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[math-fun] Sex, Lies and Government Conducted Surveys
by David Gale 28 Sep '05

28 Sep '05

On September 15 the government released a report "Sexual Behavior and Selected Health Measures" reporting on a survey "conducted by the Centers for Disease Control and Prevention's [sic] (CDC) National Center for Health Statistics (NCHS)" http://www.cdc.gov/nchs/data/ad/ad362.pdf The objective of the survey is to get information on public health concerns, fertility, sexually transmitted disease, etc. However I bring it up here because it contains the most glaring examples I have yet seen of published inconsistency. It's the well worn story that males have many more "sexual partners" than females. Interested people should look at the report. For example, Tables 10 and 11 of the survey show that the median number of partners "in lifetime" for males over forty is 8 while that for females is 3.8. To immediately recognize the inconsistency imagine the same survey with but with the words sexual partners replaced by spouses. For more of the same look at Figure 6 on page 6. More inconsistency: when men and women are asked for the number of partners over the past 12 months, Tables 1 and 2, the numbers come out the same, within epsilon. . As I said, this is an old story. See the following from New York Review of Books ten years ago by Richard Lewontin. http://www.nybooks.com/articles/article-preview?article_id=1923 The authors are aware of the problem and suggest explanations on pages 12 and 13 some of which are, well, amusing. "Some researchers have suggested that some of this difference is due to a small percentage of men who report very large numbers of partners," Another "explanation" is that women my have partners over age 44 who were not polled in the survey (this would of course skew it in the other direction). Is this an example of innumeracy in high places? Lewontin writes in http://www.nybooks.com/articles/1871 "The willingness of both social and natural scientists to recognize contradictions in their findings, and then to ignore them when it is convenient, is a serious disease of inquiry." David The authors

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RE: [math-fun] Multiplicative Magic Squares
by Torgerson, Mark D 27 Sep '05

27 Sep '05

Michael Kleber wrote >Q: Is it always possible to partition the integers from 2 to 2n-1 >into two sets of size n-1, such that the products of two elements, >one from each set, all distinct integers >=2n? >Seems like the answer is "yes with high probability", but can someone >change that to just "yes"? Looks like "no" is the real answer Suppose so... Let S,T be the two sets, with 2 in S. Let 2<a<n. It must be that a isin S. Given a, then 2a<=2n-1 and hence in one of the sets. If a isin T then we can make 2a two different ways. The first with 1*2a (no matter where 2a lives) and 2*a since 2 and a are not in the same set. So S={1,2,3,...,n-1,r} for some r>=n. Now for n of any size, there are a couple of instances where 2a and 2a+1 are in S and (because we don't know r) at least one case where 2(2a) and 2(2a+1) are in T. This gives two ways to get 4a(2a+1). The cheese ball way to get the job done is to set S={1,2,...,n} and T={1,p1,...,p(n-1)} where the pi are the n -1 smallest primes bigger than n. Mark

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RE: [math-fun] Multiplicative Magic Squares
by Lee Sallows 27 Sep '05

27 Sep '05

>I promise to explain my "secret" algorithm (but there is no great secret...) >when it will be proved enough good and optimized to successfully answer to >the 5x5 question. >Christian Hello folks, I don't know how Christian does it, but to take 3x3 as an example, I'd start with a generalization of all 3x3 multiplicative magic squares, such as: z*x z*x^2*y^2 z*y z*y^2 z*x*y z^x^2 z*x^2*y z z*x*y^2 The magic product is then x^3*y^3*z^3 = 216 when z = 1, x = 2, y = 3, the smallest integer assignmments. Stepwise incrementing of these values while skipping those results showing repeated entries will then yield squares with the remaining products on Christian's list. Ditto for 4x4. But I must say, 5x5 looks tricky. Lee

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RE: [math-fun] Multiplicative Magic Squares
by dasimov＠earthlink.net 27 Sep '05

27 Sep '05

I love the idea of multiplicative magic squares. Using n^2 unknown but distinct vectors in R^n that are indexed by (i,j) for 1 <= i,j <= n, it's the same as finding nonnegative integer coordinates for these vectors such that all vectors (i, j0) for 1 <= i <= n sum to the same as all vectors (i0,j) for 1 <= j <= n (for all choices of 1 <= i0,j0 <= n). (Or did someone already mention this?) I'm interested in how magic these can be. I find the old rule of having all rows & columns plus the 2 diagonals sum to the same sum as rather dorky: the diagonals are kind of random. 1) Better here would be all rows & columns and broken diagonals (i.e., diagonals on the torus) multiply to the same product. 2) Best of all would be for simply all affine lines on Z_n x Z_n multiply to the same product. (This is when you repeat the same step (K,L) on the torus and first come back to your starting point with exactly n steps. (There are 4x4 additive magic squares with this property; I'm not sure if there are for any other n.) Are 1) or 2) possible for a multiplicative magic square (MMS)? (And is there a better name for an MMS than multiplicative magic square?) --Dan

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RE: [math-fun] Announcement: Atlas of Natural Numbers
by dasimov＠earthlink.net 27 Sep '05

27 Sep '05

David Wilson wrote: << In the near future, I intend to begin serious development on my Atlas of Natural Numbers, a web site devoted to collecting and organizing interesting information about individual natural numbers. >> This sounds great. Can you answer a question I've had for some time? I'd like to know the smallest positive integer that cannot be described with fewer than fifteen English words. --Dan

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[math-fun] Atlas Replies + Help
by David Wilson 26 Sep '05

26 Sep '05

In deference to the Math-Fun and Seqfan lists, I would ask that you address any questions to about the Atlas directly to me at davidwwilson(a)comcast.net, and not copy to math-fun or seqfan lists. I am still looking for a free or nominal-charge mailing list server for an Atlas mailing list. -------------------------------- - David Wilson

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[math-fun] Geometry book "Divine Proportions"
by Joerg Arndt 26 Sep '05

26 Sep '05

A colleague has pointed me to the book "Divine Proportions: Rational Trigonometry to Universal Geometry" by N J Wildberger (Assoc Prof UNSW Sydney) See http://wildegg.com/products.htm I am not into geometry but some people on the list surely are. Therefore this posting. -- p=2^q-1 prime <== q>2, cosh(2^(q-2)*log(2+sqrt(3)))%p=0 Life is hard and then you die.

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RE: [math-fun] Sex, Lies and Government Conducted Surveys
by dasimov＠earthlink.net 26 Sep '05

26 Sep '05

David Gale writes: << . . . The objective of the survey is to get information on public health concerns, fertility, sexually transmitted disease, etc. However I bring it up here because it contains the most glaring examples I have yet seen of published inconsistency. It's the well worn story that males have many more "sexual partners" than females. Interested people should look at the report. For example, Tables 10 and 11 of the survey show that the median number of partners "in lifetime" for males over forty is 8 while that for females is 3.8. To immediately recognize the inconsistency imagine the same survey with but with the words sexual partners replaced by spouses. For more of the same look at Figure 6 on page 6. More inconsistency: when men and women are asked for the number of partners over the past 12 months, Tables 1 and 2, the numbers come out the same, within epsilon. . . . >> I'm not entirely sure what the researchers were supposed to do -- they are merely reporting the results of their survey and attempting to interpret the inconsistencies, which to their credit they acknowledge. It is a well-known fact that people's unverifiable self-descriptions are biased toward making themselves look good (or at least better than reality), and so are prone to inconsistency. Many simple explanations are possible. One is the truism that it is often considered an indication of virility for men to have had numerous sexual partners (up to a point), whereas for women this is often frowned upon. Hence, men would have an incentive to report higher, and women lower, numbers, than actual fact. (But when only the past year is considered, the numbers are relatively small, so there may be less incentive to mis-report -- and also a clearer memory of what actually happened.) I don't get why replacing "sexual partners" with "spouses" makes any inconsistency clearer. It seems easy to believe that unmarried sexual behavior tends to be different from married. --Dan

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RE: [math-fun] Multiplicative Magic Squares
by Schroeppel, Richard 26 Sep '05

26 Sep '05

There's a standard proof that the center of a 3x3 magic square is K/3, where K is the row sum. (Add up the four lines through the center, subtract the whole square.) Of course this works for multiplication too, so the magic product is always the cube of the center. There's a collection of similar results for a 4x4 square, such as "the sum of the four corners is K" etc. Although the arguments offered so far are plausible, I think a bit more proof is in order before claiming minimality of the various squares. Maybe a program? There aren't that many potential products < 5040 with 16 divisors, and we can also require the exponents in the prime factorization form a descending staircase. Allowing 0 as an entry doesn't seem helpful. I suspect that allowing negatives will turn out to be equivalent to the positive case with duplications allowed (but not triplications & up). But I don't see the proof that minus signs can always be attached to a positive square in a consistent way. Rich rcs(a)cs.arizona.edu -----Original Message----- From: math-fun-bounces+rschroe=sandia.gov(a)mailman.xmission.com [mailto:math-fun-bounces+rschroe=sandia.gov@mailman.xmission.com] On Behalf Of Christian Boyer Sent: Thursday, September 22, 2005 9:02 AM To: 'math-fun' Subject: RE: [math-fun] Multiplicative Magic Squares Of course replace "magic sum" by "magic product", twice in my previous message... -----Message d'origine----- De : math-fun-bounces+cboyer=club-internet.fr(a)mailman.xmission.com [mailto:math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com] De la part de Christian Boyer Envoyé : jeudi 22 septembre 2005 16:30 À : 'math-fun' Objet : RE: [math-fun] Multiplicative Magic Squares In his old book on recreative mathematics, Boris Kordiemski described exactly the Michael's method (using two latin squares) for 4x4 multiplicative squares. He also described a method for 3x3 multiplicative squares: a b² a²b a²b² ab 1 b a² ab² With a=2 and b=3, you get 2 9 12 36 6 1 3 4 18 Magic sum = 216 (*). It is the smallest possible multiplicative square. In 1667 (a long time ago...), Arnauld gave a 3x3 multiplicative square. Perhaps the oldest published multiplicative square? Using powers of 2, its magic sum was bigger : 4096. Christian. (*) 216 is also the smallest cube being also sum of three cubes. 216 = 6^3 = 3^3 + 4^3 + 5^3 _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ 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] Frost visits the Gulf on a blustery evening
by Hilarie Orman 26 Sep '05

26 Sep '05

> >> A front-page Sat., Sept. 17 story on the NY Times website, > >> found at http://snipurl.com/hqxi, claims that FEMA has > >> delivered 177 million tons of ice to Louisiana, Mississippi and > >> Alabama in the aftermath of hurricane Katrina. Some say the Gulf will end in water, Some say in ice. >From what I've witnessed of Katrina, I hold with those who favor FEMA. But if it had to perish twice, I think I know enough of weight, To say that for destruction ice Is also great And would suffice. Hilarie, With apologies to RF.

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