You have initiated an interesting topic concerning the decision
whether to consider the 3rd person view or the 1st person view to be
fundamental. It is also natural to say that our experiences or qualia
are fundamental, and that the existence of an external universe that
we inhabit merely is a theoretical construct. But on the one hand, the
sciences assuming the existence of an external universe have had great
success, and if we want to apply the power of mathematics, it seems
much more promising to study the external universe than to study
personal experiences or qualia.
I have always been hopeful that both approaches will finally turn out
to be equivalent. Those who prefer the 3rd person view are interested
in the question which universe we---being observers---must expect,
leading to the self-sampling assumption. The fact that we are
interested in 1st person views is also expressed by the anthorpic
principle. So, the transition is made by the anthropic principle in
combination with the self-sampling assumption.
You, starting from the first person view, must give an answer to the
question why the assumption of an external universe is so successful.
You give this answer with the help of your "World-Index-Compression
Postulate". Thus, this postulate is somehow complementary to the self-
sampling assumption and the anthropic principle.
So far, I'm no supporter of the idea imagining our universe (or our
experiences) being the output of a Turing Machine. I feel more
satisfied with the idea that everything exists per se which I justify
using my "no-justification" or, since I know of it, also using the
"zero information principle". This is why I let it to others to
analyse your ideas in detail. I'll prefer the role of the interested
Nonetheless, I have one critical remark. I cannot accept your
reasoning against previous approaches to solve the measure problem.
You wrote: "But if both the Goldilocks Universe and the blackbody
radiation universe are infinite in size, then both have an infinite
number of observers. [...] Maybe we say, 'The Goldilocks Universe
produces more observers per
cubic meter.' "
The considerations trying to solve the measure problem have not been
that primitive, but much better. The concept of a cubic meter won't
make sense in most of the universes, and to compare infinities in a
rigorous manner is nothing new to mathematicians. Both, Standish and
Schmidhuber (and surely others, too) have given well-advised attempts
to solve the problem.
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