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Uncomputability, unsolvability and anxiety
Dec. 9th, 2004 09:12 amIn the middle of this lovely Making Light discussion about fanfic, sex in literature, and the Id Vortex, commenter "clew" makes a completely off-topic observation:
There's a related phenomenon that I noticed when I was in graduate school (I think John Baez has also written about it somewhere). In arguments between physicists and/or mathematicians (unfortunately I can't think of specific examples at the moment), it's common for somebody to beat down a line of speculation by citing some no-go theorem or other, in the form "Paper X proved that you can't do that"—ignoring the fact that the no-go theorem actually relies on very specific assumptions that are not entirely necessary to the line of speculation. Impossibility theorems gradually accumulate this nightmarish folk status that they do not actually deserve.
There's some kind of realistic-but-optimistic medium between techie triumphalism and anxious obsession over impossibilities, which would presumably be optimal for dealing with the world. But it's difficult to hit it exactly. It may even be possible to prove that it's impossible to come up with a decision procedure to hit it exactly.
There is a sermon lurking somewhere in here about the social/psychological function of faith (religious or otherwise). There are many sorts of problems that can actually be solved, but have to be divided into parts in order to solve them, the parts considered one at a time, and some of the parts sometimes delegated to other people or left purely to chance, fate, God or whatever you want to call it; but in order to do this it's necessary to have an abstraction mechanism in our heads that lets us assume, if only for the sake of argument, that we don't have to worry about this or that part of the problem just now (and maybe not ever). I'm pretty sure that this is what is useful about faith. Whether it's yoked to a metaphysics or not (and I tend to think that the metaphysics is the least necessary part), it becomes pathological only when the decision to delegate is blatantly contrary to evidence.
(I was trying to explain Chaitin's Maximally Unknowable Number to a buncha high-octane tech geeks a while ago; was startled that many hadn't even studied Computability & Unsolvability, and therefore hadn't been cured of the characteristic techies' belief that any problem you can state clearly enough must have a solution.... I feel this gap in their educations may help to explain the goofier branches of techno-libertarianism. I am now hopelessly off point.)A problem I run into is that (possibly because of my own educational background, which is more in math and science and less in engineering) I am perhaps too aware of this. In my daily life, whether I'm thinking about work or politics or personal problems, I spend a lot of time fretting about the existence of unsolvable problems and worrying that I have fallen into one (my thinking about my love life back in my early twenties seemingly consisted almost entirely of this sort of fretting). There's an irrational anxiety that sets in, say, when I'm trying to debug some software problem and the first ten things I've tried had no effect: I can start thinking that maybe nothing I do has any effect, and have a hard time believing in the insight that finally comes until I actually run the last build. I can lose sight of the fact that, regardless of the existence of uncomputability and unsolvability, an amazing variety of problems, including most of the ones that people encounter on a daily basis, are actually solvable.
There's a related phenomenon that I noticed when I was in graduate school (I think John Baez has also written about it somewhere). In arguments between physicists and/or mathematicians (unfortunately I can't think of specific examples at the moment), it's common for somebody to beat down a line of speculation by citing some no-go theorem or other, in the form "Paper X proved that you can't do that"—ignoring the fact that the no-go theorem actually relies on very specific assumptions that are not entirely necessary to the line of speculation. Impossibility theorems gradually accumulate this nightmarish folk status that they do not actually deserve.
There's some kind of realistic-but-optimistic medium between techie triumphalism and anxious obsession over impossibilities, which would presumably be optimal for dealing with the world. But it's difficult to hit it exactly. It may even be possible to prove that it's impossible to come up with a decision procedure to hit it exactly.
There is a sermon lurking somewhere in here about the social/psychological function of faith (religious or otherwise). There are many sorts of problems that can actually be solved, but have to be divided into parts in order to solve them, the parts considered one at a time, and some of the parts sometimes delegated to other people or left purely to chance, fate, God or whatever you want to call it; but in order to do this it's necessary to have an abstraction mechanism in our heads that lets us assume, if only for the sake of argument, that we don't have to worry about this or that part of the problem just now (and maybe not ever). I'm pretty sure that this is what is useful about faith. Whether it's yoked to a metaphysics or not (and I tend to think that the metaphysics is the least necessary part), it becomes pathological only when the decision to delegate is blatantly contrary to evidence.