Bruno wrote: *** Let me insist because some people seem not yet grasping fully that idea. In fact that 1/3-distinction makes COMP incompatible with the thesis that the universe is a machine. If I am a machine then the universe cannot be a machine. No machine can simulate the comp first person indeterminacy. This shows that the Wolfram-Petrov-Suze-... thesis is just inconsistent. If the universe is a (digital) machine then there is level of description of myself such that I am a machine (= I am turing-emulable, = comp), but then my most probable neighborhood is given by a sum over all computational histories going through my possible states, and by godel (but see also the thought experiments) that leads to extract the probable neighborhood from a non computable domain, in a non computable way. In short WOLFRAM implies COMP, but COMP implies NOT WOLFRAM(*). So WOLFRAM implies NOT WOLFRAM, so NOT WOLFRAM. Eventually physics will be reduced into machine's machine psychology. If octonion play a fundamental role in physics, it means, with comp, that octonions will play a fundamental role in psychology. ***

Unfortunately, I do not follow your argument in spite of some significant effort. When you say "sum over all computational histories", what if we just fix a bound N, and then say "sum over all computational histories of algorithmic info. content <= N." Finite-information-content-universe, no Godel problems. So what's the issue? *** And, dear Ben, I should still read how you link octonions and the "deep aspect", as you say, of the mind. BTW, I would be also glad if you could explain or give a rough idea how quaternions play a role in the mondane aspect of the mind, as you pretend in one of your paper, if you have the time. *** I'll address this in a later post, unfortunately I have to catch a plane and don't have time at the moment ben