BM:
(1) The universe is more complex than current physics
makes it out and may not be computable, and in comparison,
(2) Our ability to comprehend things is quite limited.
But these two together imply that is quite possible
that we live in a simulation.
In a n-dimensional Hilbert space, one needs n^2 -1
real parameters to specify the information content,
that is to say a density matrix, hermitean,
with tr(rho)=1.
Since human measurements, within a specific basis set,
give n-1 independent probabilities, one needs n+1
unbiased basis sets to provide the required
number n^2 - 1. (Note that n+1 unbiased basis sets
exist if n is _prime_, as far as I remember).
Are the great simulators number theorists?
:-)
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Received on Mon Feb 26 2007 - 13:29:11 PST