January 2004 - mathfun@mailman.xmission.com

Re: [math-fun] Tenuous Associations
by asimovd＠aol.com 19 Jan '04

19 Jan '04

<< I was wondering if there is a name for the practice of drawing tenuous assocations between unassociated entities from a rich association domain, and specifically, the practice of drawing mathematical associations between mathematically unrelated numbers? >> This is called either "numerology" or "lying with statistics", depending on which one is applicable. --Dan -- NOTE: Please direct any responses to <asimov(a)msri.org>, since I may not keep this AOL e-address much longer -- thanks.

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[math-fun] Forwarded mail.... Mixed Doubles
by Richard Guy 19 Jan '04

19 Jan '04

Colleague Aiden Bruen suggests that the following may be relevant. R. (89f:51059) Fuji-Hara, R.(J-TSUKS-SO); Vanstone, S. A.(3-WTRL-B) Hyperplane skew resolutions and their applications. J. Combin. Theory Ser. A 47 (1988), no. 1, 134--144. 51E30 (05B25) References: 0 Reference Citations: 0 Review Citations: 0 A resolution class of an affine geometry $\roman{AG}(n,q)$ is a set of lines which partitions the points; a resolution class $S$ is called a hyperplane skew resolution class if the points of the hyperplane $H$ at infinity which are not incident with any line of $S$ are the points of an $(n-2)$-dimensional subspace $\Gamma(H,S)$. A resolution of $\roman{AG}(n,q)$ is a partition of the lines into resolution classes; a hyperplane skew resolution is a resolution with the following properties: (i) all resolution classes are hyperplane skew; (ii) if $S$ and $S'$ are distinct classes, then $\Gamma(H,S)\not=\Gamma(H,S')$. The main purpose of the paper under review is to construct such resolutions; in fact, the authors construct infinite classes of hyperplane skew resolutions. Moreover, the authors point out the connection to the packing problem in projective spaces. Reviewed by Albrecht Beutelspacher

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[math-fun] Re: When liberals do science ...
by MCKAY＠vax2.concordia.ca 19 Jan '04

19 Jan '04

Eugene S. writes questioning that human activity causes global temperature increases... What happens is that the energy in the atmosphere increases thus causing moer extreme weather. This may manifest itself in many ways, one by excessive cold somewhere. I live near Quebec City and it seems to me that winters are less formidable than they used to be. John McKay .

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[math-fun] http://www.renyi.hu/staff/highermath.html
by MCKAY＠vax2.concordia.ca 19 Jan '04

19 Jan '04

Click on Research staff link. John McKay

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Re: [math-fun] Mixed Doubles
by Richard Guy 18 Jan '04

18 Jan '04

Lack-a-day! R. On Sun, 18 Jan 2004, Ed Pegg Jr wrote: > Unfortunately, it doesn't work -- A plays against a more than > once. > > --Ed > > > Aj.Ja Bi.Ib Ch.Hc Dg.Gd Ef.Fe > > Ab.Ba Cj.Jc Di.Id Eh.He Fg.Gf > > Ac.Ca Db.Bd Ej.Je Fi.If Gh.Hg > > ..... ..... ..... ..... ..... > > Ai.Ia Jh.Hj Bg.Gb Cf.Fc De.Ed > > > > --- does that work?? > >

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[math-fun] Midlevels Conjecture
by N. J. A. Sloane 17 Jan '04

17 Jan '04

I posted this question to the seq-fan mailing list yesterday. I got some replies, which are mentioned below. In Peter Winkler's very nice new book "Math Puzzles" he mentions an unsolved problem, which is related to a possibly new sequence: a(n) = number of ways to cycle through all the subsets of size n and n+1 of a set of size 2n+1 by adding or deleting one element at a time The conjecture is that a(n) is always > 0. a(1) is 2, because the two cycles are 1 13 3 23 2 12 1 ... and its reverse. Yesterday Edwin Clark <eclark(a)math.usf.edu> wrote to say: a(n) = 2b(n) where b(n) is the number of Hamiltonian cycles in the so-called bipartite Kneser graph H(2n+1,n) whose vertices are the subsets of size n and n+1 of a set of size 2n+1. A is adjacent to B iff one set is contained in the other. Using the Hamiltonian cycle finder in the program Groups & Graphs, I got b(2) = 24. Then when I tried the case n = 3, I got the reply: "Too much output. Logging of Hamiltonian cycles is being terminated. 10382 cycles were found so far." So all I can say is b(3) >=10382. So all I know at the moment is that the sequences a(n) and b(n) begin 2, 48, >=20764 1, 24, >=10382 Also, Peter Winkler says: I'm delighted to see this sequence in your sights. My old colleague Bob Roth (laker(a)mathcs.emory.edu) once computed some terms, you might ask him if he still has the results after 25 years or so! So far I have not heard back from Bob Roth. Can anyone supply more terms? Neil

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[math-fun] online Museum of Mathematics
by David Gale 17 Jan '04

17 Jan '04

I hope I'm not misusing or abusing our network, but I'm hoping some one of you may be able to help me on a project. Before I start here's something more in the math-fun spirit. I'm offering two hundred bucks ($200) for a solution of the following Nim varient. There are 4 piles, ordinary Nim rules, the only difference being that the game ends when three of the four piles are empty. To get down to business, I've received a small grant from the Sloan Foundation to look into the possibility of creating an on line Museum of Mathematics. Yes, I know there are lots of very nice mathematical sites, some belonging to members of this group, that already exist, (and I'm eager to learn about more of them) but this project is a little different. Primarily, my exhibits must be highly interactive like this link from the San Francisco Exploratorium (which unfortunately has nothing to do with mathematics). http://www.exploratorium.edu/exhibits/mix_n_match/ In fact I what I'm trying to make is a sort of on line mathematical Exploratorium, which will give you an idea of the intended audience. (I thought of calling it The Mathematics DiscoverySite.) The present modest aim of the project is to create two or three high quality, that is to say, "cool" prototype exhibits. The theory is that if these are sufficiently impressive then other members of the math community who are currently creating things on their own web sites will want to think up and contribute exhibits, and in this way the Museum would continue to expand and evolve over time. Last year with the help of two bright undergraduates we started on this prototype project. Due to limitations of time and resources we didn't get very far. In fact the main lesson from the links below is that they show what not to do. Nevertheless I think the ideas were good. The first exhibit is pure math, illustrating the Glur-Hadwiger Theorem which says that any two polygons of the same area are "equidecomposable" and moreover the corresponding pieces in the two dissections are congruent either by translation or central reflection. This allows for lots of clicking and dragging, animation etc. as you can imagine. http://mathmuseum.math.berkeley.edu/triangle/triangle_square.html The second applied math link is intended to give the visitors some idea of what sorting theory is about. http://tacnode.com/dev/sorting/beta/Sorting.html My first goal is to create really good applets for these two exhibits (which probably involves starting over). So please, if any of you know of some good programmers who might want to get involved in this enterprise could you put me in touch with them.? Thanks, David

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Re: [math-fun] When liberals do science...
by MCKAY＠vax2.concordia.ca 16 Jan '04

16 Jan '04

In a UNESCO Science journal they have an article on volcanic activity from about 1700 onwards. It (like the CO2 graph) shows a linear increasing line with time. Examined carefully, we see that there is next to no activity for several years after both 1914 and 1940. This suggests that the graph is related to the adequacy of the observations being made. John McKay From: IN%"math-fun(a)mailman.xmission.com" "math-fun" 16-JAN-2004 16:45:45.52 To: IN%"math-fun(a)mailman.xmission.com" "math-fun" CC: Subj: RE: [math-fun] When liberals do science... Return-path: <math-fun-bounces+mckay=vax2.concordia.ca(a)mailman.xmission.com> Received: from clyde.concordia.ca (clyde.Concordia.CA [132.205.1.1]) by vax2.concordia.ca (PMDF V6.2 #30759) with ESMTP id <01L5H25RFSG4006IPV(a)vax2.concordia.ca> for mckay(a)vax2.concordia.ca (ORCPT mckay(a)vax2.concordia.ca) Fri, 16 Jan 2004 16:45:45 -0400 (EDT) Received: from mailman.xmission.com (mailman.xmission.com [198.60.22.29]) by clyde.concordia.ca (8.12.10/8.12.10) with ESMTP id i0GLjXkE100619 for <mckay(a)vax2.concordia.ca>; Fri, 16 Jan 2004 16:45:33 -0500 (EST) Received: from localhost ([127.0.0.1] helo=mailman.xmission.com) by mailman.xmission.com with esmtp (Exim 3.35 #1 (Debian)) id 1Ahbbe-0001jK-06 for <mckay(a)vax2.concordia.ca>; Fri, 16 Jan 2004 14:34:18 -0700 Received: from web40710.mail.yahoo.com ([66.218.78.167]) by mailman.xmission.com with smtp (Exim 3.35 #1 (Debian)) id 1AhbbV-0001iY-00 for <math-fun(a)mailman.xmission.com>; Fri, 16 Jan 2004 14:34:09 -0700 Received: from [66.81.144.236] by web40710.mail.yahoo.com via HTTP; Fri, 16 Jan 2004 13:33:38 -0800 (PST) Date: Fri, 16 Jan 2004 13:33:38 -0800 (PST) From: Eugene Salamin <gene_salamin(a)yahoo.com> Subject: Re: [math-fun] When liberals do science... In-reply-to: <6.0.1.1.2.20040116103315.02d5d008(a)pop.pipeline.com> Sender: math-fun-bounces+mckay=vax2.concordia.ca(a)mailman.xmission.com To: math-fun <math-fun(a)mailman.xmission.com> Errors-to: math-fun-bounces+mckay=vax2.concordia.ca(a)mailman.xmission.com Reply-to: math-fun <math-fun(a)mailman.xmission.com> Message-id: <20040116213338.60545.qmail(a)web40710.mail.yahoo.com> MIME-version: 1.0 Content-type: text/plain; charset=us-ascii Precedence: list X-BeenThere: math-fun(a)mailman.xmission.com X-Mailman-Version: 2.1.1 X-Scanned-By: MIMEDefang 2.35 List-Post: <mailto:math-fun@mailman.xmission.com> List-Subscribe: <http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>, <mailto:math-fun-request@mailman.xmission.com?subject=subscribe> List-Unsubscribe: <http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>, <mailto:math-fun-request@mailman.xmission.com?subject=unsubscribe> List-Archive: <http://mailman.xmission.com/cgi-bin/mailman/private/math-fun> List-Help: <mailto:math-fun-request@mailman.xmission.com?subject=help> List-Id: math-fun <math-fun.mailman.xmission.com> Original-recipient: rfc822;mckay(a)vax2.concordia.ca --- Henry Baker <hbaker1(a)pipeline.com> wrote: > Aside from the deceptive graphing (see Tutte), my > problem with these alarmist graphs is that we know > nothing about what they mean. Since we have only > been gathering data for 30 years or so, we have no > idea what the "natural range" for this variable is. > In fact, we have no idea what the natural range of > temperatures for the Earth is -- e.g., do we really > know what the mean temperature during the Roman Empire > was? Have a look at the paper "Environmental Effects of Increased Atmospheric Carbon Dioxide" by Arthur Robinson et. al., on-line at http://www.oism.org/pproject/s33p36.htm The paper has a plot showing that temperatures were warmer than they are today back around 1000 AD, and warmer yet around 500 BC and 1000 BC. It seems plausible that the causes of that warm temperature are operative today, though not as strongly. Another interesting plot shows a close correlation (from 1750 to 2000) between average temperature and solar magnetic cycle length. As there is no conceivable way human activity could have the slightest influence on the sun, this does seem to put a good part of the blame for global temperature variation upon the sun. This paper was the basis of a petition, which gathered 17000 signatures, opposing the Kyoto treaty. > We don't know where CO2 comes from, or where it is > stored. A recent article indicated that the ocean > stores enormous amounts of CO2, CO and other gasses. > > I bought gas saving cars for years, but then discovered > that all my liberal friends (big donors to the Sierra > Club) drove gas-guzzling SUV's. One known environmental effect of increased atmospheric CO2 is a surge in the growth rate of trees. Experiments show that when the CO2 reaches 600 ppm (which is Robinson's guess), we may expect the growth rate to triple. What we are doing is taking this carbon, sequestered underground for a hundred million years, and returning it to the biosphere. Why are the tree-hugging Sierra Clubbers not pleased by this prospect? > Scientists are paid to be alarmist -- that's how they > get funding -- e.g., looking for asteroids that might > hit the Earth. But that doesn't mean that I'm going > to drop everything every time they scream that the sky > is falling. Scientists have cried wolf about 10^6 times > too often, and they've used up all their credibility. > They've become yet another political lobbying group -- > just look at any issue of Scientific American for the > past 10 years or so. Yes. A while ago the American Physical Society moved its headquarters from New York City to College Park MD. I suspect the reason was to locate their lobbyists closer to Congress. Bully for the American Mathematical Society; they've remained in Providence RI. > At 09:23 AM 1/16/2004, Ed Pegg Jr wrote: > >Can you laugh away this graph? > >http://www.cmdl.noaa.gov/ccgg/figures/co2obs.jpg > > > >Eventually, we're going to find out what happens > >when this graph hits 420, or higher. A conservative, > >in my mind, would be happy with the current levels > >of carbon dioxide, and would not want to take the > >risk of ever higher levels. > > > >--Ed Pegg Jr. > > > >--- Eugene Salamin <gene_salamin(a)yahoo.com> wrote: > >> This little chuckle pales in comparison to the damage done by the > >> pervasive belief that nuclear power is unsafe, or that human > activity > >> is casusing global temperatures increases. > >> > >> Gene __________________________________ Do you Yahoo!? Yahoo! Hotjobs: Enter the "Signing Bonus" Sweepstakes http://hotjobs.sweepstakes.yahoo.com/signingbonus _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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[math-fun] A prime gap of 1001548
by Richard Schroeppel 16 Jan '04

16 Jan '04

An interesting tidbit from the Number Theory List. Of course, the average spacing between primes must be logN, from the prime number theorem. I don't know anything about the variance of the spacing: Is it poisson?, How unusual is a 10x normal gap? The first gap of 100 is around 10^6, making a 7x gap. I think Shanks posed the question "Where do we expect to find the first gap of 1M?" Rich rcs(a)cs.arizona.edu --------- Date: Thu, 15 Jan 2004 20:56:07 -0500 From: Jens Kruse Andersen <jens.k.a(a)get2net.dk> Subject: A prime gap of 1001548 To: NMBRTHRY(a)LISTSERV.NODAK.EDU Hans Rosenthal and I have found a prime gap of 1001548 between two probabilistic primes (prp's) with 43429 digits. Sieving for small factors used the GMP multiple precision library, and prp testing of the remaining numbers was performed by the program PrimeForm/GW. The logarithm of the primes is 99997 so the gap is 10.02 times the "typical" gap by the prime number theorem. I think that regardless of relative size, this is the first known prime "megagap" with identified (probabilistic) primes as gap ends. The primes have no simple expression. See more details at http://hjem.get2net.dk/jka/math/primegaps/megagap.htm -- Jens Kruse Andersen

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Re: [math-fun] When liberals do science...
by Dan Hoey 16 Jan '04

16 Jan '04

> Can you laugh away this graph? .... I can't laugh away the fact that you are helping Gene make math-fun a list I don't want to read. He did, as usual, spew his political credo uninvited and with only his word for support. That's his habitual practice (and the last time I pointed this out, he called it a left-wing rant, which makes him a liar, too). But you can't convince him--he has all the non-facts on his side, and he is his own ultimate authority. So please don't try to debate his issues--the debate is much larger than you can answer on math-fun, unless you turn this into the political list Salamin is slavering for. Dan Hoey(a)AIC.NRL.Navy.Mil

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