On 28 Nov 2017, at 14:50, Jason Resch wrote:
On Tue, Nov 28, 2017 at 6:06 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 27 Nov 2017, at 04:04, Jason Resch wrote:
Richard Feynman in "The Character of Physical Law" Chapter 2 wrote:
"It always bothers me that according to the laws as we understand
them today, it takes a computing machine an infinite number of
logical operations to figure out what goes on in no matter how tiny
a region of space, and no matter how tiny a region of time. How can
all that be going on in that tiny space? Why should it take an
infinite amount of logic to figure out what one tiny piece of space/
time is going to do?"
Does computationalism provide the answer to this question,
Yes. :)
Very nice. It seems then Feynman's intuition was in the right place.
The second half of the above quote was:
"So I have often made the hypothesis ultimately physics will not
require a mathematical statement, that in the end the machinery will
be revealed and the laws will turn out to be simple, like the
checker board with all its apparent complexities. But this is just
speculation."
So it looks like that simple machinery is the machinery of the
universal machine and the simple laws are those of Peano (or
Robinson?) Arithmetic.
Any first order specification of a universal (Church-Turing)
machinery will do. But it seems to me that we should avoid using
induction axioms for the ontology (as I could explain someday, I
discovered this more recently). So it is Robinson Arithmetic, and it
is better to avoid Peano (for the ontology). Then, the
"observer" (which is also a believer, knower, ...) we can use PA
(whose existence is a theorem in RA).
But we could use combinators, of Lamdda Expressions. In fact any
inductive structure who terms admits laws making it into a universal
machinery will do. Iuse the numbers only because we are all familiar
with them.
I have recent reason to suspect that if we put the induction axioms in
the ontology, we can no more hunt away the white rabbit.
Unfortunately, to prove this is not easy.
in the sense that even the tiniest region of space is the result of
an infinity of computations going through an observer's mind state
as it observes the tiniest region of space?
That might be OK, if space was something entirely physical, which is
suggested by the physics of the vacuum, or general relativity, but
with Mechanism, spece and time might be less physical than here
suggested. The reason is that it is not clear how "empty space"
could make a computation different from another,
I think what I was thinking here were "closed loop feyman diagrams",
where any possible diagram might be drawn in the tiniest area of
space, so long as it is closed, e.g. fluctuations/particle creations
are permitted so long as they all cancel out. So if space is
physical, and enables any of these fluctuations to happen, then this
noise can take any possible value from the observer's point of view
(like the polarization of a photon).
That could make sense. But I am still not at ease with quantum field
theory enough, notably on how to interpret the "virtual particles". I
would treat them as superposition, but some remark by Brent sometimes
ago made me doubt this. I am not enough competent on this to get my
hand to it.
and so space could be only a marker differentiating some
computations, like time seems to be in the indexical approach. All
this would need big advance in the mathematics of the intelligible
and sensible arithmetical matter. I expect space to be explained by
quantum knot invariant algebra due to subtil relation between BDB
and DBD logical operators (I mean []<>[] and <>[]<>). Kant might be
right on this, apparently space and time are really in the
"categorie de l'entendement", I don't know Kant in English sorry,
but this means mainly that they belong to the mind).
Thanks I very much appreciate these additional insights. I do
subscribe to the belief that time is an illusion created by the
mind. I have a little more trouble seeing that when extended to
spacetime as a whole. Though perhaps what's come closest to helping
me see this picture is Amanda Gefter's excellent book "Trespassing
on Einstein's Lawn"--I would recommend it to everyone on the
Everything list. It takes the approach that only things that are
invariant are real, and from there proceeds to deconstruct almost
all of physics.
Thank you, it seems interesting, I might try to take a look (when time
permits),
Bruno
Jason
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