Almost all my work as a numerical analyst has an experimental side. I have an idea, I try it on the computer, I adjust the idea. This happy cycle has worked for me since my undergraduate thesis 42 years ago. I like to tell people that numerical analysis is an experimental science, but whereas other experimentalists need weeks or months or years to get an experiment running, we can do it in an hour.

Lately I have noticed that our situation is even more special than I had realized, since even in numerical analysis, before the days of laptops and Matlab, the time scales were so much longer. The closing sentence from a 1968 paper by Rice and Usow gives an idea of what it used to be like:

If one has a reliable least-squares approximation program, then one can write and debug a program for either one of these algorithms rather quickly (in a few days).

A few days! How awful!  I’m not just luckier than the physicists and biologists, but also than my numerical colleagues of the past.

I am sure the speed has consequences. As I argued in my “Ten Digit Algorithms” essay, when the time scale for carrying out an experiment matches that of the experimenter, more experiments inevitably get done, and the results are more reliable.

[29 August 2019]

Here on the Yorkshire Wolds Way, we’ve walked by many fields of wheat waving in the breeze. It’s beautiful how at any given moment, twenty patches are waving left and another twenty are waving right. Back and forth, forth and back, each plant coupled to some friends nearby but uncoupled to those ten feet away.

What makes this possible is that each stem of wheat, viewed as an oscillator, is in the underdamped regime. If the damping were stronger, we’d see much less motion, with the plants bending placidly in proportion to the local wind speed. The waving back and forth reveals that the damping is subcritical.

[25 August 2019]