When Math Left Medicine

I'm now in my second year of medical school at Indiana University and I attend every class every day. The professors are certainly some of the top-educated humans in the world, and yet simple mathematical concepts have completely left them.

For example, Suppose you have a patient with Familial Adenomatous Polyposis (FAP) and on his colon there are 1000 polyps. Given that the chance any one of those polyps will become malignant is 1/1000 what is the chance that this patient will develop a malignancy?

The class says 100% and the professor agrees. I shamefully said nothing because I unfortunately couldn't do the math in my head to give the correct answer. But it breaks down like this:

The chance of developing malignancy(P(m)) is equal to one minus the chance of it not becoming malignant (~P(m)) so that is:
1 - ~P(m)

We use (~P(m) because it is easy to calculate and is equal to the chance the first polyp remains benign times the chance the second polyp remains benign times the third, fourth, fifth, ... , nine hundred ninetyninth times the One thousanth polyp.

So:

P(m) = 999/1000 * 999/1000 * 999/1000 ... = (999/1000)^1000 ~= .3677

The chance this patient develops a malignancy is then (1-.3677) = .6323 or 63.23%



Another professor had a line graph with 4 sets of data points graphed. All of them were more or less parallel, but two of them were translated up several units on the graph. The statement was made that while these lines (on the bottom of the graph) were increasing, the lines up here (points to top of graph with the parallel lines) were increasing exponentially.

Um...wrong. They are increasing linearly and the R^2 value of the graph with respect to a straight line through the datapoints would have been extremely close to 1. The data points were merely greater than the other ones. Exponentially doesn't mean larger.

Oh well, someone once said that grad students go to school to learn more and more about less and less until they know everything there is about nothing at all.
MDs go to school to learn less and less about more and more until they know nothing about everything.