Category Archives: Math

The War on the War on Christmas

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Halfway There: Happy Humbug!

Therefore I was less than impressed when Prager lamented the death of “Merry Christmas” as a holiday greeting. He declared, with great assurance, that pressure from anti-religious pressure groups had brought nonsectarian greetings like “Happy Holidays” into prominence in preference to speaking of our (not his) dear savior’s birth. Instead of taking Prager’s word for it, I decided to do a little checking. What does Google’s Ngram viewer show?

I’m not sure how authoritative Google’s database is, but if their sampling is close to random, “Merry Christmas” isn’t suffering the fate that some would have you think it is.

“Happy Holidays” is inclusive.
“Merry Christmas” is exclusive.

Not surprising to me the general association of who uses what, and what group is upset about their sense of entitlement being challenged.

NonOedipal Snakes On a NonOedipal Plane.

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You need to a flashplayer enabled browser to view this YouTube video

But here’s the thing: if someone asked me five minutes ago what tangled-up snakes demented checkerboards and crazy twisty surfaces have in common, what would you have answered?

This is why I love mathematics. The moment when you realize that something seemingly arbitrary and confusing is actually part of something. It’s better than the cleverest possible ending to any crime show or mystery novel, because that’s only the beginning.

There’s more wonderful doodling at her website, or on youtube. All full of math-y goodness, puns, denunciation of poor teaching, stop-action video and a remarkable lack of commas. (Does she ever inhale?)

Binary trees
Infinity elephants
Stars

You can show these to people, and it’s possible they won’t know they learned some math. Sneaky.

A Matter of Perspective

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The Virtuosi: The Law and Large Numbers

The US budget, deficit and the ludicrous “Youcut” program (which has been rightly lambasted almost everywhere in the science blogohedron)

I just want to point out again, claiming that cutting NPR funding makes a dent in the US budget is similar to claiming you’ve moved closer to Orlando (while in LA) by crossing the room

…

In my undergraduate physics lab, the instructor had a mantra: “A number without context is meaningless”. Now, he originally meant the statement to be a lesson on how important it is to quote errors on your measurements, but I think I can adapt it to apply to giving out numbers like 7 billion without a sense of scale.

(I think the motivation for “cutting NPR” has less to do with budget than ideology, and NPR doesn’t actually get any direct appropriations from the government, but it’s still a nice example of scale)

Attack of the Math Monster

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Uncertain Principles: Two Cultures Within Science

[No equations in a paper] is almost completely inconceivable to me (at the risk of leaving myself open to the Vizzini joke). In my part of science, a paper without an equation is suspect, and I’m not exactly the world’s most mathematically inclined physicist. Physics is so intimately connected to math, and the business of doing physics is so inherently mathematical that its difficult to imagine a scientific paper about physics that doesn’t contain at least one equation. A press release or popular article, sure, but to a physicist, the equations aren’t some offal to be avoided en route to the science. The equations are the science. Objecting to the presence of an equation in a scientific paper is like objecting to the presence of meat in a steak sandwich.

I had the serendipity of reading another post just before reading Chad’s, related to the closing remarks concerning physicists sometime needing to learn some less “standard” math to do the physics they are interested in pursuing:

Medical researcher discovers integration, gets 75 citations

My more reasonable friends claim that this abstract isn’t really as amusing as I make it out to be. And to be sure, they’re right.

Murray Gell-Mann developed the “eight-fold way” to explain the spectrum of hadrons in the 1960s. It wasn’t until after he’d developed this formalism that he discussed his model with mathematicians, who then told him that he’d rediscovered group (representation) theory. This ushered ina new era in the history of particle physics where symmetry became our guiding light and group theory became a necessary tool for any particle theorist. Though, to be fair, in the 1960s group theory—unlike calculus—wasn’t something that physicists were expected to take during high school.

I’m also aware of a few instances of some of my colleagues struggling through some new way of analyzing clock performance, only to find out that the math is standard analysis of some other sort of problem. As they say, math is the language of physics.

There's a Chance This Would Work

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Some ideas on communicating risks to the general public

Relative risk statements speak of risk increasing or decreasing by a percentage, for instance, that mammography in women over 40 reduces the risk of breast cancer by 25%. But all percentages erase the frequencies from which they were derived. We cannot tell from the relative risk reduction what is the absolute risk reduction: by how much does the risk of breast cancer actually decrease between those who get mammographies and those who do not: the answer is .1%

Relative risk information does not give information on how many people need to undergo a treatment before a certain benefit is obtained. In particular, based on the relative risk information, can one say how many women must be screened before a single life is saved? If your intuition tells you 4, you are again far off, as 1000 women must be screened to save the one life. In this way, relative risk information can cause people to misjudge the effectiveness of treatments

Sacking Some Statistics

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Thanksgiving and Football: Why you should always go for it on 4th and short

[I]f teams that decide to kick when they are on their opponents’ 30 yard line make the field goal an average of 33% of the time, then the benefit of kicking is assigned a point value of 1 (since a field goal is worth 3 points, and 33 percent of 3 points is 1 point). Since teams that only have one yard to go when they are on the 30 yard line convert for a first down 64% of the time, and teams that are inside the 30 yard line score a touchdown about 40% of the time, the benefit of going for a first down is assigned a value of 1.8 (0.64 x 0.40 = 0.24, or a 24% chance of scoring a touchdown by going for it on 4th and 1, and 0.24 x 7 points = 1.8 points). This means that “going for it” should result in scoring almost twice as many points than kicking

One problem is that the chance of making a 47-yard field goal is about twice the value used here. It varies from year to year, of course, but field goals from 50+ yards are made at about a 50-50 clip (almost 53% last year), and 40-49 yards is north of 60% (73% last year). Which makes the expected gain from a field goal attempt from that distance about the same as from going for the first down, and perhaps slightly higher.

Also, the distribution of the abilities of offenses and defenses play a role. The average chance of scoring might be 40%, but I’ll bet that the e.g. Colts, Patriots and Saints are higher than that, and teams trying this against the Ravens are lower. And add to that situational details, such as whether a field goal increases your lead to more than one score, or it gives you a lead or ties the game.

Statistics are all well and good, but there’s a problem with looking at them without context, and not understanding what they mean. It’s also not a good idea to just retrieve a number from a dark place in order to make your conclusion look good, when the correct numbers are available.

The Cryptic Kryptos

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Clues to Stubborn Secret in C.I.A.’s Backyard

Jim Sanborn, the sculptor who created “Kryptos” and its puzzles, is getting a bit frustrated by the wait. “I assumed the code would be cracked in a fairly short time,” he said, adding that the intrusions on his life from people who think they have solved his fourth puzzle are more than he expected.

So now, after 20 years, Mr. Sanborn is nudging the process along. He has provided The New York Times with the answers to six letters in the sculpture’s final passage. The characters that are the 64th through 69th in the final series on the sculpture read NYPVTT. When deciphered, they read BERLIN.