On Wed, Feb 5, 2020, 7:25 PM TimTyler <[email protected]> wrote: > On 2020-02-05 13:22:PM, Matt Mahoney wrote or quoted: > > > Occam's razor also likely applies in toy finite worlds, such as those >> modeled by >> cellular automata. >> >> I don't think it has much to do with infinity. >> > > Turing machines are useful models of computation even though they cannot > exist in a finite universe. > > What do you think is the reason Occam's Razor works, if not math? > > > Well, math permits worlds not bound by > > Occam's razor, such as the world where > > all sequences of a given length are > > equiprobable. So, the answer is probably > > physics. Locality and the speed of light limit, > > in particular. -- >
Math allows strings of equal length to be equally likely, which is what a Solomonoff distribution assumes. It does not allow a uniform distribution over an infinite set of strings of different lengths. Occam's Razor suggests that the origin of the laws of physics is that all possible universes exist and we necessarily observe one where intelligent life is possible. For example, if the masses of the proton and neutron were different then stars would not shine or supernovas would not produce the right elements needed for life chemistry. Those universes exist but are not observable. It takes a few hundred bits to describe the physics of the universe we observe but not all possible universes. So Occam's Razor drives physics, not the other way around. ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T353f2000d499d93b-Ma5dd9f706b77234a77d58750 Delivery options: https://agi.topicbox.com/groups/agi/subscription
