At 13:08 13/04/04 -0700, George Levy wrote:

Put in another way, *either* the massive computer simulates the exact
laws of physics (exact with comp = the laws extractible from the
measure on all 1-computations) in which case we belong to it but
in that case we belong also to all its "copy" in Platonia, and our
prediction or physics relies on all those copies (so that to say
we belong to the massive computer has no real meaning: if it stops,
nothing can happen to "us" for example); *or* the massive
computer simulates only an approximation of those laws (like a
brain during the night), and then we can in principle make the
comparison, and find the discrepancies, and conclude we inhabit
a fake reality ... OK?


This is a very interesting method of testing what I thought was untestable. However, I see some problems. The number of simulations within Platonia is likely to be infinite. In addition, you may be simulated at more than one level, possibly at an infinite number of levels, including at the "base" level in Platonia if there is such a thing.

OK. Although I am not sure by what you mean by "base" in Platonia.

While the number of instances of "you" in the computer may be limited, the number of computers in Platonia may be infinite. In addition, the number of "real you" in Platonia is also likely to be infinite.

Yes. Plausibly 2^aleph_0 (the power of the continuum).

Your existence at the base level in Platonia is much more likely than the existence of a simulation computer (because the computer is presumably much more complex than you) and therefore, your measure in Platonia will swamp out your measure in the computers.


Your proposed test idea is interesting but it should be designed to cancel out these infinities.

If that is possible. The translation of the reasoning in arithmetic leads me to think that these
infinities are not cancellable. Comp would predict that the "toe" cannot be renormalizable.
It is too early to make definite conclusion however.


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