Bruno Marchal wrote:
On 06 Jan 2010, at 01:21, Nick Prince wrote:
Hi Brent
Perhaps Bruno could give some clarification here. Just prior to his
conclusion on the sane paper I quoted from was this:
"So if we keep comp at this stage, we are forced to relate the inner
experience only to
the type of computation involved. The reason is that only those types
are univocally related to
all their possible counterfactuals. This entails that, from a first
person point of view, not only
the physical cannot be distinguished from the virtual, but the virtual
can no more be
distinguished from the arithmetical. Now DU is emulated
platonistically by the verifiable
propositions of arithmetic. They are equivalent to sentences of the
form ‘‘it exists n such that
P(n)’’ with P(n) decidable. Their truth entails their provability, and
they are known under the
name of Sigma1 sentence.
If comp is correct, the appearance of physics must be recovered from
some point of
views emerging from those propositions. Indeed, taking into account
the seven steps once
more, we arrive at the conclusion that the physical atomic (in the
Boolean logician sense)
invariant proposition must be given by a probability measure on those
propositions. A
physical certainty must be true in all maximal extensions, true in at
least one maximal extension (we will see later why the second
condition does not follow from the first) and
accessible by the UD, that is arithmetically verifiable. Figure 8
illustrates our main
conclusion, where the number 1 is put for the so called Sigma1
sentences of arithmetic."
It sounds as if Bruno thinks that the computations of the UD invoke
our inner experiences and also our understanding of physics. Both
come from arithmetical platonicism ( because thats what the UD is all
about). So the pictures in the "film" are stiched together by the
arithmetical (computation necessity) rather than the laws of of
physics... Hmm not what I thought and said earlier!!
So according to Bruno the laws of physics come from something
intrinsic in the computation? Not quite sure how. I just can't
figure out any more at the moment and hope Bruno will give me a hint
here.
But the quote you give is the conclusion of step 7 and 8. Except that
I use a bit the vocabulary which will help to understand the
"interview" of the Löbian machine.
Normally at step seven you understand that COMP + concrete UD => "I am
already in UD*" and the physical laws have to result from a sum on my
first person (hopefully plural) indeterminacy in UD*. (step 1 ->6 + 7)
Then step 8, MGA, shows (is supposed to show) that COMP makes any
concrete running of the UD irrelevant.
(but the MGA thread in this list is better, I may send a new version
of MGA). MGA = Movie Graph Argument.
This is not *just* because UD* is represented, remarkably enough, in
the elementary consequences of addition and multiplication, but mainly
because, by MGA, comp together with the physical supervenience thesis
makes it necessary to confuse a computation and a description of a
computation.
I think you need to carefully explicate your teminology here. Logicians
and mathematicians tend to use "description" like "model" to mean
exactly the opposite of what engineers and physicists mean by the
terms. The physicists thinks of the physical computer running as the
computation and the program as a description of what it is (supposed to
be) doing. But I don't think that's what you mean.
Brent
The computation has to consist in the logical relations, not in this
or that implementation, (which, btw, can only be a reduction to a
particular universal machine).
Do you see that COMP + concrete UD leads to an Everett-DeWitt shock?
We am multiplied by 10^100+ at each instant. COMP leads, naively, to
Aleph_zero + multiplication, or even 2^aleph_zero (in a sense)?
Then MGA is the next and last difficulty. (before the machine
interview, if interested).
Bruno
http://iridia.ulb.ac.be/~marchal/
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