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jacobt comments on You only need faith in two things - Less Wrong
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But... no.
"The sun rises every day" is much simpler information and computation than "the sun rises every day until Day X". To put it in caricature, if hypothesis "the sun rises every day"is:
XXX1XXXXXXXXXXXXXXXXXXXXXXXXXX
(reading from the left)
then the hypothesis "the sun rises every day until Day X" is:
XXX0XXXXXXXXXXXXXXXXXXXXXX1XXX
And I have no idea if that's even remotely the right order of magnitude, simply because I have no idea how many possible-days or counterfactual days we need to count, nor of how exactly the math should work out.
The important part is that for every possible Day X, it is equally balanced by the "the sun rises every day" hypothesis, and AFAICT this is one of those things implied by the axioms. So because of complexity giving you base rates, most of the evidence given by sunrise accrues to "the sun rises every day", and the rest gets evenly divided over all non-falsified "Day X" (also, induction by this point should let you induce that Day X hypotheses will continue to be falsified).
You're making the argument that Solomonoff induction would select "the sun rises every day" over "the sun rises every day until day X". I agree, assuming a reasonable prior over programs for Solomonoff induction. However, if your prior is 99% "the sun rises every day until day X", and 1% "Solomonoff induction's prior" (which itself might assign, say, 10% probability to the sun rising every day), then you will end up believing that the sun rises every day until day X. Eliezer asserted that in a situation where you assign only a small probability to Solomonoff induction, it will quickly dominate the posterior. This is false.
Not sure exactly what this means, but the ratio between the probabilities "the sun rises every day" and "the sun rises every day until day X" will not be affected by any evidence that happens before day X.