond as I see ?. For all anybody knows,> James could be a nice guy. I think he is a tool. JayI know someone who acts like him who has a hyper- mania diagnoses, which isa form of psychoses. But, , not this extreme and in public. Ive mixedwith people with diagnoses quite a bit over the years, I try to humour themor ignore them if they are similar to James. But, yes they can bug you ifyou let them, and then you ?d yourself biting back. But, these areobviously just impressions, who the hell could possibly know what is goingon in his mind or his motivations. I wonder if he has any insight into hisbehaviour, I doubt it.But, my earlier impressions were that I thought some people might be usinghim purely as a source of comic relief which I think re?badly on them,but judging from your post you are not one of them. But, yes, Im ?ding ita bit comical as well, likely some others here are as well, even though Iveseen this behaviour a lot in the past in some people I know.See a shrink would not react to his behaviour they would keep an objectivedistance and just classify his symptoms. Ive got mixed feelings as I have amental health diagnoses, on the one hand I feel some empathy for him, on theother I ?d him comical.But, I know how people like James can bug you and be very grating if you areover exposed to them or they ?ate on you and give you a hard time. > > > > Someone who wasnt already familiar with you might be taken in by most> of> > the pack of lies you posted. But your last three sentences demonstrate> > clearly why nothing you say deserves to be taken seriously.> > > (Has anyone else noticed that James tends to post his most> obscenity-laden> > diatribes on Sunday afternoons? My theory is that Sunday is his> favorite> > drinking-day. I suggest he try church instead; it would be a much less> > self-destructive use of his time.)> I did not notice that, but let me guess as to the motivation.> > Possibly JSH can chime in if he spots any errors in my reasoning.> The few people remaining who can tolerate JSH in person have jobs to> > Monday through Friday, those who are not sick of James are unable to> > listen to his diatribes against the sci.math machine. He knows he> > will be all alone for the upcoming week. He becomes disconsolate on> > Sunday after fully realizing both this and the fact that he struck out> > bigtime with the ladies on Friday and Saturday night.> He may have noticed (or may not, it is JSH after all) that he holds> > court for a smaller and smaller group of regulars -- some of them may> > not reappear the next weekend. If he does notice, he will, of course,> > attribute that to something other than his asinine personality.> > Rather than reassess his [lack of] social standing or scour the want> > ads for a job, James hits the bottle.> Suf?iently looped, James lashes out at David Ullrich. :):):) David> > and the rest (myself a willing specator/occasional participant in this> > trainwreck) then have a weekly party at James expense.> What amazes me is that anybody responds to the mathematics in his> > posts. IMO, JSH deserves *only* the ridicule he gets, and none of the> > help/corrections.> Bye, Jay> of your responses to me earlier, I should have realized what the> > quotes signify. So, with your instructions in mind, I retract calling> > you a tool in favor of calling you a tool. I know you may disagree,> > but to me you are a total loser. Keep up the good work. Idiot> P.P.S. JSH, no hard feelings. Please let me state that this is a> > psychological experiment I am performing on you. It is part of entertainment and experimentation as well. At least youve> progressed to psychological experiments on other people now your a grown> up.>> You are kidding, right? Jim was correct in my intentions.>James self-diagnosed narcisstic personality disorder.Well I did think that I had the disorder in the past. > James has repeatedly stated that he is testing the group, or> performing an experiment on it (sociological or psychological, or> whatever he thinks at the moment).Im testing mathematicians real love of mathematics, especially puremath since they often claim that they value mathematics for its ownsake, and further make claims about beauty in mathematics.Given the extremely hostile reaction, where insults are seen as aproper form of communication, that Ive seen from mathematicians andpeople I call math groupies, it makes sense to see how far outsidemainstream social norms they lie.After all, mathematics is a VERY important subject, and I think itimportant if *modern* mathematicians have gone off the path of properintellectual endeavor.My guess is that they have too much power today, and have learned thatmodern society doesnt know what theyre really doing and is afraid tochallenge them to prove their worth.>James took pride in the crank label, and now he wants everubody to> revisit it in numerous curent posts. He disowns that pride now and> dismisses it because he used quotes around the term. Hence, I did the> same, albeit with some sarcasm.I dont take pride in a negative and insulting label.I do take pride in challenging people in the tradition of Socrates.Remember him?He was considered a gad?his time as he asked questions.I ask questions.>James has repeatedly requested that others refrain from posting to> his threads, as if he owned them. David Ullrich, in particular,> receives this request.David Ullrich is a special case as anyone who bothers to do a David Ullrich in the author ?ld and racial slur in theexact phrase ?ld, will ?d out.Being someone who repeatedly engages in negative attacks against me,who was called on his bad behavior, David Ullrich appeals to the crowdas a victim.Granted, some might think I do the same, but he comes to me. That is,David Ullrich makes sure to come to my threads and reply to my posts,and then whines when I tell him to go away.Hes a tag-along that just wont go away when hes told that hes notwanted.Im sure those of you who are successful in some way have had to dealwith such people.>James posted one un?ished short story and posted to alt.writing,> requesting help. Immediately, *he* starting attacking the critics,> who were there for the sole purpose to critique his writing style. > Immediately, he came across as the arrogant expert (in his own mind). > One un?ished story and he alienated many within days.Well thats one point of view on the subject.Short stories are subjective to a large extent.I posted a draft and had critiques. I didnt like some things about apost by *one* of the critiquers, expressed that opinion, and faced alot of criticism on the group alt.?tion.original as a result.It seems to me that Jay Petrulis has spent some effort in his post topaint a picture, and I want readers to ask themselves, why.Math society in pushing insults and personal attacks as legitimatebehavior reveals its own true values.Those of you who might have considered mathematicians better than youin some way, need only look in my threads and see the reality.The Socratic Method is a trying one, and many of you might not beaware of it in this modern world. I suggest you look it up, andremember what happened to Socrates.Being a true intellectual is a lot about learning to think for*yourself* without being dependent on people telling you what is true.My hope is that I might have in some small way helped some of youunderstand that being an adult is a continual process.It doesnt get any easier from here.James HarrisMy math discoveries, found for pro?http://mathforpro?.blogspot.com/ >Im testing mathematicians real love of mathematics, especially pure>math since they often claim that they value mathematics for its own>sake, and further make claims about beauty in mathematics.Maybe their idea of beauty does not coincide with yours. And maybetheir idea as to what is a useful contribution to mathematics doesnot correspond to yours.>Given the extremely hostile reaction, where insults are seen as a>proper form of communication, that Ive seen from mathematicians and>people I call math groupies, it makes sense to see how far outside>mainstream social norms they lie.Try talk.origins if you want to see the sparks ? comparison,sci.math is tame. And there are groups far worse thattalk.origins. narcisstic personality disorder. Well I did think that I had the disorder in the past. > James has repeatedly stated that he is testing the group, or> performing an experiment on it (sociological or psychological, or> whatever he thinks at the moment). Im testing mathematicians real love of mathematics, especially pure> math since they often claim that they value mathematics for its own> sake, and further make claims about beauty in mathematics. Given the extremely hostile reaction, where insults are seen as a> proper form of communication, that Ive seen from mathematicians and> people I call math groupies, it makes sense to see how far outside> mainstream social norms they lie. After all, mathematics is a VERY important subject, and I think it> important if *modern* mathematicians have gone off the path of proper> intellectual endeavor. My guess is that they have too much power today, and have learned that> modern society doesnt know what theyre really doing and is afraid to> challenge them to prove their worth. > James took pride in the crank label, and now he wants everubody to> revisit it in numerous curent posts. He disowns that pride now and> dismisses it because he used quotes around the term. Hence, I did the> same, albeit with some sarcasm. I dont take pride in a negative and insulting label. I do take pride in challenging people in the tradition of Socrates. Remember him? He was considered a gad?his time as he asked questions. I ask questions. > James has repeatedly requested that others refrain from posting to> his threads, as if he owned them. David Ullrich, in particular,> receives this request. David Ullrich is a special case as anyone who bothers to do a with David Ullrich in the author ?ld and racial slur in the> exact phrase ?ld, will ?d out. Being someone who repeatedly engages in negative attacks against me,> who was called on his bad behavior, David Ullrich appeals to the crowd> as a victim. Granted, some might think I do the same, but he comes to me. That is,> David Ullrich makes sure to come to my threads and reply to my posts,> and then whines when I tell him to go away. Hes a tag-along that just wont go away when hes told that hes not> wanted. Im sure those of you who are successful in some way have had to deal> with such people. > James posted one un?ished short story and posted to alt.writing,> requesting help. Immediately, *he* starting attacking the critics,> who were there for the sole purpose to critique his writing style.> Immediately, he came across as the arrogant expert (in his own mind).> One un?ished story and he alienated many within days. Well thats one point of view on the subject. Short stories are subjective to a large extent. I posted a draft and had critiques. I didnt like some things about a> post by *one* of the critiquers, expressed that opinion, and faced a> lot of criticism on the group alt.?tion.original as a result. It seems to me that Jay Petrulis has spent some effort in his post to> paint a picture, and I want readers to ask themselves, why. Math society in pushing insults and personal attacks as legitimate> behavior reveals its own true values. Those of you who might have considered mathematicians better than you> in some way, need only look in my threads and see the reality. The Socratic Method is a trying one, and many of you might not be> aware of it in this modern world. I suggest you look it up, and> remember what happened to Socrates. Being a true intellectual is a lot about learning to think for> *yourself* without being dependent on people telling you what is true. My hope is that I might have in some small way helped some of you> understand that being an adult is a continual process. It doesnt get any easier from here.James, as one sufferer to another possible sufferer. I think you should getsome help for the mental state you seem to be in.Also, you seem to know a lot more maths than most people, but judging by thethreads you are no expert. Why dont you get some help, get yourselfthinking straighter, then you might be able to learn a lot more about maths,and even do some interesting work for people to appreciate? After all, mathematics is a VERY important subject, and I think it> important if *modern* mathematicians have gone off the path of proper> intellectual endeavor. My guess is that they have too much power today, and have learned that> modern society doesnt know what theyre really doing and is afraid to> challenge them to prove their worth.Bad guess. The correct answer is that you are an idiot.--There are two things you must never attempt to prove: the unprovable -- and the obvious.--Democracy: The triumph of popularity over principle.--http://www.crbond.com >I neither know nor care how his mind works, but I see two primary ways>to ignore the trolls: ignore them or insult them. Most of the time I>choose to ignore. On this occasion, I just wanted to illustrate the>JSH hypocrisy.If everyone would ignore him, he *might* go away after a coupleweeks or months. Insulting him only inspires him.>James is a crank because he produces oodles of erroneous math and does>not correct any mistakes when they are repeatedly shown to him. He>continues to wail about the injustice and the conspiracies against>him.Yes, he is clearly a crank for these reasons.>James is clearly a troll, too. He baits others and then does it some>more when they respond. Again, I am amazed at the help that his>mathematics receives. He doesnt deserve any help. Yet, in direct>refutation of his claims that mathematicians are out to get him, he>does receive help on the occasional post that contains mathematics. >It *should* indicate that the math community -- David Ullrich is the>spokesperson :):) -- is not out to get him, but it doesnt register.Yes, he is a superb troll.Now can we just ignore him? Please? DO NOT FEED TROLLS!--Dan Grubb > [...]> P.P.S. JSH, no hard feelings. Please let me state that this > is a psychological experiment I am performing on you. It is > part were a kid for entertainment and experimentation as well. At > least youve progressed to psychological experiments on other > people now your a ?grown up.Pat -- Im pretty sure Jays PPS was an intentionally lamejusti?ation for the rest his post, because it is very muchin the mold of the (intentionally?) lame excuses that Jamesuses for his own similar or worse insults. Putting it in thoseterms _should_ remind James of his own posting history andmake it harder for him to point the Finger of Shame from someremains to be seen.The reference to marketing , at least, is very fresh, from only Jim Burns [...]> > P.P.S. JSH, no hard feelings. Please let me state that this> > is a psychological experiment I am performing on marketing class.> you were a kid for entertainment and experimentation as well. At> least youve progressed to psychological experiments on other> people now your a ?grown up. Pat -- Im pretty sure Jays PPS was an intentionally lame> justi?ation for the rest his post, because it is very much> in the mold of the (intentionally?) lame excuses that James> uses for his own similar or worse insults. Putting it in those> terms _should_ remind James of his own posting history and> make it harder for him to point the Finger of Shame from some> remains to be seen. The reference to marketing , at least, is very fresh, from only Jim BurnsI see. Well, I think, concerning some of the people here, an element of whatfollowing this over the last few days, I see in his behaviour, judging by myimpression of his posts, what I see directly in someone whom I know verywell that has a mental health diagnoses. I think people should just ignorehim they are feeding his obsession by replying. I dont see the point in theendless repetition. It is no joke what he could be going through. As can be seen by the number of posts in this thread,and the references to his web site in thousands of other posts,a computer programmer, who took some data processing classesat a third rate California college, has become a highly regarded expertin math, physics, and other science disciplines, andmany people, who pretend to be rational, intelligent, open-mindedscientists (Or at least, pretend to have a scienti? mind.),frequently use this programmer as a major reference.I assert that this indicates that science,is pretty much like show business and politics,and that the ideas that get elevated to high statusare those that are promoted best.I suggest that those folks,who feel passionate about their ideas, and want to promote them,should ?st set up a web site much like the highly regarded crank.net,and after they become recognized as a highly regarded expert,to slowly incorporate their ideas into the web site,and take sly shots at competing ideas.As it would be helpful to new readers to knowwho the sociopaths are in the newsgroups,another web site that would be popularwould be one that puts the internet ? in the spotlight,by posting some of their posts, and their backgrounds.--Tom Potter http://tompotter.us > As can be seen by the number of posts in this thread,> and the references to his web site in thousands of other posts,> a computer programmer, who took some data processing classes> at a third rate California college, has become a highly regarded expert> in math, physics, and other science disciplines, and> many people, who pretend to be rational, intelligent, open-minded> scientists (Or at least, pretend to have a scienti? mind.),> frequently use this programmer as a major reference. What third rate California college? Who rated it? What criteria?Hey Wormley,as you use this programmers web site as your primary rederence,it seems to me that you should know what college your resident expertattended.If you want to know how this college rates,I suggest that you learn how to use Google.Ill give you some hints.Caltech and Stanford and ?st rate California colleges.The college that Baez teaches at is a second rate college.Your expert took some data processing classes at a third rate college.> Most scientist are computer programmers... are you knocking us Potter?Wormley,why do you always try to identify yourself with some group?Does identifying yourself with a group make you feel more secure,or do you think [sic] that it lends strength to your position?Do you have the courage to express any independent ideas you have(Assuming that you have an independent idea.),or the knowledge to address the point of a dichotomy,rather than try to position an opponents pointagainst some group that you identify with?In other words Wormley,are you a man or a mouse?--Tom Potter http://tompotter.us instigates con?nd war for power and wealth?WHO instigated the class wars of the 1900s?WHO is instigating the religious wars of the 2000s?WHO has a well organized propaganda machine?WHO gang attacks all who expose their agenda and methods?Visit my web site, and download the worlds best physics tutorial! number of posts in this thread,>> and the references to his web site in thousands of other posts,>> a computer programmer, who took some data processing classes>> at a third rate California college, has become a highly regarded expert>> in math, physics, and other science disciplines, and>> many people, who pretend to be rational, intelligent, open-minded>> scientists (Or at least, pretend to have a scienti? mind.),>> frequently use this programmer as a major reference.>> What third rate California college? Who rated it? What criteria?Hey Wormley,>as you use this programmers web site as your primary rederence,>it seems to me that you should know what college your resident expert>attended.If you want to know how this college rates,>I suggest that you learn how to use Google.I suggest you learn how to use Usenet.Jim > As can be seen by the number of posts in this thread,> and the references to his web site in thousands of other posts,> a computer programmer, who took some data processing classes> at a third rate California college, has become a highly regarded expert> in math, physics, and other science disciplines, and> many people, who pretend to be rational, intelligent, open-minded> scientists (Or at least, pretend to have a scienti? mind.),> frequently use this programmer as a major reference. What third rate California college? Who rated it? What criteria?Hey Wormley,as you use this programmers web site as your primary rederence,it seems to me that you should know what college your resident expertattended.If you want to know how this college rates,I suggest that you learn how to use Google.Ill give you some hints.Caltech and Stanford and ?st rate California colleges.The college that Baez teaches at is a second rate college.Your expert took some data processing classes at a third rate college.> Most scientist are computer programmers... are you knocking us Potter?Wormley,why do you always try to identify yourself with some group?Does identifying yourself with a group make you feel more secure,or do you think [sic] that it lends strength to your position?Do you have the courage to express any independent ideas you have(Assuming that you have an independent idea.),or the knowledge to address the point of a dichotomy,rather than try to position an opponents pointagainst some group that you identify with?In other words Wormley,are you a man or a mouse?--Tom Potter http://tompotter.us instigates con?nd war for power and wealth?WHO instigated the class wars of the 1900s?WHO is instigating the religious wars of the 2000s?WHO has a well organized propaganda machine?WHO gang attacks all who expose their agenda and methods?Visit my web site, and download the worlds best physics tutorial! sorry but I didnt know where else to post it. Iam trying to convert between Octal, Hex, and Decimal and got a question. Ifor octal to break the number into 3 digit groups like so 100011010001becomes 100 011 010 001 and then ?d the octal represenation for hex itsays to break it into 4 digit groups. If the number is not a multiple itsays to leave the last set a one, two, or three digit binary number like so01001011 becomes 010 010 11. This makes sense to me and comes out to 223number is not a multiple of 3 or 4 you add a zero to left to make it so. 01001011 becomes 001001011 this is 113 in decimal and hex. Which way iscorrect? The ?st makes more sense to me but the ?st site is aMicrosoft programming resource center and the second is a math professors-Matty- > This may be OT if so I am sorry but I didnt know where else to post it. I> am trying to convert between Octal, Hex, and Decimal and got a question. I> for octal to break the number into 3 digit groups like so 100011010001> becomes 100 011 010 001 and then ?d the octal represenation for hex it> says to break it into 4 digit groups. If the number is not a multiple it> says to leave the last set a one, two, or three digit binary number like so> 01001011 becomes 010 010 11. I think you misinterpreted how to group. You always group from right to left(from least signi?ant to most signi?ant). The proper grouping of 01001011 is01 001 011> This makes sense to me and comes out to 223> number is not a multiple of 3 or 4 you add a zero to left to make it so. > 01001011 becomes 001001011 this is 113 in decimal and hex. 113 in octal. It would be 75 in decimal and 4B in hex.> Which way is correct? The two ways are equivalent. Adding a 0 to the left to make a 9-digit numbermakes the grouping001 001 011which is still 113 in octal.> The ?st makes more sense to me but the ?st site is a> Microsoft programming resource center and the second is a math professors>-Matty- > This may be OT if so I am sorry but I didnt know where else to post it. I> am trying to convert between Octal, Hex, and Decimal and got a question. I> for octal to break the number into 3 digit groups like so 100011010001> becomes 100 011 010 001 and then ?d the octal represenation for hex it> says to break it into 4 digit groups. If the number is not a multiple it> says to leave the last set a one, two, or three digit binary number like so> 01001011 becomes 010 010 11. This makes sense to me and comes out to 223> number is not a multiple of 3 or 4 you add a zero to left to make it so. > 01001011 becomes 001001011 this is 113 in decimal and hex. Which way is> correct? The ?st makes more sense to me but the ?st site is a> Microsoft programming resource center and the second is a math professors>-Matty- The second one is the correct one. 5 = 05 = 005 = 000...00005. Adding zeros to the left doesnt change the value of the number, whichever way you read it.Would be interesting to know which was the ?st site, though.And now, the long explanation. Binary notations is a shorthand like any other notation. It actually means multiplying by a power of the base, and adding the results.So 10110 = 1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 1 * 2^1 + 0 * 2^0 = 1 * 16 + 0 * 8 + 1 * 4 + 1 * 2 + 0 * 1 = 16 + 4 + 2 = 22Dividing the number into groups simply uses the fact that:x*2^(2+3n) + y*2^(1+3n) + z*2^(0+3n) = 2^3n * (x*2^2 + y*2^1 + z*2^0) = 8^n * (x*2^2 + y*2^1 + z*2^0).Since x*2^2 + y*2^1 + z*2^0 < 8 for any x,y,z binary digits, we can give each combination a name (000 = 0, 001 = 1, 010 = 2 ... 111 = 7), and get the octal notation.However, everything relies on the fact that we multiply by 2^3n, so we must divide the number into groups of three digits *from the right*, and not from the left. Thats why you should add zeros to the left, or simply divide from the right (i.e. 10110 = 10 110 = 26).Hope this helps. Supposed I have to intersect a nurbs representation of a cylinder witha given plane. How can the 2D parameter curve for the 3D intersectioncurve in the domain of the nurbs cylinder be calculated? Does someoneknow a good reference which describes something like that? Or cansomeone give an algorithm doing the calculation? Given a set S = { (1,2),(1,3),(1,4)...(k-1,k)}, is it possible topartition the above set into ?k subsets such that the elements of each subset are pairwise-disjoint? The elements of set S areunordered pairs so that (i,j) = (j,i) and the elements of a set arepairwise-disjoint if (i,j) and (m,n) belongs to S_i implies i != m, i!= n, j != m and j != n.For instance, if k = 5 -S = {(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)}. We can partition S into 5 disjoint sets as -S_1 = {(1,2),(3,5)}S_2 = {(1,3),(2,4)}S_3 = {(1,4),(2,5)}S_4 = {(1,5),(3,4)}S_5 = {(2,3),(4,5)}I am looking for any previous for your time and help. --Pradip >i am doing a report on aristotle>what did he contriute to math?Nothing.-- This address is for information only. I do not claim that these viewsare those of the Statistics Department or of Purdue University.Herman Rubin, Department of Statistics, Purdue University >i am doing a report on aristotle>what did he contriute to math?>Nothing.Thats not quite true, but its mostly true. He was probably the?st formal logician; he ?ured out how the Aristotelian Formswork.So if logic counts as a branch of mathematics, then he had somethingto do with it. He is responsible for such theorems as:[(x) Px & Qx] -> (x) Px & (x) QxThomasX-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Pose: george_cox@btinternet.comX-Punge: Micro$oft dhguy23@yahoo.com (Davis Howard) said:>The Lorentz group is the group of all linear transformations of the>variables x, y, z, and t which leave invariant the quadratic form s =>c^2t^2 - x^2 - y^2 - z^2.Youve got a con?ith what follows. If you want an explicitfactor c^2 here then it needs to appear in the metric tensor. Thatsone os the reasons that physicists often wok in natural units withx_0=ct, s = x_0^2 - x_1^2 - x_2^2 - x_3^2, or with the opposite signconvention.Note that in older literature you may also see x_0 = ict.-- Shmuel (Seymour J.) Metz, SysProg and JOATReply to domain Patriot dot net user shmuel+news to contact me. Donot reply to approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hB9DDpU05714; >
Im sorry to disturb anyone with such a
stupid question, but can someone write>>back showing how to
?d the percent difference between 9905.9 and 9390.9.>>The
way I went about ?ding this is ?stly ?ding the difference
between>>9905.9 and 9390.9 which is 515. Then I took the
average between the two>>values which is 9648.4. Then I solved
the following equation:>>% difference = 515 / 9648.4 * 100 %>>
= 5.33 %>>You may want to set the mathematics aside for a
moment and think>about the words and their meanings. percent =
abbreviation of per centum = per hundredNow take your sentence
?d the percent difference between 9905.9 and 9390.9and
replace percent by the equivalent per hundred: ?d the
per hundred difference between 9905.9 and 9390.9See what is
wrong? You are not specifying per hundred of WHAT.>The
sentence as it stands is neither grammatically correct
not>mathematically meaningful.You may reformulate your
question as follows: A quantity is incremented from 9390.9 to
9905.9. Compute > the change per hundred of the starting
value.You may replace the last three words by the ending
value, or by>the average of the starting and ending values,
or whatever suits>you.If you insist in using the word percent
rather than per hundred ,>you can say: A quantity is
incremented from 9390.9 to 9905.9. Compute > the percent
change measured with respect to the starting value.-- >Rouben
Rostamian Mr. Rostamian, you were not
at all helpful to the person who posed the question, only
critical. Youre ?ng your knowledge, and that is all.
You should set aside your semantics for someone who needs
them, when they are appropriate. 
> >>Im sorry to disturb
anyone with such a stupid question, but can someone
>>write>>back showing how to ?d the percent difference
between 9905.9 and 9390.9.There are, generally, two posssible
answers, depending on which number is considered the base
number, or divisor:The percent difference FROM 9905.9 TO
9390.9 assumes 9905.9 as base, and is calculated as
(100*(9390.9 - 9905.9)/9905.9) per cent.This is probably what
is expected in this case.The percent difference FROM 9390.9 TO
9905.9 assumes 9390.9 as base, and is calculated as
(100*(9905.9- 9390.9)/9905.9) per cent. Note that this result
is negative.There is not, unfortunately, any standard way of
calculating percent differences which is not dependent on
which number is chosen as base, although your averaging of the
numbers would be a reasonable candidate for such a
standard.
> >>
>Im sorry to disturb anyone with such a
stupid question, but can someone write>back showing how to
?d the percent difference between 9905.9 and 9390.9.>>The
way I went about ?ding this is ?stly ?ding the difference
between>9905.9 and 9390.9 which is 515. Then I took the
average between the two>values which is 9648.4. Then I
solved the following equation:>% difference = 515 / 9648.4
* 100 %> = 5.33 %>You may want to set the mathematics aside
for a moment and think>>about the words and their meanings.>>
percent = abbreviation of per centum = per hundred>>Now take
your sentence>> ?d the percent difference between 9905.9 and
9390.9>>and replace percent by the equivalent per
hundred:>> ?d the per hundred difference between 9905.9 and
9390.9>>See what is wrong? You are not specifying per hundred
of WHAT.>>The sentence as it stands is neither grammatically
correct not>>mathematically meaningful.>>You may reformulate
your question as follows:>> A quantity is incremented from
9390.9 to 9905.9. Compute >> the change per hundred of the
starting value.>>You may replace the last three words by the
ending value, or by>>the average of the starting and ending
values, or whatever suits>>you.>>If you insist in using the
word percent rather than per hundred ,>>you can say:>> A
quantity is incremented from 9390.9 to 9905.9. Compute >> the
percent change measured with respect to the starting
value.>>-- >>Rouben Rostamian 
Mr.
Rostamian, you were not at all helpful to the person who posed
the question, only critical. Youre ?ng your knowledge,
and that is all. You should set aside your semantics for
someone who needs them, when they are appropriate. > Mr.
jkljk,In this case semantic is everything. Taking a similar,
but exaggerated problem demonstrates it:Whats the percent
difference between 50 and 100?Its not grammatically correct,
and it doesnt have a mathematical meaning. If your salary
went up from $50 to $100, you got a 100% raise. If your salary
was reduced from $100 to $50, you took a 50% wage cut. If you
take the average (75), and divide the difference by the
average, you get the meaningless number 2/3 (0.6666666...),
which has no connection to the question.Semantic here is
everything - it gives meaning to the different
support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
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>> Can somebody point
me to a fast, sequential implementation>>of the ?mimimum
vertex cover problem in C/C++ ?>>Murthy
support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision: 1.9 primary) id hB9Eb8q11928;
>Does teaching
science in the classroom open doors towards the reading and
language arts subjects?If so, how?I feel that science is a
gateway to all subjects. There are many aspects to consider.
One can write lab reports, ?dings of a research report, and
approve@localhost) by support1.mathforum.org
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Im trying to solve the complex equation
z^(2i) + z^i + 1 = 0 for z.First I substitute y = z^i to
get:y^2 + y + 1 = 0>y = (1/2)(+/-Sqrt(3)i - 1)So we have:z^i =
(1/2)(+/-Sqrt(3)i - 1)>z^i = e^(i*(+/-2pi/3 + 2pi*n)) for all
integers n.>e^(i*ln(z)) = e^(i*(+/-2pi/3 + 2pi*n))At this
stage I get a bit confused. I think the right hand side
should>really be e^(i*(ln(z) + 2pi*m)) for all integers m,
however the>solutions I have do not do this. The solutions I
i*(+/-2pi/3 + 2pi*n)>ln(z) = +/-2pi/3 + 2pi*n>z = e^(+/-2pi/3
+ 2pi*n)> = e^(2pi(+/-(1/3) + n)However, I cant see how for
two complex numbers a and b, e^a = e^b><=> a = b is
necessarily true. What about the
following>counter-example:e^(i*2pi) = e^(i*4pi) <=> 2i*pi =
4i*piWhich is clearly incorrect. Surely this renders the above
solution to>the aforementioned equation incorrect? Have I
missed something?>Richard Hayden.You sure have missed
something, Richard.Your last statement is false, because
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>Does teaching science in the classroom open
doors towards the reading and language arts subjects?If so,
how?Science teaching can open doors. Writing is a must in our
world. Without writing there would be no reading. With no
reading there would be no science. You can easily tie in all
teaching areas into a science classroom.
How do you prove
the converse of this theorem?If a right triangle is inscribed
in a semicircle then the hypoteneuse is thediameter of the
circle
> How do you prove the converse of this theorem?>If
a right triangle is inscribed in a semicircle then the
hypoteneuse is the> diameter of the circlelooks like
homework, so as a start, draw a line from the centre of
thecircle to the apex of the triangle. should be
straightforward from there.
>How do you prove the converse
of this theorem?If a right triangle is inscribed in a
semicircle then the hypoteneuse is the>diameter of the
circle>Converse: (?) If a triangle is inscribed in a circle
with one side asa diameter, then the triangle is a right
triangle.Proof is almost trivial. Let A and B be the ends of
the diameter and Cthe third vertex, with corresponding angles
a, b, and c. Draw theradius to C, forming two isosceles
subtriangles. Then c = a + b and a+ b + c = 180 so 2c = 180
and c is a right angle.--Lynn
That is the theorem...but the
converse is:If a triangle is inscribed in a semicircle with the
angle opposite to thehypoteneuse as 90 then the hypoteneuse is
the diameter...How would you prove that ? I tried it many
times and I get stuck
Mr. Harris has lately been posting
asking why people consider him acrank. I think it comes from
his inability to recognize when he hasmade a mistake even when
it has been pointed out to he and explainedclearly. I think
this results in people getting angry and frustrated. If JSH
would express his gratitude to the mathematicians who
havedevoted considerable time and effort to ?ding his errors
maybe therewouldnt be so much acrimony.
>> I hope that
some of you are getting the picture now from my threads>>
asking questions about my own crank status, by considering
the>> replies in those threads.>> >> Your posts are
suf?ient.> Why?The way you have reacted to those critical
replies concerning themathematical part of your posts, and
your recently adopted habit ofstarting new threads every other
day in which you bemoan missingrecognition for your
achievements and cry over all those evilmathematicians out
there, does qualify you as a crank, if nothing else does.That
being said, I should point out, that I do not favour thosesilly
posts, where people are trying to abuse you.But what makes you
think, that these posters are especially after you?> >>[...]>>
But on Usenet, you have *vicious* posters who just go on and
on, like>> consider Uncle Al who has over 29,000 posts as he
knows that he>> cant be stopped.>> >> Hes sitting somewhere
at a keyboard, insulting people day and night,>> getting away
with what he cant in person.>> >> But this is hard work.>> By
insulting people day and night, he saves me from insulting
people,>> so I can try to keep the positive image of
myself.> Well you just screwed up there Marc Olschok.Not
really. I actually meant self-image. I can keep this, even
ifnobody else does.>In any event, fostering an insulting
environment doesnt help in the> long run.I am not fostering
it. But everytime I see some stupid personal insult,I am
reminded, how stupid the poster appears after a while, when
thedust settles down. This helps me, to avoid posting stupid
insults,that would make me appear stupid after a while.Of
course, I will once in a while appear as a fool for
completelydifferent reasons, but I can live with that.>For
instance, Marc Olschok I could call you an idiot, especially
given> your support of Uncle Al, and I could proceed to
track any posts you> make on sci.physics, and reply to them
insulting you continually, but> what good would it do?In the
long run, each of your posts would be regarded as
meaningless,even if you posted something worth reading. As I
pointed out,continuing abusive posting tends to damage the
reputation ofthe poster.But this is not quite the behaviour of
Uncle Al you described.He is not on a personal vendetta
against you. As you said,Hes sitting somewhere at a
keyboard, insulting people day and night.> What Im telling
other readers is YES that IS the kind of Usenet that> people
like Marc Olschok and Uncle Al want because theyre not>
civilized!Why do you ask, if you cannot wait for an answer?>
[...]> Now Im not talking about insults here and there as
things can get> heated even among adults.>But look at posters
like Marc Olschok and Uncle Al and consider how> many of you
would promote childish behavior, like repeated and> continual
insults meant to silence others.Well, if repeated and
continual insults really had a chance ofsilencing you, I might
become weak and start promoting it.But I do not have the time,
nor do I believe that it would work.Marc
You have a very
small penis.And you mother has a large back-side.And many
sailors enjoy the back-side of the corpse of your mother.Have
a nice day!> > I hope that some of you are getting the picture
now from my threads> > asking questions about my own crank
status, by considering the> > replies in those threads.> Your
posts are suf?ient.>Why? >[...]> > But on Usenet, you have
*vicious* posters who just go on and on, like> > consider
Uncle Al who has over 29,000 posts as he knows that he> >
cant be stopped.> Hes sitting somewhere at a keyboard,
insulting people day and night,> > getting away with what he
cant in person.> But this is hard work.> By insulting people
day and night, he saves me from insulting people,> so I can
try to keep the positive image of myself.>Well you just
screwed up there Marc Olschok. In any event, fostering an
insulting environment doesnt help in the> long run. For
instance, Marc Olschok I could call you an idiot, especially
given> your support of Uncle Al, and I could proceed to
track any posts you> make on sci.physics, and reply to them
insulting you continually, but> what good would it do? Well it
might drive you off of Usenet. Is that the kind of Usenet you
want? What Im telling other readers is YES that IS the kind
of Usenet that> people like Marc Olschok and Uncle Al want
because theyre not> civilized! Now then, many of you might
?d it tolerable because you think of> yourself as part of the
group, so its Us against Them. But what do you really know
of Marc Olschok or Uncle Al? Why would you assume theyre on
your side?> Perhaps he is also working on the terrestrial
version of the> universal insulting problem, described by
Douglas Adams.> In this case it would be almost serious
research.> Marc Now Im not talking about insults here and
there as things can get> heated even among adults. But look at
posters like Marc Olschok and Uncle Al and consider how> many
of you would promote childish behavior, like repeated and>
continual insults meant to silence others. Its just not
normal behavior.> James Harris
10:51:19 EST)>The quantum of
light is the photon>The quantum of sound is the sonon
[phonon?]A bull smell arises. > The quantums of
electricity are electron, proton, positron, and>
anti-protonAgrammatical idiot. > The quantums of heat would
then be the thermon [or pyron].> Right??? If not, what is
it?? It cannot be the photon or phonon for> reasons described
lying to you.-- Uncle Alhttp://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)Quis
custodiet ipsos custodes? The Net!
nice post James, good
general FAQ or introductory material about posting.Hercnow
will anyone look at MY claim?--www.StealthHostiing.com You
rule Truman. http://tinyurl.com/iky4 Hey Trueman...love the
show. YOU ARE the Truman I heard him. Very spooky! >Is the
truman living in Townsville? Ive been hearing stuff,
yeah.Webmasters help the TRUEman by joining www.theBanner.net
Current:1
Goal:1000----------------------------------------------------
------------------------------> I hope that some of you are
getting the picture now from my threads> asking questions
about my own crank status, by considering the> replies in
those threads. Clearly there are quite a few posters who
insult ?st, and it doesnt> much matter whats being
discussed, so what gives? Of course the answer is that by
insulting people you can sometimes> control them. How many of
you are readers terri?d of posting? Dont you think that
posters know that you are? If you ever get up the nerve to
step out and present your ideas, then> there are posters who
can sense it, and can control you. Basically you can be
stopped. Your dreams of being heard, of maybe adding to the
body of knowledge,> or just putting in a different point of
view can be crushed in an> instant--on a whim. Insulting is a
powerful technique. If you post, and are insulted,> then you
are affected, which can affect what you post next, and for>
many of you, stop you from *ever* posting again at all.
Insulting posters is a tried and true technique on Usenet.
Its been> there from the beginning and itll stay here until
someone ?ures out> a way to stop it. The reason its so
powerful is that in the regular world there are> many
protections from being insulted. And if someone does step
over> the line, there are many ways to knock them back. But on
Usenet, you have *vicious* posters who just go on and on, like>
consider Uncle Al who has over 29,000 posts as he knows that
he> cant be stopped. Hes sitting somewhere at a keyboard,
insulting people day and night,> getting away with what he
cant in person. Some of you may think that Im part of the
problem as yes, I *do* at> times insult people, but mostly I
challenge them. I present work from my research for others to
consider, and run into> the insult people over, and over and
over again. However, Im not interested in letting them win. I
dont care to> allow myself to be insulted into silence. Im
not afraid to give some> back when insulted. Remember, a lot
of it is about control. People like Uncle Al dont> have
29,000 posts because theyre not usually winning. Normally
that> poster can *silence* people. Think about it!!! All he
has to do is sit wherever he is at his keyboard, posting day>
and night as he does, and he can in his own small way control
part of> your world, as youre reading this so youre probably
on Usenet, by> controlling posters. He can silence them with
insults.> James Harris
> But James, by not insulting those
people back, you are sure to show others> that youre more
mature than the ones doing the insulting. Wouldnt that> help
in your favor?That presumes that maturity and intelligent new
ideas go hand in hand,and that immaturity precludes brilliant
new ideas. When openly statedas a proposition, would you be so
bold as to say that it iscategorically true? You may assume it
sub silentio, on moral grounds,as a precondition to whether
you will listen to a persons ideas, butis your presupposition
actually true? Would you care to defend such aproposition with
facts?Very Respectfully,Ray
 > But James, by not insulting
those people back, you are sure to showothers> that youre
more mature than the ones doing the insulting. Wouldnt that>
help in your favor? That presumes that maturity and intelligent
new ideas go hand in hand,> and that immaturity precludes
brilliant new ideas. When openly stated> as a proposition,
would you be so bold as to say that it is> categorically true?
You may assume it sub silentio, on moral grounds,> as a
precondition to whether you will listen to a persons ideas,
but> is your presupposition actually true? Would you care to
defend such a> proposition with facts? Very Respectfully,>
RayWhat I meant that when he gets insulted, just to blow it
off or to reply toit kindly without cussing them or any of his
usual antics.-- David MoranChief MeteorologistOklahoma Storm
Team
Snipped.....> --> There are two things you must never
attempt to prove: the unprovable -- and the obvious.I just
want to address this this above errorent line......Its wrong
on several levels......Noone can prove anything
individually... Best you cando is supply evidence ...
Something is proven onlywhen there is concensus that the
supplied evidence isvalid and the conclusions made are, by
concensus, agreed too.Also noone can know if something is
unprovable for allonly have a knowledge base of the moment and
new informationmay at some point be dirived that allows the
proofs requiredto prove by consessus the concept that was
unprovable beforethe new information was aquired.....And the
obvious is not always obvious and when the obviousseems
obvious to some, it may very well be illusion... Ifbeing
obvious were the rule then David Copper?ld wouldnot be
drawing very many crowds.....> --> Democracy: The triumph of
popularity over principle.> --> http://www.crbond.comPaul R.
Mays----------------------------------------------------------
-------------------Some where within the Quantum
StateHttp://Paul.Mays.Com/story.htmlhttp://paul.mays.com/
mayday.htmlhttp://paul.mays.com/rainy.htmlScience tries to
answer the question: ?How? How docells act in the body? How
do you design an airplanethat will ?ter than sound? How
is a molecule o?sulin constructed? Religion, by contrast,
tries toanswer the question: ?Why? Why was man created?Why
ought I to tell the truth? Why must there be sorrowor pain or
death? Science attempts to analyze howthings and people and
animals behave; it has no concernwhether this behavior is good
or bad, is purposeful ornot. But religion is precisely the
quest for suchanswers: whether an act is right or wrong, good
or bad,and why. - Warren Weaver (1894~1978)
>
Snipped.....> --> There are two things you must never attempt
to prove: the unprovable --> and the obvious. I just want to
address this this above errorent line...... Its wrong on
several levels...... Noone can prove anything individually...
Best you can> do is supply evidence ... Something is proven
only> when there is concensus that the supplied evidence is>
valid and the conclusions made are, by concensus, agreed too.
Also noone can know if something is unprovable for all> only
have a knowledge base of the moment and new information> may
at some point be dirived that allows the proofs required> to
prove by consessus the concept that was unprovable before> the
new information was aquired..... And the obvious is not always
obvious and when the obvious> seems obvious to some, it may
very well be illusion... If> being obvious were the rule then
David Copper?ld would> not be drawing very many
crowds.....Look before you leap is also wrong on many
levels. It doesnt apply to theblind or to paraplegics, it
doesnt tell you which way to look or how long todo so and
fails to provide details on the proper distance to leap. Both
thatexpression and my signature line are aphorisms. Get over
it.--There are two things you must never attempt to prove: the
unprovable -- and theobvious.--Democracy: The triumph of
popularity over principle.--http://www.crbond.com
... > Now
Im not talking about insults here and there as things can get
> heated even among adults. > > But look at posters like Marc
Olschok and Uncle Al and consider how > many of you would
promote childish behavior, like repeated and > continual
insults meant to silence others.Look at posters like James
Harris who insults people to let them stoppostings. Who even
contacts employers to get posters to stop posting.And only
because they provide factual counterproofs of his claims.You
have called Arturo Magidin a liar many times on the way. He
neverhas insulted you. Where has Arturo been lying? Please
provide an exactreference. But you succeeded in stopping him
to post in response toyour answers. So, are your insults
intended to silence others? Youare a hypocrite. (Yes, this is
my second insult to you. Count thenumber of insults to me
uttered by you, please.)-- dik t. winter, cwi, kruislaan 413,
1098 sj amsterdam, nederland, +31205924131home: bovenover
215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
[.snip.]>Look at posters like James Harris who insults people
to let them stop>postings. Who even contacts employers to get
posters to stop posting.>And only because they provide factual
counterproofs of his claims.>You have called Arturo Magidin a
liar many times on the way. He never>has insulted you. Thats
not accurate; I have, in the past, insulted James. --
accept as reality. --- Calvin (Calvin and
Hobbes)
can be seen by the number of posts in this thread,and the
references to his web site in thousands of other posts,a
computer programmer, who took some data processing classesat a
third rate California college, has become a highly regarded
expertin math, physics, and other science disciplines, andmany
people, who pretend to be rational, intelligent,
open-mindedscientists (Or at least, pretend to have a
scienti? mind.),frequently use this programmer as a major
reference.I assert that this indicates that science,is pretty
much like show business and politics,and that the ideas that
get elevated to high statusare those that are promoted best.I
suggest that those folks,who feel passionate about their
ideas, and want to promote them,should ?st set up a web site
much like the highly regarded crank.net,and after they become
recognized as a highly regarded expert,to slowly incorporate
their ideas into the web site,and take sly shots at competing
ideas.As it would be helpful to new readers to knowwho the
sociopaths are in the newsgroups,another web site that would
be popularwould be one that puts the internet ? in the
spotlight,by posting some of their posts, and their
backgrounds.--Tom Potter http://tompotter.us
> As can be
seen by the number of posts in this thread,> and the
references to his web site in thousands of other posts,> a
computer programmer, who took some data processing classes> at
a third rate California college, has become a highly regarded
expert> in math, physics, and other science disciplines, and>
many people, who pretend to be rational, intelligent,
open-minded> scientists (Or at least, pretend to have a
scienti? mind.),> frequently use this programmer as a major
reference.> What third rate California college? Who rated it?
What criteria?>Hey Wormley,as you use this programmers web
site as your primary rederence,it seems to me that you should
know what college your resident expertattended.If you want to
know how this college rates,I suggest that you learn how to
use Google.Ill give you some hints.Caltech and Stanford and
?st rate California colleges.The college that Baez teaches at
is a second rate college.Your expert took some data processing
classes at a third rate college.> Most scientist are computer
programmers... are you knocking us Potter?Wormley,why do you
always try to identify yourself with some group?Does
identifying yourself with a group make you feel more secure,or
do you think [sic] that it lends strength to your position?Do
you have the courage to express any independent ideas you
have(Assuming that you have an independent idea.),or the
knowledge to address the point of a dichotomy,rather than try
to position an opponents pointagainst some group that you
identify with?In other words Wormley,are you a man or a
mouse?--Tom Potter http://tompotter.us
instigates con?nd war for power and wealth?WHO instigated
the class wars of the 1900s?WHO is instigating the religious
wars of the 2000s?WHO has a well organized propaganda
machine?WHO gang attacks all who expose their agenda and
methods?Visit my web site, and download the worlds best
physics tutorial!
readers terri?d of posting?: Dont you think that posters
know that you are?: If you ever get up the nerve to step out
and present your ideas, then: there are posters who can sense
it, and can control you.: Basically you can be
stopped.Everything Ive ever posted here on sci.math has been
kindly received andcommented on by the most polite of people.
A cheerful exchange hasresulted and everyone walked away
satis?d.Justin
-------------------------------------------
--------------------------------------- : How many of you are
readers terri?d of posting?> : Dont you think that posters
know that you are?> : If you ever get up the nerve to step out
and present your ideas, then> : there are posters who can sense
it, and can control you.> : Basically you can be stopped.
Everything Ive ever posted here on sci.math has been kindly
received and> commented on by the most polite of people. A
cheerful exchange has> resulted and everyone walked away
satis?d.>thats because youre quoting text book problems in
here, try saying anythingagainst the grain and youll get
your head shot offHerc
No, thats not true.Justin: thats
because youre quoting text book problems in here, try
sayinganything : against the grain and youll get your head
shot off:
Herc
cite?-------------------------------------------------
---------------------------------> No, thats not true.
Justin : thats because youre quoting text book problems in
here, try saying> anything : against the grain and youll get
your head shot off : Herc>
Im currently reading Michael
Spivaks Calculus on Manifolds. Inthe very beginning of the
chapter called Integration on Chains he----- If V is a
vector space (over R), we will denote the k-fold product V x V
x ... x V by V^k. A function T : V^k --> R is called
multilinear if for each i with 1 <= i <= k we have:
T(v_1,...,v_i + v_i,...,v_k) = T(v_1,...,v_i,...,v_k) +
T(v_1,...,v_i,...,v_k) T(v_1,...,a * v_i,...,v_k) = a *
T(v_1,...,v_i,...,v_k) A multilinear function T : V^k --> R is
called a k-tensor on V and the set of all k-tensors, denoted
J^k(V), becomes a vector space (over R), if for S,T in J^k(V)
and a in R we de?e: (S+T)(v_1,...,v_k) = S(v_1,...,v_k) +
T(v_1,...,v_k) (aT)(v_1,...,v_k) = aT(v_1,...,v_k) There is
also an operation connecting the various spaces J^k(V). If S
is in J^k(V) and T in J^l(V), we de?e the tensor product S*T,
in J^k+l(V), as: (S*T)(v_1,...,v_k,v_k+1,...,v_k+l) =
S(v_1,...,v_k) T(v_k+1,...,v_k+l)-----Now my problem is that I
cannot reconcile this with my previous notionof tensors. I
dont know much about tensors, but I always thought oftensors
as a collection of n^k quantities that are indexed by kindices
that range from 1 to n. Also, these quantities have totransform
in a certain way.I thought a second-rank tensor was a matrix
and an (m x n)-matrix is alinear mapping from V^n --> V^m. I
cannot see, how a matrix is amultilinear function from V^k -->
R. (I dont even know what k shouldbe in this case.)So, Im
thoroughly confused.Boris-- boris@uncommon-sense.net -
No one can go back and make a
brand new start, my friend, but anyone canstart from here and
make a brand new end. -- Carl Bard
of tensors. I
dont know much about tensors, but I always thought of>tensors
as a collection of n^k quantities that are indexed by k>indices
that range from 1 to n. Also, these quantities have
to>transform in a certain way.>I thought a second-rank tensor
was a matrix and an (m x n)-matrix is a>linear mapping from
V^n --> V^m. I cannot see, how a matrix is a>multilinear
function from V^k --> R. (I dont even know what k should>be
in this case.OK, several points to clear up.1) A second rank
tensor wouldnt be a linear map of V^n to V^m.Remember that V
is the vector space here, so V=R^n. Because of this,a nxm
matrix is a linear map from R^m to R^n. These are two
differentvector spaces. If we keep the same V, we are only
talking about square matices. (BTW, I put the matrices on the
left of the vectors when I multiply.)2) The de?ition given
doesnt work for tensors with bothcovariant and contravariant
indices. Hence a matrix (which hasone of each) is not a tensor
of the type de?ed. More on this below.3) If we have V=R^n,
then a basis of V has n elements, so a vector inV has n
*components* in this basis. If we change to a different
basis,the components of the vector change in a certain way.
This is thetransformation law for vectors.4) A tensor T on V
of rank k will be a multi-linear map of V^k to R.If we have a
basis of V, the tensor will be determined by itsvalues at
basis elements. If V has dimension n, there will be
n^kpossible combinations of basis elements over the k ?slots
of T. This collection of n^k elements of R constitute the
*components* of the tensor T in that basis.5) If we change the
basis of V, the components of T will also change.The
transformation law describing this change is the one you
arefamiliar with. Essentially, your previous de?ition of
tensors focusedon the components in different bases, not on
the tensor itself.6) To de?e tensors with both covariant and
contravariant indices,we dont use a multi-linear map on just
V^k. We also have to considerthe dual vector space V*. Then a
tensor on V of type (k,l) will bea multi-linear map from V^k x
(V*)^l to R. It is important in this toremember that V** is
isomorphic to V. Thus, a tensor of type (1,0)is an element of
V* and one of type (0,1) can be considered to bean element of
V. Now the components of a tensor have k lower indicesand l
upper indices (if I got everything right, that is...vectors
havecomponents with upper indices).7) Now, a tensor of rank
(1,1) is a multi-linear map from VxV* into R. It turns out
that this is equivalent to being a linear map fromV to V, and
hence a square matrix.8) To consider nxm matrices, you have to
look at multi-linearmaps with different vector spaces, eg a
multi-linear map fromVxW* to R where V is m dimensional and W
is n dimensional.I hope this helps!--Dan Grubb
>Im
currently reading Michael Spivaks Calculus on Manifolds.
In> the very beginning of the chapter called Integration on
Chains he>-----> If V is a vector space (over R), we will
denote the k-fold product> V x V x ... x V by V^k. A function
T : V^k --> R is called> multilinear if for each i with 1 <=
i <= k we have:> T(v_1,...,v_i + v_i,...,v_k) =
T(v_1,...,v_i,...,v_k) +> T(v_1,...,v_i,...,v_k)> T(v_1,...,a
* v_i,...,v_k) = a * T(v_1,...,v_i,...,v_k)> A multilinear
function T : V^k --> R is called a k-tensor on V and> the set
of all k-tensors, denoted J^k(V), becomes a vector space>
(over R), if for S,T in J^k(V) and a in R we de?e:>
(S+T)(v_1,...,v_k) = S(v_1,...,v_k) + T(v_1,...,v_k)>
(aT)(v_1,...,v_k) = aT(v_1,...,v_k)> There is also an
operation connecting the various spaces J^k(V). If> S is in
J^k(V) and T in J^l(V), we de?e the tensor product S*T, in>
J^k+l(V), as:> (S*T)(v_1,...,v_k,v_k+1,...,v_k+l) =
S(v_1,...,v_k) T(v_k+1,...,v_k+l)> ----->Now my problem is
that I cannot reconcile this with my previous notion> of
tensors. I dont know much about tensors, but I always thought
of> tensors as a collection of n^k quantities that are indexed
by k> indices that range from 1 to n. Also, these quantities
have to> transform in a certain way.aaarggh! This is the
physicists way of thinking of tensors ---reduce everything to
a ?ed basis. Spivak is avoiding this by givinga basis-free
de?ition (I think this makes everything easier!).In physics
the space V is usually a tangent space on your
manifold(usually space-time) and what Spivak is de?ition is
knownas covariant tensors of rank k (or maybe contravariant
tensors ofrank k --- I cant remember which is which :-) ) in
physics jargon.If you are desperate to see your indices....
pick a basis v_1,... ,v_nof v and write T_{i_1 ... i_k} (or
should it be T^{i_1 ... i_k}?)for T(v_{i_1}, ..., v_{i_k}).
This gives your beloved n^k quantities.(Knowing them de?es T
by multilinearity ...).-- Robin Chapman,
www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the
last laugh. Alan Partridge, _Bouncing Back_ (14 times)
 :
: > NR invited people to think about the path category over
THE AFFINE : > plane. IF one thinks instead about a path
category over the 2d PROJECTIVE : > IN THAT plane (which they
ARE NOT in the plane that NR was talking about) : Points and
non-vertical lines are dual in the af?e plane.Thats
ridiculous. In the af?e plane, there is no such thingas
vertical. If you want to put a co-ordinate system on itand
do analytic geometry, ?e, but that duality comes from
theco-ordinate system and not from the underlying geometry. :
Anyway, my point had nothing to do with path categories
speci?ally : it was entirely about your refusal to accept the
general phenomenon that : different ways of looking at the
same mathematical objects can lead to : better insights about
those objects.All I can say to that, frankly, is that you are
starting to deserveinsults at the same level at which you are
dishing them out.I DO NOT refuse to accept the general
phenomenon thatdifferent ways of looking at the same
mathematical objects canlead to better insights about those
objects. But in anysituation where things are dual, they are
still DIFFERENT.They are NOT the same. In projective
geometry, pointsand lines are REALLY dual. In the af?e plane,
the merefact that you can create an isomorphism between 2
classesof things does NOT suf?e to make them dual. : Why do
you want to blinker us?I dont. The general thrust of this
thread is aboutrepresentation theorems, not blinkering.The
fact that you can reprsent any group via an isomorphismwith a
permutation group does not mean that you are being
blinkeredfrom seeing all the others. It just means that the
permutation groupsare in some sense closer to explaining the
core of the concept.You will in some sense have focused on
some important aspect ofa group if you bother to separate it
into the relevant permutationgroup and the isomorphism between
that and itself. You will notgain any insight into the nature
of a point by thinking about itas an in?ite collection of
lines, especially not if you aregoing to arbitrarily exclude
one of the lines.-- --- Its dif?ult ... you need to be
united to have any strength, but internal issues have to be
addressed. --- E. Ray Lewis, on liberalism in America
> :
Anyway, my point had nothing to do with path categories
speci?ally> : it was entirely about your refusal to accept
the general phenomenon that > : different ways of looking at
the same mathematical objects can lead to > : better insights
about those objects.>All I can say to that, frankly, is that
you are starting to deserve> insults at the same level at
which you are dishing them out.What insult?> I DO NOT refuse
to accept the general phenomenon that> different ways of
looking at the same mathematical objects can> lead to better
insights about those objects. But in any> situation where
things are dual, they are still DIFFERENT.> They are NOT the
same. In projective geometry, points> and lines are REALLY
dual.Perhaps your understanding of projective duality is
different from mine.In my understanding, the dual of a
con?uration of points and lines consists of the same objects,
but the objects that were points now get called lines and the
objects that were lines now get called points. A projective
geometry is a system of objects with incidence relations
satisfying certain axioms and when you rename the objects they
still satisfy the appropriate axioms. The only difference is in
the human terminology for the objects, not in their
mathematical behavior or identity.To get back to an earlier
point, one possible way of forming objects satisfying the set
of projective geometry axioms is to have points that are just
points (atomic from the point of view of the geometry) while
the lines are sets of points and the point-line incidence
relation is set membership. Projective duality tells us that
we could instead view the lines as being atoms, and the points
as being sets of lines through them, with incidence again being
equivalent to set membership. As someone who has personally
gained insight into geometry problems by applying projective
duality, despite dualitys inability to change the underlying
mathematical objects involved, I ?d your claim You will not
gain any insight into the nature of a point by thinking about
it as an in?ite collection of lines to be counterfactual and
strange. Why are you trying to tell me not to apply a technique
that I know from personal experience has worked?-- David
Eppstein http://www.ics.uci.edu/~eppstein/Univ. of California,
Irvine, School of Information & Computer Science
I just
thought I would save George some time: To get back to an
earlier point, one possible way of forming objects> satisfying
the set of projective geometry axioms is to have points that>
are just points (atomic from the point of view of the
geometry) while> the lines are sets of points and the
point-line incidence relation is> set membership. Projective
duality tells us that we could instead view> the lines as
being atoms, and the points as being sets of lines through>
them, with incidence again being equivalent to set membership.
As> someone who has personally gained insight into geometry
problems by> applying projective duality, despite dualitys
inability to change the> underlying mathematical objects
involved, I ?d your claim You will> not gain any insight
into the nature of a point by thinking about it as> an in?ite
collection of lines to be counterfactual and strange. Why> are
you trying to tell me not to apply a technique that I know
from> personal experience has worked?>What follows is from a
recent off-group correspondence:>>When all is said and done,>>
the membership relation is just an incidence>>relation:George
replied:>And you are just an idiot. JEEzus.>What you are
presenting is indeed an incidence relation, but>equating it
with the membership relation is JUST SILLY.>THAT is a LOCAL
idiolectic AND idiotic usage.Sorry, David. Im sure your
opinions are more highly regarded than mine. Mysomewhat more
absolute statement comes from several years of studying set
theoryand concluding that the concept of language invariance
described in TopologicalModel Theory by Flum and Ziegler is
the mathematically important issue thatarises from set
theory.(What I presented was an incidence matrix for the
trivial af?e plane becauseit was easy to cut-and-paste from
recent material I had written. Like a goodmathematician,
George visualized the af?e geometry from the presentation.
Mywords explaining otherwise made no difference.):-)mitch
 :
Why do you want to blinker us? I dont.Give it a break George.
You know what you are doing.> The general thrust of this
thread is about> representation theorems, not blinkering.Now
who is lying?You bring ridiculous concepts like burden of
proof concerning metaphysicalpositions like foundationalism
to mathematical discussions and arent honest aboutit to the
people with whom you are in discussion. The fact that you can
reprsent any group via an isomorphism> with a permutation
group does not mean that you are being blinkered> from
seeing all the others.Usual a natural language term like us
is usually not a reference to mathematicalentities.> It just
means that the permutation groups> are in some sense closer
to explaining the core of the concept.combinatorial topology
and Betti group invariants, maybe) You will in some sense have
focused on some important aspect of> a group if you bother to
separate it into the relevant permutation> group and the
isomorphism between that and itself. You will not> gain any
insight into the nature of a point by thinking about it> as an
in?ite collection of lines, especially not if you are> going
to arbitrarily exclude one of the lines.Perhaps not. But you
will gain an in?ite amount of knowledge about the
geometricinsights Frege leveraged just before revolutionizing
analytical philosophy.Hey guys... (not to you George). You need
to be looking at Pluckers work inalgebraic geometry and its
relationship to triple systems to understand why Georgegets
to use logic like a battle axe. Truth tables are essentially a
tetrahedralsimplex. The independence criterion, namely(x_1 -
x_0),(x_2 - x_0),(x_3 - x_0)being linearly independent
vectors, is tantamount to specifying the representationof the
complete NOR connective.To understand the discussion you are
actually in folks, you must make inferencesfromExcuse me for
having BEEN pedagogued thatway, but since I was, I think that
that direction isJust Fine, and that YOURS is the onethat is
mistaken.andThere never wouldve been any relativity if
thestudy of the ether hadnt come before it. Therenever
wouldve been any chemistry if phlogistonhadnt come before
it. There never wouldvebeen any heliocentric astronomy if
Ptolemaicepicycles hadnt come before it. Good riddanceto
all.In other words, you will have to be willing to overturn
the rationalizations ofanalytical philosophy in order to
avoid blinkering and enjoin constructivemathematical
discourse. Moreover, as the remark above indicates, you will
havelittle success invoking any authority which might be
commonly respected. Nor, willyou be informed of what
authoritative material is legitimate even if you ask.Why then
am I so sure this goes back to the algebraic geometry preceding
Frege?Everything you are saying here is ENTIRELY analogousto
the fact that [the domain of] A MODEL OF a[consistent] set of
?st-order axioms can be just aboutanything.which means that
a model is practically nothing at all.He is just not quite as
elegant as Frege,It is dif?ult to avoid an expression that
has universalcurrency, before you learn of the mistakes it can
giverise to. It is extremely dif?ult, perhaps impossible,
totest every expression offered us by language to seewhether
it is logically innocuous. So, a great part ofthe work of a
philosopher consists--or at least oughtto consist--in a
struggle against language. But perhapsonly a few people are
aware of the need for this.Instead, you get someone with a
philosophy background insisting that you engage
injusti?ationalism (hey, now there is a word that belongs on
sci.math),There is simply no way (nor desire) to bindor
restrict the potential universe of applicability. Butsaying
set all over the place DOES tend to do that,because naive
set theory wont work; if you are going tosay set then you
are going to, whether you want to or not,invoke SOME set
THEORY and associated restrictionsand complexities that ARE
necessary to a coherent notionof set but that you do NOT
want to respect as far asapplicability of your structure.Now,
if you look at the literature on triple systems, you will ?d
that it isrelates to orientability in combinatorial topology.
And if you consider what Isaid about the tetrahedron, you will
realize that the coherence to which Georgerefers is actaully
derivative from the coherence between vertices and
theiropposing face.One thing I can assure everyone in this
thread: it is not about representationtheorems.:-)mitch
>
: Points and non-vertical lines are dual in the af?e
plane.>Thats ridiculous. In the af?e plane, there is no such
thing> as vertical. If you want to put a co-ordinate system
on it> and do analytic geometry, ?e, but that duality comes
from the> co-ordinate system and not from the underlying
geometry.The distinction between vertical and non-vertical can
be quite useful, when one is doing statistics such as ?ting a
line to data with one independent variable (the x-coordinate)
and one dependent variable (the y-coordinate) -- a vertical
line does not predict the y-coordinate as a function of the
of problem from a coordinate-free af?e-invariant point of view
can lead to statistical methods that are highly robust against
outliers and other kinds of errors (e.g. see Rousseeuws
notion of regression depth).In fact in this setup one is using
a restricted group of af?e transforms that preserve the family
of vertical lines, but I dont know of a good word for this
other than af?e.-- David Eppstein
http://www.ics.uci.edu/~eppstein/Univ. of California, Irvine,
School of Information & Computer Science
> Why do you want
to blinker us?lol:-)mitch
>I have a hard problem in what I
suppose is plane geometry. It might >require some
machine-assisted computation. Any help would be appreciated.I
worked on this question a little more. I think it has no
solutionbut I havent got a proof. What Im wondering about,
now that Ivelooked at it, is how to phrase the problem and
its obstruction elegantly.This seems to be a problem in Af?e
Geometry (or Projective Geometry)but I cant quite pinpoint
the relevant classical con?uration.Let me explain. Youve
given quite a few constraints, and asked usto draw a picture
consistent with all of them. My claim is that thedata are
contradictory, and in fact a contradiction results from
arather smaller set of constraints.You asked us to draw 8
lines in the plane; that we can do. You add atiny constraint
that no two be parallel; no problem. That means thateach pair
of lines has a unique point of intersection, giving 28
pointsaltogether.Now, if we label the lines A, B, C, D, E, F,
G, H then on each linewe ?d the seven points of intersection
with the other lines, occurringin some order as we read from
left to right (or bottom to top). Theordering data you
provided specify unambiguously the sequence ofthe intersection
points on each line. (Your partial order speci?smore, in fact,
but I believe there is already a contradiction fromthis more
limited information.) If, as in some cases, we dont
reallycare whether the points occur in one order or the
reverse order, we cannote the points of intersection in
brackets as you do. Actually, I believethere is already a
contradiction even if these more relaxed constraints are
imposed.Let me illustrate ?st with two examples. If you
wanted us to drawthree lines A, B, C, then you would have to
specify the orderings ofthe intersection points on each line.
For example, on line A you mightwant B to be to the left of C,
which we could write this way: A : B, CBut if you arent choosy
about whether the points of intersection onany particular line
show up left-to-right or right-to-left, you mightwrite the
constraint this way: A : [B, C]Of course, when there are only
three lines, this means the only possibleset of constraints of
this form would be A : [B, C] B : [A, C] C : [A, B]and these
constraints are satis?ble (e.g. by the lines x=0, y=0,
x+y=1).Next consider an example with four lines. Can we draw
lines with theseincidence data? A : [D, B, C] B : [D, A, C] C
: [A, B, D] D : [A, C, B]I claim not. If we could do this, we
could translate the picture so thatA & B meet at the origin.
Applying a linear transformation, we couldassume A and B are
the x- and y- axes, respectively. Applying re?ns as
needed, we could assume C meets these lines above andto the
right of the origin; applying scalings we could assume C isthe
line x + y = 1. And now where is the line D ? If it meets A
atthe point (x0, 0) and meets B at (0, y0), then the ?st
twoconstraints imply that x0 < 0 and that y0 < 0,
respectively. You canwork out where C and D cross (hint: D is
the line x/x0 + y/y0 = 1)but youll ?d that under these
conditions x y < 0, that is, the pointof intersection is in
the second or fourth quadrants; on the other handa point
between the other intersection points (x0,0) and (0, y0)
wouldlie in the third quadrant. So the constraints on D are
incompatiblewith the constraints on A and B . (And I havent
even used theconstraints on C !)Note that I am using only the
incidence relations of the lines, andinvariance under the
group of af?e maps (linear maps and translations);that makes
this a question of Af?e Geometry. With the addition of
atechnical axiom or two, af?e geometry really is coordinate
geometryover some ?ld (a very nice theorem!). We have used
nothing else here,really, except the condition that the ?ld
be ordered. So there oughtto be some more classical way of
stating that there is a contradictionhere. (Its not
Desarguess con?uration, nor Pappuss, nor ... Whose is
it?)By the way, you can also ask whether the con?uration can
be constructedin Projective Geometry. There, lines have no
ends, so the incidence datacan be read not only
left-to-right or right-to-left, but also with anycyclic
permutation. In that setting, any four-line problem is
solvablebut I suppose there is a corresponding ?e-line
con?uration which is not.After this very long preamble, I
can state your problem in this languageand make some
suggestions as to how to prove it impossible. I think Iwould
like to name the lines as follows: A = your points # 1, 2, 3,
4, 5, 6, 7 B = 1, 9, 10, 8, 11, 12, 13 C = 20, 22, 19, 21, 9,
14, 3 D = 20, 16, 27, 26, 11, 5, 23 E = 25, 28, 7, 13, 27, 18,
22 F = 25, 23, 4, 15, 10, 24, 19 G = 2, 14, 15, 8, 17, 18, 16 H
= 28, 6, 12, 26, 17, 24, 21(Ive written them in the order they
seem to appear in my sketches.)Reading either your (corrected)
partial orders on the x-coordinatesor on the y-coordinates, we
then have these incidence constraints: A : [B, G, C, F, D, H,
E] B : [A, C, F, G, D, H, E] C : [D, E, F, H, B, G, A] D : [C,
G, E, H, B, A, F] E : [F, H, A, B, D, G, C] F : [E, D, A, G, B,
H, C] G : [A, C, F, B, H, E, D] H : [E, A, B, D, G, F, C]You
can come pretty close to achieving these as follows: make C
and Dnearly vertical, meeting very high above the origin (C
has a positive slope,D a negative slope); rotate these about
a third of a circle counterclockwiseto obtain A and B
respectively, and rotate C and D clockwise abouta third of a
circle to obtain E and F respectively. Jiggle as needed.Line G
can be made to pass these from the lower left (between A and
C)to the upper right (between D and B). Then line H can be
drawn fromthe right side (between E and A) to the upper left,
emerging betweenE and F, EXCEPT THAT the intersection of H
with F is way off base.I think that by drawing the pairs
{A,B}, {C,D}, {E,F} nearly parallel,its possible to have H
and F meet either far off to the left or faroff to the right,
but not somewhere in the middle, as it needs to be.Of course
my failure to satisfy the constraints need not imply
theycannot be satis?d. We could try to emulate the proof I
gave for thefour-line problem above: without loss of
generality we may assumeA is the horizontal axis and D is the
vertical axis (point 5 is now atthe origin) and we can assume
line G is the line y = x + 1, say.There are ?e more lines
whose intersections with the axes we can name,giving ten
variables x_B, y_B, x_C, ..., y_H for us to play with.We can
compute the intersections of pairs of the lines, giving us
42inequalities to be satis?d by these 10 variables. (For each
lineother than A and D, it suf?es to write the constraints in
termsof either the x- or y-coordinates of intersection.) For
example, fromline A we learn that x_B < -1 < x_C < x_F < 0 <
x_H < x_Eand from line B we learn that x_B < (y_B - y_C) x_B
x_C/(y_B x_C - y_C x_B) < (y_B - y_F) x_B x_F/(y_B x_F - y_F
x_B) < (y_B - y_G) x_B x_G/(y_B x_G - y_G x_B) < 0 < ...(Note
that our conventions have resolved the ambiguity of the
orderin which the intersections with B are to be read. For
instance thecontraints read from line D must be in this
direction: y_C > 1 > y_E > y_H > y_B > 0 > y_F .)There are
other ways to capture the constraints in terms of
rationalexpressions of multiple variables. But I should stress
that if wethink that we can obtain a contradiction by (say)
adding a string o?equalities together, its going to be a
complicated sum, since asI noted it IS possible to satisfy
almost all the constraints at once.The contradiction is only
going to come from using essentially ALLthe inequalities
together.But as I said earlier, it may not be necessary at all
to proceedalgebraically; there may well be a nice
incidence-geometric principlewhich shows that this
con?uration is impossible.OR -- could it be that youve made
another typo? Maybe your desired ordering of the intersections
is wrong...Since I have just taught a course in linear
geometries, I wouldbe very interested in hearing the context
in which this problem arose.dave
Is there any other name
used to denote groups of order p^a q^b, p andq prime (like the
abbreviation p-groups)? It seems that thereshould be quite a
bit of literature on them given Burnsides theoremthat they
are solvable. Maybe Im looking for the wrong words.Also, does
anyone know if when you search on MathSciNet if the enginethe
words? When I enter anything even without quotes it appears as
astring on the results page.
> Where the hypotenuse (c) of a
right triangle is the square root of a> future Fibonacci number
where sides (a) and (b) are any sequential> pair of Fibonacci
numbers (excluding) the ?st term = ( 0 ) as one of> the
pair.>The proof is, any sequential pair of the Fibonacci
sequence where > Fn^2 + F(n+1)^2 = a future larger Fib. #.Its
easy enough to prove.It is known that Fn = (phi^n -
(-phi)^(-n)) / sqrt(5)Using the identity that phi^2 + 1 = phi
+ 2 = phi * sqrt(5), it isstraightforward to show that (Fn)^2
+ (F(n+1))^2 = F(2n+1) > Each succeeding c^2 ratio converges
to (phi +1) where phi = golden> meanThe ratio F(n+1) / Fn has
long been known to converge to phi.Therefore, F(n+2) / Fn
would obviously converge to phi^2 = phi + 1 .-- Daniel W.
Johnsonpanoptes@iquest.nethttp://members.iquest.net/~panoptes/
039 53 36 N / 086 11 55 W
<1g5p9kk.wqiq16p4vslcN%panoptes@iquest.net>
 > Where the
hypotenuse (c) of a right triangle is the square root of a>
future Fibonacci number where sides (a) and (b) are any
sequential> pair of Fibonacci numbers (excluding) the ?st
term = ( 0 ) as one of> the pair.> The proof is, any
sequential pair of the Fibonacci sequence where> Fn^2 +
F(n+1)^2 = a future larger Fib. #. Its easy enough to prove.
It is known that Fn = (phi^n - (-phi)^(-n)) / sqrt(5) Using
the identity that phi^2 + 1 = phi + 2 = phi * sqrt(5), it is>
straightforward to show that (Fn)^2 + (F(n+1))^2 = F(2n+1)A
proof that uses integers only, but it looks better if you
use2-by-2 matrices:Let A =[0 1][1 1]then A^n =[F(n-1) F(n)
][F(n) F_(n+1) ]where F(-1)=1, and this is done by
induction.Then (A^n)^2 = A^(2*n) will give you the result
F(n)^2 + F(n+1)^2 = F(2*n+1)in the lower right corner.[Nothing
else added by me.]> Each succeeding c^2 ratio converges to (phi
+1) where phi = golden> mean The ratio F(n+1) / Fn has long
been known to converge to phi.> Therefore, F(n+2) / Fn would
obviously converge to phi^2 = phi + 1 .> --> Daniel W.
Johnson> panoptes@iquest.net>
http://members.iquest.net/~panoptes/> 039 53 36 N / 086 11 55
W>
Yes, this is known and there is more on this at my Fib
and Phi website
atwww.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/?maths.html
#nonpythIt uses teh Fibonacci identity thatF(n)^2 + F(n+1)^2 =
F(2n+1) and F(2n+1) is there are no Fiboanccisquare numbers
beyond F(12)=144 Every Fibonacci-type sequence has Phi
(1.618..) as the limit of theratios of consecutive terms
F(n)/F(n-1), n>0 (and -phi=-0.618...) asthe limit as n gets
more negative. Also, take any two numbers A and B, and the
next two in aFibonacci-type series: A+B and B+(A+B). These 4
are simply combinedto make a Pythagorean triangle by
multiplying the outer 2, doublingthe product of the inner two
and the third side is the sum of thesquares of the inner
two.So 1,2,3 and 5 give sides 1x5=5, (2x3)x2=12 and 2^2+3^2=13
- the5,12,13 triangle. All Pythagorean trianes are derivable
this way. Theres a calculator for this on the web page
too,Ron Knott> I dont recall if I posted this at an early
date so please excuse me> if I did.> > Is this known about the
Fibonacci sequence?> I did web lookups with no hits. >Where the
hypotenuse (c) of a right triangle is the square root of a>
future Fibonacci number where sides (a) and (b) are any
sequential> pair of Fibonacci numbers (excluding) the ?st
term = ( 0 ) as one of> the pair.>The proof is, any sequential
pair of the Fibonacci sequence where > Fn^2 + F(n+1)^2 = a
future larger Fib. #.>Below are the ?st ten examples of right
triangles.>1) a = 1 2) a = 1 3) a = 2> b = 1 b = 2 b = 3 > c =
sqrt(2) c = sqrt(5) c = sqrt(13)>4) a = 3 5) a = 5 a = 8 > b =
5 b = 8 b = 13> c = sqrt(34) c = sqrt(89) c = sqrt(233)>7) a =
13 8) a = 21 9) a = 34> b = 21 b = 34 b = 55> c = sqrt(610) c
= sqrt(1597) c = sqrt(4181)>10) a = 55> b = 89> c =
sqrt(10946) etc.>Etc.>Where m=2,3,4,5,6,7..m and where n= the
nth Fibonacci number then > fn = n = 2,3,4,5,6,7..n> Starting
with (c)^2 =2 where m=2 and fn = n = 2 then thereafter the>
next (c)^2 is (f(n+m)).>Each succeeding c^2 ratio converges to
(phi +1) where phi = golden> mean>Strange how a simple additive
number sequence such as the Fibonacci> sequence can have so
many profound properties including this one.>Maybe there is
some connection to the Pythagorean triples, but here> (a) and
(b ) are integer pairs from the Fibonacci sequence and (c)is>
an integer square root of a larger Fibonacci number!>Also this
sequence which is related to the Fibonacci sequence
-->1,2,5,12,29,70,169,408,985... (silver mean sequence) does
the same> thing. The ratio between its terms is the silver
mean.> > In fact there are an in?ite number of these
sequences (metal mean> sequences) that have this unusual
relationship to the right triangle.> > Dan
>Yes, this is
known and there is more on this at my Fib and Phi web> site
at>
www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/?maths.html#
nonpyth> It uses teh Fibonacci identity that> F(n)^2 +
F(n+1)^2 = F(2n+1) and F(2n+1) is there are no Fiboancci>
square numbers> beyond F(12)=144> Every Fibonacci-type
sequence has Phi (1.618..) as the limit of the> ratios of
consecutive terms F(n)/F(n-1), n>0 (and -phi=-0.618...) as>
the limit as n gets more negative.> Also, take any two numbers
A and B, and the next two in a> Fibonacci-type series: A+B and
B+(A+B). These 4 are simply combined> to make a Pythagorean
triangle by multiplying the outer 2, doubling> the product of
the inner two and the third side is the sum of the> squares of
the inner two.> So 1,2,3 and 5 give sides 1x5=5, (2x3)x2=12 and
2^2+3^2=13 - the> 5,12,13 triangle. All Pythagorean trianes are
derivable this way. > Theres a calculator for this on the web
page too,>Ron KnottVery interesting site.Dan>I dont recall if
I posted this at an early date so please excuse me> if I did. Is this known 
about the Fibonacci sequence?> I did web
lookups with no hits. >Where the hypotenuse (c) of a right
triangle is the square root of a> future Fibonacci number
where sides (a) and (b) are any sequential> pair of Fibonacci
numbers (excluding) the ?st term = ( 0 ) as one of> the
pair.>The proof is, any sequential pair of the Fibonacci
sequence where > Fn^2 + F(n+1)^2 = a future larger Fib.
#.>Below are the ?st ten examples of right triangles.>1) a =
1 2) a = 1 3) a = 2> b = 1 b = 2 b = 3 > c = sqrt(2) c =
sqrt(5) c = sqrt(13)>4) a = 3 5) a = 5 a = 8 > b = 5 b = 8 b =
13> c = sqrt(34) c = sqrt(89) c = sqrt(233)>7) a = 13 8) a = 21
9) a = 34> b = 21 b = 34 b = 55> c = sqrt(610) c = sqrt(1597) c
= sqrt(4181)>10) a = 55> b = 89> c = sqrt(10946)
etc.>Etc.>Where m=2,3,4,5,6,7..m and where n= the nth
Fibonacci number then > fn = n = 2,3,4,5,6,7..n> Starting with
(c)^2 =2 where m=2 and fn = n = 2 then thereafter the> next
(c)^2 is (f(n+m)).>Each succeeding c^2 ratio converges to (phi
+1) where phi = golden> mean>Strange how a simple additive
number sequence such as the Fibonacci> sequence can have so
many profound properties including this one.>Maybe there is
some connection to the Pythagorean triples, but here> (a) and
(b ) are integer pairs from the Fibonacci sequence and (c)is>
an integer square root of a larger Fibonacci number!>Also this
sequence which is related to the Fibonacci sequence
-->1,2,5,12,29,70,169,408,985... (silver mean sequence) does
the same> thing. The ratio between its terms is the silver
mean.> > In fact there are an in?ite number of these
sequences (metal mean> sequences) that have this unusual
relationship to the right triangle.> > Dan
Consider : X_1,
X_2, ... is a sequence of independent random variables
with?ite variances and a common distribution F such that F(0)
= 0. Nowconsider the productZ_n = product (from k = 1 to n) of
{ (2(X_k)^2) / ( (X_{k-1})^2 +(X_{k-2})^2 ) }In order to
analyze Z_n, Id like to talk about 2E[(X_n)^2]
andE[1/((X_{n-1})^2 + (X_{n-2})^2]. What is the relationship
between these twoexpectation? Is one always bigger than the
other?Then ?ally Id like to show that Z_n converges with
probability one to arandom variable that is ?ite with
probability one.Any ideas?Henrique
Suppose that the random
variables X_i are independent and P(X_i = 2^k) =2^(-k) for all
k >= 1.Show that (X_1 + X_2 + ... + X_n)/(n*log(n)) converges
in probability tolog(2).Prove or disprove that limsup (X_1 +
... + X_n)/(n*log(n)) = in?itywith probability 1.Anyone can
19072
id like a function f: O : --> R , O denotes an open
set in R^2,such that ? C^infty , f(tv) = t f(v), f(0) = 0,
there exist v, w in O such that f ( v + w ) =/= f(v)+ f(w).Can
you halp me, please?Tern
> id like a function f: O : --> R>
, O denotes an open set in R^2,>such that f>is C^infty , f(tv)
= t f(v), f(0) = 0> , there exist v, w in O such that f ( v +
w ) =/= f(v)+ f(w).Try functions of the form f(rcos(t),
rsin(t)) = r*g(t), on O = R^2 {0}, where g is C^oo and 2Pi
periodic on R.
> id like a function f: O : --> R> , O
denotes an open set in R^2,> such that f> is C^infty , f(tv) =
t f(v), f(0) = 0> , there exist v, w in O such that f ( v + w )
=/= f(v)+ f(w). Try functions of the form f(rcos(t), rsin(t)) =
r*g(t), on O = R^2 {0},> where g is C^oo and 2Pi periodic
on R.(x,y)--> sqrt{x^2+y^2} cos (arctg y/x) if x=/=0 0
else?
...> the 3-by-3 case has at least 6 solutions (where
I stopped counting);> but the 4-by-4 grid has (I believe I
proved, perhaps) only 2 solutions.> (I am referring to the
back-and-forth variation of the puzzle.)>(You can try to ?d
the 4-by-4 solutions yourself.> More fun, and not too hard, is
trying to prove that there > are ONLY 2 solutions for the
grid.> Extra credit if you ?d more than 2 solutions!)There
are 4 solutions at n=4:1 2 3 4 aabb aabb aabb aabb8 7 6 5 aacc
cdee aacd cdef9 10 11 12 aacc cdee aacd cdef16 15 14 13 ddcc
ffee eecf ggehof solutions for n=3...7; some solution times in
seconds;and some solution-sizes, ie, number of rectangles in
solutions:n #sols time Solution-sizes3 9 0.001 3 5 64 4 0.005
4 6 85 154 0.15 3 5 7 9-146 837 10 8 10 11-197 24 175 11 13 15
17 198 >2330 >5400 14 16-27(n=8 has run about 1.5 hours so far,
on my 450MHz Athlon)-jiw
> A simple not-too-hard puzzle:>>
Write the integers 1 through 25 in a 5-by-5 grid in a
back-and-forth> manner like this:>> 1 2 3 4 5>10 9 8 7 6>11 12
13 14 15>20 19 18 17 16>21 22 23 24 25>>Subdivide this grid
into 11 rectangles, each rectangle of any> integral{1 to 5}
width and height, so that the integers in each> rectangle sum
to a prime.>> There are at least 2 similar solutions.>> And,
for further research:> Ideally, someone will not only ?d
other solutions, but solutions> using fewer rectangles.>>
Which sized squares, with the integers written in the above>
back-and-forth manner, have solutions???>Generally:> How many
as noted, there are multiple solutions. > I myself found a
couple 9-rectangle solutions earlier today. >If we have any
such grid of integers, > whatever n (>= 2) is (and no matter >
if every row increases or {as here} alternates > between
increasing and > decreasing consecutive terms), then the only
> *widths* that the rectangles can have are 1 or 2.> And if
the width is 2, then the height > must be odd.>> As for my
question asking what the # of solutions > is for the n-by-n
grid,>(somewhat) interestingly, > the 3-by-3 case has at least
6 solutions (where > I stopped counting);> but the 4-by-4 grid
has (I believe I proved, perhaps) > only 2 solutions.> (I am
referring to the back-and-forth variation of the puzzle.)
>(You can try to ?d the 4-by-4 solutions yourself. > More
fun, and not too > hard, is trying to prove that there are
ONLY 2 solutions> for the grid. > Extra credit if you ?d more
than 2 solutions!)> >> OB puzzle (that I have not solved
myself):>For the n= 5 case, place the integers 1 through 25>
into the grid AS YOU WISH so as to:> 1) maximize the number of
prime-rectangles you can> subdivide the square into.> 2)
minimize the number of prime-rectangles you can> subdivide the
square into.>If there is no obvious way to PROVE the number of
primes is > minimal/maximal, then we might as well make a
contest out> of this for sci.math/rec.puzzles posters...>
puzzle, perhaps this would be more fun for n = 6, or higher.Let
Quet
> For the n= 5 case, place the integers 1 through 25>
into the grid AS YOU WISH so as to:[maximize or minimize]> the
number of prime-rectangles you can subdivide the square
into...> As for the OB puzzle, perhaps this would be more fun
for n = 6, or higher....In the late 1980s the following
appeared in Scienti? AmericansMathematical Games (or perhaps
Metamagical Themas, dont rememberwhich): Place copies of
digits 0...9 as you like in a square grid, one digit per cell.
Reading all sets of vertically or horizontallyadjacent digits
both ways as decimal numbers, maximize the number of primes. A
3x3 example: 173937139has primes 17, 7, 173, 71, 73, and 37 in
the top rowand primes 19, 19, 191, and 191 in the left column.
Etc.(I dont remember if any prime-uniqueness requirements
applied.)For the 6x6 case, the best squares found have 188
primes, iirc,and I dont remember any results for other
sizes.-jiw
|-|erc  schreef
in bericht>
-------------------------------------------------------------
--------------------- > |An hour ago I put a pie in the oven,
then was lost in time doing some> |website reviews when I came
across this page : Traf? Rank for> |pagewolf.com: 1,314,826
unburnt! Herc true story>
|http://www.alexa.com/data/details/traf?_details?q=&url=
pagewolf.com> > and what do you make of this? is it just some
sort of funny> coincidence, or is there more to it than
that?>I just posted it for the coincidence, but pi does follow
me around, I tendto look> at clocks at 3:14.No you dont.You
*remember* the times when its 3:14 when you watch the watch,
and youforget the rest.
So far it seems that all solutions
to B6 were based on a discrete version. Here is a more direct
proof:Denote by I the unit interval and let m be the Lebesque
measure on the real line. Then th double integral
is:int_{R_+} 2( m(f>t)m(f>-t) + m(ft) + m(f<-t) dt(use Fubini for
both).Now, for each t, the ?st integrand is larger or equal
than the second.This is in fact equivalent to:for t larger or
equal than 0,m( -tSo
far it seems that all solutions to B6 were based on a discrete
>version. You havent been paying attention very
carefully...>Here is a more direct proof:Denote by I the unit
interval and let m be the Lebesque measure on the >real line.
Then th double integral is:int_{R_+} 2( m(f>t)m(f>-t) +
m(fThe single integral
is:int_{R_+} m(f>t) + m(f<-t) dt>(use Fubini for both).I
certainly see how the second equality follows from Fubini,but
I dont see the ?st one.>Now, for each t, the ?st integrand
is larger or equal than the second.>This is in fact equivalent
to:for t larger or equal than 0,m( -tCiprian
Pop************************David C. Ullrich
>So far it
seems that all solutions to B6 were based on a discrete
>>version. >> You havent been paying attention very
carefully...Sorry if I was out of sync.>Here is a more
direct proof:>>Denote by I the unit interval and let m be the
Lebesque measure on the >>real line. Then th double integral
is:>>int_{R_+} 2( m(f>t)m(f>-t) + m(f> Why
is this? If chi denotes the indicator function,
then|f(x)+f(y)| =int_R ( chi_[-f(y),f(x)] (t) +
chi_[f(y),-f(x)] (t) ) dt(exactly one of the two indicator
functions is essentially zero).The use Fubini to get an
integral over the real line of an even function...I hope this
helps.>The single integral is:>>int_{R_+} m(f>t) + m(f<-t)
dt>>(use Fubini for both).>> I certainly see how the second
equality follows from Fubini,> but I dont see the ?st
one.>Now, for each t, the ?st integrand is larger or equal
than the second.>>This is in fact equivalent to:>>for t larger
or equal than 0,>>m( -t> Its not
clear to me whether this is just a typo,> but in fact that
last inequality is backwards.Yes, it was a typo.>Ciprian
Pop>> ************************>David C. UllrichCiprian
Just
multiply sec (x) by (sec (x) + tan (x))/(sec (x) + tan (x))
then make a u-substitution (u = sec (x) + tan (x))>>In order
to integrate sec(x), >>Note sec(x) = cos(x)/(1-sin(x)^2)>> =
(1/2)*(1/(1-sin(x)) + 1/(1+ sin(x)))*cos(x)Certainly, if you
know what the integral is, this arcane multiplicationand
substitution might be somewhat obvious, but its a lot more
obvious,and almost as simple, to multiply numerator and
denominator of dx/cos(x)by cos(x) to get cos(x)dx/cos^2(x) =
dsin(x)/(1-sin^2(x)) which is quitesimple by partial
fractions.I would always teach Virgils method to a student
learning calculus.What you suggest looks too much like magic
and would probably serve toincrease any math anxiety that
already exists.Rob Johnson take out the
trash before replying
>There are various versions of this.
I give three possible solutions at the>end. Please
comment.In?itely many balls, each numbered (#1,#2,#3, etc.)
are to be placed into>a bucket, ten at a time, by the scheme
given below. Immediately after each>group of ten are placed
in the bucket, one is removed and discarded. The>process is as
described below.11am: Balls #1 - #10 placed into the bucket.
Ball #1 is removed>and discarded.11:30am: Balls #11-#20 placed
into the bucket. Ball #2 removed and>discarded.11:45am: Balls
#21-#30 placed into the bucket. Ball #3 removed
and>discarded.11:52.5am: Balls #31-#40 placed into the bucket.
Ball #4 is removed and>discarded.Etc.The process continues by
halving the remaining time until 12 noon. Then ten>are placed
in and one is removed and discarded by the above scheme.
The>remaining time is halved again, etc. There is a ?of
activity just>prior to 12 noon. The process does not continue
at or beyond 12 noon.Question: How many balls remain in the
bucket at 12 noon?There are three common, though not
necessarily correct, replies.1) In that the net gain is +9
balls per event, and there are in?itely>many events, there
are in?itely remaining balls in the bucket.2) None remain.
Any given ball, say ball #k, is removed and discarded at
a>speci? time prior to 12 noon.3) The question is
meaningless as the process can not be extended to or>beyond 12
noon.Comments?Almost 4 years ago, there was a very long thread
on this very topic.See the thread starting at
news.globalcenter.netAs you mention, there are three ways to
approach this problem; eachboils down to a question of
convergence. If we have a sequence {a_n},we might ask what
happens to that sequence as n tends to in?ity, andthus, pass
to the limit to de?e what happens at in?ity. However,to
de?e a limit, we must ?st de?e a topology.Reply
1-------There are standard topologies on both the reals and
the integers, sothat if the a_n are reals or integers, we use
those topologies.For example, let a_n be the number of balls
in the bucket after the n^thplacement/removal. That sequence
converges to in?ity as n tends toin?ity.Reply 2-------Let us
de?e a_n to be the function, after the n^th
placement/removal,which maps the set of balls to {0,1}, where
1 means that ball is in thebucket and 0 means it is not. If we
use the topology of pointwiseconvergence on these functions,
the sequence {a_n} converges to thefunction which maps all the
balls to 0, since at some point, each ballis removed from the
bucket, never to be put back.Reply 3-------Consider the same
sequence of functions {a_n} de?ed for Reply 2, butlet us use
the discrete topology on this sequence. With this topology,the
functions converge to a function f if after some point, all the
a_nare equal to f. Thus, using this topology, the {a_n} do not
converge.Thus, each of the replies is correct depending on how
you de?e theconvergence. Since the question asks, how many
balls, it seems to meit is looking at the topology described
for Reply 1. So in this case,I would say an in?ite number. If
the question were which balls,that would indicate the
topology for Reply 2, and then I would say noballs.Rob Johnson
take out the trash before
replying
>>There are various versions of this. I give three
possible solutions at the>>end. Please comment.>>In?itely
many balls, each numbered (#1,#2,#3, etc.) are to be placed
into>>a bucket, ten at a time, by the scheme given below.
Immediately after each>>group of ten are placed in the
bucket, one is removed and discarded. The>>process is as
described below.>>11am: Balls #1 - #10 placed into the bucket.
Ball #1 is removed>>and discarded.>>11:30am: Balls #11-#20
placed into the bucket. Ball #2 removed
and>>discarded.>>11:45am: Balls #21-#30 placed into the
bucket. Ball #3 removed and>>discarded.>>11:52.5am: Balls
#31-#40 placed into the bucket. Ball #4 is removed
and>>discarded.>>Etc.>>The process continues by halving the
remaining time until 12 noon. Then ten>>are placed in and one
is removed and discarded by the above scheme. The>>remaining
time is halved again, etc. There is a ?of activity
just>>prior to 12 noon. The process does not continue at or
beyond 12 noon.>>Question: How many balls remain in the bucket
at 12 noon?>>There are three common, though not necessarily
correct, replies.>>1) In that the net gain is +9 balls per
event, and there are in?itely>>many events, there are
in?itely remaining balls in the bucket.>>2) None remain. Any
given ball, say ball #k, is removed and discarded at
a>>speci? time prior to 12 noon.>>3) The question is
meaningless as the process can not be extended to or>>beyond
12 noon.>>Comments?> Almost 4 years ago, there was a very long
thread on this very topic.> See the thread starting at>
news.globalcenter.net> As you mention, there are three ways
to approach this problem; each> boils down to a question of
convergence. If we have a sequence {a_n},> we might ask what
happens to that sequence as n tends to in?ity, and> thus,
pass to the limit to de?e what happens at in?ity. However,>
to de?e a limit, we must ?st de?e a topology.But the
question can be answered without appealing to any sort
oftopology.> Reply 1> -------> There are standard topologies
on both the reals and the integers, so> that if the a_n are
reals or integers, we use those topologies.> For example, let
a_n be the number of balls in the bucket after the n^th>
placement/removal. That sequence converges to in?ity as n
tends to> in?ity.But that has nothing to do with the question
that was asked.> Reply 2> -------> Let us de?e a_n to be the
function, after the n^th placement/removal,> which maps the
set of balls to {0,1}, where 1 means that ball is in the>
bucket and 0 means it is not. If we use the topology of
pointwise> convergence on these functions, the sequence {a_n}
converges to the> function which maps all the balls to 0,
since at some point, each ball> is removed from the bucket,
never to be put back.If we view a_n to be a function de?ed in
the time domain rather than inthe domain of natural numbers,
such that a_n(t) = 1 if ball n is in thebucket at time t and
a_n(t) = 0 otherwise, then we ?d that a_n(t_0) = 0for each n,
where t_0 = noon. Thus a(t_0) = sum_n=1^oo a_n(t_0) =
0.Although this reasoning leads to the same conclusion as your
argument,there is an essential difference. Your argument uses
limits as t->t_0,but mine does not. The only limit that
appears in my argument is the onethat says the sum of an
in?ite collection of zeros is zero. Yourargument depends on
justifying the step of introducing a pointwisetopology and
using it to answer the original question, while my
argumentdepends on no such arti?e.> Reply 3> ------->
Consider the same sequence of functions {a_n} de?ed for Reply
2, but> let us use the discrete topology on this sequence. With
this topology,> the functions converge to a function f if after
some point, all the a_n> are equal to f. Thus, using this
topology, the {a_n} do not converge.Again, I dont see that
this argument has anything to do with thequestion that was
asked.> Thus, each of the replies is correct depending on how
you de?e the> convergence. Since the question asks, how many
balls, it seems to me> it is looking at the topology described
for Reply 1. So in this case,> I would say an in?ite number.
If the question were which balls,> that would indicate the
topology for Reply 2, and then I would say no> balls.And this
is strong evidence that there is something wrong in
yourreasoning. If you know which balls, then you
automatically know howmany balls. Every set has a
cardinality. If your reasoning leads toinconsistent answers,
then your reasoning is wrong.-- Dave SeamanJudge Yohns
mistakes revealed in Mumia Abu-Jamal
ruling.
And what if the numbering fades so that
all appear as blank white balls?> There are various versions
of this. I give three possible solutions atthe> end. Please
comment. In?itely many balls, each numbered (#1,#2,#3, etc.)
are to be placedinto> a bucket, ten at a time, by the scheme
given below. Immediately aftereach> group of ten are placed in
the bucket, one is removed and discarded. The> process is as
described below. 11am: Balls #1 - #10 placed into the bucket.
Ball #1 is removed> and discarded. 11:30am: Balls #11-#20
placed into the bucket. Ball #2 removed and> discarded.
11:45am: Balls #21-#30 placed into the bucket. Ball #3 removed
and> discarded. 11:52.5am: Balls #31-#40 placed into the
bucket. Ball #4 is removed and> discarded. Etc. The process
continues by halving the remaining time until 12 noon.
Thenten> are placed in and one is removed and discarded by the
above scheme. The> remaining time is halved again, etc. There
is a ?of activity just> prior to 12 noon. The process
does not continue at or beyond 12 noon. Question: How many
balls remain in the bucket at 12 noon? There are three common,
though not necessarily correct, replies. 1) In that the net
gain is +9 balls per event, and there are in?itely> many
events, there are in?itely remaining balls in the bucket. 2)
None remain. Any given ball, say ball #k, is removed and
discarded ata> speci? time prior to 12 noon. 3) The question
is meaningless as the process can not be extended to or> beyond
12 noon. Comments?> L
Get a black hole and try it out :-)--
Hauke Reddmann <:-EX8 For our chemistry workgroup,remove
>
There are various versions of this. I give three possible
solutions at the> end. Please comment.>In?itely many balls,
each numbered (#1,#2,#3, etc.) are to be placed into> a
bucket, ten at a time, by the scheme given below. Immediately
after each> group of ten are placed in the bucket, one is
removed and discarded. The> process is as described
below.>11am: Balls #1 - #10 placed into the bucket. Ball #1 is
removed> and discarded.>11:30am: Balls #11-#20 placed into the
bucket. Ball #2 removed and> discarded.>11:45am: Balls #21-#30
placed into the bucket. Ball #3 removed and>
discarded.>11:52.5am: Balls #31-#40 placed into the bucket.
Ball #4 is removed and> discarded.>Etc.>The process continues
by halving the remaining time until 12 noon. Then ten> are
placed in and one is removed and discarded by the above
scheme. The> remaining time is halved again, etc. There is a
?of activity just> prior to 12 noon. The process does not
continue at or beyond 12 noon.>Question: How many balls remain
in the bucket at 12 noon?Ill-posed problem; Youre clearly not
modeling a physical process here, as (1) there arent in?itely
many balls, and (2) you cant perform theseactions at unbounded
speed. So the stuff about 12 noon and halving the time etc is
metaphor, and the underlying process seems to be forming a
sequence of ?ite sets of positive integers. Lets call the
n-th setA_n; it can be numerated as {n+1, n+2, ..., 10*n}. The
most usual limit notions for such a sequence are the elements
in in?itely many of the sets (lim sup) the elements in all
but a ?ite number of the sets (lim inf) and when these two
are equal, the limit.If you mean any of these, the answer is
that the limit is empty, asyou indicate in your alternative
2:> 2) None remain. Any given ball, say ball #k, is removed
and discarded> at a speci? time prior to 12 noon.
>There
are three common, though not necessarily correct, replies.1)
In that the net gain is +9 balls per event, and there are
in?itely>many events, there are in?itely remaining balls in
the bucket.I would say this assumes, without justi?ation, a
sort of continuitycondition as t -> noon, which is invalid. If
n(t) is the numberremaining at time t, why should the limit of
n(t) as t -> noon equaln(noon)?>2) None remain. Any given
ball, say ball #k, is removed and discarded at a>speci? time
prior to 12 noon.Correct.>3) The question is meaningless as the
process can not be extended to or>beyond 12 noon.Not physically
of course, but ideally it makes sense. There is noquestion that
t = noon happens. So the guy removing the balls has towork
pretty fast :-)--Lynn
> >There are three common, though not
necessarily correct, replies.>1) In that the net gain is +9
balls per event, and there are in?itely>many events, there
are in?itely remaining balls in the bucket.>I would say this
assumes, without justi?ation, a sort of continuity> condition
as t -> noon, which is invalid. If n(t) is the number>
remaining at time t, why should the limit of n(t) as t -> noon
equal> n(noon)?>>2) None remain. Any given ball, say ball #k,
is removed and discarded at a>speci? time prior to 12
noon.>Correct.> >3) The question is meaningless as the process
can not be extended to or>beyond 12 noon.>Not physically of
course, but ideally it makes sense. There is no> question that
t = noon happens. So the guy removing the balls has to> work
pretty fast :-)>--Lynn> Doesnt guy adding balls have to work
10 times as fast?
>3) The question is meaningless as the
process can not be extended to or>beyond 12 noon.>Not
physically of course, but ideally it makes sense. There is no>
question that t = noon happens. So the guy removing the balls
has to> work pretty fast :-)But they guy adding the balls
works ten times faster! Yet still theycome out
even.............Of course there is a variant:11am: Balls #1 -
#10 placed into the bucket. Ball #10 isremovedand
discarded.11:30am: Balls #11-#20 placed into the bucket. Ball
#20 removed anddiscarded.11:45am: Balls #21-#30 placed into
the bucket. Ball #30 removed anddiscarded.11:52.5am: Balls
#31-#40 placed into the bucket. Ball #40 removed
anddiscarded.Etc.-- G. A. Edgar
http://www.math.ohio-state.edu/~edgar/
But they guy adding
the balls works ten times faster! Yet still they>come out
even...>You have to pay that guy more than the other guy.
:-)--Lynn
>>But they guy adding the balls works ten times
faster! Yet still they>come out even...> > You have to pay
that guy more than the other guy. :-)>--Lynn>Depends on
whether you pay by the ball or by the minute...Wait, both ways
they get the same pay!-- G. A. Edgar
http://www.math.ohio-state.edu/~edgar/
 >I am in the
Statistical Analysis Department of an HMO. Our CFO asked>us if
we could do some completion tables to better project
claim>dollars that have been incurred but not paid (IBNR) or
even havent>been incurred yet. Would this be similar to
Mortality tables. What>advice and instruction would you start
with for this project? Any>information would be greatly
appreciated! IBNR is commonly not, incurred but not paid,
but rather incurred butnot> reported. This normally has two
components: Claims that have been incurred (the occurrence that
gives rise to theclaim> has happened), but the claim has not
yet been reported to the insurancecompany> (or HMO) (this is
soemtimes called pure IBNR), and Claims that have been
reported, but for which the current estimate ofthe> value of
the claim is not equal to what the ?al ultimate cost of
theclaim> will be (sometimes called IBNER for incurred but
not enough reported). You have to be very careful about
terminology here, as practices vary, andnot> everyone
recognizes that their use of terms is not standard.>mortality>
tables. A common way to estimate IBNR is to arrange your
historical data intocertain> triangular arrays and complete
the square.Called claim triangles.> If someone has done a
similar> project at your company in the past, imitate what
they did with updateddata. Otherwise, you need the advice of
an actuary. If there are no actuariesin> your company, get
advice from a consultant.Go ahead and hire a consultant
anyway. But hire him (or her) to set up thesystem for you to
analyze claim patterns, not to calculate the reserves foryou.
You could call AutoZone in Memphis and see who they use for
theirbattery warranty claim reserves. (Do I have to insert a
disclaimer here?Well, just assume the appropriate disclaimer
is inserted.)Alternatively, consult with the actuary who
calculates your capitationrates. (They are set actuarially,
arent they? With medical costs rising12-25% a year (depending
on coverage) you cant afford to just follow themarket and hope
everyone else is right.)Jon Miller
I have done the following
calculation and wanted to knowwhether its correct or not.
:###task: expressing the term below through an in?ite
continuation.(x-1)^(-1) + (x+1)^(-1) = -(1-x)^(-1) + ( 1-(-x)
)^(-1)= -sum(x^k, k, 0, in?ity) + sum( (-x)^k, k, 0,
in?ity)= sum( (-x)^k - x^k, k, 0, in?ity)###Did I miss
something or did I do it right?Karl.
>I have done the
following calculation and wanted to know> whether its correct
or not. :> ###> task: expressing the term below through an
in?ite continuation.>(x-1)^(-1) + (x+1)^(-1) = -(1-x)^(-1) +
( 1-(-x) )^(-1)> = -sum(x^k, k, 0, in?ity) + sum( (-x)^k,
k, 0, in?ity)> = sum( (-x)^k - x^k, k, 0, in?ity)>
###>Did I miss something or did I do it right?>> Karl.> It is
ok for |x| < 1.But note that (-x)^k - x^k = 0 for even k and
(-x)^k - x^k = -2*x^k for odd kAn alternate approach might
start with (x-1)^(-1) + (x+1)^(-1) = 2*x/(x^2-1)
> It is ok
for |x| < 1.So, I forgot to tell for which ?x I can substitute
thesequence-formula.But why is it ok for |x| < 1 only?Why cant
I say, its ok for x =|= 1 and x =|= -1? > An alternate
approach might start with> (x-1)^(-1) + (x+1)^(-1) =
2*x/(x^2-1)Sorry that I didnt tell you before. But I had
given2*x/(x^2-1) as the original formula and decomposed itin
the fractions above.My original approach had been:2*x/(x^2-1)
= A*(x-1)^(-1) + B*(x+1)^(-1).And how does your alternate
approach look like?Karl.
Shuttle tragedy, I received these
3 posts, all recorded in
-------------------------Randi will test you when you
properly apply to be tested. Sign up
here:http://www.randi.org/research/challenge.html-------------
----Rich
ShewmakerCNoteWandaRust---------------------------------------
-----------------------------------------It really all
depends on the situation.-----------------ShanxSee You In Hell
My Friend.SomeoneGreg
Neill---------------------------------------------------------
-----------------------If ever I actually found myself in
that situation, Id hold it upright,with the intent of
attacking my assailants knife
hand.-----------------cliff86RustShanxNormDePloom-------------
--------------------------------------------------------------
-----If you ?found yourself in a knife ?ht, work with the
grip
that...
////////////////////////////////////////
//Look at the 1st post : http://tinyurl.com/nd52 Herc>Randi
will test you when you properly apply to be tested. Sign up
here:http://www.randi.org/research/challenge.html--Rich///////
///////////////////////////
Can you tell this post
is paranormal ?Check here where in sci.math people can guess
the author to the post!http://tinyurl.com/ygt8> Randi will
test you when you properly apply to be tested.> Sign up here:
http://www.randi.org/research/challenge.html
-----------------> Rich Shewmaker> CNote> Wanda> Rust>I pick
the ?st. But this isnt much of a test.To do this properly
would require 10 names, all of a****** thats all it takes to
prove paranormal ******Herc--www.StealthHostiing.com You rule
Truman. http://tinyurl.com/iky4 Hey Trueman...love the show.
YOU ARE the Truman I heard him. Very spooky! >Is the truman
living in Townsville? Ive been hearing stuff, yeah.Webmasters
help the TRUEman by joining www.theBanner.net Current:1
Goal:1000----------------------------------------------------
------------------------------
face, groaned, pushed hard,
and farted out the following message in> Can you tell this post
is paranormal ?Wait, wait... detecting... Yep! Youre right!
Paranormal! Right there! See, it says paranormal! Its been
proven. |-|erc, I bow down to your magni?ence.-- Mekkala,
Atheist #2148Atheism is ... the bed-rock of sanity in a world
of madness.--Emmett F. Fields
> Can you tell this post is
paranormal ? Wait, wait... detecting... Yep! Youre right!
Paranormal! Right there!> See, it says paranormal! Its been
proven. |-|erc, I bow down to your> magni?ence.>Just actually
click on the link this time to peruse the post. It has
alreadybeen demonstrated to have a unique property,
you_can_guess_the_authors_name.from 1,000 author options,
which you could, then its aONE IN 1000 COINCIDENCE or
paranormal cause.i.e. there is only 1 chance in 1000 its NOT
paranormal(once people demonstrate how many names it can be
spotted fromas a measure of the subjective attribute)Do you
know what 3 consecutive 1 in 1000 coincidences on the same day
makes?If you can ?d ONE reply to you that you can spot the
author from 100 postsconsistently then SHOW ME!Do you atleast
admit the post has a peculiar nature to
it????????????????????????click on itand dont set forwards
on
me
//////////////////////////////////////////Look
at the 1st post : http://tinyurl.com/nd52 Herc>Randi will test
you when you properly apply to be tested. Sign up
here:http://www.randi.org/research/challenge.html--Rich///////
///////////////////////////
face, groaned,
pushed hard, and farted out the following message in> >> Can
you tell this post is paranormal ?>> Wait, wait...
detecting... Yep! Youre right! Paranormal! Right>> there!
See, it says paranormal! Its been proven. |-|erc, I bow>>
down to your magni?ence.>Just actually click on the link this
time to peruse the post. It has> already been demonstrated to
have a unique property,> you_can_guess_the_authors_name. If
you can guess that RICH SHEWMAKER> could, then its a >ONE IN
1000 COINCIDENCE or paranormal cause.>i.e. there is only 1
chance in 1000 its NOT paranormal> (once people demonstrate
how many names it can be spotted from> as a measure of the
subjective attribute)No, no, I was agreeing with you! You
misunderstood me!Its *obviously* paranormal, especially since
the people trying to guess the author couldnt possibly have
noticed the great similarity between RICH SHOWMAKER and
RICH SHEWMAKER and guessed based on that... no, quite
obviously they guessed it using psychic powers. I fully agree,
|-|erc. Its stunning proof of magic in our time!-- Mekkala,
Atheist #2148Atheism is ... the bed-rock of sanity in a world
of madness.--Emmett F. Fields
> No, no, I was agreeing with
you! You misunderstood me! Its *obviously* paranormal,
especially since the people trying to> guess the author
couldnt possibly have noticed the great similarity> between
RICH SHOWMAKER and RICH SHEWMAKER and guessed based on>
that... no, quite obviously they guessed it using psychic
powers. I> fully agree, |-|erc. Its stunning proof of magic
in our time!>were actually getting somewhere here, you
basically agree the post hasa quality to it that lets anyone
guess the name right? RIGHT?then how come I got 3 posts just
like that in 1 day?try this one
:-------------------------------------------------------------
-------------------It really all depends on the
situation.-----------------ShanxSee You In Hell My
Friend.SomeoneGreg
Neill---------------------------------------------------------
-----------------------Herc
Look whos off their
meds again.---
Mr Ules is my other alias Herc Ules.Searched
Groups for proof of god author:mr author:ules from 2 Feb 2002
to 3 Feb 2002. Results1 - 7 of 7. Search took 1.57
seconds.Sorted by relevance Sort by dateproof of god 0202
2002http://www.skeptics.com.au/ ASS - we are a skeptic society
that test peoplewho claim to have paranormal ability Herc - Id
like to be tested, I have ...ping dick smith, tell him proof
of god and skeptics use carrot-- ? ???) ?~ proof of God-- ?
FFRRAAUUDDSSIVE ALLREADY SENT YOU A NOTARISED APPLICATION
PROOF OF GOD 0202 2002 guy atshop slipped in a free banana
milk, ...i PASSED a one in a million preliminary... Smith, you
owe me one handred grand Mr Randi, you owe me one million US
EVERYONE,saturday was 2 millenia, 2 year, 2 month, 2 day i
posted proof of god in uk ...1000 to one would do it pope,
xmen, willisee, anyone?... days break with jen hmmm, not one
homosapien thinks im worth more than 100$ a week,written 50
phds oh well, its a new dawn people, proof of god on 0202 2002
...man silverstreak is dumb... your question was one in 10
trillion :( hey silverstreak , silver - 2nd proof ofgod
posted on 0202 2002 homosapien2 --
<^>--www.StealthHostiing.com You rule Truman.
http://tinyurl.com/iky4 Hey Trueman...love the show. YOU ARE
the Truman I heard him. Very spooky! >Is the truman living in
Townsville? Ive been hearing stuff, yeah.Webmasters help the
TRUEman by joining www.theBanner.net Current:1
Goal:1000----------------------------------------------------
------------------------------X-Cise:
tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate:
admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Pose:
george_cox@btinternet.comX-Punge: Micro$oft
 at 09:24 PM,
mattinglyz@yahoo.com (Zac Mattingly) said:There is a
difference between justifying the curriculum and motivatinga
fourth grader.>My fourth graders are always asking why?A
certain amount of that is good.>Why do we need to learn that?A
certain amount of that is good.>Why is this important?A certain
amount of that is good. Especially if the examples you giveare
all different, rather than the same example in multiple
guises.>Thye want to know if there is a profession that does
not require>math?Kneecapper? Most professions require at least
arithmetic.-- Shmuel (Seymour J.) Metz, SysProg and JOATReply
to domain Patriot dot net user shmuel+news to contact me.
> My fourth
graders are always asking why? Why do we need to learn that?
Why is this important? Thye want to know if there is a
profession that does not require math?Depending on how
desperate you are:bright/rich/cool/higher-class and
stupid/poor/lower-class,and that the higher people are the
ones that tend toappreciate abstract subjects also without
applicationsbeing given; only the lower species of people
needs to knowabout applications ?st, before they can
understand anything.It might work, you never know.:-)Herman
Jurjus
> My fourth graders are always asking why? Why do we
need to learn> that? Why is this important?Because math keeps
you from getting cheated. If you cant add ormultiply, youll
get cheated at the cash register.If you cant do probablity,
youll get cheated all the time.If you cant understand
complex budgetary issues, youll get cheatedat the polls.And
so forth.Thomas
> If you cant understand complex budgetary
issues, youll get cheated> at the polls.And since no one
understands them, we all get cheated at the polls, all
thetime.Or do you mean complex budgetary issues like, If you
spend more than youtake in, your debt will grow to the point
where debt service kills you -- oryou devalue your currency
and zap the population.? I understand that one,and I still
get cheated at the polls.Jon Miller
> Or do you mean
complex budgetary issues like, If you spend more than you>
take in, your debt will grow to the point where debt service
kills you -- or> you devalue your currency and zap the
population.? I understand that one,> and I still get cheated
at the polls.An excellent example of someone not understanding
a complex budgetaryissue.Are you saying that a budget de?it
one year will necessarily resultin that horrible
conclusion?Most businesses use debt as a cash-?nagement
technique.Governments wisely do the same.What I ?d really
perverse is that huge budget de?its are thehallmark of
Republican administrations in this country. If you dontwant a
de?it, then the solution is simple: stop cutting
taxes.Thomas
> And since no one understands them, we all
get cheated at the polls, all the> time.I understand them.
Sorry.> Or do you mean complex budgetary issues like, If you
spend more than you> take in, your debt will grow to the
point where debt service kills you -- or> you devalue your
currency and zap the population.? I understand that one,>
and I still get cheated at the polls.No, I dont mean that.
YesX-Coriate: admin@interspeed.co.nzX-Ecrate:
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Micro$oft
>After much struggle, I ?ally reached page 31.
>AXIOM OF COMPREHENSION: For any condition P(x) on x there
exists a>set which contains exactly those elements x which
ful? this>condition.That would lead to Russells Paradox.
However, For any set A and anyproposition P, there is a set
{X /in A|P(x)} works, as does[1] Forany well-formed
proposition P, there is a set {X /in A|P(x)}, forappropriate
de?ition of well formed. Presumably the authors
wereexplaining why they did *not* use the axiom you quoted.[1]
Quinne used that-- Shmuel (Seymour J.) Metz, SysProg and
JOATReply to domain Patriot dot net user shmuel+news to
>
Dont you mean: given a set S, and a condition P(x) on x,
there> exist a set which contains exactly those elements x
->which belong> to S<- and ful? this condition?> >That is
one of the ZF axioms, but I dont think its called the
axiom>>of comprehension. > >Actually, I have seen this
called the Scheme of Comprehension, e.g., in Kunen.-- Stephen
J. Herschkorn herschko@rutcor.rutgers.edu
>>That is one of
the ZF axioms, but I dont think its called the axiom>>of
comprehension.> Actually, I have seen this called the Scheme
of Comprehension, e.g.,> in Kunen.Damn. And so the distinction
I imagined between Comprehension andSeparation goes up in
smoke. Good think I didnt bet anything onthat.
>That is
one of the ZF axioms, but I dont think its called the
axiom>of comprehension.>> > Actually, I have seen this
called the Scheme of Comprehension, e.g.,>> in Kunen.> Damn.
And so the distinction I imagined between Comprehension and>
Separation goes up in smoke. Good think I didnt bet anything
on> that.I have heard Separation called Bounded
Comprehension.-- Dave SeamanJudge Yohns mistakes revealed in
Mumia Abu-Jamal
ruling.
<0312071423430.10086-100000@gandalf.math.ukans.edu>


<0312090303010.19188-100000@gandalf.math.ukans.edu>
>of
comprehension.> Actually, I have seen this called the
Scheme of Comprehension, e.g.,> in Kunen.> Damn. And so the
distinction I imagined between Comprehension and>>
Separation goes up in smoke. Good think I didnt bet
anything on>> that. I have heard Separation called Bounded
Comprehension.Sometimes, Ive also heard separation called
either comprehension orbounded comprehension. On many
occasions, Ive been very close to thespeaker using those
terms. In his shoes, in fact.-- What Ive learned is that
[mathematicians are] the gatekeepers, andseem to have almost
absolute power when it comes to mathematics. -- James Harris,
on All I Really Ever Needed to Know I Learned in
/Ghostbusters/. 
<87fzfvnma8.fsf@becket.becket.net Is there a formulation
of set theory that does not have a pairing axiom?> Yes, ZF
with the pairing axiom left out, which is equivalent to ZF.
Huh? Are you saying that the pairing axiom can be proven from
the> other axioms of ZF?>Yes, from replacement and power
setand nulset from comprehensionand comprehension from
replacement.
> > Is there a formulation of set theory that
does not have a pairing axiom?> Yes, ZF with the pairing
axiom left out, which is equivalent to ZF.> Huh? Are you
saying that the pairing axiom can be proven from the> other
axioms of ZF?> Yes, from replacement and power set> and nulset
from comprehension> and comprehension from
replacement.(axiom-schema) is introduced...along with power
set...pairing isredundant, they advocate keeping it because it
is elementary andessential for the sequential development and
even for a scheme thatshuns replacement, pairing makes sense.
I think they are suggestingthat set theory even without
replacement is strong enough for almostall practical purposes.
What do you think?
> (axiom-schema) is introduced...along
with power set...pairing is> redundant, they advocate keeping
it because it is elementary and> essential for the sequential
development and even for a scheme that> shuns replacement,
pairing makes sense. I think they are suggesting> that set
theory even without replacement is strong enough for almost>
all practical purposes. What do you think?Oh, I see, Im used
to the shunning replacement version, because Imused to GBN
set theory. So I think of replacement+comprehension asjust
GBNs comprehension, but of course, that isnt quite right,
andthis is an example why.I believe that in GBN set theory,
pairing *is* required, is it not?Thomas
>How so?> The
pairing axiom is provable using replacement and power set.
This> is just a pointless technicality, of no interest.Im
afraid I still dont see it. Can you explain, since its so
easy?
 > Im afraid I still dont see it. Can you explain,
since its so > easy? You can ?d proofs on the net, in
homework collections and elsewhere.Just look for proof pairing
power set replacement. 


<874qwax0n3.fsf@becket.becket.net > How so?> The pairing
axiom is provable using replacement and power set. This> is
just a pointless technicality, of no interest. Im afraid I
still dont see it. Can you explain, since its so
tb@becket.becket.net
> Basically it goes like this:How do
you get the function from {nulset, {nulset}} to {a,b}?X-Cise:
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In
, on at
10:57 PM, Tim Smith 
said:>Wouldnt that be pretty much everyone except Erdos?No.
Consider the 2nd greatest Mathematician in Europe, Gausss
wastebasket.-- Shmuel (Seymour J.) Metz, SysProg and JOATReply
to domain Patriot dot net user shmuel+news to contact me. Donot
In sci.math, Arturo
Magidin:>>I know guys like Abel and Galois did
their best work early and then died, As opposed to dying and
->then<- doing their best work?>No, Im *not* going to voice
the obvious punchline here..... :-)-- #191,
ewill3@earthlink.netIts still legal to go .sigless.
> I
know guys like Abel and Galois did their best work early and
then died,> but can people give me some examples of
mathematicians who did their best> work in their early 20s
(say), then continued to work for a long time butIIRC, the
conventional wisdom is that mathematicians do their
most*creative* work in their 20s. So it would be interesting
to examinethe various sense of best work. E.g., was
Weierstrass work deeplycreative, even if it was very good in
other senses.Dale
> I know guys like Abel and Galois did
their best work early and then died,> but can people give
me some examples of mathematicians who did their best> work
in their early 20s (say), then continued to work for a long
time but>>Wouldnt that be pretty much everyone except
Erdos?Well, no; that would mean that, say, JSH is in your
category of did>their best work in their early 20s (say).
Im not sure how to ?d the>greatest element in an empty
set.Well, that would mean that JSH is an example of a
mathematician, and I dontthink either party is inclined to
be associated with the other :).>>As opposed to dying and
->then<- doing their best work?Hey, you can make a career
studying things like decay, and decompositions...Theres
Cholesky decomposition, and then theres Cholesky
decomposition! -- Erick
>>I know guys like Abel and Galois
did their best work early and then died,>>As opposed to dying
and ->then<- doing their best work?Hey, you can make a career
studying things like decay, and decompositions...Checking the
index of _Calculus of Elementary Functions_ byAbelson, Fellman,
and Rudolph (Harcourt, Brace and World, 1970),I see that
despite Hal Abelsons best efforts, we did not manageto slip
growth-and-decay theory past the copyeditors and into the
text. Tant pis.Lee RudolphX-Cise:
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In
,
on>Is this an acceptable proof?It might get marked down for
lack of elegance. Its certainly not theshortest or clearest
proof. But in most circles it is correct.-- Shmuel (Seymour
J.) Metz, SysProg and JOATReply to domain Patriot dot net user
shmuel+news to contact me. Donot reply to
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kramsay@aol.com (KRamsay) said:>Conesetters remark was in
reply to David Ullrich, who said that the>analytic
continuation construction produced a unique
Riemann>surface.Which it does.>not even independent of
homotopy.?>Note that if something (like the function element
reached by>continuing along a path which depends on the
homotopy class of the>path), it follows logically that also it
depends on the path.uniqueness. What you get depends on the
path. What makes theconstruction unique is precisely the fact
that it does not depend onthe path within the homotopy class.
You have to read his depends incontext.>Shmuel Metz seems to
enjoy saying no to people. :-)He also enjoys saying yes ;-)--
Shmuel (Seymour J.) Metz, SysProg and JOATReply to domain
Patriot dot net user shmuel+news to contact me. Donot reply to
<87llpozxni.fsf@phiwumbda.org> 
X-Cise:
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 at 01:28 PM,
George Greene  said:>That is
not only not interesting, it is the opposite of reasonable.>If
the object is itself something as trivial and structureLESS as
a>point, to begin with, asking ANYbody to think of it as
something>BIGGER (e.g., the collection of all arrows ending at
it) is simply>RIDICULOUS.The duality principal in Projective
Geometry was quite productive. Itis RIDICULOUS to pretend
otherwise.-- Shmuel (Seymour J.) Metz, SysProg and JOATReply
to domain Patriot dot net user shmuel+news to contact me.



X-Cise:
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 at 01:07 PM,
George Greene  said:>but my
point is simply that grownups know that sets>are just
irrelevant period. Thats a rather childish perspective. Its
comparable to saying thatonly children use GBN and adults use
ZFC. The fact that you prefer itdoes not make it more adult
than other approaches.-- Shmuel (Seymour J.) Metz, SysProg and
JOATReply to domain Patriot dot net user shmuel+news to contact
I hate having
to strongly agree and weakly disagree at the same time.I
strongly agree with the following: : anyway its true that
when there are a bunch of more or less : equivalent viewpoints
from which to understand a subject i often like : to seize on
one of them and push it as far as possibleThe trick, of
course, is ?uring out *which* of these viewpoints*merits* the
push. The fact that they really are equivalent is precisely
what makes that ?uring *hard*, and entitles you to feel
better about your teaching skills, if you can convince people
that thisone viewpoint is more equivalent than others.In
further agreement: : ... whereas i like my philosophy because
i think it makes : math seem like a game for ordinary mortals:
once you learn the grand : equivalences between different
viewpoints, thats basically an excuse : for going back to
always seeing things from your old favorite : viewpoint,
secure in the knowledge that its really equivalent to all :
those other viewpoints.I completely endorse this viewpoint.I
did, after all, stress the relevance, early on, of the
factthat from one viewpoint, ANY n-dimensional vector space
is reallythe ordered n-tuples over its ?ld, and ANY group
is reallya permutation group.That was the strong
agreement.The weak disagreement is with this: (in this case
the all groups/all categories are concrete viewpoint). This
needs to be contrasted with the two examples *I* gave.N-tuples
of ?ld-elements are in some sense smaller and simplerthan some
other things that could be vectors. Permutation groupsin some
sense forget a lot of implementation detail of the
othergroups they can be isomorphic to. They are simpler
subspaces ofthe overall class, even though everything in the
class is isomorphic to one.Concreteness simply does not
have this property. It is arguablyMORE detailed and MORE hairy
than any absrtact counterparts. Thespace of concrete groups or
concrete categories is not fundamentallysimpler at ANY level,
than any bigger richer space that includes more abstractions.
Saying you can represent any group as a concrete groupis
going in the OPPOSITE direction from saying you can
representany group as a permutation group.We in some sense
know a reasonable, right smaller space of
representativesfor groups and vector spaces. The question
of a prototype for categoriesgets much more complex,
though, for the sole and simple reason that categoryin
general is a suf?iently MINIMALLY-de?ed kind of structure
that A WIDEVARIETY OF THINGS fall under it. In particular,
every group is ALREADY a category already.But it only has 1
object. If we are going to look for prototypes,if we are going
to have a primary among nominees for election to a house
ofrepresentatives of categories, then maybe we need to look
SEPARATELYfor prototypes of a) categories with a ?ite number
of objects (butlarger than 1, since weve solved THAT case),
and b) cateogories withan in?ite number of objects.
>
Actually category theory started out as a way to de?e
``natural > transformation [There is a quote by Mac Lane to
this effect. I dont > have the precise reference handy.]...>
The fundamental importance of naturality in homology and >
homotopy is impossible to overstate.Well,if the path category
in the Euclidean plane isprototypical, what are the simplest
natural transformationsthat are most directly relevant to
it?
PLEASE READ THIS POST UNTIL ITS LAST WORD, BEFORE YOU
REPLY, THANK YOU.Let us check these lists.P(2) =
{{},{0},{1},{0,1}} = 2^2 = 4and also can be represented
as:00011011P(3) = {{},{0},{1},{2},{0,1},{0,2},{1,2},{0,1,2}} =
2^3 = 8and also can be represented
as:000001010011100101110111Let us call any 0,1 list,
combinations list.When we use Cantors Diagonalization
function on the combinations listof 2^power_value and get some
output result, we ?d that this resultis already somewhere in
the list.The formula that gives us the number of combinations
, which are outof the range of Cantors Diagonalization
function, is:2^n - nCombinations are ?st of all structural
changes, based on at leasttwo parameters:a)The number of
different notations.b)The number of places that have been
given to permute thesenotations.We get our list of in?itely
many places, by using the ZF Axiom o??ity induction, on the
left side of our combinations list (bychanging
power_value).When we have in?itely many places to combine our
two differentnotations, then the number of combinations, which
are out of the rangeof Cantors Diagonalization function
is:2^aleph0 - aleph0 = E where by E we mean that there are E
possiblecombinations, which are out of the range of Cantors
Diagonalizationfunction, where one of these combinations, is
Cantors Diagonalizationfunction result.Therefore Cantors
Diagonalization function result is not a
newcombination.Because the aleph0 long Cantors
Diagonalization function resultcannot cover the 2^aleph0 list,
it means that 2^aleph0 > aleph0, butwe can de?e a map between
any unique combination and some naturalnumber, therefore
2^aleph0 = aleph0. Therefore (2^aleph0 >= aleph0) = {}, and we
have a proof saying thatBoolean Logic cannot deal with
in?itely many objects. Doron Shadmi
> 2^aleph0 - aleph0 =
E where by E we mean that there are E possible> combinations,
which are out of the range of Cantors Diagonalization>
function, where one of these combinations, is Cantors
Diagonalization> function result.> Therefore Cantors
Diagonalization function result is not a new> combination.You
dont seem to understand what the theorem says.> Because the
aleph0 long Cantors Diagonalization function result> cannot
cover the 2^aleph0 list, it means that 2^aleph0 > aleph0, but>
we can de?e a map between any unique combination and some
natural> number, therefore 2^aleph0 = aleph0. Cantors theorem
says that if X is any set, then |X| < 2^|X|. Inparticular, if X
happens to be the set of natural numbers, then thisreduces to
aleph_0 < 2^aleph_0. To show that it is enough to show thatif
f: X -> 2^X is any injection from a set to its power set, then
f isnot a surjection.Notice that in the case X = N we are
talking about an injection f: N ->2^N, which means the domain
of the function is N, not 2^N. In short,there is no such thing
as a 2^aleph_0 list that has anything to do withthe proof.
The proof only concerns aleph_0 lists.> Therefore (2^aleph0 >=
aleph0) = {}, and we have a proof saying that> Boolean Logic
cannot deal with in?itely many objects.Wrong. In fact, the
proof of Cantors theorem works precisely the samewhether the
set X happens to be ?ite or in?ite.-- Dave SeamanJudge
Yohns mistakes revealed in Mumia Abu-Jamal
ruling.Actually ?ding paranormal would put the
company out of business. Thats possible i guess....but more
likely *no one* can come up with the> goods..thats a simpler
explanation. Wouldnt all the gurus out there jump at the
chance to prove themselves ??> ... dont ya think all to bozos
claiming *powers* and milking people of> their money is a much
bigger business that than those investigating ?? - who> has
more to lose ?>could be both but who knows?Skeptic companies
actively promote the non investigation of paranormal
claims.The only people they test are already making steady
incomes or celebrities.Look at the millions of hate posts made
by skeptics, did you know alt.astrologyis called kook watcher
central. Here is Wally Anglesea, one of 100s of
devoutskeptics that ? off the prestige of Skeptic
companies that has plagued mein a half dozen paranormal
related newsgroups.Searched Groups for kook author:wally
author:anglesea. Results 1 - 10 of about 1,580.Up 100 on last
week.Herc
: The only people they test are already making
steady incomes orcelebrities.Hey netkook, I can understand
wanting people who make a steady income,but whyshould they
care about people who make
celebrities?
----------------------------------------------
------------------------------------> : The only people they
test are already making steady incomes or> celebrities. Hey
netkook, I can understand wanting people who make a steady
income,> but why> should they care about people who make
celebrities?what are you talking about? 90% of people in each
newsgroup here know meand Ive never heard of you, well not as
an alias anywayHerc
>Actually ?ding paranormal would put
the company out of business.> Thats possible i guess....but
more likely *no one* can come up with the>> goods..thats a
simpler explanation.>> Wouldnt all the gurus out there jump at
the chance to prove themselves ??>> ... dont ya think all to
bozos claiming *powers* and milking people of>> their money
is a much bigger business that than those investigating ?? -
who>> has more to lose ?>>could be both but who knows?Skeptic
companies actively promote the non investigation of paranormal
claims.>The only people they test are already making steady
incomes or celebrities.>Look at the millions of hate posts
made by skeptics, did you know alt.astrology>is called kook
watcher central. Here is Wally Anglesea, one of 100s of
devout>skeptics that ? off the prestige of Skeptic
companies that has plagued me>in a half dozen paranormal
related newsgroups.Hey, nutjob. I was actively posting to
usenet long before you got your?st ?puter.You came in ?g
your arms about with crap claims of paranormalpowers. Get back
on your meds.Searched Groups for kook author:wally
author:anglesea. Results 1 - 10 of about 1,580.Up 100 on last
week.For those that dont know yet, Herc is subject to a
restraining order.Hes unemployed, suffers a mental condition
(his own admission),cannot get laid which is unsurprising,
considering the kinds ofapproaches he makes to female posters
on usenet, and to cap it off, hethinks hes Truman, and we are
all part of the truman showMy purpose, and the purpose of
many skeptics apparently, is to be thenasty guys in the
script.-- Find out about Australias most dangerous Doomsday
Cult:http://users.bigpond.net.au/wanglese/pebble.htmYou cant
fool me, its turtles all the way down.
kook author:wally
author:anglesea. Results 1 - 10 of about 1,580.nutjob? you
didnt even increase your count.Stay out of paranormal
discussion forums with your abuse.Herc
Sonnyboy, dont you
even know what groups youre posting to?: kook author:wally
author:anglesea. Results 1 - 10 of about 1,580.:: nutjob? you
didnt even increase your count.:: Stay out of paranormal
discussion forums with your abuse.::
Herc:::
www.StealthHostiing.com You rule Truman.
http://tinyurl.com/iky4 Hey Trueman...love the show. YOU ARE
the Truman I heard him. Very spooky! >Is the truman living in
Townsville? Ive been hearing stuff, yeah.Webmasters help the
TRUEman by joining www.theBanner.net Current:1
Goal:1000----------------------------------------------------
------------------------------> Sonnyboy, dont you even know
what groups youre posting to?Ive spent months at each
separately on the same topic, here ishow it links
upsci.skeptic : paranormal claimsci.math : statistical
correlation requires validationrec.org.mensa : the proof is in
the form of a puzzlealt.atheism : proof of god, help get me off
the truman showHercthe proof is very obvious, George Bush
points a very painful satellite at my head 24/7,if you dont
follow up and give me some bene? of doubt I will suffer for
severalyears longer. once you can see you can *measure* the
statstic, and that noonecan *compete* against me getting
replies to give away the author, the paranormalclaim is a
sinch. 10% of Randis million to those who try to justify my
claim.
>>Actually ?ding paranormal would put the company
out of business. > Thats possible i guess....but more likely
*no one* can come up with the> goods..thats a simpler
explanation.> Wouldnt all the gurus out there jump at the
chance to prove themselves??> ... dont ya think all to bozos
claiming *powers* and milking people of> their money is a much
bigger business that than those investigating ?? -who> has
more to lose ?>could be both but who knows? Skeptic companies
actively promote the non investigation of
paranormalclaims.Skeptic companies? WTF? Can you name 10?> The
only people they test are already making steady incomes
orcelebrities.I would, because theyre cheating people the
most.> Look at the millions of hate posts made by skeptics,
did you knowalt.astrology> is called kook watcher
central.Makes sense.> Here is Wally Anglesea, one of 100s of
devout> skeptics that ? off the prestige of Skeptic
companies that hasplagued me> in a half dozen paranormal
related newsgroups.Skeptic companies. What is their product?
Who is their market?> Searched Groups for kook author:wally
author:anglesea. Results 1 - 10of about 1,580. Up 100 on last
week.Must be lots of kooks to respond to.Denis
Loubetdloubet@io.comhttp://www.io.com/~dloubet
------------
--------------------------------------------------------------
--------> Skeptic companies actively promote the non
investigation of paranormal> claims. Skeptic companies? WTF?
Can you name 10?Help support the JREF through donations,
grants, gifts and memberships. Click here to learn
more.Australian Skeptics Inc.To subscribe see: Online Store
and How To JoinASKE The annual fee, currently 8, (10 for
overseas members) is renewable on January 1st eachyearThats
the 3 that offer prizesHercstrange all 3 out of 3 run
businesses from it, must be a coincidence??
> Anyone know
why Grad Schools will not accept your application unless> you
have a Bachelors? Is it not possible to have the required>
knowledge and no degree? Is it so very hard to verify that
ones claim> of knowledge. some reasons: 1. it invalidates the
whole college education schtick.> 2. lack of institutional
admissions exams.> 3. the general population lacks the
discipline to pull off such> thing as self-education. now to
address your latter question. it woulnt be very hard to
verify knowledge, but it is politically> incorrect and
somewhat costly and time-consuming.Which is why grad schools
cant be bothered unless you indicate that you arespecial.
You dont get special consideration unless youre a
specialperson.Jon Miller
 >I have never reviewed material
for exams when I took the>course. I like to say that a test
which can be studied for is not worth> giving (or taking).Been
to a medical doctor lately? Im glad mine studied for their
exams.Jon Miller
> >I have never reviewed material for
exams when I took the> >course.> I like to say that a test
which can be studied for is not worth> giving (or
taking).>Been to a medical doctor lately? Im glad mine
studied for their exams.What is the graduate with the lowest
GPA in a Medical School classcalled?Doctor.A license to
practice medicine isnt meaningful until the doctor doesyears
of clinical work supervised by nurses (re green lieutenants
andseargents) and senior doctors. The sciences require a whole
lot o?me - and that is only foreplay to practicing
professionally. There are savants, and thats ?e. If you have
to read the books,then reading the books isnt nearly enough.--
Uncle Alhttp://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for
children and most mammals)Quis custodiet ipsos custodes? The
Net!
> All degrees, credentials, etc., should be by
comprehensive> examinations ALONE. Anything else is
anti-educational.Written by someone with a degree which is a
result of a long paper.Jon Miller
> And money is surely not
the reason to print more diplomasWell, its not like printing
more of them will devalue them.Jon Miller
> >> And money is
surely not the reason to print more diplomas>Well, its not
like printing more of them will devalue them.Actually, it IS
like that. Its exactly what weve beenexperiencing. Afterall
_something_ devalued the diploma, andif it wasnt
proliferation, what do you think it was?Bart
 > Or have
they put in more? If you want to understand> mathematics, the
books you should read are not of that> type. There are few
good books; the market for them> is very poor. Students do not
want courses which will> make them think. Some suggestions
please (for a good, well rounded, general course of self>
study)!!Buy one or more of Ian Stewarts books, _The Problems
of Mathematics_ and_Another Fine Math Youve Got Me Into_
springing to mind. Just startreading them, work all the
problems. Read slow, and think of additionalquestions. Try to
solve the additional questions. Then start with
thereferences.This has the advantage that the parts are
independent, and if somethingisnt interesting, you can just
skip it, and if it is, you can dig as deepas you want.Also,
the Columns section of MAA Online http://www.maa.org/. Again,
this isjust light reading unless you work on it yourself and
refer to thereferences.Of course, if you need to get some
papers out because theres a tenurecommittee meeting coming
up, this is probably the wrong way to go about it.Jon
Miller
 > Yes, but are there many examples of people who
have been admitted with> no BA at all?> It seems likely to me
that math departments would be more tolerant of> degree
de?iencies than most other departments, but I wonder if
anyone> has some concrete examples. When I began graduate
school in math at Harvard in 1970, one of the> other ?st-year
graduate students (a Putnam Fellow, Alan Beale) had> come there
after 3 years as an undergraduate without waiting to ?ish> a
bachelors degree. He left Harvard after one year, and I do
not know> what happened to him...Which illustrates (but
doesnt prove) one of the reasons for requiring aBA/BS. Proof
that you can ?ish something.Employers want one for the same
reason. And for employers, it stillindicates some pro?iency
in reading and writing.Jon Miller
> When I began graduate
school in math at Harvard in 1970, one of the>> other
?st-year graduate students (a Putnam Fellow, Alan Beale)
had>> come there after 3 years as an undergraduate without
waiting to ?ish>> a bachelors degree. He left Harvard after
one year, and I do not know>> what happened to him...Which
illustrates (but doesnt prove) one of the reasons for
requiring a>BA/BS. Proof that you can ?ish
something.Employers want one for the same reason. And for
employers, it still>indicates some pro?iency in reading and
writing.>Perhaps Mr. Beale is working with Bill Gates at
Microsoft? I sometimes wonderif Mr. Gates could still get a
job at his own company? Probably not. Makes sense to me.
rich
> Anyone know why Grad Schools will not accept your
application unless> you have a Bachelors? Is it not possible
to have the required> knowledge and no degree? Is it so very
hard to verify that ones claim> of knowledge.>What is wrong
with buying the College books, reading them at home at> your
leisure and then sending in the Grad School Application? That
way> you avoid having to sit in class and watch the professors
make painful> mistakes -- book-writers gave gone over things
multi times and weeded> out most errors!It isnt necessary to
have a bachelors degree to enter graduateschool. A former
colleague of mine had a Ph.D. in math from theUniversity of
Chicago but had no bachelors degree nor even a highschool
diploma. He went straight from his junior year of high
schoolinto the U. of C., moved from their undergrad program
(without?ishing) into the grad program where he completed his
Ph.D. at theage of 21!Id say that if you have the stuff you
can get a graduate degreewithout having a bachelors degree.
Youll need to convince thegraduate faculty that you really do
have the stuff, not such an easytask, unfortunately. Though
plenty of inept students get bachelorsdegrees professors can
and do write recommendations that have forceand meaning and
allow graduate school admission committees to know thetrue
ability of an applicant. Id say your best bet is to ?d
aUniversity near you that has a math faculty person whom you
respect.Then take a graduate level course or two from that
person to establisha relationship, explain your goal to
him/her, and go from there.Good luck!
>Even then, I am,
in general, against this. That is, I would>rather not give
them credit hours toward degree completion,>but I am
perfectly happy to give them credit as having >prerequisites
for higher level courses.>>If you give ANY student who sits
through hours of classes,>>hands in homework, and takes tests
credit for something,>>you should be willing to give anyone
who knows the material>>the same credit. >Im not sure what my
own position is on these questions, but I>note that the
conclusion to be drawn depends on the choice of>axioms
used.>Axiom A : The purpose of awarding a college degree is to
indicate the >attainment of a certain level of
understanding/knowledge/enlightenment.>Corollaries:> 1.
College degrees should be withdrawn if a recipient forgets
what> has been learned.I would not go THAT far, but I object
to the use of degreesand other such credentials unless they
can provide reasonableassurance that the person has a good
share of the importantknowledge and ability.> 2. There is no
reason not to award a college degree to a person who> has just
received the comparable degree from another institution.>(I
think HR starts from this axiom to derive his position.)Unless
there is something to be gained by attaining multipledegrees,
what is the point? But I also stated that theknowledge and
ability needs to be demonstrated; see the aboveto see my
questioning whether the attainment of a degree isgood
evidence.>Axiom B: The purpose of awarding a college degree is
to indicate the >completion of a certain collection of tasks
(or jumping of certain hurdles).>Corollaries:> 1. Possession
of a college degree cannot be assumed to imply that the>
degree-holder has actually learned anything.> 2. Those who
have mastered a subject at a certain level may be denied> a
degree until they have later completed work at a lower
level.>(I believe I have seen others in this thread begin with
this axiom.)-- This address is for information only. I do not
claim that these viewsare those of the Statistics Department
or of Purdue University.Herman Rubin, Department of
Statistics, Purdue University
> 2. There is no reason not
to award a college degree to a person who> has just received
the comparable degree from another institution. >(I think HR
starts from this axiom to derive his position.) Unless there
is something to be gained by attaining multiple> degrees, what
is the point?As long as a Harvard degree carries more weight
than a Purdue degree, itsworthwhile to make a cost-free
exchange if possible. (A real-lifeapplication of arbitrage
theory?)Jon Miller
> I would not go THAT far, but I object
to the use of degrees> and other such credentials unless they
can provide reasonable> assurance that the person has a good
share of the important> knowledge and ability.I know of no
graduate program which relies on a BA alone as itsadmissions
criterion. So indeed, they all work pretty hard to makesure
one has gotten that knowledge and ability.
>>Anyone know
why Grad Schools will not accept your application
unless>>you have a Bachelors? Is it not possible to have
the required>>knowledge and no degree? Is it so very hard to
verify that ones claim>>of knowledge.>>What is wrong with
buying the College books, reading them at home at>>your
leisure and then sending in the Grad School Application? That
way>Just a thought here is that the student, to earn a
Bachelors degree, >spends four or ?e years in pretty
intensive study. Theres always >homework to do, ?ish it up
for one class and theres always another. >Always pushing
against deadlines, staying at home to study while his
>friends go out to play, bringing homework to work to do
during breaks...>>Why? There is no point for a good student in
most of the>>trivial homework assigned; a good student, left
alone, will>>do too many problems anyhow, and should rarely do
any easy>>problems. And why push against deadlines? One does
not>>really learn on a schedule, especially concepts. This
is>>why the schools do not teach or grade on concepts, only
on>>memorization and routine, which are not really
important.>Im refering simply to the amount of time spent
with the material. The >student cannot cover a great deal of
material unless he spends a great >deal of time with it. If
the school-less student were to study it at his >leisure, how
old would he be by the time hes ready to enter grad school?At
age 12, I encountered an algebra text. I tested out ofalgebra,
and while taking a good plane geometry course andother high
school courses, studied mathematics, not tooef?iently. Within
one year, I would have been close toready for graduate school
in mathematics. With the betterbooks today, and very little
guidance, I would have beenready for todays graduate schools.
And this includedbeing able to do the computational material.I
did take one worthwhile undergraduate course, which BTWis not
given any more. It is true that some of the graduatecourses I
took, some before graduating high school, would now be
undergraduate courses, but I certainly would not have had any
problems in reading the material on my own ina short time. The
professors did add some insight; that iswhat one can get from
scholars who understand the subject.As for statistics, in
which I am reasonably well known, Ihave never had even one
course. The same holds in set theory.With a program, someone
with the ability to understand shouldbe able to learn more
mathematics than is taught in good universities in two years.
Only the upper division theorycourses are really important,
anyhow.-- This address is for information only. I do not claim
that these viewsare those of the Statistics Department or of
Purdue University.Herman Rubin, Department of Statistics,
Purdue University
>$30lk@odds.stat.purdue.edu:>> The degree
should require the knowledge of 120 credit>> hours. How it is
obtained should be irrelevant. If >> you think that sitting
through classes results in this,>> you are sadly mistaken.
Give a surprise exam in just>> about anything to a student who
has credit for it, and>> you will know what I mean.>> No, you
should examine him, as you should examine those>> students you
have passed through those 120 credits,>> usually with no
understanding.>Cynicism is learned helplessness. Please get
out of education>as quickly as possible.Get the educationists
out; those who have tried to educate,rather than to teach what
machines can do, and which willbe forgotten anyhow, are the few
who should remain.-- This address is for information only. I do
not claim that these viewsare those of the Statistics
Department or of Purdue University.Herman Rubin, Department of
Statistics, Purdue University
>> If the student is in this
situation, it is questionable>> whether that person can ever
do decent graduate work.>> Unfortunately, the teachers in
the elementary and high>> schools, who do not understand any
mathematics, but just>> computation, have fostered this type
of student.>Some teachers in elementary and high schools do
*not* have this>lamentable property.Fortunately, no procedure
can guarantee ONLY bad results.But are they even allowed to
teach concepts? And willtheir efforts be largely undone by
those others.-- This address is for information only. I do not
claim that these viewsare those of the Statistics Department or
of Purdue University.Herman Rubin, Department of Statistics,
Purdue University
>> Anyone know why Grad Schools will not
accept your application unless>> you have a Bachelors? Is it
not possible to have the required>> knowledge and no degree?
Is it so very hard to verify that ones claim>> of
knowledge.>> What is wrong with buying the College books,
reading them at home at>> your leisure and then sending in the
Grad School Application? That way>> you avoid having to sit in
class and watch the professors make painful>> mistakes --
book-writers gave gone over things multi times and weeded>>
out most errors!>Getting a bachelors degree is a bit of
work;>buying the College books, reading them at home at your
leisure, isnt.It is not work that matters, but being able
to think.Reading the books is not enough; understanding them
iswhat is needed. Memorizing the textbook should not beenough
to pass a decent course, but alas, too many do.It is hard to
verify, but almost as hard (and sometimesharder) to verify for
those who do get college degrees.>A bachelors degree, besides
being a claim of knowledge,>is also a claim of achievment.What
achievement? Taking a set of irrelevant and badlytaught
courses and getting grades in them? Learning tostudy for exams
and forget the material afterward?>It represents keeping a
commitment for a number of years.>Thats the ability that the
Grad Schools are most interested in.This might be what the
administrators of the graduateschools are interested in; it is
not what good faculty orgood departments care about. I have
been on the facultyside of this for a long time.-- This
address is for information only. I do not claim that these
viewsare those of the Statistics Department or of Purdue
University.Herman Rubin, Department of Statistics, Purdue
University
> achievement> What achievement? Taking a set
of irrelevant and badly> taught courses and getting grades in
them? Learning to> study for exams and forget the material
afterward?Learning to show up for work every day and eat up
the nonsense the bossdishes out.An important achievement.Jon
Miller
> ..................>Very nicely said. Now, since
we had a debate in our Faculty Senate on this
just>yesterday, where do you stand on giving credit for
life experience (the>wording varies from place to
place)Life experience is irrelevant. What is relevant is
what >academic material is known and can be used. I suggest
that,>instead of using grades, etc., for admission to
graduate>school, we use a long examination with no multiple
choice,>and few short answer, questions.>Would depend on what
the criteria were - on what sort of life >>experience counted
as replacement for what courses.>Like a person with a lot of
experience as a computer programmer>>might reasonably be given
credit for intro programming classes,>>etc. With that, possibly
credit for even some graduate courses.How does the grad program
determine that the life experienceincludes the ability to
program? I knew a lot of programmers;just because their title
had that word did not mean thatthey could do the work. If your
grad study is going to bein computer science, then a life
experience of programmingshould never be used to skip
classes; remember, were talkingabout degree study and the
classes that could possibly be skippedare undergrad intros. In
some cases, I can see where those undergrad intro courses might
be a requirement for the lifeexperienced person because s/he
didnt work with that particularlanguage or numerical recipe
or...Now, if the degree program is in a hard science which has
a requirementof the FOOBAR programming language _and_ the life
experience of thestudent was based on programming using the
FOOBAR language, thenthe requirement of setting in class
learning how to set up adata structure in that language is
probably a waste of that studentstime. However, the student
has to demonstrate an ability of usingthe FOOBAR language and
not just with writing a baby problem. Thereason for the
programming language requirement is because its goingto be
used as a tool for the hard science study./BAH
>> >>My
agenda is to question absolute agreement over matters which at
the>>end of the day are just theories. That is where a lecture
could get>>interesting -- when the professor states the
standard theory as stated>>in the text, then goes on to sow
doubts on its being true based on his>>original thinking.>> >>
Which has absolutely nothing to do with whether or not
undergraduate>> lectures are frequently errorfree. >> >Yes,
but it does address the issue of the lecture vs.
textbook.Whoop de doo. People can also shout epithets at
others to address the topicof racism, but that doesnt mean
that theyre helping.Doug
> >>Cynicism is learned
helplessness. >Thats snappy, to the point, and meaningless.
You should write bumper> stickers.That wasnt the intent at
all. This is the de?itionof cynicism (the sort displayed by
HR, not the the ancientGreek variety.) One acquires such an
attitude, say, aboutgovernment, after having been continuously
beaten by it, as a defense mechanism. One learns to _expect_
the worstin order to not have ones hopes dashed. Some people
think cynics are cute. I think they need help.They sure
shouldnt be passing on their dispair to students.Bart
>
Axiom A : The purpose of awarding a college degree is to
indicate the > attainment of a certain level of
understanding/knowledge/enlightenment.>Corollaries:> 1.
College degrees should be withdrawn if a recipient forgets
what> has been learned.This corrolary does not follow from
Axiom A. No amount of forgettingcould change the fact that one
has attained a certain level ofunderstanding. Just as a
mountain climber who later becomes disabledhas still climbed a
given mountain. > 2. There is no reason not to award a college
degree to a person who> has just received the comparable
degree from another institution.This corrolary follows only if
one hinges upon a certain ambiguity inAxiom A. Axiom A should
really be phrased The purpose of a collegedegree at
institution foo is to indicate the attainment, at foo, of
acertain level of ... In otherwords, foo certi?s that the
degree inquestion has been earned at foo. Other schools do not
need to awardnew degrees, though they do recognize the degree,
and at their school,treat degree holders similarly even if the
degree was not locallyearned. (Which is not universal, however;
Cambridge is famous for notletting degree holders from other
schools wear their proper academicdress.) > Axiom B: The
purpose of awarding a college degree is to indicate the >
completion of a certain collection of tasks (or jumping of
certain hurdles).>Corollaries:> 1. Possession of a college
degree cannot be assumed to imply that the> degree-holder has
actually learned anything.This Corollary does not follow from
Axiom B; one of the tasks in thecollection may well be a
demonstration that the degree holder haslearned something.> 2.
Those who have mastered a subject at a certain level may be
denied> a degree until they have later completed work at a
lower level.This Corollary does not follow; it assumes a
single list of tasks,when in fact, there is considerable
variability in the tasks (whilenot complete variability), so
that it is often the *number* of taskscompleted that matters,
and a higher task can be substituted for alower
one.Thomas
I am teaching myself Applied Combinatorics by
Alan Tucker, and I cameacross 2 problems on page 246 that I
cant ?ure out...1) Find a generating function for a_r, the
number of ways n distinct dicecan show a sum of r.2) Find a
generating function for a_r, the number of ways a roll of
sixdistinct dice can show a sum of r if : a) The ?st three
dice are odd and the second three even. b) The ith die does
not show a value of i.Can someone solve these in detail?Note :
> I am teaching
myself Applied Combinatorics by Alan Tucker, and I came>
across 2 problems on page 246 that I cant ?ure out... 1)
Find a generating function for a_r, the number of ways n
distinct dice> can show a sum of
r.(x+x^2+x^3+x^4+x^5+x^6)^neach role is like a choice of
1,...,6, n roles... 2) Find a generating function for a_r, the
number of ways a roll of six> distinct dice can show a sum of r
if :> a) The ?st three dice are odd and the second three
even.> b) The ith die does not show a value of i.Here is (a),
I wont spoil (b)(x+x^3+x^5)^3 . (x^2+x^4+x^6)^3First 3 roles,
you can get 1, 3 ,5, the next three 2,4,6> Can someone solve
these in detail?I dont know how much detail there is in my
answers, but anything more isjust being verbose. Note : This
is NOT for a classlook up generatingfunctionology (available
Steve
Thomas Bushnell, BSG says...>> > Again I am making a
simple point. For any formal system there is a>> > recursive
ordinal that is the limit of the recursive ordinals>> >
de?able within that system.>> > Ok, for ZFC, what is the
ordinal in question?>> >> If I could answer that question I
would be up for the next Fields mdal in>> mathematics. In>>
my youth I did try for a while.Ok, you didnt take my bait. I
will prove to you that there is no>such last ordinal.Suppose K
is the last ordinal de?able within ZFC.Paul misspoke. Rather
than talking about the largestordinal de?able within ZFC, you
should instead talkabout the smallest ordinal that is *not*
de?ablein ZFC.There are only countably many formulas in ZFC,
and sothere are only countably many de?able ordinals.
Butthere are uncountably many ordinals. So there must besome
ordinal that is not de?able in ZFC.>But what do you mean by a
recursive ordinal?Heres one de?ition: A recursive ordinal
is an ordinal that canbe coded using the natural numbers. In
particular, alpha is arecursive ordinal if there is a countable
enumeration beta_0,beta_1, ... of all the ordinals less than
alpha, and there is arecursive function r(i,j) on naturals
such that r(i,j) = 1 if beta_i < beta_j = 0 otherwise--Daryl
McCulloughIthaca, NY
> Paul misspoke. Rather than talking
about the largest> ordinal de?able within ZFC, you should
instead talk> about the smallest ordinal that is *not*
de?able> in ZFC. Why? Surely he had in mind the
proof-theoretic ordinal of atheory, the smallest recursive
ordinal for which the inductionprinciple is not provable in
the theory, although there arevarious complications connected
with this.
>> Paul misspoke. Rather than talking about the
largest>> ordinal de?able within ZFC, you should instead
talk>> about the smallest ordinal that is *not* de?able>> in
ZFC. Why? Surely he had in mind the proof-theoretic ordinal
of a>theory, the smallest recursive ordinal for which the
induction>principle is not provable in the theory, although
there are>various complications connected with this.Youre
probably right.--Daryl McCulloughIthaca, NY
Thomas
Bushnell, BSG says...>> This is incorrect. It depends on what
you mean by consequences. If>> the laws and initial conditions
are known, then *by de?ition* the>> future state of the system
can be computed. Thats exactly what we>> mean by
deterministic physical law>> >> I made it clear by example
that I was taking about ultimate consequences.>> Will a
computer ever begin accepting input?What is an ultimate
consequence?It was clear to me what Paul was talking about.
Suppose you havean algorithm that allows you to compute the
state of the universeat time t given the state of the universe
at time 0. You still maynot be able to answer questions of the
form If the universe is in state s0 at time 0, then will there
ever be a time in which the universe is in state s1?The
quanti?ation over all future times implicit in the
questioncan make the question undecidable even if the
evolution is perfectlyalgorithmic.Paul makes an analogy with a
Turing machine. Given a description ofa Turing machine and the
tape at time 0, you can compute the state atany future time.
But you still may not be able to answer the question:Does
there exist a time at which the Turing machine halts?--Daryl
McCulloughIthaca, NY
 > > Again I am making a simple point.
For any formal system there is a> > recursive ordinal that is
the limit of the recursive ordinals> > de?able within that
system.> Ok, for ZFC, what is the ordinal in question?> > If I
could answer that question I would be up for the next Fields
mdalin> mathematics. In> my youth I did try for a while. Ok,
you didnt take my bait. I will prove to you that there is no>
such last ordinal. Suppose K is the last ordinal de?iable
within ZFC.I did not say there was a last ordinal. I said
there is a limit ordinalthat is the union of all the recursive