On 25 Jun 2016, at 03:12, Jason Resch wrote:
On Fri, Jun 24, 2016 at 9:56 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 24 Jun 2016, at 03:25, Jason Resch wrote:
On Thu, Jun 23, 2016 at 12:55 PM, John Clark <johnkcl...@gmail.com>
wrote:
On Thu, Jun 23, 2016 at 1:34 AM, Jason Resch <jasonre...@gmail.com>
wrote:
>> I would say it would have to have SOMETHING physical as
we know it or it wouldn't be another physical universe as we know
it.
> So according to you, does every physical universe has to
have hadrons, electrons and photons, and 3 spatial dimensions?
No, according to me every physical universe must have
something physical in it or it wouldn't be a physical universe.
> What in your mind delineates the physical from the
mathematical?
"Mathematics" is the best language minds have for thinking about
the physical universe.
And "physical" is anything that is NOT nothing.
And "nothing" is anything that is infinite, unbounded,
and homogeneous in both space and time.
So if a Game of Life computation qualifies as a physical universe,
I am guessing so would other cellular automata systems would. Some
linear cellular automata systems are even Turing universal: http://mathworld.wolfram.com/UniversalCellularAutomaton.html
When we envision (imagine) a GoL emulation, we interpret it as a
grid of cells with changing states, but an equally consistent view
would be to imagine the grid as a binary number, whose bits flip
from one step to another according to finite rules. For example,
the game tic-tac-toe (a.k.a. naughts and crosses) is often
envisioned as completing a line, or diagonal with X's or O's, but a
mathematically equivalent view of the game is the players complete
for selecting unique numbers from 1 to 9, such that the sum of
their selected numbers adds to 15 ( https://www.mathworks.com/moler/exm/chapters/tictactoe.pdf
).
All this is to say that a "physically existing GoL universe" is
from the inside of that world, no different (in any testable way)
from a recursive function operating on an integer. So can anyone
truly differentiate a "physically existing GoL universe" from a
"platonically existing recursive computation" when both are
equivalent and for all intents and purposes identical--sharing all
the same internal relations isomorphically?
If a GoL universe exists and contains a Turing machine executing
the universal dovetailer, no conscious entities within the programs
executed by the universal dovetailer could ever know their ultimate
substrate happens to be a GoL universe.
That would even have no sense, as here the GOL would only be a tool
for us to have some precise view of the UD. In fact we could not
distinguish the UD made by that GOL from the UD made by a GOL made
by a UD made by a Diophantine polynomial. Fortunately, the measure
is formalism independent. We need one, but anyone will do. Then it
happens that we all believe, in the relevant sense, in one of them,
when we decide to not take our kids at school when a teacher told
them that there are infinitely many primes.
Wouldn't different formalisms lead to different frequencies of
occurrences of different programs? It is not immediately clear to me
that it wouldn't.
By the compiler theorem it would not. if phi_i and phi'_j are two
computable enumerations of the partial recursive functions, there is a
computable function h such that for all phi_i, phi'_(h(i)) = phi_i,
and vice versa. The relative computations will be the same in both
structure.
You can see this in this way, imagine than a *special* UD is needed,
then, in all others UDs, that special UD will be executed, and has to
be the solution of the winning measure problem when we start any UD,
which exists independently of us, as we assume the equivalent of the
sigma_1 arithmetical reality (the "arithmetical UD"). So, if a special
UD is needed, it is part of the mind-body problem to justify its need
from any other UD base.
Now, the closure of diagonalization, and the Turing equivalence
between all universal machine, and all creative sets (Post), and 1-
complete set, and m-complete set, assures the solidity and sense of
Church-thesis, and of the very general notion of universal system. To
choose one among all, to explain what we see, is about the same
cheating than doing physics and saying that's the fundamental reality.
Computationalism made obligatory to justify the appearances of this or
that type of reality (the biological, the physical, the chemical, the
psychological, the theological, etc.) from the first person
intrinsically internal to any universal system.
All universal numbers reflects all universal numbers, and all have all
computable and non computable relations between each others, with
relative relations invariant for the choice of the universal
dovetailing.
Note that physics cannot been a priori Turing emulable, as it is
given by a first person limit on the FPI on the whole universal
deployment (entirely determined by a tiny part of the arithmetical
reality). The miracle here is that an infinite addition leads to
subtraction of probabilities, a bit like with Ramanujan sum. The
explanation of this is in the math of self-reference.
Is this without assuming imaginary measures? Or do imaginary numbers
somehow fall out of the infinities?
Well my comparison with Ramanujan formula (1+2+3+4+5+6+ ... = -1/12)
was an analogy.
That was just a way to suggest that the argument: "with comp all
probabilities are added, but with QM sometimes they are subtracted (or
their amplitudes), so comp cannot lead to QM" is an (erroneous)
extrapolation from the finite to the infinite.
Then such argument forgets that we have to structure the probability
space from the UDA-definition of "observable" translated in arithmetic
using only what a machine can prove and guess about itself.
We get three versions of this: []p & p, []p & <>t, []p & <>t & p.
Which makes 5 "physical theories" ("[]p & p" does not split in two
theories on the G-G* separation). When p is sigma_1, as it should be
to work on the UD basic ontology (the universal computation, the
splashed Turing machine, as I call it once, the universal dovetailing,
or just the sigma_1 arithmetical reality, actually already obtained
semi-recursively by the weak theory RA (see three nice versions in the
Tarski, Mostowski, Robinson paper.
So, to sum up: ontology = RA, and the epistemology is given by the
belief system having induction axioms. So the observer are PA, ZF and
all recursive (machine) sound extensions of RA, having enough
"induction power" (beliefs in induction axioms, like (P(0) & (n)(P(n) -
> P(n+1)) -> (n)P(n)). (I abbreviate "for all x" by (x).
I am interested in the arithmetic of enlightenment. My oldest theory
was that this occurred in PA, when PA proves PA's incompleteness, i.e.
the löbian knowledge of personal incompleteness.
My less old theory was that it occurs when the machine recognizes
itself in the primary hypostases (p, []p, []p & p), and "abandons" the
material hypostases (the one with "<>t" in). But the salvia experience
suggests (!) that it is when PA reminds being RA, and abandon the
induction axioms, which makes it the exact contrary of my oldest theory!
Everything is very tricky here, but the use of the G and G* separation
helps to avoid the easy "blasphemes" (asserting truth which get wrong
once taken as an axiom or theorem).
I still don't know if making the induction axiom epistemological only
is mandatory or obligatory. That might be a candidate for being
absolutely undecidable for all machines.
I am amazed that Nelson could believe that PA was inconsistent, and
that others took the time to find the bug in his proof! The bug has
been found of course (of course?).
Is PA consistent? Personally I have few doubt it is, but can I prove
it? Of course I can prove it, but only by using something less
trustful than PA. Humans have usually much stronger beliefs than PA.
We are usually OK with analysis or second order induction (where P(n)
above would mean (n belongs to the (arbitrary) set P), accepting a
transfinite (2^aleph_0) induction axioms at once!).
From it you can prove easily the soundness (and consistency) of PA,
and study the models of PA.
Bruno
What is a Number that a Man May Know It and a Man that He May know a
Number? (McCulloch)
Jason
Bruno
Jason
>>Cells and particles are physical.
> Would you say it is a particle even when the particles have
only 1 bit of information associated with them "exists in this cell"
Yes I would and that's why you're not talking about nothing,
you're talking about something, you're talking about the physical.
You use plural words like "particles" and "them". So there is more
than one. So neither particles nor cells can be infinite,
unbounded, and homogeneous in both space and time. So it can't be
nothing. So it must be physical.
John K Clark
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