A second answer, more precise.
On 25 Jun 2016, at 03:12, Jason Resch wrote:
On Fri, Jun 24, 2016 at 9:56 AM, Bruno Marchal <[email protected]>
wrote:
On 24 Jun 2016, at 03:25, Jason Resch wrote:
On Thu, Jun 23, 2016 at 12:55 PM, John Clark <[email protected]>
wrote:
On Thu, Jun 23, 2016 at 1:34 AM, Jason Resch <[email protected]>
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.
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?
Normally, the imaginary numbers and the whole quantum linear stuff
should come from the semantics of the logic of the observable (Z1*,
etc.).
By incompleteness, you can't take []p as "p has probability one". You
might be in cul-de-sac world, where the probabilities make no sense,
and that is why we add the "<>t" conjunctive attachment ([]p & <>t) to
get the bettable. On p sigma_1, we get a quantum logic (Z1*), and if
it is correct, this should have a semantics such that we get the
equivalent of Gleason theorem, and the quantum formalism.
Now we get three quantum logics, even five, generalizing the notion of
quantum logic.
It seems the only way to avoid the white rabbits in the infinite
multiplication of computations consists in phasing them, going from
from sum of Ht to sum of e^iHt. For this you need a good proximity
space and a cosine. The universal machines got the proximity space,
and the quantization, but it is a hell of a difficulty to extract the
cosine, and the imaginary numbers. The quantum win by phasing out the
relatively aberrant computations. Intuititively.
If number theory get closer to arithmetic, like with Matiyazevich,
Analytical number theory might put light on this too. Number theorist
loves the complex plane, as it provide many information already on the
diophantine equation. There will be something like analytical computer
science. Better to get -1/12 than a computer crash :)
Bruno
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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