> Hutter's only assumption about AIXI is that the environment can be simulated by a Turing machine.
That is already too strong to me. Can our environment be simulated by
a Turing machine? Why?
There are currently no widely accepted laws of physics that cannot
be simulated by a Turing machine (in the general sense of the word,
i.e. I include monotone machines with access to a source of random
bits) to an arbitrary degree of accuracy.
Of course this doesn't "prove" that the universe is computable, however
it is enough evidence to put the onus onto you to prove otherwise.
Before some other people jump in with the usual objections (by the
way the perspective I am advocating is the mainstream one) here's
some replies:
Q: What about quantum theory and quantum computers?
They are both Turing computable (with great effort I might add).
Quantum computers can do things with lower time complexity,
but they can't perform incomputable computations.
Q: What about chaos?
Again, Turing computable but with great effort. You might need
the initial conditions to an amazing accuracy and a vast amount
of computation time, but there is no indication that what happens
is in any way fundamentally incomputable.
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