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.
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. 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.
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.
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. 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.
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.
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. There is no change or movement
involved. Arithmetic is completely static, as are the relations between
numbers.
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.
Bruce
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