Face Recognition

In the five days I was out of town, Benjamin's weight shot up 10%, his cheeks lost their acne, he perfected his roundhouse and he learned to warble like a Black Capped Thrush. If Catalina weren't here to vouch for the boy, I'd swear he had been abducted by Chinese pirates and replaced by a crude Fatboy knockoff. As it is, I'm still a little sketched: perhaps they took only the chassis, left the paneling?

It is ironic that my difficulties in recognizing my son come hot on the heels of a conference whose driving concern was facial recognition. Machines are still very bad at this task, it seems, at least relative to humans (which, in light of my struggles to absorb the changes in Benny II, makes me wonder where exactly I fit on the Andropoid-Thingamajig spectrum.) Part of the difficulty may have to do with the level of mathematical hocus pocus that is brought to bear on this problem. Vast realms of theory are distilled into simple algorithms any unbaked sophomore can implement but whose intuitive connection to the task remains totally opaque to all but a handful of hoary old fossils at Harvard. The result is a raft of special purpose recognition schemes whose domain of applicability extends exactly as far as the artificial conditions specified by the author ("potential application" is a phrase one hears a lot), with spotty performance and inscrutable convergence properties. Though I shouldn't admit this, I actually view the relative lack of progress as a good thing: it means, among other things, that there's still a lot to do, i.e. more papers to write, more theorems to prove, more opportunity to play in what the greatest mathematician of the 19th century called a "paradise", the realm of pure structure, severed from function and inured to responsibility. It also means that the Artist still trumps the Processor in certain privileged spheres, and that an effective police state is still at least several years off.

The conference itself provided another opportunity for facial recognition, in the form of that favorite game "find the luminary." Context: the Institute for Mathematics and Its Applications is one of a handful of federally funded, university-affiliated institutions across the country designed to support collaborative interplay between mathematicians and their quantitative counterparts in science and engineering. As major repositories of NSF funding, these institutes draw high powered people, so that any given conference is likely to be studded with a luminous cast of optimizers, implementers, purse-holders and theory-mongers. Even among this technical glitterati, however, a truly powerful mind stands out: it charges the air, polishes the dialogue, raises the intellectual temperature. I had never met Charles Fefferman, and never seen his picture, but I knew his story (full professor at 22, Fields medalist for work done by the time he was 24) and knowing he would be present, I sought him out. It took me all of about five minutes: there he sat, bearded and smiling, his speech formal, his wit shy. He sat calm and erect, just listening, not taking notes, and seemed at times to sleep, or dream, or perhaps just take a mental walkabout, zooming off in the spaceship of his imagination, dipping a wing to reality before blasting into a galaxy where the life forms have six-eyes and rubbery tentacles. He asked "what is M?" twice, in fifteen minutes; he diffused an increasingly shrill argument about mathematical models with an arcane reference to epicycles; he said "I assume, of course, that a computer is a Turing machine." Now in his late fifties, the man spoke with the kind of reckless modesty that is the hallmark of a psyche totally untouched by doubt or failure.

Watching Fefferman was a welcome reminder that there are many ways to be a mathematician. I trained in the austere environment of Pure Theory, under mentors who had bad haircuts, mismatched socks, and no computers. I learned to say irrefutable things about irrelevant objects in a syntax that was both spare and bulletproof; I subscribed to the Suessian ethos that "a question's a question, no matter how small;" I inferred that it was better to delay publishing until you had worked out a considerable body of theory, and that it was OK to spend your life in a dark office contemplating sets of measure zero as long as posterity judged you well. How different this new world! This real world, of real applications, real money, all those realtime pressures for real results. The haircuts are sharper, the shoes are black and polished, and most people carry their laptops to the talks, either to fine tune their code or check their email, but in any case so as to occupy themselves with something more fruitful than listening to other people's theories. In this charged ambiance of powerful people, all striving to prove their relevance with a torrential publication record, multiple grants, invited addresses and commercial contracts, it is difficult to remember why I entered this field in the first place: a love of form, a talent for dreams, a belief in beauty. At the core of the original dream lay the idea of noble failure, a vision of the mathematician maudit in dogged and doomed pursuit of the Truth.

Most people who leave their radical roots to become Republicans once they accrete property and power end up saying that it was the political landscape that shifted, not their views. As I reflect on the shift in my mathematical environs, I wonder if I would be falling into the same trap if I were to suggest that the shift is symptomatic of a broader disciplinary trend? I think most mathematicians would agree that the days of insouciant theorem proving in a vacuum are gone, or at least ending: even at undergraduate institutions, the movement is towards student research, with tenure-stingy deans wanting to see if you can lead it, how well, and with what federal backing. Ultimately, the race is for grant funding, it having become well known that grants determine rankings, rankings draw people, and people pull in grants, in a vicious, money-and-power centered circle that threatens to overlook a basic, utopian mission of the university. But even as I condemn what I see to be a national shift towards an ugly and stultifying pragmatism, the good praktischer mensch in me sympathises with its motives. The world is melting. We need mathematicians who are capable of solving intractable technical problems, people who are both good theorists and able experimentalists, who can formulate the pressing problems of the world in clean mathematical terms and solve them in polynomial time. Why shouldn't governmental structures be set up to support such things, and why shouldn't mathematicians step to the plate? Thus rants a small but shrill voice in my higher conscience. From across the brain, there is a counter volley, also a small voice, but subdued: the risk, it warns, is that this pressing sense of mission can arise only in exactly the sort of arcadian environment in which it has no hope of a practical solution.

It's a lazy Sunday. My plans to reprocess conference threads, read papers, and start projects were mostly eaten up by the new-and-improved Zoogle, whose main link to the old Zoogle are an insatiable appetite and a binary watched-or-crying mode. We went for three walks in Frick Park today, and each time I was dazzled by the change in the look of the ravine, once a shock of impenetrable green, now a kaleidoscope of color in which dotty and garish old leaves hold on by their fingernails, defying the Great Plunge for a few more days. Like my son, and like my discipline, these woods are molting. My associated sense of loss betrays my susceptibility to the Fallacy of Perpetual Form, the idea that there is something sacred and intrinsic in the appearances of the moment, this sun-drenched knoll with its moss and catepillars, this nook in the stacks among the original sources, this clean smell of sweet milk. Under pressure, I would agree that there is something like ontological continuity, but for me identity is increasingly fantasmal, a whispy object of syntax and statistics. I am back with Heraclitus on the banks of his river. And though I though I've been forbidden to bathe again, I get wet, soap off, and I recognize the bank and the willow and my reflection, everything, indeed, but Recognition itself, the meaning behind this whirlwind of labels with which Man the Namegiver builds his kingdom. It will be many years, I believe, before a computer can imitate this sort of incomprehension.