The Numbers Behind Numb3rs

My students sometimes ask me whether the mathematics in the television show Numb3rs is real. This question, among others, is explored in a fascinating book, The Numbers behind Numb3rs: Solving Crime with Mathematics, by mathematicians Keith Devlin and Gary Lorden. Most of the book consists of excursions into specific mathematical topics that arise in various episodes of the show; these excursions are really spinoffs, as they take an idea (that might be mentioned in passing or might be the entire basis of an episode) and discuss it in an accessible manner that goes far beyond anything on the show. If you’re interested in real-world applications of math, these chapters are well worth reading for their own sake, even if you’ve never watched Numb3rs.

But I specifically want to comment on my students’ question with regard to what’s in this book. Not surprisingly, the authors get asked the same question that I do. Here are some excerpts from their answer:

Is the math in Numb3rs real?

Both of us are asked this question a lot. The simplest answer is “yes.” The producers and writers go to considerable lengths to make sure that any math on the show is correct…

A more difficult question to answer is whether the mathematics shown could really be used to solve a crime in the way depicted. In some cases the answer is a definite “yes.” Some episodes are based on real cases where mathematics actually was used to solve crimes…. But even when an episode is not based ona real case, the use of mathematics depicted is generally, though not always, believable — it could happen… The skepticism critics express after viewing an episode is sometimes based on their lack of awareness of the power of mathematics and the extent to which it can be applied.

In many ways, the most accurate way to think of the series is to compare it to good science fiction: In many cases the depiction in Numb3rs of a particular use of mathematics to solve a crime is something that could, and maybe even may, happen someday in the future.

So there! Read the book for more details.

But the views of Devlin and Lorden may be out of date. A more recent and contrarian view comes from Mark Bridger, a mathematician at Northeastern University who maintains a blog about Numb3rs, from which these excerpts are taken:

January 3, 2009:

Last Friday’s Numb3rs was a repeat of the exciting episode “The Chinese Box” — aired December 14, 2007. This was yet another show where either the math consultants made a bunch of mistakes or the writers garbled the technicalities…

Since the Numb3rs folks eliminated independent script reviewers — mathematicians such as yours truly — the show’s math has gotten very sloppy, to put it politely. As far as I know, the math these days is injected exclusively by the Wolfram people. They seem prone to making mistakes, but Big companies such as CBS-Paramount like to deal with other Big companies such as Wolfram, not with individuals whom they have no control over. (And Wolfram gets to advertise its product Mathematica on the CBS website.) So what else is new?

December 15, 2007:

…Charlie whines that people are dissing him, and that he sees exactly what’s going on but can’t put it into words. This is an aspect of Charlie’s personality we have not seen before. The whole point of mathematics is to elucidate the structure of things. To say “I see things but can’t explain them” is pre-mathematical; Charlie can hardly expect people to recognize an expertise that he can’t communicate…

Now we come to some actual mathematical topics. Charlie describes a game called “Chomp” in which players take turns removing cookies from a grid… Exactly how this is relevant to the situation in the elevator is unclear, but at least there is mathematics here. Charlie identifies Sinclair with the “first player,” who makes his first move by getting into the elevator. Of course, we already know that it is not known what a winning first move is in Chomp, so I don’t see the analogy. Then Charlie throws in a real clinker: “Chaos Theory holds that outcome is sensitive to initial conditions. We must restore the decision making process to the man who started it.” This is a total non-sequitur. Yes, it’s true that a chaotic process is very sensitive to initial conditions: a small change in the beginning set-up can result in a tremendous change in the outcome. But how do we know that the Chomp game — or the elevator hostage situation — is chaotic? It would seem just the opposite: we simply don’t know what effect the first player’s first move will have: we just know that, as the game progresses, the first player can force a win. Furthermore, Sinclair stepping or not stepping into the elevator can hardly be described as a small change in initial conditions. On the other hand, Charlie’s conclusion turns out to be exactly correct: return the decision-making process to Sinclair. That’s exactly what the FBI doesn’t do, nearly resulting in Sinclair’s death (only his bullet-proof vest saves him).

All this reflects a disturbing trend in the show. Instead of using mathematics to solve the kind of physical or logical problems that are its natural setting, Charlie is trying to apply it to human behavior in complex situations. This is over-reaching, and the results simply do not ring true. In the early days of Numb3rs (season I, May 6, 2005) there was an episode called “Sacrifice” in which a young computer scientist kills his boss because the senior scientist is developing a program that uses mathematics to profile neighborhoods — this in order to determine where federal education money would be best spent. Charlie is admonished to look at the nature of his own research to see if he is not misusing mathematics to make social projections. It is interesting that he is, in recent shows, routinely using game theory, profiling, and data-mining to do just that: predict how humans will behave. We see once again, as in the “Chinese Room,” that the nature of human thought, behavior and language is very complicated and difficult to pin down. It can be very dangerous to exaggerate what we know and (think) we can predict.

Categories: Books, Math, Movies & (occasionally) TV, Teaching & Learning