Complexity theory is a tricky subject. While classical computability theory pretty successfully explains what can be computed and what can’t, the question seems to get much more difficult when you ask what can be computed in a certain amount of time or space. This difficulty is epitomized by the famous P versus NP problem: informally, is it more efficient to recognize the solution to a problem than it is to generate a solution? Although this problem has been around for far less than a century, the Clay Mathematics Institute has named it one of a handful of Millenium Problems. The P versus NP question seems so hard, in fact, that before locking oneself in one’s attic and succumbing to obsession, I think it’s worthwhile asking whether it is the right question in the first place. For one thing, deciding whether P equals NP might not have much impact on the real world: it may be that P does not equal NP, but for all intents and purposes we can solve typical instances of NP problems efficiently; on the other hand, maybe P does equal NP, but the boolean satisfiability problem (SAT), for example, requires deterministic time n 100 on average, leaving it practically infeasible. For another thing, it may be impossible or virtually impossible to resolve whether they are equal: some have suggested that it is independent of Peano arithmetic, but even if it’s not maybe P = NP, but it requires an algorithm so complicated that it’s too much for our modest brains.