Saturday, February 19, 2005

Factoring NUMB3RS

Scott Aaronson weighs in on last night's NUMB3RS episode "Prime Suspect". Mild Spoiler Warning.

Last night's NUMB3RS again centered around complexity. A brilliant mathematician (not Charlie) tells his friends that he's on the verge of proving the Riemann hypothesis -- and not only that, but his proof will somehow yield a fast factoring algorithm. When the bad guys get wind of this, they kidnap the mathematician's six-year-old daughter, demanding the algorithm as ransom. But the mathematician refuses to cooperate with the FBI investigation of the kidnapping. The reason, we later learn, is that the mathematician has fooled himself: he doesn't have a proof or an algorithm, and he's terrified the bad guys will find out. (One thing that has to be said for NUMB3RS: in contrast to, say, Good Will Hunting, it does get across the idea that math problems are hard.) So Charlie has the improbable task of helping the other mathematician fake a factoring algorithm -- apparently, the bad guys won't be savvy enough to run whatever they get on a few random instances!

In a way, this episode represents a retreat from the premise that "math helps us solve crimes" -- I mean, no duh it helps, if the crimes in question happen to involve polynomial-time factoring algorithms! But in my opinion, the fact that math was actually integral to the plot helped to make this the most effective episode so far. In contrast to the P versus NP episode, this time they actually explained a little about prime numbers, RSA, and factoring, and did a fairly non-egregious job by TV standards. Admittedly, an RH proof leading to a factoring algorithm seems pretty farfetched, but what path to efficient factoring isn't farfetched? (Other than building a quantum computer, of course.)

My main criticism is that, whenever Charlie and the other academics open their mouths, I feel like I'm listening to foreigners speaking perfectly grammatical sentences that no native speaker would ever utter. The phrasing is just too pretentious -- a trivial example being that everyone calls the Riemann hypothesis "Riemann's hypothesis." If they wanted to, the writers could easily fix this problem by reading the scripts to mathematicians, and seeing which lines pass the cringe test.


  1. I think scott is a bit confused here. I think the reason that the father didnt want the FBI in the loop was because he was afraid that the kidnappers might do something to his daughter and he was certain that he had solved the Riemann Hypothesis. Its only later when Charlie stopped by and showed him that his math was flawed that they had to create a fake algorithm.

  2. Now that I think about it, the show never gave a compelling explanation for why the father didn't want the FBI involved initially, but probably a better one than what I offered is just that he saw it as irrelevant. He knew what his task was -- namely to distill his proof into an algorithm -- and the fact that he didn't have a proof meant that this wasn't going to terminate any time soon.

  3. There's a saying my playwriting teacher once told me: Never let the truth get in the way of telling a good story.

    I'm not sure why they don't seem to be motivated to get the little facts right, other than the fact that even getting the everyday facts straight can be a challenge for shows: "Did he have his hat on the car seat before?", "did we already say this detail about this character?".

  4. If they wanted to, the writers could easily fix this problem by reading the scripts to mathematicians, and seeing which lines pass the cringe test.If this were standard practice, the typical TV show would be even less compelling than the vast wasteland that it already is. I'm sure that most shows have some sort of consultant that helps them out; but to fact check every detail like that is unnecessary. Do you think Cop shows accurately portray day-to-day law enforcement activities? That lawyer shows reflect the true atmosphere in a courtroom? Are sitcoms good standards by which one could judge the average american household? Hardly.

    Television is (generally) meant to appeal to the lowest common denominator so as to capture the broadest possible audience and (ultimately) the highest possible ratings.

    Real lawyers will continue to perform real law and read real law journals and mathematicians, computer scientists and every other discipline will do the same while television will continue to entertain (at least those who do not wisely turn off the dial).

  5. They actually use real mathematicians as consultants: Gary Lorden, Dinakar Ramakrishan, Rick Wilson and Nathan Drunfield (and two graduate students) of Caltech. Lorden is a probabilist/statistician, Ramakrishan a number theoretician, Wilson a combinatoralist and drunfeld a topologist.
    I don't know why they did not catch the odd naming of the Riemann hypothesis.

  6. Gosh, TV intended for the lowest common denominator? You think so?

    My point was that, given that the NUMB3RS writers decided to get some things right that most viewers wouldn't notice, they might as well go whole hog and get most of them right. As far as I can tell, this would involve minimal effort and wouldn't affect the show's general entertainment value one way or another.

    I also knew that mathematicians were involved as consultants. But I have no idea what their exact role is -- and it's possible that when the show moves from scripting to filming, a lot gets changed without their input. Maybe next time I should sit in front of the TV with pen and paper, and make a list of 30 examples of what I'm talking about...

  7. "My point was that, given that the NUMB3RS writers decided to get some things right that most viewers wouldn't notice, they might as well go whole hog and get most of them right."

    I think you are too harsh on them scott. They're trying to make a show which makes mathematics what if they made some errors? Even Lance did a mea culpa about all of the papers in which he had made errors after publishing. People are human and not machines. Have you never made a mistake?

  8. Numb3rs is the greatest show ever! Check out my site about it @!

  9. Wouldn't it be incredibly anal to make up a list of minor nitpicks? Oh well, I sure hope you have better things to do with your life but judging from your posts here, that seems unlikely.

  10. Just got through watching the RH episode of NUMB3RS and what a treat! This show enthralled my entire family and had the guts to deal w/this subject matter in network TV. The math was motivational and uncompromising, it had me re-reading the Millenium Problems book chapter on Internet security and its relationship to RH. The human interest story w/the dad & brother is, as always, excellent. Thanks for quality TV.