God tweets about playing dice

There's a book coming out in November, The Last Testament: A Memoir by God. "God" tweets at TheTweetOfGod, and "He" just twote:

Do you ever lose when you play cards?" Remember Einstein! I play not cards, but dice. And I never lose. The dice are loaded. And so am I.

There you have it, folks. The title of this blog is correct.

Bad word problems

An example of a bad word problem, from Frank Quinn's article The Nature of Contemporary Core Mathematics, who is at Virginia Tech:

Bubba has a still that produces 700 gallons of alcohol per
week. If the tax on alcohol is $1.50 per gallon, how much tax will Bubba pay in amonth? [Set up and analyze a model, then discuss applicability of the model.]

I have given an example with obvious cultural bias because I am not sure I could successfully avoid it. At any rate students in my area in rural Virginia would think this problem is hilarious. We have a long tradition of illegal distilleries and they would know that Bubba has no intention of ever paying any tax.

This blog needs a new title

The word "probability" does not appear in the Bible, or so we learn from Conservapedia's List of missing words in the Bible.

I can only conclude that Einstein was right, and God does not play dice.

How most mathematical proofs are written

From Abstruse Goose: How most mathematical proofs are written, dramatized as people driving around and getting lost.

Sometimes I've wondered what an actual map of the various possible proofs of certain results would look like.

Eponyms in mathematics

Let S be the standard Smith class of normalized univalent Matcuzinski functions on the unit disc, and let B be the subclass of normalized Walquist functions. We establish a simple criterion for the non-Walquistness of a Matcuzinski function. With this technique it is easy to exhibit, using standard Hughes-Williams methods, a class of non-Walquist polynomials. This answers the Kopfschmerzhaus-type problem, posed by R. J. W. (“Wally”) Jones, concerning the smallest degree of a non-Walquist polynomial.

This fake abstract of a paper is from Merv Henwood and Ivan Rival, Eponymy in Mathematical Nomenclature: What's in a Name, and What Should Be? (PDF), from the Mathematical Intelligencer in 1980. It sounds to me like slight caricature -- but only slight. Henwood and Rival point out that such names are lazy. Names have at least two important functions -- to describe and to label -- and eponyms only label.

Perhaps such abstracts would be more common in areas which are small enough that all the major players talk to each other. I imagine that Smith, Matcuzinski, Walquist, etc. know each other.

Also of interest is David Rusin's list of eponyms occurring in the MSC classification. These names in general seem a bit less obscure than the names one would find in the abstract of a random paper, which isn't surprising as they're names of concepts big enough to get areas named after them.

(And can someone confirm or refute the story that Banach, in the paper in which he introduced Banach spaces, called them "spaces of type B" in an effort to get them named after himself? I've heard this one a few times but always unsourced.)

Fields of onions

The Onion, commenting on Sarah Palin's resignation as governor of Alaska, writes that "Nothing can distract her laser focus from the ultimate prize: the Fields Medal.”

But Palin is 45, and the age limit for the Fields is 40. Perhaps she should aim for the Abel Prize instead?

(Note to the humor-impaired: this is not meant to disparage the Abel Prize.)

A meta-proof

A meta-proof of P=/!=NP, from the Geomblog in 2004. (That's "equals or does not equal".)

Note that you don't need to know anything about the P vs. NP problem to find it funny.

(via Michael Trick.)

News from Course XVIII-P

Glimpi's conjecture, the Holy Grail of numeric set lassitude mathematics, has been proven.

"Roommates" is a euphemism?

I'm at the Cornell Probability Summer School. (This announcement is too late for anybody who wants to find me here, as it's almost over! But I have been tracked down by at least one fan.)

In a lecture here this morning, Ander Holroyd spoke about the stable marriage problem and variations of it involving point processes (see this paper of Holroyd, Pemantle, Peres, and Schramm, which I've mentioned before, for details). The goal of the problem is to pair up n men and n women in such a way that no two people who aren't married to each other prefer each other to their current partners; this is called a "stable matching" and one always exists.

The original paper on the stable marriage problem is that of Gale and Shapley, in 1962. This paper also talks about the "stable roommates" problem, which is the analogous problem where everybody is of the same gender. Rather surprisingly, I never realized that "roommates" might be a euphemism here, which is something that Holroyd pointed out this morning to quite a bit of laughter.

Bears, pigs, and the like

The blog's been slow. I've been off writing real mathematics, thinking for and preparing for the class I'm teaching this summer, and so on. But I'm still here!

And while I'm here, you should read Chad Orzel on the faulty thermodynamics of children's stories. In the story of Goldilocks and the three bears, one would expect that the papa bear is the largest, then the mama bear, and then the baby bear. Furthermore, you'd think that the larger the bear, the larger the bowl of porridge, and the slower it should cool off. But it doesn't seem to work that way! Read the comments come up with some interesting explanations.

Exercise for the scientifically-inclined reader: comment on the physical implications of the Three Little Pigs.

Exercise for the not-so-scientifically-inclined reader: what's with all the animals coming in threes?

Global octahedron

The Onion, in its fictional world, is owned by Global Tetrahedron. Their logo is a dodecahedron.

(The title of this post splits the difference.)

Billions and millions

Yes, I'm still alive. I got out of the blogging groove somehow.

Today's xkcd makes an interesting point about the difference between "billion" and "million".

And although this isn't about math, Carl Sagan's Cosmos can be watched online at hulu.com. (Thanks to Blake Stacey for the pointer.)

Knuth on solitaire

I'm browsing through Knuth's The Art of Computer Programming (Volume 1, Volume 2, Volume 3), because it's Spring Break, so I have time. I'm reading the mathematical bits, which are perhaps half the work; I'm less interested in the algorithms.

Anyway, we find on page 158 of Volume 2: "Some people spend a lot of valuable time playing card games of solitaire, and perhaps automation will make an important inroad in this area." This is part of Chapter 3, on the generation and testing of random numbers. Of course, this book was published in 1969; Windows Solitaire didn't exist then. (It's also amusing to see Knuth describing things that will be in, say, Chapter 10; he's currently working on Chapter 7, which will be the first half of Volume 4.)

Does algeblah confuze u?

Algeblah confuzez mi, from I Can Has Cheezburger.

Square root day

Today, it appears, is "square root day", 3/3/09. 3 is, of course, the square root of 9.

From 360; it was also pointed out there that square roots, i. e. root vegetables cut into squares, do not taste as good as pi(e). So I will wait until next Saturday for my mathematical holiday needs.

On the combinatorics of tourism

Tourists Not Leaving Landmark Until All Permutations Of Groups And Cameras Exhausted, from The Onion.

The Arbesman limit

Samuel Arbesman talks how to get something named after yourself. Of course, he names something after himself -- the "Arbesman limit", which is the number of things that one person can have named after themselves. (Gauss, Euler, etc. provide a lower bound for this limit.)

Supposedly Banach originally named his spaces "spaces of type B" or something like that, figuring that people would see the B, assume it standed for Banach, and start calling them Banach spaces. If that's true, it worked.

Read today's Foxtrot

You should read today's Foxtrot comic strip. (I won't tell you why, because if I told you why you won't follow the link.)

Universality theory for cranks

From the geomblog, in 2004: a meta-proof of P=/!=NP. With very slight modifications this could be a meta-proof of the Riemann hypothesis, or any other outstanding open problem in mathematics, theoretical CS, theoretical physics, or other heavily mathematical fields. The cranks work in roughly the same way regardless of the specific question.

Pólya and Szegö take a dim view of authority

George Pólya and Gabor Szegö, in Problems and Theorems in Analysis I: Series, Integral Calculus, Theory of Functions, define the "maximum term" of a power series with all coefficients p_i positive,

p₀ + p₁ x + p₂ x² + ...,

as that term for which p_i xⁱ is largest. (Obviously this depends on x.) They then ask:

[Part 1, Problem] 120. [Prove that] the subscript of the maximum term increases as x increases. (One might consider this situation as somewhat unusual: in the course of successive changes the position of maximum importance is held by more and more capable individuals.)

Problem 119 is to prove that for an everywhere convergent power series which is not a polynomial, the subscript of the maximal term goes to ∞ with x. Pólya and Szegö offer no commentary.