In Tegmark's paper,
in section 2G, he makes a crucial point that the fewer axioms
you use to define your mathematical structure, the larger is
the ensemble. This provides a concrete justification for the
principle of Occam's Razor. Similarly to the argument given
above, we would expect to find ourselves in worlds with fairly
few laws of physics, since those admit the most SAS's. You
can always add any bizarre behavior to the structure by adding
ad hoc axioms, but worlds in which that is the case
have a smaller measure than those that do not.
This line of reasoning also explains why, in a general sense,
we find that our universe behaves sensibly from moment to moment.
Many philosophers have pondered the question of why everything
doesn't disintegrate into chaos in the next instant. What holds
the world together such that things persist and our memories
match our external reality? The answer is that the structure(s)
we are in obey physical laws, not because they were cast by
fiat from some omnipotent being, but simply because the structures
that do obey physical laws are more numerous than those that do
not, and hence we are likely to find ourselves in those.
--
Chris Maloney
http://www.chrismaloney.com
"Knowledge is good"
-- Emil Faber
Received on Sat Jun 05 1999 - 05:27:07 PDT