Devlin's Angle

January 2007

DNA math and the end of innocence

In September and October last year, I devoted this column to a discussion of the reliability calculations that accompany the use of DNA profiling in criminal investigations and in court cases. My beef was not the math, which for the most part is non-debatable. (The one exception here is that there is an unresolved debate between frequentists and Bayesians as to what is the most appropriate calculation to perform when it comes to presenting DNA profile evidence in court following a Cold Hit identification of the defendant.) Rather I was concerned at the way mathematics was sometimes presented in such cases, and in what I believe is a significant likelihood that judges and jurors would misunderstand the math, perhaps even to the extent of reaching an unjust verdict. (I actually got into this whole DNA business when a lawyer asked me to help prepare a submission to help judges understand the often highly subtle issues involved.)

Some interesting correspondence ensued, ranging from those who broadly shared my concerns to others who were clearly affronted that anyone should question the current practice. But when that died down, I thought the matter was over, and apart from working from time to time on a largely descriptive paper on the subject (available in unfinished - and hence unpolished - form, doubtless with some errors, at ) I moved on to other things.

But it seems that I must have come too close to the mark for some people. A few days ago, a colleague pointed me to the blog of a legal consultant who had posted a lengthy commentary on my two columns.

Now, as a scientist, I am used to debate and disagreement. But usually this takes the form of one party analyzing what the other has said or written. Having clearly strayed into non-scientific territory, the game was clearly played differently. Instead of analyzing my two articles, the blogger started out by stating I had claimed something that appeared nowhere in my article, and indeed is flat counter to the much more detailed version of my columns that appears in the unfinished paper just referenced. (In brief, he took statements I had made about how laypeople often present and understand certain probabilities, and then proceeded to demonstrate that those lay beliefs were false - which indeed they are, being counter to what I had written in my more substantial account referenced above). The desired intention of such a strategy is, of course, that the average reader will then discount the entire original article. This is a familiar rhetorical device people adopt when faced with an argument that leads to a conclusion they don't like but are unable to counter on its merits. Proponents of intelligent design do it all the time.

It would of course make this column a whole lot juicier if I were to provide a link to the blog in question, but I'm not going to provide free publicity for such gross misrepresentation. Those who choose to will clearly be able to find it, and those who want to dig deeply enough can read all the components of this episode and see for themselves exactly what is going on.

But here is where I am going with this. (Like anyone who writes a lot, particularly for diverse audiences, I've had my share of attacks and usually I just ignore them.) Time was when mathematicians could stay clear of the political, legal, military, and quasi-religious realms (the latter as in the ID movement). At least, most of us felt we could. But mathematics has now permeated most walks of life to an extent that we can no longer claim to be separate. Those axiom-based, pure abstractions we work with connect to the world and have real consequences in the world.

Homeland Security uses mathematics to make daily threat assessments. The military uses mathematics to plan its actions. Political parties uses mathematics to plan and run election campaigns. Marketers use mathematics to plan advertising campaigns. Global corporations use mathematics in their strategic planning. Two presidential elections ago, what a statistical analysis subsequently demonstrated beyond any doubt to be a major electoral irregularity in one Florida county, swung an election and changed the course of world history in what we now see to be major way. Doubtless there are people dead today who would have been alive had that statistical analysis been carried out sooner (and understood by those who make the decisions on such matters). (There may also have been people now alive who would have been dead had that election turned out otherwise; we can never know what that alternative world-line would have led to.) Future elections are likely to depend on the security and integrity of automatic voting systems that only mathematics can supply and verify. And, to bring my column full circle, we must now accept that we and our subject are now part of the criminal justice system.

If ever there was a time when physicists could stand aloof from the messy everyday world, that era came to an end when the first atomic bomb was detonated. It may have been an illusion that we mathematicians were able to remain pure for a few decades longer, but illusion or not, we can no longer maintain such an attitude.

Outside of mathematics, arguments are not conducted, and decisions are not made, on the basis of logical correctness, as is ultimately the case in our chosen world. In the world outside mathematics, rhetoric rules. It's all about convincing others - regardless how that end is achieved. We'd better get used to it; and if we want our voice to be heard, we'd better get good at it.

Devlin's Angle is updated at the beginning of each month.
Mathematician Keith Devlin (email: [email protected]) is the Executive Director of the Center for the Study of Language and Information at Stanford University and The Math Guy on NPR's Weekend Edition. Devlin's most recent book, THE MATH INSTINCT: Why You're a Mathematical Genius (along with Lobsters, Birds, Cats, and Dogs) was published last year by Thunder's Mouth Press.