Integrals fall from the sky

Back when we were slogging through Calculus, my friends and I used to complain that there was no practical use to what we were learning.  What were the chances, for instance, of encountering a Taylor expansion in a dark alleyway?  Or of an integral falling from the sky?  Except in my world, of course, where this happens all the time.

Suppose, just for instance, that you are designing an auditory stimulus with certain statistical properties and you want to know what the overall power in the stimulus will be.  Or that you make a new stimulus composed of lots of independently fluctuating signals at different frequencies and you want to know what happens when you make the individual signals vary more (answer: the mean power across frequencies increases).  Or that you can measure a signal after it’s been slowed down by an odor delivery device, or by an odor delivery device plus a neuron, and you want to figure out how much of the slowing is due to the neuron.  I swear those integrals are everywhere.

Around year 2 of graduate school I got very depressed about the fact that I was never going to be the sort of person who could look an integral in the eye and not blanche.  The nadir was the Computation Neuroscience course at Woods Hole, where well-meaning theorists liked to comment that those of us running experiments had no idea what our data meant and Haim Sompolinsky would pop by in the evenings to drop off fun problems and to glower menacingly when we couldn’t solve them on the spot.

Towards the end of grad school I came to terms with the fact that—although I’d never be the kind of person who could solve the integral myself— I could at least be the sort of person who recognized when there was an integral there to solve.  Thanks to Matlab (and many years in a windowless closet) I have a pretty good visual intuition for a number of mathematical concepts.  I am—if not at home in frequency domain—at least able to read the road signs and ask for directions.  And when an integral falls from the sky I know to call my Dad.

The beauty of asking a mathematician for help is that they send you the answer in Tex, which makes it look deeply professional and well thought-out, and gives me the lovely impression that what I’m doing must be Real Science.  Either that, or on napkins, which is if anything even more bad-ass.

I know I don’t post about science much, even though it’s up there with art and sewing on the masthead and is ostensibly what I do all day.  But I just wanted to say thanks, Dad.  You’re the best.  And I’ve still got those napkins from grad school.