mm-3149 ==== > David's point is a good one. Apart from exhaustively testing > an implementation with all possible inputs of length less than > 1000 digits, I see no way to prove an implementation attains > your goal of establishing primality in the given time limit of no > more than a few hours. ... > For this reason the tests commonly used in cryptographic > applications might be said to be probabilistic in name only. > If you're asking me, I was responding to the original poster's quest > for primality testing software. See the OP's requirements, which > were left in my response, specifying that inputs up to a thousand > digits should be handled in no more than a few hours. There are primality proving algorithms out (that do not rely on the truth of any hypothesis). Check APR-CL. They have been extended to way beyond the original 300 digit number for which they were designed. Proving 80 digit number primes is a question of less than a second. When I first used them on a Cray 1, proving a 200 digit number prime took 8 minutes; speed has increased quite a bit since that time... http://www.cwi.nl/~dik/ ==== What are primative rings and do they have any particular structure? ==== > What are primative rings and do they have any particular structure? A ring R is said to be left (right) primitive ring if there is a left (right) R-module V such that V is a simple faithful R-module. The term left and right here is important. There are right primitive ring which are not left pimitive (Bergman result). There is a well-known classification for pimitive rings (see I. N. Herstein, Noncommutative rings, The mathematical Association of America, 1968. Best wishes Alireza Abdollahi ==== >There is a well-known classification for pimitive rings (see I. N. >Herstein, Noncommutative rings, The mathematical Association of >America, 1968. about primitive rings. Also, not knowing what a simple faithful R-module is, I'm afraid I've not the background for his book. Additionally I was frustrated trying to locate Noncommutative Rings, at MAA. ---- ==== >> >>[rants that make my point better than I ever could snipped] >>David Ullrich got caught once in an interesting exchange where he >>called me an idiot for apologizing to a *French* newsgroup for not >>posting in French. >> >> Nope. Never happened. (Provide a citation, please). > idiot FOR APOLOGIZING TO A FRENCH NEWSGROUP FOR NOT POSTING IN FRENCH. According to the post in question, your comments were: >>Well I must say I'm impressed if Ullrich speaks French! >>Though I'd have been more impressed if he'd replied in it! To which David Ullrich replied: >> Idiot. It is clear that you were not apologizing to anybody. Therefore, you lied. Since you knew the post in question, your lie was a knowing lie. ====================================================================== Why do you take so much trouble to expose such a reasoner as Mr. Smith? I answer as a deceased friend of mine used to answer on like occasions - A man's capacity is no measure of his power to do mischief. Mr. Smith has untiring energy, which does something; self-evident honesty of conviction, which does more; and a long purse, which does most of all. He has made at least ten publications, full of figures few readers can critize. A great many people are staggered to this extend, that they imagine there must be the indefinite something in the mysterious all this. They are brought to the point of suspicion that the mathematicians ought not to treat all this with such undisguised contempt, at least. -- A Budget of Paradoxes, Vol. 2 p. 129 by Augustus de Morgan ====================================================================== Arturo Magidin magidin@math.berkeley.edu ==== I thought that I'd posted this, yesterday: is this a conjecture on the twin primes, UA? be nice! > If one looks at pairs of consecutive prime numbers separated by only > one non-prime number - 41,43; 821,823; 8087,8089 etc. - one sees that > the sum of such two primes is often divisible by 12: > > (11 + 13)/12 = 2 > (41 + 43)/12 = 7 > (821 + 823)/12 = 137 > (1931 + 1933)/12 = 322 > (8087 + 8089)/12 = 1348 > (104681 + 104683)/12 = 17447 --les ducs d'Enron! http://www.tarpley.net ==== >If one looks at pairs of consecutive prime numbers separated by only >one non-prime number - 41,43; 821,823; 8087,8089 etc. - one sees that >the sum of such two primes is often divisible by 12: (11 + 13)/12 = 2 > (41 + 43)/12 = 7 > (821 + 823)/12 = 137 > (1931 + 1933)/12 = 322 > (8087 + 8089)/12 = 1348 >(104681 + 104683)/12 = 17447 > 3,5 obviously does not work. Use your Harris big mouth to find >another pair of consecutive primes other than 3,5 whose sum is not >evenly divisible by 12. Interesting. I've never seen that before. How would you suggest going about finding the other pair other than by brute force? ==== > >[rants that make my point better than I ever could snipped] > >David Ullrich got caught once in an interesting exchange where he >called me an idiot for apologizing to a *French* newsgroup for not >posting in French. > > Nope. Never happened. (Provide a citation, please). > He called you an idiot for something else. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ ==== function? > > A simple guess would be jealousy. And it hardly makes sense that he'd > be jealous of a rehash. Oh gosh, why didn't I see all this before? Of course, everything you say just must be true. For if no-one questions its accuracy, we can be sure it's true, but if anyone does question its accuracy, the only possible explanation is jealousy, and again we can be sure it's true. Would this work for me too? function was the fastest possible. However, in its base form, it's > rather slow, as implementations find primes on their own and don't use > the information about found primes. > > For faster *algorithms* it pays to use sieves. Hmm. Can you explain the significance of the '*' round algorithms? Am I right in understanding that yours is a *function*, not an *algorithm*? > What's OP? Original Poster Brian Chandler ---------------- http://imaginatorium.org ==== ... > > Nope. Never happened. (Provide a citation, please). > > > > He called you an idiot for something else. (He might also have called you idiot savant...) -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ ==== the floating-point standard (IEEE-755, -855, I think) inherently is chaotic; and, it's impimentation is completely variable, in both software & hard. > Funny that. Your claim is that your algorithm is the fastest in the > world, so a value of 2^63 should no problem. What is more funny is that > you get it wrong again: Your Java program cannot work for values up to > 2^63, because the square root of 2^63 doesn't fit into an int (only > values up to 2^31 - 1 work). Not that it cannot be fixed, but it shows > that you are just incapable of any coherent thought. --UN HYDROGEN (sic; Methanex (TM) reformanteurs) ECONOMIE?... La Troi Phases d'Exploitation de la Protocols des Grises de Kyoto: (FOSSILISATION [McCainanites?] (TM/sic))/ BORE/GUSH/NADIR @ http://www.tarpley.net/aobook.htm. Http://www.tarpley.net/bushb.htm (content partiale, below): 17 -- L'ATTEMPTER de COUP D'ETAT, 3/30/81 23 -- Le FIN d'HISTOIRE 24 -- L'ORDEUR du MONDE NOUVEAU 25 -- THYROID STORK !?! ==== >> >>[rants that make my point better than I ever could snipped] >>David Ullrich got caught once in an interesting exchange where he >>called me an idiot for apologizing to a *French* newsgroup for not >>posting in French. >> >> Nope. Never happened. (Provide a citation, please). > an idiot for apologizing to a French newsgroup for not posting in French. I called you an idiot for saying you'd be impressed if _I_ had posted in French, like a working knowledge of that language is a big deal, attained by only a few geniuses. A quote from the post you refer to here: [James] >>Well I must say I'm impressed if Ullrich speaks French! >>Though I'd have been more impressed if he'd replied in it! [Ullrich] >> Idiot. Once again we see how accurate your version of events is. It's curious - you say something happpened, I say it never happened and ask for a reference. You give a reference that _shows_ it never happened, but you don't seem to notice that fact... >>When informed that he was on a French newsgroup >>making his posts, he gave some excuse about not knowing, Btw, this never happened either. >>but never >>apologized to me nor to the newsgroup. >>And ask yourself, how does it all relate to the poster who noted the >>nitpick? _This_ is _very_ curious. _You_ brought the whole thing up just now, now _you_ are asking about its relevance? >>James Harris >> >> ************************ >> >> David Ullrich is a math professor at Oklahoma State University. He is >therefore paid by the state and by American taxpayers as I'm sure the >school receives funds from the federal government. My point is that he should be held to *some* standard, where at a >minimum public lying is frowned upon. James Harris ************************ ==== >[...] >Seems like James Harris has an algorithm for counting primes >which is correct, even if perhaps not totally novel and not >the fastest available today. Yes (although the word totally is perhaps overly polite.) >If he has come up with the algorithm >himself, clearly he is bright enough to do mathematical work of >more importance, perhaps given some mentor and of course, actual >interest on his part. Yes. Nobody has ever denied this. In fact it's happened many times that people have pointed out exactly what you say here and suggested that he actually study some mathematics. But he doesn't appear to have any interest in doing so. One conjectures that this is because if he were to start a serious study of mathematics he would first have to admit to himself that he's _not_ at present one of the top number theorists in the world (one of the many curious things he's stated many times). >(Anybody wanna offer him a graduate >fellowship so he has more interesting things to deal >with and stops posting?) Re on-topic vs off-topic, I think meta-comments about >a discussion are relevant to the discussion. The topic >itself is only marginally relevant to Java as such, but >the comparison to C++ seems to have generated some interest. ************************ ==== > He has responded to such statements many times, simply stating > that it's not so. But it is. > > That is a false statement. > > Ultimately Ullrich's case seems to rest on the fact that my work gives > the same answers as others. But, given that, for instance, there are > 4 primes up to 10, which are 2, 3, 5, and 7, prime counting methods, > and any correct prime counting function will give the same answer. > > I am more than happy to go into details about why my prime counting > function is significant and is NOT a rehash. Well, what advantage does your method provide over existing methods? Is it significantly faster? Tables of primes already exist on the web for very large number of primes. One could simply do a table search to see if a number is a prime or not. The only advantage one might see for a new method is for assisting in the computation of even newer and larger primes. If your method is faster, the people computing new primes and building tables will be happy to use it, I am sure. You might want to contact and convince such people. But if your method is not _seriously_ faster than what they are already using (faster enough to justify rewriting their programs,) you won't hear a peep back from them. And there is nothing else in it for you. Primes are old stuff. In today's age, it's not something for which somebody is going to put you in history books or give you large amounts of grant money. There isn't a nobel prize in it, either. So why waste your good cheer over it? Nobody seems to be arguing seriously that your method is incorrect. Even if they are ornery enough not to have come out right away and told you that your method was correct -- that's kind of expected on the usenet. So be happy that your method is correct, and nobody has found an actual fault in it. After that, if you want to emulate Newton and fight like a bitch over credit, that's your business. It's a personal choice, is it worth it to you, enough to get into these fights that deterioriate into sleaze quickly, and pull you and everyone else down? > David Ullrich is commenting on my issue with a post where he talked of > a racial slur being the perfectly appropriate reply to me. > > He also has an interesting post which you can find by going to > groups.google.com and checking posts where David Ullrich is the > author, and he uses the word rape. I am not sure what to make of it. You are exposing that when Mr. Ullrich thinks of particular vicious nasty crimes, he seems to think only members of a certain race are capable of them. Now if that's the case, I would say Mr. Ullrich's upbringing was sadly wanting and/or he has not been a particularly thoughtful individual since, and maybe has convinced himself Jeffrey Dahmer was framed. But none of that's really related to primes. It would be nicer if both sides had avoided attacks on character of each other. There is a context when the best of us need to be pointed out the errors in our thinking, but ideally the context is not that of attacks on each other. > What's OP? Useful new net shorthand for Original Poster. ==== > > Yes, I have been seeing this show up on comp.lang.java.advocacy, > so I am not familiar with the presumably longer history! > > Here's a quick summary: For about EIGHT YEARS James Harris has been > discoveries to sci.math (and often to other newsgroups). Much of the > time his arguments are too vague and ill-defined for people to make sense Sorry, that's not believable. Something that can be put into a Java or C++ program that can be understood by a compiler is by nature not vague or ill-defined. Frankly, vague and ill-defined are cop-outs used frequently by many incompetent and dishonest people in academia and on usenet, so you have to do better than that if you want to be taken seriously. E.g. take a crucial part of the argument and show that it rests on lack of clear definition (ill-defined) or can be interpreted in meaningfully and significantly different ways (vague.) <3c65f87.0307020542.78b862ac@posting.google.com> <9fa75d42.0307080749.707b7827@posting.google.com> <6jdmgvkm83p1mvup4lie71h55gm4u9trif@4ax.com> <9fa75d42.0307090412.28500a34@posting.google.com> ==== || || | Yes, I have been seeing this show up on comp.lang.java.advocacy, || | so I am not familiar with the presumably longer history! || || Here's a quick summary: For about EIGHT YEARS James Harris has been || discoveries to sci.math (and often to other newsgroups). Much of || the time his arguments are too vague and ill-defined for people to || make sense | | Sorry, that's not believable. Something that can be put into | a Java or C++ program that can be understood by a compiler is | by nature not vague or ill-defined. the breakthrough he claims it is. Wayne was referring to James's other mathematical arguments, such as his claimed proof of Fermat's Last Theorem, his claimed proof that Wiles's proof of FLT is invalid, and his claimed proof that 'core mathematics' has a fatal flaw because the ring of algebraic integers is 'incomplete'. -- http://www.dfan.org ==== > [...] > David Ullrich is commenting on my issue with a post where he talked of >> a racial slur being the perfectly appropriate reply to me. >> >> He also has an interesting post which you can find by going to >> groups.google.com and checking posts where David Ullrich is the >> author, and he uses the word rape. I am not sure what to make of it. You are exposing that when >Mr. Ullrich thinks of particular vicious nasty crimes, he seems >to think only members of a certain race are capable of them. Um, maybe exposing was not the word you meant - it seems to me that if you say someone's exposing something it follows that the thing being exposed is actually so. It's certainly not true that I think that only members of certain races are capable of certain nasty crimes. (Maybe espousing is what you meant? Not sure I spelled that right.) In case you _do_ think that the posts James is referring to demonstrate that I think what you say James is exposing, let me just clarify: Long ago James told us he was black. Some time later, still long ago, he said something particularly insulting and dehumanizing - it occured to me at the time that a racial slur in reply would be appropriate, simply to illustrate the idea that there is such a thing as you're not supposed to talk to people that way. I refrained, because it wouldn't have been something I meant, and because of course I'm _not_ supposed to talk to people that way. Then some time later, still long ago, in reply to some other egregious insult, I said what I say in the previous paragraph, about things I once considered saying and why, and why I did not say them. Again, my point was simply to say that there is such a thing as ways one is simply not supposed to talk to people - James had stepped way over that line and I wanted to point out that there was in fact such a line. In my post I included a statement as above, to the effect that I once (briefly) considered the idea that a racial slur would be appropriate - pointed out that of course I decided it wasn't, in fact it's not something I said. James replied that a racial slur was _never_ appropriate. This statement is of course ridiculous; I pointed out that for example, to take an extreme case, if someone had broken into my home, tied me up and was about to rape my daughter, if I thought that calling him a nasty name might distract him until the police arrived then a racial slur would be not only appropriate, refraining from making such a comment would be positively wrong. And since then he's accused me of thinking that blacks are rapists, or that rapists are all black, or whatever - he never puts it quite so baldly, just points to that post as evidence of my attitudes. Which of course is twisting things - the rapist in the imaginary scenario is in fact black (or a member of some other unspecified minority, let's say black for simplicity's sake), but that's not because I think that rapists tend to be black, it's because the _question_ was whether it's correct to say that a racial slur is _never_ appropriate - a hypothetical example illustrating that that's not so is necessarily going to involve a minority. I mean, duh. >Now if that's the case, I would say Mr. Ullrich's upbringing >was sadly wanting and/or he has not been a particularly thoughtful >individual since, and maybe has convinced himself Jeffrey Dahmer >was framed. But none of that's really related to primes. >It would be nicer if both sides had avoided attacks >on character of each other. There is a context when >the best of us need to be pointed out the errors in >our thinking, but ideally the context is not that >of attacks on each other. > What's OP? Useful new net shorthand for Original Poster. ************************ ==== > ... > > > Nope. Never happened. (Provide a citation, please). > > > > > > > He called you an idiot for something else. > > (He might also have called you idiot savant...) Hmmm...so Ullrich calls me an idiot for noting that I'd be impressed if he'd written in French in posting to a French newsgroup, and first you claim it was for something else, and *then* you reply again to claim that he actually *was* posting in French!!! Fascinating. James Harris ==== >> >> Yes, I have been seeing this show up on comp.lang.java.advocacy, >> so I am not familiar with the presumably longer history! >> >> Here's a quick summary: For about EIGHT YEARS James Harris has been >> discoveries to sci.math (and often to other newsgroups). Much of the >> time his arguments are too vague and ill-defined for people to make sense Sorry, that's not believable. Something that can be put into >a Java or C++ program that can be understood by a compiler is >by nature not vague or ill-defined. He was not referring to the Prime Counting Function, rather to James purely mathematical breakthroughs (things like his proof of Fermat's last theorem, his Object-Oriented Mathematics, his Advanced Polynomial Factorization, etc. Years and years of stuff, all of it in fact vague and ill-defined. Like object- oriented mathematics sounds interesting, but he's never given a coherent definition of the basic concepts. (yes, he will call what I just said a lie. He doesn't know what a _coherent definition_ _is_ - he _thinks_ he's given them.)) >Frankly, vague and >ill-defined are cop-outs used frequently by many incompetent and >dishonest people in academia and on usenet, so you have to do >better than that if you want to be taken seriously. E.g. take >a crucial part of the argument and show that it rests on >lack of clear definition (ill-defined) or can be interpreted >in meaningfully and significantly different ways (vague.) How about when James uses a technical term, it's clear that whatever he means by it is not what the term usually means, and for _years_ (literally) he simply ignores requests for an explanation of what he _does_ mean by the term? Would you consider that using vague and ill-defined terms? You really need to do some research on sci.math for the last eight years, at google, say. ************************ ==== >> >> Yes, I have been seeing this show up on comp.lang.java.advocacy, >> so I am not familiar with the presumably longer history! >> >> Here's a quick summary: For about EIGHT YEARS James Harris has been >> discoveries to sci.math (and often to other newsgroups). Much of the >> time his arguments are too vague and ill-defined for people to make sense > Sorry, that's not believable. Something that can be put into > a Java or C++ program that can be understood by a compiler is > by nature not vague or ill-defined. Frankly, vague and > ill-defined are cop-outs used frequently by many incompetent and > dishonest people in academia and on usenet, so you have to do > better than that if you want to be taken seriously. E.g. take > a crucial part of the argument and show that it rests on > lack of clear definition (ill-defined) or can be interpreted > in meaningfully and significantly different ways (vague.) Only a tiny fraction of James' output can be put into a Java or C++ program that can be understood by a compiler or has anything at all to do with computers. I'm not talking specifically here of his prime-counting algorithm but of the whole body of his work, most of which consists of failed attempts to prove Fermat's Last Theorem. There are numerous examples of his vague or ill-defined terminology in the threads archived in Google; of which his use of factor is a prime (pun intended) example. (He uses expressions in his proofs like x has a factor of y sometimes to mean y divides x and sometimes to mean there is a factor, z, that divides both y and x. The intended meaning usually is left for the reader to guess. He also has a habit of using ring operations without clearly identifying the ring in which he's working, or assuming that because an argument holds in one ring, it also holds in another; this unspoken assumption can cause people to spend days trying to puzzle out his meaning, especially when they can't tell which ring he thinks he's using.) I'm not going to start looking up choose; but here are links to a few recent examples to get you started, if you're interested: http://www.google.com/groups?selm=be7qih%249li%241%40agate.berkeley.edu http://www.google.com/groups?selm=bef8oc%241vi7%241%40agate.berkeley.edu http://www.google.com/groups?selm=36024859.0307080736.58977a6f%40posting.goo gle.com Basically, what I've been saying is that the presumably longer history with which you said you were not familiar demonstrates just why many people have no confidence in Harris or his work. Because of that richly-deserved opinion, anything he does (including programming) is greeted with extreme skepticism by many of us. I'm really not trying to prove anything to you here -- reject everything I've said if you prefer -- I'm just making you aware of the general opinion of himself James has created over a period of years on USENET. -- Wayne Brown | 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 ==== > Seems like James Harris has an algorithm for counting primes > which is correct, There seems to be some dispute about that > even if perhaps not totally novel and not > the fastest available today. If he has come up with the algorithm > himself, clearly he is bright enough to do mathematical work of > more importance, ! > perhaps given some mentor and of course, actual > interest on his part. !! > (Anybody wanna offer him a graduate > fellowship so he has more interesting things to deal > with and stops posting?) !!! -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html The League of Gentlemen ==== >> Yes, I have been seeing this show up on comp.lang.java.advocacy, >> so I am not familiar with the presumably longer history! >> >> Here's a quick summary: For about EIGHT YEARS James Harris has been >> discoveries to sci.math (and often to other newsgroups). Much of the >> time his arguments are too vague and ill-defined for people to make sense > > Sorry, that's not believable. No, it happens to be true. > Something that can be put into > a Java or C++ program that can be understood by a compiler is > by nature not vague or ill-defined. You are asserting that JSH's various alleged proof of Fermat's Last Theorem can be put into a Java or C++ program that can be understood by a compiler. Please justify this. > Frankly, vague and > ill-defined are cop-outs used frequently by many incompetent and > dishonest people in academia and on usenet, And they are also inevitable when commenting on many USENET postings :-( > so you have to do > better than that if you want to be taken seriously. He has done. Have you? > E.g. take > a crucial part of the argument and show that it rests on > lack of clear definition (ill-defined) or can be interpreted > in meaningfully and significantly different ways (vague.) Been done wish JSH (frequently). -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html The League of Gentlemen ==== > > He has responded to such statements many times, simply stating > that it's not so. But it is. > > That is a false statement. > > Ultimately Ullrich's case seems to rest on the fact that my work gives > the same answers as others. But, given that, for instance, there are > 4 primes up to 10, which are 2, 3, 5, and 7, prime counting methods, > and any correct prime counting function will give the same answer. > > I am more than happy to go into details about why my prime counting > function is significant and is NOT a rehash. > > Well, what advantage does your method provide over existing > methods? Is it significantly faster? Tables of primes > already exist on the web for very large number of primes. > One could simply do a table search to see if a number > is a prime or not. You're focusing on algorithms, which isn't a surprise as I take it you're a computer scientist. But remember I'm arguing with mathematicians. I doubt Ullrich would be caught dead in a computer lab unless he was going in to toss something into the trash if he wandered by it and no other was handy. However, my prime counting function maps out the entire distribution of prime numbers over infinity by telling you how to get them over infinity in a difference equation that you can easily transfer from to a partial differential equation. It may disprove some interesting assertions in mathematics like that the prime distribution crosses li(x) an infinite number of times by proving that it *never* crosses li(x). It may disprove Riemann's entire approach which is the basis for the famous Riemann Hypothesis by showing that certain of his assumptions were flawed. I say may because I'm not sure. But if mathematicians can fight to not even properly acknowlede the mathematics, how will anyone know? > The only advantage one might see for a new method is for assisting > in the computation of even newer and larger primes. If your method > is faster, the people computing new primes and building > tables will be happy to use it, I am sure. You might > want to contact and convince such people. And you've been caught in the assumption that it's just some algorithm. However, the reality is that it's a mathematical function that's apparently never been seen before, which just might give a new approach to a lot of high level mathematics. But if it *has* been discovered before but never put in references or textbooks that just emphasizes my point. The mathematicians you see me talking about or who you see posting in reply to me don't know everything. For all any of us know, someone a hundred years from now might be the one capable of putting things together in some important way. But if these mathematicians can get away without even acknowledging my work, then you open up the possibility that some person down the line never even sees the function as it's not in a textbook. How could any of you defend them not even giving proper acknowledgement? > But if your method is not _seriously_ faster than what they > are already using (faster enough to justify rewriting > their programs,) you won't hear a peep back from them. > And there is nothing else in it for you. Primes are old > stuff. In today's age, it's not something for which > somebody is going to put you in history books or give > you large amounts of grant money. There isn't a nobel > prize in it, either. So why waste your good > cheer over it? There's more to the prime distribution than counting primes. And it's not just about prizes or money. Don't any of you care about knowledge? Why allow mathematicians to just pick and choose at their whim? > Nobody seems to be arguing seriously that your method > is incorrect. Even if they are ornery enough not > to have come out right away and told you that your method > was correct -- that's kind of expected on the usenet. > > So be happy that your method is correct, and nobody > has found an actual fault in it. After that, if you want > to emulate Newton and fight like a bitch over credit, that's > your business. It's a personal choice, is it worth it to > you, enough to get into these fights that deterioriate > into sleaze quickly, and pull you and everyone else down? If necessary I'll tear down the entire mathematical world as it's currently known. > David Ullrich is commenting on my issue with a post where he talked of > a racial slur being the perfectly appropriate reply to me. > > He also has an interesting post which you can find by going to > groups.google.com and checking posts where David Ullrich is the > author, and he uses the word rape. > > I am not sure what to make of it. You are exposing that when > Mr. Ullrich thinks of particular vicious nasty crimes, he seems > to think only members of a certain race are capable of them. Standards. I say that a university professor should be held to some standard, and people argue with me. > Now if that's the case, I would say Mr. Ullrich's upbringing > was sadly wanting and/or he has not been a particularly thoughtful > individual since, and maybe has convinced himself Jeffrey Dahmer > was framed. But none of that's really related to primes. > It would be nicer if both sides had avoided attacks > on character of each other. There is a context when > the best of us need to be pointed out the errors in > our thinking, but ideally the context is not that > of attacks on each other. Well if you wish to give him a title why don't you address him as Professor? He is a professor at Oklahoma State University, after all. I dare you to stop calling him Ullrich or Mr. Ullrich and from now on address him as professor Ullrich. Like I'm sure his students do in Oklahoma. > What's OP? > > Useful new net shorthand for Original Poster. James Harris ==== which computerized proofs do you believe, by the lights of thier adequate documentation? in other words, you've got to be kidding. > Sorry, that's not believable. Something that can be put into > a Java or C++ program that can be understood by a compiler is > by nature not vague or ill-defined. Frankly, vague and > ill-defined are cop-outs used frequently by many incompetent and > dishonest people in academia and on usenet, so you have to do > better than that if you want to be taken seriously. E.g. take --A church-school McCrusade (Blair's ideals?): Harry-the-Mad-Potter want's US to kill Iraqis?... For a 1000-year anglo-american hegemony? HEY, JIMMY; LET'S US and SU FIGHT -then-PM of England & Zbiggy http://www.tarpley.net/bush25.htm (Thyroid Storm ch.) http://www.rwgrayprojects.com/synergetics/plates/plates.html http://quincy4board.homestead.com/files/curriculum/Cosmo.PCX ==== [snip] > However, my prime counting function maps out the entire distribution > of prime numbers over infinity by telling you how to get them over > infinity in a difference equation that you can easily transfer from to > a partial differential equation. It may disprove some interesting assertions in mathematics like that > the prime distribution crosses li(x) an infinite number of times by > proving that it *never* crosses li(x). It may disprove Riemann's entire approach which is the basis for the > famous Riemann Hypothesis by showing that certain of his assumptions > were flawed. I say may because I'm not sure. But if mathematicians can fight to > not even properly acknowlede the mathematics, how will anyone know? Even when you *are* sure, you're usually wrong. Of all the things your work may do, I'll place my money on it confirming that you don't know what you're talking about -- not that your ignorance ever kept you from talking before. Your brain appears to be on a permanent vacation, while your mouth still works overtime. -- 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 ==== > > Yes, I have been seeing this show up on comp.lang.java.advocacy, > so I am not familiar with the presumably longer history! > > Here's a quick summary: For about EIGHT YEARS James Harris has been > discoveries to sci.math (and often to other newsgroups). Much of the > time his arguments are too vague and ill-defined for people to make sense > > Sorry, that's not believable. Something that can be put into > a Java or C++ program that can be understood by a compiler is > by nature not vague or ill-defined. You've misunderstood. Prime-counting is only one tiny piece of what James claims he has done to revolutionize mathematics. The 8 years of postings are overwhelmingly concerned with proofs of Fermat's Last Theorem and have nothing to do with Java, C++, or algorithms. The vague and ill-defined nature of these arguments has been discussed at great length in sci.math. One needn't read too far into any of James' arguments to get to a point where you haven't the foggiest idea of what he's trying to say. If you read some of the threads in sci.math, you'll find many explicit discussions about precisely what terms James is being vague about (one of his favorites is has a factor of), what the possible meanings are, how his meaning does not correspond to accepted definition, or how his meaning shifts during the course of an argument. - Randy ==== unless you believe every thing taht is put out by the Second British Church of Christ, Isaac, or by the state schools as opposed to directly by the church schools (Public Schools), that is only apt in that he did aglomerate a lot of credit, after the putative fact (and AI .-) try searches on American Almanac, in my sig. > to emulate Newton and fight like a bitch over credit, that's --Dec.2000 'WAND' Chairman Paul O'Neill, reelected to Board. Newsish? http://www.rand.org/publications/randreview/issues/rr.12.00/ http://members.tripod.com/~american_almanac ==== Hash: SHA1 [..] >> David Ullrich is commenting on my issue with a post where he talked of >> a racial slur being the perfectly appropriate reply to me. >> >> He also has an interesting post which you can find by going to >> groups.google.com and checking posts where David Ullrich is the >> author, and he uses the word rape. > > I am not sure what to make of it. You are exposing that when > Mr. Ullrich thinks of particular vicious nasty crimes, he seems > to think only members of a certain race are capable of them. > > Now if that's the case, I would say [snippety-snip] Spoken like a reasonable person. If, however, you continue to entertain the idea that JSH may be a reasonable person, you would IMHO double the size of the minority which holds that as a viable hypothesis. I conclude[1] that JSH's major contribution, if any, is likely to be as part of a case-study for someone trying to find a more precise description of JSH's condition than kook. Jens JSH) quote from a recent JSH missive, message-ID <3c65f87.0307090953.43098f6d@posting.google.com> : ================= > >[rants that make my point better than I ever could snipped] David Ullrich got caught once in an interesting exchange where he >called me an idiot for apologizing to a French newsgroup for not >posting in French. > > Nope. Never happened. (Provide a citation, please). ================== - -- Key ID 0x09723C12, j.tingleff@ieee.org/jens_tingleff@yahoo.com http://www.imaginet.fr/~jensting/ +44 1223 211 585 iD8DBQE/DcfqimJs3AlyPBIRAhKxAKDQ3DdFDUNwRck/f6MIj0QA2RX8ZwCg3SBm xi42SJhnUKBuVbWdTiiJmkk= =BtDH ==== [newsgroups trimmed] >> >> Yes, I have been seeing this show up on comp.lang.java.advocacy, >> so I am not familiar with the presumably longer history! >> >> Here's a quick summary: For about EIGHT YEARS James Harris has been >> discoveries to sci.math (and often to other newsgroups). Much of the >> time his arguments are too vague and ill-defined for people to make sense Sorry, that's not believable. Something that can be put into >a Java or C++ program that can be understood by a compiler is >by nature not vague or ill-defined. Frankly, vague and >ill-defined are cop-outs used frequently by many incompetent and >dishonest people in academia and on usenet, so you have to do >better than that if you want to be taken seriously. E.g. take >a crucial part of the argument and show that it rests on >lack of clear definition (ill-defined) or can be interpreted >in meaningfully and significantly different ways (vague.) Searching google using James Harris usenet kook reveals the following #1 world wide web page devoted to James Harris: http://www.crank.net/harris.html Which might provide a degree of familiarization with the longer history referred to. George Maydwell -- Modern Cellular Automata: www.collidoscope.com/modernca Collidoscope Hexagonal Screensaver: www.collidoscope.com ==== > > In case you _do_ think that the posts James is referring to > demonstrate that I think what you say James is exposing, > let me just clarify: > > Long ago James told us he was black. Some time later, > still long ago, he said something particularly insulting > and dehumanizing - it occured to me at the time that > a racial slur in reply would be appropriate, simply to > illustrate the idea that there is such a thing as you're > not supposed to talk to people that way. I refrained, > because it wouldn't have been something I meant, > and because of course I'm _not_ supposed to talk > to people that way. Ah, people are not supposed to say what they're thinking? Okay, David. I haven't gone back to the old postings far enough, but what you say here confirms what I have suspected. Something in your personal duel with James reminds me of the classic story The President's Speech by Oliver Sacks. It has been so popular that it was easy to find a fine summary of it, so I don't have to give a summary myself: http://www.konformist.com/2001/mickeyz-05.htm (scroll down to find Sack's name, and then read to end). I also recommend reading the original story. ==== > > [...] > >> David Ullrich is commenting on my issue with a post where he talked of >> a racial slur being the perfectly appropriate reply to me. >> >> He also has an interesting post which you can find by going to >> groups.google.com and checking posts where David Ullrich is the >> author, and he uses the word rape. I am not sure what to make of it. You are exposing that when >Mr. Ullrich thinks of particular vicious nasty crimes, he seems >to think only members of a certain race are capable of them. > > Um, maybe exposing was not the word you meant - it seems > to me that if you say someone's exposing something it > follows that the thing being exposed is actually so. It's > certainly not true that I think that only members of certain > races are capable of certain nasty crimes. (Maybe espousing > is what you meant? Not sure I spelled that right.) > > In case you _do_ think that the posts James is referring to > demonstrate that I think what you say James is exposing, > let me just clarify: > > Long ago James told us he was black. Some time later, > still long ago, he said something particularly insulting > and dehumanizing - it occured to me at the time that > a racial slur in reply would be appropriate, simply to > illustrate the idea that there is such a thing as you're > not supposed to talk to people that way. I refrained, > because it wouldn't have been something I meant, > and because of course I'm _not_ supposed to talk > to people that way. > > Then some time later, still long ago, in reply to some > other egregious insult, I said what I say in the previous > paragraph, about things I once considered saying > and why, and why I did not say them. Again, my point > was simply to say that there is such a thing as ways > one is simply not supposed to talk to people - James > had stepped way over that line and I wanted to point > out that there was in fact such a line. > > In my post I included a statement as above, to the > effect that I once (briefly) considered the idea that a > racial slur would be appropriate - pointed out that of > course I decided it wasn't, in fact it's not something I > said. James replied that a racial slur was _never_ > appropriate. This statement is of course ridiculous; > I pointed out that for example, to take an extreme case, > if someone had broken into my home, tied me up > and was about to rape my daughter, if I thought > that calling him a nasty name might distract him > until the police arrived then a racial slur would be > not only appropriate, refraining from making such > a comment would be positively wrong. > > And since then he's accused me of thinking that > blacks are rapists, or that rapists are all black, > or whatever - he never puts it quite so baldly, just > points to that post as evidence of my attitudes. > Which of course is twisting things - the rapist > in the imaginary scenario is in fact black (or a > member of some other unspecified minority, > let's say black for simplicity's sake), but that's > not because I think that rapists tend to be black, > it's because the _question_ was whether it's > correct to say that a racial slur is _never_ > appropriate - a hypothetical example illustrating > that that's not so is necessarily going to involve > a minority. I mean, duh. > >Now if that's the case, I would say Mr. Ullrich's upbringing >was sadly wanting and/or he has not been a particularly thoughtful >individual since, and maybe has convinced himself Jeffrey Dahmer >was framed. But none of that's really related to primes. >It would be nicer if both sides had avoided attacks >on character of each other. There is a context when >the best of us need to be pointed out the errors in >our thinking, but ideally the context is not that >of attacks on each other. > What's OP? Useful new net shorthand for Original Poster. > > ************************ > > Ok, there is a complex history here. Sorry if I caused offense. I would agree with your point too -- if anything at all can be said to stop a criminal until police gets there, what was said is not a valid object of criticism. ==== > Only a tiny fraction of James' output can be put into a Java or C++ > program that can be understood by a compiler or has anything at > all to do with computers. I'm not talking specifically here of his > prime-counting algorithm but of the whole body of his work, most > of which consists of failed attempts to prove Fermat's Last Theorem. > There are numerous examples of his vague or ill-defined terminology > in the threads archived in Google; of which his use of factor is a Ok, I get it. > http://www.google.com/groups?selm=be7qih%249li%241%40agate.berkeley.edu I dunno, this still seems a little like nitpicking to me: g has a factor of 5, you really mean not that 5 divides g, but rather that there is an algebraic integer which divides both 5 and g, then the STANDARD AND CORRECT way of saying it is g and 5 have a common factor [in the ring of all algebraic integers]. I would say a certain amount of informal neologism is ok in usenet posts as long as the meaning is not lost. > Basically, what I've been saying is that the presumably longer history > with which you said you were not familiar demonstrates just why many > people have no confidence in Harris or his work. Because of that > richly-deserved opinion, anything he does (including programming) is > greeted with extreme skepticism by many of us. I'm really not trying to > prove anything to you here -- reject everything I've said if you prefer > -- I'm just making you aware of the general opinion of himself James > has created over a period of years on USENET. Overall, I guess after seeing some of the self-evaluation and the intent and self-assurance to tear down the entire mathematical world over the subtle advantages of a new prime counting function/method and what it may (and presmuable may not) do, I suppose I have to agree with the general opinion... ==== >> >>[...] Ok, there is a complex history here. Yup. _If_ for whatever reason you want to understand what's going on in all this then like I keep saying, you need to look at a lot of posts on sci.math for the last seven or eight years. Of course there's no reason you should actually do that, but until you do you need to realize that you cannot take anything James says about the complex history at face value - his version of who said what, when and why is always different from everyone else's. >Sorry if I caused offense. Okie dokie. >I would agree with your point too -- if anything at all can be said >to stop a criminal until police gets there, what was said is not a >valid object of criticism. ************************ ==== > > ... > > I dare you to stop calling him Ullrich or Mr. Ullrich and from now on > address him as professor Ullrich. > > Like I'm sure his students do in Oklahoma. How very quaint. Don't university students in the States call their profs by their first names? GC ==== >> >> He has responded to such statements many times, simply stating >> that it's not so. But it is. >> >> That is a false statement. >> >> Ultimately Ullrich's case seems to rest on the fact that my work gives >> the same answers as others. But, given that, for instance, there are >> 4 primes up to 10, which are 2, 3, 5, and 7, prime counting methods, >> and any correct prime counting function will give the same answer. >> >> I am more than happy to go into details about why my prime counting >> function is significant and is NOT a rehash. >> >> Well, what advantage does your method provide over existing >> methods? Is it significantly faster? Tables of primes >> already exist on the web for very large number of primes. >> One could simply do a table search to see if a number >> is a prime or not. You're focusing on algorithms, which isn't a surprise as I take it >you're a computer scientist. But remember I'm arguing with >mathematicians. I doubt Ullrich would be caught dead in a computer >lab unless he was going in to toss something into the trash if he >wandered by it and no other was handy. Your cluelessness remains amazing, as always. Last time you said something in this direction I clarified things for you - maybe you didn't see that post. Lemme just say this about that: _my_ programs do not give incorrect answers because of roundoff errors. >However, my prime counting function maps out the entire distribution >of prime numbers over infinity by telling you how to get them over >infinity in a difference equation that you can easily transfer from to >a partial differential equation. That pde is not a pde, and more important you've _never_ given _any_ reason to suspect that it has anything to do with counting primes. >It may disprove some interesting assertions in mathematics like that >the prime distribution crosses li(x) an infinite number of times by >proving that it *never* crosses li(x). It may do that, even though there's absolutely nothing novel about it mathematically, and you give _no_ reason why someone would think it might do that. >It may disprove Riemann's entire approach which is the basis for the >famous Riemann Hypothesis by showing that certain of his assumptions >were flawed. Same comment, squared. >I say may because I'm not sure. You're not sure? In fact you have no reason whatever to think either of those two assertions may be so. > But if mathematicians can fight to >not even properly acknowlede the mathematics, how will anyone know? > >> The only advantage one might see for a new method is for assisting >> in the computation of even newer and larger primes. If your method >> is faster, the people computing new primes and building >> tables will be happy to use it, I am sure. You might >> want to contact and convince such people. And you've been caught in the assumption that it's just some >algorithm. However, the reality is that it's a mathematical function that's >apparently never been seen before, Never seen before, until about 200 years ago you mean. Never seen since then, except by people who've studied well-known algorithms for counting primes. Nothing like it has ever been seen, except by the 20% of the grad students in the field that _you_ tell us you were told come up with something analogous. >which just might give a new >approach to a lot of high level mathematics. But if it *has* been >discovered before but never put in references or textbooks that just >emphasizes my point. The mathematicians you see me talking about or who you see posting in >reply to me don't know everything. [...] If necessary I'll tear down the entire mathematical world as it's >currently known. sanity or lack thereof then don't say things that sound totally crazy. Seems simple enough. >> David Ullrich is commenting on my issue with a post where he talked of >> a racial slur being the perfectly appropriate reply to me. >> >> He also has an interesting post which you can find by going to >> groups.google.com and checking posts where David Ullrich is the >> author, and he uses the word rape. >> >> I am not sure what to make of it. You are exposing that when >> Mr. Ullrich thinks of particular vicious nasty crimes, he seems >> to think only members of a certain race are capable of them. Standards. I say that a university professor should be held to some >standard, and people argue with me. > Now if that's the case, I would say Mr. Ullrich's upbringing >> was sadly wanting and/or he has not been a particularly thoughtful >> individual since, and maybe has convinced himself Jeffrey Dahmer >> was framed. But none of that's really related to primes. >> It would be nicer if both sides had avoided attacks >> on character of each other. There is a context when >> the best of us need to be pointed out the errors in >> our thinking, but ideally the context is not that >> of attacks on each other. Well if you wish to give him a title why don't you address him as >Professor? He is a professor at Oklahoma State University, after all. I dare you to stop calling him Ullrich or Mr. Ullrich and from now on >address him as professor Ullrich. Like I'm sure his students do in Oklahoma. > What's OP? >> >> Useful new net shorthand for Original Poster. James Harris ************************ ==== > Don't any of you care about knowledge? Get off it -- if you truly cared about knowledge rather than credit, you would have shut up long ago and gone on to other things. What you had to say is out there. It's sitting on archives, you have generated enough noise about it, if it has any truth and super-lasting value to it, it will be found by those who need it. But you are just looking for credit over something, if not for Fermat's theorem, then by convincing yourself that what you maybe have is very significant. The material is not truly interesting to you, *you* are. So let's don't pretend you are in it for knowledge. ==== > I dare you to stop calling him Ullrich or Mr. Ullrich and from now on > address him as professor Ullrich. > > Like I'm sure his students do in Oklahoma. > > How very quaint. Don't university students in the States call their > profs by their first names? I was amazed quite a few years ago when I was taken to task by someone because I had suggested that a professor (whom I called by his first name) was making a serious error. The professor acknowledged his error later. I think it is cultural. Some students think very highly of their professors and think they are not making mistakes, and would never dare to address them by their first name. They are putting them on a pedestal. Of course, in general they know more than the students, but are liable to make mistakes and errors just like everybody else. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ ==== > ... > > > Nope. Never happened. (Provide a citation, please). > > > > > > > He called you an idiot for something else. > > (He might also have called you idiot savant...) > > Hmmm...so Ullrich calls me an idiot for noting that I'd be impressed > if he'd written in French in posting to a French newsgroup, and first > you claim it was for something else, and *then* you reply again to > claim that he actually *was* posting in French!!! Ah, vous .90tes un idiot. You claimed he said that because you apologised for not writing in French. But as you *now* so aptly remark, it was for writing you'd be impressed if he'd written in French. And indeed, the latter is something else. Yes? You are an idiot for a few reasons. The first is that when you find a posting by David in a French newsgroup that is not in French, your only reply is about his French abilities in that newsgroup (and you know nothing about his abilities in that field), not about the content. Second is your assumption that posting in English in a French (or German or whatever) newsgroup is frowned upon. I have posted in English in both French and German newsgroup, simply because I do not feel comfortable writing in those languages, especially when it is technical. I have no problem either reading or speaking those languages. None of my English postings has been frowned upon. And the third reason is of course that you (not so) subtly changed the allegation in order to make me look a fool. Idiot, va-t'en. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ ==== > > ... > > I dare you to stop calling him Ullrich or Mr. Ullrich and from now on > address him as professor Ullrich. > > Like I'm sure his students do in Oklahoma. > > > How very quaint. Don't university students in the States call their > profs by their first names? > > GC Depends on the professor. Come on, Americans aren't so easily boxed, you know. James Harris ==== > [newsgroups trimmed] > > >> >> Yes, I have been seeing this show up on comp.lang.java.advocacy, >> so I am not familiar with the presumably longer history! >> >> Here's a quick summary: For about EIGHT YEARS James Harris has been >> discoveries to sci.math (and often to other newsgroups). Much of the >> time his arguments are too vague and ill-defined for people to make sense Sorry, that's not believable. Something that can be put into >a Java or C++ program that can be understood by a compiler is >by nature not vague or ill-defined. Frankly, vague and >ill-defined are cop-outs used frequently by many incompetent and >dishonest people in academia and on usenet, so you have to do >better than that if you want to be taken seriously. E.g. take >a crucial part of the argument and show that it rests on >lack of clear definition (ill-defined) or can be interpreted >in meaningfully and significantly different ways (vague.) > > Searching google using James Harris usenet kook reveals the > following #1 world wide web page devoted to James Harris: > http://www.crank.net/harris.html > Which might provide a degree of familiarization with the longer > history referred to. > > George Maydwell Well I just checked the page and while it's clearly meant to be insulting, it seems that it's just insults like crank scattered around the page, as the links provided don't say much. I'm curious as to whether anyone can find real justification on the page for the assertion that I'm a crank. Consider it a dare. James Harris ==== > Don't any of you care about knowledge? Get off it -- if you truly cared about knowledge rather than >credit, you would have shut up long ago and gone on >to other things. What you had to say is out there. >It's sitting on archives, you have generated enough noise >about it, if it has any truth and super-lasting value to it, >it will be found by those who need it. But you are just looking for credit over something, if >not for Fermat's theorem, then by convincing yourself >that what you maybe have is very significant. The >material is not truly interesting to you, *you* are. So let's don't pretend you are in it for knowledge. An unusually fast disillusionment cycle. Usually it takes a week or so. - Randy ==== > Only a tiny fraction of James' output can be put into a Java or C++ >> program that can be understood by a compiler or has anything at >> all to do with computers. I'm not talking specifically here of his >> prime-counting algorithm but of the whole body of his work, most >> of which consists of failed attempts to prove Fermat's Last Theorem. >> There are numerous examples of his vague or ill-defined terminology >> in the threads archived in Google; of which his use of factor is a Ok, I get it. > http://www.google.com/groups?selm=be7qih%249li%241%40agate.berkeley.edu I dunno, this still seems a little like nitpicking to me: g has a factor of 5, you really mean not that 5 > divides g, but rather that there is an algebraic integer which divides > both 5 and g, then the STANDARD AND CORRECT way of saying it is g and 5 have a common factor [in the ring of all algebraic > integers]. I would say a certain amount of informal neologism is ok in usenet posts >as long as the meaning is not lost. Certainly. But (i) the meaning _is_ lost - it happens all the time that when he says a has a factor of b someone foolishly assumes that what he means is that a has a factor of b! So they reply, pointing out that what he's just said is wrong. Of course whatever he's said typically _is_ wrong, but not for the reason someone thinks, because the someone was not familiar with his private language. The irritating and irrational aspect of all of this is that it has been pointed out to him _many_ times that he's not saying what he means, and that this leads to confusion - you'd think he'd say oh, and start using the language correctly. But instead when people point out that he's not saying what he means he insists that his terminology is correct and that the way the language is used by everyone else is wrong, and he continues to speak his own private language. (You might note that since we're talking just about what words and phrases _mean_, it's literally impossible for him to be right and everyone else wrong - that's possible although unlikely regarding matters of fact, but what words mean is defined by consensus, the majority _is_ right, by definition. But he doesn't seem to care about that.) (ii) He's not consistent - _sometimes_ when he says a has a factor of b he means that a has a factor of b, and sometimes he means that a and b share a factor. A certain amount of neoligism is fine. In mathematics _any_ amount of neologism is fine as long as things are clearly defined. But things are never clearly defined in his stuff - there's always some question as to exactly what something means in one of his proofs. [Noting that of course sentences containing the word always are always exaggerations...] >> Basically, what I've been saying is that the presumably longer history >> with which you said you were not familiar demonstrates just why many >> people have no confidence in Harris or his work. Because of that >> richly-deserved opinion, anything he does (including programming) is >> greeted with extreme skepticism by many of us. I'm really not trying to >> prove anything to you here -- reject everything I've said if you prefer >> -- I'm just making you aware of the general opinion of himself James >> has created over a period of years on USENET. Overall, I guess after seeing some of the self-evaluation and >the intent and self-assurance to tear down the entire mathematical world >over the subtle advantages of a new prime counting function/method >and what it may (and presmuable may not) do, I suppose I have to >agree with the general opinion... That's not a good thing. He's stated that he's going to sic the Army on us if we don't shape up (he has the power to do this because generals like him). Presumably now that you've said you suppose you have to agree with the general opinion you've become part of the establishment that's going to be fired or worse when the Truth finally comes out. Good luck with that. ************************ ==== >[...] Ah, vous .90tes un idiot. > [...] Idiot, va-t'en. French. I'm impressed. ************************ ==== > Don't any of you care about knowledge? Get off it -- if you truly cared about knowledge rather than >credit, you would have shut up long ago and gone on >to other things. He talks a lot about how we have no regard for Truth. But _he_ is the _only_ person I've ever seen state explicitly in a usenet post that if what he'd just said was wrong people shouldn't bother to say so because he didn't want to know: <824hn8$i61$1@nntp9.atl.mindspring.net> 1999/12/01 > If you're worried that maybe you can't judge its correctness for yourself, > especially since all these real mathematicians would just as soon let me > mouth off as produce any actual math in objection, I'll help you out. Where > I have p in the proof, use 3. That is, try it out with p=3. But if it > fails, don't tell me. I don't want to know. >What you had to say is out there. >It's sitting on archives, you have generated enough noise >about it, if it has any truth and super-lasting value to it, >it will be found by those who need it. But you are just looking for credit over something, if >not for Fermat's theorem, then by convincing yourself >that what you maybe have is very significant. The >material is not truly interesting to you, *you* are. So let's don't pretend you are in it for knowledge. ************************ ==== [snip] > Well I just checked the page and while it's clearly meant to be > insulting, it seems that it's just insults like crank scattered > around the page, as the links provided don't say much. The term crank isn't an insult, it's an identification. If someone want to insult you they they will call you a jackass. > I'm curious as to whether anyone can find real justification on the > page for the assertion that I'm a crank. Consider it a dare. James Harris Check your track record of postings to the internet. Your prior history is sufficient proof. -- It takes a village to raise an idiot. -- Democracy: The triumph of popularity over principle. -- http://www.crbond.com ==== > ... > > > > Nope. Never happened. (Provide a citation, please). > > > > > > > > > > He called you an idiot for something else. > > > > (He might also have called you idiot savant...) > > > > Hmmm...so Ullrich calls me an idiot for noting that I'd be impressed > > if he'd written in French in posting to a French newsgroup, and first > > you claim it was for something else, and *then* you reply again to > > claim that he actually *was* posting in French!!! > > Ah, vous .90tes un idiot. Nope. You're a math groupie, so you fight for Ullrich even when he displayed his true coarseness when I was being diplomatic. Readers should see: Now consider that in the previous post--the one to which Ullrich replied--I said: Well I must say I'm impressed if Ullrich speaks French! Though I'd have been more impressed if he'd replied in it! Unfortunately I do not speak French so I won't try. Now in thinking back I saw that as an apology to the newsgroup for not speaking French, in which I also was pointing out that I wasn't speaking French because I don't know it. > You claimed he said that because you apologised for not writing in French. > But as you *now* so aptly remark, it was for writing you'd be impressed > if he'd written in French. And indeed, the latter is something else. > Yes? You are an idiot for a few reasons. The first is that when you > find a posting by David in a French newsgroup that is not in French, your > only reply is about his French abilities in that newsgroup (and you know > nothing about his abilities in that field), not about the content. That's irrational. If someone were posting here completely in French, wouldn't that be pertinent? How welcoming are all of you to non-English speakers who post? In noting my inability to speak French I was at *least* acknowledging that fault, and explaining why I couldn't go to French. > Second is your assumption that posting in English in a French (or German > or whatever) newsgroup is frowned upon. I have posted in English in > both French and German newsgroup, simply because I do not feel comfortable > writing in those languages, especially when it is technical. I have no > problem either reading or speaking those languages. None of my English > postings has been frowned upon. And the third reason is of course that > you (not so) subtly changed the allegation in order to make me look a > fool. Which is an expression of arrogance, as if the fact that others tolerated your not posting in the language of the newsgroup, it's ok. Well let someone come on one of these newsgroups and post entirely in French, or Russian or German, and see the treatement they get. > Idiot, va-t'en. But then again, English speakers seem to be quite vicious and impolite with each other anyway. It's as if so many not only lack proper manners, but they enjoy informing the world. James Harris ==== > ... I dare you to stop calling him Ullrich or Mr. Ullrich and from now on > address him as professor Ullrich. Like I'm sure his students do in Oklahoma. > How very quaint. Don't university students in the States call their > profs by their first names? GC > > Depends on the professor. Come on, Americans aren't so easily boxed, you know. > > James Harris I know nothing about pugilism. But you all call your fathers sir don't you? Very odd. GC ==== > Which is an expression of arrogance, as if the fact that others > tolerated your not posting in the language of the newsgroup, it's ok. > > Well let someone come on one of these newsgroups and post entirely in > French, or Russian or German, and see the treatement they get. Generally they get their questions answered, as you'd know if you've ever read any threads but your own. I've seen French, Spanish, Italian, German and Dutch. I think I've seen Polish as well. Occasionally Finnish, but only in response when somebody posted from a *.fi address. - Randy ==== > Now consider that in the previous post--the one to which Ullrich > replied--I said: > > Well I must say I'm impressed if Ullrich speaks French! That certainly isn't an apology to the newsgroup for not speaking French. > > Though I'd have been more impressed if he'd replied in it! Nor is that. > > Unfortunately I do not speak French so I won't try. Nor is that. > > Now in thinking back I saw that as an apology to the newsgroup for not > speaking French, in which I also was pointing out that I wasn't > speaking French because I don't know it. It is a statement about not speaking French. Not an apology though, nor does it seem addressed to the French newsgroup. [snip] > That's irrational. If someone were posting here completely in French, > wouldn't that be pertinent? > > How welcoming are all of you to non-English speakers who post? > [snip] > Well let someone come on one of these newsgroups and post entirely in > French, or Russian or German, and see the treatement they get. http://groups.google.com/groups?ie=ISO-8859-1&as_umsgid=%3Cb4e32a30.03012119 50.47133406%40posting.google.com%3E http://groups.google.com/groups?dq=&hl=en&lr=lang_fr&ie=UTF-8&threadm=200208 211233.g7LCXQK14034%40proapp.mathforum.org&prev=/groups%3Fsafe%3Dimages%26ie% 3DISO-8859-1%26as_ugroup%3Dsci.math%26lr%3Dlang_fr%26num%3D50%26hl%3Den Exchanges in other languages are not hard to find either, but I confined myself to posts in sci.math in the last year or so where the original query was not in English. - Randy ==== >> >> Now in thinking back I saw that as an apology to the newsgroup for not >> speaking French, in which I also was pointing out that I wasn't >> speaking French because I don't know it. > It is a statement about not speaking French. Not an > apology though, nor does it seem addressed to the > French newsgroup. In the Harris-Universe it counts as an apology, in the same way that well, maybe you weren't lying this time serves as an apology for calling someone a liar. -- Wayne Brown | 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 ==== ... > Well I just checked the page and while it's clearly meant to be > insulting, it seems that it's just insults like crank scattered > around the page, as the links provided don't say much. > > The term crank isn't an insult, it's an identification. If > someone want to insult you they they will call you a jackass. I disagree; it is no insult to call a jackass a jackass. I've given this matter some thought, and now feel certain that along such lines there is nothing one can say to Harris that would be an insult. It seems that what you have to do if you want to insult him is to ask him a civil question. -jiw > I'm curious as to whether anyone can find real justification on the > page for the assertion that I'm a crank. Consider it a dare. James Harris ... [Page referred to is http://www.crank.net/harris.html] ==== > > Don't any of you care about knowledge? Get off it -- if you truly cared about knowledge rather than >credit, you would have shut up long ago and gone on >to other things. > > He talks a lot about how we have no regard for Truth. > But _he_ is the _only_ person I've ever seen state > explicitly in a usenet post that if what he'd just said > was wrong people shouldn't bother to say so because > he didn't want to know: JSH is a discoverer. He doesn't need to have his errors pointed out to him. Here's how it's supposed to work: - JSH makes a (wrong) discovery - JSH posts this discovery on sci.math - the mathematicians _fix_ what's wrong - JSH takes the credit Trouble is, you guys arne't doing step three properly. JSH wants you to correct his problems, not simply prove that they are wrong. No wonder he's so frustrated, you're not cooperating. The fact that his discoveries aren't fixable is irrelevant. > > <824hn8$i61$1@nntp9.atl.mindspring.net1999/12/01 > > If you're worried that maybe you can't judge its correctness for yourself, > especially since all these real mathematicians would just as soon let me > mouth off as produce any actual math in objection, I'll help you out. > Where > I have p in the proof, use 3. That is, try it out with p=3. But if it > fails, don't tell me. I don't want to know. > >What you had to say is out there. >It's sitting on archives, you have generated enough noise >about it, if it has any truth and super-lasting value to it, >it will be found by those who need it. But you are just looking for credit over something, if >not for Fermat's theorem, then by convincing yourself >that what you maybe have is very significant. The >material is not truly interesting to you, *you* are. So let's don't pretend you are in it for knowledge. > > ************************ > > ==== > > Now consider that in the previous post--the one to which Ullrich > replied--I said: > > Well I must say I'm impressed if Ullrich speaks French! > > That certainly isn't an apology to the newsgroup for > not speaking French. > > > Though I'd have been more impressed if he'd replied in it! > > Nor is that. > > > Unfortunately I do not speak French so I won't try. > > Nor is that. I'll concede that you can argue that it's not an apology. I thought of it as an apology, but I'll back down from the assertion that it is an apology, as I can see where others can reasonably disagree. > > Now in thinking back I saw that as an apology to the newsgroup for not > speaking French, in which I also was pointing out that I wasn't > speaking French because I don't know it. > > It is a statement about not speaking French. Not an > apology though, nor does it seem addressed to the > French newsgroup. My point was that it would have been polite to reply in French on a French newsgroup, or at least to acknowledge in some way that some might be bothered by posting in English. My explanation for the group was that I didn't know French, or I would have posted at least partly in French. My sense that was apologetic can be reasonably disputed by others as I noted above. James Harris ==== > ... > Well I just checked the page and while it's clearly meant to be > insulting, it seems that it's just insults like crank scattered > around the page, as the links provided don't say much. > > The term crank isn't an insult, it's an identification. If > someone want to insult you they they will call you a jackass. > > I disagree; it is no insult to call a jackass a jackass. > I've given this matter some thought, and now feel certain > that along such lines there is nothing one can say to Harris > that would be an insult. It seems that what you have to do > if you want to insult him is to ask him a civil question. > -jiw As if posters usually ask me a civil question!!! Consider that there's more below... > I'm curious as to whether anyone can find real justification on the > page for the assertion that I'm a crank. Consider it a dare. James Harris > ... > [Page referred to is http://www.crank.net/harris.html] So go ahead and check the link. Consider that a double dare. James Harris ==== [snip] > [Page referred to is http://www.crank.net/harris.html] So go ahead and check the link. Consider that a double dare. James Harris OK, now what? Your own track record of publicly flaunting your mistakes, gaffes, blunders, errors, oversights, omissions, ambiguities, solipsisms, non-sequiters, gaps, slip-ups, fallacies, etc. has elevated your status as a crank from convincingly evident to conclusively proven. In my dictionary the term crank has your picture for a definition. -- 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 ==== > > [...] > >> David Ullrich is commenting on my issue with a post where he talked of >> a racial slur being the perfectly appropriate reply to me. >> >> He also has an interesting post which you can find by going to >> groups.google.com and checking posts where David Ullrich is the >> author, and he uses the word rape. I am not sure what to make of it. You are exposing that when >Mr. Ullrich thinks of particular vicious nasty crimes, he seems >to think only members of a certain race are capable of them. > > Um, maybe exposing was not the word you meant - it seems > to me that if you say someone's exposing something it > follows that the thing being exposed is actually so. It's > certainly not true that I think that only members of certain > races are capable of certain nasty crimes. (Maybe espousing > is what you meant? Not sure I spelled that right.) > > In case you _do_ think that the posts James is referring to > demonstrate that I think what you say James is exposing, > let me just clarify: > > Long ago James told us he was black. Some time later, > still long ago, he said something particularly insulting > and dehumanizing - it occured to me at the time that > a racial slur in reply would be appropriate, simply to > illustrate the idea that there is such a thing as you're > not supposed to talk to people that way. I refrained, > because it wouldn't have been something I meant, > and because of course I'm _not_ supposed to talk > to people that way. Well, a while back I ended up in a debate with a poster from South Africa--before Apartheid was ended--and during that discussion information about my race was pertinent so I gave it. I don't remember David Ullrich participating in that discussion but he apparently gathered the information from it, based on the timing of his comments that he mentions later. Since then I have made other posts where I've talked of my race. As for this remark he claims was so insulting and dehumanizing it was my stating that he'd acted as my lapdog in an instance. > Then some time later, still long ago, in reply to some > other egregious insult, I said what I say in the previous > paragraph, about things I once considered saying > and why, and why I did not say them. Again, my point > was simply to say that there is such a thing as ways > one is simply not supposed to talk to people - James > had stepped way over that line and I wanted to point > out that there was in fact such a line. Remember Ullrich is talking now about my saying he'd acted as my lapdog in an instance, and now notice the paternalistic tone. > In my post I included a statement as above, to the > effect that I once (briefly) considered the idea that a > racial slur would be appropriate - pointed out that of > course I decided it wasn't, in fact it's not something I > said. James replied that a racial slur was _never_ > appropriate. This statement is of course ridiculous; > I pointed out that for example, to take an extreme case, > if someone had broken into my home, tied me up > and was about to rape my daughter, if I thought > that calling him a nasty name might distract him > until the police arrived then a racial slur would be > not only appropriate, refraining from making such > a comment would be positively wrong. Given Ullrich's claim above I went into the Google archives. I found that I'd said: Now how many of you think that it's the most natural thing in the world that calling someone a racial slur might be appropriate? Later I found that I'd said: Possibly you believe that you are doing yourself and Professor Ullrich of Oklahoma State University a favor by a post which I believe indicates that you agree with him that a racial slur may be in some cases the appropriate response. Now then as to Ullrich's example of a someone breaking into his house about to rape his daughter the implication is obvious enough, but it's actually nonsensical. If you could even imagine such a thing, do you think you'd be hurling racial slurs if one would apply? If you had a gun, you might use it, but not your mouth. Why would Ullrich even come up with such an example? And why use his own daughter? > And since then he's accused me of thinking that > blacks are rapists, or that rapists are all black, > or whatever - he never puts it quite so baldly, just > points to that post as evidence of my attitudes. > Which of course is twisting things - the rapist > in the imaginary scenario is in fact black (or a > member of some other unspecified minority, > let's say black for simplicity's sake), but that's > not because I think that rapists tend to be black, > it's because the _question_ was whether it's > correct to say that a racial slur is _never_ > appropriate - a hypothetical example illustrating > that that's not so is necessarily going to involve > a minority. I mean, duh. Now Ullrich refuses to acknowledge that noxious smell of the implication, and seeks to attack me instead, accusing me of twisting things. What should fascinate you is that Ullrich consistently has gotten away with his comments as many posters on sci.math were stalwart in defense of him. For me that makes the case fascinating as they apparently have a *perception* of power based on their refusal to acknowledge truths that don't suit them. I had the feeling that they thought that they were in some way controlling me, or at least hurting my feeling deeply, which I found extraordinary. If you find that hard to believe, consider the other post in reply to Ullrich's comments here, from soft-eng. >Now if that's the case, I would say Mr. Ullrich's upbringing >was sadly wanting and/or he has not been a particularly thoughtful >individual since, and maybe has convinced himself Jeffrey Dahmer >was framed. But none of that's really related to primes. >It would be nicer if both sides had avoided attacks >on character of each other. There is a context when >the best of us need to be pointed out the errors in >our thinking, but ideally the context is not that >of attacks on each other. > What's OP? Useful new net shorthand for Original Poster. > > ************************ > > So what's the synopsis? Ullrich acknowledges his statements about a racial slur being the perfectly appropriate reply but continues to defend himself. He also defends his scenario involving an intruder about to rape his daughter with the position that a racial slur would be an appropriate response with the implication that the intruder is someone to whom a racial slur would apply. He bases his arguments at one point on the assertion that I delivered an egregious insult, for stating that he had acted as my lapdog in an instance. What he doesn't add is that once I found he was so upset, deduced from replies that came later, I apologized. I've maintained that David Ullrich as a professor at a state university should be held to some standard, and repeatedly posters have argued with me. They've also become extremely upset at my actually registering a complaint to Oklahoma State University about David Ullrich's *public* statements. And in fact I've registered several complaints and even chatted once with the head of the math department at Oklahoma State University on the phone. It's a fascinating case that just keeps going. I wouldn't be surprised if more comes later as I want to remind the readers that *Ullrich* brought the subject up in this thread. James Harris ==== > > ... > Well I just checked the page and while it's clearly meant to be > insulting, it seems that it's just insults like crank scattered > around the page, as the links provided don't say much. The term crank isn't an insult, it's an identification. If > someone want to insult you they they will call you a jackass. I disagree; it is no insult to call a jackass a jackass. > I've given this matter some thought, and now feel certain > that along such lines there is nothing one can say to Harris > that would be an insult. It seems that what you have to do > if you want to insult him is to ask him a civil question. > -jiw > > As if posters usually ask me a civil question!!! [snip] No referent database exists to justify any class of reply except derision. You are a troll, a crackpot, woefully and irremediably ignorant, and vigorously entertain delusions of personal competence. http://www.apa.org/journals/psp/psp7761121.html Unskilled and Unaware of It: How Difficulties in Recognizing One's Own Incompetence Lead to Inflated Self-Assessments http://insti.physics.sunysb.edu/~siegel/quack.html When some git (look in a mirror, Harris) repeatedly presents brilliant discovery trivially demonstrated to be crap, then we all justifiably shout http://w0rli.home.att.net/youare.swf Hey Harris, can you pass the Space math test? Fill in the following, including signs (the first one is mercy humped): (+1)(+1) = +1 (-1)(+1) = ? (+1)(-1) = ? (-1)(-1) = ? Uncle Al can ce in the pale moonlight, http://www.mazepath.com/uncleal/eotvos.htm 1) Footnotes, 2) Footnotes that connect to literature references; 3) Internally self-consistent, 4) Consistent with all empirical observation; 5) New predicted phenomena, 6) New predicted phenomena that are testable against empirical observation in existing qualified apparatus. Your posts - every one of your posts - fall short in categories (1)-(4), and short of (6) at your own insistence. You post , Harris, you post . What sort of civil question do you thereafter expect? Uncle Al ays, Evolution is a hoot if you are one of the survivors. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) Quis custodiet ipsos custodes? The Net! ==== [snip] > Well, a while back I ended up in a debate with a poster from South > Africa--before Apartheid was ended--and during that discussion > information about my race was pertinent so I gave it. [snip] Usenet is blind. You are what you present. You are loathsome, boring, ignorant, and ineducable. You are the Bell Curve personified (p. 279, softcover). You are a credit... nah, we won't go there, but... so is Uncle Al - except at the right side of the bell rather than the left, amidst his own kind in turn. What made this country great? It was spics and niggers and wops and kikes with noses as long as you arm! Firesign Theatre. And chinks and micks and bohunks and frogs (mostly Canukistan - poor bottom line) and squidjiggers and squareheads and norsks and svensks and the occasional WASP. Excise the Liberals and it's a pretty good country. (Hey folks, the new AT&T $0.99 monthly charge is bull. Call the 800 number and tell them you won't pay it. The first time they hang up on you. The second time they have a special plan that is the same as your current plan, but without the new monthly fee. Uncle Al got to scream into the handset, I'm mad as Hell and I'm not going to take it any more! It was a lot of fun when the fungible corporate asset at the other end got into the spirit of the thing.) -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) Quis custodiet ipsos custodes? The Net! ==== > which computerized proofs do you believe, > by the lights of thier adequate documentation? > in other words, > you've got to be kidding. ??? If you have been frustrated by someone's adequate documentation, I can understand that. But something put into a program can NEVER be vague or ill-defined, though it can be incorrect for its purpose. At worst, it could be obfuscated and hard to understand. Which is not at all related to being vague and ill-defined. This is because (useful) programming languages have to be implemented by compilers or interpreters so every possible nuance has to have been defined to exact precision. Even more so than mathematics, where a certain amount of hand-waving can possibly escape the attention of people. ==== So how can such stuff go on for EIGHT years? You folks must not have enough entertaining material on sci.math, to want to provide enough feedback to keep the flames on for so long! Does anybody know the relevance of alt.writing here? ==== > > ... > Well I just checked the page and while it's clearly meant to be > insulting, it seems that it's just insults like crank scattered > around the page, as the links provided don't say much. The term crank isn't an insult, it's an identification. If > someone want to insult you they they will call you a jackass. I disagree; it is no insult to call a jackass a jackass. > I've given this matter some thought, and now feel certain > that along such lines there is nothing one can say to Harris > that would be an insult. It seems that what you have to do > if you want to insult him is to ask him a civil question. > -jiw > > As if posters usually ask me a civil question!!! > [snip] > > No referent database exists to justify any class of reply except > derision. You are a troll, a crackpot, woefully and irremediably > ignorant, and vigorously entertain delusions of personal competence. > > http://www.apa.org/journals/psp/psp7761121.html > Unskilled and Unaware of It: How Difficulties in Recognizing One's > Own Incompetence Lead to Inflated Self-Assessments > http://insti.physics.sunysb.edu/~siegel/quack.html > When some git (look in a mirror, Harris) repeatedly presents > brilliant discovery trivially demonstrated to be crap, then we all > justifiably shout > > http://w0rli.home.att.net/youare.swf > > Hey Harris, can you pass the Space math test? Fill in the > following, including signs (the first one is mercy humped): > > (+1)(+1) = +1 > (-1)(+1) = ? > (+1)(-1) = ? > (-1)(-1) = ? > > Uncle Al can ce in the pale moonlight, > > http://www.mazepath.com/uncleal/eotvos.htm > > 1) Footnotes, > 2) Footnotes that connect to literature references; > 3) Internally self-consistent, > 4) Consistent with all empirical observation; > 5) New predicted phenomena, > 6) New predicted phenomena that are testable against empirical > observation in existing qualified apparatus. > > Your posts - every one of your posts - fall short in categories > (1)-(4), and short of (6) at your own insistence. You post , > Harris, you post . What sort of civil question do you > thereafter expect? > > Uncle Al ays, Evolution is a hoot if you are one of the survivors. Uncle Al, You fracture me, man. Outrageous! ==== > So how can such stuff go on for EIGHT years? You folks > must not have enough entertaining material on sci.math, > to want to provide enough feedback to keep the flames on > for so long! Every time someone succeeds in convincing James that there is an error. He goes away -- for a while. Then he comes back as if nothing had happened and starts proliferating threads. > Does anybody know the relevance of alt.writing here? I don't even know why he posts to any group other than: alt.delusions.of.grandeur. -- 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 ==== ... > You claimed he said that because you apologised for not writing in French. > But as you *now* so aptly remark, it was for writing you'd be impressed > if he'd written in French. And indeed, the latter is something else. > Yes? You are an idiot for a few reasons. The first is that when you > find a posting by David in a French newsgroup that is not in French, your > only reply is about his French abilities in that newsgroup (and you know > nothing about his abilities in that field), not about the content. > > That's irrational. If someone were posting here completely in French, > wouldn't that be pertinent? Yup, it would be pertinent. And it does happen. > How welcoming are all of you to non-English speakers who post? there are only a few that are *not* welcoming. I have myself answered some of them. > In noting my inability to speak French I was at *least* acknowledging > that fault, and explaining why I couldn't go to French. was not posting in French in a French newsgroup, rather you would have been impressed when he had done so. As an afterthought you mention that you did not write in French either. David's idiot was *not* in response to that afterthought. > Second is your assumption that posting in English in a French (or German > or whatever) newsgroup is frowned upon. I have posted in English in > both French and German newsgroup, simply because I do not feel comfortable > writing in those languages, especially when it is technical. I have no > problem either reading or speaking those languages. None of my English > postings has been frowned upon. And the third reason is of course that > you (not so) subtly changed the allegation in order to make me look a > fool. > > Which is an expression of arrogance, as if the fact that others > tolerated your not posting in the language of the newsgroup, it's ok. How could I communicate otherwise in a French or German newsgroup when I do not feel comfortable posting in French or German? If you seriously limit the languages used in a newsgroup to the main languages used in that group, you are seriously losing quite a bit of international communication. > Well let someone come on one of these newsgroups and post entirely in > French, or Russian or German, and see the treatement they get. There are only a few that give them a hard treatment. > Idiot, va-t'en. > > But then again, English speakers seem to be quite vicious and impolite > with each other anyway. Oh, well, as I am not an English speaker this does not apply to me, it appears. > It's as if so many not only lack proper manners, but they enjoy > informing the world. Yup, you are a prime example. Invading a French newsgroup only to inform the readers (but not in French) that you would be impressed if a particular poster had written something in French. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ ==== ... > Well, a while back I ended up in a debate with a poster from South > Africa--before Apartheid was ended--and during that discussion > information about my race was pertinent so I gave it. I think this is quite strange. Apartheid ended in South Africa in 1993, that was years before you started your quest on FLT. (Nelson Mandela was released in 1990 and three years after his release Apartheid ended.) -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ ==== > >[rants that make my point better than I ever could snipped] David Ullrich got caught once in an interesting exchange where he >called me an idiot for apologizing to a *French* newsgroup for not >posting in French. > > Nope. Never happened. (Provide a citation, please). >When informed that he was on a French newsgroup >making his posts, he gave some excuse about not knowing, but never >apologized to me nor to the newsgroup. And ask yourself, how does it all relate to the poster who noted the >nitpick? >James Harris > > ************************ > > David Ullrich is a math professor at Oklahoma State University. He is therefore paid by the state and by American taxpayers as I'm sure the school receives funds from the federal government. My point is that he should be held to *some* standard, where at a minimum public lying is frowned upon. James Harris ==== >So how can such stuff go on for EIGHT years? You folks >must not have enough entertaining material on sci.math, >to want to provide enough feedback to keep the flames on >for so long! Although some of his talents exist only in his imagination he _is_ a world-class troll. >Does anybody know the relevance of alt.writing here? Only James. ************************ ==== > ... > > Well, a while back I ended up in a debate with a poster from South > > Africa--before Apartheid was ended--and during that discussion > > information about my race was pertinent so I gave it. > > I think this is quite strange. Apartheid ended in South Africa in 1993, > that was years before you started your quest on FLT. (Nelson Mandela > was released in 1990 and three years after his release Apartheid ended.) You're right. I actually went back to the thread and also found out that the other poster merely mentioned being part Afrikaaner. So in recollecting I got several things wrong, which looks like a sexing up to me, as in fact, Apartheid had ended, and the poster's I should have gone back and checked instead of relying on memory. James Harris ==== > >So how can such stuff go on for EIGHT years? You folks >must not have enough entertaining material on sci.math, >to want to provide enough feedback to keep the flames on >for so long! > > Although some of his talents exist only in his imagination > he _is_ a world-class troll. > >Does anybody know the relevance of alt.writing here? > > Only James. > ************************ Some words from James on the subject: >> You see, I looked for major discoveries using very simple mathematics >> because I feared that mathematicians and the people who worship them, >> might too easily avoid the truth, if I couldn't explain it to people >> outside of the math club. >> They don't play fair. I point out simple neat mathematical truths; >> they try to deliver low blows. >> On sci.math that's often all you need to handle people labeled >> cranks. >> >> I'm hoping that alt.math.undergrad and sci.skeptic are different. >> >> And as for alt.writing, writers rule the earth, so prudence dictates >> that I include them. - Randy ==== http://www.msnusers.com/AmateurMath/Documents/CountViewer.html Very stupid to put it at a MSN site... like most reasonable people, I don't > have a Microsoft Passport account so I can't go to your site. And I'm really > not going to create a Passport account... =- Brian Dickens, the Netherlands I have also tried try the applet, and I also do not intend to create a Passport account. It seems to me, that if Harris is interested in folks seeing his works, that he should make them more accessible. -- Tom Potter http://tompotter.us ==== > Conjecture: > For every prime p, the multiplicative group Z(modulo p) contains at least > one prime q

> It fails for p=2 :-) ==== I don't think it works for p = 3 either. Lurch Conjecture: > For every prime p, the multiplicative group Z(modulo p) contains at least > one prime q

It fails for p=2 :-) > ==== > I don't think it works for p = 3 either. <2> = {2, 1} Z modulo 3. GREG Lurch Conjecture: > For every prime p, the multiplicative group Z(modulo p) contains at > least > one prime q

It fails for p=2 :-) > ==== > > If one looks at pairs of consecutive prime numbers separated by only > one non-prime number - 41,43; 821,823; 8087,8089 etc. - one sees that > the sum of such two primes is often divisible by 12: > The post by Rasmus Villemoes settles that splendidly, but your even > posing the problem shows you've forgotten that all primes over 3 are of the > form 6x+1 or 6x-1, so prime pairs are one of each. > Or else you hoped this Harris guy would waste major time > looking for a counterexample -- _Bad_ Uncle Al! Baaad! Stupidity should be lethal, Robert A. Heinlein. Think of my original post as evolution in action. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) Quis custodiet ipsos custodes? The Net! ==== Al Littlebigmanwearingbigboypants admits to trolling: > Al Littlebigmanwearingbigboypants trolls: > If one looks at pairs of consecutive prime numbers separated by only > one non-prime number - 41,43; 821,823; 8087,8089 etc. - one sees that > the sum of such two primes is often divisible by 12: > The post by Rasmus Villemoes settles that splendidly, but your even > posing the problem shows you've forgotten that all primes over 3 are of the > form 6x+1 or 6x-1, so prime pairs are one of each. > Or else you hoped this Harris guy would waste major time > looking for a counterexample -- _Bad_ Uncle Al! Baaad! > Stupidity should be lethal, Robert A. Heinlein. > Think of my original post as evolution in action. Do unto others as you've done unto yourself..... LOL ==== Conjecture 1: If p is any odd prime & p-1 contains at least 1 Quadratic non-residue, then at least one prime q which divides p-1 is a primitive root. Conjecture 2: If p is any prime bigger than 3, then the multiplicative group Z(modulo p-1) contains at least one primitive root of p. Conjecture 3: Suppose p is any odd prime and p-1 is of the form 2q^x, where q is an odd prime. If g is a quadratic non residue of both p and p-1, then g is a primitive root. -- So, I'm looking for counterexamples, or reasons why these wouldn't be true. So far, I'm thinking that both 1 & 3 are false, and 2 is true - although I haven't found any counterexamples, or been able to prove them either way. Any help would be great. GREG ==== I have a function proportional to a probability distribution of interest that is giving me fits. y = x * I(1-(x^2); y, 1/2) where 'I' is the regularized beta function. What I need is the form of this distribution as y->+oo and x>0. For large y, it looks awfully like a gamma or beta distribution, and I'd really like to know if it *is* one of those (or something similar). Can anyone help with this? Zeus ==== Suppose X, Y, Z are positive random variable with the pdf f_X(t), f_Y(t), f_Z(t), respectively. And F_X(t), F_Y(t), F_Z(t) are respective cdf function. The quantity a is a positive real number. I need to evaluate the following probabiltiy. P( X > Suppose X, Y, Z are positive random variable with the pdf f_X(t), f_Y(t), > f_Z(t), respectively. And F_X(t), F_Y(t), F_Z(t) are respective cdf > function. The quantity a is a positive real number. I need to evaluate the > following probabiltiy. > > P( X > I develop the following expresion. > > P( X =int_{0}^{a} f_X(t) F_Y(t) [1-F_Z(t) ] dt > > No. As you have stated it, you have definite values for Y and Z, such that 0 < Y < X < min(a,Z) Why the last inequality? Because if a < Z then X < a guarantees x < Z, and vice-versa. Of course the probability must be 0 if min(a,Z) < Y . Thus P( Y < X < min(a,Z) ) = int _Y ^{min(a,Z)} {dt f_X (t) ) = [ F_X ( min(a,Z) ) - F_X (Y) ] theta ( min(a,Z) - Y ) You can then multiply by the pdf's f_Y (u) and f_Z (v), and integrate over u and v to get the probability of finding an X that satisfies the restrictions. -- Julian V. Noble Professor Emeritus of Physics jvn@spamfree.virginia.edu ^^^^^^^^ http://galileo.phys.virginia.edu/~jvn/ Science knows only one commandment: contribute to science. -- Bertolt Brecht, Galileo. ==== In Madrid, 25 > I think this is a wellknow problem but I'm not sure: A street has a length of 10 car lengths. How many cars can be parked on > average if each arriving car parks on a random available spot? ==== > >>I think this is a wellknow problem but I'm not sure: >>A street has a length of 10 car lengths. How many cars can be parked on >>average if each arriving car parks on a random available spot? > > > 10 > Not if cars park across a car-length boundary. Of course. But the OP didn't specify that. Very often, the available spots are explicitly marked with painted rectangles. > > For example, if the street is two car lengths long, > and a car parks right in the middle, no more cars can park. ==== >Message-id: In Madrid, 25 I've heard it said (about circles) It doesn't work in theory, but it's a tribute to European drivers that it works in practice. >> I think this is a wellknow problem but I'm not sure: >> A street has a length of 10 car lengths. How many cars can be parked on >> average if each arriving car parks on a random available spot? -- Mensanator 2 of Clubs http://members.aol.com/mensanator666/2ofclubs/2ofclubs.htm ==== >> >I think this is a wellknow problem but I'm not sure: A street has a length of 10 car lengths. How many cars can be parked on >average if each arriving car parks on a random available spot? >> >> >> 10 >> Not if cars park across a car-length boundary. > > Of course. But the OP didn't specify that. Very often, the available > spots are explicitly marked with painted rectangles. And very often, people completely ignore those painted rectangles :p ==== > >> >I think this is a wellknow problem but I'm not sure: A street has a length of 10 car lengths. How many cars can be parked on >average if each arriving car parks on a random available spot? >> >> >> 10 >> Not if cars park across a car-length boundary. > > Of course. But the OP didn't specify that. Very often, the available > spots are explicitly marked with painted rectangles. > > And very often, people completely ignore those painted rectangles :p But less so when parking meters are present. ==== Hey, Im curious, what would you guys/gals say the probability of someone entering a Ph.D. program in Math or Stats and not finishing it. i.e. dropping out. ==== >Im curious, what would you guys/gals say the probability of someone >entering a Ph.D. program in Math or Stats and not finishing it. i.e. >dropping out. Of not leaving with a Ph.D.? 75% would be my guess, based on the eight years I've been at Colorado. Doug ==== >Hey, Im curious, what would you guys/gals say the probability of someone >entering a Ph.D. program in Math or Stats and not finishing it. i.e. >dropping out. Wouldn't know about stat, but sad to say a large majority of the people who enter the PhD program in math here at OSU end up without a PhD, one way or another. ************************ ==== Im curious, what would you guys/gals say the probability of someone >entering a Ph.D. program in Math or Stats and not finishing it. i.e. >dropping out. Of not leaving with a Ph.D.? 75% would be my guess, based on the eight > years I've been at Colorado. Doug Depends a lot on the school, of course. If you want the highest probability, I would guess in the states it might be University of Montana or University of Idaho or Idaho State. Not disparaging, that's just how they are. ==== > Hey, > > Im curious, what would you guys/gals say the probability of someone > entering a Ph.D. program in Math or Stats and not finishing it. i.e. > dropping out. I just read that it was about 50-50. Long ago, I heard that it is another 50-50 that one who finishes will do nothing after their thesis. This suggests that a lot of theses are written by the advisor. ==== > Hey, Im curious, what would you guys/gals say the probability of someone > entering a Ph.D. program in Math or Stats and not finishing it. i.e. > dropping out. I just read that it was about 50-50. Long ago, I heard that it is > another 50-50 that one who finishes will do nothing after their > thesis. This suggests that a lot of theses are written by the > advisor. Not in the least. In graduate school you are surrounded by excellent mathematicians and the spirit of mathematics. Mathematics is everywhere; it is the whole world. Everybody around you thinks that it's the only thing worth learning. Then you get a job at Podunk, and discover that your newfound colleagues think that knowing mathematics is knowing the difference between addition and subtraction. Discussions in the faculty lounge are about football. You teach 12 to 15 credits a week, same old stuff year after year. You get numb and tired and disillusioned (Pirsig mentions this in Zen and the Art of Motorcycle Maintenance). You have no real contact with the living world of mathematics and mathematicians; all you've got is your Calculus I textbook and your colleagues. With great effort you can scare up money to go to the occasional convention. Some people overcome these obstacles, bless them. ==== ... >> I just read that it was about 50-50. Long ago, I heard that it is >> another 50-50 that one who finishes will do nothing after their >> thesis. This suggests that a lot of theses are written by the >> advisor. Not in the least. In graduate school you are surrounded by excellent >mathematicians and the spirit of mathematics. Mathematics is everywhere; it >is the whole world. Everybody around you thinks that it's the only thing >worth learning. Then you get a job at Podunk, and discover that your newfound colleagues >think that knowing mathematics is knowing the difference between addition >and subtraction. Discussions in the faculty lounge are about football. You teach 12 to 15 credits a week, same old stuff year after year. You get >numb and tired and disillusioned (Pirsig mentions this in Zen and the Art of >Motorcycle Maintenance). You have no real contact with the living world of >mathematics and mathematicians; all you've got is your Calculus I textbook >and your colleagues. With great effort you can scare up money to go to the >occasional convention. Some people overcome these obstacles, bless them. I like to believe that the advent of Usenet, later the web, arxiv.org, etc., are helping more people overcome those obstacles more effectively. Lee Rudolph ==== >> Hey, >> >> Im curious, what would you guys/gals say the probability of someone >> entering a Ph.D. program in Math or Stats and not finishing it. i.e. >> dropping out. I just read that it was about 50-50. 50-50 for finishing or not finishing? ;-) -- Rouben Rostamian ==== > I just read that it was about 50-50. Long ago, I heard that it is > another 50-50 that one who finishes will do nothing after their > thesis. This suggests that a lot of theses are written by the > advisor. Most of those PhDs go to positions where research is not encouraged, rather teaching and service are encouraged. 4-year colleges, community colleges, even high schools. That could also be a reason for not writing more papers. The idea that writing no research papers equals doing nothing shows a warped view of the world. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ ==== Not in the least. In graduate school you are surrounded by excellent >mathematicians and the spirit of mathematics. Mathematics is everywhere; it >is the whole world. Everybody around you thinks that it's the only thing >worth learning. Then you get a job at Podunk, and discover that your newfound colleagues >think that knowing mathematics is knowing the difference between addition >and subtraction. Discussions in the faculty lounge are about football. You teach 12 to 15 credits a week, same old stuff year after year. You get >numb and tired and disillusioned (Pirsig mentions this in Zen and the Art of >Motorcycle Maintenance). You have no real contact with the living world of >mathematics and mathematicians; all you've got is your Calculus I textbook >and your colleagues. At this point I would suggest: Guy's UPINT, GP/PARI, some decent coffee, a supply of good Scotch Whiskey, and a great wife. Perhaps time on a trout stream just outside Podunk two evenings a week may be of some benefit. A summer working the wheat harvest might help also. Clearly Podunk ain't MSRI. Southwest will, however, get you to Oakland for $99. I don't know what AC Transit costs these days, but it can't be much. Even the numb and tired and disillusioned have choices, I would think. Rich ==== > >Im curious, what would you guys/gals say the probability of someone >entering a Ph.D. program in Math or Stats and not finishing it. i.e. >dropping out. > > Of not leaving with a Ph.D.? 75% would be my guess, based on the eight > years I've been at Colorado. > > Doug Wow, i never would have thought it be that high. I would have guessed maybe 30% drop out rate. I figured after someone got their Masters in Mathematics, got straight A's in their graduate courses that it would be sufficient to prepare them for the doctorate program in mathematics /or statistics. ==== > I just read that [chance of completing Ph.D.] was about 50-50. Long > ago, I heard that it is another 50-50 that one who finishes will do > nothing after their thesis. You mean 50% of mathematics Ph.D.s are unemployed, spending their entire lives sitting in their room staring at the walls? I think not. Perhaps there is a much more narrow (-minded) interpretation of the word nothing? I'm going to speculate that nothing is interpreted along the lines not inconsistent with the simple observation that something on the order of 50% of math or science Ph.D. graduates enter careers other than academics. > This suggests that a lot of theses are written by the advisor. I would suggest that one for whom this is suggested by the 50-50 figure should consider investing some time in the study of logic or statistics. Kevin. ==== > >Im curious, what would you guys/gals say the probability of someone >entering a Ph.D. program in Math or Stats and not finishing it. i.e. >dropping out. > > Of not leaving with a Ph.D.? 75% would be my guess, based on the eight > years I've been at Colorado. > > Doug > > Wow, i never would have thought it be that high. I would have guessed > maybe 30% drop out rate. I figured after someone got their Masters in > Mathematics, got straight A's in their graduate courses that it would > be sufficient to prepare them for the doctorate program in mathematics > /or statistics. One thing is that most people enter without a Masters degree in the first place and switch to a Masters rather than finish the PhD. That accounts for a big portion of the discrepancy you think is present. I on the other hand was one of the few people that had passed most of the hurdles of a math PhD program without actually getting such a degree. I believe there was one other out of maybe two or three dozen PhD graduates during the five year period I was trying for a PhD. Karl Hallowell ==== > think that knowing mathematics is knowing the difference between addition >and subtraction. Discussions in the faculty lounge are about football. You teach 12 to 15 credits a week, same old stuff year after year. You get >numb and tired and disillusioned (Pirsig mentions this in Zen and the Art of >Motorcycle Maintenance). You have no real contact with the living world of >mathematics and mathematicians; all you've got is your Calculus I textbook >and your colleagues. With great effort you can scare up money to go to the >occasional convention. Some people overcome these obstacles, bless them. > > I like to believe that the advent of Usenet, later the web, > arxiv.org, etc., are helping more people overcome those obstacles > more effectively. I believe that is quite accurate. I currently (to be cured in a few months) have no access to a nearby college library, community, etc. The nearest college is more than fourty miles away and there I have only a few informal contacts in the aerospace engineering community. My real connections (as such) are online. Any serious math or physics concept is available online. Ie, I can google for Borel subgroups, Kaluza Klein models, the inverse Galois problem, or the Eight Vertex model and quickly find relevant research and expository material. The USENET might not be able to answer my questions, but they never have failed to come up with some insight. I'm still trying to figure out how to use arXiv.org (even after years of playing with it), but it's proving to be an amazing research tool even with my limited experience. Karl Hallowell ==== >> >>Im curious, what would you guys/gals say the probability of someone >>entering a Ph.D. program in Math or Stats and not finishing it. i.e. >>dropping out. >> >> Of not leaving with a Ph.D.? 75% would be my guess, based on the eight >> years I've been at Colorado. >> >> Doug Wow, i never would have thought it be that high. I would have guessed >maybe 30% drop out rate. I figured after someone got their Masters in >Mathematics, got straight A's in their graduate courses that it would >be sufficient to prepare them for the doctorate program in mathematics >/or statistics. Again, I have no idea how things are in stat, but no that's not how it is in math at all. A master's degree requires that you learn a certain amount of mathematics - how much and how well you're required to learn it varies from place to place. A PhD requires _much_ more. First, it requires that you learn much more mathematics - much deeper mathematics, and you're required to understand it much better than a master's student (to oversimplify that last point, a master's student gets credit for knowing facts, while a PhD student only gets credit for knowing how to _prove_ those facts). And then there's the much more significant difference: A PhD requires a thesis, which is supposed to be significant original research. Of course some theses are more significant and original than others, but regardless, it's a totally different sort of requirement from anything that's required in a typical master's degree - at least theoretically, when you finish your PhD there's supposed to be _something_ that you understand better than anyone else on the planet. ************************ ==== ... > I just read that it was about 50-50. Long ago, I heard that it is > another 50-50 that one who finishes will do nothing after their > thesis. This suggests that a lot of theses are written by the > advisor. >>Not in the least. In graduate school you are surrounded by excellent >>mathematicians and the spirit of mathematics. Mathematics is everywhere; it >>is the whole world. Everybody around you thinks that it's the only thing >>worth learning. >>Then you get a job at Podunk, and discover that your newfound colleagues >>think that knowing mathematics is knowing the difference between addition >>and subtraction. Discussions in the faculty lounge are about football. >>You teach 12 to 15 credits a week, same old stuff year after year. You get >>numb and tired and disillusioned (Pirsig mentions this in Zen and the Art of >>Motorcycle Maintenance). You have no real contact with the living world of >>mathematics and mathematicians; all you've got is your Calculus I textbook >>and your colleagues. With great effort you can scare up money to go to the >>occasional convention. >>Some people overcome these obstacles, bless them. I like to believe that the advent of Usenet, later the web, >arxiv.org, etc., are helping more people overcome those obstacles >more effectively. It can certainly help people stay in touch, or at least that seems plausible. Hard to see how it can help with the huge teaching loads at Podunk, though. >Lee Rudolph ************************ ==== >>I like to believe that the advent of Usenet, later the web, >>arxiv.org, etc., are helping more people overcome those obstacles >>more effectively. It can certainly help people stay in touch, or at least that seems >plausible. Hard to see how it can help with the huge teaching >loads at Podunk, though. Why, by providing the students^Wclients^Wenrollees at Podunk with sci.math to do their homework for them, of course. And if you'd read Hyman Bass's report to the Carnegie Foundation in the latest _Notices_, you'd realize that teaching load is a doubleplusungood phrase. Time to talk about research burden instead! Lee Rudolph ==== > > Most of those PhDs go to positions where research is not encouraged, > rather teaching and service are encouraged. 4-year colleges, community > colleges, even high schools. That could also be a reason for not > writing more papers. The idea that writing no research papers equals > doing nothing shows a warped view of the world. Adding to this ... A PhD program in mathematics that ONLY prepares the participant for writing research papers is a seriously incomplete program at best. Data shows that only about 20% of math PhDs in the US will end up at PhD-granting universities. ==== >> >> Most of those PhDs go to positions where research is not encouraged, >> rather teaching and service are encouraged. 4-year colleges, community >> colleges, even high schools. That could also be a reason for not >> writing more papers. The idea that writing no research papers equals >> doing nothing shows a warped view of the world. Adding to this ... A PhD program in mathematics that ONLY prepares the >participant for writing research papers is a seriously incomplete >program at best. Data shows that only about 20% of math PhDs in the US >will end up at PhD-granting universities. There is neither a logical nor a pragmatic connection between your last two sentences. Many universities and colleges which do not grant PhDs (in mathematics) nonetheless have (however unreasonably and/or unrealistically) a requirement that their (mathematics) faculty members write and publish research papers, at least if they expect to get tenure and/or merit raises. Lee Rudolph ==== > >Im curious, what would you guys/gals say the probability of someone >entering a Ph.D. program in Math or Stats and not finishing it. i.e. >dropping out. > > Of not leaving with a Ph.D.? 75% would be my guess, based on the eight > years I've been at Colorado. > > Doug Well, at my University you need an A average in your graduate courses to be aloud entrance into the PH.D. program. Would it still be a 75% failure rate you think ?? ==== >> Hey, >> >> Im curious, what would you guys/gals say the probability of someone >> entering a Ph.D. program in Math or Stats and not finishing it. i.e. >> dropping out. >I just read that it was about 50-50. Long ago, I heard that it is >another 50-50 that one who finishes will do nothing after their >thesis. This suggests that a lot of theses are written by the >advisor. How in the hell does it suggest that? If I go into industry after finishing, maybe I'm not writing papers, but that doesn't mean that my thesis was written for me. Doug ==== > Clearly Podunk ain't MSRI. Southwest will, however, get you to Oakland for > $99. I don't know what AC Transit costs these days, but it can't be much. > Even the numb and tired and disillusioned have choices, I would think. if you've got the patience to ride the bus from Oakland, kudos to you. It's only $2.25, but it takes over an hour and a half just to get to downtown Berkeley. if you take the BART, it's 4.25 total, and worth the $2. Ben ==== >> Most of those PhDs go to positions where research is not encouraged, >> rather teaching and service are encouraged. 4-year colleges, community >> colleges, even high schools. That could also be a reason for not >> writing more papers. The idea that writing no research papers equals >> doing nothing shows a warped view of the world. >Adding to this ... A PhD program in mathematics that ONLY prepares the >participant for writing research papers is a seriously incomplete >program at best. Data shows that only about 20% of math PhDs in the US >will end up at PhD-granting universities. Such a program will only prepare the participant for doing research in a narrow area. Unfortunately, these seem to be most of what is being done now, especially in statistics. The emphasis on interdisciplinary programs mainly produces those who do not know the basics of anything, but these programs have high rates of finishing. Students are not getting the basics of set theory, algebra, analysis, and topology these days. Learning how to compute and how to solve certain types of problems fails if basic material not covered in that is needed. Abstract concepts are needed for understanding, even if the details of them are not used. -- 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, Deptartment of Statistics, Purdue University ==== >Hey, >Im curious, what would you guys/gals say the probability of someone >entering a Ph.D. program in Math or Stats and not finishing it. i.e. >dropping out. No one seems to have mentioned it, but I think it may depend on the specific university and what its criteria are for being admitted into the program. Averaging over all U.S. schools would probably not provide a meaningful statistic. My guess is that there is a significant variation. Hard data could be obtained by asking the Director of Graduate Studies for various programs. At my school I'll ask him the next time we're on the tennis courts. -- John E. Prussing University of Illinois at Urbana-Champaign Department of Aerospace Engineering http://www.uiuc.edu/~prussing ==== available online in PDF format at http://www.ams.org/employment/asst.pdf Everyone thinking about graduate school in mathematics should look at this booklet. For example, the first institution that I looked at in the booklet had 72 full time graduate students, 15 part time graduate students, and 15 full time first year graduate students. The department had graduated 18 MS students in the past year, and an average of 3 PhD's per year gets an MS, but only about one in five entering graduate students goes on to get a PhD. Of course, you should go back to previous years booklets to see whether there have been any significant changes in enrollment patterns. Looking at about a dozen schools in this booklet, the ratio of full time first year graduate students to PhD's per year (note that PhD's for the last four years are given in the book, so this has to be divided by four) runs from about 5-to-1 down to 2-to-1. Of course, some students enter the graduate program intending to get an MS degree. Unfortunately, I can't think of any way to distinguish those students from students who were given an MS as a consolation prize. In many cases, the total number of MS and PhD degrees per year is very similar to the number of full time first year students, indicating that most students get at least an MS. In other cases, far fewer degrees are awarded than there are entering students. For the big picture, it's worth pointing out that there are approximately 15,000 graduate students in PhD granting departments of math and statistics in the US, and that these departments produce something like 1,000-1,200 PhD graduates per year. These numbers haven't changed dramatically in the last 10 years. (See the latest AMS annual survey report for the numbers.) -- Brian Borchers borchers@nmt.edu Department of Mathematics http://www.nmt.edu/~borchers/ Socorro, NM 87801 FAX: 505-835-5366 -- Brian Borchers borchers@nmt.edu Department of Mathematics http://www.nmt.edu/~borchers/ Socorro, NM 87801 FAX: 505-835-5366 ==== > In <1eb18a7f.0307180852.4f4c5c6b@posting.google.com >Hey, Im curious, what would you guys/gals say the probability of someone >entering a Ph.D. program in Math or Stats and not finishing it. i.e. >dropping out. No one seems to have mentioned it, but I think it may depend on the > specific university and what its criteria are for being admitted into > the program. Averaging over all U.S. schools would probably not provide > a meaningful statistic. My guess is that there is a significant variation. Hard data could be obtained by asking the Director of Graduate Studies > for various programs. At my school I'll ask him the next time we're on > the tennis courts. -- > John E. Prussing > University of Illinois at Urbana-Champaign > Department of Aerospace Engineering > http://www.uiuc.edu/~prussing I did mention it, when this thread started. I also suggested a few schools where I guessed (I have no data) that the probability of finishing might be highest. ==== >Wow, i never would have thought it be that high. I would have guessed >maybe 30% drop out rate. I figured after someone got their Masters in >Mathematics, got straight A's in their graduate courses that it would >be sufficient to prepare them for the doctorate program in mathematics >/or statistics. But that ability to do well in classes is not particularly well correlated with the ability to generate new mathematical ideas. You don't get a PhD for taking a lot of classes, you know. (In some places, you don't take _any_ classes to get a PhD.) I would also object to a phrase like drop out. In secondary school and below, there is a clear expectation that degree completion is the necessary goal for everyone of that age. At the graduate level, and even at the undergraduate level, leaving a program is not necessarily an indication of some kind of failure. Students' eyes are opened in school to the reality of the career choices for which they are preparing, and they may well decide they don't like that image -- even if they're doing well and can continue to do well. Even if your mathematical skills are superb, if what you want to do is make a lot of money, or to have time to raise a family, or to work with some of the world's needy people, then you would be making a mistake to complete a PhD in mathematics. dave ==== This suggests that a lot of theses are written by the advisor. Right. After all, why *wouldn't* a professor want to forego his or her own research activities for a couple years to write an enormous paper under a student's name? Maybe you meant to say something less hilarious. -- Kevin ==== > Hey, Im curious, what would you guys/gals say the probability of someone > entering a Ph.D. program in Math or Stats and not finishing it. i.e. > dropping out. I just read that it was about 50-50. Long ago, I heard that it is > another 50-50 that one who finishes will do nothing after their > thesis. This suggests that a lot of theses are written by the > advisor. > > Not in the least. In graduate school you are surrounded by excellent > mathematicians and the spirit of mathematics. Mathematics is everywhere; it > is the whole world. Everybody around you thinks that it's the only thing > worth learning. > > Then you get a job at Podunk, and discover that your newfound colleagues > think that knowing mathematics is knowing the difference between addition > and subtraction. Discussions in the faculty lounge are about football. > > You teach 12 to 15 credits a week, same old stuff year after year. You get > numb and tired and disillusioned (Pirsig mentions this in Zen and the Art of > Motorcycle Maintenance). You have no real contact with the living world of > mathematics and mathematicians; all you've got is your Calculus I textbook > and your colleagues. With great effort you can scare up money to go to the > occasional convention. > > Some people overcome these obstacles, bless them. Ok, let me put it this way. I KNOW that a lot of PhD theses are written by the advisors. Let me see, I have had 8 PhD students. Of had only the most minimal help; four had a lot of help and explanation described a PhD thesis as a work by the advisor under adverse circumstances and I know for a fact that that was true in his case. Wherever I have been there is always one supervisor who is known to write all or nearly all of his students' theses. One once complained that he didn't mind writing them, it was having to explain them that he objected to. But yes, there are other explanations for why people don't go on to do their own work, but as I look at my students there is a strong correlation between what they did in grad school and what they did afterwards. ==== >> This suggests that a lot of theses are written by the advisor. Right. After all, why *wouldn't* a professor want to forego his or >her own research activities for a couple years to write an enormous >paper under a student's name? Maybe you meant to say something less hilarious. A lot of people have pointed out that this does not necessarily suggest that. Barr just posted a reply, saying let me put it this way and then asserting that in _fact_ a lot of PhD theses are written by advisors. That's not really putting it another way, it's a separate assertion. And whether you believe it or not, it's a _fact_ that a lot of PhD theses are essentially written by the advisor. Barr says he's seen a lot of this - so have I. Have you spent a lot of time on the faculty in a PhD-granting math department, or is your disbelief just motivated by your wonderment as to why a professor would do such a thing? (Regarding why a professor would do such a thing: First, it doesn't mean he's putting his own research on hold for those years. Anyway, there are all sorts of reasons: you have a student who possibly should have been kicked out years ago but wasn't - after the guy's been here for five or six years, passed his exams and courses and all, you really hate to kick him out just because he can't do the thesis. Or in more cynical vein: If none of the students get degrees then sooner or later the bean counters will remove the PhD program from the department, and then the professor will have to teach trigonometry instead of advanced course. All sorts of reasons it happens. Not that _I_'ve ever done such a thing of course...) ************************ ==== >> Hey, >> >> Im curious, what would you guys/gals say the probability of someone >> entering a Ph.D. program in Math or Stats and not finishing it. i.e. >> dropping out. I just read that it was about 50-50. > > 50-50 for finishing or not finishing? > > ;-) Yes. ;-) ==== >> >> And whether you believe it or not, it's a _fact_ that a lot of >> PhD theses are essentially written by the advisor. Yes, there's something significant hidden in the word essentially. >I am certainly willing to believe that theses are written with highly >variable degrees of guice from the advisor, from here's a concept >look at so why don't we meet again in two months to for tomorrow, >why don't you try showing this class of functions is uniformly >continuous, and I'd suggest you start by using these estimates I >highlighted in this paper I photocopied for you---you'll want to take >beta=1/2 in this formula (and beyond). In any event, Michael said he'd read that only 50% of those who finish >their PhDs go on to do any useful research after the thesis and then >inferred that lots of theses were written by the advisor. Whether the >inference was logically correct or not, the implication was that >Michael figured somewhere around 50% of theses (let's be charitable >and say about 25% or so) are written by advisors, a claim I find >difficult to swallow, especially without the word essentially to >dicker over, since Michael didn't quality written by. At a guess---and I admit it is a guess---I would say that somewhere >around 1% of theses (in math and stats departments, let's say) are >written by the advisor in the sense that it would be considered >substantial plagiarism in a different context. Significantly more, >say 5% (or perhaps even 10%), involve the advisor leading the student >by the nose to the extent that it would be obvious to an unbiased >observer that the student hasn't demonstrated *any* capability to do >independent research. These seem to be the cases you have in mind >when you say essentially written. I imagine that substantially more often, perhaps in as many as 50% of >the cases, the advisor contributes most of the important ideas, rough >statements of most main results, and just generally mostly or even >completely determines the overall direction of the research with the >student primarily filling in the details. Am I being naive? You seem to think the last estimate should be >somewhere close to 100%. Huh? How do you get from a lot of to close to 100%? For the record, when I said a lot of I wasn't referring to a large _percentage_ of PhD theses. (Otoh in the cases I had in mind the percentage of the thesis written by the advisor is indeed _very_ close to 100%.) >> Have you spent a >> lot of time on the faculty in a PhD-granting math department, I have spent a lot of time (too much time) as a Ph.D. student in a >statistics department interacting with both stats and math >Ph.D. students at that institution. I've also spent some time as a >postdoc in a math department interacting with faculty and their >Ph.D. students. The students that I remember (even a few lifers >who'd been there many years) were obviously writing their own theses >in any reasonable sense. I was probably fortunate enough to interact >mostly with strong (though sometimes slow-working!) students. ************************ ==== > Does a Ph.D. program for Mathematics have a time period for validly > completing > the program? At my university, one must finish within four years. -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html The League of Gentlemen ==== > > Huh? How do you get from a lot of to close to 100%? question: >Do you mean that the advisor has contributed >almost every original idea in the thesis? with: > Yes. Sometimes it appears to be somewhat more > than almost every. and I didn't read carefully enough. I mistakenly thought you were saying that it sometimes seemed to you that this happened in almost every case. > For the record, when I said a lot of I wasn't referring to > a large _percentage_ of PhD theses. Yes, now I understand. -- Kevin ==== Does a Ph.D. program for Mathematics have a time period for validly completing > the program? It depends on the university and even the department. My department (stats at Wisconsin---Madison) had various deadlines you had to meet to indicate progress. You had to take a certain series of core courses within two or three semesters of starting. You had to take and pass your written qualifying exam within four semesters of completing that series of courses, and a pass on your qualifying exam was only good for a limited amount of time (five years, maybe?). On the other hand, if you let that lapse, you could always take and pass your qualifying exam again. I believe there were requirements to take a full course load up until the time you passed your preliminary exam (an oral defense of the first part of your thesis, essentially). After that, you had dissertator status, and I'm not aware that there was any particular reason a student couldn't go on indefinitely passing a qualifying exam every five years as long as his or her advisor continued to indicate satisfactory progress. The graduate school was considering introducing some time limits at some point. I don't know if anything came of it. For the most part, it's probably not worth the trouble. Lifers are prominent fixtures because of their longevity, not their numbers. They aren't particularly a drain on the university; in some cases, they may be a source of cheap teaching or research labour, as pointed around campus doing odd jobs for low wages, why go out of your way to regulate against the practice? -- Kevin ==== > > One wonders also about the ethics of the department. People > have brains and can use them to make decisions on a case by > case basis, and that's why we have extensions. But oh how easy > it is to take advantage of these lifers as cheap help. On the flip side, the lifers have brains, too. If they really thought they were being taken advantage of, they could always get real jobs. The fact is, a university campus is a wonderful place to be for a bright person with a wide variety of interests. (Less charitably, these people undoubtedly have laziness and directionless in somewhat larger shares than other students, but even these qualities aren't wholly without their virtues.) That kind of person, in that kind of environment, may see no earthly reason for rushing to finish a thesis when there are so many other neat things to do every day. There undoubtedly are graduate students that are taken advantage of, but I suspect it's easier to take advantage of a student that desperately wants or needs to graduate quickly. A department doesn't have as much leverage over a lifer. > It is a disservice to a graduate student to not only let him > waste 7 years of his life pretending to write his disseration, I wasn't a lifer, but I took my time. I'd hardly consider the many interesting things I did while pretending to write my dissertation a waste of my life. (Since my marriage was one of them, I imagine my wife would agree.) > When things are down to the wire, he ought to be _supported_ in his > efforts by a department interested in the furthering of the > discipline, not _distracted_ from them by a department interested in > avoiding hiring a faculty member at 4 times the cost. I think most departments are extremely supportive of students who actually want to graduate. In fact, half of this thread has been concerned with advisors who are far *too* supportive of those students. I really think you've got it all wrong. These aren't poor, dumb kids who don't know any better than to let the greedy corporate university steal all their money. These are grown men and women who happen to love the life they're leading and have found a mutually beneficial arrangement with a cash-strapped institution to allow them to lead that life. If anyone feels taken advantage of, I'll bet it's the poor soul who agreed to be a lifer's advisor many, many years ago and has regretted it ever since. Are there any lifers (or near-lifers) out there that feel differently? -- Kevin ==== > I really think you've got it all wrong. These aren't poor, dumb kids > who don't know any better than to let the greedy corporate university > steal all their money. These are grown men and women who happen to > love the life they're leading and have found a mutually beneficial > arrangement with a cash-strapped institution to allow them to lead > that life. I would only have it all wrong if I thought that all the cases were that way. I've just seen _some_ lifers who would have benefitted from a kick in the pants, who's wives would have dearly loved to see the quadrupling of the salary, who would have continued to do essentially the same work in the same environment, but with the the quadrupled salary and quadrupled respect, but it was just too easy for all involved to shirk their responsibility. And yes, I'm with you and Dear Abby on this one. Someone can't walk all over you unless you let them. My point was that the departments should not enable (in the Alcoholics Anonymous sense of the word) slacking behavior. These are stipends, not salaries. In my case, the department got in big hurry to rush people through. While there was a generous time allowance for finishing the program, there was only a short allowance for stipends. Finish quickly or get your support somewhere else was the message. I resented this also, for some of the reasons you hint at. I was busy trying to study mathematics, and this was my chance. I wasn't at a diploma factory, and it wasn't my goal to help a department boost their statistics. This was my only chance to take courses from and interact with certain talented mathematicians. I would go off and likely end up at a small college with no colleagues or library. Here was my one shot, and some administrator wanted to make sure it was as antiseptic as possible. So I did mine in 5 years. Another year would have been nice, so I know what you're saying. Dammit, it was _my_ Ph.D., so I was, by golly, going to forge it _my_ way, at least to some extent. But my post was addressing other cases. There are adults who allow people to take advantage of them. That doesn't mean it's A-OK for departments to use them. If a student is not making progress on his degree then he is not really a student, and he doesn't deserve a stipend. He's stagnant. There's an ethical question here: The department believes, in theory, that every professor is engaged in research at some level. At least they expect it. And every TA is chasing a degree. So everyone teaching courses is an _active_ participant in the pursuit of knowledge. We advertize that this is important in the classroom. Even the smallest of colleges insist on professional development for promotion and tenure. In academia, we're against stagnance (is that a word?) We want (don't we?) people who are excited pursuers of truth and beauty teaching others to be excited pursuers of truth and beuaty. Just to be clear, I don't think every 12-year Ph.D. student is stagnant. I said at the beginning that we have brains and we should use them to make decisions. It's that I think that some of those decisions are made in favor of slave labor. Bart ==== Consider the product h = n(n+1)(n+2)(n+3) for integer n>0, and assume h=a^b for some positive intgers a and b. Any prime p>3 that divides n cannot divide the other n+i factors, so p^b must divide n, from which it follows n= (product of primes >3 dividing n)^b * 3's and 2's. Similarly for the other factors. Thus we can write n = 2^i 3^j (prod primes p>3)^b n+1 = 2^x 3^y (prod primes q>3)^b giving that 1+2^i 3^j (prod primes p>3)^b = 2^x 3^y (prod primes q>3)^b Analyze this last equation. If i or x is nonzero, divide both sides by 2^min(i,x), giving one side to be in integer, and the other not, a contradiction. Thus i=x=0. Similarly, j=y=0. Thus we have two bth powers of integers that differ by 1, which is impossible, i.e. 1+c^b=d^b has no integer solutions for b>1, c>0,d>0, since bth powers differ by more than 1. Thus no product of 4 consecutive integers is a poerfect power. Chris Lomont > Does anyone know of a simple, elementary proof for the result that the > product of four consecutive positive integers is never a perfect power > (exponent >= 2)? I know that Erdos and Selfridge proved a more > general result, but their proof was neither elementary nor simple. > ==== [...] > Thus no product of 4 consecutive integers is a poerfect power. > Chris Lomont Chris, nicely done and nicely explained. ==== Surely, either n or n + 1 is even, so how can i = x = 0? What am I missing? Robert Consider the product h = n(n+1)(n+2)(n+3) for integer n>0, and assume > h=a^b for some positive intgers a and b. Any prime p>3 that divides n > cannot divide the other n+i factors, so p^b must divide n, from which it > follows n= (product of primes >3 dividing n)^b * 3's and 2's. Similarly > for the other factors. Thus we can write n = 2^i 3^j (prod primes p>3)^b > n+1 = 2^x 3^y (prod primes q>3)^b giving that 1+2^i 3^j (prod primes p>3)^b = 2^x 3^y (prod primes q>3)^b Analyze this last equation. If i or x is nonzero, divide both sides by > 2^min(i,x), giving one side to be in integer, and the other not, a > contradiction. Thus i=x=0. Similarly, j=y=0. Thus we have two bth powers > of integers that differ by 1, which is impossible, i.e. 1+c^b=d^b has no integer solutions for b>1, c>0,d>0, since bth powers differ by more > than 1. Thus no product of 4 consecutive integers is a poerfect power. > Chris Lomont Does anyone know of a simple, elementary proof for the result that the > product of four consecutive positive integers is never a perfect power > (exponent >= 2)? I know that Erdos and Selfridge proved a more > general result, but their proof was neither elementary nor simple. ==== Consider the product h = n(n+1)(n+2)(n+3) for integer n>0, and assume >h=a^b for some positive intgers a and b. Any prime p>3 that divides n >cannot divide the other n+i factors, so p^b must divide n, from which it >follows n= (product of primes >3 dividing n)^b * 3's and 2's. Similarly >for the other factors. Thus we can write n = 2^i 3^j (prod primes p>3)^b >n+1 = 2^x 3^y (prod primes q>3)^b giving that 1+2^i 3^j (prod primes p>3)^b = 2^x 3^y (prod primes q>3)^b Analyze this last equation. If i or x is nonzero, divide both sides by >2^min(i,x), giving one side to be in integer, and the other not, a >contradiction. Thus i=x=0. You have only shown that min{i, x} = 0. John Roberts-Jones ==== Good, you just shortened the proof a bit. Similarly, you can't have both n and n+1 being a multiple of 3. > Surely, either n or n + 1 is even, so how can i = x = 0? What am I missing? > Robert Consider the product h = n(n+1)(n+2)(n+3) for integer n>0, and assume > h=a^b for some positive intgers a and b. Any prime p>3 that divides n > cannot divide the other n+i factors, so p^b must divide n, from which it > follows n= (product of primes >3 dividing n)^b * 3's and 2's. Similarly > for the other factors. Thus we can write n = 2^i 3^j (prod primes p>3)^b > n+1 = 2^x 3^y (prod primes q>3)^b giving that 1+2^i 3^j (prod primes p>3)^b = 2^x 3^y (prod primes q>3)^b Analyze this last equation. If i or x is nonzero, divide both sides by > 2^min(i,x), giving one side to be in integer, and the other not, a > contradiction. Thus i=x=0. Similarly, j=y=0. Thus we have two bth powers > of integers that differ by 1, which is impossible, i.e. 1+c^b=d^b has no integer solutions for b>1, c>0,d>0, since bth powers differ by more > than 1. Thus no product of 4 consecutive integers is a poerfect power. > Chris Lomont Does anyone know of a simple, elementary proof for the result that the > product of four consecutive positive integers is never a perfect power > (exponent >= 2)? I know that Erdos and Selfridge proved a more > general result, but their proof was neither elementary nor simple. ==== > Chris, nicely done and nicely explained. But not, unfortunately, correct. Eg 1 + 2^3 = 3^2. -- Timothy Murphy tel: +353-86-233 6090 ==== 1+2^i 3^j (prod primes p>3)^b = 2^x 3^y (prod primes q>3)^b Analyze this last equation. If i or x is nonzero, divide both sides by >2^min(i,x), giving one side to be in integer, and the other not, a >contradiction. Thus i=x=0. I think you mean, If BOTH i and x are nonzero then ... [ same ]. Thus > either i = 0 or x = 0. But now you've got more work to do! Ah yes, correct :) I only spent a few minutes thinking..... Actually, since one is n, and one is n+1, then only one of them has any factor of two anyways... So exactly one of i and x are nonzero. Also, since n and n+1 are relatively prime, at most one of j and y can be nonzero, and the p are distince from the q. You might be able to complete this proof using these facts. For example, if the 2 and 3 are with the n, then noting that each of n+1 , n+2, and n+3 must be (prod primes)^b times some 2 or 3 factors, you might get contradictions since powwers of b should be large... But I have no proof, and must work now. Perhaps after work I'll finish this if possible Chris Lomont Obviously if both i and x are zero, you've got 1 + odd = odd, which > is already a contradiction. dave > ==== > [...] Thus no product of 4 consecutive integers is a poerfect power. > Chris Lomont Chris, nicely done and nicely explained. > doodled with it again this afternoon, but it is harder than I thought. Chris Lomont ==== I have found an elegant proof that the derivative of sin(x) is cos(x). I have studied two a-levels in maths and read lots of math books but have not come across this particular proof before. Obviously, this is not a groundbreaking proof, it is simply a different way of proving a fundamental result. (without using limits or infintesimals). However, for personal interest I would like to know if it is original. Is there anywhere I can find a catalogue of existing proofs for the derivative of sin(x)? If it turned out this proof was original should I consider getting it published or is it not worth it, since it is such a tiny proof. Among these things, I am also working on some integration techniques. Again, I have a similiar problem: I do not know whether this stuff I am finding is original. I have done 6 modules of pure maths at school so I am not a complete novice, but on the other hand I am aware that there is many things that I do not know of pure maths since I have yet to start my maths degree. Can anyone suggest a website that provides information on advanced integration techniques, and for that matter information on higher level maths? Any responses to the above would be gratefully received. Flame. ==== > I have found an elegant proof that the derivative of sin(x) is cos(x). Put your money where your mouth is. > If it turned out this proof was original should I consider getting it > published or is it not worth it, since it is such a tiny proof. > Don't count your chickens before they hatch. > Among these things, I am also working on some integration techniques. > Again, I have a similiar problem: I do not know whether this stuff I > am finding is original. Apply William's Metatheorem: Whatever math I dream up is already old hat. > Any responses to the above would be gratefully received. > Let us know when or if you've the courage for a peer review. ==== > I have found an elegant proof that the derivative of sin(x) is cos(x). > I have studied two a-levels in maths and read lots of math books but > have not come across this particular proof before. > > Obviously, this is not a groundbreaking proof, it is simply a > different way of proving a fundamental result. (without using limits > or infintesimals). Hmmm. The definition of differentiation involves limits .... > However, for personal interest I would like to know > if it is original. Why not post it? For such a basic result it's probably unlikely that it's totally new, but who knows? > Is there anywhere I can find a catalogue of existing proofs for the > derivative of sin(x)? Sounds a bit unlikely. > If it turned out this proof was original should I consider getting it > published or is it not worth it, since it is such a tiny proof. If you have a novel angle on any elementary mathematics, the Mathematical Gazette might publish it. -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html The League of Gentlemen ==== I have found an elegant proof that the derivative of sin(x) is cos(x). > I have studied two a-levels in maths and read lots of math books but > have not come across this particular proof before. Obviously, this is not a groundbreaking proof, it is simply a > different way of proving a fundamental result. (without using limits > or infintesimals). However, for personal interest I would like to know > if it is original. Is there anywhere I can find a catalogue of existing proofs for the > derivative of sin(x)? If it turned out this proof was original should I consider getting it > published or is it not worth it, since it is such a tiny proof. Among these things, I am also working on some integration techniques. > Again, I have a similiar problem: I do not know whether this stuff I > am finding is original. I have done 6 modules of pure maths at school > so I am not a complete novice, but on the other hand I am aware that > there is many things that I do not know of pure maths since I have yet > to start my maths degree. Can anyone suggest a website that provides > information on advanced integration techniques, and for that matter > information on higher level maths? Any responses to the above would be gratefully received. Flame. Learning by doing has helped many, including myself - along with learning by questioning. Don't get discouraged when you find out that often you are re-discovering. Could you share your proof of the derivative result? It will not diminish your claims to originality, if that is indeed the case. (I wonder how the use of limits can be avoided!) There are journals of high-school mathematics; in Canada, there is Crux Mathematicorum with Mathematical Mayhem, published by the Canadian Mathematical Society; there should be a counterpart known facts, although the main part of its contents are competition type problems, with best solutions published. And there is American Mathematical Monthly, of course. Best wishes, ZVK(Slavek). ==== > >> I have found an elegant proof that the derivative of sin(x) is cos(x). >> I have studied two a-levels in maths and read lots of math books but >> have not come across this particular proof before. >> >> Obviously, this is not a groundbreaking proof, it is simply a >> different way of proving a fundamental result. (without using limits >> or infintesimals). > > Hmmm. The definition of differentiation involves limits .... > Yeah, I'm kind of wondering also. I think what he means is that there is no limit explictly being taken, i.e. you don't take the difference quotient of sine and then compute it directly. For example, here's a nice little proof that derivative of sine is cosine that may be what he's talking about: Consider the unit circle in R^2, with some parametrization t |--> (x(t), y(t)). The derivative (x'(t), y'(t)) must be orthogonal to the position vector (x(t), y(t)) (by differentiating the equation x(t)^2 + y(t)^2 = 1). So (x'(t), y'(t)) = ( -f(t)y(t), f(t)x(t) ) for some function f. However, if we had taken the parametrization by arc length, then we would have unit speed, i.e. f = 1. So we can assume that x'(t) = -y(t), y'(t) = x(t). Also, since we've parametrized by arc length, we see that (x(t), y(t)) makes angle t with the x axis (going counterclockwise). This is precisely the definition of cosine and sine (or equivalent to whatever your definition is). Therefore we have shown derivative of cosine is -sine and derivative of sine is cosine. >Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html > The League of Gentlemen I presume this is from the graphic novel by Alan Moore. But the question is, is the movie any good? ==== >>Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html >> The League of Gentlemen > > I presume this is from the graphic novel by Alan Moore. But the question > is, is the movie any good? Oh, never mind; I noticed that I misread The League of Gentlemen as The League of Extraordinary Gentlemen. The former is apparently a British TV show. ==== I have found an elegant proof that the derivative of sin(x) is cos(x). > I have studied two a-levels in maths and read lots of math books but > have not come across this particular proof before. Obviously, this is not a groundbreaking proof, it is simply a > different way of proving a fundamental result. (without using limits > or infintesimals). However, for personal interest I would like to know > if it is original. I too would like to see your proof. > Is there anywhere I can find a catalogue of existing proofs for the > derivative of sin(x)? If it turned out this proof was original should I consider getting it > published or is it not worth it, since it is such a tiny proof. Among these things, I am also working on some integration techniques. Since you say ... also working on some integration techniques I hope that your reasoning is not circular. (Actually the pun is not intended) > Again, I have a similiar problem: I do not know whether this stuff I > am finding is original. I have done 6 modules of pure maths at school > so I am not a complete novice, but on the other hand I am aware that > there is many things that I do not know of pure maths since I have yet > to start my maths degree. Can anyone suggest a website that provides > information on advanced integration techniques, and for that matter > information on higher level maths? Use google. To find information about different disciplines you could look at some to the links mentioned in this news group. Some of the links are cranks, but by reading the responses to various post, you will determine which ones are worth while. Enjoy the discovery. > Any responses to the above would be gratefully received. Flame. ==== > -------------------------------------------------------------------------- > Learning by doing has helped many, including myself - along with > learning by questioning. Don't get discouraged when you find out > that often you are re-discovering. > > Could you share your proof of the derivative result? It will not > diminish your claims to originality, if that is indeed the case. > (I wonder how the use of limits can be avoided!) -------------------------------------------------------------------------- Before I begin, a correction: I have made no claims to originality. Obviously I hope it to be original, but do not know this, hence me posting onto this group. I will post this proof onto this newsgroup since I noticed a ring of pessimism in some of the replies. However, before this, how can I be sure I wont lose the claim to its discovery? (if, of course, its original). Note: I apologise for any confusion when I said no limits were used. I meant this in the sense that limits or infintesimals were not used explicitly (not by first principles or otherwise) The integration techniques I referred to are not related to this proof this is a separate thing I am working on. I am currently working on other areas of pure maths, and I am frequently finding new things that I have not come accross before. I am confident at least one of these things is quite significant, but do not know what to do with them. Should I just send them off somewhere to get published? I do not have a clue in this area, I am only in my teens. ---------------------------------------------------------------------------- --- > There are journals of high-school mathematics; in Canada, there > is Crux Mathematicorum with Mathematical Mayhem, published by > the Canadian Mathematical Society; there should be a counterpart > known facts, although the main part of its contents are > competition type problems, with best solutions published. > ---------------------------------------------------------------------------- ---- Crux Mathematicorum with Mathematical Mayhem: I have not been able to find a counterpart to this. Can anyone suggest a UK publication similiar to this? thank you all for your time in replying, Flame. <9a85593f.0307120419.3ad90f2e@posting.google.com> ==== > Before I begin, a correction: I have made no claims to originality. > Obviously I hope it to be original, but do not know this, hence me > posting onto this group. I will post this proof onto this newsgroup since I noticed a ring of > pessimism in some of the replies. However, before this, how can I be > sure I wont lose the claim to its discovery? (if, of course, its > original). > It's published here with date stamp and your alias. If you want your name on it, then publish it here with your name. Records of news groups are kept for some years, so you can lay claim to your notions via the archives of sci.math. Otherwise go thru hassle of archiving which is much less hassle than copy writing or publishing. yourself. Post office time stamps envelopes and as long as you don't open it, upon public opening, it will give you some claim to authorship of your fantasies. > I am currently working on other areas of pure maths, and I am > frequently finding new things that I have not come across before. I > am confident at least one of these things is quite significant, but do > not know what to do with them. Should I just send them off somewhere > to get published? I do not have a clue in this area, I am only in my > teens. You'll need to have you ideas peer reviewed. You'll need to have presentation that'll be noticed by the referee as notable and worth his volunteer efforts to consider your paper for publishing. Claim what you may, The proof of the pudding is in the eating. So again I remind you of William Metatheorem Whatever math I dream up is already old hat. I've never been able to produce a counterexample and I bet you won't either. Yet it's not certain William Metatheorem has no unnoticed loop holes. ==== > > Crux Mathematicorum with Mathematical Mayhem: I have not been able to > find a counterpart to this. Can anyone suggest a UK publication > similiar to this? I already did: The Mathematical Gazette. -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html The League of Gentlemen ==== I have found an elegant proof that the derivative of sin(x) is cos(x). >I have studied two a-levels in maths and read lots of math books but >have not come across this particular proof before. Obviously, this is not a groundbreaking proof, it is simply a >different way of proving a fundamental result. (without using limits >or infintesimals). However, for personal interest I would like to know >if it is original. Is there anywhere I can find a catalogue of existing proofs for the >derivative of sin(x)? If it turned out this proof was original should I consider getting it >published or is it not worth it, since it is such a tiny proof. Among these things, I am also working on some integration techniques. >Again, I have a similiar problem: I do not know whether this stuff I >am finding is original. I have done 6 modules of pure maths at school >so I am not a complete novice, but on the other hand I am aware that >there is many things that I do not know of pure maths since I have yet >to start my maths degree. Can anyone suggest a website that provides >information on advanced integration techniques, and for that matter >information on higher level maths? Any responses to the above would be gratefully received. Flame. > > 1. There's no money in math. So if someone steals your idea, you haven't lost any money. 2. If you're doing original work, you'll continue to do original work. If someone steals an idea, just stay away from that person in the future and keep doing your original work. 3. The only fame you can expect from doing math is among other mathematicians. 4. There is money in applying mathematical ideas to other disciplines. Not deep mathematical ideas, but a little math and some logic and organization to business problems (and translating your results to English for your colleagues) will keep you steadily employed at quite reasonable rates. Thinking original thoughts is using time that could be spent thinking profitable thoughts. (Of course, if you get paid well enough, you can afford to spend some time thinking original thoughts. It's much easier to take the lower salary and be a university professor.) Jon Miller ==== > I have found an elegant proof that the derivative of sin(x) is cos(x). >I have studied two a-levels in maths and read lots of math books but >have not come across this particular proof before. Obviously, this is not a groundbreaking proof, it is simply a >different way of proving a fundamental result. (without using limits >or infintesimals). However, for personal interest I would like to know >if it is original. Is there anywhere I can find a catalogue of existing proofs for the >derivative of sin(x)? If it turned out this proof was original should I consider getting it >published or is it not worth it, since it is such a tiny proof. Among these things, I am also working on some integration techniques. >Again, I have a similiar problem: I do not know whether this stuff I >am finding is original. I have done 6 modules of pure maths at school >so I am not a complete novice, but on the other hand I am aware that >there is many things that I do not know of pure maths since I have yet >to start my maths degree. Can anyone suggest a website that provides >information on advanced integration techniques, and for that matter >information on higher level maths? Any responses to the above would be gratefully received. Flame. > 1. There's no money in math. So if someone steals your idea, you > haven't lost any money. I made no reference to money. To quote myself: ...for personal interest I would like to know if it is original > 2. If you're doing original work, you'll continue to do original work. > If someone steals an idea, just stay away from that person in the > future and keep doing your original work. If someone steals an idea as you put it, then i would lose priority as the discoverer. I think that as unfair, strange though it may sound. > 3. The only fame you can expect from doing math is among other > mathematicians. I do not expect fame. I do not understand where you derived this idea from my post. > 4. There is money in applying mathematical ideas to other disciplines. Please see my response to 1. > Not deep mathematical ideas, but a little math and some logic and > organization to business problems (and translating your results to > English for your colleagues) will keep you steadily employed at quite > reasonable rates. Thinking original thoughts is using time that could > be spent thinking profitable thoughts. Please see my response to 1. (Of course, if you get paid well > enough, you can afford to spend some time thinking original thoughts. > It's much easier to take the lower salary and be a university professor.) > > Jon Miller I am currently making enquiries with other professional mathematicians regarding my work so far. If any developments occur, I will post them here along with my work. Flame ==== And don't forget that I've provided access to my work at one location where you can go to see the mathematics that underpins so many of these discussions: 1. The short proof of Fermat's Last Theorem where you see the power of techniques that are also used in the paper Advanced Polynomial Factorization. 2. THE prime counting function, or my prime counting function as I differentiate it from those so-called prime counting functions. At my website you can see the function, get a C++ program to run it, read some of my thoughts on it, join the group and get a Java algorithmic implementation, and most importantly, see the partial differential equation for the J function, which is a prime suspect for the connection between the prime distribution and the continuous functions like li(x) and x/ln x. 3. Join the group and you can access the pdf file to read my paper Advanced Polynomial Factorization, where a polynomial factorization into non-polynomial factors proves an error in taught mathematics. http://groups.msn.com/AmateurMath See what all the arguing is about, judge for yourselves the mathematics presented, and step away from just waiting for people to tell you what to think. Mathematics is not owned by any group of people. It's beautiful in that logic and consistency rule the day, while unfortunately, people can lie about just about anything, even mathematics. And they can even lie when they're mathematicians. Yes, even mathematicians can lie. James Harris ==== [a lot not worth quoting] And they can even lie when they're mathematicians. Yes, even > mathematicians can lie. > And even laymen can be fools. /Rasmus Irrelevant group 'sci.physics' removed from list. -- ==== > And don't forget that I've provided access to my work at one location > where you can go to see the mathematics that underpins so many of > these discussions: > > 1. The short proof of Fermat's Last Theorem where you see the power > of techniques that are also used in the paper Advanced Polynomial > Factorization. > > 2. THE prime counting function, or my prime counting function as I > differentiate it from those so-called prime counting functions. At my > website you can see the function, get a C++ program to run it, read > some of my thoughts on it, join the group and get a Java algorithmic > implementation, and most importantly, see the partial differential > equation for the J function, which is a prime suspect for the > connection between the prime distribution and the continuous functions > like li(x) and x/ln x. > > 3. Join the group and you can access the pdf file to read my paper > Advanced Polynomial Factorization, where a polynomial factorization > into non-polynomial factors proves an error in taught mathematics. > > http://groups.msn.com/AmateurMath > > See what all the arguing is about, judge for yourselves the > mathematics presented, and step away from just waiting for people to > tell you what to think. > > Mathematics is not owned by any group of people. It's beautiful in > that logic and consistency rule the day, while unfortunately, people > can lie about just about anything, even mathematics. > > And they can even lie when they're mathematicians. Yes, even > mathematicians can lie. > > > James Harris I just went for a stroll, as advised. Much of your work is based on your object math. The problem is, you have something called an operator that you haven't clearly defined. Your definition of Objects is also unclear at best. Why not either use the same math as everyone else or be clear and use examples? If all your work is based on this, it's no wonder you are making very little progress in convincing people. -- Will Twentyman ==== [snip] > 2. THE prime counting function, or my prime counting function as I > differentiate it from those so-called prime counting functions. [snip] Hey ing imbecile Harris, Uncle Al will give you a discrete prime number task to redeem yourself and your incredible manure pile of bull theories and proofs. If one looks at pairs of consecutive prime numbers separated by only one non-prime number - 41,43; 821,823; 8087,8089 etc. - one sees that the sum of such two primes is often divisible by 12: (11 + 13)/12 = 2 (41 + 43)/12 = 7 (821 + 823)/12 = 137 (1931 + 1933)/12 = 322 (8087 + 8089)/12 = 1348 (104681 + 104683)/12 = 17447 3,5 obviously does not work. Use your Harris big mouth to find another pair of consecutive primes other than 3,5 whose sum is not evenly divisible by 12. Put up and demonstrate your claimed expertise, or shut up for being the dysfunctional ing imbecile that you are. Uncle Al bets that you don't have the balls or the brains to perform. Are you going to run crying to your mama, Harris? -- Uncle Al http://www.mazepath.com/uncleal/eotvos.htm (Do something naughty to physics) ==== > Put up and demonstrate your claimed expertise, or shut up for being > the dysfunctional ing imbecile that you are. Uncle Al bets that > you don't have the balls or the brains to perform. Are you going to > run crying to your mama, Harris? Can you refer me to a proof (in the literature) that consective primes whose sum is >= 12 add up to a number divisible by 12. Is this a known theorem or is this an open problem? Bob Kolker ==== > Put up and demonstrate your claimed expertise, or shut up for being >> the dysfunctional ing imbecile that you are. Uncle Al bets that >> you don't have the balls or the brains to perform. Are you going to >> run crying to your mama, Harris? Can you refer me to a proof (in the literature) that consective primes > whose sum is >= 12 add up to a number divisible by 12. Is this a known > theorem or is this an open problem? > Well, if you accept this is literature, here is a proof: Let p be an odd prime such that p+2 is also a prime, and assume p /= 3. If p == 1 (mod 4) we have 2p == 2 (mod 4) and consequently p + p+2 = 2p+2 == 0 (mod 4), that is, 4 divides 2p+2. If p == 3 (mod 4) we also have 2p == 2 (mod 4), so also in this case we have that 4 divides 2p+2. Now 3 does not divide p; thus p == 1 or p == 2 (mod 3); but since p+2 is also prime, 3 does not divide p+2, from which we may conclude that p == 2 (mod 3) and p+2 == 1 (mod 3); then 2p+2 == 0 (mod 3), and 3 divides the sum. Since 3 and 4 are coprime, and they both divide 2p+2, 3á4=12 divides 2p+2. QED (quite elementary, actually). /Rasmus -- ==== > And don't forget that I've provided access to my work at one location > where you can go to see the mathematics that underpins so many of > these discussions: > > 1. The short proof of Fermat's Last Theorem where you see the power > of techniques that are also used in the paper Advanced Polynomial > Factorization. > > 2. THE prime counting function, or my prime counting function as I > differentiate it from those so-called prime counting functions. At my > website you can see the function, get a C++ program to run it, read > some of my thoughts on it, join the group and get a Java algorithmic > implementation, and most importantly, see the partial differential > equation for the J function, which is a prime suspect for the > connection between the prime distribution and the continuous functions > like li(x) and x/ln x. > > 3. Join the group and you can access the pdf file to read my paper > Advanced Polynomial Factorization, where a polynomial factorization > into non-polynomial factors proves an error in taught mathematics. I think that is speled undermines! ==== > > Put up and demonstrate your claimed expertise, or shut up for being > the dysfunctional ing imbecile that you are. Uncle Al bets that > you don't have the balls or the brains to perform. Are you going to > run crying to your mama, Harris? > > Can you refer me to a proof (in the literature) that consective primes > whose sum is >= 12 add up to a number divisible by 12. Is this a known > theorem or is this an open problem? If by consective you mean primes p and q with q-p = 2 then I would refer you to the use of your brain instead of looking for a proof in the literature. Two minutes without using pen and paper maximum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Every prime except 2 and 3 is of the form 6k-1 or 6k+1. If p and q are primes, q = p+2, and p is not equal to 3, then p is of the form 6k-1 and q of the form 6k+1, so p+q = 12k. ==== > > > Put up and demonstrate your claimed expertise, or shut up for being >> the dysfunctional ing imbecile that you are. Uncle Al bets that >> you don't have the balls or the brains to perform. Are you going to >> run crying to your mama, Harris? Can you refer me to a proof (in the literature) that consective primes > whose sum is >= 12 add up to a number divisible by 12. Is this a known > theorem or is this an open problem? > Well, if you accept this is literature, here is a proof: > > Let p be an odd prime such that p+2 is also a prime, and assume p /= > 3. > > If p == 1 (mod 4) we have 2p == 2 (mod 4) and consequently p + p+2 = > 2p+2 == 0 (mod 4), that is, 4 divides 2p+2. > > If p == 3 (mod 4) we also have 2p == 2 (mod 4), so also in this case > we have that 4 divides 2p+2. > > Now 3 does not divide p; thus p == 1 or p == 2 (mod 3); but since p+2 > is also prime, 3 does not divide p+2, from which we may conclude that > p == 2 (mod 3) and p+2 == 1 (mod 3); then 2p+2 == 0 (mod 3), and 3 > divides the sum. Since 3 and 4 are coprime, and they both divide 2p+2, > 3á4=12 divides 2p+2. QED (quite elementary, actually). Very elegant! Must I now propose something new for Harris to be an ineffectual jackass about, or do you think the original challenge is still sufficient? 8^>) -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) Quis custodiet ipsos custodes? The Net! ==== Put up and demonstrate your claimed expertise, or shut up for being > the dysfunctional ing imbecile that you are. Uncle Al bets that > you don't have the balls or the brains to perform. Are you going to > run crying to your mama, Harris? >> Can you refer me to a proof (in the literature) that consective primes >> whose sum is >= 12 add up to a number divisible by 12. Is this a known >> theorem or is this an open problem? > >Well, if you accept this is literature, here is a proof: Let p be an odd prime such that p+2 is also a prime, and assume p /= >3. If p == 1 (mod 4) we have 2p == 2 (mod 4) and consequently p + p+2 = >2p+2 == 0 (mod 4), that is, 4 divides 2p+2. If p == 3 (mod 4) we also have 2p == 2 (mod 4), so also in this case >we have that 4 divides 2p+2. Now 3 does not divide p; thus p == 1 or p == 2 (mod 3); but since p+2 >is also prime, 3 does not divide p+2, from which we may conclude that >p == 2 (mod 3) and p+2 == 1 (mod 3); then 2p+2 == 0 (mod 3), and 3 >divides the sum. Since 3 and 4 are coprime, and they both divide 2p+2, >3á4=12 divides 2p+2. QED (quite elementary, actually). > Nice, very nice. Mati Meron | When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same ==== >> Put up and demonstrate your claimed expertise, or shut up for being >> the dysfunctional ing imbecile that you are. Uncle Al bets that >> you don't have the balls or the brains to perform. Are you going to >> run crying to your mama, Harris? Can you refer me to a proof (in the literature) that consective primes > whose sum is >= 12 add up to a number divisible by 12. Is this a known > theorem or is this an open problem? > Well, if you accept this is literature, here is a proof: Let p be an odd prime such that p+2 is also a prime, and assume p /= > 3. If p == 1 (mod 4) we have 2p == 2 (mod 4) and consequently p + p+2 = > 2p+2 == 0 (mod 4), that is, 4 divides 2p+2. If p == 3 (mod 4) we also have 2p == 2 (mod 4), so also in this case > we have that 4 divides 2p+2. Now 3 does not divide p; thus p == 1 or p == 2 (mod 3); but since p+2 > is also prime, 3 does not divide p+2, from which we may conclude that > p == 2 (mod 3) and p+2 == 1 (mod 3); then 2p+2 == 0 (mod 3), and 3 > divides the sum. Since 3 and 4 are coprime, and they both divide 2p+2, > 3á4=12 divides 2p+2. QED (quite elementary, actually). Let me suggest a simpler statement of the last part. p+1 must be divisible by 3, since neither p nor p+2 are. Therefore: 2(p+1) = 2p+2 must be divisible by 3. I was working on a similar statement to show that 2p+2 must be divisible by 4, and decided to check what had already been posted. Good work. ==== > Put up and demonstrate your claimed expertise, or shut up for being >> the dysfunctional ing imbecile that you are. Uncle Al bets that >> you don't have the balls or the brains to perform. Are you going to >> run crying to your mama, Harris? Can you refer me to a proof (in the literature) that consective primes > whose sum is >= 12 add up to a number divisible by 12. Is this a known > theorem or is this an open problem? > Well, if you accept this is literature, here is a proof: Let p be an odd prime such that p+2 is also a prime, and assume p /= > 3. If p == 1 (mod 4) we have 2p == 2 (mod 4) and consequently p + p+2 = > 2p+2 == 0 (mod 4), that is, 4 divides 2p+2. If p == 3 (mod 4) we also have 2p == 2 (mod 4), so also in this case > we have that 4 divides 2p+2. Now 3 does not divide p; thus p == 1 or p == 2 (mod 3); but since p+2 > is also prime, 3 does not divide p+2, from which we may conclude that > p == 2 (mod 3) and p+2 == 1 (mod 3); then 2p+2 == 0 (mod 3), and 3 > divides the sum. Since 3 and 4 are coprime, and they both divide 2p+2, > 3á4=12 divides 2p+2. QED (quite elementary, actually). Very elegant! Must I now propose something new for Harris to be an > ineffectual jackass about, or do you think the original challenge is > still sufficient? 8^>) Does he understand the notation p == 2 (mod3)? ==== > Every prime except 2 and 3 is of the form 6k-1 or 6k+1. Of course. I should remember this trick for puzzles for the kids (yesterday they understood my explanation of the proof of why there can be no largest prime number). This is obvious once I read it, but not something I previously knew (or remembered). The resulting proof is then obvious. > If p and q are > primes, q = p+2, and p is not equal to 3, then p is of the form 6k-1 and > q of the form 6k+1, so p+q = 12k. ==== > Can you refer me to a proof (in the literature) that consective primes > whose sum is >= 12 add up to a number divisible by 12. Is this a known > theorem or is this an open problem? If p>3 is prime, then p is congruent either to 1 or to -1 modulo 6. Likewise p+2 is congruent to either 1 or -1 modulo 6; if p=1 (mod 6) we have p+2 = 3 (mod 6). So, p = 6k-1, p+2 = 6k+1, and p+p+2 = 12k. <3F0C968B.5A575899@hate.spam.net> ==== >> >> > Put up and demonstrate your claimed expertise, or shut up for being > the dysfunctional ing imbecile that you are. Uncle Al bets that > you don't have the balls or the brains to perform. Are you going to > run crying to your mama, Harris? >> Can you refer me to a proof (in the literature) that consective primes >> whose sum is >= 12 add up to a number divisible by 12. Is this a known >> theorem or is this an open problem? >> >> Well, if you accept this is literature, here is a proof: >> >> Let p be an odd prime such that p+2 is also a prime, and assume p /= >> 3. >> >> If p == 1 (mod 4) we have 2p == 2 (mod 4) and consequently p + p+2 = >> 2p+2 == 0 (mod 4), that is, 4 divides 2p+2. >> >> If p == 3 (mod 4) we also have 2p == 2 (mod 4), so also in this case >> we have that 4 divides 2p+2. >> >> Now 3 does not divide p; thus p == 1 or p == 2 (mod 3); but since p+2 >> is also prime, 3 does not divide p+2, from which we may conclude that >> p == 2 (mod 3) and p+2 == 1 (mod 3); then 2p+2 == 0 (mod 3), and 3 >> divides the sum. Since 3 and 4 are coprime, and they both divide 2p+2, >> 3á4=12 divides 2p+2. QED (quite elementary, actually). Very elegant! Must I now propose something new for Harris to be an > ineffectual jackass about, or do you think the original challenge is > still sufficient? 8^>) > Well, assuming he can interpret _standard_ mathematical arguments in _standard_ terminology and using the usual meaning of words like divides, conclude, sum etc., you should find something else for him to do. I leave it for you to decide... /Rasmus -- http://home.imf.au.dk/burner/ <3f0c3c90$1@cpns1.saic.com> ==== Let me suggest a simpler statement of the last part. p+1 must be divisible > by 3, since neither p nor p+2 are. Therefore: 2(p+1) = 2p+2 must be > divisible by 3. I was working on a similar statement to show that 2p+2 must be divisible by > 4, and decided to check what had already been posted. Good work. > Well, you're almost already there. Being divisible by 4 is the same as being divisible by 2 twice. But 2p+2 is even, and so is (2p+2)/2 = p+1, since p is odd. So 4 divides 2p+2. Good work to you too; and thanks for the simplification. /Rasmus -- ==== >And don't forget that I've provided access to my work at one location >where you can go to see the mathematics that underpins so many of >these discussions: You should send your texts to your local FBI. They like to hear from scientists like you. --- I spewed bodily fluids. - Shydavid http://www.skeptictank.org/ http://www.RonTheNut.ORG/ -- You love drugs! You love drugs, don't you?! You better not say anything about my mother! Don't you DARE say anything about my mother! -- Scientology's International President (Audio files of this nutter at http://www.linkline.com/personal/frice ==== > I think that is speled undermines! > I think that is spelled spelled. Gib ==== > > > I think that is speled undermines! > > > I think that is spelled spelled. > > Gib > ==== > > Can you refer me to a proof (in the literature) > that consecutive primes > 3 have sum divisible by 12. > Is this a known theorem or is this an open problem? Twin primes p, p+2 have sum divisible by 12 if p > 3. It's well-known and easy. Let x|y denote x divides y. METHOD 1: It's obvious every prime p > 3 has form 6n+-1, so twin primes > 3 have form 6n-1, 6n+1 with sum 12n. METHOD 2: Suppose p, p+2 are both primes > 3. Then 4|2(p+1) since p odd => p+1 even and 3|2(p+1) since not 3|p, not 3|p+2 => 3|p+1 Thus 12|2(p+1) = p + p+2 i.e. 12 divides the sum of two twin primes > 3. You said consecutive primes but surely you meant twin primes since it's obviously false for consecutives, e.g. not 12|7+11. -Bill Dubuque ==== | Can you refer me to a proof (in the literature) that consective primes | whose sum is >= 12 add up to a number divisible by 12. Is this a known | theorem or is this an open problem? Twin primes is a better term than consecutive primes. 13 and 17 are consecutive in the sequence of primes, but of course this is not what we're talking about. | Let p be an odd prime such that p+2 is also a prime, and assume p /= 3. | | If p == 1 (mod 4) we have 2p == 2 (mod 4) and consequently p + p+2 = | 2p+2 == 0 (mod 4), that is, 4 divides 2p+2. | | If p == 3 (mod 4) we also have 2p == 2 (mod 4), so also in this case | we have that 4 divides 2p+2. | | Now 3 does not divide p; thus p == 1 or p == 2 (mod 3); but since p+2 | is also prime, 3 does not divide p+2, from which we may conclude that | p == 2 (mod 3) and p+2 == 1 (mod 3); then 2p+2 == 0 (mod 3), and 3 | divides the sum. Since 3 and 4 are coprime, and they both divide 2p+2, | 3á4=12 divides 2p+2. QED (quite elementary, actually). I think it's a little better if you don't divide into the cases where p is of the form 4n+1 and of the form 4n+3. Because p is of the form 2n+1, p+(p+2) is 4n+4 which is divisible by 4. A slightly different approach is to consider the remainder left by p when you divide it by 6 (or equivalently the congruence class of p mod 6). If p is of the form 6n, 6n+2, or 6n+4 it's even, and 2 is the only even prime. If p is of the form 6n+3 it's a multiple of 3, and 3 is the only such prime. For p>3, p is always of the form 6n+1 or 6n+5. In order to be a twin prime, p has to be of the form 6n+5, and p+(p+2)=12n+12 is divisible by 12. An exercise is to see what one can say about prime triples, either three primes of the form p, p+2, and p+6, or of the form p, p+4, p+6. It's a famous conjecture that given a sequence a1=0,...,an of integers, there exist infinitely many p such that p+a1,p+a2,...,p+an are primes if and only if there doesn't exist a prime q such that the a1,...,an leave all q possible remainders on division by q. That's in turn just a special case of a more general conjecture on the thickness of the set of m such that A1(m),...,An(m) are simulataneously prime, where A1,...,An are polynomials in m. The upshot is that the kind of quite elementary reasoning Rasmus Villemoes just gave us is expected to be good enough to answer a whole related family of questions about primes, when the answer is that there are only finitely many examples. On the other hand, even to show that there are infinitely many examples of twin primes is already extremely hard and hasn't been done, so the possibility that all large enough twin primes p have p+(p+2) divisible by 120 can't be ruled out; it just seems rather implausible. Keith Ramsay ==== > > METHOD 2: Suppose p, p+2 are both primes > 3. > > Then 4|2(p+1) since p odd => p+1 even > > and 3|2(p+1) since not 3|p, not 3|p+2 => 3|p+1 > > Thus 12|2(p+1) = p + p+2 i.e. 12 divides the sum of two twin primes > 3. Alternatively 6|p(p+1)(p+2) via binomial coef (p+2:3) integral. So it must be 6 | p+1 since 6 coprime to p & p+2 (primes > 3). Finally then 12|2(p+1) = p + p+2. More simply: Among any n or more consecutive integers must occur a multiple of n. So among p, p+1, p+2 occurs a multiple of 2 and 3; it must be p+1 in both cases since p and p+2 are primes > 3. So 6|p+1 => 12|2(p+1) = p + p+2. -Bill Dubuque ==== >> >> METHOD 2: Suppose p, p+2 are both primes > 3. >> >> Then 4|2(p+1) since p odd => p+1 even >> >> and 3|2(p+1) since not 3|p, not 3|p+2 => 3|p+1 >> >> Thus 12|2(p+1) = p + p+2 >> i.e. 12 divides the sum of two twin primes > 3. Alternatively 6|p(p+1)(p+2) via binomial coef (p+2:3) integral. >So it must be 6 | p+1 since 6 coprime to p & p+2 (primes > 3). >Finally then 12|2(p+1) = p + p+2. More simply: Among any n or more consecutive integers >must occur a multiple of n. So among p, p+1, p+2 occurs >a multiple of 2 and 3; it must be p+1 in both cases since >p and p+2 are primes > 3. So 6|p+1 => 12|2(p+1) = p + p+2. > Lovely. Mati Meron | When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same ==== > > And don't forget that I've provided access to my work at one location > where you can go to see the mathematics that underpins so many of > these discussions: > > 1. The short proof of Fermat's Last Theorem where you see the power > of techniques that are also used in the paper Advanced Polynomial > Factorization. > > 2. THE prime counting function, or my prime counting function as I > differentiate it from those so-called prime counting functions. At my > website you can see the function, get a C++ program to run it, read > some of my thoughts on it, join the group and get a Java algorithmic > implementation, and most importantly, see the partial differential > equation for the J function, which is a prime suspect for the > connection between the prime distribution and the continuous functions > like li(x) and x/ln x. > > 3. Join the group and you can access the pdf file to read my paper > Advanced Polynomial Factorization, where a polynomial factorization > into non-polynomial factors proves an error in taught mathematics. > > I think that is speled undermines! I think he means underlies, not undermines! Also, I think you mean spelled, not speled! (...Starblade Riven Darksquall...) ==== > And don't forget that I've provided access to my work at one location > where you can go to see the mathematics that underpins so many of > these discussions: You have been thoroughly discredited, James Harris. Your attempt at a proof is a failure. It's time to take down your site as you promised. Or has any remaining ounce of integrity you once possessed long since departed? -- 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 think that is speled undermines! > I think that is spelled spelled. Gib I think its spiel myself. -- New definition of irony: 'Today's liberal Democrats are like the supporters of the Third Reich of the '30's and '40's - they absolutely trusted the government to make things right. ' -Comment made on the internet by an ardent GW Bush supporter. > ==== In sci.physics, Rasmus Villemoes : > > Put up and demonstrate your claimed expertise, or shut up for being > the dysfunctional ing imbecile that you are. Uncle Al bets that > you don't have the balls or the brains to perform. Are you going to > run crying to your mama, Harris? >> Can you refer me to a proof (in the literature) that consective primes >> whose sum is >= 12 add up to a number divisible by 12. Is this a known >> theorem or is this an open problem? Well, if you accept this is literature, here is a proof: > > Let p be an odd prime such that p+2 is also a prime, and assume p /= > 3. > > If p == 1 (mod 4) we have 2p == 2 (mod 4) and consequently p + p+2 = > 2p+2 == 0 (mod 4), that is, 4 divides 2p+2. > > If p == 3 (mod 4) we also have 2p == 2 (mod 4), so also in this case > we have that 4 divides 2p+2. > > Now 3 does not divide p; thus p == 1 or p == 2 (mod 3); but since p+2 > is also prime, 3 does not divide p+2, from which we may conclude that > p == 2 (mod 3) and p+2 == 1 (mod 3); then 2p+2 == 0 (mod 3), and 3 > divides the sum. Since 3 and 4 are coprime, and they both divide 2p+2, > 3á4=12 divides 2p+2. QED (quite elementary, actually). > > /Rasmus > Damn, you beat me to it. I need a bigger left margin.... But yeah, you must have noticed that the center number is always divisible by 6. ;-) -- #191, ewill3@earthlink.net It's still legal to go .sigless. ==== In sci.physics, Uncle Al <3F0C968B.5A575899@hate.spam.net>: [proof snipped for brevity] > Very elegant! Must I now propose something new for Harris to be an > ineffectual jackass about, or do you think the original challenge is > still sufficient? 8^>) > Well, you could ask him to prove Goldbach's Conjecture, if you're into serious sadism. :-) -- #191, ewill3@earthlink.net It's still legal to go .sigless. ==== Trivially false. 23 + 29 = 52 23,29 are consecutive primes. 12 does not divide 52 ==== > > | Can you refer me to a proof (in the literature) that consective primes > | whose sum is >= 12 add up to a number divisible by 12. Is this a known > | theorem or is this an open problem? > > Twin primes is a better term than consecutive primes. 13 and 17 are > consecutive in the sequence of primes, but of course this is not what > we're talking about. Twin primes is the proper term, and so is searchable. I gave idiot Harris the benefit of the doubt that he could use Google and trivially discover he was being made a fool, again. In retrospect this was wholly unjustified and silly. Harris is an irremediable cripple. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) Quis custodiet ipsos custodes? The Net! ==== > Twin primes is the proper term, and so is searchable. I gave idiot > Harris the benefit of the doubt that he could use Google and trivially > discover he was being made a fool, again. In retrospect this was > wholly unjustified and silly. Harris is an irremediable cripple. Do you have a reference to a proof that twin primes whose sum is greater than 12 have a sum which is divisible by 12? Bob Kolker ==== >Trivially false. 23 + 29 = 52 23,29 are consecutive primes. 12 does not >divide 52 _What_ is trivially false, exactly? Go back to the top: > If one looks at pairs of consecutive prime numbers separated by only >one non-prime number - 41,43; 821,823; 8087,8089 etc. - one sees that >the sum of such two primes is often divisible by 12: It's trivially false that 23, 29 are consecutive primes separated by only one non-prime number: 23 < 24 < 25 < 29. ************************ ==== > > >> Twin primes is the proper term, and so is searchable. I gave idiot >> Harris the benefit of the doubt that he could use Google and trivially >> discover he was being made a fool, again. In retrospect this was >> wholly unjustified and silly. Harris is an irremediable cripple. > > Do you have a reference to a proof that twin primes whose sum is greater > than 12 have a sum which is divisible by 12? > Why should anyone wish to publish such a triviality? -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html The League of Gentlemen ==== > Twin primes is the proper term, and so is searchable. I gave idiot > Harris the benefit of the doubt that he could use Google and trivially > discover he was being made a fool, again. In retrospect this was > wholly unjustified and silly. Harris is an irremediable cripple. > > Do you have a reference to a proof that twin primes whose sum is greater > than 12 have a sum which is divisible by 12? There already is a short one in this thread. Here's a summary of my scribbling, a slightly different tack, that convinced me why this is true. Let p and p+2 be two primes both >3. First of all, p + (p+2) = 2(p+1). Since p is odd, p+1 is even and 2(p+1) is a multiple of 4. What is p mod 3? It can't be 0 (p is prime, not divisible by 3). It can't be 1 (because then p+2 would be equal to 0 mod 3). So it must be 2. Thus we have p = 2 mod 3 p+2 = 1 mod 3 and p+(p+2) = (2+1) mod 3 = 0 mod 3, So p+(p+2) is divisible by both 3 and 4. - Randy We also have that p+(p+2) = 2(p+1). Since p ==== >> Twin primes is the proper term, and so is searchable. I gave idiot >> Harris the benefit of the doubt that he could use Google and trivially >> discover he was being made a fool, again. In retrospect this was >> wholly unjustified and silly. Harris is an irremediable cripple. Do you have a reference to a proof that twin primes whose sum is greater >than 12 have a sum which is divisible by 12? This is trivial - also proofs have been posted right here in this thread. Let's see if even I can figure it out. Say p and p+2 are both prime, and p > 3. Then p mod 12 must be one of 1, 5, 7, 11, as must be p + 2 mod 12; any other case would imply that p (or p+2) was not prime. Since p + 2 is two more than p it follows that p mod 12 must be 5 or 11, and in either case p + p + 2 is divisible by 12 (5 + 7 = 12, 11 + 1 = 12). I didn't read the posted proofs, but I noticed people saying they were very nice. So I imagine they are more elegant than the above... >Bob Kolker > ************************ ==== > Proof of FLT Ah, how disappointing, I figured that for Free Lunch Theorem, and guessed you'd found a way to be honored as a mathematician while acting with dishonor. No such luck, you've just added poor abused Fermet to your attempts to steal what you can't earn. xanthian. -- ==== In sci.physics, Robert J. Kolker : > > >> Twin primes is the proper term, and so is searchable. I gave idiot >> Harris the benefit of the doubt that he could use Google and trivially >> discover he was being made a fool, again. In retrospect this was >> wholly unjustified and silly. Harris is an irremediable cripple. > > Do you have a reference to a proof that twin primes whose sum is greater > than 12 have a sum which is divisible by 12? You need a reference? Try this one. If a prime p and its pair p+2 are around a number m = p+1, what is m divisible by? It turns out that m has to be divisible by 6. This is mostly because p and p+2 are both odd and neither are divisible by 3; the only numbers which satisfy both conditions are 6n - 1 and 6n + 1, for some positive n (unless one of the primes is in fact 3, of course). The sum of those numbers is 12n. QED > Bob Kolker -- #191, ewill3@earthlink.net It's still legal to go .sigless. ==== x,y and z are nonzero and coprime integers, p is an odd prime, and v is a variable integer. That's just x2+y2+vz2 = x2+y2+vz2, which might seem strange, but the point here is to allow me to introduce v, which I can set to any value I choose because it's based as it is on this beginning. Whee, what fun! You can set v to anything you want. So your proof starts with v = v from which, since v = v is already an axiom, you can deduce NOTHING! Yours, Doug Goncz, Replikon Research, Seven Corners, VA Fair use and Usenet distribution without restriction or fee Civil and criminal penalties for circumvention of any embedded encryption ==== | Let's see if even I can figure it out. Say p and p+2 are both prime, | and p > 3. Then p mod 12 must be one of [...] | I didn't read the posted proofs, but I noticed people saying they | were very nice. So I imagine they are more elegant than the above... The only real way to go is by a congruence argument, so in a sense they're all minor variations of the same thing. It's very natural to consider p mod 12, but I would say that I prefer considering p mod 6 Just a little bit. p and p+2 are of the form 6n-1 and 6n+1 for the same n, so their sum is 12n. The one approach shows that p and p+2 lie in a pair of congruence classes having the property that any two numbers p and q lying in them add up to a multiple of 12. But if we know q-p, in order to determine the congruence class of p+q mod 2n, it's enough to know the congruence classes of p and q only mod n. I have a sense that I've often seen little forks in the road in mathematical proofs which are analogous to this. Going from A to C, one either passes through B, or passes through a slightly weaker B' which however is still sufficient for C, given A. It seems like often I prefer the former argument, which in a sense disposes of the original information more quickly, but not always of course. Keith Ramsay ==== if the question seems really easy to everyone else. I wasn't sure if I had done it right. I know that between any two rational numbers there is an irrational number, and this makes sense because there are many more irrational numbers than rational ones. However, I am having problems understanding why there is always a rational number between any 2 irrational numbers (it seems like it would not work since there are more irrational numbers). ==== > I know that between any two rational numbers there is an irrational number, > and > this makes sense because there are many more irrational numbers than rational > ones. However, I am having problems understanding why there is always a > rational number between any 2 irrational numbers (it seems like it would not > work since there are more irrational numbers). > The statements should be in the form of stateintg that there is at least one rational/irrational betwen any two reals. The complete truth is that between any two distinct reals (rational or not) there are a countable infinity of rationals and an uncountable infinity of irrationals. ==== > I know that between any two rational numbers there is an irrational number, and > this makes sense because there are many more irrational numbers than rational > ones. However, I am having problems understanding why there is always a > rational number between any 2 irrational numbers (it seems like it would not > work since there are more irrational numbers). > Making sense is not good enough; for example, it makes good sense (to me) that Euler's constant should be irrational (after all, most real numbers are irrational), but so far no one has figured out whether it is irrational or not. What is important here is there are enough integer numbers to get bigger than any prescribed real number. So: suppose you give me two different real numbers (you would be interested in irrational ones); call the smaller one x and the other y. Easy case: If the interval (x,y) contains an integer number, we are done. Harder case: The interval (x,y) is too short (and too inconveniently located) to contain an integer. But among the intervals (2*x, 2*y), (3*x, 3*y), ..., (n*x, n*y), ... there will be one that is longer than 1, so it will contain an integer number; call it m (if there are more, choose the smallest of them). Then for suitable n, m: n*x < m < n*y and divide by n to squeeze m/n between x and y. (Good night, Mr. Archimedes, wherever you are...) ==== >I know that between any two rational numbers there is an irrational number, and >this makes sense because there are many more irrational numbers than rational >ones. However, I am having problems understanding why there is always a >rational number between any 2 irrational numbers (it seems like it would not >work since there are more irrational numbers). > It's because between any two distinct numbers there is a finite distance, and you can always find both a rational number and an irrational number on any finite interval. There are uncountably many irrationals and countably many rationals on EVERY finite interval. Here's one easy construction to find such a number: Consider two distinct irrational numbers, a and b. Let b be the larger of the two. Let N be the first position in which they differ, and b_N be the digit that b has in that position. Let c be a number which consists of the first N digits of b and then terminates (continues with all 0s). This number is strictly less than b, strictly greater than a, and is rational. - Randy ==== > (Good night, Mr. Archimedes, wherever you are...) I think it's time some university gave Archimedes an honorary doctorate. -- ==== obvious.. ==== > Is my solution to this question correct? Almost! The algebra is correct, the English needs some help. > ============================ > QUESTION > Consider the following recurrence relation: a(n) = a sub (n-1) + n, > with a0 = 1 > Prove by induction that a(n) = 1 + (1/2)(n)(n + 1) is a closed formed > expression for the above recurrence relation for all nonnegative > integers n. > ============================ > MY SOLUTION: > - Basic step: Show the statement is true when there is only one term. > Left: A0 = 1 > Right: 1 + (1/2)(0)(0 + 1) = 1 + 0 = 1 > 1 = 1 > A0 = 1 + (1/2)(0)(0 + 1) > - Inductive step: > Assume the statement is true. Oops! Usually expressed the strong way: Assume the statement is true for all numbers of terms up to n. Also sometimes expressed the weak way: Assume the statement is true for some number of terms n. > Show it is true when there are (n + 1) terms. > An+1 > = An + (n + 1) > = 1 + (1/2)(n)(n + 1) + (n + 1) > = 1 + (1/2)(n + 1)(n + 2) > = 1 + (1/2)(n + 1)[(n + 1) + 1] > Since it is true for (n + 1) terms, it is also true for n terms. Usually expressed: Since we have shown that it is true for (n + 1) terms assuming it is true for n terms, and since we have shown that the induction has a valid starting case n = 1, then it is true for any positive integer n. xanthian, assuming I haven't said something stupid, of course. -- ==== Of course there are several ways to *construct* the exponential function, but is there also a pure existence proof? I am very interested in such a theorem if it exists. Peace, EJ ==== >Of course there are several ways to *construct* the exponential function, but is >there also a pure existence proof? I am very interested in such a theorem if it >exists. Peace, >EJ > Off the top of my head, I would say that one of the existance proofs for ODEs guaarantees that y-y'=0 has a solution, and if you add the right intial condition, you get e^x. Larry (this space unintentially left blank ..... ==== Can someone give me a hint (not solution) on the following problem. It is number 2.29 in Rotman's Introduction to Homological Algebra. Given: g A------>B | | f| Prove the following diagram is a pushout: | V C g A-------->B | | | | f| f'| | | V g' V C-------->D Where D=(C /osum B)/W, W={(fa,-ga):a /in A}, f':b-->(0,b)+W and g':c-->(c,0)+W. What do I need to prove to prove the diagram is a pushout and what is the significance of the set W? ==== >Can someone give me a hint (not solution) on the following >problem. It is number 2.29 in Rotman's Introduction to >Homological Algebra. Given: > g > A------>B > | > | >f| Prove the following diagram is a pushout: > | > V > C g > A-------->B > | | > | | >f| f'| > | | > V g' V > C-------->D Where D=(C /osum B)/W, W={(fa,-ga):a /in A}, f':b-->(0,b)+W and >g':c-->(c,0)+W. >What do I need to prove to prove the diagram is a pushout The diagram is a pushout if it satisfies the following two conditions: 1. COMMUTATIVITY: f'g = g'f (I am applying functions on the left, so they should be read right-to-left; f'g means g first, then f'). 2. UNIVERSAL PROPERTY: Given any K and maps b:B->K, c:C->K such that bg=cf, there exists a unique map d:D->K such that b=df' and c=dg'. > and >what is the significance of the set W? You can think of a pushout as a co-equalizer; you are finding the largest object on which you can make f and g 'equal'. W is a measure of how far they are on being 'equal' (not exactly, since we are dealing with the dual notion, but maybe that makes some sense to you?). In order for f'g(a) to be equal to g'f(a) for all a, you need to make sure that (f(a),0) is the same as (0,g(a)); for them to be the same, you need to mod out by (f(a),-g(a)); so W is the closure of all those identities in Cosum B; moding out by W is the same as imposing those identities on Cosum B. ====================================================================== 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 ==== [snip] > The diagram is a pushout if it satisfies the following two conditions: > > 1. COMMUTATIVITY: f'g = g'f (I am applying functions on the left, so > they should be read right-to-left; f'g means g first, then f'). > > 2. UNIVERSAL PROPERTY: Given any K and maps b:B->K, c:C->K such that > bg=cf, there exists a unique map d:D->K such that b=df' and c=dg'. > [snip] Ok, I got the commutativity. That part was really obvious. The universal property is the part giving me the most trouble. I am assuming that one must use a previously proved universal property to obtain the one in question. I am not seeing how to construct or prove the existence of such a map d:D->K, for any K. I don't mind if you spoil the problem now, unless you think you can give me a suitable hint. Chris ==== >[snip] >> The diagram is a pushout if it satisfies the following two conditions: >> >> 1. COMMUTATIVITY: f'g = g'f (I am applying functions on the left, so >> they should be read right-to-left; f'g means g first, then f'). >> >> 2. UNIVERSAL PROPERTY: Given any K and maps b:B->K, c:C->K such that >> bg=cf, there exists a unique map d:D->K such that b=df' and c=dg'. >> >[snip] Ok, I got the commutativity. That part was really obvious. The >universal property is the part giving me the most trouble. I am >assuming that one must use a previously proved universal property to >obtain the one in question. I am not seeing how to construct or prove >the existence of such a map d:D->K, for any K. I don't mind if you >spoil the problem now, unless you think you can give me a suitable >hint. I don't follow what you mean. Assume you have an object K, and maps b:B->K and c:C->K such that bg = cf. f A ---> C | | g | | g' | | V V B ----> D f' We know that D is defined as (Boplus C)/W; so to define a map from D to K, we can define a map from Boplus C to K whose kernel contains W, and factor it through the quotient. f' and g' are the obvious inclusions, and W is the subgroup generated by all pairs (g(a),-f(a)) for a in A. So let's consider what the d HAS to be. First, we want b=df' and c=dg'. So given any x in B, we know what b(x) is (we are GIVEN the maps b and c); and we know that f'(x) = (x,0) in Boplus C. So we map (x,0) to b(x). Likewise, we will need to map (0,y) to c(y) for all y in C. That means that we need to map an element (x,y) in Boplus C to b(x)+c(y). That defines a map, call it e: B oplus C -> K. Now we need to verify that e factors through the quotient D, that is, that W is contained in the kernel of e. So let's take an element of W, which is of the form (g(a),-f(a)) for a in A. According to the definition of e, we map e(g(a),-f(a)) = b(g(a))+c(-f(a)) = b(g(a)) - c(f(a)) = bg(a) - cf(a). But we are assuming futher that b and c are such that bg=cf; so bg(a)-cf(a)=0 for all a in A. Therefore, e takes W to 0, and so W is contained in the kernel of e. Therefore, e factors through the quotient p:Boplus C -> (Boplus C)/W = D. So define d to be the unique map from (Boplus C)/W to K such that commutativity condition, b=df' and c=dg'. Moreover, since the definition of e was forced by the commutativity of the diagram, the choice of d is also forced, so that d is the only function that will fit in that diagram. Thus, d is unique. In general, when you have a universal construction, IF you have an ->explicit<- construction of the object, then the universal property is easy to verify, because you will have no choice about how to define the map in question. it should be obvious what the map has to be in an object. ====================================================================== 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 ==== ==== to this question, which has been driving me a bit nuts. Some quick background: as a role-player, I use a lot of dice. At times, the rules call for one to roll multiple dice (say, five six-sided dice, or 5d6), then to drop the lowest two and total the other three. The basic question is: is there a formula for determining the probability of rolling a certain result, given these conditions? Determining the probability of a particular outcome when just rolling multiple dice is relatively straightforward (there's a brief discussion here: http://mathforum.org/library/drmath/view/52207.html). I can find a pattern to the summation needed when dropping a single die from a set; but once I try to remove two dice from the set, the pattern disappears and I find myself lost again. (The numbers can be determined by brute force, of course, but that's neither practical nor interesting.) So, I guess the base question is: Is there a formula for calculating the probability of achieving a result R on n dice with d sides, dropping the k lowest dice? ==== Background... An exponent function fulfills an equation: f(A+B)=f(A)*f(B) For example: a^(A+B)=(a^A)*(a^B) A logarithmic function fulfills an equation f(A*B)=f(A)+f(B) For example: log(A*B)=log(A)+log(B) Question: What is the name of the following function that fulfills f(A)*f(B)=f(A)+f(B) or f(A)*f(B)=f(A*B) For example: ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B) (This kind of function indeed exists, if you (xy)-plot a hyperbola in a double logarithmic cartesian co-ordination (ln(x), ln(y) As You know the hyperbola is the product of asymptotes). Hopefully someone knows.... Tapio ==== >Background... >An exponent function fulfills an equation: >f(A+B)=f(A)*f(B) >For example: >a^(A+B)=(a^A)*(a^B) A logarithmic function fulfills an equation >f(A*B)=f(A)+f(B) >For example: log(A*B)=log(A)+log(B) Question: What is the name of the following function that fulfills >f(A)*f(B)=f(A)+f(B) or I'd call it either 0 or 2. >f(A)*f(B)=f(A*B) This might be called a multiplicative function, or a homomorphism of the group R{0} under multiplication. >For example: >ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B) ?????! Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 ==== > Background... > An exponent function fulfills an equation: > f(A+B)=f(A)*f(B) > For example: > a^(A+B)=(a^A)*(a^B) A logarithmic function fulfills an equation > f(A*B)=f(A)+f(B) > For example: log(A*B)=log(A)+log(B) Question: What is the name of the following function that fulfills > f(A)*f(B)=f(A)+f(B) or f(a)^2 = 2f(a) f(a)(f(a)-2) = 0 if some a with f(a) = 0, then for all b, f(b) = f(a) + f(b) = f(a)f(b) = 0 otherwise for all a, f(a) /= 0, hence f(a) = 2. > f(A)*f(B)=f(A*B) > Exponentation a^n b^n = (ab)^n ==== >Background... >An exponent function fulfills an equation: >f(A+B)=f(A)*f(B) >For example: >a^(A+B)=(a^A)*(a^B) A logarithmic function fulfills an equation >f(A*B)=f(A)+f(B) >For example: log(A*B)=log(A)+log(B) Question: What is the name of the following function that fulfills >f(A)*f(B)=f(A)+f(B) or I'd call it either 0 or 2. f(A)*f(B)=f(A*B) This might be called a multiplicative function, or a homomorphism of > the group R{0} under multiplication. For example: >ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B) ?????! Ah, how to get those equations? hyperbola in a double logarithmic cartesian co-ordination (ln(x), ln(y) As You know the hyperbola is the product of asymptotes). I start with two asymptotes of a hyperbola that goes through origo in double logarithmic cartesian co-ordination: ln(g) = kln(a)-t and ln(g) = -qln(a)-s where st>0 and -q and k are slopes. The equation of the hyperbola is the product of the asymptotes, like this (-qln(a)-ln(g)-s)(kln(a)-ln(g)-t)=st => (ln((a^(-q))/g)-s)(ln((a^(k))/g)-t)=st lhs is expanded by multiplication => (ln((a^(-q))/g))(ln((a^(k))/g)) -t(ln((a^(-q))/g))-s(ln((a^(k))/g))+st=st After elimination of st and after rearrangement => (ln((a^(-q))/g))(ln((a^(k))/g))=t(ln((a^(-q))/g))+s(ln((a^(k))/g)) Dividing both sides by st and collecting and grouping s and t on lhs => ((ln((a^(-q))/g))/s)((ln((a^(k))/g))/t) = Equation 1 ((ln((a^(-q))/g))/s)+((ln((a^(k))/g))/t) the coefficients 1/s and 1/t before ln() can be used as exponents like done earlier with slopes (above): ((a^(-q))/g)^(1/s) = A and ((a^(k))/g)^(1/t) =B and it follows: ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B) or 1=(1/ln(A)) +1/(ln(B)) Done, assuming there is no error. Clearly A=xB, but substitution does not help to reduce the equation. Neither e^lhs=e^rhs. I confess I'm blind to see simple solution for (a/g)=f(q,k,s,t). Of course, I can solve ln(g), but that's a standard solution, which has no common interest. Any help to develop Equation 1 further? Tapio > Robert Israel israel@math.ubc.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia > Vancouver, BC, Canada V6T 1Z2 ==== Background... > An exponent function fulfills an equation: > f(A+B)=f(A)*f(B) > For example: > a^(A+B)=(a^A)*(a^B) A logarithmic function fulfills an equation > f(A*B)=f(A)+f(B) > For example: log(A*B)=log(A)+log(B) Question: What is the name of the following function that fulfills > f(A)*f(B)=f(A)+f(B) or f(a)^2 = 2f(a) > f(a)(f(a)-2) = 0 > if some a with f(a) = 0, > then for all b, f(b) = f(a) + f(b) = f(a)f(b) = 0 > otherwise for all a, f(a) /= 0, hence f(a) = 2. Yes, You are right. My Q was badly formulated - sorry! But, starting from the product of two asymptotes ( a hyperbola) in the double logarithmic coordination system, then f(A) is not constant 2. (2*2=2+2) Please - refer my other post today. The hyperbola goes through the origo. It is true for some a , f(a)=0 , namely as a=1 and g=1 (refer my post today) when the point of the hyperbola is the origo. > f(A)*f(B)=f(A*B) Exponentation > a^n b^n = (ab)^n You are right again, but I'm too blind to apply Your result in the asymptote problem. Do You see more clear? Can You help me? Tapio ==== > Background... > An exponent function fulfills an equation: > f(A+B)=f(A)*f(B) > For example: > a^(A+B)=(a^A)*(a^B) > > A logarithmic function fulfills an equation > f(A*B)=f(A)+f(B) > For example: log(A*B)=log(A)+log(B) > > Question: What is the name of the following function that fulfills > f(A)*f(B)=f(A)+f(B) or > f(A)*f(B)=f(A*B) > > For example: > ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B) Are you claiming that this is true when ln represents the natural log, for arbitrary A and B? For instance, are you claiming that ln(2)*ln(3) = ln(2)+ln(3) and that ln(2)*ln(3) = ln(2*3)??? - Randy ==== > Background... > An exponent function fulfills an equation: > f(A+B)=f(A)*f(B) > For example: > a^(A+B)=(a^A)*(a^B) A logarithmic function fulfills an equation > f(A*B)=f(A)+f(B) > For example: log(A*B)=log(A)+log(B) Question: What is the name of the following function that fulfills > f(A)*f(B)=f(A)+f(B) or > f(A)*f(B)=f(A*B) For example: > ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B) Are you claiming that this is true when ln represents > the natural log, for arbitrary A and B? Dear Randy, The background of my Q was presented today more precisely in my reply to prof. Robert Israel. (See the thread). The equation was derived considering a hyperbola (with two asymptotes) in the double logarithmic cartesian co-ordination system. Here is a link into the similar problem. http://www.ica1.uni-stuttgart.de/Recent_publications/Papers/frank/PRE16115.p df Look at the plots and recognize the hyperbola! Maybe I have done a failure, maybe I'm blind, but I'm still tackling with the final solution. If You can give any help, it's welcome! Tapio For instance, are you claiming that ln(2)*ln(3) = ln(2)+ln(3) and that ln(2)*ln(3) = ln(2*3)??? - Randy ==== >>ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B) >> ?????! >Any help to develop Equation 1 further? The measurable functions f:(0,infinity) -> R such that f(A)*f(B) = f(A*B) are f(x) = x^c for real constants c. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 ==== >The measurable functions f:(0,infinity) -> R such that f(A)*f(B) = f(A*B) >are f(x) = x^c for real constants c. And for f:R -> R, it would be f(0) = 0, f(x) = |x|^c otherwise; or f(0) = 0, f(x) = (sgn x) |x|^c otherwise; or f(x) = 1 for all x. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 ==== > For example: >> ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B) >> Are you claiming that this is true when ln represents >> the natural log, for arbitrary A and B? Dear Randy, The background of my Q was presented today more precisely in my reply to >prof. Robert Israel. (See the thread). I posted my question after skimming through that reply. > The equation was derived considering >a hyperbola (with two asymptotes) in the double logarithmic cartesian >co-ordination system. I'm not asking about the derivation. I'm asking about what it is you claim to have proved. Are you saying that the above equations hold for the natural logarithm, for arbitrary A and B? - Randy ==== >> For example: >> ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B) >> Are you claiming that this is true when ln represents >> the natural log, for arbitrary A and B? Dear Randy, The background of my Q was presented today more precisely in my reply to >prof. Robert Israel. (See the thread). I posted my question after skimming through that reply. The equation was derived considering >a hyperbola (with two asymptotes) in the double logarithmic cartesian >co-ordination system. I'm not asking about the derivation. I'm asking about what it is you > claim to have proved. Are you saying that the above equations hold for > the natural logarithm, for arbitrary A and B? Considering the terms of the derivation from hyperbola and assuming there is no errors, then the equation should hold for A and B, but you have to recognize that A is a function of B (or vice versa) as derived in my earlier message: ((a^(-q))/g)^(1/s) = A and ((a^(k))/g)^(1/t) =B At least, it was fun to notice after derivation such a strange and unexpectable equation. At the first glance, it should not be valid at all. Therefore, I still consider an error. There are few reasons: 1) a and g are variables, but plot ln(a) against ln(g) makes hyperbola and therefore f(a)=b or vice versa. 2) slopes (-q and k) and constants (s and t) can be - in principle - any reals, which gives too many possibilities to choose them for arbitrary A and B, which results in impossible answers. As we can choose slopes and constants quite freely, they nail ln(a) and ln(g). I assume or guess, but I do not know, that iff the equation could be true, then there should be some more simple relation or function between slopes and constants and a and g. As said earlier, I still consider an error - too. Tapio > - Randy > ==== > For example: >> ln(A)*ln(B)=ln(A)+ln(B) or ln(A)*ln(B)=ln(A*B) >> Are you claiming that this is true when ln represents >> the natural log, for arbitrary A and B? Dear Randy, The background of my Q was presented today more precisely in my reply to >prof. Robert Israel. (See the thread). I posted my question after skimming through that reply. The equation was derived considering >a hyperbola (with two asymptotes) in the double logarithmic cartesian >co-ordination system. I'm not asking about the derivation. I'm asking about what it is you > claim to have proved. Are you saying that the above equations hold for > the natural logarithm, for arbitrary A and B? Some additional ideas to consider: The double logarithmic plotting that results in conic sections has general interest. Why? Physical phenomena are based on differential equations that have solutions of harmonic oscillations, i.e wave equations. For example: an overdamped harmonic oscillator has phase-space plot that is hyperbola. On the other hand, the real exponents can be sometimes considered as fractal dimensions, which can indicate the packing density etc. As may physical phenomena are exponential, it does not mean that a line in log-plot is the only solution. It's even expectable that also conic sections appear in the double logarithmic plotting of data. Tapio ==== I'm trying to find the name for the following property of a matrix norm. We have matrix norm |.| over the reals. Norm |.| has the above property, if for every pair of matrices A,B with nonnegative coefficients, |A+B| >= |A|. Also, does anyone know of matrix norms that don't have this property? Karl Hallowell ==== >I'm trying to find the name for the following property of a matrix >norm. I don't know of a name for it. >We have matrix norm |.| over the reals. Norm |.| has the above >property, if for every pair of matrices A,B with nonnegative >coefficients, |A+B| >= |A|. Also, does anyone know of matrix norms >that don't have this property? If |.|_1 is one matrix norm and U is any invertible matrix, you can get another matrix norm by |A|_2 = |U A U^(-1)|_1. Take |.|_1 to be any matrix norm satisfying your property, [ 1 1 ] [ 1 0 ] [ 0 b ] [ 1 1-b ] U = [ 0 -1 ], A = [ 0 0 ], B = [ 0 0 ], U (A+B) U^(-1) = [ 0 0 ]. Thus if 0 < b < 1, |A+B|_2 <= |A|_2 (and in most cases the inequality will be strict). Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 ==== >I'm trying to find the name for the following property of a matrix >norm. > > I don't know of a name for it. Too bad. Guess I'll look around some more. >We have matrix norm |.| over the reals. Norm |.| has the above >property, if for every pair of matrices A,B with nonnegative >coefficients, |A+B| >= |A|. Also, does anyone know of matrix norms >that don't have this property? > > If |.|_1 is one matrix norm and U is any invertible matrix, you can > get another matrix norm by |A|_2 = |U A U^(-1)|_1. Take |.|_1 to be > any matrix norm satisfying your property, > [ 1 1 ] [ 1 0 ] [ 0 b ] [ 1 1-b ] > U = [ 0 -1 ], A = [ 0 0 ], B = [ 0 0 ], U (A+B) U^(-1) = [ 0 0 ]. > Thus if 0 < b < 1, |A+B|_2 <= |A|_2 (and in most cases the inequality > will be strict). looked at these norms is that I was trying to find convexity results for matrices with nonnegative coefficients that were convex up functions of some parameter. Eg, let matrix A(x) with parameter x belonging to some real interval have nonnegative coefficients that are all convex up functions in x. Then |A(x)| is a convex up function of x, if |.| satisfies the above property. The most interesting case is the operator two norm over square matrices which is the absolute value of the largest eigenvalue of the matrix. In the case where the matrix has nonnegative coefficients then by one of the variants of the Perron-Frobenious Theorem we know that there is a largest eigenvalue which is equal to the operator two norm. Hence, for A(x) defined as above, the largest nonnegative eigenvalue is a convex up function of x. The trace of A(x) is also a convex up function of x. Karl Hallowell ==== I place a quarter (coin) on the table. Exactly how many quarters can I put around this centered quarter? ==== > > I place a quarter (coin) on the table. Exactly how many quarters can I put > around this centered quarter? Six. Think honeycomb. -- Ioannis http://users.forthnet.gr/ath/jgal/ ___________________________________________ Eventually, _everything_ is understandable. ==== > I place a quarter (coin) on the table. Exactly how many quarters can I put > around this centered quarter? Define put. ==== >I place a quarter (coin) on the table. Exactly how many quarters can I put >around this centered quarter? That depends, of course, on the size of the table. :-) -- Stan Brown, Oak Road Systems, Cortland County, New York, USA http://OakRoadSystems.com/ You find yourself amusing, Blackadder. I try not to fly in the face of public opinion. ==== >>I place a quarter (coin) on the table. Exactly how many quarters can I put >>around this centered quarter? > That depends, of course, on the size of the table. :-) It also depends on the definition of around. If we consider it in a three-dimensional sense and place noÊlimits on distance, then every quarter on Earth is around it. And since quarter isn't defined, we could take it to mean one-fourth of anything, which raises the total a bit higher... :-) -- Wayne Brown | 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 ==== hi all, I am actually trying to understand this mathematical notion that is so weird to me (I am far from being a god at maths...). could someone drop the light onto the following for me ? We will compute a rotation about the unit vector, u by an angle . The quaternion that computes this rotation is q = (s,v) s = cos(teta/2) v = u * sin(teta/2) We will represent a point p in space by the quaternion P=(0,p) We compute the desired rotation of that point by this formula: P = (0,p) Protated = qPq^-1 The first thing I don't understand at all here is where the s and v values come from ?!? It might sound stupid but I don't understand this. Any help ? thanx Sam ==== hi all, I am actually trying to understand this mathematical notion that is so weird to me (I am far from being a god at maths...). could someone drop the light onto the following for me ? We will compute a rotation about the unit vector, u by an angle . The quaternion that computes this rotation is q = (s,v) s = cos(teta/2) v = u * sin(teta/2) We will represent a point p in space by the quaternion P=(0,p) We compute the desired rotation of that point by this formula: P = (0,p) Protated = qPq^-1 The first thing I don't understand at all here is where the s and v values come from ?!? It might sound stupid but I don't understand this. Any help ? thanx Sam ==== Can someone please tell me how to remove old posts. I still have post from ==== > Can someone please tell me how to remove old posts. I still have post from Is that the post we were all laughing at yesterday? ====