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endoself comments on A potential problem with using Solomonoff induction as a prior - Less Wrong
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When we do enough testing, K could get arbitrarily large and, therefore, arbitrarily complex so, unless you, like Solomonoff induction, essentially assign infinite complexity to anything uncomputable, there exists a K such that "Halts within K" is more complex than "never halts".
At this stage, an uncomputable universe is an extraordinary hypothesis, that would require extraordinary evidence to support. A finite string of numbers seems like poor evidence for uncomputability. It seems much easier to believe that it is a computable approximation. So, I am inclined to side with Solomonoff induction here.
The uncomputable is always infinite. Our observations are always finite. I don't see how making such a leap could be justified.
So if a simple setup you can do at home with some liquid nitrogen, a laser and a kumquat appeared to allow direct hypercomputation - could instantaneously determine whether a particular Turing machine halted - and you were able to test this against all sorts of extraordinary examples, you would never come to the conclusion that it was a hypercomputation engine, instead building ever-more-complex computable models of what it was doing?
I would never conclude that, because the proposition that I'm in a simulation and the DLotM are messing with me is about as plausible on the evidence.
A hotline to a computable halt-finding machine seems much more plausible than something uncomputable, yes. We have no idea how something uncomputable could possibly work. You should not give weight to the uncomputable while computable approximations exist.
So how many cycles of
would you have to go through before concluding the universe was not computable?
I have to confess that I don't really see what's so special about the bottom of the compute hierarchy that you would be so certain that's where the universe is.
I'm not talking about "this stage", I'm talking about what would happen in principle, after we make enough observations.
Are you saying that you assign literally 0 probability to an uncomputable universe? How could you possibly be so sure? Remember there are an infinite number of possible computable universes, so there must be computable universes with probability less than epsilon, for all epsilon > 0.