On 06 Apr 2015, at 13:25, Bruce Kellett wrote:
Bruno Marchal wrote:
On 06 Apr 2015, at 07:02, Bruce Kellett wrote:
Bruno Marchal wrote:
On 05 Apr 2015, at 01:19, Russell Standish wrote:
Then what is your definition of a recording? In my eyes, UD* is a
recording, particularly a finite portion of it, such as the first
10,000 steps of the first 10,000 programs.
You confuse description of computations, which exists in the
"movies" obtained by filming the boolean graph, and the
computations themselves, with involves semantic, that is a
reality (be it the static standard model of Peano Arithmetic) or
a physical reality.
Where is the dynamics necessary for computations themselves (as
opposed to descriptions of computations) in the static standard
model of Peano Arithmetic? I know where the dynamics reside in
physical reality.
In the truth of the elementary relations which implements a
relation between some universal Turing system (universal number)
and the program that is implemented.
That 'truth' is static. The implementation of a program might be
dynamic, but that is because it is implemented on a physical
computer that has a physical clock cycle.
No, it is dynamic in virtue of a universal machine running it step by
step. The physical clock cycle is used in physical implementation, but
other can use computable injection in N.
I remind you that 'dynamic' means "of or relating to force
producing motion" or "active, potent, energetic, forceful;
characterized by action or change." In other words, the opposite
of static.
That is a physicalist account of dynamics. It could be the correct
one---I don't know. But even if is the correct one, you have to
agree that a diophantine approximation of, let us say the evolution
of the milky way + andromeda can exists (unless you presuppose at
the start that the Milky Way + andromeda use non computable
functions).
I don't know that is uses functions at all. Even the three-body
problem in Newtonian gravitational dynamics does not have a general
closed form solution.
Which is a symptom that its set of rational approximations might be
Turing universal.
But the inverse is easier to prove: a Turing universal machine can
emulate all rational approximations of the three-body problem.
It is not a 'function' in any standard sense. The system can only be
approximated by perturbation theory, and the calculations are
different for every set of starting values. There is not a
'function' to be evaluated over some input domain.
?
What is the set of staring values, if not the domain of inputs?
So your type of dynamics would exist somewhere in the dynamics of
some game-of-life pattern, and would appear in the running of a
game-of-life
"Running" a game-of-life? Any dynamics there comes from the running
-- the clock cycles of the computer on which it is run. It is not
intrinsic.
I am sorry but you are wrong on this. Computations can be defined in
the arithmetical language. It is not intrinsic, but it is intrinsic
relatively to a universal number, or to the system assumed at the base
(arithmetic, or combinators, etc).
pattern emulating the universal dovetailer, which run all game-of-
life pattern. Then it would exist in the block-description of the
dynamics (digital, discrete) of the universal game of life patter,
that you can see as a static infinite cone of some sort. In that
case, your acceptance of a block universe, and the way to recover
the dynamics internally would work for that pattern.
No, it doesn't work like that. The block universe idea arises from
special relativity theory -- the fact that Lorentz transformations
alter the way in which space and time are interrelated. There is no
universal 'time' parameter in that picture, only a local variable
't' that depends on the frame of reference.
But that will occur for all emulation of evolving interacting set of
universal machine. The UD is intensionally universal: sigma_1
arithmetic emulate all computable processes, indeed, even with
oracles. Different notion of times can be defined from inside, in a
relative way. Lorentz invariance is a particular case, and it is not
excluded nor directly relevant with the fact that arithmetic emulates
all computable dynamics.
If you accept computationalism, you can understand that a machine
emulated cannot feel the difference if the is emulate by a physical u,
or an arithmetical u. Yet the point is that by observation they might
find evidence that comp is false, because below its computationalist
substitution level, the math has to be a sum on all computations (and
in that sense QM confirms computationalism).
The useful dynamical concepts in relativity are the Lorentz
invariants -- quantities that do not depend on the way you slice up
separate time and space variables. Time is part of a coordinate
system, and you do not have a space-time model that can be spanned
by a coordinate system.
You have still local tensor and metric (g_ij). But if you accept
computationalism, the brain dynamics is captured at some level by a
Turing emulable process, and this one is provably emulated in
arithmetic. If you believe that 2+2=4 independently of you, then you
must believe that the emulation of your current emulation existe,
infinitely distributed in the sigma_1 arithmetical reality.
The FPI makes this a bit more complex, because from the point of
view of the self-aware entities emulated in the universal pattern,
their "real future" is not really defined by some location in the
pattern, but from all their infinitely many locations in that
pattern.
That is, again, an entirely static concept. You have not introduced
any time parameter.
Yes, I do. It is the variable x, which is for the natural number.
My clock is static, but that's the point: the time are illusion/
experience related in the computations. Sigma_1 arithmetic contained
already a web of dreams. So much that we will have a problem to solve,
actually.
To be more precise, I should explain you how "computations" and
"emulation" is defined in arithmetic, in term of the truth of
elementary number theoretical relations. A computation will exist
through the fact that it is true that some numbers divide some
other numbers, and other facts like that. On the contrary, a
description of a computation will be a number from which we can
extract the description of a sequence of states, but that is
different from the states existence being the result of a set of
true relation.
So you can use these terms in that way. But that does not make
'computation' a dynamical concept.
It is not a physical time related concept. But computer, or universal
number (or universal combinators) needs only a discrete static "time":
0, 1, 2, 3, ..
There is no change or movement involved. Arithmetic is completely
static, as are the relations between numbers.
Block universe are static too. It is the point of a relativity theory.
Time and space comes from comparison between clock and meter, nothing
can prevent the sigma_1 reality to emulates all those comparisons ,
and by assuming computationalism, of the conscious entities which make
sense of the comparisons.
It is very much like the difference between the Gödel number of the
sentence "3 divides 6", and the true fact that the number 3 divides
6. The first one is a number, and needs some encoding; the second
is a truth involving the number 3 and 6, and which does not needs
any encoding to be true (only to be communicated).
'Communicated'? A transition from a state of not knowing to a state
of knowing? But that is a temporal concept, and you have no time
variable in your model. The truth that 6 is divisible by 3 does not
involve time in any sense at all. It is not a dynamical calculation
unless you implement the operation on a computer, and even then the
'truth' is static, it is only the computer (physics) that is dynamic.
Each universal system defines a sort of absolute timing, by the
stepping of the computations that it emulates.
Most such computations are even irreversible: from an output = to 5
you can't guess from + and the u, if the inputs were 1 and 4 or 2 and 3.
The problem is more in justifying the reversibility of the apparent
"natural universal computation", the universal unitary transformation/
quantum computers.
A computation is a dynamic. You can always describes them by a
sequence of states S1 -> S_2 -> S_3 -> ..., with the "->" carried by a
universal number.
You want a dynamic like in physics, a function from time to space, but
in computer science, and to understand the problem here, the dynamics
are given by function from N to "mind states".
You need to give magical ability to a turing machine so that she can
distinguish (by its consciousness, in a first person way) the
difference between a physical emulation, and an arithmetical
emulation. The physical will give rise to the right measure, but not
by magic, only because the physical is run by the sum on all
computations below its substitution level.
But all this is not needed to get the reversal in step seven. So I
guess again that you are OK with step seven and see that if a primary
physical universe exists and run the UD, then physics is reduced to
arithmetic (seen from inside). Do you see that. With occam, a believer
in comp can already stop here, and work on the measure problem.
But a phsysicalist can still conclude that there is a primary unique
universe, and that it can't run the UD, nor any significant part.
The step 8 address this situation and shows precisely why invoking a
primary physical universe makes it magical, with neuron needing
prescience, and movie getting experiences, and indeed nothing getting
all experiences.
It is good news, as it suggest we might understand the origin of the
physical laws, from non physical things, the gluing properties of
universal numbers' dreams.
Bruno
Bruce
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