May 2009 - mathfun@mailman.xmission.com

[math-fun] Return of Monte Hall
by Bernie Cosell 24 May '09

24 May '09

In a recent Math Intelligencer, AS Landsberg posed a variation on Monte Hall [paraphrased]: There are three doors, behind which are a car, a car key and a goat. There are two players, the car-player and the key-player. Each player gets to pick two doors to see if they can find their corresponding prize. Each player acts independently and with no information from the other. If they can each find their corresponding prize, the two drive off in their new car. He mentions a proof that with a sufficiently clever strategy the two will be able to drive off in their car 2/3rds of the time. I just can't see how to make that work! If they each pick randomly, I get the odds of their winning the car as 4/9. It is fairly easy to come up with strategies that up the odds to 1/2. But I just don't see how to get it all the way to 2/3rds. /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--

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[math-fun] Math (or is it English?) phobia institutionalized
by rwg＠sdf.lonestar.org 24 May '09

24 May '09

Los Altos Library Volunteer Application [...] I understand that there is no pay or other numeration for my services as a volunteer and that I am not an employee for the library. Signature_____________________

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[math-fun] Ford circles and intuition
by rwg＠sdf.lonestar.org 22 May '09

22 May '09

The usual proof that the rationals have measure zero in the reals has always bugged me. If you surround every point in a dense subset of [0,1] with a finite interval, however small, the intervals ought to overlap like crazy and cover the unit interval many times over, no? And if, instead of surrounding the nth rational (for some ordering) by epsilon/2^n, you surround every rational n/d by epsilon/d^2, the overcovering ought to be even worse, no? No. Admittedly, pictures can deceive, but check out the epsilon=1 case on page 11 of http://www.tweedledum.com/rwg/rectarith12.pdf . Clearly every n/d can be surrounded (by how many intervals?), and the the area sum is finite. --rwg

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Re: [math-fun] Zipf's law
by Henry Baker 20 May '09

20 May '09

Interesting article, but some of the comments posted below it indicate its flaws. In particular, there appear to be dimensional problems (of the usual "cgs" sort) in some of the arguments. About all I could conclude after reading both the article & all of the comments was the usual: "there are fractal sets with differing fractal dimensions". At 01:14 PM 5/20/2009, Dan Asimov wrote: >Interesting math column in today's NY Times about Zipf's law, >which I'd thought applies only to word frequencies: > >< http://judson.blogs.nytimes.com/2009/05/19/math-and-the-city/ > > >One paragraph: > ><< >The mathematics of cities was launched in 1949 when George Zipf, a linguist working at Harvard, reported a striking regularity in the size distribution of cities. He noticed that if you tabulate the biggest cities in a given country and rank them according to their populations, the largest city is always about twice as big as the second largest, and three times as big as the third largest, and so on. In other words, the population of a city is, to a good approximation, inversely proportional to its rank. Why this should be true, no one knows.

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[math-fun] Zipf's law
by Dan Asimov 20 May '09

20 May '09

Interesting math column in today's NY Times about Zipf's law, which I'd thought applies only to word frequencies: < http://judson.blogs.nytimes.com/2009/05/19/math-and-the-city/ > One paragraph: << The mathematics of cities was launched in 1949 when George Zipf, a linguist working at Harvard, reported a striking regularity in the size distribution of cities. He noticed that if you tabulate the biggest cities in a given country and rank them according to their populations, the largest city is always about twice as big as the second largest, and three times as big as the third largest, and so on. In other words, the population of a city is, to a good approximation, inversely proportional to its rank. Why this should be true, no one knows. _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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[math-fun] OOPS. Re: Now they tell me: Mathematica for $295
by Dan Asimov 20 May '09

20 May '09

Meant to change the Subject line to Zipf's law _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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Re: [math-fun] Now they tell me: Mathematica for $295
by Dan Asimov 20 May '09

20 May '09

Interesting math column in today's NY Times about Zipf's law, which I'd thought applies only to word frequencies: < http://judson.blogs.nytimes.com/2009/05/19/math-and-the-city/ > One paragraph: << The mathematics of cities was launched in 1949 when George Zipf, a linguist working at Harvard, reported a striking regularity in the size distribution of cities. He noticed that if you tabulate the biggest cities in a given country and rank them according to their populations, the largest city is always about twice as big as the second largest, and three times as big as the third largest, and so on. In other words, the population of a city is, to a good approximation, inversely proportional to its rank. Why this should be true, no one knows. >> _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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[math-fun] x^2=0 but x=1
by deutsch 20 May '09

20 May '09

I am interested in an analytic device to handle the following simple situation. I have a polynomial P in several variables, x,y,z,u, say. It is of degree 2 in each variable. I would like to evaluate the polynomial when x^2 = 0, y^2 = 0, z^2 = 0, u^2 = 0 BUT x=y=z=u=1. Many thanks for any comment, hint, input. Emeric P.S. Sorry, previous message had no subject.

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Re: [math-fun] x^2=0 but x=1
by deutsch 20 May '09

20 May '09

I think we may assume commutativity, associativity, distributivity. Here is a simple example with 2 variables: P(x,y) = 2 + 2xy + x^2 + y^2. Letting x^2 = y^2 = 0 and then x = y = 1, the answer is 4. This is the number I am after in this particular example. Emeric > Are we to assume x,y,z,w are members of some kind of ring? > > --Dan > > > Emeric wrote: > > << > I am interested in an analytic device to handle the > following simple situation. I have a polynomial P in > several variables, x,y,z,u, say. It is of degree 2 in each > variable. I would like to evaluate the polynomial when x^2 > = 0, y^2 = 0, z^2 = 0, u^2 = 0 BUT x=y=z=u=1. > Many thanks for any comment, hint, input. > >> > > __________________________________________________________ > ___________ "It don't mean a thing if it ain't got that > certain je ne sais quoi." --Peter Schickele > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >

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Re: [math-fun] Now they tell me: Mathematica for $295
by Dan Asimov 20 May '09

20 May '09

I asked about how it might differ from the expensive ("Professional") edition. In the small print, linked to "Q & A", it's stated that it doesn't: << Q: How is Mathematica Home Edition different from the professional version of Mathematica? Mathematica Home Edition is a fully functional version of Mathematica Professional with the same features. >> So "full-featured" apparently here means "full-featured". (The only catch, for me, is that I bought my Mac just before they went to an Intel chip, and this "Home Edition" is available for Macs only if they use Intel. Rats. --Dan ------------------------- Robert Baillie wrote: << I wish I had known about this before I shelled out big bucks. But maybe others can benefit from this. For $295, you can get a full-featured 32-bit version of Mathematica for use at home. Commercial uses are prohibited. So is using it for the class you teach at a school. But for true math nerds, like me, who consider Mathematica to be recreational software that we use at home, this sounds like a great bargain! http://www.wolfram.com/products/mathematicahomeedition/ >> _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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