On 29 Nov 2017, at 20:45, Brent Meeker wrote:
On 11/29/2017 2:27 AM, Bruno Marchal wrote:
On 28 Nov 2017, at 14:52, Jason Resch wrote:
On Tue, Nov 28, 2017 at 7:50 AM, Jason Resch
<jasonre...@gmail.com> 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.
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).
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.
Jason
I wanted to add, it also shows that the function (if you can call
it that) of practically every physical law is to ensure
consistency between observers. I think you would like it.
That is needed to have first person plural realities, but truth is
also very useful. "just consistency" is good for multi-user video
game, but the truth requires sound proposition,
What does "sound" mean?
In our context, a theory T is sound if its theorems are true in the
standard model of arithmetic. i.e. when (T proves A) -> [ (N, 0, +,
*) satisfies A].
"True" is not definable in logic.
Truth about a first order logic theory is definable in second-order
logic, or in set theory. Set theoretical truth is not definable in ZF,
but is definable in ZF + kappa. Truth theory is a vast sub-branch of
mathematical logic.
ISTM it's just a marker "t" for the rules of inference, i.e. those
transformations that preserve "t". Without empiricism or something
like it "t" has no interpretation.
Don't confuse the constant boolean t, which in our context can be
interpreted by 1 = 1, and the predicate "true", which by
incompleteness (à-la Tarski) needs a richer theory to be defined. We
use such richer theory all the times in many part of science, no need
to do "bad philosophy". truth is not a problem when handled with some
caution.
Bruno
Brent
and consistency is too cheap (PA + []f is consistent), that is why
we need both nuances: []p & <>t and []p & <>t & p.
So yes, I like what you say, and it is the main motivation for the
Z1* logic ("intelligible matter", []p & <>t), but the X1* logic
(sensible matter, []p & <>t & p) requires some notion of Truth/God/
One.
Bruno
Jason
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