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Manfred comments on Thought experiments on simplicity in logical probability - Less Wrong Discussion
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So what do you think happens in thought experiment 3?
I think P(eval(random_expression(n)) = 42) will go to a positive limit when n goes to infinity, because expressions like (short expression that evaluates to 42) + 0 * (arbitrary long expression) will tend to be a constant fraction.
That's a good point. I'm not sure if it goes through, though, because rather than length, we want to order sentences by apparent complexity, and the sentences you describe are only (apparently) as complex as the prefix.
There might still be tricks that exploit the weakness in our method for evaluating apparent complexity [...]
EDIT: Okay, I thought of a trick - rather than "0", multiply the suffix by an expression that evaluates to 0 but is too complicated for the checker to evaluate. This allows the positive limit of probabilities to be fairly big (well, relative to 0).
Anyhow, great, the probability that some apparently-complex expression equals 42 doesn't go to zero. What happens when the expression is just as complex as "42"? Is the probability that it equals 42 higher then? Lower?
I think you're confusing the complexity of the sentence with the complexity of what the sentence evaluates to. The sentence "0 * random_expression" is still roughly as complex as random_expression, even though it evaluates to 0.
Whoops, you're right.