Category Archives: Math

What Are the Odds?

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DNA’s Dirty Little Secret

In Puckett’s case, where there were only five and a half markers available, the San Francisco crime lab put the figure at one in 1.1 million—still remote enough to erase any reasonable doubt of his guilt. The problem is that, according to most scientists, this statistic is only relevant when DNA material is used to link a crime directly to a suspect identified through eyewitness testimony or other evidence. In cases where a suspect is found by searching through large databases, the chances of accidentally hitting on the wrong person are orders of magnitude higher.

The reasons for this aren’t difficult to grasp: consider what happens when you take a DNA profile that has a rarity of one in a million and run it through a database that contains a million people; chances are you’ll get a coincidental match. Given this fact, the two leading scientific bodies that have studied the issue—the National Research Council and the FBI’s DNA advisory board—have recommended that law enforcement and prosecutors calculate the probability of a coincidental match differently in cold-hit cases. In particular, they recommend multiplying the FBI’s rarity statistic by the number of profiles in the database, to arrive at a figure known as the Database Match Probability. When this formula is applied to Puckett’s case (where a profile with a rarity of one in 1.1 million was run through a database of 338,000 offenders) the chances of a coincidental match climb to one in three.

It’s scary that a judge didn’t find these statistics relevant, and scarier still that the FBI is denying database access to scientists who might confirm that their statistics are right or wrong.

I wonder, though, if the defense asked if the police had tracked down the other ~300 suspects who would have fit the DNA profile in the US, and if that would have raised reasonable doubt?

Tinker, Tailor …

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Tale of a Would-Be Spy, Buried Treasure, and Uncrackable Code

When officials searched the aspiring spy, they found a paper tucked under the insole of his right shoe. On it were written the addresses of several Iraqi and Chinese embassies in Europe. In a trouser pocket they discovered a spiral pad in which Regan, who had been trained in cryptanalysis by the Air Force, had written 13 seemingly unconnected words — like tricycle, rocket, and glove. Another 26 words were written on an index card. In his wallet was a paper with a string of several dozen letters and numbers beginning “5-6-N-V-O-A- I …” And in a folder Regan had been carrying, they found four pages filled with three-digit numbers, or trinomes: 952, 832, 041, and so on. The spiral pad, the index card, the wallet note, and the sheets of trinomes: The FBI suddenly had four puzzles to solve.

Lots and Lots

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Physics Buzz: How Much Snow did Washington DC REALLY Get?

Washington DC looks like a 10 x 10 mile square with a bite taken out of it. All together the city is 68.3 square miles. It’s not too hard to figure out the total volume of snow dumped on the city so far.

55.6″ depth of snow x 68.3 square miles roughly equals 8,820,000,000 cubic feet of snow, or 249,000,000 cubic meters. If you were to build a giant cube of snow that big it would be 2,066 feet, or 629 meters on each side. That’s almost two fifths of a mile or two thirds of a kilometer per side. That’s the volume of about 238 Empire State Buildings. That’s a lot of snow.

I Wonder How it Ends?

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Kottke three-fer

Insanely deep fractal zoom

The final magnification is e.214. Want some perspective? a magnification of e.12 would increase the size of a particle to the same as the earths orbit! e.21 would make a particle look the same size as the milky way and e.42 would be equal to the universe. This zoom smashes all of them all away. If you were “actually” traveling into the fractal your speed would be faster than the speed of light.

(Spoiler alert … The butler did it, and the chick is really a guy, and they faked their deaths to pull off the con)

Graphic Images

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Arts: Photographer Loves Math, Graphs Her Images

Graziano, a math and photography student at Rochester Institute of Technology, overlays graphs and their corresponding equations onto her carefully composed photos. “I wanted to create something that could communicate how awesome math is, to everyone,” she says. Graziano doesn’t go out looking for a specific function but lets one find her instead. Once she’s got an image she likes, Graziano whips up the numbers and tweaks the function until the graph it describes aligns perfectly with the photograph.

A little like Matt’s Sunday Function over at Built on Facts, only with pretty pictures in addition to the graphs.

One Fish, Two Fish

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From Fish to Infinity

I have a friend who gets a tremendous kick out of science, even though he’s an artist. Whenever we get together all he wants to do is chat about the latest thing in evolution or quantum mechanics. But when it comes to math, he feels at sea, and it saddens him. The strange symbols keep him out. He says he doesn’t even know how to pronounce them.

In fact, his alienation runs a lot deeper. He’s not sure what mathematicians do all day, or what they mean when they say a proof is elegant. Sometimes we joke that I just should sit him down and teach him everything, starting with 1 + 1 = 2 and going as far as we can.

Crazy as it sounds, over the next several weeks I’m going to try to do something close to that. I’ll be writing about the elements of mathematics, from pre-school to grad school, for anyone out there who’d like to have a second chance at the subject — but this time from an adult perspective. It’s not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it.

How to Kill Mathematicians

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Give them pizza, apparently. They’ll starve.

The perfect way to slice a pizza

They can’t think about sharing a pizza, for example, without falling headlong into the mathematics of how to slice it up. “We went to lunch together at least once a week,” says Mabry, recalling the early 1990s when they were both at Louisiana State University, Shreveport. “One of us would bring a notebook, and we’d draw pictures while our food was getting cold.”

The problem that bothered them was this. Suppose the harried waiter cuts the pizza off-centre, but with all the edge-to-edge cuts crossing at a single point, and with the same angle between adjacent cuts. The off-centre cuts mean the slices will not all be the same size, so if two people take turns to take neighbouring slices, will they get equal shares by the time they have gone right round the pizza – and if not, who will get more?

If you really want to mess them up, serve a pizza which isn’t round, and you need to value the crust differently than the rest! That’s like the sheet cake problem — trying to fairness-optimize the volume of cake and surface area of icing. (Gee, I wonder if round food was invented to keep the peace amongst the mathematicians, and allow them to solve other problems)

Or, you could give them a ham sandwich.

(To be fair, I can easily see many scientists falling into a similar analytic trap.)