Eliezer: Sorry to harp on something tangential to your main point, but you keep repeating the same mistake and it’s bugging me. Evolution is not as slow as you think it is.
In an addendum to this post you mention that you tried a little genetic algorithm in Python, and it didn’t do as badly as you would have expected from the math. There is a reason for this. You have the math completely wrong. Or rather, you have it correct for asexual reproduction, and then wrongly assume the limit still applies when you add in sex. As has been pointed out before, genetic algorithms with sex are much, much, much faster than asexual algorithms. Not faster by a constant factor; faster in proportion to the square root of the genome length, which can be pretty damn big.
The essential difference is that as a genome gets more fit, the odds of a mutation hurting rather than helping fitness go up, which limits your acceptable mutation rate, which limits your search rate for asexual reproduction. But if you rely on crossover (sex) to produce new individuals, (1) the expected fitness of the child is equal to the average fitness of the parents, even if the parents are already very fit; and (2) mutation isn’t the main thing driving the search anyway, so even if your mutation rate is very low you can still search a large space quickly.
And just for fun, but here’s another way to look at it that I haven’t seen described before. Asexual evolution, as you’ve pointed out a few times, relies on mutations to generate new candidates, so it’s just doing a random walk to adjacent positions in search space. But if you take two parent genomes and do a random crossover, you’re effectively taking the hypercube (in the search space of genome strings) whose corners are the two parents, and randomly picking a different corner. So you’re taking a much larger step. Mutations are now only necessary to prevent the population from collapsing into a lower-dimensional search space; they aren’t the driver of innovation any more.
Eliezer: Sorry to harp on something tangential to your main point, but you keep repeating the same mistake and it’s bugging me. Evolution is not as slow as you think it is.
In an addendum to this post you mention that you tried a little genetic algorithm in Python, and it didn’t do as badly as you would have expected from the math. There is a reason for this. You have the math completely wrong. Or rather, you have it correct for asexual reproduction, and then wrongly assume the limit still applies when you add in sex. As has been pointed out before, genetic algorithms with sex are much, much, much faster than asexual algorithms. Not faster by a constant factor; faster in proportion to the square root of the genome length, which can be pretty damn big.
The essential difference is that as a genome gets more fit, the odds of a mutation hurting rather than helping fitness go up, which limits your acceptable mutation rate, which limits your search rate for asexual reproduction. But if you rely on crossover (sex) to produce new individuals, (1) the expected fitness of the child is equal to the average fitness of the parents, even if the parents are already very fit; and (2) mutation isn’t the main thing driving the search anyway, so even if your mutation rate is very low you can still search a large space quickly.
Once again I’ll point to MacKay’s Information Theory, Learning, and Inference Algorithms for a much better explanation of the math (from an information theory standpoint) than I’m capable of.
And just for fun, but here’s another way to look at it that I haven’t seen described before. Asexual evolution, as you’ve pointed out a few times, relies on mutations to generate new candidates, so it’s just doing a random walk to adjacent positions in search space. But if you take two parent genomes and do a random crossover, you’re effectively taking the hypercube (in the search space of genome strings) whose corners are the two parents, and randomly picking a different corner. So you’re taking a much larger step. Mutations are now only necessary to prevent the population from collapsing into a lower-dimensional search space; they aren’t the driver of innovation any more.