mm-4409 === Subject: Re: JSH: What is surrogate factoring? Once more. >IN arguing about research I call surrogate factoring, I bump into this >weird thing where posters seem to be lost on what is actually going >on, so I thought I'd start a thread informing, yet again, what >surrogate factoring is. Years ago, while thinking about RSA encryption, I wondered to myself >if instead of directly attacking a large number that you wanted to >factor, you might instead factor some other number and in that way >factor the target. I termed the concept: surrogate factoring. So, to repeat, years ago, as in about four years ago I think it was, I >was just kind of wondering about factoring because I was thinking >about RSA encryption, and I wondered if you might go after a large >composite that was otherwise hard to factor, by instead factoring some >other number. To me a good name for the concept was surrogate factoring, so it was >called surrogate factoring. Now years later I have finally settled in my own mind that >mathematically the concept reduces to considering x^2 = y^2 mod T and k = 2x mod T and equations that result from those two basic congruences, where T is >the target, which took me about three years to figure out. With those two relations I found that my surrogate to factor is given >by deriving (x+k)^2 = y^2 + 2k^2 + nT as then the surrogate S, is S = 2k^2 + nT and the big question is, how do you pick k and n? It is indeed the big question. For those of you who wonder how it works from there, it's trivial >algebra that if you let 4f_1*f_2 = 2k^2 + nT Why the 4? There is no guarantee that S is a multiple of 4 unless you constrain k and n appropriately. Why not just say: S = f_1 * f_2 = 2k^2 + nT >then x+y = 2f_1 - k and x-y = 2f_2 - k or x + y = f_1 - k x - y = f_2 - k rossum >so once you factor the surrogate S, you just loop through solutions >for x+y and x-y, by going through the various possible values for f_1 >and f_2, and check the gcd with T. James Harris === Subject: How to identify (regression) bugs in _Maple_ (a rule of index) (* NOT applicable to any computer algebra system *) 1. Put your index on (virtually) any Maple function. 2. Dig insistently enough. 3. Voila! Example. Maple 11: # a tip of the tip of the Maple bug iceberg evalf(Int(exp(-z^(1/5)), z= 0..infinity)); evalf(Int(exp(-z^(1/6)), z= 0..infinity)); evalf(Int(exp(-z^(1/7)), z= 0..infinity)); evalf(Int(exp(-z^(1/8)), z= 0..infinity)); 120.0000000 720.0000000 5040.000000 Float(infinity) Best wishes, Vladimir Bondarenko VM and GEMM architect Co-founder, CEO, Mathematical Director http://www.cybertester.com/ Cyber Tester, LLC http://maple.bug-list.org/ Maple Bugs Encyclopaedia http://www.CAS-testing.org/ CAS Testing === Subject: Re: How to identify (regression) bugs in _Maple_ (a rule of index) > (* NOT applicable to any computer algebra system *) 1. Put your index on (virtually) any Maple function. > 2. Dig insistently enough. > 3. Voila! Example. Maple 11: # a tip of the tip of the Maple bug iceberg evalf(Int(exp(-z^(1/5)), z= 0..infinity)); > evalf(Int(exp(-z^(1/6)), z= 0..infinity)); > evalf(Int(exp(-z^(1/7)), z= 0..infinity)); > evalf(Int(exp(-z^(1/8)), z= 0..infinity)); 120.0000000 > 720.0000000 > 5040.000000 > Float(infinity) Oh m.8an, you newwer l.9arn it ... Plotting shows very slow decay and computing where the tail becomes less than 1e-13 (I work with 14 Digits) gives z beyond 1e-10, so I am not too astonished that a numerical integrator might give up: it estimates the integrand as no longer decaying, I guess. For slow decay & no oscillations the double exponential method is a good first idea, so one uses that more specific command instead: evalf(Int(exp(-z^(1/8)), z= 0..infinity, method = Dexp)); 40319.999998902 Otherwise increase precision (and MMA does it internally by 10 Digits IIRC, no?). === Subject: Re: How to identify (regression) bugs in _Maple_ (a rule of index) <5ju1k7F19v9cU1@mid.individual.net> This is nothing but lack of competence on part of Maplesoft. Consider Mathematica 6.0.1 NIntegrate[Exp[-z^(1/8)], {z, 0, Infinity}] 40320. Voila! AV> Otherwise increase precision Oh no. This devours my time, my main life resource. This SHOULD be done automatically. And this can be done. AV> (and MMA does it internally by 10 Digits IIRC, no?). Anything Mathematica does without wasting my time is good if I enjoy a correct answer... or at least a warning that the answer might be incorrect - which situations are quite typical with Mathematica. By the way, I'd like to add that Mathematica 6 became a really better system as compared with Mathematica 5.2. As a Maplesoft customer, I am unhappy that Maple fails at a wide range of computations. I'd prefer to have 2 competing CASs. But with the current Maplesoft direction of movement, they will make Maple fairly soon uncompetitive in the marketplace. This example is just a single grain of sand taken from Maple's defect sanddrift rising. Unlike you and the other slow human being customers, we are equipped with an expert high-performance QA system which gives us the basis for the claim I have done. Something should be done with the situation of the gap between Mathematica and Maple powers increasing... AV> Oh maen, you newwer loern it ... This your remark shows your blessed soul of a Mathematician. Many Cyber Tester's messages are not only about mathematics; they are quite often includes a business component. In mathematics, most probably you cannot change the situation via speaking out many times some resembling things, you cannot add some extra value. But, in contrast, in business you can. Best wishes, Vladimir Bondarenko VM and GEMM architect Co-founder, CEO, Mathematical Director http://www.cybertester.com/ Cyber Tester, LLC http://maple.bug-list.org/ Maple Bugs Encyclopaedia http://www.CAS-testing.org/ CAS Testing > (* NOT applicable to any computer algebra system *) > 1. Put your index on (virtually) any Maple function. > 2. Dig insistently enough. > 3. Voila! > Example. > Maple 11: # a tip of the tip of the Maple bug iceberg > evalf(Int(exp(-z^(1/5)), z= 0..infinity)); > evalf(Int(exp(-z^(1/6)), z= 0..infinity)); > evalf(Int(exp(-z^(1/7)), z= 0..infinity)); > evalf(Int(exp(-z^(1/8)), z= 0..infinity)); > 120.0000000 > 720.0000000 > 5040.000000 > Float(infinity) Oh man, you newwer lorn it ... Plotting shows very slow decay and computing where the tail becomes > less than 1e-13 (I work with 14 Digits) gives z beyond 1e-10, so I > am not too astonished that a numerical integrator might give up: > it estimates the integrand as no longer decaying, I guess. For slow decay & no oscillations the double exponential method is a > good first idea, so one uses that more specific command instead: evalf(Int(exp(-z^(1/8)), z= 0..infinity, method = _Dexp)); 40319.999998902 Otherwise increase precision (and MMA does it internally by 10 Digits > IIRC, no?). === Subject: Re: Solutions Guides Does anyone have solutions manuals for the following books: > Byrd, C., & Chen, I. (2007). Canadian Tax Principles. Toronto: Pearson > Education (2006-2007 ed.). > ISBN-10: 0132325314; ISBN-13: 978013235318 > (4th ed.). Toronto: Prentice Hall. > Romney, M., & Steinbart, P. (2006). Accounting information systems > (10th Ed.). Upper Saddle River, NJ: Pearson Education, Inc. ISBN > 0-13-147591-6 What a stupid question. Obviously Pearson Education has the 1st and 3rd > ones, and Prentice Hall has the second one. Duh. B. -- > Cheerfully resisting change since 1959. I am just wondering if anyone has electronic copies of these solutions guide. === Subject: Re: Solutions Guides > I am just wondering if anyone has electronic copies of these solutions > guide. Of course _someone_ does, and that, again, would be the publisher. So, again, duh. (Yes, I know that you really just want to commit a crime, and that, in the end is what pisses me off.) B. -- Cheerfully resisting change since 1959. === Subject: Re: Math mnemonics Anyone know any good math mnemonics? > >How I wish I could calculate pi. --- Christopher Heckman > The one I know is: How I want a drink (alcoholic, of course) after the eight chapters involving quantum mechanics. -- Stephen J. Herschkorn sjherschko@netscape.net === Subject: Re: Math mnemonics <46D9CF7E.3030601@netscape.net> On Sep 1, 1:45 pm, Stephen J. Herschkorn Anyone know any good math mnemonics? >How I wish I could calculate pi. > --- Christopher Heckman The one I know is: How I want a drink (alcoholic, of course) after the eight chapters > involving quantum mechanics. -- > Stephen J. Herschkorn sjhersc...@netscape.net Good one. I know there is at least one man who can accurately state pi to 20,000 places. He tells whether big numbers are prime as well plus a lot of other math. He was featured on a Discovery Channel documentary. He doesn't memeorize as least not in any way that can be determined. What he is able to do is associate numbers and apparently their positions with a shape, color and feeling, so that the number 7 might look something like a taco but be light blue and feel warm to him. That was no gimmick. He went on to learn a language in a week....Icelandic, a language they were fairly sure he had no exposure to. Unlike some of the people who are Savants, he seems normal. The mind is amazing. It makes me wonder if somewhere hidden in the recesses of our minds are every experience, thought and vision we have had, read or heard, just awaiting the right trigger or drug to return them to consciousness? === Subject: Re: Math mnemonics > It makes me wonder if somewhere hidden in the recesses of our minds > are every experience, thought and vision we have had, read or heard, > just awaiting the right trigger or drug to return them to > consciousness? Hopefully not. -- Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: Math mnemonics <46D9CF7E.3030601@netscape.net> <87odgmyqpf.fsf@huxley.huxley.fi> On Sep 1, 3:18 pm, Aatu Koskensilta It makes me wonder if somewhere hidden in the recesses of our minds > are every experience, thought and vision we have had, read or heard, > just awaiting the right trigger or drug to return them to > consciousness? Hopefully not. -- > Aatu Koskensilta (aatu.koskensi...@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus Richtig. Blessed is the man, who, having nothing to say abstains from giving in words evidence of the fact. (George Elliot), or It is better to be thought stupid and remain silent, then to speak out and remove all doubt. dkw === Subject: Re: best braking technique as one approaches red light On Aug 31, 11:42 am, jeremy rutman > |the assumption is fixed red length with some > probability > |p(t)dt to change in dt. > |It looks like no one can actually answer this so it > looks like I must > |give up on the math forum as a source of answer. I hope you'll excuse my pointing out that you've > jumped to conclusions here about the abilities > of the people you're dealing with, are you assuming i made an overestimate or underestimate >You seem to have an odd idea of how > to go about getting answers to questions on > usenet. by asking a question? i guess it would strike some as odd but that fact strikes me in turn as odd. does that make me odd or are we even > More often > questions are to some extent open-ended, like this > one, and we'll start with some partial answer, and > then refine it with feedback from the person > asking the question. yes this is what happened more or less except no one cracked the nut yet. maybe it will eventually occur but it seems most discussion here is not actually about math questions (this post case in point). > For example, sometimes, at least, the kind of > answer I gave is what the person actually wanted. > There are also various ways to refine the answer > I gave you. it could be i am still working on it. > Someone might want to have it further explained > how to maximize P(t)/t. Because of your mention of > having tried some techniques, I figured you > probably knew some calculus already, and would be > able to figure out that maximizing P(t)/t is > equivalent to finding a solution to tp(t) = P(t). > You might well already know a numerical method for > computing a root of that. And, surprise, that's > about as much of an answer as it's possible to > get. I don't agree. My feeling is there is lurking here some sort of variational technique [Cauchy Riemann] that will answer the question but it is nonstandard as far as i know and therefore hard. >In general, there's no closed-form expression > for t. This is very commonplace. If p(t) is a > Gaussian, for example, P(t) is a special function, > and you might as well compute t numerically. It is called Gauss error function erf(x) and numerical is fine or answer in terms of erf(x) > hardly seemed worth the trouble to present you > with a tutorial on this kind of thing when it > seemed fairly likely from your initial message > that you would know all that already. fair enough > In any case, you didn't bother to say what further > you wanted, which is why you didn't get more. Just the right answer...I will go over yours again and see if I'm convinced this time. I appreciate your time and aplogize if I offended. === Subject: sup, inf how would one go about proving that sup(A/B) = sup A / inf B, with A,B >= 0 ? i'm not sure that following the same argument i used for sup (AB) = sup A sup B will work. any suggestions? === Subject: Re: sup, inf > how would one go about proving that sup(A/B) = sup A / inf B, with A,B > = 0 ? i'm not sure that following the same argument i used for sup > (AB) = sup A sup B will work. any suggestions? If C = 1/B, then sup(A/B) = sup(AC) = sup A sup C = ... ? Kiuhnm === Subject: Re: sup, inf > how would one go about proving that sup(A/B) = sup A / inf B, with A,B>= 0 ? i'm not sure that following the same argument i used for sup (AB) = sup A sup B will work. any suggestions? I presume that A,B are sets of nonnegative real numbers, and A/B = { s/ t : s in A, t in B }, with the convention that s/0 = +oo. Outline: Take s/t in A/B. Show s/t <= sup A / inf B. Now take x < sup A / inf B. Show that there exists s/t in A/B with s/t > x. (Hint: x * inf B < sup A, so there exists s in A with s > x * inf B. Now s/x > inf B...) If you get stuck, ask again. === Subject: Re: sup, inf > how would one go about proving that sup(A/B) = sup A / inf B, with A, > B>= 0 ? i'm not sure that following the same argument i used for sup > (AB) = sup A sup B will work. > any suggestions? I presume that A,B are sets of nonnegative real numbers, and A/B = { s/ > t : s in A, t in B }, with the convention that s/0 = +oo. Even if s = 0? I don't think so. David === Subject: Re: sup, inf > how would one go about proving that sup(A/B) = sup A / inf B, with A,B >= 0 ? i'm not sure that following the same argument i used for sup > (AB) = sup A sup B will work. any suggestions? Is one to assume that A and B are sets of non-negative numbers and that AB is the set of all products {a*b: a in A and b in B}? === Subject: Re: sup, inf how would one go about proving that sup(A/B) = sup A / inf B, with A,B >= 0 ? i'm not sure that following the same argument i used for sup > (AB) = sup A sup B will work. > any suggestions? Is one to assume that A and B are sets of non-negative numbers and that > AB is the set of all products {a*b: a in A and b in B}? A and B are >= 0 in R, and A/B = {a/b | a in A, b in B}. [[AB is, incidentally, as you've defined it, but my question stems from sup (A/ B), not sup (AB).]] === Subject: COME ON !!! 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(Two mountain peaks). I want to find 1) The straight line distances from a to b. (*Not* the distance > along the circumference of the earth, which I can get from the > Haversine formula) > 2) The bearing of 'a' when viewed from 'b'. > The Web page you refer to below mentions two kinds of > bearings: > (1) The initial bearing (at 'b') for an arc of a great-circle from 'b' > to 'a'. > (2) The rhumb line bearing, where a rhumb line or loxodrome is a path > of constant bearing . The rhumb line route in general is > longer than > the arc of great circle route. > Of the two, I think #1 is easier to compute than the rhumb line > bearing. But the distance I want is I believe shorter than even the arc of the > great circle, as that is (I believe) the distance you would travel if > you drove a car from a to b, rather than tunnel through the earth which > would give a shorter distance. I believe the distance r = sqrt(dx*dz + dy*dy + dz*dz) is the correct distance - i.e. the distance the crow would fly. Yes, I understand. Above, I was assuming altitudes of 0 for a and b, and the choice of an arc of great circle route *or* a loxodrome route, both on the surface of the globe, to simplify the explanation of bearings of type #1 and #2. I think the rhumb line bearing (type #2) was of interest to navigators at sea from, say, 1400-1900 (+/- whatever). I think you're probably more interested in the type #1 bearing. > 3) The vertical angle - i.e how many degress above the horizon is 'a' > when viewed from 'b'. (alt_a > alt_b). > So I guess for the horizon you mean the plane perpendicular > to a plumb line ... If I interpret what you say correctly, then you mean 90 deg away from > vertical, i.e. horizontal. That is indeen what I mean by horizon. Fine. The vertical in physics is often taken as the plumb line direction. > If the altitude values are included, and the > bearing of 'a' when viewed from 'b' is measured as the crow flies or > would > fly, I believe the altitudes don't matter and > the initial bearing for an arc of a great-circle from b0 to a0 can be > used, > where a0 (resp. b0) has the same latitude/longitude as a (resp. b) but > altitude 0... > For the the elevation, consider the points a, b and O, the center of the > earth. The lengths of the three sides of triangle abO can be computed. Yes, I think I can do that. I know the xyz coordinates of all points. > Then I think the elevation, from my assumption about the horizon, > would be the measure of the angle of the triangle at 'b' minus 90 > degrees. That is interesting. I'll look into that and calculate that. I have done this for a couple of places a and b and get an elevation > angle of about 30 degrees. Someone else gets about 80 degrees - clearly > a huge difference. I don't know what method he is using. I've done it like this. 1) Calculated the radial distance r from r = sqrt(dx*dz + dy*dy + dz*dz) (we agress on that one.) Yes, in other words, r is the length of the side ab of the triangle. > 2) Assumed a right-angled with a hypotenuse of the length r, which is > known from above. In the general case, none of the angles of the triangle abO will be exactly 90 degrees. But the lengths of the three sides are already known. Any of the three angles can be computed from the law of cosines. The law of cosines is explained here: http://en.wikibooks.org/wiki/Trigonometry:Law_of_Cosines and there is a page on solving triangles (three known sides being one solvable case) here: http://en.wikibooks.org/wiki/Trigonometry:Solving_Triangles David Bernier === Subject: Re: Latitude / longitude distance and bearing. > In the general case, none of the angles of the triangle abO will be > exactly 90 degrees. But the lengths of the three sides are > already known. > That's true, the way you defined ab0. But there must be a point at sea level that is directly below point a - lets call that c. i.e c has the same latitude and longitude of a, but is at an altitude of 0. Hence the vertical side ac is of length alt_a - just the altitude of point a. The triangle abc is a right angled one. I then know Length of ac = alt_a length of ab = r If my logic is correct, then I can find the length cb (horizontal distance between a and b) very easily. If my logic is flawed, feel free to correct me. When I did the calculation this way (which I have only checked at one point), I get the same result as the great circle distance at http://www.movable-type.co.uk/scripts/latlong.html I suspect given the small distances involved, the effect of curvature of the earth is very small indeed and would lost in the very few significant digits given in that calculator. I just seem to get a VERY different value for the elevation angle to someone else, which is a bit worrying. > Any of the three angles can be computed from the law of > cosines. The law of cosines is explained here: > http://en.wikibooks.org/wiki/Trigonometry:Law_of_Cosines something about the law of cosines is my studies in the dim and distant past - I finished my first degree some 20 years ago. Maths never was my strongest subject. > and there is a page on solving triangles (three known > sides being one solvable case) here: > http://en.wikibooks.org/wiki/Trigonometry:Solving_Triangles David Bernier Chers. -- Dave (from the UK) It is always of the form: month-year@althorne.org Hitting reply will work for a few months only - later set it manually. http://chessdb.sourceforge.net/ - a Free open-source Chess Database === Subject: Re: Latitude / longitude distance and bearing. > In the general case, none of the angles of the triangle abO will be > exactly 90 degrees. But the lengths of the three sides are > already known. That's true, the way you defined ab0. But there must be a point at sea level that is directly below point a - > lets call that c. i.e c has the same latitude and longitude of a, but is > at an altitude of 0. Hence the vertical side ac is of length alt_a - just the altitude of > point a. The triangle abc is a right angled one. I then know I drew a figure for triangle abc. Perhaps you're thinking that abc will have a right angle at c ... the horizon as seen from c, because as you say, ac is vertical. > Length of ac = alt_a > length of ab = r If my logic is correct, then I can find the length cb (horizontal > distance between a and b) very easily. If my logic is flawed, feel free to correct me. When I did the calculation this way (which I have only checked at one > point), I get the same result as the great circle distance at http://www.movable-type.co.uk/scripts/latlong.html I suspect given the small distances involved, the effect of curvature of > the earth is very small indeed and would lost in the very few > significant digits given in that calculator. The vertical shifts by one degree for every 69 miles traveled on the equator. > I just seem to get a VERY different value for the elevation angle to > someone else, which is a bit worrying. I'm pretty sure relatively few adults would get as far as you did on this problem. > Any of the three angles can be computed from the law of > cosines. The law of cosines is explained here: > http://en.wikibooks.org/wiki/Trigonometry:Law_of_Cosines something about the law of cosines is my studies in the dim and distant > past - I finished my first degree some 20 years ago. Maths never was my > strongest subject. > and there is a page on solving triangles (three known > sides being one solvable case) here: > http://en.wikibooks.org/wiki/Trigonometry:Solving_Triangles > David Bernier Chers. > === Subject: Re: @good mathematicians only ... cos(x) = x x cannot be written in closed form in terms of > standard functions. but can x be expressed as a ' simple ' infinite > series ?? yes , i know 'simple' is vague ... but i would like to see such series ... > You might look up: Lagrange Inversion [or Reversion] > Theorem [or Formula]. > A formal series solution for x = a f(x) [with x=0 for > a=0] is > x = sum_{k=1}^infty a^k/k! (d/dt)^(k-1) > (f(t)^k)|_{t=0} Thus the solution of x = a cos(x) near 0 is a - 1/2 a^3 + 13/24 a^5 - 541/720 a^7 + 9509/8064 a^9 > + ... This converges for a close enough to 0, but > unfortunately not for a = 1. > -- > Robert Israel > israel@math.MyUniversitysInitials.ca > Department of Mathematics > http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, > BC, Canada not for a = 1 no ... so the question remains open ... tommy1729 === Subject: Re: solutions <5fnARlaovWWb77p3WOURF0a+G98i@4ax.com >hello, >i would greatly appreciate it if you would send me several solutions >manuals if you have them. I'm looking for the following: >Geology for Engineers and Environmental Scientists by Kehew (3rd ed) >Mechanics of Materials by Hibbeler (7th ed) >I realize that at least one of these is a new book and if you don't >have the current edition, I will also gladly take the previous >edition. > I happen to have all of those books, but pray tell, why should I send > them to you? --Lynn- Hide quoted text - - Show quoted text - because i could really use them. === Subject: Re: Silence is golden BOGUS NEILIST , YOU WHERE NEVER SILENT > On Aug 30, 2:43 pm, tommy1729 where is neilist now ?? > and david C. Ullrich ?? > and denisfeldman?? > it seems they accepted this set geometry (snicker) > yeah sure this is better than my set theory or > cantor > lol > why not be rude now neilist ?? > i guess you accept this set geometry :-) > and why cant professor (snicker) david see this > set geometry is bogus ? > i guess the perfect spelling maybe (lol) > and where is denis feldmann ? > math bruder ? > 666 ? > and all the other big critics ?? > nowhere , they accepted this > yeah really this set geometry is the best ever. > way better than any post i ever made (snicker) > the OP does not even accepts the reals as an > uncountable set (lol) > yet doesnt seem to bother neilist , or david c > ullrich or denis feldmann ... ( the others in that > category ) > btw just as i predicted denis feldmann left > the pattern described in my post of critics towards > me sure is a rule ! > to be honest the only decent geometry post done > recently is by galathaea > maybe the OP wants to compare notes with denis > feldmann , neilist , the prof and JSH. > tommy1729 > ps : one thing i do have to admit : cantor's math > was better than this :-) Ah, wouldn't some like silence, perhaps from yours > truly? :-) And to not hear Tommy's sloppy drivel. And for Tommy > to actually > believe his ridiculous proposition that > silence=acceptance of his > pompous declarations of greatness ala James Harris. In the realm of law, silence may be imputed to > acceptance or > acquiescence. See A Man For All Seasons with Paul > Scofield. An > excellent movie. But in the realm of ordinary people, such as this > newsgroup, silence > can be a sign of NON-acceptance of either the posting > OR the POSTER. Now, if someone else stated some of these > propositions, then maybe I'd > pay attention, or give it a bid of credibility. But from YOU? You don't even know the definition of integral as > used in normal and > proper mathematics. Can't source your WRONG > definition, can't admit > you're WRONG, and can't accept the fact that YOU'RE > PWNED!!! And Tommy, if you can't source your WRONG definition, > don't even > attempt to respond. It'll just put you in deeper and > deeper Pwn-dom- > ness, Tommy. (pwn-dom-ness? I should submit that to the Urban > Dictionary) So go join James Harris and Bassam Ass-King with your > grandiose > theories and mathematics, you Pwn-boy Tommy-typo. And have a great weekend everyone!! > BOGUS neilist , you just dont offend the OP because accept the post or because the OP is not me ... there was no silence towards me , so dont pretend to be a wise silent man , you just forgot to insult once , thats not silence !! and as for the integral look that up decently: integral x dx = x^2 /2 + C and every sain man on this forum will accept that integral as written above ... yet ullrich , you and a few others dont accept and dont know the integral of x. so the jokes on you actually. go ahead look it up in topic integral zeta : ullrich computed the integral different !! but i assume you will snip my defense and simply dribble and insult instead , as usual ? tommy1729 === Subject: Tommy's prices are INSAIN !!!!!!! <29913925.1188683624571.JavaMail.jakarta@nitrogen.mathforum.org> even cantor doubted there were things like > aleph_2 or aleph_3 and assumed C = aleph_1 > Very true. He was led to these doubts upon noticing > the diagonal > method is flawed as we can always just insert the > diagonal to the > list. Alas, cantor was too much of a coward to > publicly admit the > error his ways, singing all the way to the bank, > and thus we are left > with the swindle of set theory, sneakily rotting > the brains of poor > impressionable youths. No, Cantor was not a coward. proof ? According to a report by > Kowalewski thats no proof. > (which however is not confirmed in other sources) not a coincidence of course. [G. > Kowalewski: > Bestand und Wandel, 1950, p. 202] by accidents fans of cantor ... the following > happened after the > (erroneous) proof by Koenig: After the lecture Cantor > took the floor > with deep emotion. Among other things he thanked God > that he had the > privilege of living to see the refutation of his > errors. refutations ... Further Cantor emphasized that numbers which are not > finiteley > definable are nonsense (Letter to Hilbert, August > 8,1906) see the comment of aatu and me it implies that aleph_2 and _3 dont exist or are nonsence by the diagonal argument. If he had > recognized (as every modern scientist does) that most > uncountable > reals are of this kind, he would have withdrawn his > theory with no > doubt. thats no proof , lol if --> then maybe --> i assume ... btw the reals are already definable so i dont agree with you and i wont waste time on thinking about if's -> then's Aatu Koskensilta (aatu.koskensi...@xortec.fi) > Wovon man nicht sprechen kann, daruber muss man > schweigen > - Ludwig Wittgenstein, Tractatus > Logico-Philosophicus Why don't you quote Wittgenstein on set theory? despite we dont agree tommy1729 === Subject: Re: tommy set theory / cantor simplified and corrected > see the comment of aatu and me it implies that aleph_2 and _3 dont exist or are nonsence > by the diagonal argument. Right. I'm well known for my vehement opposition to Cantor and the innumerable incontrovertible refutations of the diagonal proof I've presented. It seems you're doing such a swell job yourself you're in no need of my help. I'll leave you to it. -- Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: LWALKE ACCEPTS AND EXPLAINS tommy set theory TO ULLRICH ! > On 29 Aug., 15:29, tommy1729 ( and understood my post ! ) > ( i know he visited the university of cambridge and > the university of brussels ( in my country :-) ) so i > guess he's a researcher/ prof ? ) > On Aug 26, 8:33 am, tommy1729 > in tommy set theory there are only 2 types of > actual infinity. > countable infinity > uncountable infinity = continuum = C > So far, this sounds like the Pocket Set Theory to > which I > referred in another thread. >http://math.boisestate.edu/~holmes/holmes/pocket.txt > yes that was an intresting remark. > and indeed Pocket Set Theory is consistant and has > a lot in common with Tommy Set Theory. > It has primitive predicates of membership and > classhood and the > following axioms: > I. Classes with the same members are the same; > non-classes (if there > are any) have no members. > this is why i added [a] = a > same member a. > this is the only significant difference with Pocket > Set Theory as you pointed out below... > We define set as class which is a member. > II. Any condition whatever that we can express > on > elements (including > non-class elements) defines a class. > This is, formally speaking, an impredicative > class > comprehension > scheme; it allows definitions of classes of sets > (or > sets and > non-class elements) which may involve > quantification > over all classes. > Notice that we get a unique empty class in > addition > to any > non-classes. > III. There is a set I and relation P such that > for > each x in I, > there is exactly one y in I such that Pxy and > for > each y in I, there > is at most one x such that Pxy and for some x, > for > all y, not Pyx. > I is a Dedekind infinite set. It is > straightforward > to prove that I > has any concrete finite number of distinct > elements. > We define proper class as class which is not a > set. > IV. All proper classes are the same size. > V. The infinite sets are exactly the classes > such > that there are > class bijections witnessing the fact that they > are > the same size as > I. > As its author points out, all sets are countable > (including > finite), while all proper classes have the > cardinality of > the continuum, so the OP's intuition that there > exist > only > two types of infinity applies to PST. > consistant and in agreement with TST. > nice definitions. > although im sure DAVID C ULLRICH can disproof what > you said :p > i will give proof that R -> R^2 WITHOUT CANTOR. > Indeed, in PST both R and R^2 are proper classes, > so > they > trivally have the same cardinality by Axiom IV. > there is no need for axioms , and there is a > construction. > (!!!!) > The proof you give actually works in ZFC as well, > though > one must deal with the 0.999...=1.000 caveat. > in ZFC as well -> it is not needed. > and 0.999999 is not a problem in TST and neither in > PST. Interesting to hear. > A proof of that claim within an axiomless theory > might be even more interesting. no problem , that can be done. all you need to do is accept the reals exist. ** intresting remark ** when i talked about 0.99999 a few mounths ago , neilist liked my post. that was during the time i was on his side against bassam. so did he lie back then , or is he going to lie now and deny he ever liked that post ? or is he mentally instable ? there are only these 3 possibilities if you think about it ... you cant just like someone and agree and not anymore later if your mentally stable and honest. **end remark** im happy someone finally understood that there are > proofs of R -> R^2 without cantor , and mine is a > consistant one. > Well, in PST that is almost an axiom, and you buy the > fact with the > problem > thet R is a subset of R but not an element of > powerset(R). not really ; i dont totally agree 100 % on PST i have TST but PST is quite good , better than cantor id say. > After all - even though it is an interesting subject > - there is a > reason > why it is called Pocket Set Theory and not > Super-Duper Set Theory. SDST ?? :p even stronger using PST or TST it is probably the > shortest possible proof ! and without the axiom of > choice ! Any theorem has the shortest possible proof in a > theory where it is an > axiom. yes of course, but there are no axioms in TST unless you dont accept the difference between countable and uncountable... and even if we do accept ZFC it is STILL A PROOF > without needing cantor's method. > At this point Prof. Ullrich asks: > Let P = P(R), the set of all subsets of R. Is > P > finite? Is P countable? Or does P have > cardinality C? > what's worse ; he thinks he can ask a trick > question to debunk me or any other set theory apart > from cantor set theory ... > yet he did not even understand my proof of R-> R^2; > even gave a counterproof LOL ... > Because R is uncountable, R is a proper class -- > not > a > set -- in PST. Obviously P must also be a proper > class > and so it also has cardinality C by Axiom IV. It > may > seem strange that a class has the same > cardinality as > its power class, but remember that V, the class > of > all > sets, is equal to its own power class P(V). > Cantor's > theorem only applies to sets, not proper classes, > and > the class of reals is proper (not a set) in PST. > Returning to the OP: > [a]=a for all sets > This is the first statement made by the OP in > this > thread which fails in PST. > you have beaten David C. Ullrich :-) > and you have explained my set theory mainly. > of course David C. Ullrich wont agree ( the > stubborn fool) > so i hope you are a professor indeed. > thank you for that post > and if you ever visit belgium again , let me know > :-) > tommy1729 > anticantorian > ps : you see david ? people do agree with me ! > and im talking cambridge people here :-) > and nobody accepts your disproof (snicker) > in fact they accept my proof of R -> R^2 > and i got many emails of support too > so what's your next step ?? > going to start about the O in WO like neilist ? > starting about history and spelling mistakes if you > cant handle the math ? > lol > tommy1729 nice to have you here on the forum :-) tommy1729 === Subject: A new wiki site to Organize and Share Calls For Papers Hi All, I would like to recommend a new web site, www.wikicfp.com, which could help you to organize and share Calls for Papers. Why not have a try? http://wikicfp.com/cfp/servlet/tool.search?kwstr=mathematics What's special with WikiCFP ? - You can have your own customized CFP list. - It's easy to share your list with others. - You can organize your list by sorting on various fields. - You can browse CFPs with respect to categories. - You can search CFPs by title, location or category. - There are many other useful features. I sincerely hope this new site will be helpful to you. Best wishes, Evie === Subject: Re: JSH: Contradictory behavior, issue of math fraud > So I went to the factoring problem. > And never solved it. > Maybe not, but what is your proof? > I gave a proof in another post, but my newsreader seems to have fallen > apart in the last ten minutes, so it might not exist. > Select k=9, n=0 for T = 23457634568903458768912756896234625612456734523. > The largest factor your method will find is 1. That violates no > constraint of your method. Therefore your method as stated doesn't work. > If as I say mathematicians routinely lie about math, and I do come up > with a viable factoring approach then it stands to reason that they > would CONTINUE to lie, but other people might use the research anyway. > That is irrelevant, since you will never come up with a viable factoring > approach faster than the known ones. > And you have a crystal ball? > No, but your past antics indicate that you do not have sufficient > mathematical ability beyond anyone else working on the problem. I can > say P = NP, and give some rationale, but I can never *prove* it because > I do not have the sufficient mathematical abilities. > If my retirement dollars depend on the answer, what are you giving me > so that I can feel safe? > A naive Bayesian classifier trained on your previous performance as data > says you won't. > But then again, I might simply be unable to come up with a viable > approach to the factoring problem. > You *will* be unable to come up with a viable approach to the factoring > problem faster than the known ones. > And if I do, will you personally vouch for the money lost for those > who lose their savings? > *Who* will lose their savings? Almost all serious cryptography has > passed up factoring and started using stuff like elliptic-curve. Many of > the secure algorithms most people use have been shown to be breakable, > but we still use them. Best examples: RC4 and MD5. Fine. So Santos can pledge his entire life savings, every penny he > owns to anyone who might lose money if he and you are wrong. Based on your analysis he is perfectly safe, right? So he should do the pledge, and anyone else of you I ask should do it > as well. I want a pledge of every dime you have, so that you put enough out > there that people can know where you stand, without question. And what would be *your* pledge here? So that people can know where you stand, without question. What about a pledge of every dime you have in the case you have not factored any of the RSA challenge numbers until August the 31st 2008? Jose Carlos Santos === Subject: Re: JSH: Contradictory behavior, issue of math fraud <5jtmbnF17r3tU1@mid.individual.net> <5ju8fcF1acs9U1@mid.individual.net > So I went to the factoring problem. > And never solved it. > Maybe not, but what is your proof? > I gave a proof in another post, but my newsreader seems to have fallen > apart in the last ten minutes, so it might not exist. > Select k=9, n=0 for T = 23457634568903458768912756896234625612456734523. > The largest factor your method will find is 1. That violates no > constraint of your method. Therefore your method as stated doesn't work. > If as I say mathematicians routinely lie about math, and I do come up > with a viable factoring approach then it stands to reason that they > would CONTINUE to lie, but other people might use the research anyway. > That is irrelevant, since you will never come up with a viable factoring > approach faster than the known ones. > And you have a crystal ball? > No, but your past antics indicate that you do not have sufficient > mathematical ability beyond anyone else working on the problem. I can > say P = NP, and give some rationale, but I can never *prove* it because > I do not have the sufficient mathematical abilities. > If my retirement dollars depend on the answer, what are you giving me > so that I can feel safe? > A naive Bayesian classifier trained on your previous performance as data > says you won't. > But then again, I might simply be unable to come up with a viable > approach to the factoring problem. > You *will* be unable to come up with a viable approach to the factoring > problem faster than the known ones. > And if I do, will you personally vouch for the money lost for those > who lose their savings? > *Who* will lose their savings? Almost all serious cryptography has > passed up factoring and started using stuff like elliptic-curve. Many of > the secure algorithms most people use have been shown to be breakable, > but we still use them. Best examples: RC4 and MD5. > Fine. So Santos can pledge his entire life savings, every penny he > owns to anyone who might lose money if he and you are wrong. > Based on your analysis he is perfectly safe, right? > So he should do the pledge, and anyone else of you I ask should do it > as well. > I want a pledge of every dime you have, so that you put enough out > there that people can know where you stand, without question. And what would be *your* pledge here? So that people can know where you > stand, without question. What about a pledge of every dime you have in the case you have not > factored any of the RSA challenge numbers until August the 31st 2008? > No. I pledge nothing. Jose Carlos Santos Fine Jose Carlos Santos. Refuse to put your money up for something you claim is not a threat to anyone else. But do you really think you can keep people from just taking it if you are wrong? Do you believe you have that power? If the world comes and says, pay up, how can you stop them? I don't need you to show responsibility to make my point, and I really like what I said in a previous post about con artists only caring about money. It makes them predictable. How can anyone not wonder that maybe you will not take that pledge to protect the only thing you actually care about? Why really do you reply as you do to me? If not to convince others, then why? Now then, let's try again. What makes you so certain there is nothing to surrogate factoring? James Harris === Subject: Re: JSH: Contradictory behavior, issue of math fraud <5jtmbnF17r3tU1@mid.individual.net > MY position is that modern math people routinely lie and don't > actually care about math except as a tool to use to get what they > want--employment for acting like mathematicians. James Harris MY position is that you always lie and don't actually care about math except as a tool to use to get what you want--girls and wealth for acting like mathematicians. You are a liar, cheat, charlatan, crank, troll and crackpot - that about covers it. === Subject: Re: JSH: Contradictory behavior, issue of math fraud However, if I come up with an approach then if it is NOT viable then > mathematicians, supposedly brilliant, should be able to settle it, and > simply proclaim me as just being the crackpot who has nothing--and > prove it. James Harris BINGO! === Subject: Re: integral zeta > On 31 Aug., 12:35, David C. Ullrich > To tommy1729: > If you insist that primitives are uniquely > determined > simply by the > concept of just set C=0, you are going to > run > into > some problems. > For example, let f(x )= e^x - x. > Let's integrate f(x) two different ways .... > method (1) [standard Calc 1 approach]: > int f(x) dx = e^x - x^2/2 + C > Setting C=0 yields e^x - x^2/2 > method (2) [using power series]: > e^x = 1 + x + x^2/2 + x^3/6 + x^4/24 + ... > f(x) = e^x - x = 1 + x^2/2 + x^3/6 + > x^4/24 + > ... > int f(x) dx = (x + x^3/6 + x^4/24 + x^5/120 + > ... > ... ) + C > Setting C=0 yields x + x^3/6 + x^4/24 + > x^5/120 + > 0 + ... > which equals e^x - x^2/2 - 1. > So which one is the unique primitive? > quasi >intresting argument. :-) >first note : i have already defined integral > zeta > by a series. >although perhaps there might be discussion > about the > analytic continuation or riemann surface .... >but anyways integral zeta is already > defined... > First, it _had not_ been defined at the point > where > you started insulting people for not knowing > what you > meant. Second, that series does not converge > except > for Re(z) > 1, and it has many _different_ > continuations > to larger regions - hence that series does _not_ > specify where the zeroes in the plane are - > where the > zeroes in the plane are depends on what > particular > continuations we're talking about. Saying that > there > might be discussion about analytic > continuation > is progress, but it shows you still have no idea > what you're talking about - the question of > non-uniqueness of analytic continuation is > crucial > here. >in your argument, perhaps a good way to clarify > is > this >f(0) = INTEGRAL f(0)dx if possible by changing > C. >so f(x) = exp(x) - x >f(0) = 1 = integral f(0) >therefore the integral is method(1). >another reason for avoiding series is the > taylor > expansion of exp(x^2) at 0 ... >you know what happens there dont you ? >a bit off topic perhaps but can you give nice > examples of an integral which can take 3 or more > values ... >just for fun :-) >tommy1729 > ************************ > David C. Ullrich >ok , so you FINALLY accepted the series. > Huh? What does it mean to accept a series? >the continuation is arguable yes. >i admit that. >but there are zero's that are in common with any > possible continuation ; critical ones. >correct me if im wrong about that >( would surprise me ; the wrong , not the > correction ) >( critical is not the same here as usual ; not > referring to a line but the zero' s that are in > common to all continuations ) >i never claimed to be an expert on continuation > though ... > In fact you know nothing whatever about it, but > that > doesn't stop you from making statements about it. > I'll give you a hint, so you can realize exactly > how absurd you're being here: > Hint: What you're claiming is this: If f is a > function > defined in a certain region and g is defined in the > same region by g = f + 2 pi i then f and g have > certain zeroes in common. Indeed. > And to allow tommy1729 to learn something: > zeta(s) has one pole, of residuum 1. Loosely speaking, this allows us to look at integral > zeta mod 2pi. > In other words, the research question is: DEFINITION1 : > f:U->C is called a tommy-function if > - U is a region in C > - 0 in U, 1 not in U > - f holomorphic on U > - f(0)=0 > - f'(s)=zeta(s) fr all s in U DEFINITION 2: > If f:U->C is a tommy-function, a point z in C is > called > a tommy-point for f if z in U and f(z) is an integer > multiple of 2pi. tommy's objective is to study tommy-points. Trivial LEMMA: tommy-pointnesss does not depend on > the choice of f (and/or U). Which allows DEFINITION 3: > z in C{1} is called a tommy-point if there exists > a tommy-function of which z is a tommy-point So, now there is something defined. > Next question: What is interesting about > tommy-points? hagman > hahaha hagman tommy-points lol your making stuff up i never said , just like david. i assume its a parody :-) if not , well then you made that up ( tommy points) ... and yes zeta(1) has a pole since it is the harmonic series 1+1/2+1/3+... you have outlined a clearer similar version of the topic , yet ullrich ignores it ... just as he ignored the series i gave him ... instead he invents stuff ala tommy-points :-) tommy1729 === Subject: Re: Mathematics: art or science? > That a system of axioms is not strong enough to prove > its own consistency (Godel) does not render untrue the > results deduced from that system. That is indeed fortunately so. Do you think anyone has thought it did? > So, to your question: The theory PA + 'PA is inconsistent' is consistent. > Does it follow that it is true that PA is inconsistent? It follows, metamathematically. It follows metamathematically that it's true that PA is inconsistent from the fact that the consistent theory PA + PA is inconsistent proves PA is inconsistent? What does that mean? > We don't know of a stronger system of axioms than Dedekind-Peano. It's obscure what you have in mind. We do know all sorts of theories, such as second-order arithmetic, Zermelo set theory, Zermelo-Fraenkel set theory, and so on, that are stronger than Peano arithmetic, after all. > Philosophy of mathematics is to mathematics as book review is to > book. Luckily no philosophy of mathematics enters to the purely mathematical observation that the consistency of a theory does not guarantee the truth of its theorems. -- Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Newtons law revisited I'm trying to rewrite newtons law in terms of how the mass density changes at a point instead how it moves from point to point. (Mainly I'm actually dealing with the gravitational law and I sorta mix up this term with newtons) First let me define a few terms, p(x,t) is the mass density at point x(x is in general a vector) and time t. F(r) is a odd function about r = 0 and is finite for all r. I'm mainly using functions like r*e^(-|r|^2) or r*e^(-|r|). This is to replace the standard 1/r^2 because it does not deal with the singularity at r = 0 and its not so hard to integrate it symbolically. I know there are other forces that are more representative of reality but I'm not concerned with its function form ATM except that it is reasonable and doesn't introduce any signularities. Attractive Force at point x due to point y is p(x,t)*p(y,t)*F(x - y). This proportionate it to it). The Total Attractive Force at point x is F(x,t) = p(x,t)*int(p(y,t)*f(x - y), y=in V). V is the space under consideration. Now newtons law as p(z(t),t)*z''(t) = F(z(t),t). This representation finds how how a point mass moves through time. z(t) is the path that it moves due to the forces acting on it. Now this is all fine and dandy if you want to follow an object through space as we can assume that the object's mass is not changing along the path z(t) and then we essentially have a differential equation in z(t) which can be used to find z(t). What I want to know is what if I only care about how the mass density changes with time at a fixed point z that is independent of t? So if I'm standing at point z and measuring the mass density(or mass) and plotting it over time. I don't care which object the mass belongs or which path it will flow from. Obivously the mass density at point z will change due to the total attractive force acting on it. This force will cause some of the mass(Actually all of it) at point z and time t to move to a new point z+dz at time t + dt. We can figure out dz by newtons law. What I'm interested in doing, if possible, is figuring out p(z,t) given p(z,0). So I the mass density and I would easily be able to evolve the system by computing the forces on each point and seeing how much the density changed at that point(and it had to go somewhere so by knowing all the changes we can easily know where it went). I believe that one can write some expression that depends only on the mass density and equate it to the total attractive force and then recover newtons law. I think that newtons law would be a specific case of following a point mass as it moves... Actually I think it would probably have to do with grad(p(z,t)) because grad(p) would point in the direction of the maximum mass density change... to me this sounds like it would correspond to a macroscopic change in mass and probably represent x(t) in some way(not directly). In any case I'm at a dead end in figuring out the solution as nothing seem to work. I know I can use newtons law to update the different points but in this case I'm essentially computing the trajectories of every point. Of course I could be wrong and maybe there is no way to find an expression for the total attractive force in terms of the mass density at a point. (Although chances are if there is, it is going to more complicated than newtons law) What I invision is that if I have a density graph plotted and evolve the system that I would see what newtons law at work but I wouldn't be computing newtons law on each element(I wouldn't be tracking each element). So this could be a better method for a very large number of elements because it doesn't keep a path per element but depends only on the partition of space. It would also be independent of the complexity of the paths because, again, it doesn't depend on the paths. Although because of that fact one think of some examples where this might happen). Any of this make sense? Any ideas if it does? Jon === Subject: Re: Newtons law revisited > I'm trying to rewrite newtons law in terms of how the mass density changes > at a point instead how it moves from point to point. (Mainly I'm actually > dealing with the gravitational law and I sorta mix up this term with > newtons) [cut] > This is to replace the standard > 1/r^2 because it does not deal with the singularity at r = 0 and its not so > hard to integrate it symbolically. Poisson beat you to it, back in the early 1800s. Gauss also contributed, iirc. This stuff is old enough so that a lot of books covering it are out of copyright, and have been digitised and are available on www. Look for phrases like potential theory, theory of attraction, mathematical theory of attraction. Do you want to include other forces? Cohesive forces giving you rigid bodies? Liquid? Gas? Or just a swarm of point masses only interacting through gravity, with the (average) mass density being proportional to the number per unit volume? You can probably find the last two in astrophysics stuff - for example, anything dealing with the collapse of gas or dust clouds. If you only want the answer, it'll be easier to look it up than do it from scratch. If you want the journey rather than the answer, have fun! Yes, it basically makes sense. Remember that the change in mass density depends on the velocity field as well as the force per unit volume - just consider a solid object moving through empty space. If you want to do computational modelling, it should be possible using a generic finite element package. Or some finite difference approximation. You're basically talking about field theory, a matter of solving PDEs. As soon as you talk about a field (ie mass density as a function of r, velocity as a function of r) rather than point masses (a finite number of positions and momenta or velocities), you have infinite degrees of freedom. But some kind of discretisation should give a working approximate solution. [moved] > F(r) is a odd function about r = 0 and is finite for all r. F(r) is a vector valued function of the vector r. I can see what you mean, but I don't know if your terminology is correct. -- Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/ E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html === Subject: Re: Newtons law revisited > I'm trying to rewrite newtons law in terms of how the mass density > changes > at a point instead how it moves from point to point. (Mainly I'm actually > dealing with the gravitational law and I sorta mix up this term with > newtons) > [cut] > This is to replace the standard > 1/r^2 because it does not deal with the singularity at r = 0 and its not > so > hard to integrate it symbolically. Poisson beat you to it, back in the early 1800s. Gauss also contributed, > iirc. This stuff is old enough so that a lot of books covering it are out of > copyright, and have been digitised and are available on www. Look for > phrases like potential theory, theory of attraction, mathematical > theory of attraction. Do you want to include other forces? Cohesive forces giving you rigid > bodies? Liquid? Gas? Or just a swarm of point masses only interacting > through gravity, with the (average) mass density being proportional to the > number per unit volume? You can probably find the last two in astrophysics stuff - for example, > anything dealing with the collapse of gas or dust clouds. If you only want the answer, it'll be easier to look it up than do it from > scratch. If you want the journey rather than the answer, have fun! Yes, it basically makes sense. Remember that the change in mass density > depends on the velocity field as well as the force per unit volume - just > consider a solid object moving through empty space. If you want to do computational modelling, it should be possible using a > generic finite element package. Or some finite difference approximation. > You're basically talking about field theory, a matter of solving PDEs. As > soon as you talk about a field (ie mass density as a function of r, > velocity as a function of r) rather than point masses (a finite number of > positions and momenta or velocities), you have infinite degrees of > freedom. But some kind of discretisation should give a working approximate > solution. [moved] > F(r) is a odd function about r = 0 and is finite for all r. F(r) is a vector valued function of the vector r. I can see what you mean, > but I don't know if your terminology is correct. > Thinks, I'll look it up. I do have some books on some of this but I never recall seeing anything described in the way I though. Its possible that the possion equation is exactly what I want. I guess if it works for the electric field it should work for gravity too. (I was actually going to go look at maxwells equations and see if I could derive something from it). Right now I'm doing some simple modeling using newtons law but for a large number of masses it is quite slow. Suppose I wanted to model a real object with, say, 10^10 points, then thats impossible, AFAIK, with newtons law. Not only that, its unnecessariy for my purposes because I do not care about the individual masses or there trajectories but only the motion of the system as a whole. So I figure that if I partitioned the space up I would come out with less elements than points(say 1000x1000 = 10^6 for 2D). Of course in this manner for large N. I'll look into it a little more and see what I can come up with. Jon === Subject: Re: Newtons law revisited possion equation is exactly what I want. I guess if it works for the > electric field it should work for gravity too. (I was actually going to go > look at maxwells equations and see if I could derive something from it). Historically, Poisson did it for gravity first (and Laplace and Gauss did their stuff for gravity first, too). Gravitation is our first modern field theory, and electromagnetism sucked up the maths and the PDEs. > Right now I'm doing some simple modeling using newtons law but for a large > number of masses it is quite slow. Suppose I wanted to model a real object > with, say, 10^10 points, then thats impossible, AFAIK, with newtons law. Not > only that, its unnecessariy for my purposes because I do not care about the > individual masses or there trajectories but only the motion of the system as > a whole. So I figure that if I partitioned the space up I would come out with less > elements than points(say 1000x1000 = 10^6 for 2D). Of course in this manner > for large N. Sounds feasible. That's basically what classical hydrodynamics and gas dynamics are all about - don't keep track of every molecule, just approximate them, on average, with a field theory. Even classical thermodynamics is this kind of animal. Perhaps it might be possible to get some compressible fluid dynamics code (ie gases) and replace the forces due to pressure with self-gravitation? Or just add gravity? I haven't looked into this, but it's possible that boundary conditions might be problematic. -- Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/ E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html === Subject: Re: Newtons law revisited > Its possible that the > possion equation is exactly what I want. I guess if it works for the > electric field it should work for gravity too. (I was actually going to go > look at maxwells equations and see if I could derive something from it). Historically, Poisson did it for gravity first (and Laplace and Gauss did >their stuff for gravity first, too). Gravitation is our first modern field >theory, and electromagnetism sucked up the maths and the PDEs. > Right now I'm doing some simple modeling using newtons law but for a large > number of masses it is quite slow. Suppose I wanted to model a real object > with, say, 10^10 points, then thats impossible, AFAIK, with newtons law. Not > only that, its unnecessariy for my purposes because I do not care about the > individual masses or there trajectories but only the motion of the system as > a whole. > So I figure that if I partitioned the space up I would come out with less > elements than points(say 1000x1000 = 10^6 for 2D). Of course in this manner > for large N. Sounds feasible. That's basically what classical hydrodynamics and gas >dynamics are all about - don't keep track of every molecule, just >approximate them, on average, with a field theory. Even classical >thermodynamics is this kind of animal. Perhaps it might be possible to get some compressible fluid dynamics code >(ie gases) and replace the forces due to pressure with self-gravitation? >Or just add gravity? I haven't looked into this, but it's possible that >boundary conditions might be problematic. http://www.mpa-garching.mpg.de/galform/millennium/ Ask them. === Subject: Re: Newtons law revisited Newtons law revisited *************** Didn't he have more than one? === Subject: Re: Newtons law revisited > In any case I'm at a dead end in figuring out the solution as nothing seem > to work. This may not be an easy problem to solve. The n-body problem (http://en.wikipedia.org/wiki/N-body_problem) is already difficult, but you would have us look at continuous densities instead of what ought to be simpler: n discrete points. This is not quite a proof, but it may be a warning sign. === Subject: Re: Newtons law revisited > In any case I'm at a dead end in figuring out the solution as nothing > seem > to work. This may not be an easy problem to solve. The n-body problem > (http://en.wikipedia.org/wiki/N-body_problem) is already difficult, but > you would have us look at continuous densities instead of what ought > to be simpler: n discrete points. This is not quite a proof, but it may > be > a warning sign. > No, you need to read what I said. I'm not solving the N body problem. I'm different. In a sense, newtons equations are like you are following along with the least... kinda hard to explain.) === Subject: Re: Newtons law revisited >I'm trying to rewrite newtons law in terms of how the mass density changes >at a point instead how it moves from point to point. What's wrong with the field equations [del.G = -4piG_newton*rho, del x G = 0] or Poisson's equation [del^2G = -4piG_newton*rho] ? [...] === Subject: Re: Newtons law revisited >I'm trying to rewrite newtons law in terms of how the mass density changes >at a point instead how it moves from point to point. What's wrong with the field equations [del.G = -4piG_newton*rho, del x > G = 0] or Poisson's equation [del^2G = -4piG_newton*rho] ? > Probably nothing. I'll have to look at this as they might be exactly what I want. Jon === Subject: Re: Newtons law revisited : I'm trying to rewrite newtons law in terms of how the mass density changes : at a point instead how it moves from point to point. (Mainly I'm actually : dealing with the gravitational law and I sorta mix up this term with : newtons) : : First let me define a few terms, : : p(x,t) is the mass density at point x(x is in general a vector) and time t. : : F(r) is a odd function about r = 0 and is finite for all r. I'm mainly using : functions like r*e^(-|r|^2) or r*e^(-|r|). This is to replace the standard : 1/r^2 because it does not deal with the singularity at r = 0 and its not so : hard to integrate it symbolically. I know there are other forces that are : more representative of reality but I'm not concerned with its function form : ATM except that it is reasonable and doesn't introduce any signularities. : : Attractive Force at point x due to point y is p(x,t)*p(y,t)*F(x - y). This : proportionate it to it). : : The Total Attractive Force at point x is F(x,t) = p(x,t)*int(p(y,t)*f(x - : y), y=in V). V is the space under consideration. : : Now newtons law as p(z(t),t)*z''(t) = F(z(t),t). This representation finds : how how a point mass moves through time. z(t) is the path that it moves due : to the forces acting on it. : : Now this is all fine and dandy if you want to follow an object through space : as we can assume that the object's mass is not changing along the path z(t) : and then we essentially have a differential equation in z(t) which can be : used to find z(t). : : What I want to know is what if I only care about how the mass density : changes with time at a fixed point z that is independent of t? : : So if I'm standing at point z and measuring the mass density(or mass) and : plotting it over time. I don't care which object the mass belongs or which : path it will flow from. : : Obivously the mass density at point z will change due to the total : attractive force acting on it. Why is this obvious? Give an example. This force will cause some of the : mass(Actually all of it) at point z and time t to move to a new point z+dz : at time t + dt. We can figure out dz by newtons law. : : What I'm interested in doing, if possible, is figuring out p(z,t) given : p(z,0). So I the mass density and I would easily be able to evolve the : system by computing the forces on each point and seeing how much the density : changed at that point(and it had to go somewhere so by knowing all the : changes we can easily know where it went). : : I believe that one can write some expression that depends only on the mass : density and equate it to the total attractive force and then recover newtons : law. I think that newtons law would be a specific case of following a point : mass as it moves... Actually I think it would probably have to do with : grad(p(z,t)) because grad(p) would point in the direction of the maximum : mass density change... to me this sounds like it would correspond to a : macroscopic change in mass and probably represent x(t) in some way(not : directly). : : In any case I'm at a dead end in figuring out the solution as nothing seem : to work. I know I can use newtons law to update the different points but in : this case I'm essentially computing the trajectories of every point. Of : course I could be wrong and maybe there is no way to find an expression for : the total attractive force in terms of the mass density at a point. : (Although chances are if there is, it is going to more complicated than : newtons law) : : What I invision is that if I have a density graph plotted and evolve the : system that I would see what newtons law at work but I wouldn't be computing : newtons law on each element(I wouldn't be tracking each element). : : So this could be a better method for a very large number of elements because : it doesn't keep a path per element but depends only on the partition of : space. It would also be independent of the complexity of the paths because, : again, it doesn't depend on the paths. Although because of that fact one can : think of some examples where this might happen). : : Any of this make sense? Any ideas if it does? : : Jon === Subject: Re: how to list all of the real numbers <87ps16tcue.fsf@phiwumbda.org> Actually I define iota as a least positive real number, in terms of > R^bar, R^umlaut, and R^bar_umlaut. > You certainly can try to construct an axiomatic system with a least > positive real number, but it would be very different system then a > the real numbers. For example, the real numbers are complete whereas > a system such as one you suggest would not be (your's has a hole where > iota/2 should be). > I don't know what bar, umlaut and bar_umlaut mean. Maybe the umlaut goes _under_ the R. > GIF! GIF! -- > Dave Seaman > Oral Arguments in Mumia Abu-Jamal Case heard May 17 > U.S. Court of Appeals, Third Circuit > I think that for example using the LaTeX typesetting language it would be something along the lines of using the stackrel operator and then placing the umlaut over the bar in indication of the real or true set of real numbers that somehow meets all the perceived properties of continuum as background of motion and complete ordered field. Ross -- Finlayson Consulting === Subject: Re: how to list all of the real numbers Actually I define iota as a least positive real number, in terms of > R^bar, R^umlaut, and R^bar_umlaut. You certainly can try to construct an axiomatic system with a least > positive real number, but it would be very different system then a > the real numbers. For example, the real numbers are complete whereas > a system such as one you suggest would not be (your's has a hole where > iota/2 should be). I don't know what bar, umlaut and bar_umlaut mean. > Then, there is a difference between sums and multiples of iota-values, > where summing n many is not the same as multiplying by n. So, not only are you redefining a number system, you are also altering > the definitions of these operations. > In the sense of being a nilpotent infinitesimal in that the square is > zero, actually I see it as more of a fluxion, where its square is simply > relatively infinitesimally small. How can that be? If your iota is the smallest possible number, what > is iota^2? Since iota < 1, then iota^2 cannot be greater than iota. > You are saying that iota^2 is not nilpotent, so it must be greater > than 0. Are you thus saying iota^2 = iota? > Also I think the hyperreals are the reals, hyperintegers integers, > etcetera. Incorrect. The hyperreals are incomplete, whereas the reals are > complete. Also, all integers are finite, whereas this is false with > hyperintegers. > ... That's a good point. If iota were the least positive real then it would not be the fluxion infinitesimal. Infinitesimals are in regular use throughout application, and generally their meaning is as the differential. That pedantically infinitesimal means as a result of applying the inductive limit over finite differencdes does not change the fact that for no finite difference is that difference the differential, which non-zero, is thus infinitesimal. Basically the notion of R as complete ordered field, R^bar, contiguous sequence of points, R^umlaut, or both, R^bar^umlaut, is graphically indicated by those notational marks. Also there is a line of argument that the natural integers, as a set, for example, contain themselves, that N E N, for example from the notion that incompleteness results about the natural integers would show the natural integers to contain nonstandard (read: infinite) natural integers. Then, the hyperreals, incomplete, would represent a proper subset of the reals, complete, that describe the continuum, also complete. Ross -- Finlayson Consulting === Subject: Re: how to list all of the real numbers So, with that out of the way, then there is the consideration of ZF as > a theory and the notion that it fulfills the properties of being a set. ZF itself is not a set, it's a theory. > For any subset of any set in ZF, it's a subset of ZF, for any > element or set in ZF, it's an element of ZF. ZF is defined by its > elements, ZF is a set. Incorrect. ZF is not defined by its elements. As a theory, there > are no elements native to it. Your elements live in models, and > there are many models of ZF. For example, there are nonstandard > models of ZF which contain infinitesimals, whilst there are standard > models that do not. ZF is a theory, and thus defined by its axioms alone. Your remaining post is rendered moot by this error. > Jonathan Hoylehttp://www.jonhoyle.com ZF is defined by a collection of axioms, which define a collection of sets, which is a unique collection of sets, else ZF's axioms would not be pairwise independent. A conjecture here is that given the collection of sets that comprise a set theory's universe, the axioms could be derived, basically saying that the axioms that establish the existence of objects of discourse are specifically reflected by those objects. There is no model of ZF in ZF, where there's no ordinal sufficient to model the entirety of the collection of sets in ZF, a set. When you say infinitesimals, Jon you generally mean specifically the Robinsonian hyperreals, and none other, where, there are a wide variety of other interpretations of what comprise the infinitesimals, that correctly used give perfect analytical results (true results). Does ZF have a universe over which quantification is possible? Skolemize, it's countable. That is to say that, for example, using model theory, there's a generic extension N^G containing no elements not in N, the natural numbers, that bijects to R, the real numbers, that there does exist a set, of ordered pairs of elements from N^G and R, that establishes the equivalency of N^G and R. Ross -- Finlayson Consulting === Subject: Re: how to list all of the real numbers A discussion point is that the collection of sets that comprise ZF, in > any supertheory containing more sets than ZF, would be the Russell set > and irregular. > It might be a set in that supertheory, but what guarantees that it will > be the set of all of the sets of that supertheory? Or if it contains all > the sets, that it might not itself be a set but only a class, as in NBG? > Well, it seems that if the properties of it as a set didn't hold, > then, it would not be a theory. It may seem so to you, but your judgement in such cases is notoriously > unreliable. > Until Ross can produce such a supertheory, any claim that one exists is > irregular. > It seems you admit that the theory ZF is a collection of all the sets > of ZF. > It is both more, and less. > In a way it is much less, being reducible to a collection of axioms. > In what way is it more, simply the recursive definition and > redefinition of set-theoretic operations upon itself? Please expand. The rules by which one establishes that certain sets exist in ZF are > part of ZF but are not themselves sets of ZF, so they make ZF more than > just sets. > There is no ur-axiom that requires any set theory to conform to Ross' > dually-self-intraconsistent null axiom theory nor that any set need > have a universal compliment. Ross is off in some sort of unreal world > again. > Yeah, there isn't. Your insult doesn't seem a reasonable statement. > It was more in the nature of an observation that Ross is again relying > on the existence of things like a dually-self-intraconsistent null > axiom theory for which there is no evidence of existence, and > considerable reason to doubt such existence. > There is quite some evidence of its existence. Not in mathematics, there isn't! > Yes, there is. That, for example, the construct or lack thereof known as the empty set exists is quite parallel to the notion of existence or lack thereof of the void as is known in a variety of theories, philosophical theories of creation, or for example Hegel's Nothing. In the conflation of those notions, which is not unreasonable, evidence can be inferred/deduced, from a quite minimal collection of primary assumptions. > (It is not actually novel to suggest the physical > universe contains itself, in a sense.) > But it is quite novel to suggest that the physical universe is a set > theory. > No, it's not. > It is to mathematicians, especially set theorists. > No, I think there has been that notion since antiquity, consider for > example the gematria, number-theoretical notions,or how the ancient > geometers believed geometry essentially perfect, explaining all. Many > contemporary mathematicians see a mathematical universe as self- > evident, in a philosophical way. None of which is at all relevant to the suggestion that > the physical universe is a set theory. > having equivalent properties (element, subset, definition by elements) as a set thus that it waas a set, thus that as a set for any set A in ZF that A E ZF, A < ZF, and ZF is defined by the collection of sets that comprise it, which include, as generally mathematical structures in set theory are modelled as sets, all mathematical structures representable in a set theory, then, yes that seems to further the notion that the theory, specified in so few axioms (or axiom schemata), is a collection, and a set. I'm reminded of discussion some time ago of Boucher's definition of the natural integers as zero and successors, quite similar to Peano/ Presburger, except Andrew was forwarding the notion of a system where Goedelian incompleteness doesn't hold, as there was a completion of sorts of the natural integers. The consideration was whether asserting those axioms was the same as asserting the existence of {0, 1, 2, ...}, specified explicitly. Then, in this context, it's not so difficult to conceive of the notion of ZF the theory being a collection of sets that satisfies the properties matching the definition of a set, and thus is a set, except for those perhaps so blind as they will not see, who care. That is where that the axioms would describe the sets that thus exist, generally with the notion of the cumulative hierarchy in a generative process, would find that the same set of axioms would be possible to deduce given the contents of the collection, or that no other set of independent axioms would be so derivable. Consider the notion that physical objects could be mapped to mathematical objects, and fields among them to functions among them, and there would be infinitely many, and the universe and physical existence would be a counterexample to the powerset result. A wide variety of cosmologists have the opinion that the universe is infinite, some even in extent. Whether it's so or not (which it is) is immaterial to the argument, in that presupposing some finite that the functions between those would have functions between those and etcetera, ad infinitum. Then, there's the consideration of the description of the equivalency function EF(n) = n/d, n randing from zero to d, d->oo. It ranges from zero to one, via a simple argument it's shown dense in the unit interval, and, it's well-ordered by the real numbers' natural order. That is where, it might be considered that standardly in analysis: EF(n) = 0 for each n < oo. Yet, algebraically, EF(m)/EF(n) = (m/d)(d/ n) = m/n, and for m > n, m/n > 1. That helps justify the notion that EF(n+1) > EF(n). So, on the way to infinity, where as n->d, EF(n)->1, the function is monotone strictly increasing. Then, where the difference between EF(n) and EF(n+1) basically vanishes, and EF(d) = 1, it is deduced that the sequence of points is equidistributed in [0,1], then, the elements of the range are dense in [0,1]. Ross -- Finlayson Consulting === Subject: Math man Atle Selberg dead at 90: posted by Akhila Raman Math man Atle Selberg dead at 90: posted by Akhila Raman -Akhila Raman === Subject: Re: JSH: Final Elimination of , > Time is up. > Everybody is fed up with JSH. > No progress, no math. > YEARS and YEARS of bull. > Just little girly bitching so he might get noticed. > The poof even had to redefine a math proof, into a spoof. > Always in error, never in doubt (UA) > Trolls die horrible deaths. Is your last name Dickus? He has a wife--you know? -- Michael Press === Subject: Re: JSH: Surrogate factoring, periodic behavior Factored trying 5 surrogates on the fifth surrogate using k=1 where >the start was with n=7. I ran my usual tests again on 500 random composite odd numbers that > are multiples of two different primes, each in the range 500 to 1000. > The results are compared to Fermat's method, trial factorisation (both > forward and reverse) and random picking. Fermat average = 7.58 probes. > JSH average = 1635.83 probes. > Probe ratio = 1 : 215.752 > Trial average = 118.52 probes. > Reverse average = 12.12 probes. > Random average = 727.79 probes. 500 trials, 0 misfactors found. Here is output from my program and a run I just did testing out some new theory. Here for various reasons I won't explain I'm using k=30, starting with n=1, and there is a lot wrong with this example from my standpoint as by my theory I don't think it should have factored at this point. java Factor 34587541 n_max=0 Number factored. Total all combinations: 21 Time: 0 Time/combination: 0.0 Surrogate: ( 11^2 )( 13 )( 19 )( 8101 ) Product: 242114587 Surrogate combinations checked: Initial Factorization: f_1=307 f_2=112663 Now checking its factors... Success! Factors: ( 307 )( 112663 ) Product: 34587541 In coming is 34587541 Factored for k : 3 Not factored for k: 4 Factored fuel percentage: 42% Factored fuel : 3 Fuel not factored: 4 Factored fuel percentage: 42% Processing time: 78 Number of digits: 8 bitLength=26 The program I use loops through trying to factor the surrogate and if it can't fully factor it just keeps on going, where in this case it says it factored 3 fully and could not fully factor 4, so I guess it checked 7, but now I'm not sure what. As it looks like to me it only tried one surrogate, so I'm not sure why it says it checked seven unless, um, the code is doing something I'm not sure about which wouldn't be a surprise. I'm kind of half-heartedly hacking at it because I think it stupid that the world should suffer because you people lie. How is that fair? In any event, it's an example of what I mean of the kind of behavior I see all the time with dinky numbers. Totally not random. > Average k's tried per factorisation: 1.000 > Average n's tried per factorisation: 47.040 k was fixed at 1 and n was 7, 8, 9, ... >Part of the problem I've run into with comments about surrogate >factoring have been repeated claims it works only as good as trial >division, but hey, I programmed the damn thing. Any chance of seeing your code? > No. But you know I'm rather fascinated by this entire process as it reminds me of when I was working on prime counting, and eventually posters just went to lying about my research. But this time if I figure out what's going on I can just factor big numbers, and see if you try to lie your way out of that, which makes the situation different. Your only hope is that I'm bluffing. Ok, I'm bluffing. Sleep ok tonite. That's my present to you. James Harris === Subject: Re: JSH: Surrogate factoring, periodic behavior Ok, I'm bluffing. Sleep ok tonite. > But where's the hammer?! :-o === Subject: Re: JSH: Surrogate factoring, periodic behavior [JSH ] > ... > Surrogate factoring is kind of mysterious because people can do these > checks as they have posted about that indicate very much worse than > random! But how is that possible? Isn't random the bottom? Jimmy, Jimmy, Jimmy. You've heard it before, but just in case you really wonder today: you should take a break from research long enough to learn something about the topics you claim to be so intrigued by. Honestly, over a decade you manage to stumble into less that's actually true than most students can pick up in a week just by reading. Sure, you're a self- proclaimed super genius, and they're not, but not even a super-genius like you can overcome their huge advantage of starting with what's already known. So take a week off to study, then try answering your own questions above. You can do it if you really try -- they're not hard questions. > Sigh. Years ago I wondered, might you be able to factor one number by > instead factoring another? As if you were the first to wonder this -- LOL. > ... === Subject: Re: Comprehensive Solution Manual for Textbooks Communications by Goldsmith. === Subject: Roots to Polynomials and Power Series http://mypeoplepc.com/members/jon8338/roots_to_polynomials_and_power_series/ === Subject: Re: PARADISE LOST: Debunking Cantor's theory M = > 1 > 11 > 111 > ... M' = > 111... > 11 > 111 > ... > However, the ordinal numbers you are dealing with are > the lengths of the sequences of ones in the rows, > not the numbers of columns in a row. > No. > O.K. A is the set of second indexes in M'. > In that case, A does not contain omega and > A+1 does not contain omega+1. > The fact that M' extended contains a line of length > omega, means that M' contains a line of length > omega. The fact that M' contains a *line of length* > omega does not mean that M' contains an *second index* > omega. Correct. A sequence does not contain an index omega but can be an > ordered set of order omega. > Extending a sequence means to get a an ordered set of order omega + 1. > M' does not contain a second index omega. A does > not contain an element omega. A+1 does not contain > omega + 1. But by extending all rows of M' we get a set of order omega + 1. Don't > we get at least one non-natural index, necessarily? Yes. However extending all rows of M' is not the same thing as adding 1 to each second index in M'. If we extend all rows of M' we get a second index omega +1. If we add one to every second index of M' we do not get omega + 1. A+1 does not contain omega + 1. - William Hughes === Subject: Re: PARADISE LOST: Debunking Cantor's theory If we add the ordinal 1 to every element of A and to every element of > B, > then A + x contains omega + 1 > No it does not. A does not contain > 111... > so A does not contain omega. > B does not contain omega either. > Correct. Neither A nor B contains omega. > And contrary to what you claim > A + 1 = B + 1 So appending one 1 to 111... does not introduce an element with index > omega + 1? Appending one 1 to 111... does indeed introduce an element with index omega +1. However, appending one 1 to 111... is not adding 1 to any element of set of second indexes. It is extending a line of length omega. A and B are sets of second indexes. So the fact that appending one 1 to 111... introduces an element with index omega+1 has nothing to do with A+1 or B+1. Neither A nor B contains omega so neither A+1 nor B+1 contains omega+1. Note that A+1 equals B+1 - William Hughes === Summary: UDP === This server is temporarily under UDP because of recent massive hipcrime attacks, until the problem is solved by their administrators. We are sorry for the inconvenience. See news.admin.net-abuse.policy and news.admin.net-abuse.usenet for more details. === Subject: Re: Number of matching sock pairs, how low does it go? >While pondering the lack of matching pairs in my sock drawer, I >thought of the following way to frame it -- suppose you start with k >matching pairs of socks. Each week you lose 2*l socks at random, and >buy l new pairs. Suppose each pair is unique. What is the expected >number of matching pairs in the drawer after a while? > I don't care for using an ASCII lower case ell as a variable, so I change that to an em. Let X_n be the the number of complete pairs before the addition of new pairs at the end of week n (so X0 = k - m). We wish to determine the limiting value e of e_n = EX_n.. Note that we start week n + 1 with X_n + m complete pairs. For i = 1, 2,..., X_n + m, let I_i indicate the presence of the complete pair i at the end of the week. Then X_(n+1) = sum(i=1..X_n + m, I_i), and X is a Markov chain. So E[X_(n+1) | X_n] = sum(i=1..X_n + m, EI_i) = (X_n + m) EI1 EI1 is the probability that neither sock in pair 1 is lost. This is p = C(2k - 2, 2m) / C(2k, 2m) = (k - m) [2(k - m) -1] / [k (2k - 1)], where C(n, r) denotes the binomial coefficient, n choose r. So e_(n+1) = EE[X_(n+1) | X_n] = p (e_n + m). Therefore, e = p (e + m), which implies e = p m / (1 - p) = (k - m) [2 (k - m) -1] / (4k -2m -1), modulo my algebra. Nice problem. You might want to submit it to Mathematics Magazine. Maybe ask for the variance as well. -- Stephen J. Herschkorn sjherschko@netscape.net Math Tutor on the Internet and in Central New Jersey and Manhattan === Subject: Re: Number of matching sock pairs, how low does it go? alt.math.recreational,alt.sci.math.probability,sci.math: >While pondering the lack of matching pairs in my sock drawer, I >thought of the following way to frame it -- suppose you start with k >matching pairs of socks. Each week you lose 2*l socks at random, and >buy l new pairs. Suppose each pair is unique. What is the expected >number of matching pairs in the drawer after a while? > I don't care for using an ASCII lower case ell as a variable, so I > change that to an em. Ouch. In fact I read it as a one, thereby significantly simplifying the problem. [...] Brian === Subject: Re: Complete Electronic Solution Manual in pdf! Get'em Quick! > I have the comprehensive solutionsmanualin electronic format for the > following textbooks. They include complete solutions to all the > problems in the text, except where noted below in the listing. Payment > is through Paypal if you have a paypal account or Propay if you prefer > to pay with credit card over a secured internet https protocol and do > not have a Paypal account, for the amount of US $7-$15 per item (about > 4 of my newestsolutionmanuals are a little higher than $15). Email > me calgirl22[at]gmail.com but please DO NOT POST HERE because I will > not be able to help you, but instead email and ask me for thesolution > that you need. Also, if you want other solutions for other books that > are not listed here, email me and ask. > A Course in Game Theory by Osborne, Rubinstein > A Course in Algebraic Number Theory by Cohen > Adaptive Filter Theory, 4th Edition, by Haykin > Adaptive Control, 2nd. Ed., by Astrom, Wittenmark > Advanced Engineering Mathematics, 8th Editoin, by Erwin Kreyszig (even > solutions) > Advanced Engineering Mathematics, 9th Edition, by Erwin Kreyszig (even > solutions) > Advanced Macroeconomics, David Romer > Advanced Mathematical Concepts Precalculus With Applications by > Holliday [ISBN: 0028341759] > Advanced Modern Engineering Mathematics, 3rd Ed., by G. James > A First Course In Differential Equations, 7th Edition, by Zill, Cullen > Analog Integrated Circuit Design, 1st Ed., by Johns, Martin (text > ebook andsolutionmanual) > Analysis and Design of Analog Integrated Circuits, 4th Ed., by Gray, > Hurst, Lewis, Meyer > Analytical Mechanics, 7th Edition, by Fowels, Cassiday > An Interactive Introduction to Mathematical Analysis, by Jonathan > Lewin > An Introduction to the Mathematics of Financial Derivatives, 2nd Ed., > by Neftci [ISBN: 0125153929] > Antenna Theory, 2nd Ed., by Balanis > Antennas for all Applications, 3rd Edition, Kraus, Marhefka > Applied Linear Statistical Models, 5th Ed., by Neter (Selected Sol.) > Applied Numerical Analysis, 6th Edition, by Gerald, Wheatley > Applied Numerical Methods with MATLAB for Engineers and Scientists, > 1st Ed,. by Chapra > Applied Statistics and Probability for Engineers, 3rd Ed., by > Montgomery, Runger (Selected Solutions) > Applied Strength of Materials, 4th Edition, by Mott > A Transition to Advanced Mathematics, 5th Edition, by Smith, Eggen, > Andre > Automatic Control Systems, 8th Edition, by Kuo, Golnaraghi > Basic Business Statistics: Concepts and Applications, 10th Ed., by > Berenson, Krehbiel, Levine (chap1-18) > Basic Engineering Circuit Analysis, 7th Ed., by J. David Irwin > Basic Engineering Circuit Analysis, 8th Ed., by J. David Irwin, Nelms > (Missing a chapter or 2) > Bioprocess Engineering Principles by Doran > Calculus Early Transcendental, 5th Ed., by James Stewart > Calculus - Early Transcendentals, 7th Ed., by Anton, Bivens, Davis > Calculus: Graphical, Numerical, Algebraic, 3rd Ed., Waits, Finney, > Demana, Kennedy > Calculus: Multivariable, 5th Edition, by James Stewart > Calculus: Single Variable, Early Transcendental, 5th Edition, by James > Stewart > Calculus, Single and Multivariable, 3rd Ed., by Hughes-Hallett, > McCallum > Calculus: Study and Solutions Guide, Vol. 1, 7th Ed., by Larson, > Hostetler, Edwards > Chemical and Engineering Thermodynamics, 3rd Ed., Stanley I. Sandler > Chemical Engineering Volume 1, Sixth Edition, by Richardson, Coulson, > Backhurst, Harker > Thornton > College Physics, Volume 1: 7th Edition, by Serway, Faugh > College Physics, Volume 2: 7th Edition, by Serway, Faughn > Communications Systems, 4th Ed., by Haykin > Communications Systems Engineering, 2nd Edition, by Proakis > Computational Techniques for Fluid Dynamics by Srinivas, Fletcher > Computer Networks, 4th Ed., by Andrew S. Tanenbaum > Computer Networks: A Systems Approach, 3rd Edition, by Davie > Control Systems Engineering, 4th Ed., by Norman Nise > Corporate Finance, 6th Edition, by Ross > C++ How to Program: Intro Object-Oriented Design with the UML, 3rd > Ed., by Deitel, Nieto > Data and Computer Communications, 8th Edition by Stallings > Database Management Systems, 3rd Ed., by Ramakrishnan, Gehrke (Sol. > for Chapters 2-21, odd only) > Design of Analog CMOS Integrated Circuits, 1st Edition, by Razavi > Design of Analysis of Experiments, 6th Edition, Montgomery (missing > chapter 6-8) > Design of Machinery, 3rd Ed by Robert L. Norton > Design With Operational Amplifiers and Analog Integrated Circuits, 2nd > Ed., by Sergio Franco > Design With Operational Amplifiers and Analog Integrated Circuits, 3rd > Ed., by Sergio Franco > Device Electronics for Integrated Circuits 3rd Edition by Muller > Differential Equations with Boundary Value Problems, 2nd Ed., by > Polking, Arnold Digital And Analog Communication Systems 7th Ed., Leon > W. Couch > Digital Communications, 4th Edition, by Proakis > Digital Communications: Fundamentals and Applications, 2nd Ed, Skylar > Digital Design, 4th Edition, by Mano, Ciletti > Digital Image Processing, 2nd Edition, by Gonzalez, Woods > Digital Integrated Circuits, 2nd Ed., by Rabaey (Solutions ONLY for > Chapters 3, 5, 6, 10) > Digital Signal Processing: A Computer Based Approach, 1st Ed., by > Mitra > Digital Signal Processing: A Computer Based Approach, 2nd Ed., by S. > Mitra > Digital Signal Processing: A Computer Based Approach, 3rd Ed., by S. > Mitra > Digital Signal Processing: Principles, Algorithms and Applications, > 3rd Edition, by Proakis > Discrete Time Signal Processing, 2nd Edition, Oppenheim > Dynamics of Mechanical Systems by C.T.F. Ross > Econometric Analysis, 5th Edition, by Greene > Wooldridge > Econometrics of Financial Markets, by Adamek, Cambell, Lo, MacKinlay, > Viceira > Electrical Properties of Materials, 7th Ed., by D. Walsh, L. Solymar > Electric Circuits 6th Ed. by Nilsson > Electric Circuits 7th Ed. by Nilsson > Electric Machinery, 6th Ed., Fitzgerald, Kingsley, Umans > Electric Machinery Fundamentals, 4th Ed by Chapman > Electromagnetic Fields and Waves by Iskander (...) > Electronic Circuit Analysis, 2nd Ed., by Donald Neamen > Electronics, 2nd Ed., by Allan R. Hambley > Elementary Differential Equations, 8th Edition, by Boyce, DiPrima > (some odd/even) > Elementary Principles of Chemical Processes, 3rd Ed., by Felder, > Rousseau > Elements of Chemical Reaction Engineering, 3rd Ed., by H. Scott Fogler > Engineering and Chemical Thermodynamics, by Koretsky [ISBN: > 0471385867] (No sol. for chapt 6) > Engineering Circuit Analysis, 6th Edition, Hyat > Engineering Electromagnetics, 6th Ed W. Hayt, J. Buck > Engineering Electromagnetics, 7th Ed., Hayt, Buck > Engineering Fluids Mechanics 7th Edition by Crowe > Engineering Fluids Mechanics 8th Edition by Crowe > Engineering Mathematics, 4th Ed., by John Bird > Engineer Mechanics: Dynamics, 4th Ed., by Bedford > Engineering Mechanics: Dynamics, 10th Ed., by Russell C. Hibbeler > Engineering Mechanics: Dynamics 11th Ed. by Hibbeler > Engineering Mechanics: Dynamics 5th Ed. by Meriam, Kraige > Engineering Mechanics: Statics, 4th Edition - A. Bedford, Wallace > Fowler > Engineering Mechanics: Statics, 5th Ed., Meriam, Kraige > Engineering Mechanics: Statics, 6th Ed., Meriam, Kraige > Engineering Mechanics: Statics, 10th Ed., by Russell C. Hibbeler > Engineering Mechanics: Statics 11th Ed. by Hibbeler > Experiments with Economic Principles by Bergstrom, Miller > Feedback Control of Dynamic Systems, 4th Edition, by Powell, Emami- > Naeini > Financial Accounting, 4th Ed., by Libby, Short (Chap1-14) > Financial Accounting: An International Introduction, 2nd Ed., by > Alexander, Nobes > Finite Element Techniques in Structural Mechanics by Ross > Fluid Mechanics - 5th Edition by Frank M. White > Fluid Mechanics and Thermodynamics of Turbomachinery, 5th Ed., by S. > L. Dixon [ISBN: 0750678704] > Essentials of Fluid Mechanics: Fundamentals and Applications, 1st Ed., > by Cengel & Cimbala > Fluid Mechanics with Engineering Applications, 10th Edition, by > Finnemore > Fundamentals of Aerodynamics, 3rd Edition, by J. D. Anderson, Jr. > Fundamentals of Applied Electromagnetics, 1st Ed., 2001 Media Edition, > by Ulaby > Fundamentals of Applied Electromagnetics, 5th Ed., 2008 Media Edition, > by Ulaby > Fundamentals of Digital Logic with Verilog Design, 1st Edition, by > Brown, Vranesic > Fundamentals of Digital Logic with VHDL Design by Stephen Brown, > Zvonko Vranesic > Fundamentals of Electric Circuits, 2nd Edition, by Alexander > Fundamentals of Electromagnetics with Engineering Appls by Wentworth > Fundamentals of Fluid Mechanics, 5th Ed. by Munson, Young.. > Fundamentals of Heat and Mass Transfer, 4th Ed by Incropera... > Fundamentals of Heat and Mass Transfer, 5th Ed by Incropera... > Fundamentals of Heat and Mass Transfer, 6th Ed by Incropera... > Fundamentals of Logic Design, 5th Ed., by Roth Jr. > Fundamentals of Machine Component Design, 3rd Ed., by Juvinall > Fundamentals of Machine Component Design, 4th Ed., by Juvinall > Fundamentals of Machine Elements, 2nd Ed., Hamrock, Jacobson, Schmid > Fundamentals of Physics by Halliday, 7th Ed., Walker, Resnick > Fundamentals of Semiconductor Devices, 1st Edition by Anderson > Fundamentals of Structural Analysis, 2nd Ed., Chia-Ming Uang, Kenneth > Leet > Fundamentals of Thermal-Fluid Sciences, 2nd Ed. by Cengel > Fundamentals of Thermal-fluid Sciences, Int'l 2nd Ed. by Cengel > Fundamentals of Engineering Thermodynamics, 5th Ed. by Shapiro > Fundamentals of Thermodynamics, 5th Ed., by Sonntag, Borgnakke... > Fundamentals of Thermodynamics, 6th Ed., by Sonntag > Geometry, 04 Edition, by McGraw-Hill [ISBN: 0078296374] > Guide to Energy Management, 5th Edition, by Pawlik > Heat Transfer: A Practical Approach - ... read more ? I need Solutions Manual: Fluid Mechanics with Engineering Applications Finnemore 10th Edition. === Subject: Re: Quaternions as a representation of four-vectors > As I can understand from wikipedia, the idea of using there 'hyper- > complex' number simply as a replacement for the four-vectors in > physics (I'm thinking about special relativity) is new. (Sorry if I'm > wrong.) This was already old and essentially rejected when I was in school >30 years ago. Tensor approaches have proved to be MUCH more effective, and of MUCH wider applicability. > Position four-vector: R = (ct,x,y,z) [...] One problem with this approach is that this is not really a 4-vector (though it sometimes masquerades as one in elementary books). The basic attractiveness of quaternions is that their norm is naturally the same as the norm of a 4-vector in the Minkowski coordinates of SR. But AFAIK they are completely unable to sensibly and simply handle other coordinates -- we physicists often use spherical and cylindrical coordinates, and quaternions no longer have the same norm naturally. And then there are the curved manifolds of GR.... > Position four-vector in one spatial direction: > R = ct + j*x > When transformed with the Lorentz-transform: > R' = ct'+j*x' = 1/(1-(v/c)^2) (ct+j*x) > -Just so much easier than usual with vectors and matrix. Hmmm. Count degrees of freedom in the transform and you'll find they are the same as the matrix method (of course!). Not really simpler, merely different. Please remember the world has 3+1 dimensions, not 1+1. So write the Lorentz transform in an arbitrary direction: you'll find it gets complicated and quite messy (with a hyper-complex constraint equation to ensure it is a valid Lorentz transform) -- Not really easier is it? BTW theoretical physicists almost never perform a Lorentz transform -- they work with invariants most of the time so there is no need. Experimenters, of course, often use them because the theory is usually expressed in the center-of-mass frame, but the detectors are in the laboratory frame, and those are often not at all the same. Note, however, that quaternions and especially octonions have other applications in physics. Not as 4-vectors but because of their group properties. I am not an expert in this.... Tom Roberts === Subject: Re: Pi in non-euclidiean spaces Nntp-Posting-Host: hera.cwi.nl ... > The Greeks also defined, for example, sqrt(2) as the length of the > diagonal of a unit square. Does the sqrt function therefore also change > in different geometries? Does sqrt(8) sometimes not equal 2*sqrt(2)? No, they must've defined the diagonal of a unit square as sqrt(2) > because pythagorean theorem requires sqrt a priori. The Greeks did not define sqrt, as far as I know. And the Pythagorean theorem does not require it at all. The theorem (originally) was: Given a triangle with a right angle. The area of the square on the hypothenusa is the sum of the areas of the two squares on the other two sides. There does exist beautiful geometric proofs of this theorem. *But* the theorem only holds in Euclidean geometry. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Pi in non-euclidiean spaces days. My association with the Department is that of an alumnus. > So you should really talk about the ratio, not pi. > No, the OP had it right and everyone here got it wrong. > Pi IS the ratio of the circumference of a circle to its diameter - > that's how the Greeks defined it, that's what they meant by it. This > is obvious as pi predates the discovery of the irrational numbers. > If you want to separate the number pi from pi then it's you who > needs to make the distinction, not the OP. > Pi takes on separate values in non-Euclidean geometries. > Oh, well if the *Greeks* defined it that way, then there's nothing we > can do about it. The definition is fixed forever. You are free to define it anyway you like, just not impose your >definitions over those who defined it first (unless qualified by some >statement). I had no idea that the original poster was an ancient greek! Of course, if he happens not to be an ancient greek posting from the past, then how are we impos[ing] this new definition on those who defined it first? > The Greeks also defined, for example, sqrt(2) as the length of the > diagonal of a unit square. Does the sqrt function therefore also change > in different geometries? Does sqrt(8) sometimes not equal 2*sqrt(2)? No, they must've defined the diagonal of a unit square as sqrt(2) >because pythagorean theorem requires sqrt a priori. Yeah, they must have done that, even though one can state the pythagorean theorem without invoking square roots, and even though the existence of inconmeasurable quantities predates the pythagorean theorem. But they must have done it exactly like you say... -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: Pi in non-euclidiean spaces [...] > Yeah, they must have done that, even though one can state the > pythagorean theorem without invoking square roots, and even though the > existence of inconmeasurable quantities predates the pythagorean > theorem. But they must have done it exactly like you say... square root ;-). === Subject: Re: Pi in non-euclidiean spaces days. My association with the Department is that of an alumnus. >[...] > Yeah, they must have done that, even though one can state the > pythagorean theorem without invoking square roots, and even though the > existence of inconmeasurable quantities predates the pythagorean > theorem. But they must have done it exactly like you say... square root ;-). I once read (don't remember exactly which book it was, but I believe it was Martin Gardner's Fads and Fallacies in the Name of Science) of some crank in the U.S. who claimed to have solved the problem of trisecting the angle. Upon review, his proof consisted of taking a given angle, constructing an angle that was triple the size of the original, and then constructing a new angle that was of the same measure as the original from the two figures. I wonder what in your response made me think of that... -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: solution manual does anyone have a solution manual for SWITCHING AND FINITE AUTOMATA THEORY KY ZVI KOHAVI .IF YES PLEASE LET ME KNOW. === Subject: Re: Error det & corr Nntp-Posting-Host: hera.cwi.nl > Can any one help me out to find me what methods are exactly used to do > following: Many. > 1. 2-bit error correction > 2. 2-bit error detection > 3. 3-bit error correction > 4. 3-bit error detection In general the methods for correction are more elaborate than those for detection. There is a whole field of mathematics devoted to this. Look for coding theory. For instance, for 1-bit error detection you can append the xor of all the bits to the message, and you are done. But in general the method used depends on the size of the message. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Single dimensional geometry I just want to check the rationale, in geometry, of using N dimensional domain to visualize the dependencies among N variables. How about representing the N variables using a single dimension (or may be 2 in case of complex variables)? I just want to stick to the notion of the single straight-line to represent all real numbers. For example, what is the geometrical notion for 6 multiplied by 4? Is it a rectangle measuring 6 and 4 on its orthogonal sides? Does that rectangle represent the number 24? How can we represent 6,4 and 24 on R-line while having a geometrical construction that can show the relationship among these 3 numbers? Well, logarithmic scaling of the R can possibly show the multiplication, but it fails to show the simple additions. For a start, i considered a general equation which can behave as x+y=constant or xy=constant based on the a third variable. Ofcourse, it is trivial to find several equations such as (x +y)cos(t) + xy.sin(t) which would suffice my requirements. However, I need a geometrical construction which can locate the variables x and y on the same line and represent the given equation. For example, Consider the following sketch. If xPy is a right angle, then it follows that xy = constant, and if the angle is very small, then x+y = constant. This is again a very trivial example. I'm looking for geometrical means of visualizing the functions of N variables, where all variable are located on the same line. This avoids using multi- dimensional spaces. | | P /| / | / | / | / | -------/-----+----------- x o y The basic problem seems to be in the notion of representing, for example, 2x3x4 as a 3-D block measuring 2,3 and 4 on its sides, and number of all unit cubes in it indicating the result of this operation. I wonder if we can't stick to a single straight line for visualizing numbers and their operations, without increasing dimensions or changing shape of number line or space. - venkat === Subject: x^a + y^a = 1 as a circle arc I was trying to find the equation for the mirror reflection of the unit circle arc (x^2 + y^2 = 1) in the first quadrant (0 I was trying to find the equation for the mirror reflection of the > unit circle arc (x^2 + y^2 = 1) in the first quadrant (0 using x+y=1 as the mirror. The third quadrant of the circle (x-1)^2 + > (y-1)^2 = 1 would be the arc I'm looking for. However I need it in the > form of x^a + y^a = 1, where a < 1. That's not possible. > I'm trying to find the value of a. > The value 0.5645... seems to be nearest one, The value of a you seem to have had in mind is precisely -2 log(2)/log(3/2 - sqrt(2)) or approximately 0.5644763825. > but then this curve can only touch the circle at three places > tangentially. Can this be proven that we can't find such value? Essentially, you _already_ have that proof. David === Subject: Re: Paul R Halmos, Measure Theory, Sec 36, Question (2) Read the problem more carefully and then fubinate. -- Ignorantly, Allan Adler * Disclaimer: I am a guest and *not* a member of the MIT CSAIL. My actions and * comments do not reflect in any way on MIT. Also, I am nowhere near Boston. === Subject: Re: Tommy is an embarassment to whatever educational system attempted to teach him English Nntp-Posting-Host: hera.cwi.nl > ... > Alas, the poor Dutch, having TOMMY among them (snicker). I do think tommy is *not* Dutch. > ... > So don't embarass the Dutch by identifying with them. He doesn't. ... > By He doesn't, do you mean Tommy doesn't embarass the Dutch, or > Tommy doesn't identify with them? Both. > Okay, Dutch may be ambiguous. Not at all. > But Tommy says above he speaks Dutch and implies that he's from > Belgium (alas for Belgium). Yup. So he is not Dutch. > I think Tommy is some sloppy person from the United States, and I can > say that since I'm from the United States. I think not. I think Tommy really is from Belgium. > Tommy should GO BACK TO SCHOOL FOR ENGLISH! You have no idea about the schooling system in Europe, where there is a plethora of languages. I think Tommy's first language is Dutch (or Flemish if you wish), and his second language French. (For me it was, in order, Dutch, French, English/Latin and German, with final exams both oral and in writing, in all except Latin.) You did note that I utilise the British spelling? > So then maybe Tommy can learn English AND learn to use English (happy, > Joshua Cranmer?), and then Tommy can USE English properly. I note that you have not been able to thank me properly in Dutch, although you used a lot of languages (and tried, I think, Dutch, but that was German). In general, language problems should not be a point of discussion. But one reason I think Tommy is indeed Belgian is that he uses Bourbaki-ist definitions. When I was a student in Amsterdam the courses were about one half Bourbaki-ist and one half Anglo-Saxon (this made you at least aware of the differences). I think the Bourbaki method is still used in France, Belgium and French speaking Switzerland. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Online dictionaries are disappointing you used a lot of languages (and tried, I think, Dutch, but that was > German). Sorry, Dik, but I tried. It wasn't (meant to be) German. I accessed an online dictionary for the Dutch word for thank 9r thank you, and got the word I used. I won't try again to thank you in Dutch, since I doubt I'll find the right word. Online dictionaries are disappointing as to accuracy or you need the context to use the right word. I absolutely do not pretend to know other languages fluently, like others who think they know English. I do know some French - I learned it in school for a career in mathematics, since French is (was?) one of the primary languages of mathematics. I know some Spanish, too. I got it mostly from U.S. television! BUT, I'll just stick with English, and thank you in that manner. === Subject: Re: Tommy is an embarassment to whatever educational system attempted to teach him English > On Aug 31, 6:52 pm, Dik T. Winter > ... > Alas, the poor Dutch, having TOMMY among them > (snicker). > I do think tommy is *not* Dutch. > ... > So don't embarass the Dutch by identifying with > them. > He doesn't. > -- > dik t. winter, cwi, kruislaan 413, 1098 sj > amsterdam, nederland, +31205924131 > home: bovenover 215, 1025 jn amsterdam, > nederland;http://www.cwi.nl/~dik/ By He doesn't, do you mean Tommy doesn't embarass > the Dutch, or > Tommy doesn't identify with them? Okay, Dutch may be ambiguous. But Tommy says above he speaks Dutch and implies that > he's from > Belgium (alas for Belgium). In another thread, Tommy says: and if you ever visit belgium again , let me know > :-) I imagine Tommy skulking around Belgium, confusing > and confounding all > of those people in Belgium he encounters. Poor, poor > Belgium. Well, I think Tommy is some sloppy American. And I > can say that, > since I'm American. Okay, let me not be ambiguous, > since Canadians > and people in Latin America don't like the United > States co-opting the > word American (ooo, those evil imperialistic > United-States-ians!). I think Tommy is some sloppy person from the United > States, and I can > say that since I'm from the United States. Tommy should GO BACK TO SCHOOL FOR ENGLISH! (note my allcaps for emphasis). So then maybe Tommy can learn English AND learn to > use English (happy, > Joshua Cranmer?), and then Tommy can USE English > properly. and when will neilist learn math ?? i will learn english 2 days before neilist learns math. go to sci.english.spelling neilist and stay there since you never post math anyways. and yes i might be sloppy and dont read before i press post... so what ?? i can speak english very good by the way. go to sci.english.spelling and not sci.english.grammar , your not that good according to others :-) so have fun discussing spelling , since you dont like to do math anyways... as for dik T winter wat is dat voor zever kerel ? waarom zou ik niet van belgie zijn ? toch niet omdat ik typfouten maak ? of omdat ik niet herlees voor ik een bericht verzend ? wedden voor 5000 euro dat ik van belgie ben ? kom het geld maar brengen zou ik zo zeggen , het is toch niet zo ver. tommy1729 === Subject: Re: Tommy is an embarassment to whatever educational system Nntp-Posting-Host: hera.cwi.nl ... > as for dik T winter wat is dat voor zever kerel ? waarom zou ik niet van belgie zijn ? Waar schrijf ik dat? Het enige dat ik schreef is dat je niet Nederlands was. Maar je moet echt beter lezen wat geschreven wordt. Of ben je nu met mijn voeten aan het spelen? In dat geval ben je niet meer dan een trol. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Poor teaching of econ Absolutely. Why because you agree with him more? Krugman is so tainted with political > spin in his column he forgets about economics all together. Sure. > Krugman has violated the unwritten standard of neutrality in research and LOL! The ole myth of pure positivism in economics. Economists who engage in objective and positive economic science make an implicit ethical statement. How can it be any other way? By presuming to engage in positive science one is ignoring ethical considerations and therefore being unethical! Normative priors are required before engaging in economic research as the subject matter of economics is humans and their economic behaviour, not electrons. I think it was Hume who said, one cannot derive ought from is but economists do it all the time. === Subject: Re: Poor teaching of econ > On Aug 31, 1:13 pm, professorchaos [ Ignorant non sequiturs and lies - deleted. ] I checked. Card and Kruger (1995), as their title suggests, do not > construct an extended time series out of the individual analyses > they examine. > No they examined 30 different time series studies. I haven't looked it back up so I am taking your work that there were 30. It said as the time series( in the time series studies that OTHERS CONSTRUCTED) got longer the effect of a minimum wage on employment went to zero. This does not mean they added any data or did any of the time series analysis themselves just that they compared studies with different length time series. Neither you nor I ever said they constructed the time series. The meta analysis was a look at 30 time series studies. Do you understand the difference? Regardless of what you thought they did or meant by adding more data, it does not change the fact that time series analysis can fall into the CP trap. It doesn't control for the possibility that labor demands are shifting over the period. Like I said before there is no surprise that a time series would eventually show zero effect of the minimum wage on employment. It doesn't take many yearly observations before the series is observing the long run, in which the prediction is no longer valid, and expanding labor demands offset the loss of employment. There is nothing indicating that the effect of no employment over a period of time was not due to the trend of increasing labor demand or the fact we are likely looking at the long run. So when you are ready to argue this and have a real discussion instead said this or did not say this on minor issues that avoid the main argument let me know. Well it is 8:30 pm and I am feeling better so I am going to enjoy the long weekend. Have funny piddling away with your amateur research. === Subject: Re: Poor teaching of econ > Yeah, he was really thick when he correctly adduced the cause of the > California energy crisis (viz, power generators cutting supply to create > huge spikes in spot prices) or when he critiques Bush's Iraq disaster. > A. That is not the correct reason for the California energy crisis. It was a symptom of the price caps and the lack of competition the government fostered after deregulation. It is Krugman spinning it for the Dems who want government in control of business. Compare to Texas where PRIOR TO deregulation competition was fostered and new companies came in building power plants before deregulation hit. There have been no problems in Texas. B. Criticizing the policy in Iraq has little to do with economics. I haven't seen Krugman once comment on the economic policy instituted. He has stepped into the party line that those democrat leaning people who pay his check want him though. Only in universities do we find economist coming anything close to being apolitical. Tenure and academic freedom allows them to draw a paycheck to research unbiased. Anyone being paid by a paper has to fall into the paper's bias or get fired. Whether that paper be influenced by those who agree with the Republicans or those agree with the democrats. === Subject: Re: Poor teaching of econ > How do you define it, observe it, measure > it? How do you scientifically distinguish > between moral, immoral, and amoral? > By reference to accepted norms. > Whose accepted norms? Yours? Muslim norms? Jewish norms? Buddhist norms? > You see the problem. No, actually, there is no problem, because the claim that there's _no > universal norms_ rooted in a bedrock, general, universal human nature is a > crock. > Certainly there are some norms that are universal but stating that lack of cooperation in a prisoner's dilemma is categorically amoral is wrong. For instance, in Islam the Koran says roughly cooperate to do good but you should not cooperate for the purpose of sin or evil. Judaism and Christianity which Islam is an extension from make the same claim. Just not as simply in one nice verse that is easy to quote. So what is amoral about the findings of the paper Rob posted? Care to explain. So far everyone has just it is amoral and you know it. I certainly do not see the amorality. What do you find amoral about the results of the paper? > I would still like an answer from you or Rob as why failure to cooperate > in the prisoner's dilemma game is amoral. I would still like an answer to > what behaviors you take offense to and why rather than everyone knows it > is amoral. If you want to argue amoral then lets have a philosophical Certainly not everyone knows it's amoral. > Include me in that. So I ask again what do or Rob or Roy find amoral about the findings in the paper. What leads Roy to the conclusion that the paper shows Economics students are the most amoral on campus. Roy has been curiously silent since I asked that question. > Everyone with a _good understanding_ of these things, however, does realize > that the only explanation that anyone ever came up with for the biological > evolution of human morality---in particular, why human are one of the few > species marked by non-kin altruism---is that iterated prisoner's dilemmas. > Not the games presented in the paper. > The ole myth of pure positivism in economics. Uh huh. Sure. Economists came up with nonsense with real business cycle > theory only because they're positive scientists, not (largely) a bunch of > normative hacks working on behalf of the powerful. The Real Business cycle theory is not well accepted and it was a response to the lack of theoretical underpinnings in the Keynesian model. The Real Business cycle theory has not stood up to the test of data. Economist liked RBC because it explained fluctuations in terms of micro markets. Fluctuations came from swings in labor supply and labor demand. Calibration attempts for RBC and most economist reject the theory now. It is hard to find in a textbook. The New Keynesians have done a much better job of providing micro foundations for business cycles. And how is it that Martin Feldstein, President of NBER, didn't violate this > standard when he argued (incorrectly, as it turned out---but data never > stops these handmaidens to the powerful, does it?) that Clinton's 1993 > income tax hike would create a recession? > He didn't because he was using standard macroeconomic theory that raising taxes decreases aggregate demand. He did fall into the ceteris paribus fallacy trap but that statement is grounded in theory not opinion. Feldstein simply failed to see other factors occurring other than Clinton's tax increase. Like the Fed backing off of raising interest rates, growth in investment, or even growth in consumption. Falling into the CP trap does not mean you were automatically being political like Krugman does. Krugman and Wells has a good section on policy lags but yet he gives Clinton credit for the economic sucess in his administration from day and no credit to Reagan and Bush policies that lags were causing to be coming into effect during the Clinton Presidency. Then blames Bush for the 2001 recession that occurred almost the day he took office despite the fact that no policy that Bush had even envision had been passed by congress or giving time to take effect. Feldstein was quoting textbook macro theory. He would have said the same to make a political statement. > Uh huh. Sure. Krugman's point that power generators had an incentive to > cut supply to drive spot electricity prices out the roof during the > California energy crisis had no theory or evidence behind it, only partisan > animus, and the reverse is true of whatever genius economists came up with > the deregulatory program to begin with. > You don't see the partisan spin do you? Correct the policy gave incentive for that to happen but it was California's energy policy did not allow for competition. He curiously omits the fact that green power laws had not allowed the building of new power plants and that the windmills were even brought down because enviromentalist were concerned with birds. He omits that due to this that California allowed for unregulated monopolies. They said we are lifting regulations and there is competition but they did not let anyone build new power plants. Compare that to Texas where when the deadline for deregulation was set, Texas started approving companies to come in and build power plants and foster competition. Krugman was being dishonest in spinning deregulation as bad rather than California's screwed up policy on energy and deregulating without allowing competition. This is Krugman leaving out facts and trying to spin it the way the democrat spin doctors who pay his check wanted it to be spun. No major media columnist is immune to the political whims of whom they work for. === Subject: Re: math is a physical process <3bc70$46ca97d1$82a1e228$24521@news1.tudelft.nl> <3udlc3d29ickupj87kkddln5gj4fv7mn6t@4ax.com> <5dbb7$46cad8ce$82a1e228$32721@news1.tudelft.nl> <2limc3983vfpimvmapj1co5kknkqvgbllk@4ax.com> <32a7a$46d2a330$82a1e228$4614@news1.tudelft.nl> <87inhc7o5.fsf@hod.lan.m-e-leypold.de> <31DAi.13010$OM1.8447@trnddc07> On Aug 27, 9:30 pm, Markus E L > Markus E L Math is the software running within the hardware of Reality. > I'd like to make this quote immortal! > Han de Bruijn > ----------------- > and in to many cases > the ware of relality! > will there be no end to that stupid arrogance > of crook methematiciance ?? > and who is the crimminal teachers > that educated those pomous farters ?? > Y.P > And who is the criminal who tought you spelling? > - M > then you may utter your critisim. Otherwise Schnauze. You're looking too many WW II films. > So, attack him on other grounds, like his Physik. Versteh! Which physics? The physics of bad spelling, bad language and trollish > claims? Gimme a break ... And BTW: I'm a physicist by education. So there :-). - M- Hide quoted text - - Show quoted text - ------------- and who thought you your 'physics' physics was it Josef Goebelsss ?? what was you or your father or your uncle doing during WW2 ??.... i tlook squite clear that this i sth ereal reason why you opened your 'shnauze '!! (now he will demnd that i will write shnautze correcrly ... (:-)!!) (i am quite sure that Goete would not speak as Makus (Aurelius) is speaking ) even markus urelious whold not speak (physics ..) as this Markus is speaking . so dear Markus as for our thread matrhematicians as is for now lead us nowhere for some advance in physics anmd even a parrot like you is leading us no where !! and the quicker yo uand other parrots will get it -- the better now as for my spelling i could easyly operate jsut now the good spell chacker but for you i tis good enough with all my spelling mistakes the fact is that you understand nicely (and should do ) anything i write !! spelling i s not the main issue for a physics ng unless you are **personally** hostile and looking for pretexts to attack me personally Y.P ------------------- === Subject: Re: math is a physical process > On Aug 27, 9:30 pm, Markus E L > Markus E L > On Aug 27, 1:10 pm, Han de Bruijn I'd like to make this quote immortal! > Han de Bruijn > ----------------- > and in to many cases > the ware of relality! > will there be no end to that stupid arrogance > of crook methematiciance ?? > and who is the crimminal teachers > that educated those pomous farters ?? > Y.P > And who is the criminal who tought you spelling? > - M > then you may utter your critisim. Otherwise Schnauze. > You're looking too many WW II films. > So, attack him on other grounds, like his Physik. Versteh! > Which physics? The physics of bad spelling, bad language and trollish > claims? Gimme a break ... > And BTW: I'm a physicist by education. So there :-). > - M- Hide quoted text - > - Show quoted text - ------------- [Porat to Markus] > and who thought you [Mark] your 'physics' physics > was it Josef Goebelsss ?? > what was you or your father or your uncle doing during > WW2 ??.... > [hanson] ... Shhh, Yehiel... Don't turn Mark into an Anti-Semite now. It would be your fault. What's done is done. He wasn't even born when it happened. > [Porat to Markus] > i tlook squite clear that this i sth ereal reason why you > opened your 'shnauze '!! > [hanson] ... But , Yehiel, think about it, it is possible that they **still** do not like Juden Physik. After all, the Unis in Bayern make it no longer mandatory (since 1996) to take relativity courses to study physics. Times are changing... Even your Landsman, Baez, said, when he visited Germany last week, at the Erwin Schroedinger Institut, August - September 2007, I learned that I've really been falling behind the times when it comes to classical mechanics and quantization! ... Times are changing, Yehiel. Take care, old friend. -- hanson > ------- [Porat to Markus] > (now he [Markus] will demnd that i will write > shnautze correcrly ... (:-)!!) > (i am quite sure that Goete would not speak > as Makus (Aurelius) is speaking ) > even markus urelious whold not speak (physics ..) > as this Markus is speaking . so dear Markus > as for our thread > matrhematicians as is for now > lead us nowhere for some advance in physics > anmd even a parrot like you > is leading us no where !! > and the quicker yo uand other parrots will get it > -- the better > now as for my spelling > i could easyly operate jsut now the good spell chacker > but for you i tis good enough with all my spelling mistakes > the fact is that you understand nicely > (and should do ) anything i write !! > spelling i s not the main issue for a physics ng > unless you are **personally** hostile > and looking for pretexts to attack me personally Y.P > ------------------- > === Subject: Re: math is a physical process <3bc70$46ca97d1$82a1e228$24521@news1.tudelft.nl> <3udlc3d29ickupj87kkddln5gj4fv7mn6t@4ax.com> <5dbb7$46cad8ce$82a1e228$32721@news1.tudelft.nl> <2limc3983vfpimvmapj1co5kknkqvgbllk@4ax.com> now you can see > why methematicians cannot be > leaders of physics > their hubris is a dsiaster to the advance physics No, it is the physicists who don't know how to use the math, nor how to > find the right math to use, that are the disaster to the advance of > physics. Mathematicians, by and large, have no desire to be leaders of physics. E.g., G.H. Hardy. ----------- so who has or can be the leader of physics ?? iow can mathematics **by itself (' per se' )lead to new breakthoughs in physics as physics is now ?? Y.Porat ------------------------- === Subject: #31e zircon crystal Hawaii mantle; proving that Earth is about 2X older than Jupiter Re: ATOM TOTALITY (Atom Universe) THEORY REPLACES BIG BANG THEORY IN PHYSICS I did a Google search for zircon crystal Hawaii mantle and received these hits: Multi-Stage Modification of the Northern Slave Mantle Lithosphere ... Zircon crystals isolated from Jericho eclogites generally have low uranium ...... high-MgO Group A (e.g. eclogite xenoliths from Salt Lake crater, Hawaii; ... petrology.oxfordjournals.org/cgi/content/full/47/4/821 - Similar pages - Note this [PDF] Multi-Stage Modification of the Northern Slave Mantle Lithosphere ... File Format: PDF/Adobe Acrobat 10 zircon crystals. The longest zircon crystal in this photo is 2 mm in length. ...... eclogite xenoliths from Salt Lake crater, Hawaii; Green, 1966) and ... petrology.oxfordjournals.org/cgi/reprint/egi097v1.pdf - Similar pages - Note this [ More results from petrology.oxfordjournals.org ] PSRD:: SaU169 Lunar Meteorite Lead-lead ages of 12 zircon crystals from the impact melt portion .... A. (2000) Major lunar crustal terranes: Surface expressions and crust- mantle origins. ... www.psrd.hawaii.edu/Oct04/SaU169.html - 38k - Cached - Similar pages - Note this Rates and Timescales of Magmatic Processes II - Volcanology ... U-series Isotopic Evidence for Remelting of Kilauea Volcano's Mantle Source .... Moreover, two zircon crystals from the youngest granite overlap in age ... www.agu.org/meetings/fm04/fm04-sessions/fm04_V52B.html - 30k - Cached - Similar pages - Note this Lithos : The granite-upper mantle connection in terrestrial ... This conclusion is currently questioned, as the zircon crystals collected in ..... glass collected in the Alae lava lake of Hawaii (Wright and Peck, 1978). ... linkinghub.elsevier.com/retrieve/pii/S0024493704002865 - Similar pages - Note this Helium isotopic evidence for episodic mantle melting and crustal ... The main zircon age peaks are at 1.2, 1.9, 2.7 and 3.3 Gyr (Fig. 2). As the continental crust was extracted from the mantle by partial melting3, ... www.nature.com/nature/journal/v446/n7138/full/nature05691.html - Similar pages - Note this Mantle Samples Included in Volcanic Rocks: Xenoliths and Diamonds Crystals typically 0.2 mm with equant or tabular shapes, irregular grain boundaries, .... phlogopite and ilmenite most common, zircon and olivine rarer. ... A COMPARISON BETWEEN THE ERUPTION STYLE AND PRODUCTS OF KILAUEA ... Hotspots are the expression of thermal plumes in the mantle which may .... with minor constituents of biotite, quartz, zircon, apatite and magnetite. ... www.es.ucl.ac.uk/research/planetary/undergraduate/mcmillan/eruption/pinatub. htm - 21k - Cached - Similar pages - Note this Pacific Museum of the Earth -- Exhibits Mantle Plumes: Here a lava lamp serves as a model for how giant bodies of hot .... (There is a zircon crystal in Wisconsin which is 4.4 billion years old, ... www.eos.ubc.ca/resources/museum/exhibits.html - 22k - Cached - Similar pages - Note this What I am thinking is that the best way to prove the Sun and Inner Planets are about 2X older than the Outer planets is via zircon crystals and from my understanding that Hawaii has the best batches of zircon crystals from the mantle of Earth. So I am guessing that this is perhaps the best place to find a zircon that is 6 or 7 or 8 or 9 or 10 billion years old. But perhaps some other geological location on the globe my offer some very old zircon crystals such as Australia. But it struck me as to what if we do find a zircon crystal which dates to say 10 billion years old, and how are we going to find a zircon crystal in any of the Outer Planets to compare? So we are in a jam here. So we find a zircon that dates Earth to 10 billion years old and never able to find a zircon on the Outer Planets. This is where we compare cores and the relative abundance of radioactive elements from Earth compared to the Outer Planets. It is the finding of a zircon crystal from Earth's mantle that is 10 billion years old that proves the Earth is much older than the usual cited age of 4.6 to 5 billion years. Once we prove Earth is much older then we use the core data and abundance of radioactive elements data to prove that Jupiter, Saturn, Uranus, Neptune are 1/2 as old as Earth. At least that is what my plan of logic scheme of things to work out. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: #31F Does Dirac Radioactivity in the form of cosmic rays create an Earth in 5 billion years?? Re: ATOM TOTALITY (Atom Universe) THEORY REPLACES BIG BANG THEORY IN PHYSICS There is another way to evaluate whether our Solar System was created from Dirac Radioactivity or whether the Nebular Dust Cloud theory is true. What we do here is evaluate how much cosmic rays and cosmic gamma rays penetrate Earth over a day time period. How much energy and mass is imparted upon Earth in a 24 hour period from that of cosmic rays and cosmic gamma rays? And then multiply that by 5 billion years and then multiply it by 10 billion years. Can we create the planet Earth from simply the accrual of cosmic rays and gamma rays. There is a hitch in this calculation in that Jupiter receives much more cosmic rays per day than does Earth so the rate of accrual is variable and not constant. And the rate of accrual depends on the magnetic field of the astro body. So the present Earth mass is 6 x 10^27 grams and there are approx 2.5 x 10^15 minutes in 5 billion years. So what I need is a rate of cosmic ray and cosmic gamma rays of about 2.5 x 10^12 grams per minute. Does Earth or the Sun or Jupiter receive about that much mass per minute from cosmic rays and cosmic gamma rays? I am going to have to look up that information but I think it is too high. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: #31G Dirac Radioactivity in the form of cosmic rays of 1/cm^2sec forms Earth over 5 billion years Re: ATOM TOTALITY (Atom Universe) THEORY REPLACES BIG BANG THEORY IN PHYSICS > There is another way to evaluate whether our Solar System was created > from Dirac Radioactivity > or whether the Nebular Dust Cloud theory is true. What we do here is evaluate how much cosmic rays and cosmic gamma rays > penetrate Earth > over a day time period. How much energy and mass is imparted upon > Earth in a 24 hour period > from that of cosmic rays and cosmic gamma rays? And then multiply that > by 5 billion years > and then multiply it by 10 billion years. Can we create the planet > Earth from simply the accrual > of cosmic rays and gamma rays. There is a hitch in this calculation in that Jupiter receives much > more cosmic rays per day than > does Earth so the rate of accrual is variable and not constant. And > the rate of accrual depends > on the magnetic field of the astro body. So the present Earth mass is 6 x 10^27 grams and there are approx 2.5 > x 10^15 minutes in > 5 billion years. So what I need is a rate of cosmic ray and cosmic > gamma rays of about > 2.5 x 10^12 grams per minute. Does Earth or the Sun or Jupiter receive > about that much > mass per minute from cosmic rays and cosmic gamma rays? > I am going to have to look up that information but I think it is too > high. > Gladly I was mistaken. Looking through this website: They give a figure for Cosmic Ray Intensity at 1/cm^2 sec ,or, 1 ev/ cm^3 They say that most Cosmic Rays, or 90%, are protons and about 9% are helium nuclei. I saw no Intensity figure for Cosmic Gamma Ray Bursts on that website. But I think I can get 2.5 x 10^12 grams per minute from the figure 1/ cm^2 sec and then some. So what we see here, is how to create and build Earth from purely just the Cosmic Rays and Cosmic Gamma Rays that impact Earth every minute of over day and year. So we never needed a Nebular Dust Cloud to create our Solar System when it can be created purely from the Cosmic rays impacting on the astro bodies of our Solar System. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: #31H So how did Earth get its heavy elements via Dirac Radioactivity Re: ATOM TOTALITY (Atom Universe) THEORY REPLACES BIG BANG THEORY IN PHYSICS Sadly we were taught in school that Earth and the Sun and planets got their heavy elements in the Nebular Dust Cloud formed from some ancient supernova. So that the gold or platinum or uranium that we find on Earth originated in some supernova explosion. So if our Earth and Solar System was not created from a Nebular Dust Cloud, how did we end up with gold and platinum and uranium found on Earth? Well the Dirac Radioactivity in the form of Cosmic Rays and Cosmic Gamma Ray Bursts easily produces the heavier elements. Some Gamma Ray bursts are so energetic that they can create a whole entire rock or insect. Some Gamma Ray bursts have been measured to have 10^17 MeV (if memory is correct) and some years back a Gamma Ray was seen that could incinerate our Solar System if it had bursted near our Solar System. So we are talking about huge amounts of energy. And so a high energy gamma ray burst on Earth could easily transmute a hydrogen or helium or oxygen atom into a uranium atom. So we never needed a Nebular Dust Cloud theory to create our Solar System when all we needed was an accounting of the Cosmic Rays and Cosmic Gamma Rays. Now if anyone still believes that the Nebular Dust Cloud theory formed and created and built our Solar System, well, obviously they would have to explain why Earth is not twice as large and twice as massive as it currently is, because if you believe the Nebular Dust Cloud, you are going to have to explain where all that mass from Cosmic Rays and Gamma Rays went in those past 5 billion years. Are you going to say that the Cosmic Rays and Gamma Rays were nonexistant for the past 5 billion years and only recently did they begin to strike Earth. Because at the rate of impact of Cosmic Rays today, gives a Earth of the same size and mass it currently possess. Also, the building of heavier elements via Gamma Ray Bursts makes sense in the fact that the surface of Earth is in large supply of heavier elements. Whereas if the Nebular Dust Cloud theory were true that the surface of Earth would have been depleted via erosion over billions of years so that the surface would have few heavy elements around. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: Two results of set geometry > Only the fact that the first column has a lot of finite initial > segments and an infinite initial segment while the rows are all finite > may be raising some suspicion. What this is stating, precisely is: > That the ordered set of natural numbers has a lot of finite initial > segments and one infinite initial segment, while the set of natural > numbers is infinite may be raising some suspicion. > Yes, I knew all along that you distrust the axiom of infinity. Well, > reject it, and go on. I do not reject the axiom of infinity. I assume that every initial > segment of the first column (including the complete first column) > corresponds to (is in bijection with) a natural number. Now you are using (again) your very own terminology. There is a bijection between the initial segments (including the complete first column) with the natural numbers. There are lots of them. But you are not talking about bijections, but about oder-preserving bijections between ordered sets. And, no, there is no order-preserving bijection between the ordered set of initial segments and the ordered set of natural numbers. > That is incorrect. Each partner on the one side is a number of natural > numbers and on the other side each partner is a natural number. I > tried to express that by the variables {1,2,3,...,n} <--> n. Again, you lost me here. The partners where both the set of natural > numbers. The partners include {1,2,3,...}. That is not a natural number. I disrember the start. As far as I remember the partners where the set of natural numbers. {1, 2, 3, ...} is not in the set of {1, 2, 3, ..., n}. > In fact I do not add something to the set the column is bijected witd, > but I do neither add something to the column. The initial segments on > the left hand side change from > 1, 11, 111, ..., 111... to > 11, 111, ..., 111..., 111...1. There is no last row, so where does the 111...1 come from? There are omega initial segments of the first *column*. Adding one 1 > to every initial segment supplies 11, 111, ..., 111..., 111...1, the > last one having ordinal omega + 1. Again, adding again a one to the initial segment that is the first column. Which row has that complete initial segment? > If they rermain in bijection with the sequences in the rows, then the > set {2, 3, 4, ...} has ordinal omega + 1. It is based on your assumption that there is a last row. There is none, > so now what? No. There is no last row. But every initial segment of the first > column is said to have a partner in the set of sequences in the rows. Who said that? There is not such partner for the *complete* first column. That could only be true it there *was* a last row. > We have a bijection between natural numbers and ordinal numbers of > sets of natural numbers. Oh. I did not know that. As far as I know, in this part we were talking > about matrices and of bijections between lines and columns. You switch > point of view from one to another without consistency. The natural numbers are represented by the sequences in the rows. The > ordinal numbers are represented by the initial segments of the first > column. O. Which initial segment represents 0? And to which line does it correspond? > I said *replaced*. But let's see whether I do understand you: > a natural number n has the set of second indices {1, 2, 3, ..., n} > a set of natural numbers {n1, ..., nk} has the set of second indices > U{l = 1, ..., k} {1, 2, 3, ..., l} = {1, 2, 3, ..., k}. The set of > natural numbers has as second indices {1, 2, 3, ...} = N. If we add > that infinite number 111..., we have that that number has the set > of indices {1, 2, 3, ...} = N. So, yes, the sets of second indices > is the same. Initially you were of opposite opinion. Perhaps. But as you do not clearly state what you mean it is easy to be set on a wrong footing. > I do not see why that should be a problem. If you add a sequence which is larger than any finite sequence, then > you do not add any index? Why is that a problem? > That hints to the fact that you add nothing. > The infinite sequence does not provably existt, because there is no > indication (no piece of circumstantial evidence) that you have done > anything at all. You have done something. Namely adding a line with *all* indices. But of course you can not prove that an infinite line exists. It is there due to the axiom of infinity (which you consistently reject, although you state you do not). > Again the negation of the axiom of infinity. There is no problem once > you are able to distinguish between natural numbers and ordinal numbers. > Properly speaking, the first ordinal number is 0, not 1. So each > ordinal number is the order number of the ordered set of all preceding > ordinal numbers. And once you see that, there is no problem at all. Wrong. Repeat twice adding a 1 to all partners of the bijection. Then > you see the problem again. Your context is so far away that I do not even understand what you mean. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Two results of set geometry Nntp-Posting-Host: hera.cwi.nl > ... > But in order to shorten the discussion: It is impossible to > define or construct a bijection between the set of constructible reals > and N. Again you are guilty of abuse of terminology. Using common mathematical > terminology, it is possible to construct a bijection between N and the > response to your garbage. I did not see it. (By the way, do I have the point?) But if you can, > then define it and take the diagonal number which then is defined too. No, you did not see it, but commented on it. Using common mathematical terminology a constructible number is a number that can be constructed using finitely many operations of a certain class. The diagonal number can not be constructed with finitely many operations, and so is not inherently constructible. As I said: abuse of terminology. You do not mean constructible numbers. > But you mean finitely defined. State so > when you mean that. And be aware that that notion holds a lot of > problems. Perhaps there are problems in matheology but not in mathematics. Any > number which can be defined, i.e., which can be addressed as an > individuum, is a finitely definable number. (Becausen non-finite > definitions are not definitions.) Which makes clear that you do *not* intend constructible numbers. cbrt(2) is finitely definable but not constructible. So why do you persist to write constructible when you mean finitely definable? > It is sufficient when you show an *injection* between the paths and N. Every separation requires a node. There cannot be more separated paths > than nodes. The bijection between nodes and natural numbers is > obvious. So what do you not understand? We have talked about this before. Your assertion there cannot be more separated paths than nodes is in question. And again (just like you, I am getting repetitive): (1) For each two pair of paths there is a node that separates them. (2) There is a level where all paths are separated. You state (2) which does not follow from (1). You argue with the number of separated paths at each node, but as at each not infinitely many paths come in and infinitely many paths go out at each edge, that is not an argument. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Two results of set geometry I've been trying to figure out the best axioms to reconcile what WM is trying to post. We can try the same trick I used earlier with tommy1729, by denying the Axiom of Infinity and allowing proper classes. We notice that since V_omega is a model for ZF-Infinity, it follows that V_(omega+1) is a model for NBG-Infinity, and the infinite sets of V_(omega+1) correspond to infinite proper classes in NBG-Infinity. And they are all countable, so it follows that every proper class has the same countable cardinality. But what about the reals, and the binary tree? If we were to identify a path by its set of nodes, then, since all _sets_ (as opposed to proper classes) are finite, it follows that the proper class of all paths has only finite paths as elements, since the elements of any class must be _sets_. The class of all paths is indeed countable, but then that class only counts the finite paths, which are indeed countable. But then you don't have the class of reals but only the dyadic rationals (i.e., the ring formed by appending 1/2 to Z). > Put aside Robinson and Conway. Please answer only this single > question: Do you believe that there can be more *separated* paths in > the tree than nodes? I'm not sure what you mean by a _separated_ path. Depending on your definition of separated, there may indeed be only countably many separated paths. If every path has a leaf node, then there is trivally a bijection between the class of paths and the class of nodes, but if some paths lack leaf nodes -- as the infinite paths in ZFC do -- then it is possible that there can be more paths than nodes. The reason I mentioned Conway is that in the binary tree of surreals, every path -- including the infinite paths -- do have leaf nodes. But then again, I'm not sure what would happen if one tried to construct the surreals without the Axiom of Infinity. === Subject: Re: What's with the solution manuals? Did something happen, like a message in the newsgroup >alt.how.to.cheat.at.math, which said that you could ask for them? --- Christopher Heckman Student cheats who spend moore time trying to cheat than it would take to work the problems! Well, so much for the proffessor's side. I don't doubt what you described happens. Still, let me give you a student's side. I don't think the scenario described by the posters necessarily the case, tho it may happen. There are also teachers who order these manuals, in order to not have to come up with their own problems. On top of that, I have taken classes in which the proffessor follows the books to the letter, making it pointless to take the class, and often, even in this case, explanations are poor. All of you who commented on this may be dedicated teachers, but, believe me, the image of the dedicated teacher , losing sleep over wether students learn is, at least in my experience mostly a myth , even when I acknowledge that the teachers is supposed to be a facilitator , i.e, without my having the expectation that just by sitting in class I will learn. === Subject: Re: What's with the solution manuals? Nntp-Posting-Host: hera.cwi.nl > Why are there so many solution manuals being advertised and asked for? I know that it's the beginning of the fall semester, but it wasn't > this bad this time last year, or any other previous year. Did something happen, like a message in the newsgroup > alt.how.to.cheat.at.math, which said that you could ask for them? ... > I beleive these are all from the same person - that has started a > business selling them. This person is obvious scum! They don't realize the damage they cause students, publishers, and > authors. I am not considering publishers and authors. I think a good textbook should have the answers to the exercises somewhere in the back. Why does nobody ask for the answers to the exercises of Knuth's The Art of Computer Programming? Because they are in the back. The problem is with the teachers. They give as homework do these ecercises from the book. The real homework should be either exercises produced by the teacher, or something like try the exercises such and such, and when you fail do look at the solutions and try to understand them. > Students who buy these are doing a huge dis-service to themselves as > they are missing the entire point of taking classes. Moreover, they will fail at the final exam, where the exercises are (I hope) *not* from the book. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Math Trek: Kidney Matchmaking [MATHTREK] Kidney Matchmaking A mathematical optimization strategy for pairing patients who need kidneys with willing donors could increase the number and quality of transplants. === Subject: Re: Analysis with integral. Hehe, and the Legesgue integral is even more zero. Brian I don't know what you mean: f,g are both assumed to b} f(x) dx = int{a to b} g(x) dx. ) so that f-g is also Riemann- integrable. Do you have a counterexample? (Dave Renfro's example does not apply, since CharQ is not R-integrable). So, under these assumptions, it comes down to: h=f-g is a Riemann-integrable function that is non-zero at only countably many points. Do you believe the integral of h is not zero?. Then try this: Do your Riemann sum so that in each inetrval (x_i-1,x_i) , you always choose a point x_i* where f(x_i*)=0 . Since h is Riemann- integrable , the Riemann integral is zero. Do you disagree? be zero Still, I do give you that I was sloppy in my explanation, specially the last part. === Subject: solutions manual can you please email me > * Solutions manual for Advanced Engineering Mathematics, 9th Edition, by Erwin Kreyszig (even solutions) to lookpong2210@yahoo.com === Subject: Re: solutions manual <1895899.1188464091378.JavaMail.jakarta@nitrogen.mathforum.org I have the following solutions manuals in pdf. If you need any of them, send me email at abole...@yahoo.com > I accept paypal payments only * Solutions manual for Analysis and Design of Analog Integrated Circuits, 4th Ed., by Gray,Hurst, Lewis, Meyer > * Solutions manual for Analytical Mechanics, 7th Edition, by Fowels, Cassiday > * Solutions manual for An Interactive Introduction to Mathematical Analysis, by Jonathan Lewin > * Solutions manual for An Introduction to the Mathematics of Financial Derivatives, 2nd Ed.,by Neftci [ISBN:0125153929] > * Solutions manual for Antenna Theory, 2nd Ed., by Balanis > * Solutions manual for Antennas for all Applications, 3rd Edition, Kraus, Marhefka > * Solutions manual for Applied Linear Statistical Models, 5th Ed., by Neter (Selected Sol.) > * Solutions manual for Applied Numerical Analysis, 6th Edition, by Gerald, Wheatley > * Solutions manual for Applied Numerical Methods with MATLAB for Engineers and Scientists,1st Ed,. by Chapra > * Solutions manual for Applied Statistics and Probability for Engineers, 3rd Ed., by Montgomery, Runger (Selected Solutions) > * Solutions manual for Applied Strength of Materials, 4th Edition, by Mott > * Solutions manual for A Transition to Advanced Mathematics, 5th Edition, by Smith, Eggen,Andre > * Solutions manual for Automatic Control Systems, 8th Edition, by Kuo, Golnaraghi > * Solutions manual for A Course in Game Theory by Osborne, Rubinstein > * Solutions manual for A Course in Algebraic Number Theory by Cohen > * Solutions manual for Adaptive Filter Theory, 4th Edition, by Haykin > * Solutions manual for Adaptive Control, 2nd. Ed., by Astrom, Wittenmark > * Solutions manual for Advanced Engineering Mathematics, 8th Editoin, by Erwin Kreyszig (even solutions) > * Solutions manual for Advanced Engineering Mathematics, 9th Edition, by Erwin Kreyszig (even solutions) > * Solutions manual for Advanced Macroeconomics, 1st Ed., by David Romer > * Solutions manual for Advanced Mathematical Concepts Precalculus With Applications by Holliday [ISBN: 0028341759] > * Solutions manual for Advanced Modern Engineering Mathematics, 3rd Ed., by G. James > * Solutions manual for A First Course In Differential Equations, 7th Edition, by Zill, Cullen > * Solutions manual for Analog Integrated Circuit Design, 1st Ed., by Johns, Martin (text ebook and solution manual) > * Solutions manual for Basic Business Statistics: Concepts and Applications, 10th Ed., by > Berenson, Krehbiel, Levine (chap1-18) > * Solutions manual for Basic Engineering Circuit Analysis, 7th Ed., by J. David Irwin > * Solutions manual for Basic Engineering Circuit Analysis, 8th Ed., by J. David Irwin, Nelms (Missing a chapter or 2) > * Solutions manual for Bioprocess Engineering Principles by Doran > * Solutions manual for Calculus: Study and Solutions Guide, Vol. 1, 7th Ed., by Larson,Hostetler, Edwards > * Solutions manual for Chemical and Engineering Thermodynamics, 3rd Ed., Stanley I. Sandler > * Solutions manual for Chemical Engineering Volume 1, 6th Edition, by Richardson, Coulson,Backhurst, Harker > * Solutions manual for College Physics, Volume 1: 7th Edition, by Serway, Faugh > * Solutions manual for College Physics, Volume 2: 7th Edition, by Serway, Faughn > * Solutions manual for Communications Systems, 4th Ed., by Haykin > * Solutions manual for Communications Systems Engineering, 2nd Edition, by Proakis > * Solutions manual for Computational Techniques for Fluid Dynamics by Srinivas, Fletcher > * Solutions manual for Computer Networks, 4th Ed., by Andrew S. Tanenbaum > * Solutions manual for Computer Networks: A Systems Approach, 3rd Edition, by Davie > * Solutions manual for Control Systems Engineering, 4th Ed., by Norman Nise > * Solutions manual for Corporate Finance, 6th Edition, by Ross > * Solutions manual for C++ How to Program: Intro Object-Oriented Design with the UML, 3rd Ed., by Deitel, Nieto > * Solutions manual for Calculus Early Transcendental, 5th Ed., by James Stewart > * Solutions manual for Calculus - Early Transcendentals, 7th Ed., by Anton, Bivens, Davis > * Solutions manual for Calculus: Graphical, Numerical, Algebraic, 3rd Ed., Waits, Finney,Demana, Kennedy > * Solutions manual for Calculus: Multivariable, 5th Edition, by James Stewart > * Solutions manual for Calculus: Single Variable, Early Transcendental, 5th Edition, by James Stewart > * Solutions manual for Calculus, Single and Multivariable, 3rd Ed., by Hughes-Hallett,McCallum > * Solutions manual for Device Electronics for * Solutions manual for Integrated Circuits 3rd Edition by Muller > * Solutions manual for Differential Equations with Boundary Value Problems, 2nd Ed., by Polking, Arnold > * Solutions manual for Digital And Analog Communication Systems 7th Ed., Leon W. Couch > * Solutions manual for Digital Communications, 4th Edition, by Proakis > * Solutions manual for Digital Communications: Fundamentals and Applications, 2nd Ed, Skylar > * Solutions manual for Digital Design, 4th Edition, by Mano, Ciletti > * Solutions manual for Digital Image Processing, 2nd Edition, by Gonzalez, Woods > * Solutions manual for Digital Integrated Circuits, 2nd Ed., by Rabaey (Solutions ONLY for Chapters 3, 5, 6, 10) > * Solutions manual for Digital Signal Processing: A Computer Based Approach, 1st Ed., by Mitra > * Solutions manual for Digital Signal Processing: A Computer Based Approach, 2nd Ed., by S.Mitra > * Solutions manual for Digital Signal Processing: A Computer Based Approach, 3rd Ed., by S.Mitra > * Solutions manual for Digital Signal Processing: Principles, Algorithms and Applications,3rd Edition, by Proakis > * Solutions manual for Discrete Time Signal Processing, 2nd Edition, Oppenheim > * Solutions manual for Dynamics of Mechanical Systems by C.T.F. Ross > * Solutions manual for Data and Computer Communications, 8th Edition by Stallings > * Solutions manual for Database Management Systems, 3rd Ed., by Ramakrishnan, Gehrke (Sol.for Chapters 2-21, odd only) > * Solutions manual for Design of Analog CMOS Integrated Circuits, 1st Edition, by Razavi Design of Analysis of Experiments, 6th Edition, Montgomery (missing > chapter 6-8) > * Solutions manual for Design of Machinery, 3rd Ed by Robert L. Norton > * Solutions manual for Design With Operational Amplifiers and Analog Integrated Circuits, 2nd Ed., by Sergio Franco > * Solutions manual for Design With Operational Amplifiers and Analog Integrated Circuits, 3rd Ed., by Sergio Franco > * Solutions manual for Elementary Principles of Chemical Processes, 3rd Ed., by Felder,Rousseau > * Solutions manual for Elements of Chemical Reaction Engineering, 3rd Ed., by H. Scott Fogler > * Solutions manual for Engineering and Chemical Thermodynamics, by Koretsky [ISBN:0471385867] (No sol. for chapt 6) > * Solutions manual for Engineering Circuit Analysis, 6th Edition, Hyat > * Solutions manual for Engineering Electromagnetics, 6th Ed W. Hayt, J. Buck > * Solutions manual for Engineering Electromagnetics, 7th Ed., Hayt, Buck > * Solutions manual for Engineering Fluids Mechanics 7th Edition by Crowe > * Solutions manual for Engineering Fluids Mechanics 8th Edition by Crowe > * Solutions manual for Engineering Mathematics, 4th Ed., by John Bird > * Solutions manual for Engineer Mechanics: Dynamics, 4th Ed., by Bedford > * Solutions manual for Engineering Mechanics: Dynamics, 10th Ed., by Russell C. Hibbeler > * Solutions manual for Engineering Mechanics: Dynamics 11th Ed. by Hibbeler > * Solutions manual for Engineering Mechanics: Dynamics 5th Ed. by Meriam, Kraige > * Solutions manual for Engineering Mechanics: Statics, 4th Edition - A. Bedford, Wallace Fowler > * Solutions manual for Engineering Mechanics: Statics, 5th Ed., Meriam, Kraige > * Solutions manual for Engineering Mechanics: Statics, 6th Ed., Meriam, Kraige > * Solutions manual for Engineering Mechanics: Statics, 10th Ed., by Russell C. Hibbeler > * Solutions manual for Engineering Mechanics: Statics 11th Ed. by Hibbeler > * Solutions manual for Experiments with Economic Principles by Bergstrom, Miller > * Solutions manual for Econometric Analysis, 5th Edition, by Greene > * Solutions manual for Econometrics of Financial Markets, by Adamek, Cambell, Lo, MacKinlay, Viceira > * Solutions manual for Electrical Properties of Materials, 7th Ed., by D. Walsh, L. Solymar > * Solutions manual for Electric Circuits 6th Ed. by Nilsson > * Solutions manual for Electric Circuits 7th Ed. by Nilsson > * Solutions manual for Electric Machinery, 6th Ed., Fitzgerald, Kingsley, Umans > * Solutions manual for Electric Machinery Fundamentals, 4th Ed by Chapman > * Solutions manual for Electromagnetic Fields and Waves by Iskander > * Solutions manual for Electronic Circuit Analysis, 2nd Ed., by Donald Neamen > * Solutions manual for Electronics, 2nd Ed., by Allan R. Hambley > * Solutions manual for Elementary Differential Equations, 8th Edition, by Boyce, DiPrima(some odd/even) > * Solutions manual for Fundamentals of Applied Electromagnetics, 5th Ed., 2008 Media Edition,by Ulaby > * Solutions manual for Fundamentals of Digital Logic with Verilog Design, 1st Edition, by Brown, Vranesic > * Solutions manual for Fundamentals of Electric Circuits, 2nd Edition, by Alexander > * Solutions manual for Fundamentals of Electromagnetics with Engineering Appls by Wentworth > * Solutions manual for Fundamentals of Fluid Mechanics, 5th Ed. by Munson, Young.. > * Solutions manual for Fundamentals of Heat and Mass Transfer, 4th Ed by Incropera... > * Solutions manual for Fundamentals of Heat and Mass Transfer, 5th Ed by Incropera... > * Solutions manual for Fundamentals of Heat and Mass Transfer, 6th Ed by Incropera... > * Solutions manual for Fundamentals of Logic Design, 5th Ed., by Roth Jr. > * Solutions manual for Fundamentals of Machine Component Design, 3rd Ed., by Juvinall > * Solutions manual for Fundamentals of Machine Component Design, 4th Ed., by Juvinall read more ?... Can you please email me, * Solutions manual for Engineering Circuit Analysis, 6th Edition, Hyat to skida2712@msn.com === Subject: Re: Writing solutions manual > Since I noticed there is such an interest in these books, I have decided > to write a solutions manual. I invite you to help me--we should make > 10^9s... Here are my first 3 solutions or answers... To make this joint > work (is that the new standard?), please limit your solutions to 3 per > person/day. > 1. 42 > 2. By studying > 3. Yes, it is rude to call somebody a crackpot 4. Yes, it does seem a flagrantly disrespectful to an author to > indiscriminately disseminate solutions manuals to his or her efforts > without appropriate permissions. 5. Truth is not a popularity contest--the notion of surrogate factoring is > likely not a diamond in the rough.... 6. The antiderivative of (1/cabin) is a houseboat. > 7. Absolutely no one who wants a solution manual has replied to this thread (it's almost ironic!) 8. Yes, this is a dumb thread, but it's less pitiful than requesting solution manuals. 9. American students who want solution manuals are one of the USA's weakest links.