The majority of the links on that page that work seem to lead to FLT proofs, and their discrediting. So one presumes you aren't claiming that they're still true. As for the crank label. Surely that depends on what an individual's definition of a crank is? The website seems to present evidence, from which the reader should draw should be clear: the 'crank' ones tend to be anti-establishment pieces, where the author somehow presumes to know the 'truth', and is often not persuaded by cogent arguments that they are talking cods-wallop. You perhaps should read the anti-cantor ones and decide if you think the arguments are sound (I don't think they are). Draw your own conclusions as to whether or not the author is misguided, mistaken, or something else. Can we get back to maths now? I've had plenty of ideas about the prime counting one. Including you'll be delighted to know, realizing some of my earlier criticisms were inaccurate. I would still like it if you were to rewrite your arguments in clear English. I mean, you at one point say dS(x,y) is a 'count of the composites', so what is S then? I mean, seriously, what does it do? I can guess but I'd like you to make it clear. Why is p'_y(x,y) = p'_x(y,y) or similar; that directional derivative bit? I mean a simple counter example shows it isn't. Perhaps we should read the differentials differently? p'_y(y,y) = partial d by du of p(u,v) evaluated at u=v=y? ==== I'm 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 have then go on to simply 'cancel' the e^ leaving: i*ln(z) = i*(+/-2pi/3 + 2pi*n) ln(z) = +/-2pi/3 + 2pi*n z = e^(+/-2pi/3 + 2pi*n) = e^(2pi(+/-(1/3) + n) However, I can't 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*pi Which is clearly incorrect. Surely this renders the above solution to the aforementioned equation incorrect? Have I missed something? Richard Hayden. ==== > However, I can't 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 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. As this would be a pretty easy way of earning $1M, I presume the answer is no. All the same it looks tantalizingly simple, and analogous to Fourier series if you could find some factor that would 'orthogonalize' the terms on the right when both sides 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 finite value at z = 0. It seems to me that the RHS has a pole of order 1/2 at both places. -- ==== I need to find 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 one ==== >I need to find 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 one This is possible if and only if a is a positive integer multiple of 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 x becomes 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 be integrable in closed form, that gives the answer. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University ==== >> Oh - I wasn't paying attention, sorry. If we're talking about >> sequences of integers then of course it's true that an infinite >> random sequence (with a suitable distribution) contains every >> finite sequence (with probability one.) >> >> Of course calling this the Shoenfeld theorem is a little silly, >> since it's 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. It's an immediate consequence of various well-known facts. Find a book on probability theory that contains a thing called the Law of large numbers, for example. Or a discussion of normal numbers... 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. That's exactly your theorem for subsequences of length 1. The generalization to subsequences of length greater than 1 is immediate: For example say we have a sequence of integers between 0 and 9 and we want to talk about subsequences of length 3. Take the original sequence, consider the terms in groups of 3 and you get a sequence of numbers between 0 and 999 (for example if the original sequence was 0,1,2,3,0,1,2,3,0,1,2,3,... then the new sequence is 12,301,239,123,...). The law of large numbers says that every number between 0 and 999 appears in the new sequence, which says that every 3-digit sequence appears 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. > That's 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 Schoenfeld's Theorem!!! -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html Needless to say, I had the last laugh. Alan Partridge, _Bouncing Back_ (14 times) ==== In message , John >>SCHOENFELD THEOREM: >>An infinite bounded sequence of random numbers contains all finite >>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 modifies 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 define what you mean by sequence of random numbers. >Whether or not I chose to disguise >simple concepts with excessive academic pedantry In mathematics, that's usually phrased rigorous proof. Do it, and you're unassailable. Don't, and you're 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 infinite random sequence R contains all 0's, then it is bound Bounded. >by [0,0], and the Schoenfeld Theorem remains true. Also, the Schoenfeld Theorem says sequence of random numbers not >random sequence of numbers. That's worse, until you define random numbers.. > See how clear things become when you try to state things with precision? > (As you try to do so, you will eventually find 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 infinite bounded sequence of random numbers contains all finite >>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 modifies generator, >not number. Better: A randomly selected bounded sequence of numbers... I understand random number is sometimes taken to mean a uniformly distributed random variable. >(As you try to do so, you will eventually find that the word random >almost never belongs in a carefully-worded mathematical sentence! Really? Not even in probability texts? Or number theory? ==== > >You're the best troll in the history of the Internet. >Hardly. He's not even the best troll in the history of sci.math/physics. Shhhhhh! You'll give somebody the idea it's a competition. Socks ==== > all of you if you think I'll 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 Harris No no no no no James.... YOU ing nut-job extordanirre.... K. Jones ==== > I understand your point of view, but I don't agree with it. Journal > and formalism. It forces you to review the literature in order to make > it clear how your work fits 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 can't they just holler out that they found something? Mathematicians have created an environment hostile to outsiders on the presumption that they've found everything simple enough for a non-mathematician to find. So then if you claim you've 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. That's 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. > 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 journal's 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. It's a demanding process that requires a lot of skills specific to that process alone, so if a person who's not a mathematician finds something, they're tasked with learning a lot specific to writing ability to write them over a lifetime. Besides, I've contacted math professors and graduate students specifically noting that I'm NOT a mathematician, and asking for help and advice with that process. The search for knowledge is hard enough without a discoverer having to face an antagonistic process, where *style* is used to block out substance. > 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 They don't accept papers unless you're properly affiliated, as it checks your gateway and bounces messages not from certain ones, like universities. I know because I tried to post a math paper there. James Harris ==== >> I understand your point of view, but I don't agree with it. Journal >> and formalism. It forces you to review the literature in order to make >> it clear how your work fits 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 can't they just holler out that they found something? And when those college-trained geologists look at it and see that it's a piece of common quartz crystal, and isn't worth anything no matter how shiny it happens to be, what should your amateur rockhound do then? Insist it's the biggest find since the Hope diamond? That seems to be your approach. > Mathematicians have created an environment hostile to outsiders on the > presumption that they've found everything simple enough for a > non-mathematician to find. So then if you claim you've 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. That's 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 rockhound should read a book on geology and gemstones, he should declare that he doesn't want to pollute his mind with false teachings because he's taught himself everything he needs to know about gems. He also should take it as evidence that there's a world-wide conspiracy to suppress gems found by non-professionals. -- Wayne Brown (HPCC #1104) | When your tail's in a crack, you improvise fwbrown@bellsouth.net | if you're 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 can't they just holler out that they found something? Bad analogy. Someone says they've found a gem. Lots of people look at it. Everyone who knows about gems says, That's 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 he's 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 can't they just holler out that they found something? >Bad analogy. >Someone says they've found a gem. Lots of people look at it. Everyone > who knows about gems says, That's 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 he's being ignored? Yeah, but here I can show the find: 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) = floor(x) - S(x, y) - 1, and S(x,y) is the sum of dS from dS(x,2) to dS(x,y). Reference: http://mathforprofit.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 those primes are 2, 3, 5 and 7. So it's more like someone finding a gem, and having experts claim it's glass, only to then have that person cut glass with it. I want critical thinkers to search on prime counting function and see the methods that mathematicians have on record for counting prime numbers to compare with what I just gave and see for yourselves how obvious it is that what I have isn't just junk. Remember, mathematicians are fighting to totally dismiss my result as unimportant to justify not putting it in math references. James Harris My math discoveries, found for profit http://mathforprofit.blogspot.com/ ==== > So it's more like someone finding a gem, and having experts claim it's > 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 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 scientific 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 first 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 know who the sociopaths are in the newsgroups, another web site that would be popular would be one that puts the internet flamers 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 scientific 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 programmer's 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'll give you some hints. Caltech and Stanford and first 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 point against some group that you identify with? In other words Wormley, are you a man or a mouse? -- Tom Potter http://tompotter.us =============== WHO instigates conflict and war for power and wealth? WHO instigated the class wars of the 1900's? WHO is instigating the religious wars of the 2000's? WHO has a well organized propaganda machine? WHO gang attacks all who expose their agenda and methods? Visit my web site, and download the world's best physics tutorial! =============== ==== >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 scientific 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, like physics' 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 scientific 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 first 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, that's really, since Inter-Web-Ware trash was invented in Switzerland it's just a matter of time before it collapses just like Texas's 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 flamers in the spotlight, > by posting some of their posts, and their backgrounds. ==== > I understand your point of view, but I don't agree with it. Journal > and formalism. It forces you to review the literature in order to make > it clear how your work fits 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 journal's 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, you've heard it before and ignored it, right? ==== > I understand your point of view, but I don't agree with it. Journal > and formalism. It forces you to review the literature in order to make > it clear how your work fits 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 journal's 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, you've heard it before and ignored it, right? No. I find 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 I've ignored good advice before? James Harris ==== [snip suggestion to James] > No. I find your post strange, as you seem to be assuming that I am > indeed some kind of crank, so I wonder what evidence you have. That's a *conclusion*, not an *assumption. Your posting record reveals your crankhood clearly, consistently and repeatedly. *You* have provided sufficient evidence for an unambiguous conclusion that you are, indeed, a crank -- in particular, your repeated passionate defense of your own blatant errors, which constantly drives you to attack those who point them out to you. > Can you tell me why you assume that I've ignored good advice before? *Conlude*, James, conclude. Because you have a long track record of ignoring good advice -- especially about learning the mathematics which is still over your head. > James Harris James, you are in such a serious and extreme (possibly terminal) state of denial over your own posting behavior that no one in this newsgroup is likely to be of any help. You need professional assistance, and not just from some world-class psychiatrist at Johns Hopkins or NIMH. You need a team of specialists, preferably from Vienna. Even then you won't get good odds from your readers 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 find 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 I've ignored good advice before? James Harris Do you still claim that you've found some hundred year old mistake in algebra? Are you claiming to have taken all the comments made there into account? Because they unequivocally showed you were mistaken. Yet you still decided to have it published in that unrefereed journal. I think that is ignoring good advice. You have stopped claiming FLT proofs it appears. However you asserted Wiles was wrong. Indeed there were some errors in its original form, but they were tidied up. I'm amazed, though, and would like to know where you learned enough modular form stuff to have read Wiles's paper and understood it enough to have spotted them. There are many comments on your 'prime counting function'. I can't believe you find them all too far beneath you to comment on. I put the quotation marks as an indicator that you've swapped from prime counting to composite counting. The best advice you've 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 don't know from crank but when great breakthroughs and advances are only posted on > usenet one has to draw some obvious conclusions. What conclusions do you draw? ==== > Someone who wasn't 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. Sufficiently 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 my > GAME'S THEORY. I learned it in marketing class. kid for entertainment and experimentation as well. At least you've progressed to psychological experiments on other people now your a 'grown up.' ==== > Someone who wasn't 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. > Sufficiently 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 my > GAME'S THEORY. I learned it in marketing class. >kid for entertainment and experimentation as well. At least you've > 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, 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 unfinished 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 unfinished story and he alienated many within days. James read *one* marketing book. If it were a textbook, I am reasonably sure he didn't *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 becomes the formost expert on GAME'S theory. He had his own version of the theory of games, much like his own version of mathematics, and demanded that others heed his every word. He couldn't get the terms and definitions 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 don't 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 doesn't 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 doesn't 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 fit. For all anybody knows, James could be a nice guy. I think he is a tool. Jay ==== > > > > Someone who wasn't 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. > Sufficiently 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 my > > GAME'S THEORY. I learned it in marketing class. > a > kid for entertainment and experimentation as well. At least you've > 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, 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 unfinished 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 unfinished story and he alienated many within days. James read *one* marketing book. If it were a textbook, I am > reasonably sure he didn't *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 becomes the > formost expert on GAME'S theory. He had his own version of the theory > of games, much like his own version of mathematics, and demanded that > others heed his every word. He couldn't get the terms and definitions > 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 don't 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 doesn't 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 doesn't 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 fit. For all anybody knows, > James could be a nice guy. I think he is a tool. Jay I know someone who acts like him who has a hyper- mania diagnoses, which is a form of psychoses. But, shit, not this extreme and in public. I've mixed with people with diagnoses quite a bit over the years, I try to humour them or ignore them if they are similar to James. But, yes they can bug you if you let them, and then you find yourself biting back. But, these are obviously just impressions, who the hell could possibly know what is going on in his mind or his motivations. I wonder if he has any insight into his behaviour, I doubt it. But, my earlier impressions were that I thought some people might be using him purely as a source of comic relief which I think reflects badly on them, but judging from your post you are not one of them. But, yes, I'm finding it a bit comical as well, likely some others here are as well, even though I've seen 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 objective distance and just classify his symptoms. I've got mixed feelings as I have a mental health diagnoses, on the one hand I feel some empathy for him, on the other I find him comical. But, I know how people like James can bug you and be very grating if you are over exposed to them or they fixate on you and give you a hard time. ==== > > > > Someone who wasn't 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. > Sufficiently 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 my > > GAME'S THEORY. I learned it in marketing class. >kid for entertainment and experimentation as well. At least you've > 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). I'm 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 I've 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 doesn't know what they're 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 don't 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 gadfly in 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 search at http://www.google.com/advanced_group_search?hl=en with David Ullrich in the author field and racial slur in the exact phrase field, will find 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. He's a tag-along that just won't go away when he's told that he's not wanted. I'm sure those of you who are successful in some way have had to deal with such people. >James posted one unfinished 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 unfinished story and he alienated many within days. Well that's one point of view on the subject. Short stories are subjective to a large extent. I posted a draft and had critiques. I didn't like some things about a post by *one* of the critiquers, expressed that opinion, and faced a lot of criticism on the group alt.fiction.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 doesn't get any easier from here. James Harris My math discoveries, found for profit http://mathforprofit.blogspot.com/ ==== >I'm 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 maybe their idea as to what is a useful contribution to mathematics does not correspond to yours. >Given the extremely hostile reaction, where insults are seen as a >proper form of communication, that I've 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 fly. By comparison, sci.math is tame. And there are groups far worse that talk.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). I'm 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 I've 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 doesn't know what they're 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 don't 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 gadfly in 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 search > at http://www.google.com/advanced_group_search?hl=en with David Ullrich in the author field and racial slur in the > exact phrase field, will find 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. He's a tag-along that just won't go away when he's told that he's not > wanted. I'm sure those of you who are successful in some way have had to deal > with such people. > James posted one unfinished 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 unfinished story and he alienated many within days. Well that's one point of view on the subject. Short stories are subjective to a large extent. I posted a draft and had critiques. I didn't like some things about a > post by *one* of the critiquers, expressed that opinion, and faced a > lot of criticism on the group alt.fiction.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 doesn't get any easier from here. James, as one sufferer to another possible sufferer. I think you should get some 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 the threads you are no expert. Why don't you get some help, get yourself thinking straighter, then you might be able to learn a lot more about maths, and even do some interesting work for people to appreciate? ==== [snip] > 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 doesn't know what they're 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 couple weeks 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 doesn't 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 doesn't 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 of my GAME'S THEORY. I learned it in marketing class. >you were a kid for entertainment and experimentation as well. At > least you've progressed to psychological experiments on other > people now your a 'grown up.' Pat -- I'm pretty sure Jay's PPS was an intentionally lame justification 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 Burns ==== [...] > > 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 my GAME'S THEORY. I learned it in marketing class. > you were a kid for entertainment and experimentation as well. At > least you've progressed to psychological experiments on other > people now your a 'grown up.' Pat -- I'm pretty sure Jay's PPS was an intentionally lame > justification 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 Burns I see. Well, I think, concerning some of the people here, an element of what following this over the last few days, I see in his behaviour, judging by my impression of his posts, what I see directly in someone whom I know very well that has a mental health diagnoses. I think people should just ignore him they are feeding his obsession by replying. I don't see the point in the endless 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 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 scientific 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 first 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 know who the sociopaths are in the newsgroups, another web site that would be popular would be one that puts the internet flamers 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 scientific 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 programmer's 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'll give you some hints. Caltech and Stanford and first 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 point against some group that you identify with? In other words Wormley, are you a man or a mouse? -- Tom Potter http://tompotter.us =============== WHO instigates conflict and war for power and wealth? WHO instigated the class wars of the 1900's? WHO is instigating the religious wars of the 2000's? WHO has a well organized propaganda machine? WHO gang attacks all who expose their agenda and methods? Visit my web site, and download the world's best physics tutorial! =============== ==== > > 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 scientific 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 programmer's 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 scientific 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 programmer's 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'll give you some hints. Caltech and Stanford and first 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 point against some group that you identify with? In other words Wormley, are you a man or a mouse? -- Tom Potter http://tompotter.us =============== WHO instigates conflict and war for power and wealth? WHO instigated the class wars of the 1900's? WHO is instigating the religious wars of the 2000's? WHO has a well organized propaganda machine? WHO gang attacks all who expose their agenda and methods? Visit my web site, and download the world's best physics tutorial! =============== ==== This may be OT if so I am sorry but I didn't 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 find 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 first makes more sense to me but the first 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 didn't 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 find 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 significant to most significant). The proper grouping of 01001011 is 01 001 011 > 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 number makes the grouping 001 001 011 which is still 113 in octal. > The first makes more sense to me but the first 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 didn't 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 find 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 first makes more sense to me but the first 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 doesn't change the value of the number, whichever way you read it. Would be interesting to know which was the first 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 = 22 Dividing 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. That's 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 with a given plane. How can the 2D parameter curve for the 3D intersection curve in the domain of the nurbs cylinder be calculated? Does someone know a good reference which describes something like that? Or can someone give an algorithm doing the calculation? ==== Given a set S = { (1,2),(1,3),(1,4)...(k-1,k)}, is it possible to partition the above set into 'k' subsets such that the elements of each subset are pairwise-disjoint? The elements of set S are unordered pairs so that (i,j) = (j,i) and the elements of a set are pairwise-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 results related to my question above. Many thanks in advance 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 views are 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. That's not quite true, but it's mostly true. He was probably the first formal logician; he figured out how the Aristotelian Forms work. So if logic counts as a branch of mathematics, then he had something to do with it. He is responsible for such theorems as: [(x) Px & Qx] -> (x) Px & (x) Qx Thomas X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 12:50 AM, 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. You've got a conflict with what follows. If you want an explicit factor c^2 here then it needs to appear in the metric tensor. That's one os the reasons that physicists often wok in natural units with x_0=ct, s = x_0^2 - x_1^2 - x_2^2 - x_3^2, or with the opposite sign convention. Note that in older literature you may also see x_0 = ict. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hB9DDpU05714; ==== >
I'm sorry to disturb anyone with such a stupid question, but can someone 
write
>>back showing how to find the percent difference between 9905.9 and 
9390.9.
>>The way I went about finding this is firstly finding 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
     find the percent difference between 9905.9 and 9390.9
and replace percent by the equivalent per hundred:
     find 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. You're flaunting your knowledge, and that is all. 
You should set aside your semantics for someone who needs them, when they are 
appropriate. 
====
> >>I'm sorry to disturb anyone with such a stupid question, but can someone 

>>write
>>back showing how to find 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.
====
> 
>>
>I'm sorry to disturb anyone with such a stupid question, but can someone 
write
>back showing how to find the percent difference between 9905.9 and 
9390.9.
>>The way I went about finding this is firstly finding 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
>>    find the percent difference between 9905.9 and 9390.9
>>and replace percent by the equivalent per hundred:
>>    find 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. You're flaunting 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:
What's the percent difference between 50 and 100?
It's not grammatically correct, and it doesn't 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 numbers.
X-Received: (from approve@localhost)
        by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 
1.9  primary) id hB9DDqN05731;
====
>>    Can somebody point me to a fast, sequential implementation
>>of the 'mimimum vertex cover' problem in C/C++ ?
>>Murthy Andukuri
>>
X-Received: (from approve@localhost) by 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, findings of a research report, and mathematical problems. Science is the key. X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hB9Eb9911944; ==== I'm 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 have then go on to >simply 'cancel' the e^ leaving: i*ln(z) = i*(+/-2pi/3 + 2pi*n) >ln(z) = +/-2pi/3 + 2pi*n >z = e^(+/-2pi/3 + 2pi*n) > = e^(2pi(+/-(1/3) + n) However, I can't 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*pi Which 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 exp[iu] is periodic with period = 2*pi phil X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hB9Eb8m11932; ==== >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 the diameter 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 circle looks like homework, so as a start, draw a line from the centre of the circle 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 as a diameter, then the triangle is a right triangle. Proof is almost trivial. Let A and B be the ends of the diameter and C the third vertex, with corresponding angles a, b, and c. Draw the radius 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 the hypoteneuse 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 a crank. I think it comes from his inability to recognize when he has made a mistake even when it has been pointed out to he and explained clearly. I think this results in people getting angry and frustrated. If JSH would express his gratitude to the mathematicians who have devoted considerable time and effort to finding his errors maybe there wouldn't 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 sufficient. > Why? The way you have reacted to those critical replies concerning the mathematical part of your posts, and your recently adopted habit of starting new threads every other day in which you bemoan missing recognition for your achievements and cry over all those evil mathematicians out there, does qualify you as a crank, if nothing else does. That being said, I should point out, that I do not favour those silly 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 >> can't be stopped. >> >> He's sitting somewhere at a keyboard, insulting people day and night, >> getting away with what he can't 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 if nobody else does. >In any event, fostering an insulting environment doesn't 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 the dust 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 completely different 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 of the 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, He's sitting somewhere at a keyboard, insulting people day and night. > What I'm telling other readers is YES that IS the kind of Usenet that > people like Marc Olschok and Uncle Al want because they're not > civilized! Why do you ask, if you cannot wait for an answer? > [...] > Now I'm 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 of silencing 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 sufficient. >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 > > can't be stopped. > He's sitting somewhere at a keyboard, insulting people day and night, > > getting away with what he can't 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 doesn't 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 I'm telling other readers is YES that IS the kind of Usenet that > people like Marc Olschok and Uncle Al want because they're not > civilized! Now then, many of you might find it tolerable because you think of > yourself as part of the group, so it's Us against Them. But what do you really know of Marc Olschok or Uncle Al? Why would you assume they're 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 I'm 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. It's 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 bullshit smell arises. > The quantums of electricity are electron, proton, positron, and > anti-proton Agrammatical 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 above. [snip] Go crack a physics book. Your bellybutton lint is lying to you. -- Uncle Al http://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. Herc now 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? I've 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 first, and it doesn't > much matter what's 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 terrified of posting? Don't 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. It's been > there from the beginning and it'll stay here until someone figures out > a way to stop it. The reason it's 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 > can't be stopped. He's sitting somewhere at a keyboard, insulting people day and night, > getting away with what he can't in person. Some of you may think that I'm 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, I'm not interested in letting them win. I don't care to > allow myself to be insulted into silence. I'm not afraid to give some > back when insulted. Remember, a lot of it is about control. People like Uncle Al don't > have 29,000 posts because they're 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 you're reading this so you're 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 you're more mature than the ones doing the insulting. Wouldn't 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 person's ideas, but is your presupposition actually true? Would you care to defend such a proposition with facts? Very Respectfully, Ray ==== > But James, by not insulting those people back, you are sure to show others > that you're more mature than the ones doing the insulting. Wouldn't 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 person's ideas, but > is your presupposition actually true? Would you care to defend such a > proposition with facts? Very Respectfully, > Ray What I meant that when he gets insulted, just to blow it off or to reply to it kindly without cussing them or any of his usual antics. -- David Moran Chief Meteorologist Oklahoma 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 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 Copperfield would not be drawing very many crowds..... > -- > Democracy: The triumph of popularity over principle. > -- > http://www.crbond.com Paul R. Mays ---------------------------------------------------------------------------- - Some where within the Quantum State Http://Paul.Mays.Com/story.html http://paul.mays.com/mayday.html http://paul.mays.com/rainy.html Science tries to answer the question: 'How?' How do cells act in the body? How do you design an airplane that will fly faster than sound? How is a molecule of insulin constructed? Religion, by contrast, tries to answer the question: 'Why?' Why was man created? Why ought I to tell the truth? Why must there be sorrow or pain or death? Science attempts to analyze how things and people and animals behave; it has no concern whether this behavior is good or bad, is purposeful or not. But religion is precisely the quest for such answers: 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 Copperfield would > not be drawing very many crowds..... Look before you leap is also wrong on many levels. It doesn't apply to the blind or to paraplegics, it doesn't tell you which way to look or how long to do so and fails to provide details on the proper distance to leap. Both that expression and my signature line are aphorisms. Get over it. -- 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 ==== ... > Now I'm 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 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. Where has Arturo been lying? Please provide an exact reference. But you succeeded in stopping him to post in response to your answers. So, are your insults intended to silence others? You are a hypocrite. (Yes, this is my second insult to you. Count the number of insults to me uttered by you, please.) -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: 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. That's not accurate; I have, in the past, insulted James. -- ====================================================================== It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) ====================================================================== Arturo Magidin magidin@math.berkeley.edu ==== 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 scientific 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 first 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 know who the sociopaths are in the newsgroups, another web site that would be popular would be one that puts the internet flamers 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 scientific 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 programmer's 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'll give you some hints. Caltech and Stanford and first 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 point against some group that you identify with? In other words Wormley, are you a man or a mouse? -- Tom Potter http://tompotter.us =============== WHO instigates conflict and war for power and wealth? WHO instigated the class wars of the 1900's? WHO is instigating the religious wars of the 2000's? WHO has a well organized propaganda machine? WHO gang attacks all who expose their agenda and methods? Visit my web site, and download the world's best physics tutorial! =============== ==== : How many of you are readers terrified of posting? : Don't 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 I've 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 satisfied. Justin ==== ---------------------------------------------------------------------------- ------ : How many of you are readers terrified of posting? > : Don't 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 I've 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 satisfied. > that's because you're quoting text book problems in here, try saying anything against the grain and you'll get your head shot off Herc ==== No, that's not true. Justin : that's because you're quoting text book problems in here, try saying anything : against the grain and you'll get your head shot off : Herc ==== cite? ---------------------------------------------------------------------------- ------ > No, that's not true. Justin : that's because you're quoting text book problems in here, try saying > anything : against the grain and you'll get your head shot off : Herc > ==== I'm currently reading Michael Spivak's 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 define: (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 define 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 don't 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 don't even know what k should be in this case.) So, I'm thoroughly confused. Boris -- boris@uncommon-sense.net - No one can go back and make a brand new start, my friend, but anyone can start from here and make a brand new end. -- Carl Bard ==== of tensors. I don't 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 don't even know what k should >be in this case. OK, several points to clear up. 1) A second rank tensor wouldn't 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 different vector 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 definition given doesn't work for tensors with both covariant and contravariant indices. Hence a matrix (which has one of each) is not a tensor of the type defined. More on this below. 3) If we have V=R^n, then a basis of V has n elements, so a vector in V 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 the transformation 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 it's values at basis elements. If V has dimension n, there will be n^k possible 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 are familiar with. Essentially, your previous definition of tensors focused on the components in different bases, not on the tensor itself. 6) To define tensors with both covariant and contravariant indices, we don't use a multi-linear map on just V^k. We also have to consider the dual vector space V*. Then a tensor on V of type (k,l) will be a multi-linear map from V^k x (V*)^l to R. It is important in this to remember 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 be an element of V. Now the components of a tensor have k lower indices and l upper indices (if I got everything right, that is...vectors have components 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 from V to V, and hence a square matrix. 8) To consider nxm matrices, you have to look at multi-linear maps with different vector spaces, eg a multi-linear map from VxW* to R where V is m dimensional and W is n dimensional. I hope this helps! --Dan Grubb ==== >I'm currently reading Michael Spivak's 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 define: > (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 define 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 don't 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 physicist's way of thinking of tensors --- reduce everything to a fixed basis. Spivak is avoiding this by giving a basis-free definition (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 definition is known as covariant tensors of rank k (or maybe contravariant tensors of rank k --- I can't remember which is which :-) ) in physics jargon. If you are desperate to see your indices.... pick a basis v_1,... ,v_n of 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 defines T by multilinearity ...). -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html Needless 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 affine plane. That's ridiculous. In the affine plane, there is no such thing as vertical. If you want to put a co-ordinate system on it and do analytic geometry, fine, but that duality comes from the co-ordinate system and not from the underlying geometry. : Anyway, my point had nothing to do with path categories specifically : 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. 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. In the affine plane, the mere fact that you can create an isomorphism between 2 classes of things does NOT suffice to make them dual. : Why do you want to blinker us? I don't. The general thrust of this thread is about representation theorems, not blinkering. 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. It just means that the permutation groups are in some sense closer to explaining the core of the concept. 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 infinite collection of lines, especially not if you are going to arbitrarily exclude one of the lines. -- --- It's difficult ... 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 specifically > : 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 configuration 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 duality's inability to change the underlying mathematical objects involved, I find your claim You will not gain any insight into the nature of a point by thinking about it as an infinite 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 duality's inability to change the > underlying mathematical objects involved, I find your claim You will > not gain any insight into the nature of a point by thinking about it as > an infinite 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. I'm sure your opinions are more highly regarded than mine. My somewhat more absolute statement comes from several years of studying set theory and concluding that the concept of language invariance described in Topological Model Theory by Flum and Ziegler is the mathematically important issue that arises from set theory. (What I presented was an incidence matrix for the trivial affine plane because it was easy to cut-and-paste from recent material I had written. Like a good mathematician, George visualized the affine geometry from the presentation. My words explaining otherwise made no difference.) :-) mitch ==== : Why do you want to blinker us? I don't. 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 metaphysical positions like foundationalism to mathematical discussions and aren't honest about it 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 mathematical entities. > 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 infinite collection of lines, especially not if you are > going to arbitrarily exclude one of the lines. Perhaps not. But you will gain an infinite amount of knowledge about the geometric insights Frege leveraged just before revolutionizing analytical philosophy. Hey guys... (not to you George). You need to be looking at Plucker's work in algebraic geometry and its relationship to triple systems to understand why George gets to use logic like a battle axe. Truth tables are essentially a tetrahedral simplex. 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 representation of the complete NOR connective. To understand the discussion you are actually in folks, you must make inferences from Excuse me for having BEEN pedagogued that way, but since I was, I think that that direction is Just Fine, and that YOURS is the one that is mistaken. and There never would've been any relativity if the study of the ether hadn't come before it. There never would've been any chemistry if phlogiston hadn't come before it. There never would've been any heliocentric astronomy if Ptolemaic epicycles hadn't come before it. Good riddance to all. In other words, you will have to be willing to overturn the rationalizations of analytical philosophy in order to avoid blinkering and enjoin constructive mathematical discourse. Moreover, as the remark above indicates, you will have little success invoking any authority which might be commonly respected. Nor, will you 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 analogous to the fact that [the domain of] A MODEL OF a [consistent] set of first-order axioms can be just about anything. which means that a model is practically nothing at all. He is just not quite as elegant as Frege, It is difficult to avoid an expression that has universal currency, before you learn of the mistakes it can give rise to. It is extremely difficult, perhaps impossible, to test every expression offered us by language to see whether it is logically innocuous. So, a great part of the work of a philosopher consists--or at least ought to consist--in a struggle against language. But perhaps only a few people are aware of the need for this. Instead, you get someone with a philosophy background insisting that you engage in justificationalism (hey, now there is a word that belongs on sci.math), There is simply no way (nor desire) to bind or restrict the potential universe of applicability. But saying set all over the place DOES tend to do that, because naive set theory won't work; if you are going to say set then you are going to, whether you want to or not, invoke SOME set THEORY and associated restrictions and complexities that ARE necessary to a coherent notion of set but that you do NOT want to respect as far as applicability of your structure.' Now, if you look at the literature on triple systems, you will find that it is relates to orientability in combinatorial topology. And if you consider what I said about the tetrahedron, you will realize that the coherence to which George refers is actaully derivative from the coherence between vertices and their opposing face. One thing I can assure everyone in this thread: it is not about representation theorems. :-) mitch ==== > : Points and non-vertical lines are dual in the affine plane. >That's ridiculous. In the affine plane, there is no such thing > as vertical. If you want to put a co-ordinate system on it > and do analytic geometry, fine, 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 fitting 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 x-coordinate and is therefore not a good fit. Viewing this type of problem from a coordinate-free affine-invariant point of view can lead to statistical methods that are highly robust against outliers and other kinds of errors (e.g. see Rousseeuw's notion of regression depth). In fact in this setup one is using a restricted group of affine transforms that preserve the family of vertical lines, but I don't know of a good word for this other than affine. -- 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 solution but I haven't got a proof. What I'm wondering about, now that I've looked at it, is how to phrase the problem and its obstruction elegantly. This seems to be a problem in Affine Geometry (or Projective Geometry) but I can't quite pinpoint the relevant classical configuration. Let me explain. You've given quite a few constraints, and asked us to draw a picture consistent with all of them. My claim is that the data are contradictory, and in fact a contradiction results from a rather smaller set of constraints. You asked us to draw 8 lines in the plane; that we can do. You add a tiny constraint that no two be parallel; no problem. That means that each pair of lines has a unique point of intersection, giving 28 points altogether. Now, if we label the lines A, B, C, D, E, F, G, H then on each line we find the seven points of intersection with the other lines, occurring in some order as we read from left to right (or bottom to top). The ordering data you provided specify unambiguously the sequence of the intersection points on each line. (Your partial order specifies more, in fact, but I believe there is already a contradiction from this more limited information.) If, as in some cases, we don't really care whether the points occur in one order or the reverse order, we can note the points of intersection in brackets as you do. Actually, I believe there is already a contradiction even if these more relaxed constraints are imposed. Let me illustrate first with two examples. If you wanted us to draw three lines A, B, C, then you would have to specify the orderings of the intersection points on each line. For example, on line A you might want B to be to the left of C, which we could write this way: A : B, C But if you aren't choosy about whether the points of intersection on any particular line show up left-to-right or right-to-left, you might write the constraint this way: A : [B, C] Of course, when there are only three lines, this means the only possible set of constraints of this form would be A : [B, C] B : [A, C] C : [A, B] and these constraints are satisfiable (e.g. by the lines x=0, y=0, x+y=1). Next consider an example with four lines. Can we draw lines with these incidence 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 that A & B meet at the origin. Applying a linear transformation, we could assume A and B are the x- and y- axes, respectively. Applying reflections as needed, we could assume C meets these lines above and to the right of the origin; applying scalings we could assume C is the line x + y = 1. And now where is the line D ? If it meets A at the point (x0, 0) and meets B at (0, y0), then the first two constraints imply that x0 < 0 and that y0 < 0, respectively. You can work out where C and D cross (hint: D is the line x/x0 + y/y0 = 1) but you'll find that under these conditions x y < 0, that is, the point of intersection is in the second or fourth quadrants; on the other hand a point between the other intersection points (x0,0) and (0, y0) would lie in the third quadrant. So the constraints on D are incompatible with the constraints on A and B . (And I haven't even used the constraints on C !) Note that I am using only the incidence relations of the lines, and invariance under the group of affine maps (linear maps and translations); that makes this a question of Affine Geometry. With the addition of a technical axiom or two, affine geometry really is coordinate geometry over some field (a very nice theorem!). We have used nothing else here, really, except the condition that the field be ordered. So there ought to be some more classical way of stating that there is a contradiction here. (It's not Desargues's configuration, nor Pappus's, nor ... Whose is it?) By the way, you can also ask whether the configuration can be constructed in Projective Geometry. There, lines have no ends, so the incidence data can be read not only left-to-right or right-to-left, but also with any cyclic permutation. In that setting, any four-line problem is solvable but I suppose there is a corresponding five-line configuration which is not. After this very long preamble, I can state your problem in this language and make some suggestions as to how to prove it impossible. I think I would 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 (I've written them in the order they seem to appear in my sketches.) Reading either your (corrected) partial orders on the x-coordinates or 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 D nearly vertical, meeting very high above the origin (C has a positive slope, D a negative slope); rotate these about a third of a circle counterclockwise to obtain A and B respectively, and rotate C and D clockwise about a 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 from the right side (between E and A) to the upper left, emerging between E 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, it's possible to have H and F meet either far off to the left or far off 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 they cannot be satisfied. We could try to emulate the proof I gave for the four-line problem above: without loss of generality we may assume A is the horizontal axis and D is the vertical axis (point 5 is now at the origin) and we can assume line G is the line y = x + 1, say. There are five 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 42 inequalities to be satisfied by these 10 variables. (For each line other than A and D, it suffices to write the constraints in terms of either the x- or y-coordinates of intersection.) For example, from line A we learn that x_B < -1 < x_C < x_F < 0 < x_H < x_E and 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 order in which the intersections with B are to be read. For instance the contraints 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 rational expressions of multiple variables. But I should stress that if we think that we can obtain a contradiction by (say) adding a string of inequalities together, it's going to be a complicated sum, since as I noted it IS possible to satisfy almost all the constraints at once. The contradiction is only going to come from using essentially ALL the inequalities together. But as I said earlier, it may not be necessary at all to proceed algebraically; there may well be a nice incidence-geometric principle which shows that this configuration is impossible. OR -- could it be that you've made another typo? Maybe your desired ordering of the intersections is wrong... Since I have just taught a course in linear geometries, I would be 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 and q prime (like the abbreviation p-groups)? It seems that there should be quite a bit of literature on them given Burnside's theorem that they are solvable. Maybe I'm looking for the wrong words. Also, does anyone know if when you search on MathSciNet if the engine the words? When I enter anything even without quotes it appears as a string 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 first 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. #. It's 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) > 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 <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 first 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. #. It's 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 use 2-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 web site at www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibmaths.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. There's a calculator for this on the web page too, Ron Knott > I don't 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 first 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 first 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 infinite 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/fibmaths.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. > There's a calculator for this on the web page too, >Ron Knott Very interesting site. Dan >I don't 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 first 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 first 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 infinite 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 finite variances and a common distribution F such that F(0) = 0. Now consider the product Z_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, I'd like to talk about 2E[(X_n)^2] and E[1/((X_{n-1})^2 + (X_{n-2})^2]. What is the relationship between these two expectation? Is one always bigger than the other? Then finally I'd like to show that Z_n converges with probability one to a random variable that is finite 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 to log(2). Prove or disprove that limsup (X_1 + ... + X_n)/(n*log(n)) = infinity with probability 1. Anyone can prove this problem? Sincerely, Rob Robert Kaplan Penn Valley, PA 19072 ==== i'd 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). Can you halp me, please? Tern ==== > i'd 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. ==== > i'd 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 find 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 find more than 2 solutions!) There are 4 solutions at n=4: 1 2 3 4 aabb aabb aabb aabb 8 7 6 5 aacc cdee aacd cdef 9 10 11 12 aacc cdee aacd cdef 16 15 14 13 ddcc ffee eecf ggeh of solutions for n=3...7; some solution times in seconds; and some solution-sizes, ie, number of rectangles in solutions: n #sols time Solution-sizes 3 9 0.001 3 5 6 4 4 0.005 4 6 8 5 154 0.15 3 5 7 9-14 6 837 10 8 10 11-19 7 24 175 11 13 15 17 19 8 >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 find 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 solutions for any n-by-n square? thanks, > Leroy > Quet Yes, 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 find 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 find 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... > >;) >(ascii-face is evil grin) >thanks, > Leroy Quet As for the OB puzzle, perhaps this would be more fun for n = 6, or higher. Let us try it with n = 6 for now, if you all want... thanks, Leroy 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 1980's the following appeared in Scientific American's Mathematical Games (or perhaps Metamagical Themas, don't remember which): Place copies of digits 0...9 as you like in a square grid, one digit per cell. Reading all sets of vertically or horizontally adjacent digits both ways as decimal numbers, maximize the number of primes. A 3x3 example: 173 937 139 has primes 17, 7, 173, 71, 73, and 37 in the top row and primes 19, 19, 191, and 191 in the left column. Etc. (I don't remember if any prime-uniqueness requirements applied.) For the 6x6 case, the best squares found have 188 primes, iirc, and I don't 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 : Traffic Rank for > |pagewolf.com: 1,314,826 thanks to old 314 my pie is now cooling on > |the oven top unburnt! Herc true story > |http://www.alexa.com/data/details/traffic_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 tend to look > at clocks at 3:14. No you don't. You *remember* the times when it's 3:14 when you watch the watch, and you forget 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 first 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 haven't 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 don't see the first one. >Now, for each t, the first 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 haven't 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(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 don't see the first one. >Now, for each t, the first integrand is larger or equal than the second. >>This is in fact equivalent to: >>for t larger or equal than 0, >>m( -t but in fact that last inequality is backwards. Yes, it was a typo. >Ciprian Pop ************************ >David C. Ullrich Ciprian ==== 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 multiplication and substitution might be somewhat obvious, but it's 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 quite simple by partial fractions. I would always teach Virgil's method to a student learning calculus. What you suggest looks too much like magic and would probably serve to increase 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. Infinitely 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 flurry 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 infinitely >many events, there are infinitely remaining balls in the bucket. 2) None remain. Any given ball, say ball #k, is removed and discarded at a >specific 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 http://groups.google.com/groups?threadm=38b0da2f.5767305@news.globalcenter.ne t 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 infinity, and thus, pass to the limit to define what happens at infinity. However, to define a limit, we must first define a topology. 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 infinity as n tends to infinity. Reply 2 ------- Let us define 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. Reply 3 ------- Consider the same sequence of functions {a_n} defined 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. Thus, each of the replies is correct depending on how you define 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 infinite number. If the question were which balls, that would indicate the topology for Reply 2, and then I would say no balls. Rob Johnson take out the trash before replying ==== >>There are various versions of this. I give three possible solutions at the >>end. Please comment. >>Infinitely 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 flurry 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 infinitely >>many events, there are infinitely remaining balls in the bucket. >>2) None remain. Any given ball, say ball #k, is removed and discarded at a >>specific 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 > http://groups.google.com/groups?threadm=38b0da2f.5767305@news.globalcenter.ne t > 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 infinity, and > thus, pass to the limit to define what happens at infinity. However, > to define a limit, we must first define a topology. But the question can be answered without appealing to any sort of topology. > 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 infinity as n tends to > infinity. But that has nothing to do with the question that was asked. > Reply 2 > ------- > Let us define 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 defined in the time domain rather than in the domain of natural numbers, such that a_n(t) = 1 if ball n is in the bucket at time t and a_n(t) = 0 otherwise, then we find that a_n(t_0) = 0 for 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 one that says the sum of an infinite collection of zeros is zero. Your argument depends on justifying the step of introducing a pointwise topology and using it to answer the original question, while my argument depends on no such artifice. > Reply 3 > ------- > Consider the same sequence of functions {a_n} defined 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 don't see that this argument has anything to do with the question that was asked. > Thus, each of the replies is correct depending on how you define 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 infinite 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 your reasoning. If you know which balls, then you automatically know how many balls. Every set has a cardinality. If your reasoning leads to inconsistent answers, then your reasoning is wrong. -- Dave Seaman Judge Yohn's 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 at the > end. Please comment. Infinitely 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 flurry 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 infinitely > many events, there are infinitely remaining balls in the bucket. 2) None remain. Any given ball, say ball #k, is removed and discarded at a > specific 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 math from the address For spamming, remove anything else ==== > There are various versions of this. I give three possible solutions at the > end. Please comment. >Infinitely 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 flurry 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; You're clearly not modeling a physical process here, as (1) there aren't infinitely many balls, and (2) you can't perform these actions 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 finite sets of positive integers. Let's call the n-th set A_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 infinitely many of the sets (lim sup) the elements in all but a finite 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, as you indicate in your alternative 2: > 2) None remain. Any given ball, say ball #k, is removed and discarded > at a specific 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 infinitely >many events, there are infinitely remaining balls in the bucket. I would say this assumes, without justification, 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 >specific 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 ==== > >There are three common, though not necessarily correct, replies. >1) In that the net gain is +9 balls per event, and there are infinitely >many events, there are infinitely remaining balls in the bucket. >I would say this assumes, without justification, 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 >specific 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 > Doesn't 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 they come out even... .......... Of course there is a variant: 11am: Balls #1 - #10 placed into the bucket. Ball #10 is removed and discarded. 11:30am: Balls #11-#20 placed into the bucket. Ball #20 removed and discarded. 11:45am: Balls #21-#30 placed into the bucket. Ball #30 removed and discarded. 11:52.5am: Balls #31-#40 placed into the bucket. Ball #40 removed and discarded. 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 haven't >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 but not > reported. This normally has two components: Claims that have been incurred (the occurrence that gives rise to the claim > has happened), but the claim has not yet been reported to the insurance company > (or HMO) (this is soemtimes called pure IBNR), and Claims that have been reported, but for which the current estimate of the > value of the claim is not equal to what the final ultimate cost of the claim > will be (sometimes called IBNER for incurred but not enough reported). You have to be very careful about terminology here, as practices vary, and not > everyone recognizes that their use of terms is not standard. > mortality > tables. A common way to estimate IBNR is to arrange your historical data into certain > 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 updated data. Otherwise, you need the advice of an actuary. If there are no actuaries in > your company, get advice from a consultant. Go ahead and hire a consultant anyway. But hire him (or her) to set up the system for you to analyze claim patterns, not to calculate the reserves for you. You could call AutoZone in Memphis and see who they use for their battery 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 capitation rates. (They are set actuarially, aren't they? With medical costs rising 12-25% a year (depending on coverage) you can't afford to just follow the market and hope everyone else is right.) Jon Miller ==== I have done the following calculation and wanted to know whether it's correct or not. : ### task: expressing the term below through an infinite continuation. (x-1)^(-1) + (x+1)^(-1) = -(1-x)^(-1) + ( 1-(-x) )^(-1) = -sum(x^k, k, 0, infinity) + sum( (-x)^k, k, 0, infinity) = sum( (-x)^k - x^k, k, 0, infinity) ### Did I miss something or did I do it right? Karl. ==== >I have done the following calculation and wanted to know > whether it's correct or not. : > ### > task: expressing the term below through an infinite continuation. >(x-1)^(-1) + (x+1)^(-1) = -(1-x)^(-1) + ( 1-(-x) )^(-1) > = -sum(x^k, k, 0, infinity) + sum( (-x)^k, k, 0, infinity) > = sum( (-x)^k - x^k, k, 0, infinity) > ### >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 k An 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 the sequence-formula. But why is it ok for |x| < 1 only? Why can't I say, it's 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 didn't tell you before. But I had given 2*x/(x^2-1) as the original formula and decomposed it in 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 google. ---------------------------------------------------------------------------- ---- 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 ---------------------------------------------------------------------------- ---- It really all depends on the situation. ----------------- Shanx See You In Hell My Friend. Someone Greg Neill ---------------------------------------------------------------------------- ---- If ever I actually found myself in that situation, I'd hold it upright, with the intent of attacking my assailant's knife hand. ----------------- cliff86 Rust Shanx NormDePloom ---------------------------------------------------------------------------- ---- If you 'found yourself' in a knife fight, 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 first. But this isn't much of a test. To do this properly would require 10 names, all of a ****** that's 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? I've 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! You're right! Paranormal! Right there! See, it says paranormal! It's been proven. |-|erc, I bow down to your magnificence. -- Mekkala, Atheist #2148 Atheism 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! You're right! Paranormal! Right there! > See, it says paranormal! It's been proven. |-|erc, I bow down to your > magnificence. > 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. from 1,000 author options, which you 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) Do you know what 3 consecutive 1 in 1000 coincidences on the same day makes? If you can find ONE reply to you that you can spot the author from 100 posts consistently then SHOW ME! Do you atleast admit the post has a peculiar nature to it???????????????????????? click on it and don't 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! You're right! Paranormal! Right >> there! See, it says paranormal! It's been proven. |-|erc, I bow >> down to your magnificence. >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! It's *obviously* paranormal, especially since the people trying to guess the author couldn't 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. It's stunning proof of magic in our time! -- Mekkala, Atheist #2148 Atheism is ... the bed-rock of sanity in a world of madness. --Emmett F. Fields ==== > No, no, I was agreeing with you! You misunderstood me! It's *obviously* paranormal, especially since the people trying to > guess the author couldn't 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. It's stunning proof of magic in our time! > we're actually getting somewhere here, you basically agree the post has a 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. ----------------- Shanx See You In Hell My Friend. Someone Greg Neill ---------------------------------------------------------------------------- ---- Herc ==== Look who's 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. Results 1 - 7 of 7. Search took 1.57 seconds. Sorted by relevance Sort by date proof of god 0202 2002 http://www.skeptics.com.au/ ASS - we are a skeptic society that test people who claim to have paranormal ability Herc - I'd like to be tested, I have ... ping dick smith, tell him proof of god and skeptics use carrot -- ? ???) ? ~ proof of God -- ? ???) ? JAMES RANDI and AUSTRALIA SKEPTICS rrrrrr FFRRAAUUDDSS I'VE ALLREADY SENT YOU A NOTARISED APPLICATION PROOF OF GOD 0202 2002 guy at shop 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 i'm 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 of god 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? I've been hearing stuff, yeah. Webmasters help the TRUEman by joining www.theBanner.net Current:1 Goal:1000 ---------------------------------------------------------------------------- ------ X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 09:24 PM, mattinglyz@yahoo.com (Zac Mattingly) said: There is a difference between justifying the curriculum and motivating a 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 give are 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 JOAT Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org ==== > 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 to appreciate abstract subjects also without applications being given; only the lower species of people needs to know about applications first, 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 can't add or multiply, you'll get cheated at the cash register. If you can't do probablity, you'll get cheated all the time. If you can't understand complex budgetary issues, you'll get cheated at the polls. And so forth. Thomas ==== > If you can't understand complex budgetary issues, you'll get cheated > at the polls. And since no one understands them, we all get cheated at the polls, all the time. 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. 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 budgetary issue. Are you saying that a budget deficit one year will necessarily result in that horrible conclusion? Most businesses use debt as a cash-flow management technique. Governments wisely do the same. What I find really perverse is that huge budget deficits are the hallmark of Republican administrations in this country. If you don't want a deficit, 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 don't mean that. X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== >After much struggle, I finally reached page 31. >AXIOM OF COMPREHENSION: For any condition P(x) on x there exists a >set which contains exactly those elements x which fulfil this >condition. That would lead to Russell's Paradox. However, For any set A and any proposition P, there is a set {X /in A|P(x)} works, as does[1] For any well-formed proposition P, there is a set {X /in A|P(x)}, for appropriate definition of well formed. Presumably the authors were explaining why they did *not* use the axiom you quoted. [1] Quinne used that -- Shmuel (Seymour J.) Metz, SysProg and JOAT Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org ==== > Don't 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 fulfil this condition? > >That is one of the ZF axioms, but I don't think it's 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 don't think it's 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 didn't bet anything on that. ==== >That is one of the ZF axioms, but I don't think it's 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 didn't bet anything on > that. I have heard Separation called Bounded Comprehension. -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. <0312071423430.10086-100000@gandalf.math.ukans.edu> <0312090303010.19188-100000@gandalf.math.ukans.edu> ==== >That is one of the ZF axioms, but I don't think it's 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 didn't bet anything on >> that. I have heard Separation called Bounded Comprehension. Sometimes, I've also heard separation called either comprehension or bounded comprehension. On many occasions, I've been very close to the speaker using those terms. In his shoes, in fact. -- What I've learned is that [mathematicians are] the gatekeepers, and seem 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 set and nulset from comprehension and 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 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? ==== > (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, I'm used to the shunning replacement version, because I'm used to GBN set theory. So I think of replacement+comprehension as just GBN's comprehension, but of course, that isn't quite right, and this 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. I'm afraid I still don't see it. Can you explain, since it's so easy? ==== > I'm afraid I still don't see it. Can you explain, since it's so > easy? You can find 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. I'm afraid I still don't see it. Can you explain, since it's so easy? > Basically it goes like this: Sender: tb@becket.becket.net ==== > Basically it goes like this: How do you get the function from {nulset, {nulset}} to {a,b}? X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== In , on at 10:57 PM, Tim Smith said: >Wouldn't that be pretty much everyone except Erdos? No. Consider the 2nd greatest Mathematician in Europe, Gauss's waste basket. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org ==== 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, I'm *not* going to voice the obvious punchline here..... :-) -- #191, ewill3@earthlink.net It's 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 but IIRC, the conventional wisdom is that mathematicians do their most *creative* work in their 20s. So it would be interesting to examine the various sense of best work. E.g., was Weierstrass' work deeply creative, 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 >>Wouldn't 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). I'm not sure how to find the >greatest element in an empty set. Well, that would mean that JSH is an example of a mathematician, and I don't think 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... There's Cholesky decomposition, and then there's 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_ by Abelson, Fellman, and Rudolph (Harcourt, Brace and World, 1970), I see that despite Hal Abelson's best efforts, we did not manage to slip growth-and-decay theory past the copyeditors and into the text. Tant pis. Lee Rudolph X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== In , on >Is this an acceptable proof? It might get marked down for lack of elegance. It's certainly not the shortest or clearest proof. But in most circles it is correct. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 08:30 AM, kramsay@aol.com (KRamsay) said: >Conesetter's remark was in reply to David Ullrich, who said that the >analytic continuation construction produced a unique Riemann >surface. Which it does. >not even independent of homotopy. ? >Note that if something (like the function element reached by >continuing along a path which depends on the homotopy class of the >path), it follows logically that also it depends on the path. uniqueness. What you get depends on the path. What makes the construction unique is precisely the fact that it does not depend on the path within the homotopy class. You have to read his depends in context. >Shmuel Metz seems to enjoy saying no to people. :-) He also enjoys saying yes ;-) -- Shmuel (Seymour J.) Metz, SysProg and JOAT Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org <87llpozxni.fsf@phiwumbda.org> X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== 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. It is RIDICULOUS to pretend otherwise. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 01:07 PM, George Greene said: >but my point is simply that grownups know that sets >are just irrelevant period. That's a rather childish perspective. It's comparable to saying that only children use GBN and adults use ZFC. The fact that you prefer it does not make it more adult than other approaches. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org ==== I hate having to strongly agree and weakly disagree at the same time. I strongly agree with the following: : anyway it's 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 possible The trick, of course, is figuring out *which* of these viewpoints *merits* the push. The fact that they really are equivalent is precisely what makes that figuring *hard*, and entitles you to feel better about your teaching skills, if you can convince people that this one 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, that's basically an excuse : for going back to always seeing things from your old favorite : viewpoint, secure in the knowledge that it's really equivalent to all : those other viewpoints. I completely endorse this viewpoint. I did, after all, stress the relevance, early on, of the fact that from one viewpoint, ANY n-dimensional vector space is really the ordered n-tuples over its field, and ANY group is really a 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 field-elements are in some sense smaller and simpler than some other things that could be vectors. Permutation groups in some sense forget a lot of implementation detail of the other groups they can be isomorphic to. They are simpler subspaces of the overall class, even though everything in the class is isomorphic to one. Concreteness simply does not have this property. It is arguably MORE detailed and MORE hairy than any absrtact counterparts. The space of concrete groups or concrete categories is not fundamentally simpler at ANY level, than any bigger richer space that includes more abstractions. Saying you can represent any group as a concrete group is going in the OPPOSITE direction from saying you can represent any group as a permutation group. We in some sense know a reasonable, right smaller space of representatives for groups and vector spaces. The question of a prototype for categories gets much more complex, though, for the sole and simple reason that category in general is a sufficiently MINIMALLY-defined kind of structure that A WIDE VARIETY 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 of representatives of categories, then maybe we need to look SEPARATELY for prototypes of a) categories with a finite number of objects (but larger than 1, since we've solved THAT case), and b) cateogories with an infinite number of objects. ==== > Actually category theory started out as a way to define ``natural > transformation'' [There is a quote by Mac Lane to this effect. I don't > 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 is prototypical, what are the simplest natural transformations that 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 = 4 and also can be represented as: 00 01 10 11 P(3) = {{},{0},{1},{2},{0,1},{0,2},{1,2},{0,1,2}} = 2^3 = 8 and also can be represented as: 000 001 010 011 100 101 110 111 Let us call any 0,1 list, combinations list. When we use Cantor's Diagonalization function on the combinations list of 2^power_value and get some output result, we find that this result is already somewhere in the list. The formula that gives us the number of combinations , which are out of the range of Cantor's Diagonalization function, is: 2^n - n Combinations are first of all structural changes, based on at least two parameters: a)The number of different notations. b)The number of places that have been given to permute these notations. We get our list of infinitely many places, by using the ZF Axiom of infinity induction, on the left side of our combinations list (by changing power_value). When we have infinitely many places to combine our two different notations, then the number of combinations, which are out of the range of Cantor's Diagonalization function is: 2^aleph0 - aleph0 = E where by E we mean that there are E possible combinations, which are out of the range of Cantor's Diagonalization function, where one of these combinations, is Cantor's Diagonalization function result. Therefore Cantor's Diagonalization function result is not a new combination. Because the aleph0 long Cantor's Diagonalization function result cannot cover the 2^aleph0 list, it means that 2^aleph0 > aleph0, but we can define a map between any unique combination and some natural number, therefore 2^aleph0 = aleph0. Therefore (2^aleph0 >= aleph0) = {}, and we have a proof saying that Boolean Logic cannot deal with infinitely 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 Cantor's Diagonalization > function, where one of these combinations, is Cantor's Diagonalization > function result. > Therefore Cantor's Diagonalization function result is not a new > combination. You don't seem to understand what the theorem says. > Because the aleph0 long Cantor's Diagonalization function result > cannot cover the 2^aleph0 list, it means that 2^aleph0 > aleph0, but > we can define a map between any unique combination and some natural > number, therefore 2^aleph0 = aleph0. Cantor's theorem says that if X is any set, then |X| < 2^|X|. In particular, if X happens to be the set of natural numbers, then this reduces to aleph_0 < 2^aleph_0. To show that it is enough to show that if f: X -> 2^X is any injection from a set to its power set, then f is not 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 with the proof. The proof only concerns aleph_0 lists. > Therefore (2^aleph0 >= aleph0) = {}, and we have a proof saying that > Boolean Logic cannot deal with infinitely many objects. Wrong. In fact, the proof of Cantor's theorem works precisely the same whether the set X happens to be finite or infinite. -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. ==== >>Actually finding 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 bozo's 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 florish off the prestige of Skeptic companies that has plagued me in 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 or celebrities. Hey netkook, I can understand wanting people who make a steady income, but why should 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 me and I've never heard of you, well not as an alias anyway Herc ==== >Actually finding 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 bozo's 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 florish 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 first 'puter. You came in flapping your arms about with crap claims of paranormal powers. 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 don't know yet, Herc is subject to a restraining order. He's unemployed, suffers a mental condition (his own admission), cannot get laid which is unsurprising, considering the kinds of approaches he makes to female posters on usenet, and to cap it off, he thinks he's Truman, and we are all part of the truman show My purpose, and the purpose of many skeptics apparently, is to be the nasty guys in the script. -- Find out about Australia's most dangerous Doomsday Cult: http://users.bigpond.net.au/wanglese/pebble.htm You can't fool me, it's turtles all the way down. ==== kook author:wally author:anglesea. Results 1 - 10 of about 1,580. nutjob? you didn't even increase your count. Stay out of paranormal discussion forums with your abuse. Herc ==== Sonnyboy, don't you even know what groups you're posting to? : kook author:wally author:anglesea. Results 1 - 10 of about 1,580. : : nutjob? you didn't 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? I've been hearing stuff, yeah. Webmasters help the TRUEman by joining www.theBanner.net Current:1 Goal:1000 ---------------------------------------------------------------------------- ------ > Sonnyboy, don't you even know what groups you're posting to? I've spent months at each separately on the same topic, here is how it links up sci.skeptic : paranormal claim sci.math : statistical correlation requires validation rec.org.mensa : the proof is in the form of a puzzle alt.atheism : proof of god, help get me off the truman show Herc the proof is very obvious, George Bush points a very painful satellite at my head 24/7, if you don't follow up and give me some benefit of doubt I will suffer for several years longer. once you can see you can *measure* the statstic, and that noone can *compete* against me getting replies to give away the author, the paranormal claim is a sinch. 10% of Randi's million to those who try to justify my claim. ==== >>Actually finding 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 bozo's 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. Skeptic companies? WTF? Can you name 10? > The only people they test are already making steady incomes or celebrities. I would, because they're cheating people the most. > Look at the millions of hate posts made by skeptics, did you know alt.astrology > is called kook watcher central. Makes sense. > Here is Wally Anglesea, one of 100s of devout > skeptics that florish off the prestige of Skeptic companies that has plagued 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 - 10 of about 1,580. Up 100 on last week. Must be lots of kooks to respond to. Denis Loubet dloubet@io.com http://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 Join ASKE The annual fee, currently £8, (£10 for overseas members) is renewable on January 1st each year That's the 3 that offer prizes Herc strange 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 Bachelor's? Is it not possible to have the required > knowledge and no degree? Is it so very hard to verify that one's 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 wouln't be very hard to verify knowledge, but it is politically > incorrect and somewhat costly and time-consuming. Which is why grad schools can't be bothered unless you indicate that you are special. You don't get special consideration unless you're a special person. 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? I'm 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? I'm glad mine studied for their exams. What is the graduate with the lowest GPA in a Medical School class called? Doctor. A license to practice medicine isn't meaningful until the doctor does years of clinical work supervised by nurses (re green lieutenants and seargents) and senior doctors. The sciences require a whole lot of lab time - and that is only foreplay to practicing professionally. There are savants, and that's fine. If you have to read the books, then reading the books isn't nearly enough. -- Uncle Al http://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 diplomas Well, it's not like printing more of them will devalue them. Jon Miller ==== > >> And money is surely not the reason to print more diplomas >Well, it's not like printing more of them will devalue them. Actually, it IS like that. It's exactly what we've been experiencing. Afterall _something_ devalued the diploma, and if it wasn't 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 Stewart's books, _The Problems of Mathematics_ and _Another Fine Math You've Got Me Into_ springing to mind. Just start reading them, work all the problems. Read slow, and think of additional questions. Try to solve the additional questions. Then start with the references. This has the advantage that the parts are independent, and if something isn't interesting, you can just skip it, and if it is, you can dig as deep as you want. Also, the Columns section of MAA Online http://www.maa.org/. Again, this is just light reading unless you work on it yourself and refer to the references. Of course, if you need to get some papers out because there's a tenure committee 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 deficiencies 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 first-year graduate students (a Putnam Fellow, Alan Beale) had > come there after 3 years as an undergraduate without waiting to finish > a bachelor's degree. He left Harvard after one year, and I do not know > what happened to him... Which illustrates (but doesn't prove) one of the reasons for requiring a BA/BS. Proof that you can finish something. Employers want one for the same reason. And for employers, it still indicates some proficiency in reading and writing. Jon Miller ==== > When I began graduate school in math at Harvard in 1970, one of the >> other first-year graduate students (a Putnam Fellow, Alan Beale) had >> come there after 3 years as an undergraduate without waiting to finish >> a bachelor's degree. He left Harvard after one year, and I do not know >> what happened to him... Which illustrates (but doesn't prove) one of the reasons for requiring a >BA/BS. Proof that you can finish something. Employers want one for the same reason. And for employers, it still >indicates some proficiency in reading and writing. > Perhaps Mr. Beale is working with Bill Gates at Microsoft? I sometimes wonder if 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 Bachelor's? Is it not possible to have the required > knowledge and no degree? Is it so very hard to verify that one's 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 isn't necessary to have a bachelor's degree to enter graduate school. A former colleague of mine had a Ph.D. in math from the University of Chicago but had no bachelor's degree nor even a high school diploma. He went straight from his junior year of high school into the U. of C., moved from their undergrad program (without finishing) into the grad program where he completed his Ph.D. at the age of 21! I'd say that if you have the stuff you can get a graduate degree without having a bachelor's degree. You'll need to convince the graduate faculty that you really do have the stuff, not such an easy task, unfortunately. Though plenty of inept students get bachelor's degrees professors can and do write recommendations that have force and meaning and allow graduate school admission committees to know the true ability of an applicant. I'd say your best bet is to find a University near you that has a math faculty person whom you respect. Then take a graduate level course or two from that person to establish a 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. >I'm 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 degrees and other such credentials unless they can provide reasonable assurance that the person has a good share of the important knowledge 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 multiple degrees, what is the point? But I also stated that the knowledge and ability needs to be demonstrated; see the above to see my questioning whether the attainment of a degree is good 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 views are 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, it's worthwhile to make a cost-free exchange if possible. (A real-life application 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 its admissions criterion. So indeed, they all work pretty hard to make sure one has gotten that knowledge and ability. ==== >>Anyone know why Grad Schools will not accept your application unless >>you have a Bachelor's? Is it not possible to have the required >>knowledge and no degree? Is it so very hard to verify that one's 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 Bachelor's degree, >spends four or five years in pretty intensive study. There's always >homework to do, finish it up for one class and there's 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. >I'm 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 he's ready to enter grad school? At age 12, I encountered an algebra text. I tested out of algebra, and while taking a good plane geometry course and other high school courses, studied mathematics, not too efficiently. Within one year, I would have been close to ready for graduate school in mathematics. With the better books today, and very little guidance, I would have been ready for today's graduate schools. And this included being able to do the computational material. I did take one worthwhile undergraduate course, which BTW is not given any more. It is true that some of the graduate courses 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 in a short time. The professors did add some insight; that is what one can get from scholars who understand the subject. As for statistics, in which I am reasonably well known, I have never had even one course. The same holds in set theory. With a program, someone with the ability to understand should be able to learn more mathematics than is taught in good universities in two years. Only the upper division theory courses are really important, anyhow. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University ==== >$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 will be forgotten anyhow, are the few who should remain. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University ==== >> 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 will their efforts be largely undone by those others. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University ==== >> Anyone know why Grad Schools will not accept your application unless >> you have a Bachelor's? Is it not possible to have the required >> knowledge and no degree? Is it so very hard to verify that one's 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 bachelor's degree is a bit of work; >buying the College books, reading them at home at your leisure, isn't. It is not work that matters, but being able to think. Reading the books is not enough; understanding them is what is needed. Memorizing the textbook should not be enough to pass a decent course, but alas, too many do. It is hard to verify, but almost as hard (and sometimes harder) to verify for those who do get college degrees. >A bachelor's degree, besides being a claim of knowledge, >is also a claim of achievment. 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? >It represents keeping a commitment for a number of years. >That's the ability that the Grad Schools are most interested in. This might be what the administrators of the graduate schools are interested in; it is not what good faculty or good departments care about. I have been on the faculty side of this for a long time. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University ==== > 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 boss dishes 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 experience includes the ability to program? I knew a lot of programmers; just because their title had that word did not mean that they could do the work. If your grad study is going to be in computer science, then a life experience of programming should never be used to skip classes; remember, we're talking about degree study and the classes that could possibly be skipped are undergrad intros. In some cases, I can see where those undergrad intro courses might be a requirement for the life experienced person because s/he didn't work with that particular language or numerical recipe or... Now, if the degree program is in a hard science which has a requirement of the FOOBAR programming language _and_ the life experience of the student was based on programming using the FOOBAR language, then the requirement of setting in class learning how to set up a data structure in that language is probably a waste of that student's time. However, the student has to demonstrate an ability of using the FOOBAR language and not just with writing a baby problem. The reason for the programming language requirement is because it's going to 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 topic of racism, but that doesn't mean that they're helping. Doug ==== > >>Cynicism is learned helplessness. >That's snappy, to the point, and meaningless. You should write bumper > stickers. That wasn't the intent at all. This is the definition of cynicism (the sort displayed by HR, not the the ancient Greek variety.) One acquires such an attitude, say, about government, after having been continuously beaten by it, as a defense mechanism. One learns to _expect_ the worst in order to not have one's hope's dashed. Some people think cynic's are cute. I think they need help. They sure shouldn't 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 forgetting could change the fact that one has attained a certain level of understanding. Just as a mountain climber who later becomes disabled has 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 in Axiom A. Axiom A should really be phrased The purpose of a college degree at institution foo is to indicate the attainment, at foo, of a certain level of ... In otherwords, foo certifies that the degree in question has been earned at foo. Other schools do not need to award new degrees, though they do recognize the degree, and at their school, treat degree holders similarly even if the degree was not locally earned. (Which is not universal, however; Cambridge is famous for not letting degree holders from other schools wear their proper academic dress.) > 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 the collection may well be a demonstration that the degree holder has learned 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 (while not complete variability), so that it is often the *number* of tasks completed that matters, and a higher task can be substituted for a lower one. Thomas ==== I am teaching myself Applied Combinatorics by Alan Tucker, and I came across 2 problems on page 246 that I can't figure out... 1) Find a generating function for a_r, the number of ways n distinct dice can show a sum of r. 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 first 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 : This is NOT for a class Sincerely, Steve ==== > I am teaching myself Applied Combinatorics by Alan Tucker, and I came > across 2 problems on page 246 that I can't figure 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)^n each 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 first three dice are odd and the second three even. > b) The ith die does not show a value of i. Here is (a), I won't spoil (b) (x+x^3+x^5)^3 . (x^2+x^4+x^6)^3 First 3 roles, you can get 1, 3 ,5, the next three 2,4,6 > Can someone solve these in detail? I don't know how much detail there is in my answers, but anything more is just being verbose. Note : This is NOT for a class look up generatingfunctionology (available online) by Wilf. This is a great book. Sincerely, 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 >> > definable 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 didn't take my bait. I will prove to you that there is no >such last ordinal. Suppose K is the last ordinal definable within ZFC. Paul misspoke. Rather than talking about the largest ordinal definable within ZFC, you should instead talk about the smallest ordinal that is *not* definable in ZFC. There are only countably many formulas in ZFC, and so there are only countably many definable ordinals. But there are uncountably many ordinals. So there must be some ordinal that is not definable in ZFC. >But what do you mean by a recursive ordinal? Here's one definition: A recursive ordinal is an ordinal that can be coded using the natural numbers. In particular, alpha is a recursive ordinal if there is a countable enumeration beta_0, beta_1, ... of all the ordinals less than alpha, and there is a recursive function r(i,j) on naturals such that r(i,j) = 1 if beta_i < beta_j = 0 otherwise -- Daryl McCullough Ithaca, NY ==== > Paul misspoke. Rather than talking about the largest > ordinal definable within ZFC, you should instead talk > about the smallest ordinal that is *not* definable > 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. ==== >> Paul misspoke. Rather than talking about the largest >> ordinal definable within ZFC, you should instead talk >> about the smallest ordinal that is *not* definable >> 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. You're probably right. -- Daryl McCullough Ithaca, 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 definition* the >> future state of the system can be computed. That's 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 have an algorithm that allows you to compute the state of the universe at time t given the state of the universe at time 0. You still may not 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 quantification over all future times implicit in the question can make the question undecidable even if the evolution is perfectly algorithmic. Paul makes an analogy with a Turing machine. Given a description of a Turing machine and the tape at time 0, you can compute the state at any 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 McCullough Ithaca, 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 > > definable 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 didn't take my bait. I will prove to you that there is no > such last ordinal. Suppose K is the last ordinal definiable within ZFC. I did not say there was a last ordinal. I said there is a limit ordinal that is the union of all the recursive ordinals definable in ZFC. [snip] > But what do you mean by a recursive ordinal? Try Google. Its a standard part of mathematics. -- Paul Budnik Mountain Math Software http://www.mtnmath.com ==== > But what do you mean by a recursive ordinal? Googling for recursive ordinal will give you the definition. Paul Budnik's comment makes no obvious sense, however. ==== > But what do you mean by a recursive ordinal? Googling for recursive ordinal will give you the definition. Paul > Budnik's comment makes no obvious sense, however. > Ok, let me clarify. ZFC, as a formal system, is a computer program for enumerating theorems. Among these theorems are statements of the form A is a recursive description of a recursive ordinal. Take the union of all such ordinals. This defines a recursive ordinal that is the limit of recursive ordinals whose recursive structure is definable within ZFC as a formal system. -- Paul Budnik Mountain Math Software http://www.mtnmath.com 408 353 3824 ==== >> But what do you mean by a recursive ordinal? >> Googling for recursive ordinal will give you the definition. Paul >> Budnik's comment makes no obvious sense, however. > Ok, let me clarify. > ZFC, as a formal system, is a computer program for enumerating theorems. > Among these theorems are statements of the form A is a recursive description > of a recursive ordinal. Take the union of all such ordinals. This defines a > recursive ordinal that is the limit of recursive ordinals whose recursive > structure is definable within ZFC as a formal system. The union of a *recursive* set of ordinals is recursive. The set of all recursive ordinals is not a recursive set. Proof: if the set A of such ordinals is recursive, then alpha = lim A is recursive, and so is alpha+1. Contradiction. -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. ==== >But what do you mean by a recursive ordinal? > Googling for recursive ordinal will give you the definition. Paul > Budnik's comment makes no obvious sense, however. Oh sure. I was trying to say that whatever definition Budnik was using doesn't seem to have anything to do with the normal definition. ==== > Oh sure. I was trying to say that whatever definition Budnik was > using doesn't seem to have anything to do with the normal > definition. Why not? ==== >and Maple under Windows, but I need something that can compare to those two > If you are looking for free code (under the GNU GPL of course) - you may want to try Scilab or Octave. Both of them are like MATLAB(registered trademark, or whatever the law wants me to say) and are pretty easy to use. Saikiran ==== > Oh that's nothing. I've received replies from Congressman, and even > the Office of the President of the United States--form letter replies. > I don't talk about those as they're not relevant. Also I've received replies from other notables and famous people, > which are not relevant, so I don't discuss them. Google says that you've mentioned form letters five previous times. More interesting: James has again asserted that it's only a matter of time -- an expression he's used about 10 times since September, 2001 (but I may be double counting some usages). Of course, it's never clear how much time of which it's a matter, so maybe two or so years isn't a long enough wait. [snip bit about how James was brilliant to question Iraq's so-called MWD and how everyone else was cowardly] > What were you arguing? It seems to me that you're rambling at this > point. -- I've ... contacted [some of the...] highest I.Q.'s in the country... I've even helped the FBI out a few times... I've met at least one governor..., a senator... and I've had some really good seats at sports games. My experiences are not your experiences. --JSH != you ==== First, sorry if I get some things wrong in english, my native language is german, so some translations might not fit the proper english ones. I'm currently implementing a Program for factorization of large integers using the ECM (Elliptic Curve Method). Beside the problem of finding the proper bounds for the algo, I have another problem. In some papers I read was mentioned that it would speed up the Algorithm, when the Group-Order can be devided by 4 (or 16). I can't find a proper description of how to generate such a curve. So the question is, for a given a, how do I construct the elliptic curve on b = y^2 - x^2 - ax ?? Please try to be as specific as possible, since I study Computer Science, not Mathematics, so I only know the basics of advanced mathematics stuff. greets Dennis ==== >I'm currently implementing a Program for factorization of large integers >using the ECM (Elliptic Curve Method). Beside the problem of finding the >proper bounds for the algo, I have another problem. In some papers I read >was mentioned that it would speed up the Algorithm, when the Group-Order can >be devided by 4 (or 16). I can't find a proper description of how to >generate such a curve. >So the question is, for a given a, how do I construct the elliptic curve on >b = y^2 - x^2 - ax ?? I thought I understood the question until your last line: I can tell you that an elliptic curve contains a subgroup of order 4 when it can be described by an equation y^2 = (x-r1)(x-r2)(x-r3) ; namely the points (r_i, 0), together with the identity element (at infinity) form a group isomorphic to (Z/2)x(Z/2). You can have higher torsion too; for example, the curves described by equations of the form Y^2 + X Y + t Y = X^3 + t X^2 have elements of order 4. When t is of the form (1-u^2)/16, there is a subgroup of order 16. But it looks like you want the curve to have the explicit form y^2 = x^3 + a x + b (correcting for a typo), where a has been given and you wish to choose b. Is that correct? I don't think you can necessarily force this to have subgroups of order 4 or 16 for every a. dave ==== I am bored at work, so here I go with my best work... Interpreting your problem and drawing a graph, I came up with two equations. Eq 1 for Length of fencing (and therefore, the cost) is f(x) = 3a + 2b with a being the length of the fence and b being the width of the fence. There are 3 a's since we have another length of fencing running down the middle to intersect the pens into two identical sized pens. Eq 2 for the Area is g(x) = ab and we know that g(x) = 10,000. There are too many variables for us to differentiate f(x) (at least for my Calc I knowledge) so some simple math on g(x) leads me to know that a = 10,000 / b. I substitute this back into f(x) to get rid the pesky a term giving me: f(x) = 3 (10,000 / b) + 2b We can now differentiate f(x) which gives me: f'(x) = (-30,000/b^2) + 2 Some fiddling around leads me to knowing that b = (15,000) ^ (1/2) (sq. root 15,000). Worked out b = 122.47m. Subsituting back into g(x), 10,000 = a * (122.47) so a = 81.65m. With these dimensions the length of fencing will total 612.35m but we can assume we can only buy whole meters so 613m will cost $4597.50. I wonder if this is right? Matt > Can you please explain the solution to this problem and send it to me as soon as possible. A farmer wants to create 2 identicle pens by fencing in a rectangular space and running a fence through the middle. A fencing company will build the fenc for $7.50/m. The farmer wants a total fenced area of 10000m squared. What is the LEAST that he will pay for the fence.? > ==== > test Read it anyway. It's not blank. Test failed. -- Paul V. S. Townsend Interchange the alphabetic elements to reply ==== Here is Eucleides's proof that there are infinitely many Pythagorean triplets. If n is a natural, then n^2 - (n-1)^2 = (n+n-1)(n-n+1) = 2n-1. This means that every odd natural (>1) is the difference between two squares. Some of these odd naturals are squares themselves. There are (at least) as many Pythagorean triplets as there are odd squares. And because there are infinitely many odd numbers, and an odd number's square is odd, then there are infinitely many Pythagorean triplets. Do I remember this proof correctly? -- /-- Joona Palaste (palaste@cc.helsinki.fi) ------------- Finland -------- -- http://www.helsinki.fi/~palaste --------------------- rules! --------/ My absolute aspect is probably... - Mato Valtonen ==== If I have 2 - sqrt(12)i how do I find the polar form? So far I've worked out that r = 4 and the argument is 5pi/6. The next step I'm not sure about. Do I put it in the form r(cos(theta) + isin(theta))? Making it 4(cos(5pi/6) + isin(5pi/6))? Then what do I do? BTW - what is the correct notation on here for angle theta? TIA ==== > If I have 2 - sqrt(12)i how do I find the polar form? So far I've worked out that r = 4 and the argument is 5pi/6. The next step I'm not sure about. Do I put it in the form r(cos(theta) + > isin(theta))? Making it 4(cos(5pi/6) + isin(5pi/6))? Then what do I do? BTW - what is the correct notation on here for angle theta? TIA You've done it perfectly -- David Moran Chief Meteorologist Oklahoma Storm Team ==== > I'm cross posting this to sci.physics.electromag because that may be a > more appropriate venue > You have a flashlight that holds 2 (1.5 volts) batteries. If you reverse > > just one battery the flashlight will not work if you turn on the > flashlight. > > But do the batteries get used up if you leave the switch on. When one battery is reversed, there is no potential difference overall, net 0 voltage, there is no reason for a current to flow so no, the batteries won't wear out. I bet you already knew that cos pi = -1 and such. But I was shocked to find, just now, that there appears to be a _vegetable_ in the domain of cos x. (Yes, you read that correctly. Obviously this is a silly pseudo-mathematical post, but then you could tell that from the thread's title.) What is that vegetable? What is the value of cos x there? (I guess I should wait for other people to try to answer first. But this is far too silly to be drawn out that way, and so I've given the answers below.) David S P O I L E R S P A C E The vegetable is lettuce. According to my dictionary: cos lettuce = romaine ==== I need a suggestion. I took linear algebra this semester up here in Montana (MSU-Billings). I thought that I could handle it, but I'm really struggling. In fact, I'm having to take an incomplete in the course because it's just not making any sense to me. I've always been strong in math, but matrices and vectors spaces have got me entirely stumped. Are there any good resources (either in print or online) out there that anyone knows of that would help me out. Something like Linear Algebra for Complete Morons would be nice . . . Matthew Senn Mathematics Major, MSU-Billings ==== When i did linear algbra last year in a different university we used Linear Algebra and its applications by David C .Lay there is also a study guide for it. But be sure to use it only to check your answer or see if there is a better way answering the question. You should drop by the uni libary as well and have a bit of a look through there selction of book see if any suit you. If you want online stuff i found it helpful just to search on google on a specific topic there are quite a few sites but some are abit over the undergrads head though. You should also see the lecturer and get help from them. I find it best as soon as you start to feel things get away from you. get someones help. let ====