Wednesday, October 1, 2008

Cheaper Arguments

A New York Times opinion piece spends two pages bashing classical economists for not understanding the computational aspects of economics and phase transitions. But who comes to the rescue? It is not theoretical computer scientists, with all our love of phase transitions and computational economics --- it is the damned PHYSICISTS!

Of course, 90% of this post is meant as a joke :). But I would like to point out that 10% is not.

We have witnessed a trend in TCS to focus on the philosophical implications of our work. But it should be obvious that those same philosophical implications can be obtained through cheaper arguments by other fields. When a new proposal to deregulate the Illinois energy market is made (to take the Times' example), who will be the first to point out a potential issue? The Physicists / whoever decides to run some simulations of the new market over the weekend? Or the TCS researchers, who have spent a month proving that a phase transition occurs, assuming that their precise model makes sense?

The point is that if you only want philosophical implications, a solid proof is not necessary ("Dear members of the Illinois Congress, I know you took the issues pointed out by our colleagues in the Physics Department very seriously, but you should realize they never had a complete proof before!"). Think about how hard it is to prove some things about random graphs or random SAT, even though they are obvious from experiments.

I would hate it if we became so engaged in the market for philosophical implications, that we would sacrifice our core TCS values to avoiding always coming in second place.


Anonymous said...

Should we similarly forgo the analysis of algorithms and data structures, and instead rely on empirical evidence that they work correctly and quickly?

Experiments are fine, but do not replace the understanding that mathematical proofs provide any more in emerging areas such as computational game theory, than they do in classical areas such as data structures.

Particularly if a key restriction on the model is the computational limitations of the participating agents, this seems to fall squarely within the realm of computer science theory, as well.

Mihai said...

Our long-term goal was to come up with new algorithms that work well in practical computer science, and to prove theorems that explain what practical computer science can and cannot achieve.

Now we're saying we want to provide philosophical insight into many other disciplines. We can, but it's somewhat limited, because simulations (which by the way, we're really bad at in TCS) are better and cheaper.

BTW, the grand high level theorems that you may prove by assuming a bunch of interacting agents with limited computational resources may be nice, but they will be too qualitative to be interesting to people who actually care about markets from a practical perspective.

I just don't find it so cool that we dream about helping another purely theoretical discipline (especially compared to proving theorems about computation, which is very real and important).