Re: As you mention, if somebody else uses a different reference machine their measured Kolmogorov complexity will be different, where the maximal difference is bounded by some constant. How big is this bound? Pretty small.
No, the bound is infinite. I.e. there is no bound. You have to confine your attention to a subset of possible machines before you can do any bounding. What is the rationale for considering some machines and not others? One possibile criterion is what best approximates a small hardware implementation—i.e. whether the virtual machine can be small physically. However, a physical machine has experimental access to the constants of nature, which might take up considerable space in a Turing machine—so it does not seem reasonable to claim that a simple Turing machine is a good approximation to a small physical machine. If you reject the real for the virtual, what are the grounds for doing that?
Also, if it comes down to 100 bits, that is not exactly a small probabilty difference. It’s a factor of 2^100. That might well make a big difference when comparing small theories—such as the ones often used by science.
These may not be show-stopping issues—but it seems odd to me that Solomonoff induction people seem to think they can gloss over them, perhaps to arrive all the faster at their bizarre conclusion that Solomonoff induction is the one true answer to the problem of the priors.
Re: As you mention, if somebody else uses a different reference machine their measured Kolmogorov complexity will be different, where the maximal difference is bounded by some constant. How big is this bound? Pretty small.
No, the bound is infinite. I.e. there is no bound. You have to confine your attention to a subset of possible machines before you can do any bounding. What is the rationale for considering some machines and not others? One possibile criterion is what best approximates a small hardware implementation—i.e. whether the virtual machine can be small physically. However, a physical machine has experimental access to the constants of nature, which might take up considerable space in a Turing machine—so it does not seem reasonable to claim that a simple Turing machine is a good approximation to a small physical machine. If you reject the real for the virtual, what are the grounds for doing that?
Also, if it comes down to 100 bits, that is not exactly a small probabilty difference. It’s a factor of 2^100. That might well make a big difference when comparing small theories—such as the ones often used by science.
These may not be show-stopping issues—but it seems odd to me that Solomonoff induction people seem to think they can gloss over them, perhaps to arrive all the faster at their bizarre conclusion that Solomonoff induction is the one true answer to the problem of the priors.