John Doyle gave this year’s J. Barkley Rosser Lecture at the Wisconsin Institute for Discovery; his talk was dedicated to the proposition that tradeoffs between flexibility and robustness in control systems with significant delays are in the end going to be bound by universal laws, just as the operation of a classical Turing machine is bound by laws coming from information theory and complexity theory. (A simple such one: a machine that has the potential to produce N different outputs is going to have a worst-case run time of at least log N steps.)
Doyle believes the robustness-flexibility tradeoff should be fundamental to our way of thinking of both biological and technological devices. He gave the following very illustrative example, which is so simple that you can play along as you read my blog.
Hold your hand in front of your face and wave your hand vigorously back and forth. It looks blurry, right?
Now hold your hand still and shake your head equally vigorously. No blurring!
Which is strange, because the optical problem is in some sense exactly the same. But the mechanism is different, and so the delay time is different. When your hand moves, you’re using the same general-function apparatus you use to track moving objects more generally. It’s a pretty good apparatus! But because it’s so flexible, working well for all kinds of optical challenges, it is slow, and like any system with a long delay, input that oscillates pretty fast — like your waving hand — can cross it up.
When your head moves, it’s a different story: we have a vestibulo-ocular reflex which moves our eyes in sync with our head to fix the images on our retina in place. This doesn’t pass through cognition at all — it’s a direct neural connection from the vestibular sensors in the inner ear to the muscles that control eye movement. This system isn’t flexible or adaptable at all. It does just one thing — but it does it fast.
(All this material derived from my notes on Doyle’s talk, which went pretty fast: all mistakes are mine.)
Here are the slides from Doyle’s talk. (TooManySlides.pdf is the best filename ever!)
Here’s a paper from Science that Doyle said would be especially useful for mathematicians who want to see how the tradeoffs in question can be precisely formalize. (Authors: Chandra, Buzi, Doyle.)