John Doyle on handwaving and universal laws

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.)

Imaginary Architecture

Filip Dujardin‘s digitally assembled photographs of buildings that don’t (and often couldn’t) exist are on display at the Chazen through May 16.  Worth the trip.  More Dujardin images at BLDGBLOG.

Gehry/Serra

Back from a very brief trip to Princeton. The much-maligned new science library, built by Frank Gehry, is now up. I like it — it’s very much like the Stata Center, but more humble. Here’s a small piece of it viewed from inside the Richard Serra sculpture “Fox and Hedgehog,” also much-maligned, and which I also like.

Note: this is my first attempt to blog by iPhone. I’m sitting in my car, in the back of which CJ has dozed off, and I thought I’d let him sleep instead of continuing immediately with the shopping as planned.

Voronoi diagrams at the Milwaukee Art Museum

Contemporary art involving video projection is not usually my favorite kind of contemporary art, but if you’re near Milwaukee it’s worth the effort to catch Act/React at the MAM before it closes on January 11. The small exhibition consists of eight works, each one of which records, modifies, and displays the actions of the people watching it. Brian Knep’s Healing Pool projects a vaguely biological yellow-orange pattern on the floor. When you walk on the floor, the blobby forms squirm away from your feet. With a little experimentation you can figure out how to stamp out a cleared trail, which the blobs flow in to cover as soon as you step away. As you can imagine, CJ was crazy for this — he ran around for about five minutes shouting “I’m making a circle!” which, indeed, he was. For mathematicians — and, again, three-year-olds — the highlight is Scott Snibbe’s Boundary Functions (named after Ted Kaczynksi’s Ph.D. thesis!) In this piece, the overhead camera registers the location of people walking on the floor, and the projector places a Voronoi diagram around them.

You’re enclosed in a lighted polygon consisting of all those points on the floor which are closer to you than to any other spectator. It’s simultaneously quite pretty to look at, at least somewhat thought-provoking, and a completely successful, completely wordless piece of mathematical exposition. CJ spent a long time on this one, too, “chasing the line.”

Here’s a review of the whole show from artblog Rhizome.

Of course, the Milwaukee Art Museum merits a visit just for the building; and there’s a rather good permanent collection upstairs, usually kind of underpopulated, strong on the German Expressionism, outsider art, and views of Lake Michigan.

Diversity Road

I spent last Wednesday morning working in the profoundly pleasant Prairie Cafe in Middleton Hills. This is the kind of unassuming place that you’d assume would make really first-rate breakfast and soups and maybe a heavily besprouted chicken-salad sandwich, but where you might hesitate to order a hot lunch. In fact, the corned beef hash, while homemade, was just so-so, while the reuben was really first-rate. The cold black-bean and corn salad that came alongside in lieu of coleslaw was even better, a crisp contrast to the thoroughly correct hot goopiness of the reuben.

Middleton Hills, it turns out, is a Duany Plater-Zyberk development in the “New Urbanist” style. Which means mixed retail and housing, walkability, density, stores fronting directly on sidewalks, cheap houses and expensive ones on the same block, and so on. Basically, if you take every feature of America’s soul-killing suburbs that people like to complain about, invert them, and build housing developments based on the result, you get something like New Urbanism.

As for me, I grew up in one of America’s soul-killing suburbs, and I like them! One of the nicest features of the Near West Side of Madison is that you can get on your bike and be in an authentically urban landscape in 15 minutes; or, after a 15-minute drive in the other direction, you can pull up in the oversized parking lot outside the even more oversized grocery store and load your station wagon until it groans.

Anyway, Middleton Hills. My first impression is that it’s charming; the houses all share a mild kind of Prairie style, but no two on the block look exactly alike. The main drag, Frank Lloyd Wright Boulevard, winds around a big and agreeably wild pond; lots of cattails, lots of birds, grass not too kempt. The street names do a good job of congratulating you for your participation in sustainable development — John Muir Drive, Aldo Leopold Way, and, best of all, Diversity Road.

My second impression is that it’s completely empty. You can see that the streets are laid out to encourage pedestrianism and unplanned human interaction, as in Princeton, a favorite town of Duany Plater-Zyberk’s, and mine. But at three in the afternoon, the only people I saw were a trickle of kids coming home from school, and a birdwatcher. The birdwatcher and I watched a sandhill crane for a few minutes. Then I sat down to continue revising a long-overdue paper with Michel and Venkatesh about sums of three squares. (Among other things, the paper features a careful explanation of the group structure — more properly, torsor structure — on the set of representations of a squarefree integer n as the sum of three squares. More on this when the paper’s finished.)

What makes Princeton’s streets lively and new-urban, of course, is that it has a big and interesting downtown, whose shops and restaurants serve not just Princetonians but residents of the surrounding towns. Middleton Hills has a grocery store, the Prairie Cafe, a pizza place, and a Starbucks — not enough to draw foot traffic away from Madison, or, for that matter, downtown Middleton. If this post pulls in a throng of reuben-lovers, I guess I’ll have done my bit for the New Urbanism.

In which I like brutalism

The campus of UW features a few buildings in the brutalist style; these hunker uneasily between the older buildings and are complained about by everyone, though they have some hesitant defenders. Last week I gave a number theory seminar at UIC, a campus built from scratch in the late 1960s, at the height of the vogue for concrete. Huge rectilinear concrete towers set into vast concrete plazas, not an acute angle or a brick or a natural landscape contour in sight. What’s more, I was there on a freezing cold day with overcast skies and a kind of punchy, angular snow which might have actually been extremely small hail. And you know what? It looked terrific. I take back the bad things I’ve said about this style — when your whole field of view is made out of brutalism, it ends up, if you can believe this, kind of nice. It’s like being inside a futuristic diorama. (Pictured: Walter Netsch, designer of UIC.)

Frank Lloyd Wright in bad decline

Not all of Frank Lloyd Wright’s buildings are as carefully preserved as the ones we saw last week at Taliesin. At Letter From Here, read about the FLW boathouse in James Madison park, unceremoniously demolished in 1926. And from Nadine Goff’s flickr stream, here’s a Frank Lloyd Wright house slowly decaying in the middle of downtown. (Follow the link for more information and location, not to mention more great Madison photographs.)

©  Nadine Goff, all rights reserved.

Things you could do because you live in Madison, but don’t, until visitors come: slightly out of town edition

Wednesday was excursion day; we kept CJ home from day care and daytripped around western Greater Madison. First stop was the Cave of the Mounds, about a half-hour’s drive southwest in Blue Mounds. Not the grandest cave in creation, but a good one for a little kid — easy walking, no steep drops off the side of the path, no ancient paintings to ruin. I was worried CJ would be scared, but he was quite delighted with the cave; he kept leaning up against the railing and saying “Hi, cave!”

Next we drove north through Mt. Horeb — sadly, there was no time to stop at the extremely promising Mustard Museum, because we had to rush to catch a tour at Frank Lloyd Wright’s workshop at Taliesin. We are huge FLW fans in our house, and we’ve managed to visit both famous out-of-the-way buildings (Fallingwater, the Dana-Thomas house in Springfield, IL) and pretty unfamous out-of-the-way buildings (a bank in Whitefish, MT, the College of Education Building at Wichita State University) but we’d never made it to his central workplace an hour from home. The hour-long Hillside tour, covering the school building where Wright’s students worked under his supervision, is just right if you’re traveling with a toddler; even that was a bit long for CJ, since the short drive from the cave didn’t allow him much of a nap, so he spent most of the second part of the tour outside with me digging in the gravel with a stick.

On the way home, we made an unscheduled stop at The Shoe Box in Black Earth, where I selected from the massive stock a new pair of Chuck Taylors. In 2007 is it ridiculous to have a pair of Chuck Taylors? I don’t know, but it’s been a long time since I had any and they’re still both pleasantly cheap-feeling and pleasantly cheap. Also, the Shoe Box is chock with sports memorabilia, mostly pertaining to the (baseball) St. Louis Cardinals, and there’s a dog and a parakeet walking around. Stores with loose animals and stores with identifiable rooting commitments always make me want to spend money — I suppose because they create the impression that you are doing business with a person — a Cardinals-loving, parakeet-feeding person — rather than an abstract entity.

Supplementary note on Wichita State University: If you happen to be in Wichita, certainly go visit the campus: besides the Frank Lloyd Wright building, there’s a surprisingly good collection of modern sculpture distributed around the grounds, and the original Pizza Hut!