The probability of Asian-Hispanic food

From tomorrow's New York Times: an article on the growing prevalence of Asian-Hispanic fusion food in California. It's part of a series on the Census. Orange County, California is 17.87% Asian and 34.13% Hispanic -- so the majority of the population, 52.00%, is either Asian or Hispanic. Not surprisingly there's a guy there with a food truck named Dos Chinos, which serves such food as sriracha-tapatito-tamarind cheesecake.

This is accompanied by a little map showing the sum of Asian and Hispanic population in any given county. (Well, it might be the sum; to be honest I don't know, as in the Census "Hispanic" vs. "non-Hispanic" is orthogonal to "race", which takes values White, Black, Asian, American Indian, and Native Hawaiian.) In many places in the southern half of the state it's over 50%.

But wouldn't the relevant statistic for this article be not (0.1787) + (0.3413), but 2*(0.1787)*(0.3413) = 0.1219, the probability that if two random Orange Country residents run into each other, one of them will be Asian and the other will be Hispanic? Fresno County, for example, is 50.3% Hispanic and 9.6% Asian -- that's 59.9% "Hispanic or Asian" -- but there wouldn't seem to be quite as many opportunities for such fusion as the probability of a Hispanic-Asian pair in Fresno County is only 2*(50.3%)*(9.6%) = 9.7%.

(Except that 97% of Fresno County's Asians are Hispanic, according to the frustratingly hard-to-navigate American FactFinder.So maybe some "fusion" has already taken place.)

Magic and mathematics

Sunday's New York Times has a bunch of magic tricks based on simple algebra, by Arthur Benjamin.

For some magic tricks based on "deep" mathematics, check out this mathoverflow thread. Rumor has it that Persi Diaconis thinks there's no such thing, though, and he would know.

God and some humans play dice

From Tierney Lab at the New York Times:A puzzle in which God, Einstein, and Oppenheimer play dice, and its solution.

Fermi problems

Here's a quiz full of Fermi problems (like "how many people are airborne over the US at any moment?") and an article by Natalie Angier in today's New York Times, in which she suggests that some basic quantitative reasoning skills wouldn't kill people. The article was inspired by a recent book of such problems, Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin, by John Adam and Lawrence Weinstein. Adam also has a forthcoming book entitled A Mathematical Nature Walk which may be interesting.

Check your units!

From today's New York Times, real estate section, referring to rural Normandy:

But, on average, real estate prices here generally range from 1,500 to 2,000 euros ($1,940 to $2,585) a square foot and a typical three-bedroom house sells for 250,000 euros ($323,165), according to Manuela Marques, a broker with Objectif Pierre, a local real estate agency.

Of course, this doesn't check out, unless a typical three-bedroom house is around 150 square feet (and Normandy has suddenly turned into Manhattan). The resolution is that that's a price per square meter, which is how a French real estate broker would quote things.

Sigurdur Helgason is not dead

Sigurdur Helgason dies, says the New York Times.

That's the Icelandair executive, not the MIT mathematician. The mathematician is, as far as I know, alive.

(Also, the New York Times actually refers to "Colombia University" in their obituary.)

Housing prices drop 13 percent -- what does this mean?

The New York Times reports on bad housing news:

The median price of a home plunged 13 percent from October to November, to $181,300 from $208,000 a year ago. That was the lowest price since February 2004.

They mean that house prices have gone down 13 percent in a year, i. e. from November 2007 to November 2008. That's what the National Association of Realtors press release says.

But one sees this pretty often -- the confusion between monthly declines and annual declines. And sometimes a 1% decline in a month might be reported as a "12% per year" decline -- but then the "per year" gets dropped, the statement "prices of X dropped 12% this month" is made, and those who aren't familiar with how people who care about the price of X report their numbers get confused.

Don't get me wrong -- a drop of 13% in a year is still a big deal. But a drop of 13% in a month would be a much bigger deal.

NYT profiles of Jessica Fridrich

Specializing in Problems That Only Seem Impossible to Solve , by Bina Venkataraman, in yesterday's New York Times.

This is an article about Jessica Fridrich, a professor at Binghamton University, who at one point held the world record for the fastest solving of the Rubik's Cube. She currently specializes in the research of information hiding in digital imagery.

NYT on the Netflix Prize

In this week's New York Times Magazine, Clive Thompson writes about people trying to win the Netflix Prize.

Early in 2007, Netflix, the video-rental-by-mail service, made (anonymized) data on its users preferences available, and is offering $1,000,000 to the first person or team that creates an algorithm for recommending movies that makes a certain substantial improvement upon the existing algorithms. More precisely, Netflix attempts to predict the star rating, on a one-to-five scale, that users will give to a movie; the root mean square error in their old algorithm was about 0.95 stars, and they'll pay the $1,000,000 for improvement of this by 10%. (They also pay $50,000 for improvements of 1%.)

Why are they doing this? Well, Netflix recommends movies to lots of people, and they want their recommendations to be good. And it sounds like they're getting a lot more than a million dollars worth of time from the various competitors working on this; if they actually had these people on their payroll it would cost more.

It's interesting that there are certain movies that are very difficult to predict; Napoleon Dynamite is one of the examples the article gives, which won't surprise anybody who's seen it; poking around the forums on the Netflixprize.com site I found a list of movies like that, although it's a year and a half old so there's been progress since then. (Hmm, I'm not sure if I like Napoleon Dynamite -- sometimes I do and sometimes I don't.)

Apparently one of the major mathematical tools that has emerged as being useful here is singular value decomposition. I'm not surprised that some Big Fancy Linear Algebra tool was necessary, as a lot of the algorithms essentially seem to work by identifying various dimensions along which movies can vary. (Look, it's a hidden metric space!) Hmm, I wonder if the space of movies has some nontrivial topology... no, I will not get sucked into thinking about this!

Derivation is not destiny

Arnold Zwicky at Language Log points out that the "derivative" of "financial derivatives", a word we've been hearing lots in the news lately, is not derived from the "derivative" of calculus. (This is commenting on a misunderstanding in a recently published letter to the New York Times.)

It never made sense to me that while the verb for "find the integral" is "integrate", the verb for "find the derivative" is "differentiate" -- in one case the forms are parallel and in the other they aren't. Of course the derivative involves finding a difference, but the language seems a bit inconsistent. And I've had the occasional student refer to "derivating" a function.

It probably doesn't help that they both start with d, and that every d-like symbol (off the top of my head, at least d, D, δ, Δ, and ∂) gets used for some sort of derivative/difference-like thing in some context.)

Who knew high school geometry was good for something?

Groundskeepers Display Artistry on the Diamond, September 30 (?) New York Times. David Mellor, the current head groundskeeper at Fenway Park, is the one who started the trend of mowing the grass in such a way as to create interesting-looking patterns; apparently he first did it in order to camouflage some damaged grass in Milwaukee in the early 90s. Roughly speaking, the mowing action bends the grass in one direction or another, creating contrasts of light and dark; you can see a similar effect when you vacuum your carpet. (I really mean "you" here. I can't; I have wood floors.)

And we're told that "High-school geometry classes visit [Mellor] at Fenway Park to study ways that an odd-shaped field can be divided and subdivided by straight lines and sharp angles."

Oded Schramm obituary at NYT

Yesterday's New York Times included an obituary of Oded Schramm, who died on September 1, at the age of 46. I don't know Schramm's work, but I do know that the obituary did not have me screaming things like "That's not how mathematics actually works!". Mainstream media coverage of mathematics often has such an effect on me, so the obituary is at least decently written.

There's a memorial page; if you knew him (I didn't) you probably already knew that, though.

Big numbers confuse the New York Times

From Chinese basketball builds towards podium (August 9):

"With 300,000 million people playing basketball across the country — roughly the same number as the population of the United States..."

Really? I mean, it's almost a cliche by this point that There Are Lots Of People In China -- but I didn't know there were quite that many.

Nomenclature clash

Prime Numbers for June 29 to July 5, from today's New York Times. (I don't know if this is a weekly thing; it could be but I don't recall seeing it before.)

The numbers are 46, 62000, 30, 18%, and 30000; each is important to some news story from this week. (If you want to get technical, 62000 and 30000 are approximations.)

Presumably they mean "prime" in the sense of "important". Or in the sense of "composite", but that would be a bit perverse.

Link to review of The Drunkard's Walk

Here's a review of Leonard Mlodinow's book The Drunkard's Walk. I will resist the temptation to review the review. (Although I've been meaning to write down what I think of the book. I might do so.)

For some difficult-to-explain reason it is illustrated with a couple images from Jessica Hagy's indexed.

An "algorithmic curve"?

Steampunk Moves Between Two Worlds, from today's Monkey Writes.

“There seems to be this sort of perfect storm of interest in steampunk right now,” Mr. von Slatt said. “If you go to Google Trends and track the number of times it is mentioned, the curve is almost algorithmic from a year and a half ago.” (At this writing, Google cites 1.9 million references.)

Here's the curve at Google Trends. It looks linear to me, although with a lot of noise. I suspect, though, that the speaker meant to say it was exponential (because exponentials grow really fast, so this would be in keeping with the rest of the article), then confused that with "logarithmic" (which is a pretty common mistake), and then rearranged a few letters to get "algorithmic".

And a random Google Trends fact: the number of people searching for mathematics has declined steadily over the past four years. Math has been basically flat over that time period, but shows a very large dip during the summers. Presumably the people searching for "math" are students. Maths displays what appears to be a more complicated seasonal pattern; can this be explained by the UK academic calendar. As for "mathematics" declining, I suspect people find the word too long.

A linear equation come to life

The New York Times has a delegate calculator. This consists of a slider which allows the user to set a hypothetical percentage of delegates that Obama (or Clinton) will win in the remaining primaries, and returns the percentage of the remaining uncommitted superdelegates that candidate would have to get in order to win the Democratic presidential nomination.

Of course, it varies linearly -- for each pledged delegate a candidate gets, that's one less superdelegate they need. Since things are phrased in terms of percentages, it's not quite so simple -- there are 217 pledged delegates left and 225.5 superdelegates with unknown preference. (Half a superdelegate, you ask? Democrats Abroad get delegates that each get half a vote.) So for each one percent more of the pledged delegates a candidate gets (that's roughly proportional to the popular vote, although rounding and the fact that delegates are assigned based on historic turnout as opposed to current turnout alters that), they need slightly less than one percent less of the superdelegates. (Don't try to do the arithmetic; it doesn't seem to quite work out, because I suspect the superdelegate counters and the slider-makers aren't constantly talkign to each other.)

This is an interesting wya to display the linear dependence; a graph or a table would seem more obvious, but with computers one isn't bound to static displays as one is on paper.

Breaking down inflation

An interesting informational graphic: All of Inflation's Little Parts, from Saturday's New York Times. This is a graphic that breaks up the many parts of the standard "basket" that is used by the US government to compute the inflation rate.

Of course, nobody is exactly average. To take an example dear to my heart, 0.1% of this basket is "books". But how many people do you think spend exactly that portion of their income on books? My instinct is that the distribution of "percentage of income spent on books" (and a lot of the other small items) has a long right tail. Plenty of people I know (who are of course not a uniform sample) spend, say, two or three percent of their income or more on books -- and it's my understanding that the book industry relies quite a bit on people like us.

Somewhat more seriously, 23.9% of the basket is "owner's equivalent rent" (what homeowners would pay if they were renting their homes) and 5.8% is actual rent. That means that a typical household making, say, $50,000 a year spends about $1,000 monthly on the house they own (or would, if we weren't having a housing bubble), and $250 monthly on rent. But it's very hard to imagine a household that actually does that! The mean and the mode, in distributions like this, are very different. It would be quite surprising, I think, to find someone whose spending breaks down exactly as in the graphic.

Fractions are not about pizza

Study Suggests Math Teachers Scrap Balls and Slices, from today's New York Times.

The Times article is about a study reported on in today's issue of Science (Jennifer A. Kaminski, Vladimir M. Sloutsky, Andrew F. Heckler1. The Advantage of Abstract Examples in Learning Math. Science 25 April 2008: Vol. 320. no. 5875, pp. 454 - 455). Researchers taught the idea of the group Z₃ to some students who weren't familiar with it; some learned it "abstractly" (the elements of the group were represented as funny-looking symbols) and some learned it "concretely" (by considering the slices in a pizza with three slices, or thirds of a measuring cup, or tennis balls in a three-ball can). It seems that the ones who learned the "abstract" version more easily picked up the rules of yet another "concrete" version (a children's game) than those who learned the original "concrete" version.

The Science authors claim that this is because "Compared with concrete instantiations, generic instantiations present minimal extraneous information and hence represent mathematical concepts in a manner close to the abstract rules themselves." This seems like the whole point of mathematics -- a lot of what we do as mathematicians is to strip away extraneous details of a problem while retaining those that are actually significant. If you learn about fractions by thinking about slices of pizza, perhaps you will always think that fractions are about pizza. And then whenever you hear about them, you'll think "where's lunch"?

From today's New York Times crossword

Setting numbered in multiples of the square root of 2. (Five letters.)

The answer.