Archive for the ‘non-math’ Category

Remembering Bill Thurston

August 22, 2012

Bill Thurston passed away yesterday at the far-too-young age of 65. My thoughts and prayers (for what they’re worth) are with his family.

I never read any of Dr. Thurston’s mathematical work in great detail (geometric topology never really being my thing), but from the popular surveys I read, he was of course brilliant. I can’t really do justice to his mathematical accomplishments, but I’ll quickly say for non-mathematical readers that he was probably best known for his geometrization conjecture, which helped pave the way for the proof last decade of the Poincaré conjecture.

What I did read were some of his writings on the philosophy of math; not the boring questions of how “real” mathematical entities are, but thoughts on how we do mathematics. I am incredibly grateful that I had the opportunity to let Dr. Thurston know how much those writings meant to me a couple of years ago. It’s nice to think that I contributed, even infinitesimally, to the net happiness in his life.

[ETA: Terry Tao has a much more mathematically complete obituary.]


Tonal whiplash

July 26, 2012

People who know me well know that I don’t have any particular objection to targeted advertising. Like most things, it can be used for good purposes or bad purposes, but I think on balance, it’s probably better than untargeted advertising. Either way, it’s more efficient for many advertisers, which is good, because that means they can invest more capital into developing and improving products.

I’m not sure whether YouTube targets the ads that sometimes play before videos, either based on the user or the video. But if so: YouTube, I can’t imagine that there are that many people who want to see something about “The Purina Cat Chow Real Stories Project” when they’re looking for a Nick Cave song.

I’m in love. What’s that song?

March 29, 2010

I’ve been on spring break for the past week, so this is even older news than it would have been, but Alex Chilton died earlier this month. If you don’t know who Alex Chilton is, he started off as the singer of the Box Tops, who scored a late-’60s hit with “The Letter.” But in certain circles he’s better known as the lead singer and songwriter for the defining power pop band, Big Star. Big Star’s music was a formative influnce on me as a person, if not as a mathematician, so I’m breaking from my usual routine of crackpot mathematics and expository articles to pay tribute.

Most of what I could say has already been said better, so I’ll link to some other tributes shortly. People have talked about how Big Star were a major influence on all sorts of bands in the ’80s and ’90s up to the present, from R.E.M. to the Replacements to Elliott Smith. People have talked about the timeless nature of Big Star’s songs, about how “Thirteen” is maybe the ultimate expression of what it’s like to be that age. But one thing that’s perhaps been lost in the chatter is the fact that so much of Chilton’s work with Big Star is just plain wonderful music. Witness “Nighttime” and “Blue Moon,” back-to-back tracks from Big Star’s final album, Third (also known as Sister Lover) — to my ears, two of the most achingly beautful pop songs ever recorded.

The best tribute I’ve read — maybe the definitive one — is Paul Westerberg’s in the New York Times. (Westerberg wrote and performed, with the Replacements, the song that gave this post its title.) But the best possible tribute, in my mind, would be if this blog post turned one person on to the music of the late, great Alex Chilton. It might change your life. More likely it won’t. But either way, it’s great damned music, and I hope — and expect — that it’ll live on far after I’m gone.

Is the Super Bowl a Z/2Z-graded bowl?

February 8, 2010

And if so, what’s just a regular ungraded bowl?

(Hat tip to Vladimir S. for the bad pun; new post coming soon, really, I promise.)

On bias

January 23, 2010

[From Homer the Smithers, Mr. Burns sends Smithers on a forced vacation and tasks him with finding a temporary replacement]

Smithers: I’ve got to find a replacement who won’t outshine me. Perhaps if I search the employee evaluations for the word ‘incompetent…’

[Computer beeps, screen displays “714 Matches Found’]

Smithers: 714 names?! Heh. Better be more specific. ‘Lazy,’ ‘clumsy,’ ‘dimwitted,’ ‘monstrously ugly.’

[After a couple seconds, computer beeps, screen displays ‘714 Matches Found’]

Smithers: Ah, nuts to this, I’ll just go get Homer Simpson.

Actually, I tried to find the statistical nomenclature for this kind of thing, but couldn’t. Anyone have any idea what this is? (I want to say selection bias, but that’s not quite it…)

New Extremal Toolbox post should be coming later this weekend.

Bleg: What’s the most recent day no one alive was born

January 5, 2010

Inspired by Michael Lugo’s post on reconstructing a person from their DOB, zipcode, and gender.

If you, for whatever reason, ever watch the Today show, you’ll notice that one of the recurring features is the hosts listing the names of some men and women who are turning 100. Becoming a centenarian is a reasonably big accomplishment — in the U.S., it nets you a congratulatory letter from the President, for example. But if you look into it, you’ll notice that you can find someone turning 100 on pretty much any given day. Usually not someone particularly well-known, but certainly someone. (I tried to find someone famous and vaguely math-related who just turned or is turning 100 for this post, but couldn’t; however, the fascinating economist Ronald Coase turned 99 last week.) It’s almost certainly true that on any given day, someone somewhere in the world is in fact celebrating their 100th birthday. But go ten years further, and you find almost no one who lives to 110. Actually, I know of only one supercentenarian, living or not, who is interesting for reasons apart from his longevity — the late Vietoris, the topologist, probably best known as half of the Vietoris-Rips complex and the Mayer-Vietoris sequence. Odds are pretty good that no one alive is turning 110 today, or tomorrow, or (sadly) New Years’ Day.

So… a question is starting to take shape. On every day between December 29, 1909, and today, someone was born who is still living today. But much earlier than that, and the above statement begins to be false. So what’s the most recent day that no one living was born on?



December 29, 2009

Sorry about the lack of new post; it’s coming. It turned out to be a more interesting problem than I at first thought; look for it around New Years’.

I’m working through some of the holes in my graph knowledge with my shiny new copy of Bollobas’ Modern Graph Theory. Chapter 1, Exercise 19 is a problem I’ve done before, but the way it’s presented makes me want to do it all over again:

Characterize the degree sequences of forests!

Exercise 17 is about the degree sequences of trees, and 18 extends it to forests with a fixed number of components — so this isn’t totally out of the blue. Still, it makes me wonder why more textbooks don’t end problems with exclamation marks.

An etymological question

December 18, 2009

Galois was of course the first to highly successfully use the notion of a field. However, if ones reads his papers they’ll see that he never explicity gave the concept of an algebraic structure closed under addition, subtraction, commutative multiplication, and division a name. Dedekind would be the first to do that; he gave the name Körper, or “body,” to what we’d today call a number field. A couple of decades later, E.H. Moore of Chicago would introduce the term “field” in English.

“Körper” caught on fairly quickly among Continental mathematicians, giving us the French corps, and from there it spread to Spanish and Portuguese; in the other direction, the German mutated into Hungarian “test” and Polish “ciało”, both essentially with the same meaning of “body.”

However, in Italian and most of the Slavic languages, the word for “field” is also the agricultural term. This means that the algebraic terminology didn’t solidify until considerably later, probably between the World Wars at earliest. This is understandable; while both Italy and Russia had strong mathematical communities around the turn of the last century, they were somewhat isolated and if nothing else had relatively fewer top-tier algebraists than the French or, especially, the German schools.

What’s really curious is the following: In both Italian and Russian, as I mentioned, the word for English “field” is a literal translation of “field.” In pretty much every language, the word for “ring” can also refer to a thing that you wear on your finger. But in Italian and (several of) the Slavic languages — and in these languages alone, as far as I know — the word for “skew field”, or “division ring”, translates to English as “body”! This seems to me to be a rather exceptional situation — surely either a modification of “ring” or of “field” will do, as in every other language, but it seems not to be the case. So there are two open problems here:

  1. Explain the situation that caused “field” to replace “body” to refer to a commutative division ring, but not to refer to a division ring in general, in Italian and Russian.
  2. Are there any other examples of crufty terminology that’s unique to one or two languages (or closely-related language families?)