I comment last posts by Russell, Alasdair, George.
I am very glad with the fact that people here are aware of the
flying white rabbit appearance problem in Tegmark/Schmidhuber-like
approach.

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I really think that it is not possible to solve the rabbit problem
with Tegmark hypothesis (that all mathematical structures exist),
because it makes the indeterminism domain to big. The more we
make Tegmark's hypothesis precise, the more will it be likely that
we should seen white rabbit flying ...
I agree with Russell Standish when he says that the anthropic
principle per se cannot solve the rabbit problem.
I agree with George Levy when he says that <<The ultimate anthropic
principle is relative... or relativistic with respect to the
observer and pushes the anthropic concept to its ultimate
conclusion: The Self.>>
With the computationalist hypothesis we can replace the "anthropos" by
the Universal Turing Machine, i.e. we can work with the computational
self, and the logic of self-reference.
In that case it becomes more easy to tackle the rabbit issue. The set
of all computations is well defined thanks to Church's thesis.
And there is no infinite chain of turtle problem because there is no need
for an actual implementation of the universal dovetailer as we discuss it
before. There is a "feeling of actualness" for any relative,
arithmetically
well defined, self.
The rabbit issue is thus linked to the measure definition issue.
Of course with comp we can no more distinguih in an absolute way
dream from "reality" and we must explain why some dreams seems to be
stable
and coherent (without flying rabbit).
So, of course, we are push back in the "Wei Dai" question:
should we follow the RELATIVE SSSA or the STRONG SSSA here ?
What George call rightly the crux of the matter.
To sum up : The immortality question is not linked to the measure
problem ; The white rabbit problem is definitely linked to the
measure problem (and to what I like to call the REVERSAL between
"physics" and "psychology" : with comp, it is the physical
NON-WEIRDNESS which is weird!).
Bruno