Friday, June 15, 2012

Envy and Computational Complexity

While reading this article by Sven Birkerts on artistic envy, it occurred to me that the situation of Salieri in Amadeus has some analogs in computational complexity theory, specifically, the curious dual nature of NP-hard problems. These are problems for which it is possible to recognize (verify) a solution in a reasonable amount of time, but finding that solution almost certainly takes an unreasonable (exponential) amount of time. A typical NP-hard problem involves searching through a very large space of possible solutions (eg, the possible routes a travelling salesman could take to visit all the cities on his circuit. So, given the problem of finding a route shorter than some given value, you need to examine a very large number of possibilities, which can be impossible to do in a reasonable amount of time. But checking that a given route satisfies the conditions is fast and easy.

In Amadeus, while being a genius is hard (and thus rare), recognizing genius is pretty easy. Which is the root of Salieri's problem. He can see Mozart's genius, but there is no way he can duplicate it. Recognizing genius is not necessarily a trivial capability, probably not everyone can do it, but it's a far cry from being a genius, from being able to create (or find?) works that exceed some threshold of quality from the unimaginably huge space of possible compositions. He does not have the processing power for that, and those who do seemed possessed of something supernatural, that is, beyond conceivable mortal power.

This is something of a follow-up to this post. I've been resorting my collection of old papers and grad-school detritus, and I have to say I've been fortunate to have spent a good bit of time in the presence of actual genius, at least the computer science version of it. Like Salieri, I could readily recognize it, even if I couldn't achieve it myself. I guess I was luckier than Salieri to be also almost completely clueless about social status and rank, so at least at the time it didn't occur to me to be envious, which meant it didn't interfere with my ability to learn what I could from these semi-supernatural beings.

1 comment:

jlredford said...

I remember chatting in grad school with one of the smartest guys I ever met, Lou Schaeffer, when he was reading a bio of Benjamin Franklin. He said "You know, the bifocals were pretty good, but I think I could have come up with those. I could maybe have done the stove too. But then there's the lightning-is-electricity, and the libraries, and the postal system, and the paved roads, and the Constitution, and the convincing the French to take the American side. It's just overwhelming!" So there's also a higher energy level in brilliant people, not just a faster CPU clock.