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February 21, 2006

Pirates off the Coast of Paradise

At the beginning of graduate school, few people have a clear idea of what area of research they ultimately want to get into. Many come in with vague or ill-informed notions of their likes and dislikes, most of which are due to the idiosyncrasies of their undergraduate major's curriculum, and perhaps scraps of advice from busy professors. For Computer Science, it seems that most undergraduate curricula emphasize the physical computer, i.e., the programming, the operating system and basic algorithm analysis, over the science, let alone the underlying theory that makes computing itself understandable. For instance, as a teaching assistant for an algorithms course during my first semester in grad school, I was disabused of any preconceptions when many students had trouble designing, carrying-out, and writing-up a simple numerical experiment to measure the running time of an algorithm as a function of its input size, and I distinctly remember seeing several minds explode (and, not in the Eureka! sense) during a sketch of Cantor's diagonalization argument. When you consider these anecdotes along with the flat or declining numbers of students enrolling in computer science, we have a grim picture of both the value that society attributes to Computer Science and the future of the discipline.

The naive inference here would be that students are (rightly) shying away from a field that serves little purpose to society, or to them, beyond providing programming talent for other fields (e.g., the various biological or medical sciences, or IT departments, which have a bottomless appetite for people who can manage information with a computer). And, with programming jobs being outsourced to India and China, one might wonder if the future holds anything but an increasing Dilbert-ization of Computer Science.

This brings us to a recent talk delivered by Prof. Bernard Chazelle (CS, Princeton) at the AAAS Annual Meeting about the relevance of the Theory of Computer Science (TCS for short). Chazelle's talk was covered briefly by PhysOrg, although his separate and longer essay really does a better job of making the point,

Moore's Law has fueled computer science's sizzle and sparkle, but it may have obscured its uncanny resemblance to pre-Einstein physics: healthy and plump and ripe for a revolution. Computing promises to be the most disruptive scientific paradigm since quantum mechanics. Unfortunately, it is the proverbial riddle wrapped in a mystery inside an enigma. The stakes are high, for our inability to “get” what computing is all about may well play iceberg to the Titanic of modern science.

He means that behind the glitz and glam of iPods, Internet porn, and unmanned autonomous vehicles armed with GPS-guided missles, TCS has been drawing fundamental connections, through the paradigm of abstract computation, between previously disparate areas throughout science. Suresh Venkatasubramanian (see also Jeff Erickson and Lance Fortnow) phrases it in the form of something like a Buddhist koan,

Theoretical computer science would exist even if there were no computers.

Scott Aaronson, in his inimitable style, puts it more directly and draws an important connection with physics,

The first lesson is that computational complexity theory is really, really, really not about computers. Computers play the same role in complexity that clocks, trains, and elevators play in relativity. They're a great way to illustrate the point, they were probably essential for discovering the point, but they're not the point. The best definition of complexity theory I can think of is that it's quantitative theology: the mathematical study of hypothetical superintelligent beings such as gods.

Actually, that last bit may be overstating things a little, but the idea is fair. Just as theoretical physics describes the physical limits of reality, theoretical computer science describes both the limits of what can be computed and how. But, what is physically possible is tightly related to what is computationally possible; physics is a certain kind of computation. For instance, a guiding principle of physics is that of energy minimization, which is a specific kind of search problem, and search problems are the hallmark of CS.

The Theory of Computer Science is, quite to the contrary of the impression with which I was left after my several TCS courses in graduate school, much more than proving that certain problems are "hard" (NP-complete) or "easy" (in P), or that we can sometimes get "close" to the best much more easily than we can find the best itself (approximation algorithms), or especially that working in TCS requires learning a host of seemingly unrelated tricks, hacks and gimmicks. Were it only these, TCS would be interesting in the same way that Sudoku puzzles are interesting - mildly diverting for some time, but eventually you get tired of doing the same thing over and over.

Fortunately, TCS is much more than these things. It is the thin filament that connects the mathematics of every natural science, touching at once game theory, information theory, learning theory, search and optimization, number theory, and many more. Results in TCS, and in complexity theory specifically, have deep and profound implications for what the future will look like. (E.g., do we live in a world where no secret can actually be kept hidden from a nosey third party?) A few TCS-related topics that John Baez, a mathematical physicist at UC Riverside who's become a promoter of TCS, pointed to recently include "cryptographic hash functions, pseudo-random number generators, and the amazing theorem of Razborov and Rudich which says roughly that if P is not equal to NP, then this fact is hard to prove." (If you know what P and NP mean, then this last one probably doesn't seem that surprising, but that means you're thinking about it in the wrong direction!) In fact, the question of P versus NP may even have something to say about the kind of self-consistency we can expect in the laws of physics, and whether we can ever hope to find a Grand Unified Theory. (For those of you hoping for worm-hole-based FTL travel in the future, P vs. NP now concerns you, too.)

Alas my enthusiasm for these implications and connections is stunted by a developing cynicism, not because of a failure to deliver on its founding promises (as, for instance, was the problem that ultimately toppled artificial intelligence), but rather because of its inability to convince not just the funding agencies like NSF that it matters, but its inability to convince the rest of Computer Science that it matters. That is, TCS is a vitally important, but a needlessly remote, field of CS, and is valued by the rest of CS for reasons analogous to those for which CS is valued by other disciplines: its ability to get things done, i.e., actual algorithms. This problem is aggravated by the fact that the mathematical training necessary to build toward a career in TCS is not a part of the standard CS curriculum (I mean at the undergraduate level, but the graduate one seems equally faulted). Instead, you acquire that knowledge by either working with the luminaries of the field (if you end up at the right school), or by essentially picking up the equivalent of a degree in higher mathematics (e.g., analysis, measure theory, abstract algebra, group theory, etc.). As Chazelle puts it in his pre-talk interview, "Computer science ... is messy and infuriatingly complex." I argue that this complexity is what makes CS, and particularly TCS, inaccessible and hard-to-appreciated. If Computer Science as a discipline wants to survive to see the "revolution" Chazelle forecasts, it needs to reevaluate how it trains its future members, what it means to have a science of computers, and even further, what it means to have a theory of computers (a point CS does abysmally on). No computer scientist likes to be told her particular area of study is glorified programming, but without significant internal and external restructuring, that is all Computer Science will be to the rest of the world.

posted February 21, 2006 12:06 AM in Scientifically Speaking | permalink