On 17 Jan 2014, at 21:36, Stephen Paul King wrote:
Another take is : http://arxiv.org/abs/physics/0403031
Deriving laws from ordering relations
Kevin H. Knuth
(Submitted on 3 Mar 2004)
The effect of Richard T. Cox's contribution to probability theory
was to generalize Boolean implication among logical statements to
degrees of implication, which are manipulated using rules derived
from consistency with Boolean algebra. These rules are known as the
sum rule, the product rule and Bayes' Theorem, and the measure
resulting from this generalization is probability. In this paper, I
will describe how Cox's technique can be further generalized to
include other algebras and hence other problems in science and
mathematics. The result is a methodology that can be used to
generalize an algebra to a calculus by relying on consistency with
order theory to derive the laws of the calculus. My goals are to
clear up the mysteries as to why the same basic structure found in
probability theory appears in other contexts, to better understand
the foundations of probability theory, and to extend these ideas to
other areas by developing new mathematics and new physics. The
relevance of this methodology will be demonstrated using examples
from probability theory, number theory, geometry, information
theory, and quantum mechanics.
That is very good, as Cox approach in general except for a lack of
RSSA, which seems to be introduced in Knuth's work.
We don't need it, as all this is covered by the fact that the laws
will indeed be based on the Kripke (and non Kripke) semantics of the
modal logics extracted from the machine discourse. More on this when I
will explain a bit of modal logic to Liz.
Bruno
On Fri, Jan 17, 2014 at 3:26 PM, Stephen Paul King <[email protected]
> wrote:
Dear Bruno,
You wrote:
"Physics emerges from the FPI on UD*. It is an open question if
there is a winner program, but empirically we can bet that the
winner, if it exists, can emulate a quantum universal machine. But
it might be a quantum universal machine + an oracle, or a quantum
machine defined on a ring, etc. We just still don't know."
Does the "winner" need to be absolute (over all possible
tournaments of all possible computations) or could there be winners
with respect to some finite tournaments on finite set of
computations? Think: Nash equilibria.
It seems to me that while there are no Absolute Winners, there can
be "local winners" or "Victors" in tournament between computations
in a finite set of computations that are "interacting" in some way.
Could this give us a coherent notion of a measure?
On Fri, Jan 17, 2014 at 3:20 PM, Bruno Marchal <[email protected]>
wrote:
On 17 Jan 2014, at 12:46, Stathis Papaioannou wrote:
On Friday, 17 January 2014, Bruno Marchal <[email protected]> wrote:
On 16 Jan 2014, at 19:00, meekerdb wrote:
On 1/16/2014 12:11 AM, Stathis Papaioannou wrote:
On 16 January 2014 16:26, Jason Resch <[email protected]> wrote:
The computational metaphor in the sense of the brain works like the
Intel
CPU inside the box on your desk is clearly misleading, but the
sense that a
computer can in theory do everything your brain can do is almost
certainly
correct. It is not that the brain is like a computer, but rather,
that a
computer can be like almost anything, including your brain or body,
or
entire planet and all the people on it.
Jason
I think neuroscientists have, over decades, used the computational
metaphor in too literal a way. It is obviously not true that the
brain
is a digital computer, just as it is not true that the weather is a
digital computer. But a digital computer can simulate the behaviour
of
any physical process in the universe (if physics is computable),
But Bruno concludes that physics is not computable. So does that
imply one should say "no" to the doctor?
Comp explains that physics is not *entirely* computable, that is we
cannot predict all sequences of observations. But that is already
the case thanks to QM (with our without Everett). So no worry!
Are you referring to quantum indeterminacy? But isn't even that
computable from a third person perspective, the UDA generating
every branch of the multiverse?
The UD cannot generate a non computable sequence in one branch, or
through one computation.
But the UD can dovetail on the coupling of one universal number
multiplied (coupled with) a dovetailing on *all* sequences, making
the indeterminacy recoverable statistically by the multiplied
machines. (cf the iterated self-multiplication).
- Computable means generates by one program.
- FPI-recoverable means first person "experienceable" (in the comp
usual sense) by a machine multiplied into infinity in the UD, or in
arithmetic.
Physics emerges from the FPI on UD*. It is an open question if there
is a winner program, but empirically we can bet that the winner, if
it exists, can emulate a quantum universal machine. But it might be
a quantum universal machine + an oracle, or a quantum machine
defined on a ring, etc. We just still don't know.
Bruno
But without Everett, I would perhaps not even have dared to suggest
that comp might be true.
And yes, the computable aspect of nature, even, with collapse,
might eventually be a symptom that comp is false. but up to now,
the most startling aspect of the observable reality confirms the
most startling asoect of the consequence of computationalism.
Bruno
Brent
including the behaviour of weather or the human brain. That means
that, at least, it would be possible to make a philosophical zombie
using a computer. The only way to avoid this conclusion would be if
physics, and specifically the physics in the brain, is not
computable.
Pointing out where the non-computable physics is in the brain rarely
figures on the agenda of the anti-computationalists. And even if
there
is non-computational physics in the brain, that invalidates
computationalism, but not its superset, functionalism.
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