Eliezer wrote: > James Rogers wrote: > > > > Your intuition is correct, depending on how strict you are about > > "knowledge". The intrinsic algorithmic information content of any > > machine is greater (sometimes much greater) than the algorithmic > > information content of its static state. The intrinsic AIC doesn't > > change even though the AIC of the machine state may. For this reason, > > it is not possible for a machine with a smaller AIC to perfectly model a > > machine with greater or even equal AIC. By extension, it is also not > > possible to have perfect self-knowledge. It is a common misapplication > > and/or misunderstanding to interchangeably use the intrinsic AIC of a > > machine with the AIC of the machine's state; I'm not saying that is > > happening here, but I see it regularly in other less rigorous forums and > > so it is worth bringing up. > > > > All this does not preclude a smaller machine from having a very good > > predictive model of a larger machine. Just not a perfect one. > > I'm not sure whether your definition of AIC precludes this, but it is > possible for a small physical system to perfectly model a large physical > system providing that the large physical system possesses perfect, large > regularities such that its state can be fully represented within > the small > regularities of the small physical system.
James's definition gets around the point you're making, because the definition of AIC of a machine is (roughly) the size of the smallest self-delimiting program that computes that machine.... so your large system with a lot of regularity has very low AIC... He's basically restating Chaitin's epigrammatic restatement of Godel's Theorem as: "You can't prove a 20 pound theorem with a 10 pound formal system" ;-) [poundage being algorithmic information content] -- Ben G ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/?[EMAIL PROTECTED]
