mm-248 Take the infinite series expansion for e and put it into the infinite>> series expansion of e to the power of x and multiply the terms and you>> end up with a series of aleph 1 terms> This is nonsense. Even when you multiply everything out, there are> still only countably many terms.Yes, compare countability of the rational numbers.>> that sum to a finite result e to>> the power of e. If you repete this process for e to the power of e to>> the power of e do you end up with aleph 2 terms?For series with an arbitrary number of terms, look up the term summablefamily. But a necessary condition for convergence is that at mostcountably many terms are nonzero, this follows from the archimedean axiomof the real numbers.-- reverse my forename for mail!Tobias Fritz, Student of Mathematics and PhysicsUniversity of Heidelberg, === series expansion for e and put it into the infinite>> series expansion of e to the power of x and multiply the terms and you>> end up with a series of aleph 1 terms> This is nonsense. Even when you multiply everything out, there are> still only countably many terms.> Yes, compare countability of the rational numbers.>> that sum to a finite result e to>> the power of e. If you repete this process for e to the power of e to>> the power of e do you end up with aleph 2 terms?> For series with an arbitrary number of terms, look up the term summable> family. But a necessary condition for convergence is that at most> countably many terms are nonzero, this follows from the archimedean axiom> of the real numbers.If aleph 1 is the set of all subsets of aleph 0 then take the countingnumbers the first subset is the empty set next come the sets with onlyone member that is 1,2,3 etc next is the sets with two members thesecan be arranged in a two dimensional array 1 2,1 3,1 4 etc 2 3,2 4,25 etc 3 4,3 5,3 6 etc etc all the way up to those with an infinitenumber of terms which can be arranged in an array with an infinitenumber of dimensions. Now if you want each one of these sets has acomplement however I think when you get to the sets with an infinitenumber of terms then each subset is duplica. which subset did Imiss? As for e to the power of e the first term is 1 next comes 1 + x+ (x^2)/2 + then comes 1/2 + x/2 + (x^2)/4 + , x/2 + (x^2)/2 + (x^3)/4+ , (x^2)/4 + (x^3)/4 + (x^4)/8 + etc arranged in a two dimensionalarray all the way up to those with an infinite number of terms thatcan be arranged an array with an infinite number of dimensions. youhave a one to one correspondence or at least a one to === infinite series expansion for e and put it into the infinite> series expansion of e to the power of x and multiply the terms and you> end up with a series of aleph 1 terms This is nonsense. Even when you multiply everything out, there are>> still only countably many terms.>> Yes, compare countability of the rational numbers.>that sum to a finite result e to> the power of e. If you repete this process for e to the power of e to> the power of e do you end up with aleph 2 terms?>> For series with an arbitrary number of terms, look up the term summable>> family. But a necessary condition for convergence is that at most>> countably many terms are nonzero, this follows from the archimedean axiom>> of the real numbers.>If aleph 1 is the set of all subsets of aleph 0 It's not. The _cardinality of_ the set of all subsets of aleph_0 is c,not aleph_1. But that's irrelevant. What matters is the set of _finite_ subsets of aleph_0; that has cardinality aleph_0.>then take the counting>numbers the first subset is the empty set next come the sets with only>one member that is 1,2,3 etc next is the sets with two members these>can be arranged in a two dimensional array 1 2,1 3,1 4 etc 2 3,2 4,2>5 etc 3 4,3 5,3 6 etc etc all the way up to those with an infinite>number of terms which can be arranged in an array with an infinite>number of dimensions. Now if you want each one of these sets has a>complement however I think when you get to the sets with an infinite>number of terms then each subset is duplica. which subset did I>miss? As for e to the power of e the first term is 1 next comes 1 + x>+ (x^2)/2 + then comes 1/2 + x/2 + (x^2)/4 + , x/2 + (x^2)/2 + (x^3)/4>+ , (x^2)/4 + (x^3)/4 + (x^4)/8 + etc arranged in a two dimensional>array all the way up to those with an infinite number of terms that>can be arranged an array with an infinite number of dimensions. you>have a one to one correspondence or === Mystery PuzzleI will top-post a clue, then post the spoiler below the copy/pasprevious post.Clue: If you apply the same mystery mathematical rule applied to theintegers in the puzzles' rows/columns to this list of FIVE integers:2,4,10,3,5then you get an output of:1517Puzzles' *still* did not realize I had>exchanged the two digits.>>And there is a relatively simple rule for the 3-by-3 case, which by a>certain generalization can extend to all sequences of n positive>integers.> I'm still at a loss for what the rule is, but I believe I have determined> the placement of the 4x4 grid. Will you confirm whether this is correct?> 10 11 14 15> 9 12 13 16> 8 5 4 1> 7 6 3 2> -- Erick> You are correct regarding the placement of integers.> (I should have had a rule that did not result in so much correlation> between the output integers' relative magnitudes and the relative> magnitudes of the integers in the grid.)> :/> I will reveal the rule I intended tomorrow or the next day. (As well,> I will reveal the answer then at that time for my Array Recursion> Puzzle.)>||V||V||V||V||V||VRule:If we let the integers in any particular column/row be the terms of acontinued fraction, then the output integer is the numerator === axiomatization reference?Can someone give me a reference in the literature for the followingaxiomatic characterization of the complex numbers? (1) C is a field (2) C contains a subset P of nonzero elements satisfying (a) P is closed under addition, multiplication and taking inverses. (b) If x and y are distinct elements of P, then either x-y or y-x is in P (c) If S is any nonempty subset of P, then S+P=x+P for some x in C. (3) C has a nontrivial involutive automorphism x->x*, fixing P and such that xx* is in P for any nonzero x in C.Zig === immediately below copy/pas replied-to post.> Seems as if no one has any clue...> (snicker)> So I will give a couple clues below...> We have a triangular array of integers {a(m,n)}.> a(1,1) = 0;> And, for 1 <= n <= m, m >= 2, recursively:> a(m,n) = > m-1> --- ---> 1 + > ( > mu(j) ) a(m-1,k)> / /> --- ---> k=1 j|k> j>= kn/m> Ascii-mode:> a(m,n) => 1 + sum{k=1 to m-1} (sum{j|k, j >= kn/m} mu(j)) a(m-1,k)> The inner-sum is over the divisoj, of k,> where each j is >= kn/m.> And mu() is the Mobius (Moebius) function.> Now, the array's elements can be easily described with a closed-form> (ie. non-recursive) definition.> What is this closed-form for {a(m,n)}?> I will first give a clue in a few days, then the answer a few days> after that, if no one posts an answer before I do this.>> First, every a(m,n) is a positive integer for> m >=2, 1 <= n <= m.> Second, a(m,1) DOES always = m-1,> and a(m,m) does always = 1 for m >= 2.>Answer:a(m,1) = m-1.And for n >= === Big Number GameI was directly inspired by the thread star by Joona I PalasteAbout Big Numbers( off&threadm=bp064v%24j0u%241%40oravannahka.helsinki.fi&prev=) to come up with this simple Rock/Paper/Scissors-style game.3 players each come up with expressions in-secret, as in the mentionedthread, expressions which each represent unimaginably huge finitenumbers.The winner is the player whose number is BETWEEN the other 2 players'numbers.What would be the strategy to this kind of game??(Strategy may involve psychology even more than mathematics.)But, as is seen in the alluded-to thread, actually evaluating therelative numerical orders of the players' numbers might itself be adifficult mathematical === directly inspired by the thread star by Joona I Palaste>About Big Numbers>( off&threadm=bp064v%24j0u%241%40oravannahka.helsinki.fi&prev=)> to come up with this simple Rock/Paper/Scissors-style game.>3 players each come up with expressions in-secret, as in the mentioned>thread, expressions which each represent unimaginably huge finite>numbers.>The winner is the player whose number is BETWEEN the other 2 players'>numbers.>What would be the strategy to this kind of game??>(Strategy may involve psychology even more than mathematics.)It seems like you're basically trying to GUESS their numbers. If youcould guess a single number that most accurately reflects both oftheiyou win.(I wonder if there shouldn't be a penalty for two people picking thesame number.)Anyway, 1 is too low, unless you're allowing negative numbeandthat's a mess.A trillion seems a little high. (I hear that billion isn't a wordin the UK? Does that mean that trillion isn't either?)I guess it depends what level of brainiacs you're playing with.Here's my method for predicting what type of number a guy would pick.1. Subtract 100 from the guy's IQ.2. Divide that by two.3. Raise 2 to that === Game> A trillion seems a little high. (I hear that billion isn't a word> in the UK? Does that mean that trillion isn't either?)In the UK, these words do exist, but with different meanings than those to which you might be accustomed. Billion means 10^12 (a million squared), trillion means 10^18 (a million cubed), quadrillion means 10^24 (a million to the power 4), etc etc (except in the hands of ignorant people such as politicians, businessmen, and the media).-- Richard Heathfield : binary@eton.powernet.co.ukUsenet is a strange place. - M Ritchie, 29 July 1999.C FAQ: http://www.eskimo.com/~scs/C-faq/top.htmlK&R answeC books, === Number Game <4al8rvk1fk87q049sp17kpk615bjqk022o@4ax.com> In message , Richard Heathfield >> A trillion seems a little high. (I hear that billion isn't a word>> in the UK? Does that mean that trillion isn't either?)>In the UK, these words do exist, but with different meanings than those to>which you might be accustomed. Billion means 10^12 (a million squared),>trillion means 10^18 (a million cubed), quadrillion means 10^24 (a>million to the power 4), etc etc (except in the hands of ignorant people>such as politicians, businessmen, and the media).I think Richard is referring to people born since 1940.Nick-- Nick Wedd === , Richard Heathfield>A trillion seems a little high. (I hear that billion isn't a word> in the UK? Does that mean that trillion isn't either?)>>In the UK, these words do exist, but with different meanings than those to>>which you might be accustomed. Billion means 10^12 (a million squared),>>trillion means 10^18 (a million cubed), quadrillion means 10^24 (a>>million to the power 4), etc etc (except in the hands of ignorant people>>such as politicians, businessmen, and the media).> I think Richard is referring to people born since 1940.My children (all of whom are under the age of 14) use the terms correctly. I don't see why grown-ups can't.-- Richard Heathfield : binary@eton.powernet.co.ukUsenet is a strange place. - M Ritchie, 29 July 1999.C FAQ: http://www.eskimo.com/~scs/C-faq/top.htmlK&R answeC books, === Big Number Game> My children (all of whom are under the age of 14) use the terms correctly. I > don't see why grown-ups can't.A quote from:The New Fowler's Modern English Usage, Third Edition, Edi by R. W.Burchfield, The acknowledged authority on English usage[all of that from the front of the dust jacket...]Under the topic billion:It is best now to work on the assumption that the word means 'athousand millions' in all English-speaking areas...-- === Number Game In the UK, these words do exist, but with different meanings than those to>>which you might be accustomed. Billion means 10^12 (a million squared),>>trillion means 10^18 (a million cubed), quadrillion means 10^24 (a>>million to the power 4), etc etc (except in the hands of ignorant people>>such as politicians, businessmen, and the media).I think Richard is referring to people born since 1940.> My children (all of whom are under the age of 14) use the terms> correctly. I don't see why grown-ups can't.-Arthur,i'm not good === little high. (I hear that billion isn't a word> in the UK? Does that mean that trillion isn't either?)> In the UK, these words do exist, but with different meanings than those to> which you might be accustomed. Billion means 10^12 (a million squared),> trillion means 10^18 (a million cubed), quadrillion means 10^24 (a> million to the power 4), etc etc (except in the hands of ignorant people> such as politicians, businessmen, and the media).The usage has pretty much been replaced by the US system, which is a shame.'Milliard' is the official British word for an American billion, and is alsoused elsewhere in Europe, but you'd be hard pressed to find anyone thatknows === seems a little high. (I hear that billion isn't a word> in the UK? Does that mean that trillion isn't either?)In the UK, these words do exist, but with different meanings than thoseto> which you might be accustomed. Billion means 10^12 (a millionsquared),trillion means 10^18 (a million cubed), quadrillion means 10^24 (a> million to the power 4), etc etc (except in the hands of ignorant people> such as politicians, businessmen, and the media).> The usage has pretty much been replaced by the US system, which is ashame.> 'Milliard' is the official British word for an American billion, and isalso> used elsewhere in Europe, but you'd be hard pressed to find anyone that> knows what it means.> DannyAnd billiard, trilliard etc. === Big Number Game> And billiard, trilliard etc. (although I have never heard them used).These are modern contrivances, which I'm not sure weren't just inven as a wind-up (by an American trying to discredit the European's various /mill?[ji]ardi?/ (I think that regexp covers about 10 languages.)).-- Unpatched IE vulnerability: protocol control charsDescription: Circumventing content filtersReference: http://badwebmasters.net/advisory/012/Exploit: === Big Number Game> And billiard, trilliard etc. (although I have never heard them used).> These are modern contrivances, which I'm not sure weren't just> inven as a wind-up (by an American trying to discredit the> European's various /mill?[ji]ardi?/ (I think that regexp covers> about 10 languages.)).> Aha. That might explain why I'd never heard of them until I decided tocheck if they exis. Having said that, I've never heard milliard used inconversation (although I was aware of its existence), and it must be a longtime since I heard billion === Game> [...] and it must be a> long time since I heard billion used in the British sense.I always use it in the British sense. If others are confused by what I consider to be correct usage, that's their problem, not mine.-- Richard Heathfield : binary@eton.powernet.co.ukUsenet is a strange place. - M Ritchie, 29 July 1999.C FAQ: http://www.eskimo.com/~scs/C-faq/top.htmlK&R answeC books, === American billion, and is also> used elsewhere in Europe, but you'd be hard pressed to find anyone that> knows what it === GameDanny Kodicek scribbled the followingon sci.math:>> A trillion seems a little high. (I hear that billion isn't a word>> in the UK? Does that mean that trillion isn't either?)In the UK, these words do exist, but with different meanings than those to>> which you might be accustomed. Billion means 10^12 (a million squared),>> trillion means 10^18 (a million cubed), quadrillion means 10^24 (a>> million to the power 4), etc etc (except in the hands of ignorant people>> such as politicians, businessmen, and the media).> The usage has pretty much been replaced by the US system, which is a shame.> 'Milliard' is the official British word for an American billion, and is also> used elsewhere in Europe, but you'd be hard pressed to find anyone that> knows what it means.Pretty much everything in Europe and Asia is being replaced by US thingsnowadays. Reverse occurrences are rare to the point of non-existence.-- /-- Joona Palaste (palaste@cc.helsinki.fi) ------------- Finland ---------- http://www.helsinki.fi/~palaste --------------------- rules! --------/All that flower power is no match for my glower === trillion seems a little high. (I hear that billion isn't a word>> in the UK? Does that mean that trillion isn't either?)>In the UK, these words do exist, but with different meanings than those to >which you might be accustomed. Billion means 10^12 (a million squared), >trillion means 10^18 (a million cubed), quadrillion means 10^24 (a >million to the power 4), etc etc (except in the hands of ignorant people >such as politicians, businessmen, and the media).And then for the other numbethey say thousand billion, thousandtrillion, etc.?never sounded right to my ears that a million squared was a trillion,not a === followingon sci.math:> A trillion seems a little high. (I hear that billion isn't a word> in the UK? Does that mean that trillion isn't either?)>>In the UK, these words do exist, but with different meanings than those to >>which you might be accustomed. Billion means 10^12 (a million squared), >>trillion means 10^18 (a million cubed), quadrillion means 10^24 (a >>million to the power 4), etc etc (except in the hands of ignorant people >>such as politicians, businessmen, and the media).> And then for the other numbethey say thousand billion, thousand> trillion, etc.?> never sounded right to my ears that a million squared was a trillion,> not a billion.Yes, well. There are things that are good and American, things that arebad and American, things that are good and European, and things thatare bad and European.Let me think of an example of each. Hamburgers with cole slaw (withthat yummy red onion) is good and American. The Bush administrationis bad and American. Proper football is good and European. Drivingon the left is bad and European.What we have here is an American system versus a good system. However,in today's world, whether something is good matters exactly zilch.What matters is whether it's American. So the American system winsautomatically.-- /-- Joona Palaste (palaste@cc.helsinki.fi) ------------- Finland ---------- http://www.helsinki.fi/~palaste --------------------- rules! --------/'It can be easily shown that' means 'I saw a proof of this once (which I didn'tunderstand) which I can no longer === following>on sci.math:>> And then for the other numbethey say thousand billion, thousand>> trillion, etc.?>> never sounded right to my ears that a million squared was a trillion,>> not a billion.>Yes, well. There are things that are good and American, things that are>bad and American, things that are good and European, and things that>are bad and European.>Let me think of an example of each...How about an example of all four at once? Like Paul Verhoeven? === GameJoona I Palaste grava .88 la saucisse et au marteau:> is bad and American. Proper football is good and European. Driving> on the left is bad and European.Since when are the English europeans?-- Nicolas, let === <0i29rvs65redvjh0mtv5s78j2m3fes7po2@4ax.com> > Joona I Palaste grava .88 la saucisse et au marteau:> is bad and American. Proper football is good and European. Driving> on the left is bad and European.> Since when are the English europeans?Since about 1066. :)> --> Nicolas, let the === Game> Since when are the English europeans?Do you suppose they want to be considered Americans? Or Africans? OrAsians? === Since when are the English europeans?> Do you suppose they want to be considered Americans? Or Africans? Or> Asians? Certainly not Antarcteans!They sure do not behave as if they would want to be considerd Europeans.-- houghi http://www.houghi.org/jargon It's people. Source code is made out of people! They're making our source outof people. Next thing they'll be breeding us like cattle for code. You've === Number Game> Yes, well. There are things that are good and American, things that are> bad and American, things that are good and European, and things that> are bad and European.> Let me think of an example of each. Hamburgers with cole slaw (with> that yummy red onion) is good and American. Joona, I'm amazed!How can you as a _Finn_ say such a thing? Here in Finland it's well known that the hamburger was a Polish invention (originally named Hzczambrzurszyngerschandwicz), which is in its traditional form a meat coupon in between two bread coupons.(Originally at http://softavenue.fi/u/henry.w/poland/ which was aparody of http://jpzr.com/finland/ . Henry - why have you removed it?)NB - newsgroups line has expanded somewhat.-- Unpatched IE vulnerability: window.open search injectionDescription: cross-domain scripting, cookie/data/identity theft, command executionReference: http://safecenter.net/liudieyu/WsFakeSrc/ WsFakeSrc-Content.HTMExploit: http://safecenter.net/liudieyu/WsFakeSrc/WsFakeSrc-MyPage.htm= === ==Subject: Re: Big Number Game> Driving on the left is bad and European.Joona, I assure you that driving on the left is === system. However,> in today's world, whether something is good matters exactly zilch.> What matters is whether it's American. So the American system wins> automatically.The metric system is not American and still everyone know what a kilois.-- houghi http://www.houghi.org/jargon It's people. Source code is made out of people! They're making our source outof people. Next thing they'll be breeding us like cattle for code. You've === Number Gamehoughi scribbled the followingon sci.math:>> What we have here is an American system versus a good system. However,>> in today's world, whether something is good matters exactly zilch.>> What matters is whether it's American. So the American system wins>> automatically.> The metric system is not American and still everyone know what a kilo> is.The British don't.-- /-- Joona Palaste (palaste@cc.helsinki.fi) ------------- Finland ---------- http://www.helsinki.fi/~palaste --------------------- rules! --------/And according to Occam's Toothbrush, we only need to optimise the most === Game> houghi scribbled the following> on sci.math:> What we have here is an American system versus a good system. However,> in today's world, whether something is good matters exactly zilch.> What matters is whether it's American. So the American system wins> automatically.>> The metric system is not American and still everyone know what a kilo>> is.> The British don't.On the contrary, I have it on the very highest authority (a breakfast cereal packet from the 1970s) that: Two and a quarter pounds of jam Weigh about a kilogram.So presumably it's a (rather inconvenient) unit of weight for jams and preserves.-- Richard Heathfield : binary@eton.powernet.co.ukUsenet is a strange place. - M Ritchie, 29 July 1999.C FAQ: http://www.eskimo.com/~scs/C-faq/top.htmlK&R answeC books, === Number Game <4al8rvk1fk87q049sp17kpk615bjqk022o@4ax.com> <0i29rvs65redvjh0mtv5s78j2m3fes7po2@4ax.com> scribbled the following> on sci.math:>> What we have here is an American system versus a good system. However,>> in today's world, whether something is good matters exactly zilch.>> What matters is whether it's American. So the American system wins>> automatically.> The metric system is not American and still everyone know what a kilo> is.> The === Game> houghi scribbled the following> on sci.math:>> What we have here is an American system versus a good system. However,>> in today's world, whether something is good matters exactly zilch.>> What matters is whether it's American. So the American system wins>> automatically.The metric system is not American and still everyone know what a kilo> is.The British don't.> Yes, it's 2.204 lb.Where's Gene?(i.e. there's a numerical error in that, he normally spots such things...)-- Unpatched IE vulnerability: ADODB.Stream local file writingDescription: Planting arbitrary files on the local file systemExploit: http://ip3e83566f.speed.planet.nl/eeye.html (but unrela to the === YesX-NSA-Fodder: Freeh cybercash AVN csystems SP4 Mossad infowar bce Mantis> The metric system is not American and still everyone know what a kilo> is.> The British don't.Sure we do. Its the SI prefix meaning * 10^3Oh, you meant a kilogram... Its about 4/100ths of a bushel.-- Gareth === Game> I was directly inspired by the thread star by Joona I Palaste> About Big Numbers> ( off&threadm=bp064v%24j0u%241%40oravannahka.helsinki.fi&prev=)> to come up with this simple Rock/Paper/Scissors-style game.> 3 players each come up with expressions in-secret, as in the mentioned> thread, expressions which each represent unimaginably huge finite> numbers.> The winner is the player whose number is BETWEEN the other 2 players'> numbers.> What would be the strategy to this kind of game??> (Strategy may involve psychology even more than mathematics.)las Hofstadter once proposed a game called Hruska*, in which theobject was to obtain the middle score. There was to be a series ofgames, in which the winner was not the one achieving the middle scoremost often, or least often, but (of course) the middlemost number oftimes.*named after former Senator Roman Hruska, who once gave a speechextolling the virtues of mediocre people.-- Dave SeamanJudge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. off&threadm=bp064v%24j0u%241%40oravannahka.helsinki.fi&prev=)> to come up with this simple Rock/Paper/Scissors-style game.> 3 players each come up with expressions in-secret, as in the mentioned> thread, expressions which each represent unimaginably huge finite> numbers.> The winner is the player whose number is BETWEEN the other 2 players'> numbers.> What would be the strategy to this kind of game??> (Strategy may involve psychology even more than mathematics.)> las Hofstadter once proposed a game called Hruska*, in which the> object was to obtain the middle score. There was to be a series of> games, in which the winner was not the one achieving the middle score> most often, or least often, but (of course) the middlemost number of> times.IIRC, he, or someone, analysed it in game theory terms, and it turned outthat the optimum strategy even when you allow infinitely high numbers wasonly to play numbers from 1 to 5, in a certain === 1/zeta's(I MAY have pos on this topic before, but I have a new question anyhow.)Let a(1) = 1.Let, for m >= 2, a(m) = (-m/(m-1)) sum{k|m,k= 2, is also (maybe)-1/(ln(m)) sum{k|m,k>1} a(m/k) k *Mangoldt(k)/(k-1),where Mangoldt(k) is ln(p) if p^j = k, j = positive integer, p = prime;and is 0 if k is not power of prime, Mangoldt(1) = 0.So, sum{m=1 to oo} a(m) /m^r= product{k=0 to oo} 1/zeta(k+r).I am wondering which a(k)'s are integers.(a(1), a(2), and a(6) are integers at least.)Leroy === for evaluating the prolatespheroidal wave === anyone point me toward a good method for evaluating the prolate> spheroidal wave functions?Er, the oblate case is the hardest. But if it were me, I would try tobuttonhole someone who works in acoustical engineering. PSWF's occur in thatfield, and if anybody has algorithms and software at hand, === Matt Timmermans> Can anyone point me toward a good method for evaluating the prolate> spheroidal wave functions?> Er, the === Factorization dispute, againAs it is, JSH's latest attempts appear to beLet . Then . Then> . Now [pick one: 1, 2, 4, 23]> of in are obviously divisible by> [pick one: 2, 3, 7, 11, 97] but there's only> [pick one: 1, 2, 3, 22] factors of [pick one: 2, 3, 7, 11, 97]> in the equation, therefore the algebraic numbers are equivalent> to C and . QED>LOL!In MAD magazine there used to be a variation of this where they'd give thetext of say something that was basically BS, like a politicians' speech. Inthe speech there'd be these blanks where you could use any one of 4 wordsand the thing would still make sense. Congrats, you've found the MADmagazine equivalent in === See, exactly the same as your method.>Not at all!> It's 4 things to combine, no matter how it's done.Oh, it matters a lot how it's done. Because it is done differently, itis a different method. Because it is done more easily and quicklyboth in the mind and on paper, it is a better method. Whether doing them> 2 at a time in your head (or even by rote memory) or not is irrelevant.> It's still 4.It is done more simply and quickly. Give the schoolchildren bothmethods, and ask which one they likes better.> This is 3 products (1*3, 2*4 and 3*8), not 4.> 12 * 34 = 308 + 210 - 110 = 408.>Try doing what you have done for say 12345*567809!> It's 30 pairs either way.> If you think there's anything substantially different, try doing it> with:> 234234999128098091238897289713498172389744091238412908270923478 32> x 349234230982309418209481209283409280293840293842230948230234324 23> -------------------------------------------------------------- ---Well, I can easily write some of the first and last coefficientsrelating to position with the new Vedic method that I have learnt, sowe have(6)(17)(42)(60)..........(42)(13)(6) just in my head, without needingpaper and pencil.> I know a quick way of doing this without doing ANY multiplication> whatsoever, and yet requiring about the same number of additions that> are required to combine the rows of numbers anyhow.If you are talking about digital methods relating to shiftingregisteetc. then remember that same sort of stuff can also applyto Vedic methods. In fact, the whole thing can be hardwired and wecan get the x*y products (not mod anything) in the order ofnanoseconds, for any length of N determined by hardware, with currenttechnology.> Try matching that with that ingenious Vedic method of yours.I am talking nanoseconds of computation time for any N. Mind you, thecoefficients each need not be constrained to decimal, they could be oflength n depending upon the size of the registers used. This methodis certainly ideal for parallel processing.> [Hint: c.f., dynamic === Reality>> See, exactly the same as your method.>Not at all!It's 4 things to combine, no matter how it's done.> Oh, it matters a lot how it's done. Because it is done differently, it> is a different method. Because it is done more easily and quickly> both in the mind and on paper, it is a better method.Absolutely. But:1. is it Vedic?2. is it really such a big deal?Ad 1: The expression crosswise vertical doesn't say anything about the order of addition.Ad 2: Math (at least western math) is much more than arithmetic. It sure is a cool thingto do 345 x 167 in the mind. Especially for school children. But it's not an advancein the field of mathematics. It's simply arithmetic.And for the purpose of math education, learning people calculation 'tricks'is generally considered === Mathematics --- Myth and Reality>> My father taught me in my childhood days,> 12 *> 34> --------> 48> 36> --------> 408 this is the way children are still taught in at least> Australian primary schools, and in most Indian schools as well. As> you can see, you need three lines to get this result (48, 36 and 408).> In Vedic arithmetic, you get the representation of the result in just> one line, no matter what the length of the factors. Now, in IndiaI can also do it in one line: 12 *> 34> --------> 48 36 408But seriously, this vedic method is no different as our method.> Our method is basically:2*4 + 10*4 + 2*30 + 10*30 = 48 + 360 = 408See, exactly the same as your method.> Not at all!> Wilbert> No, you don't see the difference. You have written 48 as 12*4,> whereas in the Vedic method you take only one coefficient at one time.> coefficient at the time.You just don't get it! To multiply 12 * 4 the Vedic way, you have todo (1*4+2*0)(2*4) or (4)(8) or 48.> Like, you cannot take more than one coefficient, as you have done.> Try doing what you have done for say 12345*567809! That is the very> important difference, and that which will make it much simpler for> computer calculation.> Our way (including the steps you make in your mind):> 10000*9 + 2000*9 + 300*9 + 40*9 + 5*9 + 10000*800 + 2000*800 + ...> Precisely the same as your method, only the ordering of adding > is different. Big deal.> I know it is very difficult to comprehend the simple and the> brilliant, especially when the mind has been narrowly and closely> formed.> Adding numbers in === Vedic Mathematics --- Myth and Reality>Do you know how old exactly?>And... do you have a reference for that book? (Online somewhere?)>>The 'one-register' method of multiplication is indeed very nice.>But... it is arithmetic, rather than mathematics. That may also explain>why the math teaching world is not very fond of tricks like this.>Mathematics teachers are desperately fighting the general prejudice>that mathematics is 'just' arithmetic.>I doubt this had anything to do with Vedic mathematics (though I may> just be unaware of the sources). It was a system partly inven (or> perhaps merely collec) by Jacow Trachtenberg in the twentieth> century. The standard reference in English is The Trachtenberg Speed> System of Basic Mathematics by Cutler> original German (I think). You can find it at Amazon.Has it any relation to the Vedic method? Maybe it is the same method,developed independently.> The descriptions available on the web (search for Trachtenberg and> arithmetic) mainly talk about tricks for multiplying by single digits,> 11, and 12, which is the first part of the book. Later chapters discuss> techniques of long addition, multiplication, and division.Does he do square root extraction in one line? Or long division?> there is in> Vedic maths, not just the single-register multiplication.> In the meantime i've found online sources on vedic mathematics.> It appears to be (re)discovered not before 1910 or so.The book under discussion was first published in 1965, apparently.> Convolution is older.> Nevertheless, for historic reasons it could be worth a look.> However... all they ever show is their 'crosswise-horizontal'.> If you want to know the rest, they make you buy books.> Another typical line: sorry, i'm no expert, so i'm unable> to tell more; but it's all there, in our books / courses.> Not very trustworthy...Herman JurjusI am sure you could buy the book, if you have sources in Kolkata. Iam not sure where I bought the book. You could try the AurobindoAshram on Shakespeare Sarani. I am sorry to say that I left the bookin Kolkata. I really don't know if the long division and square rootmethods really work. They were saying that the whole thing is afraud, but at least I have cleared up the multiplication angle. Noone seems to think that the method is a fraud, though you are implyingit is nothing new. There is a chance, then that the author may havepassed off the Trachtenberg method as his own. If there is anyone-line long division method being known and used by modernmathematicians, or one-line square root method, let us know. If thereis no such method being used, then the author should be completelycleared of the charge of fraud.There are so many frauds around, you see. Who is the real one, isdifficult to say.Arindam Banerjee. > -- > Stephen === Vedic Mathematics --- Myth and Reality> ...> To give a mathematical (and suitably, one-line!) definition of Vedic> multiplication: The multiplicative product of two numbers A and B> represen as a sequence of characters of length m and n> respectively, of base X, and of value A(m-1)*X^(m-1) +> A(m-2)*X^(m-2)+...+A(0)*X^0 and B(n-1)*X^(n-1) +> B(n-2)*X^(n-2)...+B(0)*X^0 will be C(m+n-1)*X^(m+n-1) +> C(m+n-2)*X^(m+n-2) +...+ C(0)*X^0, where any C(k) is found by sum of> the combinations all the A(i) and B(j) satisfying i+j=k, where i, j> and k range from 0 to m, n and m+n-1 respectively.If that's one line I'm a Dutchman. It looks like 8 lines to me.> Well, it is one long sentence, which could have been written in one> long line. Try explaining the current Western method so briefly, if> you can!> The current western method?What was taught to me, when I was young. I suppose we were taughtwhat the English knew, in our school run by Mrs Smith. My fatherwould babsit me by giving me long multiplication and long divisionsums. I would spend a lot of time working them out, the Western way,and then he would correct them very quickly. He surely knew moreabout arithmetic than I did!> If it's small, do it by inspection, else use a calculator or computer.> Much shorter, and applicable to a wider range of problems too.> This doesn't look like it differs from the standard definition> of long multiplication. > Try to be a bit more clever, please. > Sheesh, so says someone who thinks that reeordering _the same > freaking number of operations_ is clever. For the kinds of > calculations I do, your technique is _useless_. Utterly useless.> It's not clever, it's a chocolate teapot.Okay, try multiplying 12345 by 67809 in any better manner. Just do ithere.> Sorry to burst your bubble, but you, or your vedic cronies, > have taken a technique which requires theta(m*n) single-digit > multiplications, and theta(2*m*n) single-digit accumulations, > and turned it into a method that requires theta(m*n) single-> digit multiplications and theta(m*n) two-digit accumulations > -- with exactly the same multiplicative constants (where m > and n are the lengths of the numbers. That's _exactly_ the > same workload.Mumbo-jumbo. If you want to show a better method involving lesscomputation, do so. Multiply 12345 by 67809 in any better fashionthan shown by me with the Vedic method.We are not doing line-by-line computation here. That is thedifference, which makes it so much easier for mental and handcomputation. It is so much more simple and elegant. Those who tryit, will find out for themselves. I believe that schoolchildren willlike this Vedic method a whole lot better.> I'm fully aware of the 'western', 'russian peasant', 'french> peasant' and 'vedic' methods for multiplication, and on the whole > I find the 'western' one the easiest to use if I've got a piece > of paper and a pen handy, and I always have a piece of paper and > a pen handy. The 'vedic' method is basically the 'french peasant' > method with JIT multiplications (and thus not requiring the paper> scratch area for the calculations). Very good. So do you have similar french peasant methods forone-line division and one-line square root extraction? Could one knowfrom where all allgrade-school methods as well?Looks like, you are being sarcastic. > And it's _exactly_ the definition of multiplication as used in> multiplication by convolution, which is the most common method > of doing big number multiplication nowadays. Please give the reference for this, and I shall check out thesimilarity. Is that definition this brief?However, the > multiplication by convolution has an asymptotically much lower > Big-Oh than the naive counting-on-fingers technique you describe > above.Ah, so they are already using this method, you say, and calling itconvolution? But if the definitions are the same, how could mytechnique be worse...> Also, look at my explanation to> the other chap, that I just pos.> What's Vedic about it?> People who inven the method consider themselves Vedic.> And the people who propagate it I consider vedic-fanboy drones.> You're as bad as Mac-zealots and linux-weenies.Well, whatever. All I wan to do was find out whether or not theauthor of the book was a fraud, as was claimed by some. Looks like,no one has proved that he stole it from another source. Also, as Ihave shown, the method is sound and usable. Thus, I conclude that theauthor is not a fraud.> If people are too lazy to find the technique for problem solution> that suits them best then that's _their_ problem. Stop proselytising.No fear, that's the line of your type. Don't project your attitudesupon me. I think this is a great method for schoolchildren (andprobably, with more research, in computers as well). With time, thisshould === Myth and Reality> Okay, try multiplying 12345 by 67809 in any better manner. Just do it> here.bash-2.05a$ echo '12345 67809*p' | dc837102105That wasn't so hard, was it? I found it pretty darn trivial. I'll return the favour - use your vedic methods to calculate: 2 ^ (5653^16384-5653^8192) % (5653^16384-5653^8192+1)I can do that in ~200*10^9 multiplications. [*]I reckon you'll be doing 408451*3779544484*3 multiplications ~= 5*10^15 multiplications.i.e. you and your vedic method will do 25000x as many multiplications as me.Not even using the new Indel Vedium processor will help you here.> Sorry to burst your bubble, but you, or your vedic cronies, > have taken a technique which requires theta(m*n) single-digit > multiplications, and theta(2*m*n) single-digit accumulations, > and turned it into a method that requires theta(m*n) single-> digit multiplications and theta(m*n) two-digit accumulations > -- with exactly the same multiplicative constants (where m > and n are the lengths of the numbers. That's _exactly_ the > same workload.> Mumbo-jumbo. i.e. you haven't got a clue what the theta notation means.Elsewhere you display a complete ignorance of what 'convolution' is.What's worse is that _all_ of the information that anyone with any interest in learning would need in order to master the conceptsof theta notation (or Big-Oh, but theta's tighter, and I always prefer to use theta when I can), and convolution, are learn, whichis about as low as it gets, behaviour-wise, at least on the groupin which I'm reading/posting (sci.math). (Note - I don't say it'suncommon, just that it's low.)You're a fool, and you enjoy embarassing yourself by demonstratingyour foolishness on 3 newsgroups. It's been fun, but I'm just gonna have to stick you in the loony bin with Dr Jai...*_plonk_*[* The answer's 1. http://primes.utm.edu/primes/page.php?id=66398 ]-- Unpatched IE vulnerability: Basic Authentication URL spoofingDescription: Spoofing the URL displayed in the Address barReference: === Subject: Re: Vedic Mathematics --- Myth and Reality> Wrong question. The correct question is:> Try multiplying> 349123402913412309482130498213409821340982134908123094821394012 3434234-> 234234234234123094823109482310948123094812304981230948120394812 3342342-> 942309234233423423423914230491283409213840123984012398401239423 4234234> by> 234234213412340921384021934802193480213948012398402139840231984 0123433-> 234213412342134231412304981230498213412342134123421342314231423 4234233-> 985095823409852034958340295802983450943850934803498503498503495 8454434> by any method *BUT* the well-known FFT-based method.Well, dc doesn't hesitate to do so: ( I wrapped the lines ) 349123402913412309482130498213409821340982134908123094821394012 343423423423423423412309482310948231094812309481230498123094812 039481233423429423092342334234234239142304912834092138401239840 123984012394234234234234234213412340921384021934802193480213948 012398402139840231984012343323421341234213423141230498123049821 341234213412342134231423142342342339850958234098520349583402958 029834509438509348034985034985034958454434* p81776645665262905090100834428449025457762725017145598016120284 497781581332926241857587759650622403785245998354970716445468160 520692739020461843899425199790414258890476258688116163124634933 908803377126910760890214406622808729671561154492418650722624776 186731313595924669744836595048721823753507192726034874829926964 706377031617648727702103402678511391366286524547376769222708144 === from my teens, there is a book by Trachtenberg on methods of> quick arithmetic. These include long mulitplication where the> calculations are all done on one line.Very likely. After all, this is an old method. In the book on Vedic> Mathematics, they also do one-line division, square-root etc.> Do you know how old exactly?Look, I don't even have the book with me.> And... do you have a reference for that book? (Online somewhere?)No. I got it from a bookshop, selling books on Sanskrit literature. > The 'one-register' method of multiplication is seen this done anywhereelse? Also, have you seen one-line division and square-rootextraction?> But... it is arithmetic, rather than mathematics. Isn't arithmetic a part of mathematics?> That may also explain> why the math teaching world is not very fond of tricks like this.It is not a trick, it is a sound method for multiplication. It givesa very thorough insight to the whole process, once properlyunderstood. Children are likely to like this method, and teacherswill find it useful to teach.> Mathematics teachers are desperately fighting the general prejudice> that mathematics is 'just' arithmetic.Well, that is because they are not doing the arithmetic right. Oncethat is done right, following proper understanding of what numbersreally are and what they really mean, then things will be better forall === would like to know, have you seen this done anywhere> else?Yep. In a 1936 book advocating more 'adventurous' math educationfor school children. (The Dutchman Kruijtbosch, iirc.) I don't knowwhat was his source, though. He sounds as if he considered it old andcommon knowledge.Also, have you seen one-line division and square-root> extraction?Kruijtbosch also has an alternative method for square roots,but it is not as nice as his multiplication. How are the Vedic methods?Never seen them in detail. But i would be very interes.> But... it is arithmetic, rather than mathematics.> Isn't arithmetic a part of mathematics?Hardly, no (strange as that may sound).> That may also explain> why the math teaching world is not very fond of tricks like this.> It is not a trick, it is a sound method for multiplication.Yes. But i've seen a site about Vedic maths showing some other things.They really are tricks, giving a student no 'basis' or 'insight' at all.Nice tricks, mind you. But tricks.It gives> a very thorough insight to the whole process, once properly> understood.It is a welcome addition to arithmetic education.But when it comes to insight, the distributive law is much better.> Children are likely to like this method, and teachers> will find it useful to teach.Yes, i also definitely think so.> Mathematics teachers are desperately fighting the general prejudice> that mathematics is 'just' arithmetic.> Well, that is because they are not doing the arithmetic right. Once> that is done right, following proper understanding of what numbers> really are and what they really mean, then things will be better for> all concerned.Here i disagree. Worshipping vedic maths as a potential redemption === Vedic Mathematics --- Myth and Reality>> Ironically, multiplication is far easier -- almost combinatoric in fact -->> in Roman numerals. And with a minor adjustment, the system can be>> made positional (even without a zero!), with the algorithm suitable>> extended.>Try writing 123987739383883938989874 in [the above-mentioned>modification of the] Roman numerals [this reply is in reference to].> CXXIII,XIIIM,DCCXIL,CXXDIII,CXXMIII,XIILM,XIM,CXXXMIVWhat do the commas relate to? Did the Romans use commas to denotelarge numbers? What is the largest number referenced by the Romans intheir entire literature? Where is that evidence?> 123987739383883938989874>> It's not widely known,...>> do without extraneous markers (the - symbol).>They used an abacus to give a visual representaiton of a large number.> Irrelevant to what this is in reply to.No, it is highly relevant. We are talking about a very serious issuehere, that of fraud. It has been alleged that Vedic mathematics isa fraud. Now, it can be a fraud if it is inherently wrong, or copiedfrom elsewhere and passed off as original. I have shown that it isnot inherently wrong, and in fact, it is something new. The nextstage is to show whether or not it is original - after all, the mehtodcould well have been lif from the West, and passed off as Indian. As far as I can see, no one has proved that so far.Thinking of large naturals in an abstract and not physical sense (asgiven by the abacus) was natural to Vedic people, and that issuppor by the time scale underlying their osophy, and mentionedin such concepts like kalpa, which relates to a very large numberindeed. (Did the Romans have any mention of numbers as large as thekalpa?) Mathematical methods where knowledge of place value is givenprimary importance came naturally to Vedic people, and is reflec inthe multiplication algorithm. They did not need the abacus to show andmanipulate numbers.So they could show a large number, and do mathematical manipulations,down in the clumsy manner that is well known.> Did the Romans have any knowledge of algebra?> Likewise, irrelevant.Oh no, you were the one talking about algebra to begin with.> [Actually, the theory of fields and of Euclidean geometry are equivalent,> each does precisely what the other does. > So, even the Greeks knew (and> used) algebra -- and even (as recently discovered) Calculus, via> Archimedes.]We have to change the history of mathematics texts, then. So far, weknow that the Muslims introduced the Europeans to algebra. So whatnew evidence has come up within the last 30 years which should make uschange the views to which we have been brought up? Who recentlydiscovered that the Greeks knew and used algebra and calculus?>Tell us about the grade-school method.> O(N^2) pairs for two N-digit numbers.Is that the method? It looks like some information about a method,certainly not the method itself. Define the method, as I did theVedic multiplication method, and then work out an example, as I did. Then tell us about the one-line division method, that exists in yourgrade-schools. If there is any one-line divsion method, or one-linesquare-root method, that is known to you, please say so.> You have not multiplied >What it is, and how it is the same as the method given.> O(N^2) pairs for two N-digit numbers. Everything else is irrelevant.I would like to see any multiplication method that is not so.>Okay, so multiply 12345 by 67809 using FFT, right here.> Wrong question. The correct question is:No, no it is the right question. Just do it, right here, and show howit is done any better than the Vedic method. Anything else is simpleevasion. Multiply 12345 by 67809 by FFT and show how you are doing itwithout 25 multiplication processes.> Try multiplying> 349123402913412309482130498213409821340982134908123094821394012 3434234-> 234234234234123094823109482310948123094812304981230948120394812 3342342-> 942309234233423423423914230491283409213840123984012398401239423 4234234> by> 234234213412340921384021934802193480213948012398402139840231984 0123433-> 234213412342134231412304981230498213412342134123421342314231423 4234233-> 985095823409852034958340295802983450943850934803498503498503495 8454434> by any method *BUT* the well-known FFT-based method.> search.yahoo.com/search?p=FFT-Based MultiplcationOkay, I did that, and I get fromhttp://www.fifi.org/cgi-bin/info2www?(gmp)FFT+ MultiplicationThe multiplication done is x*y mod 2^N+1, for a given N. A fullproduct x*y is obtained by choosing N>=bits(x)+bits(y) and padding xand y with high zero limbs. The modular product is the native formforthe algorithm, so padding to get a full product is unavoidable.So basically the FFT is to find x*ymod2^N+1. And not x*y or M*N. Tofind the full product, you have to do the padding, as narra. So,the FFT is irrelevant in this context, where we are not talking aboutmodulo arithmetic.Yes, as I have said earlier, you can get high efficiencies by binaryarithmetic, and doing various shifting processes - really, there arevery fast methods. But I don't think those methods can be as highlyparallelised as they can be using the Vedic algorithm.In your example, you gave us x and y only, but not N! However, youare talking about O(NlnN) all the time!>Show us how it is done more simply than what I have done below.> O(N^2) vs. O(N ln(N)) operations, for 2 N digit numbers.>You have to do a lot better if you want to debunk this method,>convincingly.> No. It's O(N^2).As I said, multiply any N by M with less than NM multiplications andshow us.>> I generally go 36*49 = 1254 + 90*13 - 660 = 1764,>> or 57*28 = 1056 + 120*10 - 660 = 1596,>> or 73*39 = 2127 + 100*12 - 480 = 2847.>I don't know what you are trying to prove, here!!> Of course not. The method is O(N^log_2(3)) and is fairly well-known.> You certainly have not succeeded in multiplying 12345 by 67809> It works quite well there too.>(45) = 5*9>(36) = 4*9+5*0>(67) = 3*9+8*5+4*0>(85) = 2*9+7*5+3*0+4*8>(91) = 1*9+6*5+2*0+7*4+3*8>(61) = 4*6+1*0+2*8+3*7>(40) = 1*8+6*3+2*7>(19) = 1*7+2*6>(6) = 1*6> 25 = 5^2 multiplications; O(N^2).Absolutely. That is not the main issue. The main issues are a) it isa method which gives us a one-line answer that is easily worked out b)it is not a method taught in primary schools - if introduced there Iam sure it will make life easy for both students and teacheandalso increase interest in mathematics c) it is supposed to be anancient Indian method d) it is said to be a fraud. I personally thinkit is a great method, as it is, and could be enhanced with moderntechniques. If FFT is done with this method as a base, maybe we couldget faster x*ymodN values. Of course, it will be a whole new researchdirection.>As is evident, you always need only to take only one digit at a time. > O(N^2) operations required. Where they're done (in your head or> on paper) is irrelevant. N^2 is N^2.Well, do it better, and show us. Multiply 12345 by 67809 by anyprocess involving less than 25 multiplications, and show us. If FFTcan do that, then show how it can do that.>The whole algorithm is also very well sui for parallel processing. > FFT-based methods, that is. An O(N^2) method is very poorly sui> due to its inefficiency and the large degree of intermixing. An> FFT-based method does not require ANY crossing at all.But when padding is done to the FFT method, in order to find the fullx*y, it becomes O(N^2). If it does not, then prove it.Arindam Banerjee.> Other parallel methods exists which don't require any multiplication> whatsoever and operate === --- Myth and Reality boundary=------------020902030201060104050205----------------- ----------------------------------------------------(I've tried and failed to resist getting involved in this silly flamewar. Sigh.)> No, no it is the right question. Just do it, right here, and show how> it is done any better than the Vedic method. Anything else is simple> evasion. Multiply 12345 by 67809 by FFT and show how you are doing it> without 25 multiplication processes.See attached file linconv_5.c, with test program, which does it in 23 multiplications. This actually uses a Karatsuba variant; the advantages of FFT-based methods come mainly for larger sizes, and the O(...) notation is a statement about asymptotic speeds for large N.> So basically the FFT is to find x*ymod2^N+1. And not x*y or M*N. To> find the full product, you have to do the padding, as narra. So,> the FFT is irrelevant in this context, where we are not talking about> modulo arithmetic.You're confused. An FFT-based method computes a cyclic convolution, but you can use zero-padding to do a linear convolution, which is what non-modulo multiplication is. Equivalently, M*N is the same as M*N mod (M + N - 1).That is, to multiply an N digit number by an N digit number with an FFT, you need to zero-pad to a length of at least 2*N-1 and then muliply the FFTs. This is O((2*N-1) log (2*N-1)), which is still O(N log N).> As I said, multiply any N by M with less than NM multiplications and> show us.Download the free GNU MP library, or Bailey's arprec library, or any number of other O(N log N) multiplication implementations. See e.g. http://www.swox.com/gmp/manual/Multiplication-Algorithms.html> But when padding is done to the FFT method, in order to find the full> x*y, it becomes O(N^2). If it does not, then prove it.Zero-padding does not make it O(N^2). You're just doing an FFT of ~twice the size, with some inputs that are zeros, and it is still O(N log N). See above.How do you think people compute Pi to millions of decimal places?This is all well-known stuff.Cordially,Steven G. Johnson------------------------------------------------------- -------------- name=linconv_5.c filename=linconv_5.c/* Genera by: /homee/stevenj/cvs/fftw3/genfft/gen_conv -name conv_9 -n 5 *//* * This function contains 23 additions, 23 multiplications */typedef int R;typedef R E;void linconv5(const R A[5], const R B[5], R O[9]){ E T3; E T6; E T48; E T56; E T16; E T50; E T52; E T53; E T12; E T9; E T19; E T20; E T34; E T47; E T37; E T26; E T44; E T25; E T38; E T43; E T33; E T10; { E T13; E T14; E T15; E T1; E T29; E T31; E T2; E T4; E T11; E T5; E T8; E T41; E T36; E T24; E T18; E T32; E T23; E T7; E T42; E T30; T13 = A[2]; T14 = A[3]; T15 = T13 + T14; T1 = A[0]; T29 = B[4]; T31 = A[4]; T2 = B[0]; T4 = A[1]; T11 = B[2]; T23 = B[3]; T7 = B[1]; T5 = T1 + T4; T8 = T2 - T7; T41 = T1 * T29; T36 = T29 - T23; T24 = T11 - T23; T18 = T11 - T7; T32 = T31 * T2; T3 = T1 * T2; T6 = T5 * T2; T48 = T15 * T29; T56 = T31 * T29; T16 = T15 * T2; T50 = T14 * T36; T52 = T31 * T24; T53 = T13 * T29; T12 = T5 * T11; T9 = T1 * T8; T19 = T4 * T18; T20 = T14 * T2; T34 = T15 * T11; T47 = T31 * T11; T37 = T4 * T36; T26 = T13 * T8; T44 = T13 * T24; T25 = T1 * T24; T38 = T14 * T18; T42 = T31 * T8; T43 = T41 + T42; T30 = T5 * T29; T33 = T30 + T32; } O[0] = T3; O[8] = T56; T10 = T6 - T9; O[1] = T10; { E T51; E T55; E T49; E T54; T49 = T47 + T48; T54 = T52 + T53; T51 = T49 - T50; T55 = T49 - T54; O[6] = T51; O[7] = T55; } { E T40; E T46; E T35; E T45; E T39; T35 = T33 + T34; T45 = T43 + T44; T39 = T37 + T38; T40 = T35 - T39; T46 = T35 - T45; O[4] = T40; O[5] = T46; } { E T22; E T28; E T17; E T27; E T21; T17 = T12 + T16; T27 = T25 + T26; T21 = T19 + T20; T22 = T17 - T21; T28 = T17 - T27; O[2] = T22; O[3] = T28; }}/* test: multiply 12345 by 67809 = 837102105 */int main(void){ R a[5] = {5,4,3,2,1}, b[5] = {9,0,8,7,6}, o[9]; int i; linconv5(a,b,o); /* carry (note that a practical arbitrary-precision implementation on a binary computer would use digits that are powers of two, not 10, so this would only require shifts and not divisions. */ for (i = 0; i < 8; ++i) if (o[i] > 9) { o[i+1] += o[i] / 10; o[i] %= 10; } for (i = 8; i >= 0; --i) printf(%d, o[i]); printf(n); return === Vedic Mathematics --- Myth and Reality> Equivalently, M*N is the same as M*N mod (M + N - 1).Sorry, this should be multiplication of M digits with N digits, base b, is equivalent to multiplication modulo b^(M + N - 1), i.e. M+N-1 === Reality>Tell us about the grade-school method.> O(N^2) pairs for two N-digit numbers.>What it is, and how it is the same as the method given.> O(N^2) pairs for two N-digit numbers. Everything else is irrelevant.Better than that, it's Theta(N^2).Or do I mean 'worse than that'?-- Unpatched IE vulnerability: dragDrop invocationDescription: Arbitrary local file reading through native Windows dragDrop invocation.Reference: http://msgs.securepoint.com/cgi-bin/get/bugtraq0302/12. htmlExploit: === Vedic Mathematics --- Myth and Reality> There was an Indian mathematican called Shakuntala who toured> the west beating the computers at multiplying two large numbers - must> have used vedic methods,Must have? Must have?Cite, or retract.I'll give you a clue - if you go to her website you won't see _one_ surname's Devi, and it's the first hit IIRC.She's had my respect for about 25 yeawhich was when I firstread her The Joy of Numbe(I think that's what it's called - it was 25 years ago, rememeber). However, almost all of her computational feats have been bettered in recent decades. And none of the guys who've beaten her have claimed any usage of vedic methods either. -- Unpatched IE vulnerability: DNSError folder disclosureDescription: Gaining access to local security zonesReference: === Subject: Re: Vedic Mathematics --- Myth and Reality> My main point is to show that the writer of that book is not a fraud. > His methods can be very useful, as opposed to current methods taught> in schools. > If current methods are indeed useless, how did people build the Golden > Gate Bridge or the Queen Mary?> I did not expect this sort of response from you, Ranjit. This sort I> expect from the type of Mr Singh & Co.> I never mentioned in any post that the current methods are useless; I> said that this Vedic method is better. That did *not* imply that the> current methods are *useless*. You are twisting my words, the same way> Mr Singh does.If Mr. Singh were to use your wording and say, methods taught inschools can be very useful, as opposed to Vedic methods, would youunderstand that he never mentioned that Vedic methods are useless butthat he merely said methods taught in schools were better? The arebetter implication would have been clear only if you had saidsomething along the lines of his methods are more useful than currentmethods taught in schools.> As for your question, people built the Golden Gate Bridge and the> Queen Mary the same way the Egyptian built pyramids. It is generally> understood that the ancient Egyptians did not know trigonometry, or> any modern mathematics.FYI, people designed the bridge and ship in question WITH theapplication of trigonometry and mathematics, not without it. So, theydid not === Re: Vedic Mathematics --- Myth and Reality> My main point is to show that the writer of that book is not a fraud. > His methods can be very useful, as opposed to current methods taught> in schools. If current methods are indeed useless, how did people build the Golden > Gate Bridge or the Queen Mary?> I did not expect this sort of response from you, Ranjit. This sort I> expect from the type of Mr Singh & Co.> I never mentioned in any post that the current methods are useless; I> said that this Vedic method is better. That did *not* imply that the> current methods are *useless*. You are twisting my words, the same way> Mr Singh does.> If Mr. Singh were to use your wording and say, methods taught in> schools can be very useful, as opposed to Vedic methods, would you> understand that he never mentioned that Vedic methods are useless but> that he merely said methods taught in schools were better?Of course. > The are> better implication would have been clear only if you had said> something along the lines of his methods are more useful than current> methods taught in schools.indeed useless in your earlier post. I had never said that. However, you cunningly implied that that was what I had said, when youcurrent methods are useless. If I said they were useless, that wouldmake me look like a fool. For they do work.> As for your question, people built the Golden Gate Bridge and the> Queen Mary the same way the Egyptian built pyramids. It is generally> understood that the ancient Egyptians did not know trigonometry, or> any modern mathematics.> FYI, people designed the bridge and ship in question WITH the> application of trigonometry and mathematics, not without it.Why is it so necessary to state the obvious?> So, they> did not build them the same way Egyptians built pyramids.To build any large and complica fixed structure on this planet, youneed the same basic things like plumblines, rulers and spirit levels. Mathematics is just another thing. With better and newer maths andphysics, you can make better and more complica things. With thelevel of physics and maths the Egyptians had, they could build thepyramids. With knowledge of mechanics and slide rules, the Americansbuilt the Golden Gate Bridge. With knowledge of Archimedes Principle,thermodynamics, etc. the English built QM. With knowledge ofMaxwell's laws, they built generatoradar, etc. With knowledge ofcomputer science and technology, modern manufacturing has taken agreat leap forward, and now we take high quality for gran. Hopefully, if my new ideas in physics are right, we can make vimansand go to the stabefore very long.In the meantime, with a better multiplication method we can try tomake life easier for kids in schools. Arithmetic could be a lot morefun. They will also get a deeper and sounder insight into thedynamics of place value, and the whole business of arithmetic. It issuch a pain to learn all that, for the kids!So when they say that this method should be introduced into schools, Iwould say, why not? === Spanier's Algebraic TopologyIn Chap. 2, Sec. 5 of Algebraic Topology Spanier proves thefollowing theorem:Let p_1:X_1 ->X and p_2:X_2 -> X be objects in the category ofconnec covering spaces of a connec locally path-connec spaceX. The following are equivalent:(a) There is a covering projection f:X_1->X_2 such that p_2 circlef=p_1.(b) For all x_1 in X_1 and x_2 in X_2 such that p_1(x_1)=p_2(x_2),p_1#(pi(X_1,x_1)) is conjugate in pi(X,p_1(x_1)) to a subgroup ofp_2#(pi(X_2,x_2)).(c) There exist x_1 in X_1 and x_2 in X_2 such that p_1(x_1)=p_2(x_2)and p_1(pi(X_1,x_1)) is conjugate in pi(X,p_1(x_1)) to a subgroup ofp2#(pi(X_2,x_2)).Then he has a corollary:Two objects in the category of connec covering spaces of aconnec locally path-connec space X are equivalent if and only iftheir fundamental groups (at some two points over the same point of X)map to conjugate subgroups of the fundamental group of X (at thispoint).I don't get it. It seems to me the corollary should be:Two objects in the category of connec covering spaces of aconnec locally path-connec space X are such that there is amorphism from each to the other if and only if their fundamentalgroups (at some two points over the same point of X) map to subgroupsof the fundamental group of X (at this point) which are such that eachis conjugate to a subgroup of the other.To replace are such that there is a morphism from each to the otherwith are equivalent, you would need to prove that every morphismfrom an object to itself is an === with Spanier's Algebraic Topology> In Chap. 2, Sec. 5 of Algebraic Topology Spanier proves the> following theorem:> Let p_1:X_1 ->X and p_2:X_2 -> X be objects in the category of> connec covering spaces of a connec locally path-connec space> X. The following are equivalent:> (a) There is a covering projection f:X_1->X_2 such that p_2 circle> f=p_1.> (b) For all x_1 in X_1 and x_2 in X_2 such that p_1(x_1)=p_2(x_2),> p_1#(pi(X_1,x_1)) is conjugate in pi(X,p_1(x_1)) to a subgroup of> p_2#(pi(X_2,x_2)).> (c) There exist x_1 in X_1 and x_2 in X_2 such that p_1(x_1)=p_2(x_2)> and p_1(pi(X_1,x_1)) is conjugate in pi(X,p_1(x_1)) to a subgroup of> p2#(pi(X_2,x_2)).> Then he has a corollary:> Two objects in the category of connec covering spaces of a> connec locally path-connec space X are equivalent if and only if> their fundamental groups (at some two points over the same point of X)> map to conjugate subgroups of the fundamental group of X (at this> point).> I don't get it. It seems to me the corollary should be:> Two objects in the category of connec covering spaces of a> connec locally path-connec space X are such that there is a> morphism from each to the other if and only if their fundamental> groups (at some two points over the same point of X) map to subgroups> of the fundamental group of X (at this point) which are such that each> is conjugate to a subgroup of the other.> To replace are such that there is a morphism from each to the other> with are equivalent, you would need to prove that every morphism> from an object to itself is an automorphism.> Can anyone help me here?the maps in part a) are coverings. thus in the corollary you get two spaces A and B with surjections between each other. put this together with some other details and go from there-- Using M2, Opera's revolutionary e-mail client: === Algebraic Topology> In Chap. 2, Sec. 5 of Algebraic Topology Spanier proves the> following theorem:Let p_1:X_1 ->X and p_2:X_2 -> X be objects in the category of> connec covering spaces of a connec locally path-connec space> X. The following are equivalent:(a) There is a covering projection f:X_1->X_2 such that p_2 circle> f=p_1.> (b) For all x_1 in X_1 and x_2 in X_2 such that p_1(x_1)=p_2(x_2),> p_1#(pi(X_1,x_1)) is conjugate in pi(X,p_1(x_1)) to a subgroup of> p_2#(pi(X_2,x_2)).> (c) There exist x_1 in X_1 and x_2 in X_2 such that p_1(x_1)=p_2(x_2)> and p_1(pi(X_1,x_1)) is conjugate in pi(X,p_1(x_1)) to a subgroup of> p2#(pi(X_2,x_2)).Then he has a corollary:Two objects in the category of connec covering spaces of a> connec locally path-connec space X are equivalent if and only if> their fundamental groups (at some two points over the same point of X)> map to conjugate subgroups of the fundamental group of X (at this> point).I don't get it. It seems to me the corollary should be:Two objects in the category of connec covering spaces of a> connec locally path-connec space X are such that there is a> morphism from each to the other if and only if their fundamental> groups (at some two points over the same point of X) map to subgroups> of the fundamental group of X (at this point) which are such that each> is conjugate to a subgroup of the other.To replace are such that there is a morphism from each to the other> with are equivalent, you would need to prove that every morphism> from an object to itself is an automorphism.Can anyone help me here?> the maps in part a) are coverings. thus in the corollary you get two > spaces A and B with surjections between each other. put this together with > some other details and go from thereI'm afraid I'm still === hypothesis obviously gets a lot of goodpublicity (see, e.g., the recent nytimes sciencesection). But even as a (beginning) graduate student,I don't quite understand why it is so important.I'm guessing a complete answer is too much to put inone post, so what I'd really like to see aresubject, or any good books which discuss some of thefruitful implications the === Riemann hypothesis obviously gets a lot of good> publicity (see, e.g., the recent nytimes science> section). But even as a (beginning) graduate student,> I don't quite understand why there are a lot of important mathematicalproofs that somewhere within them have a step that includes the phrase now,assuming that Riemann's hypothesis is correct. If Riemann ultimately turnsout to be incorrect, all these other proofs will have to === IntegerRing() -> RModule(IntegerRing(), 3).Now I would like to multiply f(n) with a 3x3 matrix of complexnumbehowever Magma resists to compute the result, claiming thosearguments have incompatible coefficient rings.Your help with this problem === IntegerRing() -> RModule(IntegerRing(), 3).>Now I would like to multiply f(n) with a 3x3 matrix of complex>numbehowever Magma resists to compute the result, claiming those>arguments have incompatible coefficient rings.> f := func< n | RModule(IntegerRing(), 3)![n,2*n,4*n] >; > f(4);( 4 8 16)> C:=ComplexField(); > RModule(C,3)!f(4);The following ought to work, but doesn't:>> RModule(C,3)!f(4); ^Runtime error in '!': Illegal coercionLHS: ModFldRHS: ModEDEltElementToSequence often provides a solution for coercion problems:> v:=RModule(C,3)!ElementToSequence(f(4));> v;( 4 8 16)> M:=MatrixAlgebra(C,3)![1,i,0,2+i,1,3,-1,2,-i];> M;[ 1 i 0][2 + i 1 3][ -1 2 -i]> v*M;( 4 + 8*i 40 + 4*i 24 - 16*i)Derek === of a circle is proportional to it's radius?> How do you prove that the circumference of a circle is proportional to > it's radius?> What's the modern version and how did the greeks prove it?> /davidVery simple. It's enough to accept that equal cords substends equalarcs.If you have a circumference and an inscrit polygon, its n sides(cords) are proportional to radius. If you now have a bigger polygon,the new n arcs must increase proportional to radius. Otherwise the newcords cannot === prove that the circumference of a circle is proportional to it's radius?The police and so forth only exist insofar as they can demonstratetheir authority. They say they're here to preserve order, but in factthey'd go absolutely mad if all the criminals of the world went onstrike for only a month. They'd be on their knees waiting for acrime. That's the only existence they have.William S. Burroughs (American writer) === Numbers!> 160 years ago today, on October 16, 1843, mathematician W. R. Hamilton> inven quarternions, also known as hypercomplex numbers.Who actually uses these numbers?I mean, ordinary complex numbers are abundant, even in engineering. But> hypercomplex? Are they rela to Minkowski space, i.e. special relativity> (simply because the dimension is four). Are they used in theoretical physics> otherwise?> computing rotations in 3 dimensions. Avoid the singularities in the> Euler angles that arise when you use matrices for such rotations. But> I have no idea how common this really is in computer code for 3d> graphics (such as video games).During the late 80's I worked for Lockheed on the Space Telescopeproject. We used quaternions to calculate the rotations of thetelescope, an actual practical example of the use of quaternions.I believe that Hamilton tried to recast a great deal of physics interms of quaternions after he inven them, but later physicists didnot follow in his footsteps in this particular regard. However, theycan be used in physics, as he showed.One can define quaternion algebras in contexts that do not involve thereal numbers. I know that a lot of research has been done on thesegeneral quaternion algebras, but I don't remember much of anythingabout it except that the idea was kind of cool.Robert Israel mentions that the quaternions can be used to prove thefour-square theorem proved in a different way by Lagrange. Theycertainly give a very easy way to explicitly figure out how torepresent the product of two sums of four squares as a some of foursquares using only addition and multiplication and thus the set ofsums of four squares is closed under multiplication in any ring. Theproof is very similar to the equivalent result for sums of two squaresthat uses the complex numbers. The ideas is that you multiply acomplex number (quaternion) by its conjugates, and you get the sums ofthe squares of its coefficients. It is relatively easy to show thatthe norm function given by the product of a complex number(quaternion) by its conjugate is a multiplicative homomorphism. AGerman mathematician whose name escapes me, but I am pretty sure it isAlbrecht Pfister, proved that in a field, the set of sums of 2^nsquares is always closed under multiplication, but it only works inrings up to 8. Presumably the octonions can be used to show this in asimilar but more ious way.It is my impression that the term hypercomplex number, suitablytransla into German, is still used in Germany to represent certainalgebraic structures, possibly maximal orders in finite-dimensionalalgebras over algebraic number fields, and there is a huge and verydifficult theory about these things. This theory can be used to provethings about number theory, and I once had some idea about some suchapplications since they came up in my thesis, but it has been a verylong time and I have === Numbers!> 160 years ago today, on October 16, 1843, mathematician W. R. Hamilton> inven quarternions, also known as hypercomplex numbers.> Who actually uses these numbers?Quaternions (actually Euler parameters) are used for modellingspacecraft attitude dynamics. The attitude quaternion relates theinertial reference frame with the spacecraft body-fixed frame. Thetime derivative of the attitude quaternion can be rela to theconventional angular velocity vector. See Chapter 12 of SpacecraftAttitude Determination and === Re: 160 Years of Hypercomplex Numbers!> 160 years ago today, on October 16, 1843, mathematician W. R. Hamilton> inven quarternions, also known as hypercomplex numbers.> Who actually uses these numbers?> Quaternions (actually Euler parameters) are used for modelling> spacecraft attitude dynamics. The attitude quaternion relates the> inertial reference frame with the spacecraft body-fixed frame. The> time derivative of the attitude quaternion can be rela to the> conventional angular velocity vector. See Chapter 12 of Spacecraft> Attitude Determination and Control, J Wertz ed., Reidel Pub. Co.> --Bob Wernerhttp://www.helsinki.fi/~lounesto/CLICAL.zipSolve quaternion problems with CLICAL, the Clifford === website http://www.xs4all.nl/~plast/Jempub.htm for someapplication of S3 geometry and 4D stereographic projection to 3D rotation animation,and on Extended Euler Angles as an alternative to quaternions for singularity-freetreatment of 3D rotations.Dance, yaw, pitch and roll. Enjoy.Johan E. Mebius === involute of a circle (which approximates the Archimedes Spiral at anglesmuch larger than 1 radian) is generally given in parametric form, where itscoordinates are: x = a*cos(phi) + a*phi*sin(phi) y = a*sin(phi) - a*phi*cos(phi) ,where a is the radius of the circle and phi is the angle genera by the radius as it rotates around the origin.Is a polar coordinate relation === formula for Circle Involute?> The involute of a circle (which approximates the Archimedes Spiral at angles> much larger than 1 radian) is generally given in parametric form, where its> coordinates are:> x = a*cos(phi) + a*phi*sin(phi)> y = a*sin(phi) - a*phi*cos(phi) ,> where a is the radius of the circle and phi is the angle genera by the > radius as it rotates around the origin.> Is a polar coordinate relation possible which also gives this curve?> Gener = a*sqrt(1+phi^2), andtheta = atan((sin(phi)-phi*cos(phi))/(cos(phi)+phi*sin(phi))),at least for a > 0 and phi near enough to 0.I don't think there is any nice parametrization of theta for arbitrary phi, since the form of the representation would have to change every time x === to Berkeley Problems in Mathematics, butgeared more towards the undergraduate, and perhaps more findingstuff rather than proving stuff? I would hope the problems would beof the same relative difficulty to an undergraduate as the BPM bookwould === book Problem-Solving through Problems. It is gearedtowards Undergrads. It is pretty good, too!Lurch> Is there a book similar to Berkeley Problems in Mathematics, but> geared more towards the undergraduate, and perhaps more finding> stuff rather than proving stuff? I would hope the problems would be> of the same relative difficulty to an undergraduate as the BPM === needed?> is quo as having written:>> But aren't I a success in posting?> No, you am not.Pay no heed to this symbol-sucking === selfishly and pathetically admit I never asked for a JSH solution.A JSK solution, now that's a scary thought. Just add water and stir,voila, JSH. Who'd want that?>-- >If you *still* believe that [my proof is wrong], then I have to think>that your mind is limi [...], and it may be the case that not>everyone *can* achieve that, as the mental wiring may not be there for>the task. -- , on faculties needed to accept his === selfishly and pathetically admit I never asked for a JSH solution.>A JSK solution, now that's a scary thought. Just add water and stir,>voila, JSH. Who'd want that?Well, you know, as they say If you're not part of the JSH solution,you're part of === Deprogramming needed?>[...]>>I selfishly and pathetically admit I never asked for a JSH solution.>>A JSK solution, now that's a scary thought. Just add water and stir,>>voila, JSH. Who'd want that?>Well, you know, as they say If you're not part of the JSH solution,>you're part of the JSH precipitate.Uh-huh. Actually I didn't know that they said that === JSH: Deprogramming needed?The police and so forth only exist insofar as they can demonstratetheir authority. They say they're here to preserve order, but in factthey'd go absolutely mad if all the criminals of the world went onstrike for only a month. They'd be on their knees waiting for acrime. That's the only existence they have.William S. Burroughs === Deprogramming needed?>The police and so forth only exist insofar as they can demonstrate>their authority. They say they're here to preserve order, but in fact>they'd go absolutely mad if all the criminals of the world went on>strike for only a month. They'd be on their knees waiting for a>crime. That's the only existence they have.>William S. Burroughs (American writer)> Guardian, 1966>huffyYou got it right that time. But that other post where yousigned your name John sort of gave it away. Giggle.For about a second this morning it looked like you'dfound someone who tends to agree with you. But youhad to make him up.How sad, a grown man === Deprogramming needed?>The police and so forth only exist insofar as they can demonstrate>their authority. They say they're here to preserve order, but in fact>they'd go absolutely mad if all the criminals of the world went on>strike for only a month. They'd be on their knees waiting for a>crime. That's the only existence they have.>>William S. Burroughs (American writer)> Guardian, 1966>>huffy> You got it right that time. But that other post where you> signed your name John sort of gave it away. Giggle.> For about a second this morning it looked like you'd> found someone who tends to agree with you. But you> had to make him up.> How sad, a grown man depending on imaginary playmates that way.Your Fuffy, my === Complex Analysis books?I am surprised no one has mentioned Needham, Visual Complex Analysis. I am not familiar with the book itself, but I have read high praise of it.As always, a good thing to do is to go to a university library and examine a few of the recommended books before purchasing one.-- === The subject says it -- however, I'd like to clarify> one detail: I'm looking for a book on *analysis*, as> opposed to Calculus (i.e., that covers rigorously> the concepts and proofs on Complex numbers and> Complex variables functions).> However, I'm just a hobbyist, so I'm not looking for> the ultimate, advanced reference book (i.e., I'm not> a mathematician or even a student in Mathematics; I'm> an engineer, who already knows (at least *knew* very> well) about complex numbebut I'm beginning> to appreciate and enjoy the rigorous side of maths,> and I find that complex numbers do mentioned my favorite first book on Complex Analysis. The author is Konrad Knopp and is in two volumes. I can't rememberthe title, but it is something like Introduction to the Theory ofFunctions of a Complex Variable. Whatever. It is throroughlyreadable, beautifully clear, and actually works in more general andyet more intuitive setting than most of the first books in ComplexVariables that I have seen. I am talking about the definition of theintegral of a complex function over a curve. After giving anintuitive geometrical, but still rigorous, approach, he shows how theusual approach which is more suitable for actual calculation isequivalent to his approach in the more common situation where thecurve is piece-wise differentiable. I read it after my first coursein real analysis.Kudos for attempting to learn this kind of === Recommendations on Complex Analysis books?> The subject says it -- however, I'd like to clarify> one detail: I'm looking for a book on *analysis*, as> opposed to Calculus (i.e., that covers rigorously> the concepts and proofs on Complex numbers and> Complex variables functions)._basic complex analysisj. e. marsden and m. j. hoffman> However, I'm just a hobbyist, so I'm not looking for> the ultimate, advanced reference book (i.e., I'm not> a mathematician or even a student in Mathematics; I'm> an engineer, who already knows (at least *knew* very> well) about complex numbebut I'm beginning> to appreciate and enjoy the rigorous side of maths,> and I find that complex === books?> The subject says it -- however, I'd like to clarify> one detail: I'm looking for a book on *analysis*, as> opposed to Calculus (i.e., that covers rigorously> the concepts and proofs on Complex numbers and> Complex variables functions).I was amazed by the way you've put it. This means that for you it isobvious that Calculus is *not* rigorous and it is *not* analysis. Haveyou ever read, for instance, Michael Spivak's Calculus or Introductionto Calculus and Analysis by Richard Courant and Fritz John?> However, I'm just a hobbyist, so I'm not looking for> the ultimate, advanced reference book (i.e., I'm not> a mathematician or even a student in Mathematics; I'm> an engineer, who already knows (at least *knew* very> well) about complex numbebut I'm beginning> to appreciate and enjoy the rigorous side of maths,> and I find that complex numbers do have a great> appeal.My favorite one: Theory of === Recommendations on Complex Analysis books?> The subject says it -- however, I'd like to clarify> one detail: I'm looking for a book on *analysis*, as> opposed to Calculus (i.e., that covers rigorously> the concepts and proofs on Complex numbers and> Complex variables functions).> I was amazed by the way you've put it. This means that for you it is> obvious that Calculus is *not* rigorous and it is *not* analysis. Have> you ever read, for instance, Michael Spivak's Calculus or Introduction> to Calculus and Analysis by Richard Courant and Fritz John?[...]I think he was referring to a fairly common convention; if fact, IIRC,in the preface to the second or the third edition to his book Spivaksaid he should have called it Analysis or something like that but itwere to late to change === Analysis books?>>The subject says it -- however, I'd like to clarify>>one detail: I'm looking for a book on *analysis*, as>>opposed to Calculus (i.e., that covers rigorously>>the concepts and proofs on Complex numbers and>>Complex variables functions).> I was amazed by the way you've put it. This means that for you it is> obvious that Calculus is *not* rigorous and it is *not* analysis. No, that's not what I meant.When I say Calculus in that context, I'm referring totypical College courses in math: a Calculus course wouldtypically emphasizes on the applications, and understandingthings well enough to apply them in different contexts(i.e., it is engineering orien).Another way to put it is that I want something that ismore like analysis for mathematicians, instead ofcalculus for engineers> My favorite one: Theory of Complex Functions by === on Complex Analysis books? linux)I still like Ahlfors for this, but it's a tad more advanced thanChurchill et al.-- Howard === Recommendations on Complex Analysis books?> The subject says it -- however, I'd like to clarify> one detail: I'm looking for a book on *analysis*, as> opposed to Calculus (i.e., that covers rigorously> the concepts and proofs on Complex numbers and> Complex variables functions).> However, I'm just a hobbyist, so I'm not looking for> the ultimate, advanced reference book (i.e., I'm not> a mathematician or even a student in Mathematics; I'm> an engineer, who already knows (at least *knew* very> well) about complex numbebut I'm beginning> to appreciate and enjoy the rigorous side of maths,> and I find that complex numbers do have a great> appeal. Others have recommended Churchill, Brown, & Verhey; if you have not studied complex variables at all, I would reommend that as a *start.* Afterwards (or if you already know the equivalent of most of CBV), take a look at Conway, Functions === Complex Analysis books?>The subject says it -- however, I'd like to clarify> one detail: I'm looking for a book on *analysis*, as> opposed to Calculus (i.e., that covers rigorously> the concepts and proofs on Complex numbers and> Complex variables functions).However, I'm just a hobbyist, so I'm not looking for> the ultimate, advanced reference book (i.e., I'm not> a mathematician or even a student in Mathematics; I'm> an engineer, who already knows (at least *knew* very> well) about complex numbebut I'm beginning> to appreciate and enjoy the rigorous side of maths,> and I find that complex numbers do have a great> appeal. > Others have recommended Churchill, Brown, & Verhey; if you have not > studied complex variables at all, I would reommend that as a *start.* > Afterwards (or if you already know the equivalent of most of CBV), take > a look at Conway, Functions of One Complex Variable.THE classic text on complex functions is Ahlfo_Complex Analysis_ . BArry Mazur has recently published a popular book on complexnumbers _Imagining Numbers_. I would also recommend _Complex Numbersand Geometry_ by Hahn. Finally, a great old book: Theory ofFunctions_ by === Analysis books?> THE classic text on complex functions is Ahlfo_Complex Analysis_ .> BArry Mazur has recently published a popular book on complex> numbers _Imagining Numbers_. I would also recommend _Complex Numbers> and Geometry_ by Hahn. Finally, a great old book: Theory of> Functions_ by Caratheodory.I second the Ahlfors book. We used it as our Complex Analysistextbook when I was a grad student at the === Complex Analysis books?>>THE classic text on complex functions is Ahlfo_Complex Analysis_ .>> BArry Mazur has recently published a popular book on complex>>numbers _Imagining Numbers_. I would also recommend _Complex Numbers>>and Geometry_ by Hahn. Finally, a great old book: Theory of>>Functions_ by Caratheodory.>>I second the Ahlfors book. We used it as our Complex Analysis>textbook when I was a grad student at the University of Michigan.> I admit to never having looked at Ahlfobut I have heard that it is a rather intense book - terse, with very difficult exercises. My impression is that it would be at too high a level for a mathematical hobbyist (as the OP identified himself).-- === recommend Schaum's Outline of Complex Variables, by Spiegel.Best,Kerry Soileau> The subject says it -- however, I'd like to clarify> one detail: I'm looking for a book on *analysis*, as> opposed to Calculus (i.e., that covers rigorously> the concepts and proofs on Complex numbers and> Complex variables functions).> However, I'm just a hobbyist, so I'm not looking for> the ultimate, advanced reference book (i.e., I'm not> a mathematician or even a student in Mathematics; I'm> an engineer, who already knows (at least *knew* very> well) about complex numbebut I'm beginning> to appreciate and enjoy the rigorous side of maths,> and I find === === screwdriver Re: new way of describing ellipse for mathSubject: Robertson versus ips screwdriver Re: new way ofdescribing ellipse for math Archimedes Plutonium NOdtgEMAIL whole entire Universe is just one big atom where dots ofthe electron-dot-cloud are galaxies sci.physics, sci.physics.electromag, sci.math> (snipped)If you use two rectangles, I believe you can generate a both a unique> ellipse or circle by connecting their verticies, so long as the> rectangles do not have any identical verticies. I suppose if you were> to take a limit case, you might be able to generate some equation that> would give the result you're eight outer verticies, and you get an ellipse. As the> verticies converge on each other, you maintain the ellipse. If you> took the limit as V1 -> V1', V2 -> V2' etc, you might be able to> generate a single equation for the ellipse in terms of the verticies> of the rectangle(s).Before I leave this subject momentarily I want to add another topicwhichclosely relates to the issues above.The mathematical proof that a Robertson screwdriver is the ultimate infasteningfor screwdriver design in that the square inscribed inside the circleprovides the maximum torque. The Robertson was discovered the best inscrewing down airplane screws.A hexagonal gets into trouble in that the increasing of sides becomesalmost a circle itself and thus strip the grip. This is apparent asthescrew becomes smaller and smaller then the hexagonal is almost acircleitself and with a tiny bit of torque you get a circle inside a circleviastripping.The regular screwdriver compared to Robertson can be quantified as perareaoftorquing in that a Robertson is like having about 4 regularscrewdriverssimultaneously torquing 1 screw. I would guess it is between 3 or 4.Theips is better than a regular by about twice but that the Robertsonisbetter than the ips by about twice.The intriguing question about the above is that in an AtomTotalitysincethe entire Universe is a big atom then it has a spin. Spin of atomsisnot like a spinning top or like an Earth rotating on its axis. Spin isfundamental characteristic of atoms and no scientist has been able togivesome sort of common day description of what atomic spin may be. Butperhapsthe idea that atoms have either a spherical or elliptical geometry andplusthe idea that they may haveinternal rectangles that are Forces. Not that there is some CosmicScrewdriver that turns the AtomTotality but that the rectangles areseen asthe Robertson orips markings in the Atom geometry and these internal rectanglescausethe atom to spin. Imagine for a moment that you have a screw that isips with its markings but you do not have a screwdriver and thosemarkings alone cause the screw to rotate or spin. This above may ormay notyield some future fruit, but I give it a low probability.Archimedes Plutonium, a_plutonium@hotmail.comwhole entire Universe is just one big atom where dotsof the === physical reality Re: Robertson versus ips screwdriver === Re:Subject: what spin 1/2 is in physical reality Re: Robertsonversus ips screwdriver Re: new way of describing ellipse for math Archimedes Plutonium NOdtgEMAIL whole entire Universe is just one big atom where dots ofthe electron-dot-cloud are galaxies sci.physics, sci.physics.electromag, sci.math> (snipped)If you use two rectangles, I believe you can generate a both a unique> ellipse or circle by connecting their verticies, so long as the> rectangles do not have any identical verticies. I suppose if you were> to take a limit case, you might be able to generate some equation that> would give the result you're eight outer verticies, and you get an ellipse. As the> verticies converge on each other, you maintain the ellipse. If you> took the limit as V1 -> V1', V2 -> V2' etc, you might be able to> generate a single equation for the ellipse in terms of the verticies> of the rectangle(s).>> Before I leave this subject momentarily I want to add another topic which> closely relates to the issues above.> The mathematical proof that a Robertson screwdriver is the ultimate in> fastening> for screwdriver design in that the square inscribed inside the circle> provides the maximum torque. The Robertson was discovered the best in> screwing down airplane screws.> A hexagonal gets into trouble in that the increasing of sides becomes> almost a circle itself and thus strip the grip. This is apparent as the> screw becomes smaller and smaller then the hexagonal is almost a circle> itself and with a tiny bit of torque you get a circle inside a circle via> stripping.> The regular screwdriver compared to Robertson can be quantified as per area> of> torquing in that a Robertson is like having about 4 regular screwdrivers> simultaneously torquing 1 screw. I would guess it is between 3 or 4. The> ips is better than a regular by about twice but that the Robertson is> better than the ips by about twice.> The intriguing question about the above is that in an AtomTotality since> the entire Universe is a big atom then it has a spin. Spin of atoms is> not like a spinning top or like an Earth rotating on its axis. Spin is> fundamental characteristic of atoms and no scientist has been able to give> some sort of common day description of what atomic spin may be. But perhaps> the idea that atoms have either a spherical or elliptical geometry and plus> the idea that they may have> internal rectangles that are Forces. Not that there is some Cosmic> Screwdriver that turns the AtomTotality but that the rectangles are seen as> the Robertson or> ips markings in the Atom geometry and these internal rectangles cause> the atom to spin. Imagine for a moment that you have a screw that is> ips with its markings but you do not have a screwdriver and those> markings alone cause the screw to rotate or spin. This above may or may not> yield some future fruit, but I give it a low probability.I think I may have stumbled upon what spin 1/2 is in terms ofphysicalreality. We know it is not like a spinning top. And we know it isfundamentalparameter.So what is it??I believe the above dives into what it is. If we think of a subatomicwith 1/2 spin of quantum number. Then, what it is is that every suchhas internal parts and these internal parts have dual forces of these(1)Coulomb(2) StrongNuclear paired to WeakNuclear and (3) Gravity paired toAntigravity.And these forces take for instance Gravity paired to Antigravityinside anelectronwith spin 1/2. The insides of that electron has the force of Gravityand thepaired force of Antigravity where you take the entire electron as aellipsoidor spheroid which can have inscribed 2 rectangular solids each ofthese solidsrepresents either the Gravity Force or the Antigravity force and thatthe 2forces are like a ips head screwdriver (the crosses of the ipshead)and represent the inscribed rectangular solids.So the entire electron with its 1/2 spin is the ellipsoid and theellipsoidcan be broken down into 2 rectangular solids which is the cross in theipsheadscrewdriver. And so the ellipsoid is turned or spinned (1/2 spin)because ofthe cross inside the ellipsoid.Our nightsky of the 231Pu AtomTotality is the inside an electron(probably thelast 6 electrons) and it must have a spin. And the spin is caused bythedualing forces of gravity to antigravity.thedual forces of StrongNuclear paired to WeakNuclear.So in this manner, we can get a mental picture of what the quantumnumber ofspin is. It is caused by dual forces which create the spin.If the above is correct in part or whole, then the spin quantum numberof 1/2should have variations since the forces of Gravity to Antigravity andStrongNuclear to WeakNuclear are different and an experiment can beset upto see variations.Archimedes Plutonium, a_plutonium@hotmail.comwhole entire Universe is just one big === atom where dotsof the electron-dot-cloud are galaxiesSubject: Re: what spin 1/2 is in physical reality Re: Robertson versus ips screwdriver orbitting a globe at a fixed radiusfrom the north to the south pole.At the same time take this circular orbit andstart it precessing at twice the rate at whichthe point is travelling within the orbit.The point will make one complete trip around the globein the east-west or west-east direction (whicheverway you precessed it) by the time it getsto the south pole. Then it will make anothertrip around, cutting all the lines of longitude,on its way back up to the north pole.Place another point exactly opposite thefirst. It follows exactly the same path BUTit is THE ONLY OTHER POINT which follows thatpathway. Divide the ring into four, then eight, thensixteen points. You will find that sixteen pointscompletes the galaxy pattern:http://rapfast.petcom.com/~john/galaxypattern.gifThen consider this; growth of rings of 16can be directly rela to the Periodic Table:http://rapfast.petcom.com/~john/periodicpattern.GIFTHIS === Re: Newsgroup survey: Math and personality assessment> It seems to me that there have been debates over math concepts I> thought basic, so here's a quick survey:> 1. Before I mentioned it, had you ever heard of the distributive> property?Yes, a*(b+c) = a*b + a*c and (a+b)*c = a*c + b*c> 2. In your experience, is math quirky?quirky = adjective: informal terms; strikingly unconventionalNo.> 3. Do you think that mathematics is an extremely difficult discipline> that only experts are really good at handling?Follows from the definition of an expert.> 4. What is the distributive property?See 1.> 5. Is a math proof perfect?A proof is correct. If a perfect proof is a shortestpossible proof then not neccessarily. Can you tellwhat is a perfect proof ?> 6. Do you consider yourself to be a reasonable person?Yup, but it does not imply that I am.> 7. If a mathematical argument is explained to you in detail, using> basic algebra, if it's correct, would you admit that, even to a> hostile crowd, like even if many posters on sci.math would call you> names and insult you for admitting it?Maybe. Perhaps wouldn't bother.> === Newsgroup survey: Math and personality assessment linux)> The police and so forth only exist insofar as they can demonstrate> their authority. They say they're here to preserve order, but in fact> they'd go absolutely mad if all the criminals of the world went on> strike for only a month. They'd be on their knees waiting for a> crime. That's the only existence they have.> William S. Burroughs (American writer)> Guardian, 1966> huffyWhere huffy == John Correy (and so is self-identical)?In another post by huffy, you signed John (and clearly spoke asJohn Correy). Why the (additional) pseudonym?-- We want a single platform. We're trying to get there using thecarrot, or blackmail, or rewards, or whatever you call it. -- Madison, WI, superintendent Rainwater grasps subtlety in === Math and personality assessmentThe police and so forth only exist insofar as they can demonstrate>> their authority. They say they're here to preserve order, but in fact>> they'd go absolutely mad if all the criminals of the world went on>> strike for only a month. They'd be on their knees waiting for a>> crime. That's the only existence they have.William S. Burroughs (American writer)>> Guardian, 1966huffy>Where huffy == John Correy (and so is self-identical)?>In another post by huffy, you signed John (and clearly spoke as>John Correy). >Why the (additional) pseudonym?Most of the posts from huffy are not signed John. Seems clear tome that he's tired of having so many people disagree with himso he's inven a imaginary playmate - he slipped signing oneof huffy's posts John.Makes perfect sense - if you were him you'd probably be inventingpeople who appeared to support your positions as well. Teehee...>-- >We want a single platform. We're trying to get there using the>carrot, or blackmail, or rewards, or whatever you call it.> -- Madison, WI, superintendent Rainwater grasps subtlety in the> operating system === assessment... >Where huffy == John Correy (and so is self-identical)? >In another post by huffy, you signed John (and clearly spoke as >John Correy). >Why the (additional) pseudonym? > Most of the posts from huffy are not signed John. Seems clear to > me that he's tired of having so many people disagree with him > so he's inven a imaginary playmate - he slipped signing one > of huffy's posts John.Perhaps an idea for JSH? Setting up tens of imaginary playmates, === and personality assessment> ...>Where huffy == John Correy (and so is self-identical)?>>In another post by huffy, you signed John (and clearly spoke as>John Correy). >>Why the (additional) pseudonym?Most of the posts from huffy are not signed John. Seems clear to> me that he's tired of having so many people disagree with him> so he's inven a imaginary playmate - he slipped signing one> of huffy's posts John.> Perhaps an idea for JSH? Setting up tens of imaginary playmates, all> agreeing with him?Well, well, well! If it === survey: Math and personality assessment > ... >Where huffy == John Correy (and so is self-identical)? >In another post by huffy, you signed John (and clearly spoke as >John Correy). Why the (additional) pseudonym? > Most of the posts from huffy are not signed John. Seems clear to > me that he's tired of having so many people disagree with him > so he's inven a imaginary playmate - he slipped signing one > of huffy's posts John. > Perhaps an idea for JSH? Setting up tens of imaginary playmates, all > agreeing with him? > Well, well, well! If it === Newsgroup survey: Math and personality assessment> Well, well, well!> Corrney.Correy scores two responses. Has he found a successfulnew strategy to get people to answer his trolls? - === assessment <1217rvcn9u55s9tgjrr540q7arcchjsrpe@4ax.com> linux)> Well, well, well! If it ain't (Suk My) Dik! What's up, dude?You have on a couple of occasions now pos indignation that I oncetold you to kiss my ass. You've done this on newsgroups unrela tosci.math, so great was your offense at this verbal assault that youfelt it appropriate to warn others of my hideous crime.Now, I'm not saying you're a hypocrite, but one must be concerned withappearances, mustn't one? Isn't it a little hard to present acoherent image of justified moral outrage over my insult[1] whileusing language that the casual observer might mistake for crude abuse?Well, I suppose I shouldn't tell an expert how to proceed. No onedoes righteous indignation as well as John Correy. Or at least no onedoes it as often.Footnotes: [1] Which you refer to as a very coarse reply --- although it wasnot a reply to the post you pretend it was, indeed did not even occurin that thread, I think.-- If you have a really big idea, you can get a measure of how big it isREALLY, REALLY, *REALLY*, BIG DISCOVERY!!! --, on being === assessment> Well, well, well! If it ain't (Suk My) Dik! What's up, dude?> You have on a couple of occasions now pos indignation that I once> told you to kiss my ass. You've done this on newsgroups unrela to> sci.math, so great was your offense at this verbal assault that you> felt it appropriate to warn others of my hideous crime.> Now, I'm not saying you're a hypocrite, but one must be concerned with> appearances, mustn't one? Isn't it a little hard to present a> coherent image of justified moral outrage over my insult[1] while> using language that the casual observer might mistake for crude abuse?> Well, I suppose I shouldn't tell an expert how to proceed. No one> does righteous indignation as well as John Correy. Or at least no one> does it as often.> Footnotes: > [1] Which you refer to as a very coarse reply --- although it was> not a reply to the post you pretend it was, indeed did not === survey: Math and personality assessment > Well, well, well! If it ain't (Suk My) Dik! What's up, dude?...My, oh my. You make a joke on my name, and in response I make one on your-- === assessmentThe police and so forth only exist insofar as they can demonstrate>> their authority. They say they're here to preserve order, but in fact>> they'd go absolutely mad if all the criminals of the world went on>> strike for only a month. They'd be on their knees waiting for a>> crime. That's the only existence they have.William S. Burroughs (American writer)>> Guardian, 1966huffy> Where huffy == John Correy (and so is self-identical)?> In another post by huffy, you signed John (and clearly spoke as> John Correy).Presumably it wants to avoid killfiling. I have no idea why itthinks that the opinion of this late novelist, heroin addictand wife-murderer is at all relevant though. These huffy postsare considerably === Newsgroup survey: Math and personality assessment <87smkswqrm.fsf@phiwumbda.org> Discussion, linux)>> In another post by huffy, you signed John (and clearly spoke as>> John Correy).> Presumably it wants to avoid killfiling. I have no idea why it> thinks that the opinion of this late novelist, heroin addict> and wife-murderer is at all relevant though. These huffy posts> are considerably more ious than the rantings of D S Kabatoff.Posting the exact same quote 47 times is an odd way to avoidkillfiling.-- Jesse HughesBasically there are two angry groups. I am a harsh force ofone. Against me is a society of mathematicians. So far it's been adraw. -- JSH gives === survey: Math and personality assessment>In another post by huffy, you signed John (and clearly spoke as> John Correy).Presumably it wants to avoid killfiling. I have no idea why it>> thinks that the opinion of this late novelist, heroin addict>> and wife-murderer is at all relevant though. These huffy posts>> are considerably more ious than the rantings of D S Kabatoff.>Posting the exact same quote 47 times is an odd way to avoid>killfiling.True. And your point is what, exactly? I mean it's not like thisis the only thing we've seen him take an odd approach to...>-- >Jesse Hughes>Basically there are two angry groups. I am a harsh force of>one. Against me is a society of mathematicians. So far it's been a>draw. -- JSH gives another display of keen === assessment>In another post by huffy, you signed John (and clearly spoke as> John Correy).Presumably it wants to avoid killfiling. I have no idea why it>> thinks that the opinion of this late novelist, heroin addict>> and wife-murderer is at all relevant though. These huffy posts>> are considerably more ious than the rantings of D S Kabatoff.> Posting the exact same quote 47 times is an odd way to avoid> killfiling.Well I have now killfiled Correy under its new alias. Choosinga new username is a way of forcing one's postings on peoplewho have chosen to killfile one. Kabatoff does this too.Perhaps I should jus killfile all posts from yahoo.comas this ISP seems === Newsgroup survey: Math and personality assessment linux)> A math proof is an argument which beginning with some true statement> proceeds by logical steps to a conclusion which then must be true.James, this is not the definition of a proof. Not all proofs beginwith a true statement (read: with an axiom, I suppose). Very manyproofs begin with an assumption -- an assumption that may be provenfalse in the end.I know you're stupid. You can't even grasp the use of commas whenaddressing your correspondents. Nonetheless, try to grasp this plain,basic fact. It is not the case that a proof is an argument beginningwith some true statement.You pretend to be a logical man. In order to make the pretensionslightly more plausible, you should drop this baby definition of aproof. If you'll actually read a proof or two, you'll realize howstupidly inadequate your characterization is.-- Jesse HughesBasically there are two angry groups. I am a harsh force ofone. Against me is a society of mathematicians. So far it's been adraw. -- JSH gives another display of keen === certain posters see the sci.math newsgroup as their> personal territory, and have a territorial reaction to people posting> there. They feel they can control the newsgroup content, by> controlling posters by, you guessed it, insulting them.They don't drink it, they don't eat it, infact, they don't need it atall - but the dogs always bark when someone else touches the === Some of you may have realized that I have remarkable power to draw> attention on several newsgroups to the extent that I even have my own> dedica replielike Uncle Al or David Ullrich, who like to> obsessively insult me! Anyone have a good term for people who just> follow around a popular poster insulting him? Well I call them critic> trolls.I think critic of trolls is more accurate, as you of course are thetroll. That real mathematicians are still willing to even look atyour posts is something you ought to feel honored, since frankly theirtime is far more valuable than yours.As for calling yourself a popular poster, I'm not sure thatfrequency of posting equates to popularity. Although your infamy inpoor proof-writing has made you well known, it does not mean you areconsidered popular by any conceivable stretch of the definition.Jonathan === may have realized that I have remarkable power to draw>attention on several newsgroups to the extent that I even have my own>dedica replielike Uncle Al or David Ullrich, who like to>obsessively insult me! Anyone have a good term for people who just>follow around a popular poster insulting him? Well I call them critic>trolls.Around here we call them === mathematicians.Alan-- Defendit numerusSubject: Re: JSH: My use remarkable power to draw : >attention on several newsgroups to the extent that I even have my own : >dedica replielike Uncle Al or David Ullrich, who like to : >obsessively insult me! Anyone have a good term for people who just : >follow around a popular poster insulting him? Well I call them critic : >trolls. : : Around here we call them mathematicians.Who we? People of good will call THOSE people .That is not inconsistent with their also being mathematicians,but the overlap is a BAD thing. The people who merit mathematicianin the honorific sense in which you are trying to use it are peoplelike Dik Winter, who, even in the face of potent distractions, are willingto stay focused on mathematics.-- --- It's difficult ... you need to be uni to have any strength, but internal issues have to be addressed. --- E. Ray Lewis, on === initials>Some of you may have realized that I have remarkable power to draw>attention on several newsgroups to the extent that I even have my own>dedica replielike Uncle Al or David Ullrich, who like to>obsessively insult me! Like when I called you a ing piece of dog. Poor torturedJames.No, wait, actually it was you who called me a ing piece ofdog. Never mind...>Anyone have a good term for people who just>follow around a popular poster insulting him? Well I call them critic>trolls.>In any event, so like I said I have this drawing power, and lots of>people besides Uncle Al and David Ullrich get upset with me over>strange things, and there's little doubt there are people out there>bothered by my use of my initials JSH in subject lines, as if it's>some kind of arrogant thing, so here's the story as to how I happened>to start using my initials in subject lines.>Let me take you back a bit.>I star looking for simple yet profound math discoveries back in>1995. My thinking was that if I could look in places that others>thought were well-worked and find some spectacular, but basic result,>I could make money.>Ok, so yeah, I'm in it for the money.Indication number 37 of your utter cluelessness regarding almosteverything.>In any event, at first I talked directly to mathematicians, primarily>at math journals, and found that when I made mistakes with my>mathematics, it was embarrassing and time consuming to find someone>else to talk ro about new ideas, and then in 1996, I discovered>Usenet.>It seemed like the perfect place! I could talk about mathematics on>the newsgroup sci.math where other people were talking about math. >Maybe I'd even get some people who would be sympathetic to my idea.>What I found was a lot of hostility.>Apparently certain posters see the sci.math newsgroup as their>personal territory, and have a territorial reaction to people posting>there. They feel they can control the newsgroup content, by>controlling posters by, you guessed it, insulting them.This bit about controlling posters needs to be answered. In fact_nobody_ has _ever_ taken any steps to try to prevent you fromposting to sci.math. The _only_ person in all this who _has_ triedto control posters is _you_: You've complained to my _employer_about various things, and later admit explicitly that thereason you made those complaints was to try to get me to stopreplying to your posts.>Well I ended up in lots of arguments, but meanwhile kept posting my>ideas, as I realized that maybe I'd signed on to a really big task,>looking for a spectacular but simple proof, and I shif more to idea>generation mode, you know--brainstorming.>Well that *infuria* the territorial posters who became more>energetic in their insults, as like I said, they'd try to insult>posters like me into shutting up.>And I didn't exactly like all of those attacks, but hey, I kept at>coming up with ideas and posting them, but found myself first angry,>then intrigued when one poster--angry at *accidentally* reading my>posts--sugges that I give some identifier so that people could know>when I was the one who star a thread.>So at first I replied haughtily about my freedom of speech, and right>to post whatever subject line I wan. But then I thought, hey,>that's not a bad idea!!!>So I added my initials to the subject line to show that it was me>posting, as reques.>Now when I see a need, like now, to identify who star a thread, I>add JSH to the front, but of course, Usenet sparks imitatoso>sometimes other posters will stick *my* initials on a thread THEY>star, which is just one of those things.>In any event, in case you were wondering, no, I didn't think of>tossing my initals on subject lines--I was *ordered* to do it by a>poster angry at not always being able to tell threads that I>star!!!>Isn't Usenet a wacky, wacky world?>>My math discoveries, found for === My use of my initials Discussion, linux)> The concept of free speech encompasses the right of people to say stupid > and hateful things. The Supreme Court said you can burn the American > flag or claim that Jerry Falwell had sex with his mother in an outhouse, > and that those things are protec speech. I for one defend your right > to say whatever the hell you want.You can burn the flag, but you have no right to say that Jerry Falwellhad sex with his mother in an outhouse (unless it's true). There arelibel laws.-- Jesse Hughes If you really think there's a bug you should report a bug. Maybeyou're not using it properly... It turns out Luddites don't know howto use software properly, so you should look into that. === Assistant Professor at the University of Montana.>> The concept of free speech encompasses the right of people to say stupid >> and hateful things. The Supreme Court said you can burn the American >> flag or claim that Jerry Falwell had sex with his mother in an outhouse, >> and that those things are protec speech. I for one defend your right >> to say whatever the hell you want.>You can burn the flag, but you have no right to say that Jerry Falwell>had sex with his mother in an outhouse (unless it's true). There are>libel laws.->Context<-. Fishfry's presentation is indeed way too superficial. The case in question, which ->did<- involve a claim that JerryFalwell had had sex with his mother in an outhouse, and a suit forlibel against Hustler magazine, Hustler Magazine v. Falwell, 485U.S. 46 (1988)http://caselaw.lp.findlaw.com/scripts/getcase.pl?court= us&vol=485&invol=46decided 8-0, with Chief Justice Rehnquist writing the opinion for theCourt, involved Hustler magazine's parody of a Campari liquor adabout first times. The opinion states in part: We conclude that public figures and public officials may not recover for the tort of intentional infliction of emotional distress by reason of publications such as the one here at issue without showing in addition that the publication contains a false statement of fact which was made with actual malice, i. e., with knowledge that the statement was false or with reckless disregard as to whether or not it was true. [...] Here it is clear that respondent Falwell is a public figure for purposes of First Amendment law. 5 The jury found against respondent on his libel claim when it decided that the Hustler ad parody could not reasonably be understood as describing actual facts about [respondent] or actual events in which [he] participa. App. to Pet. for Cert. C1. The Court of Appeals interpre the jury's finding to be that the ad parody was not reasonably believable, 797 F.2d, at 1278, and in accordance with our custom we accept this finding. Respondent is thus relega to his claim for damages awarded by the jury for the intentional infliction of emotional distress by outrageous conduct. But for reasons heretofore sta this claim cannot, consistently with the First Amendment, form a basis for the award of damages when the conduct in question is the publication of a === Re: JSH: My use of my initials <87znf0wyzo.fsf@phiwumbda.org> Discussion, linux)>The concept of free speech encompasses the right of people to say stupid > and hateful things. The Supreme Court said you can burn the American > flag or claim that Jerry Falwell had sex with his mother in an outhouse, > and that those things are protec speech. I for one defend your right > to say whatever the hell you want.>>You can burn the flag, but you have no right to say that Jerry Falwell>>had sex with his mother in an outhouse (unless it's true). There are>>libel laws.> ->Context<-. Fishfry's presentation is indeed way too superficial. I didn't realize he was referring to an actual claim was not presen as afactual claim but only as part of a parody, that rather changes things.-- Run mathematicians, RUN!!! I'm coming for you. It may take a fewmonths, but I'll get [computer verification of my proof] and then yourlives will be ended as you previously knew it. -- JSH meets === concept of free speech encompasses the right of people to say stupid> and hateful things. The Supreme Court said you can burn the American> flag or claim that Jerry Falwell had sex with his mother in an outhouse,> and that those things are protec speech. I for one defend your right> to say whatever the hell you want.> You can burn the flag, but you have no right to say that Jerry Falwell> had sex with his mother in an outhouse (unless it's true). There are> libel laws.> Jesse HughesWell, I wouldn't worry about libel from JSH. His manifest bad faith, not tosay incompetence, render him incapable of harming anyone with his words.Moreover, as an ancient legal saying goes, The abuse of a humble tongue ischeap.> If money is your motivation, you'd do better selling penis enlargementpills on the Internet.A good point, not often made in Harrisland. People make money in all mannerof fraud: astrology, formulas to beat the lottery, age-reversing drugs, andso on without limit. But they make money by indulging the _buyer's_ vanityand ambition, not their own! Harris is a narcissist and narcissists wantattention, not money per se. But get famous in mathematics? Grosslyillogical. Ask the man in the street to name one living mathematician. Inall likelihood you'll get John Nash (because of the illness and the movie)or else no answer at all.There is another thing that makes math such an illogical area in which toattempt fraud: The standards of evidence are higher in this field than inany other. I theorise that someone, maybe a teacher or teacheonce toldHarris that he was good at math; when his narcissism later kicked in, mathwas therefore the area in which he assumed he must be Superman.One more bit about narcissism. In JSH's mind, these are two incontrovertibleaxioms:1) JSH is right.2) JSH is great.This at once explains JSH's inability to learn, or === initials <87znf0wyzo.fsf@phiwumbda.org> <95Isb.44352$jy.37753@clgrps13> Discussion, linux)> fishfry>> The concept of free speech encompasses the right of people to say stupid>> and hateful things. The Supreme Court said you can burn the American>> flag or claim that Jerry Falwell had sex with his mother in an outhouse,>> and that those things are protec speech. I for one defend your right>> to say whatever the hell you want.You can burn the flag, but you have no right to say that Jerry Falwell>> had sex with his mother in an outhouse (unless it's true). There are>> libel laws.>> Jesse Hughes> Well, I wouldn't worry about libel from JSH. His manifest bad faith, not to> say incompetence, render him incapable of harming anyone with his words.> Moreover, as an ancient legal saying goes, The abuse of a humble tongue is> cheap.No one was talking about whether JSH would sue for libel. -- Jesse HughesYou see 300 of something, anything, and you go `[Man], that's a lot ofstuff.' -- Jim Bigler, quo in the Pittsburgh Post-Gazette.