Over at Peter Woit’s blog there’s a lively discussion about the differences between string theory and intelligent design. There are a few obvious ones: one is based Fields Medal caliber math and the other on elementary mistakes in probability; one is studied at an Institute and the other at an “Institute”. But arguably, neither theory has yet made a clear prediction or explained what it sets out to in a non-circular way. String theorists explain the muon mass by invoking an infinite set of Calabi-Yau manifolds, some of which presumably yield the right value; ID’ers explain the complicated dance of bees by invoking a yet more complicated designer.
Of course, an important difference is that most string theorists admit the situation sucks. Many are searching for some deeper principle that would pick out a preferred vacuum (or set of vacua, or probability distribution over vacua) non-anthropically. Based on what little I know, it doesn’t sound like an enviable task. Today I had lunch with Frederik Denef, a string theorist who’s interested in the computational complexity of finding a minimum-energy vacuum, given a collection of scalar fields. He’s formulated some toy problems, all of which are provably NP-hard (or as hard as unique-SVP under a uniqueness assumption). I was impressed by Denef’s knowledge of complexity, and by his willingness to state precise problems that I could understand. But his work suggests an obvious conundrum: if finding an “optimal” Calabi-Yau is so hard, then how did Nature do it in the first place? (If the string theorists ever succeed, will a voice in the sky boom “Thanks, dudes!” just before space as we know it disappears?)
In short, if the ID’ers are armed squatters in the apartment building of science, openly scorning the materialistic concept of rent, then the string theorists are model tenants who often drop by the landlord’s office to say good afternoon, and by the way, that check from 20 years ago should clear any day. (In their defense, the other quantum gravity theorists’ checks haven’t cleared either.) To me, this raises an interesting question: does science need a notion of “resource-bounded falsifiability,” which is to Popper’s original notion as complexity is to computability?