Thursday 3 February 2011

The Birthday Problem and DNA

Keith Devlin does a variation of the birthday problem involving DNA and finds out how many people must be in a database before there are two whose DNA would match on a 9 locus match (the common judicial standard) as well as pointing out that the Body Mass Index is ....ummm...crap, stupid, not a very good predictor of obesity. 

Good lines.....

"Now, I have no problem with people disagreeing with me. Heavens, I was a mathematics department chair for four years and a dean for eight, and before that a father of two daughters growing up through adolescence to adulthood, so I have had my fair share of disagreements. What bothers me is that some folks seem (1) all too willing to accept something simply because its looks scientific and some august body advocates it, and (2) unable to adjust their intuitions when faced with evidence that they mislead us, as they do on occasion.
It bothers me because I am in the education business, and the primary goal of education is to help people develop the ability to think for themselves and to reach conclusions based on evidence and rational thought.
It bothers me particularly because, as the ancient Greeks recognized, when taught well, mathematics is one of the best mental disciplines to develop analytic thinking skills."

"The fact is, in the era of DNA identification, judges and juries simply cannot avoid getting to grips with the relevant math. Identification hinges on those calculations. There may be no way of avoiding bringing mathematicians into court to explain how the calculations are done. But for that to be effective, those judges and juries need first to learn (and accept) that human intuitions about probabilities are hopelessly unreliable. That can prepare the way, not for mathematical laypersons to learn how to do the calculations themselves - the experts can do that part - rather how to follow the calculations and evaluate the answers. For it is on those answers that justice will ultimately depend."


Steven Colyer said...

Thanks for this, and for turning us on to Devlin's work, Pat.

I imagine you'll be returning to America eventually? If and when so, you'll find that thanks to personal computing, the whole jury system has changed.

For starters, you could once get out of jury duty with a single phone call? Now? No, you have to report, and that will cost you 2 days of your life, maybe 3, even if you have a legitimate excuse not to serve. I did that recently, and the experience was not unpleasant at all. My fellow juror candidates came from all walks of life, and all were civilized and polite. Lots of waiting, but if you're a maths bookworm like me it's like a holiday.

The important bit is the "all walks of life" thing. I found that 99% of people are as Devlin says "overly impressed" with figures, and can't tell the difference between good experts and bad. The jury system has its flaws like everything else, but this is a particularly bad one, as juries ultimately decide guilt or innocence.

So once again thanks for the heads up. Yet another example of how Maths COULD save the world but if the decision makers don't understand the simplest maths then, no.

"Card Colm" Mulcahy said...

It's Keith Devlin not Bruce