Re: UDA revisited

From: Colin Geoffrey Hales <>
Date: Sun, 19 Nov 2006 13:33:13 +1100 (EST)

> Since it makes no difference in any observable respect whether we are
living in a computer simulation running on a bare substrate, as one that
is incidently computated as part of a universal dovetailer, or an
infinite chain of dovetailers, we really can make use of Laplace's ripost
to Napoleon "Sire, I have no need of that hypothesis" with
respect to a concrete computer running our world.

Sorry Russel, I disagree with this claim.

To say that the universe is computation does not imply any old substitute
computed abstraction will be identical in all respects.

In particular there is a blizzard of virtual theorems made available
because of the intrinsic parallelism of 'reality as computation'. These
are NOT explictly computed. Abstract it and all the virtual
theorems/computations are gone.

To see a computational equivalent check out ANY cellular automaton. There
is a perfectly computational but uncomputed relationship between any cell
and _all_ other cells (NOT just the local cells explicit to the rule set
used). Yet the only thing that was actually computed was the cell contents
using local cells incorporated in the cell rules. The universe is
equivalent. It is computation and can be regarded/treated as a massively
parallel CA. All the virtual theorems (computations) actually exist.

So: Computationalism is the statement that "I am a computation".

.... is correct in that the universe is computation, but incorrect in that
an abstraction on a substrate will replicate everything - is cannot/does
not replicate the virtual theorems. SO.....I have shown you a _physical_
but virtual computation that is NOT replicated by the UDA abstraction.
This makes your original assertion incorrect.

The story is bigger than this in that I hold the virtual theorems to be
the substrate for subjective experience....but my claims in this regard do
not affect my treatment of your claim in respect of computationalism. The
UDA throws away a very very very large number of virtual theorems. The
UDA does NOT do massively parallel theorem proving therefore it loses all
the virtual theorems. Note that a massively parallel computer made of
STUFF does NOT recreate the virtual theorems inherent in the actual
computation that _is_ STUFF.

Put it this way....TWO theorem-proofs actually deliver THREE truths.
TRUTH_1, TRUTH_2 and the difference between the two. Traverse TRUTH_1 back
down to the common axiom set and then back up TRUTH_2. This corresponds to
'as-if' a direct TRUTH_1_to_2 or TRUTH_2_to_1 was enacted/proven when it
was not actually proven explicitly. It comes about because TRUTH_1 and
TRUTH_2 were 'computed' in parallel by the universe-as-computation. If the
universe is computation and computes matter then the virtual theorems are
'virtual matter'.

This is the literal origin of Godel's incompleteness theorem! It's _why_
it applies - the parallelness of theorem proving is neglected by
mathematicians in the construction of calculus/logic. In the process a
whole pile of theorems become true but unprovable or conversely there's a
whole pile of truths that are provable but not actually proven, but can be
implicitly proven (via the method of 'virtual theorem proving' shown

So... if the UDA is an abstration made of 'STUFF' then it has no virtual
theorems whereas the STUFF has them. A UDA made of anything else but STUFF
is meaningless from my point of view. I want to build real AGI, not play
in ideal realms (no matter how much fun it is!).

If I can get this EC/lambda calc thing sorted I'd be able to show you
formally. All in good time.


Colin Hales

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Received on Sat Nov 18 2006 - 21:33:44 PST

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