On 03 Apr 2015, at 05:55, Bruce Kellett wrote:
Bruno Marchal wrote:
On 02 Apr 2015, at 15:04, Bruce Kellett wrote:
Bruno Marchal wrote:
On 02 Apr 2015, at 04:08, Bruce Kellett wrote:
Emulation is a dynamical process in time. I wonder where you get
a time variable for your UTM.
By a variable on the computational steps. It has nothing to do
with a physical time a priori.
What variable? A simple numbering of steps? But that will not
work, or at least, you have hidden an assumption of an external
time in your notation.
The external time is given by the universal machine running the
computation. It can be the basic level (elementary arithmetic, or
the universal dovetailer), or it can be some other universal layer,
running on some other universal layer, running on some other ....
running on the basic level.
At the basic level, we have the block mindscape, like the UD* (the
infinite "cone" of all computations).
This does not do the work you require of it. See below.
"At the end of step 27, move to step 28." That contains an
implicit notion of time -- 'ending' and 'moving' are temporal
concepts. I do not see that you can remove all traces of the idea
of an external temporal parameter. Otherwise the machine could
just halt arbitrarily at some point and never know that it had
halted.
I think you ned to flesh your ideas here out a great deal more.
Well, this is a forum, and I explain things already explained with
all details in much longer text (which sometime does not help,
because busy people tend to skip even more the long texts nowadays).
Let me try to help a bit though. Fix some universal programming
language, like Fortran, say. Enumerate all programs computing
function with 1 argument, p_0, p_1, p_2, ....
Let us denote by [p_i(j)^k] the kième step of the execution of the
ième program on argument j, by the universal dovetailer (which
dovetails then on all such [p_i(j)^k] .
Then we can define, indeed already in Robinson arithmetic, a
computation by a sequence of such steps, when i and j are fixed. So
a computation is given by the sequence
[p_456(666)^0]
[p_456(666)^1]
[p_456(666)^2]
[p_456(666)^3]
[p_456(666)^4]
etc.
This sequence is a subsequence of the general universal
dovetailing, which dovetails on all [p_i(j)^k].
It is a computation, only in virtue of the universal dovetailing,
and the universal dovetailing can be defined in arithmetic. I can
translate the proposition "the UD access to [p_345(898786)^89]"
entirely in term of arithmetic, using only the notion of addition,
multiplication, successor (of natural numbers) and 0, and predicate
logic.
The only external time used is the ordering of the natural number,
which is easily translated in arithmetic: x < y means Ez(x + z) = y).
OK?
I got this much from reading your paper and other things you have
said. But this, at best, provides and ordering (indexing if you like)
Ordering is good, for the step (here k) of the computations. Indexing
is usually used for the enumeration of the p_i.
on the computational steps. It does not provide a time parameter.
I agree.
In fact, it is entirely static, and you get no more than some
ordering imposed on sequences that can be found in any normal number.
you get the proof that the relations between numbers emulate some
computation, and the emulation comes from the "trueness" of this, (be
it realized in a universe, or in the arithmletical reality). The
emulation does not of the syntactical description of the computations,
which we need only to refer to those relation., but which alone in the
counting algorithm does not emulate any computations (in the precise
technical sense of "emulate").
The real numbets are even more full of such description, yet that
can't emulate a universal Turing machine. Diophantine polynomials on
the reals are not Turing universal, yet in the integers, and the
natural numbers they are.
Let me be more specific in my criticism.
In step 7 of your argument you introduce the dovetailer. But you
then say "Suppose now, for the sake of argument, that our concrete
and 'physical' universe is a sufficiently robust expanding universe
so that a 'concrete' UD can run forever..." Why do you need infinite
time in an expanding universe to run the dovetailer if it is not a
physical machine?
?
The 'concrete' UD is a physical UD.
By the way, I did it in 1991. I implement the UD in Lisp, and let it
run during two weeks. In step 7, I add the following assumption:
1) there is a primitive physical universe
2) it run the UD.
Then you can understand that such a universe needs to be extending for
ever, and be robust, because the universal dovetaling involves bigger
and bigger programs using greater and greater inputs.
The game of life of Conway is Turing universal. The UD can be
programmed by a two dimensional pattern in the game of life. Then its
dynamics gives a third dimensional *infinite* cone. To run that,
without stopping (the UD is a program without input and never
stopping) you need an infinitely expanding universe, and robust enough
for you to make the computations). I am not sure that such UD
execution is physically possible. But that is not relevant for the
reasoning.
You put the words 'physical' and 'concrete' in scare quotes, but
that is merely a device to mislead -- you actually are talking about
the everyday physical, concrete universe that we all know and love.
There is no Platonia here, or else why worry about time limitations
and require an infinite expanding universe in order to get all your
computations in?
To define the protocol of step seven. If you have agreed with step 6,
in step seven, you know that to predict your future first person
experience you need to take into account the infinite union of all all
finite computations going through you actual state.
Step seven shows this:
(comp + "it exists a physical universe running the universal
dovetailer")
implies
physics is reduced to statistics on computations. That is physics
emerges from a tiny part of the arithmetical reality, once you accept
Church thesis and the "yes doctor".
It means we have to extend Everett multipication of the observers into
the whole sigma_1 arithmetic. It is big. It contains all
approximations of all computable physical processes, notably. This
include the quantum computations, as they don't violate the Church
Turing thesis, but also all variants, and as I think you have intuited
in some post, we are confront to an inflation of prediction, except
that the universal dovetailing is highly mathematically structured,
and the existence of that inflation is an open problem.
In step 8 you introduce the idea that the 'physical universe' really
'exists' and is too small, in the sense of not being able to
generate the entire UD*, nor any reasonable portions of it. You call
this move /ad hoc/ and *disgraceful*, but that is again just a
rhetorical trick to divert attention from the fact that you really
are talking about a physical computer running in our physical
universe.
Not at all. A this stage, I imagine someone who want escape the
conclusion of step seven, by saying that the universe is not rich
enough to run any big portion of the UD activities. In that view,
physics remains of unknown origin, but this *apparently* saves
physicalism from the 1-7 argument. MGA shows that this won't work.
The point of the MGA will be that if you use a little physical
universe to block the conclusion of the step seven, you have to accept
some "absurdities", like: recording can be conscious, or the presence
of inactive neurons have an active role in the consciousness, or even
all experiences supervene on all machines, etc.
MGA makes "matter" being a god-of-the-gap.
Some people stop at step seven, notably in this list which find
"everything" more easy to assume than this or that particular thing.
calling a little universe is "ad hoc" for the average "everythinger".
So at step 8, I handle the case the UD is not run at all. I show you
need to put magic in matter for matter capable of winning a game
played in arithmetic since always.
In which case, at any finite time from the beginning of the universe
the dovetailer will, in general, not have generated any sequence of
computations that would correspond to us or anything else. Far from
being a disgracefully /ad hoc/ manoeuvre, this actually undoes your
whole enterprise.
You have missed the point. At step 8 the UD is not run in the
universe, but it is supposed you already undersatnd that the UD is run
in the arithmetical reality. If you agree that 2+2=4 independently of
you, you need to agree that machine 6796540023 run program 24000000000
on input 0. And this infinitely many "times", with all the relative
situations infinitely distributed themselves.
The only reason that the dovetailer might have to worry about time
limitations is if it is actually a physical computer.
It is at step 7.
It is not at step 8.
You need to enter more in the reasoning. I am not sure that you have
seen that the reversal occur at step seven.
In that case the indeterminacy is of the same type as step 3, 4, 5, 6.
Leading to the conclusion that physics is (re)defined by a statistic
on all computation in the indexical way.
Physical computers have to contend with such things as physical
laws, the finite speed of light, the properties of materials, the
generation of heat (entropy) and the need to remove that heat to a
safe distance before everything melts down. If your computer is not
a physical device, then it has none of these limitations, and there
is no such concept available as the 'speed' of the computation, the
'time for each step', or anything of this sort.
Sorry but that exists. There are many speed-up theorem in computer
science. You don't seem to have read many books on computer science.
There are normal form theorem for computation, they can all be done
doing simple procedure on the result of one exploration, and they have
machine independent law for memory space, memory time, and many other
type of measures.
To program a universal dovetailer, you have right at the start to have
good notion of "next step" for the computation, as you will dovetail
on all "next step" for all computations, infinitely many times.
From our external concrete perspective, the whole thing is
instantaneous, or it enters statis at some point and gets nowhere.
For a non-physical computer these things are equivalent.
How could the creature inside feel the difference. They can see it
indeed, that is what I show, but they can't detect the difference
between a computation being physical (and what does that mean, also)
or being arithmetical.
So without a physical computer you have no dynamics.
We have all dynamics, like in a block universal quantum universe. Too
much perhaps, but that is what I show we need to verified.
A mere ordering of states is still a static thing, and the
dovetailer does nothing useful that could not more easily be done by
referring to a normal number.
It does computation, which is exactly what is needed to support you
once you said yes to the doctor.
Referring to a normal number is simply NOT a computation.
This is why I have said several times in previous posts that you
rely on an underlying notion of physical time, and an underlying
physical computer, in order to make your computation dynamic and not
static.
This means you are not aware of (theoretical) computer science. The
dynamic of the digital machine are governed by the laws of
arithmetic. This can be proved, and has been proved, and is already
largely present in Gödel 1931, even if he will miss the thesis of
Church and Turing.
What you say above does not let you escape from this conclusion, it
merely reinforces it. The problem of time is your undoing.
I thing you must study some book in computer science.
My favorite "shorter" and "deeper" explanation is given in the book by
Matiyazevic, section 5.5, Diophantine simulation of the Turing machine.
When a computation is emulated in arithmetic, it is not in the
description of the sequence of states, it is in the trueness of the
arithmetical relation that makes those states a computation.
Pressburger Arithmetic (the numbers + the law of addition) is already
a very powerful theory, but it cannot simulate a Turing universal
machine. RA can, having addition and multiplication.
In a sense, in arithmetic, we have as many times than we have
universal numbers.
You must study the paper more seriously. I think you missed step
seven. You might need to study more of computer science.
Also, why not say "I don't understand this ... ", in place of "I have
refute your point".
How do *you* predict any (first person) event, in the protocol of step
seven?
(Nice that it looks you have no problem with step 0-6, though, you
don't say much on those).
Bruno
Bruce
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