Ben Goertzel wrote:

>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. See my web page for links to papers, and archive addresses with more explanations, including the basic results of my thesis. (Mainly the Universal Dovetailer Argument UDA and its Arithmetical version AUDA). >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? The main reason is that, once we postulate that we are turing emulable, (i.e. the computationalist hypothesis comp), then there is a form of indeterminacy which occurs and which force us to take into account the incompleteness phenomenon. Godel is not a problem. It is really Godel's incompleteness which makes comp, including the Church thesis, consistent. (Judson Webb wrote a book on that theme in 1980 " Finitism, mentalism and metamathematics, my work considerably developpes such type of reflexion). >I'll address this in a later post, unfortunately I have to catch a plane and >don't have time at the moment Thanks. I look forward to it. Take your time. I'm also very busy. Bruno