On 2/26/2012 3:50 PM, Bruno Marchal wrote:
On 26 Feb 2012, at 06:48, Stephen P. King wrote:
On 2/26/2012 12:26 AM, Stephen P. King wrote:
As I was reading an interesting paper, I ran across an equally
interesting quote from Richard Feynman:
‘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 spaces,
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?’
Bruno's idea explains this by showing that an infinite number of
computations "run" though each and every event in space-time (please
correct my wording!).
You intuit well that this need rewording. You are still talking like
I am using the Aristotelian stance as it is the only one that I see
as 1p-consistent in these discussions. The Platonist stance would have
us taking as articles of faith concepts that are not surveyable (see the
previously referenced Laplace draft that I linked previously). I
understand that you want to cover this as 3p by using the Yes Doctor and
the Teleportation discussion, but this is too context relative to truly
be 3p - as it assumes a measure and a particular level of substitution
that is functionally invariant. This is the "book-keeping" problem.
Let me put it is this way. There is no space, there is no time, there
are no events. Only the arithmetical truth. They represent all
computations, including the one which emulates the Löbian numbers'
Physical reality/realities is deep relatively persistent first person
I agree with that claim only at the deepest neutral level. My
argument is that this alone is problematic as you need to show exactly
how the observation of time (measure of change) occurs at the 1p level.
You see to think that the transitivity of numbers alone covers this, but
that is wrong headed as there exist in Platonia all possible strings of
numbers and as Kitada argues, this generates an inconsistency that can
only be overcome by adding a Hamiltonian process to 'regularize" the
inconsistency (making it an oscillator).
it would help us if you understood the problem of time, as it seems
that you do not. Sorry.
So it is not infinite number of computations which run in space-time,
it is space-time observations which emerges from arithmetical
You misunderstand me. I am considering that for each and every 1p
there is an infinite number of computations that (via universality can
act as Universal Virtual Reality Machines capable of generating its
content - D. Deutsch's idea) and, per universality, there are an
infinite number of functionally equivalent physical systems that can
implement these computations. This is consistent with both your idea and
Pratt's. The Stone-type duality here lets us identify the computations
with Boolean algebras side of the duality and the physical systems are
identified with the Stone spaces.
This gives us a natural explanation of how your result is
predictive in the physical sense in that it demands that the physical
world appear as "atoms in a void". We can then generalize the
topological spaces via the Pontryagin duality to cover all types of
observables. The open problem that I see is whether or not there is a
generalization of the Boolean algebra side of the duality; there should
be something like a Pontryagin duality for Boolean algebras.
Adding to my question: Could we equally say that an infinite number
of physical processes are running each and every instance of a
Would Feynman be happy with this answer?
Good question, and I guess the answer is yes, especially if QM is bot
computationalistic correct (= obeying S4Grz1, X1*, and Z1*) and
empirically correct (= non refuted for ever (that's different from non
It is computationally correct but we have to be sure that we obey
the Kochen-Specker and Gleason theorems, which demand that our Q-logic
is not restricted to 2 dimensional systems. Otherwise we are unable to
predict large physical structures (e.g having Hilbert spaces of
dimension < 2). Did you see my query about the LOOMIS–SIKORSKI THEOREM?
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