Remember that Wolfram assumes a 1-1 correspondence between consciousness and physical activity, which, as you, I have refuted (or I pretend I have refuted, if you prefer). the comp hyp predicts physical laws must be as complex as the solution of the measure problem. In that sense, the apparent "simplicity" of the currently known physical laws is mysterious, and need to be explained (except that QM does predict too some non computational observation like the spin up of particles in superposition states up + down.


Le 23-mai-05, à 23:59, Hal Finney a écrit :

Besides, it's not all that clear that our own universe is as simple as
it should be.  CA systems like Conway's Life allow for computation and
might even allow for the evolution of intelligence, but our universe's
rules are apparently far more complex.  Wolfram studied a variety of
simple computational systems and estimated that from 1/100 to 1/100000 of
them were able to maintain stable structures with interesting behavior
(like Life).  These tentative results suggest that it shouldn't take
all that much law to create life, not as much as we see in this universe.

I take from this a prediction of the all-universe hypothesis to be that
it will turn out either that our universe is a lot simpler than we think, or else that these very simple universes actually won't allow the creation
of stable, living beings.  That's not vacuous, although it's not clear
how long it will be before we are in a position to refute it.

I've overlooked until now the fact that mathematical physics restricts
itself to (almost-everywhere) differentiable functions of the continuum.
What is the cardinality of the set of such functions? I rather suspect
that they are denumerable, hence exactly representable by UTM programs.
Perhaps this is what Russell Standish meant.

The cardinality of such functions is c, the same as the continuum.
The existence of the constant functions alone shows that it is at least c, and my understanding is that continuous, let alone differentiable, functions
have cardinality no more than c.

I must insist though, that there exist mathematical objects in platonia which require c bits to describe (and some which require more), and hence can't be represented either by a UTM program or by the output of a UTM.
Hence Tegmark's original everything is bigger than Schmidhuber's.  But
these structures are so arbitrary it is hard to imagine SAS in them, so
maybe it makes no anthropic difference.

Whether Tegmark had those structures in mind or not, we can certainly
consider such an ensemble - the name is not important.  I posted last
Monday a summary of a paper by Frank Tipler which proposed that in fact
our universe's laws do require c bits to describe themm, and a lot of
other crazy ideas as well, .  I don't think it
was particularly convincing, but it did offer a way of thinking about
infinitely complicated natural laws. One simple example would be the fine
structure constant, which might turn out to be an uncomputable number.
That wouldn't be inconsistent with our existence, but it is hard to see
how our being here could depend on such a property.

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