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.
***

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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