Friday, January 28, 2005

Numb3rs Review: "Pilot" and "Uncertainty"

I only just got around to watching the first two episodes of Numb3rs. My plan (for as long as I can stand it) is to record any mathematical nuggets of interest that are dropped in the show. Overall, the series is decent as a CSI-type action thriller. There is far more action than I had anticipated, which is probably a good thing: makes it more crowd-friendly.

I don't know if it will last very long: the acting is a bit uneven so far, and the writers have introduced plot lines that need to be explored further (the tension between Don and his boss; the (non)romance between Charlie and his "graduate student"...)

Peeve alert: Apparently this grad student is from Madras, and her parents are arranging her marriage with a Hindu banker from Goa. Just Hindu ? Not a Vadama Iyer brahmin of an appropriate gotram ? and from Goa, of all places ? They eat meat there, for crying out loud. In any case, who lives in Goa anyway ? I thought only foreign tourists live there.

So here's the setup. Don is the FBI agent, Charlie is his "math genius almost 30yrold brother" with degrees from MIT and Stanford (not Princeton ?). There are various other irrelevant characters like the Obligatory Female Sidekick (OFS), Token agent of color (TAC), and gruff but caring dad (GCD). I don't expect to mention them much. There is also the crazy string theorist/mentor for Charlie, who for some reason needs help with his math, and has to suffer cracks like "Feynman and Witten did their own math".

WARNING: there will be spoilers; don't read this if you have a problem with that.

1. Pilot:
Main plot line revolves around determining from a set of points (locations of murders by a serial killer) the home base of the killer. Much rambling about sprinklers and how from the location of the drops one can reconstruct the location of a rotating sprinkler. The key dramatic element is familiar to anyone who knows clustering:
Make sure you know what the "right" number of cluster centers is !!!
Short story: they thought the killer had one base, but he actually had two.

Mathematical jargon:
Not too bad overall. They even resisted the urge to claim that all mathematicians atrophy after age 30, merely having the mentor point out that Charlie was at the peak of his talents and most mathematicians have only 5-6 good years in them.

There was some good stuff about the difficult of humanly generating true randomness. and the usual bashing of the lottery (Don's boss makes fun of Charlie, but has a lottery ticket in his pocket). A useful mention of Galois (the mentor was worried that Charlie was getting distracted by "unclean" human problems).

One of the writers on the show has been reading blogs. There was a line that looked like it came from Sean Carroll's Preposterous Universe: "Why do we remember the past and not the future"

Charlie allegedly "built a weak force theory" with less than 96% probabillty. Whatever that means...

2. Uncertainty:
If there was any doubt in your mind that you should watch this series, this episode should dispel all of that. This, my friends, is the famous P vs NP episode (earlier than episode 4!)

Plot: Charlie has a new equation that predicts, given a series of bank robberies, where the next one will be. When the episode opens, he is being rather cocky about it. As it turns out he is right about the next location, but the standoff ends in a bloodbath and Don is injured, shocking Charlie so much he goes into a deep depression. As it turns out, the robbers are after something more involved.

Mathematical jargon:
The first inkling of what is to come appears after Charlie returns home, shell-shocked after seeing his brother wounded. He assembles blackboards like a madman in the garage, and as he walks by one board, you see the magic words: "SUBSET SUM". A few minutes later, you see another board covered with VERTEX COVER and COLORING and CLIQUE, with lines connecting them.

Be still, my beating heart....

Mentor dude walks in, and Charlie first states a theorem (the first of the series):
Minesweeper consistency is NP-Complete.
and then mumbles something about 3SAT and coloring algorithms. Finally Don arrives, and the mystery is solved. It turns out that Charlie works on P vs NP whenever he's depressed. As OFS puts it: 'beats binge drinking and strip clubs'. Charlie is apparently so obsessed with this that when his mother was dying of cancer he spent the entire time working on it.

By the end of the episode all are happy and Charlie has realized that instead of working on P vs NP, he will work on problems that he has some hope of solving. Now there's a lesson for researchers everywhere !

What warmed the cockles of my heart was the constant referring to P vs NP as a "famous math problem". Now I would have been a little happier if this had been referred to as a "famous computer science problem", but the thought of "pure" mathematicians everywhere being driven crazy by this statement is good enough for me :)
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