When people find out I’m a mathematician, they assume I’m into numbers. I find this assumption frustrating (and a little sad) since there’s so much more to math than numbers, but the truth is that I am into numbers — so into them that I’m writing a book about them.
It’s also the case (though less than it used to be) that when people find out I’m a mathematician, they assume I’m into NUMB3RS. And I’m not.
For those who don’t know, NUMB3RS is an award-winning crime show that premiered back in 2005 and ran for six seasons. The three main characters are Don Eppes (an FBI agent), Charlie Eppes (a mathematician), and Alan Eppes (their father). Together, the brothers fight crime using Don’s Quantico training, Charlie’s mathematical genius, and a dash of worldly wisdom from dad. Or at least, that’s how things went in the pilot. I didn’t watch any episodes after that.
If you have lawyer friends who can’t stand legal dramas, or doctor friends who steer clear of medical dramas, then my lack of interest in a drama about a fictional mathematician shouldn’t surprise you.1 For one thing, no profession could possibly be as exciting as it’s made out to be in a TV series. Any TV drama that tried to portray a profession accurately would get kicked off the air after a couple of episodes; life in any profession is mostly uneventful, and uneventful is the one thing TV is not allowed to be. Even Seinfeld, a show famously about nothing, filled its dramatic void with a volley of cleverly orchestrated coincidences. What’s more, screenwriters typically don’t have deep knowledge of training-intensive professions like law, medicine, or mathematics, so they tend to get details wrong, even when consultants are on hand to try to keep things realistic. Such shows often employ lazy tropes that ring true to a general audience but irk viewers who actually work in those professions.
So you might guess that I didn’t like NUMB3RS because Charlie’s work life seemed unrealistically exciting and made my career look seriously dull by comparison, or that while watching the episode I couldn’t get past the distraction of minor details done wrong (such as misused jargon or reliance on stereotypes). Nope. What actually put me off NUMB3RS was something fairly specific in the pilot that made me it hard for me to believe in Charlie as a character and thus made it hard for me to care about him. (I was snootier back then.)
I should back up a bit and say that in episode 1, Don and Charlie are trying to catch a serial killer before he can strike again,2 and Charlie thinks he’s found a way to figure out where the perpetrator lives based on where the crimes took place. Charlie tests his model (sorry, “tests his equation”: I suspect the producers asked the writers to use words that sound math-y whenever possible) on five earlier serial cases, and in four of the five, he finds that the perpetrator lived in the “hot zone” predicted by the equation. Charlie applies his method to the case at hand and announces that there’s an 87 percent chance that the killer lives in a certain small patch of Los Angeles. FBI agents swarm the area (in that surreptitious mode of swarming that FBI agents excel at). Then new information comes in, simultaneously narrowing the hot zone and increasing the likelihood that the zone contains the killer. Now Charlie says there’s a 96 percent chance that the killer lives in an even smaller patch of Los Angeles.
The only trouble is that when Charlie bursts into the local FBI office to make this announcement, the agents under Don’s command have already looked into the backgrounds of all of the men who live in that area and cleared every single one of them.
How does Charlie react to this?
Here I’ll pause to mention that Charlie isn’t just any old first-rate mathematician: he’s one who understands probability. Probability theory is famous for its pitfalls (think of how many good mathematicians have trouble understanding conditional probabilities and get the wrong answer to the Monty Hall problem), but Charlie’s no probability neophyte. Why, when he sees that Don’s boss has bought a lottery ticket, he’s able to calculate on the spot that the odds of the ticket being a jackpot winner are one in forty-one million, so that if someone bought twenty tickets a week they’d hit the jackpot only once every forty-thousand years. (The scene plays into the stereotype of mathematician-as-lightning-calculator, but I’ll let that pass.) The point is, Charlie knows probability.
… which makes what happens next hard for me to believe.
Don: “We already cleared those twenty guys.”
Charlie: “Um, what? … No, that’s … Well, …. You must have missed him, because, uh, … Well, either you cleared someone you shouldn’t have or … No, he lives there, you just didn’t find him.”
Don: “You’re not listening to me. Okay? We cleared all males in that zone.”
Charlie: “And that means you missed him.”
Don: “Look, you just said we’re dealing with degrees of probability.”
Charlie: “Right: 96 percent! You know what that means. I helped build an entire weak force theory with less than that!”
It seemed to me then that nobody with a solid understanding of probability could mistake a prediction that’s 96 percent likely for a sure thing. (I’ll leave aside Charlie’s wacky reference to probabilistic assessment of a particle physics model since I’m trying not to be distracted by not-quite-right details, such as dialogue in which smart people seem to be trying to sound smart for no reason.) If an event has a 96 percent chance of happening, it has a 4 percent chance of not happening. And 4 percent (1 in 25) is not such low odds. As Charlie might have said, if you buy a lottery ticket every day and each ticket has a 1-in-25 chance of paying off, odds are you’ll get at least one payoff before a month has passed.
So Charlie the CalSci math professor, the black-hole-geometry consultant, the probability maven, didn’t know what a 96% chance means. That made it hard for me to believe in Charlie-the-mathematician as a character, and it made me lose faith in the show.
Here’s what I missed back then. Charlie is upset about the deaths; he needs to believe he can help prevent more deaths from happening. Maybe he’s low on sleep too. Also, in the preceding few hours, revised information about the locations of the crimes enabled him to raise the probability that the culprit lives in the hot zone from 87 percent to 96 percent. It’s easy to imagine that for him the increase from 87 to 96 is more salient than the gap between 96 and 100. And that hopeful hubris is probably what the writers of that episode were thinking about, rather than the accuracy of Charlie’s math instincts in that heated moment. Maybe they wanted to show how even brilliant people can fall into the error of thinking that statistical information can somehow, through the magic of math, be transmuted into certain knowledge.
But returning to the perspective of 2005 me: I felt that the episode never properly takes Charlie to task for this lapse in judgment. In the end it turns out that Charlie was essentially right: the culprit had lived in the hot zone during most of his killing spree, and the only reason the FBI failed to find him is that he’d moved away right before the particular killing that kicked the FBI investigation into high gear. So a 96 percent chance is certainty! Or so a viewer might be led to think. (I wonder if the writers of the show chose 96 percent to be one tick above 95 percent, a commonly-used threshhold for statistical significance.)
Also, consider where that “96%” figure comes from: a mathematical model that Charlie just invented (with help from Don). Even if the model asserts that with probability 96% the culprit lives in the hot zone, why should we (or he) believe that the model reflects reality? Charlie developed faith in his model when he tried it on five solved cases and in four of the cases the model gave a hot zone that contained the residence of the culprit. So the model is a plausible one and deserves to be tested on a larger data-set. But plausible is not the same as correct. (In fact, some statisticians would point out, correctly, that models are never “correct”; they all distort reality. The good models just do a better job of predicting events than the bad ones.) At best, “96%” is a conditional probability.
I seldom thought about the show or my dissatisfaction with it up until 2016, when some people piled onto statistician Nate Silver for failing to predict Donald Trump’s victory against Hillary Clinton. Never mind that Silver had given Clinton a lower chance of winning (71 percent) than any other public statistician; the salient fact for many was that Silver had predicted the wrong winner and so should be taken to task for this failure. See Nate Silver’s article “The Media Has A Probability Problem”. I gloomily concluded that too many people didn’t deeply understand the meaning of the phrase “71 percent chance” in the assertion “There’s a 71 percent chance that Clinton will win.” 71 is closer to 100 than it is to 0, but it’s a mistake to round 71 to 100, just as it was a mistake for Charlie Epps to round 96 to 100.
Did a 2005 TV show portraying a fictional world-class mathematician rounding 96% up to 100% increase the number of Americans in 2016 rounding 71% up to 100%? I doubt it. But the juxtaposition of these two media moments makes me feel that as a nation we’ve made depressingly little progress in understanding the meaning of assertions about probability. In a world beset by many possible dangers, probability theory is a crucial tool in helping us figure out which ones we should focus on. I like to believe that democratic processes will help us survive these dangers. But if too many people are probabilistically illiterate, then our chances become slimmer.
Here’s a Daniel-Kahneman-type question someone should investigate: Which seems like more of a sure thing to people, an event they’re told has an 87.9 percent chance of happening or an event they’re told has an 88 percent chance of happening? My guess is that the former event will seem like more of a sure thing, even though 87.9 is a smaller number, because more digits equals more precision equals more knowledge equals more certainty.
Anyway, re-watching the NUMB3RS pilot earlier this week, I was impressed by the quality of the writing and acting, and I came away thinking that I’d been too quick to judge the show back in 2005 based on just the pilot. I mean, talk about statistical blunders: what kind of statistician draws a conclusion based on a sample size of 1?! But, just as I now forgive the writers for making Charlie turn out to be right when he was more convinced of his own rightness than he had any right to be, I also forgive my snooty past self for judging those writers.
Did any of you find NUMB3RS inspiring? If so, I’d like to hear about it in the Comments! If enough fans of the show rave about the same specific episodes, maybe I’ll watch them now to see what I missed. I’m also curious how things go between Charlie and his grad-student-advisee Amita Ramanujan3; the chemistry is obvious from the get-go, but do they end up notifying HR when things start to get serious? Also, how does Charlie’s department chair get portrayed? Writers of TV shows and movies too often imagine that professors covet the opportunity to lead their departments; in my experience, it’s a form of service that faculty members do out of a sense of obligation more often than out of a desire for professional advancement. Also, department chairs don’t set their colleagues’ research agendas or salary levels. Do you crave power? Then academia may not be the best choice for you.
More seriously, I wonder whether the show went on to convey a better sense of how probability and statistics interface with the real world. It’s a tricky subject (take the continuing controversy over fingerprints, for instance); do later episodes treat the subject with the care it deserves?
The book “The Numbers Behind NUMB3RS: Solving crime with mathematics”, written by Stanford math professor Keith Devlin and CalTech mathematician Gary Lorden, talks about the real-life math that inspired specific episodes, including the pilot. Also, the Museum of Mathematics has been running a series of events called “Starring Math: the Numb3rs edition”, and the next one (coming on January 22) will be cohosted by Ingrid Daubechies, who I hope will talk about her work using wavelets to detect art forgeries, and Ed Pegg, one of the chief mathematical consultants for the show. Register at starring.momath.org.
Thanks to Sandi Gubin.
ENDNOTES
#1. I don’t know any people who work in law enforcement, so I can’t comment on whether they tend to like cop shows. But I’ve heard that a pet peeve of real-live police officers is the way TV police officers shoot while running, which is something you’re not supposed to do.
#2. Full disclosure: This is not something that has ever happened to me in my career as a mathematician.
#3. The thing I most want to know isn’t whether she’s related to Srinivasa Ramanujan. What I want to know is, is she annoyed by how often people ask?