Dear Henry, Charles and Peter,
Apparently my messages did not go through to the FOR-LIST, I can
understand because it could be slightly too technical for FOR. I let
you know my comments, and send it in cc to the everything-list in case
you want reply. We are used to discuss those matter there. Please
don't reply personally because I try to limit the personal
correspondences which force me to explain the same things to many
people. Not only I have not the times, but it makes me forget what I
say to who. Anyway, thanks for the interest.
------------------
1) Post to Henry. The message got a new title-thread: Block-Mind (was:
Free-will)
Henry Sturman wrote:
> >How would an immaterial machine distinguish between a computation and
> >a material computation? What does matter add?
>
> I would think something has to *perform* the computation. For
> example, how can a computer program be executed without hardware?
A computer program can be defined mathematically. And, like number (or
tuple of numbers) can be associated with position in physics, computer
program can be associated with number in computer science. Roughly
speaking by their encodings.
A computer program execution can be defined mathematically too. Like a
sequence of numbers, or a function, can be associated to movement in
physics, a computer execution can be defined by a sequence of numbers,
or an equivalence relation on the set of such sequences.
> >Have you a problem with the physicist notion of block universe, where
> >time does not "really" exist.
>
> No.
That is helpful. Now it is "just a bit of technic" to realize that a
tiny part of arithmetic encodes all by itself a "block-mind", once you
assume the computationalist hypothesis. All the stopping and non
stopping program executions are encoded in the arithmetical truth. So
we can define an inside point of view by the relative execution of
programs existing in arithmetic. It gives a multilayered complex
structure.
Not attibuting mind to the entities appearing there, which look like
you and me here and now, makes such complex structure full of zombies.
A priori there will be too much executions (the white rabbits).
Perhaps even so much that the comp hyp would lead to a contradiction.
Empirically, quantum mechanics entails also a class of quantum white
rabbits or some quantum Harry Potter histories, but quantum mechanics
does provide an explanation why those (quantum) rabbits are relatively
very rare.
> We don't need real space or time, because these are only abstract
> notions specifying the relation between physical/material objects.
> But the objects themselves are real, have to be real. For if they are
> not real, then we are left with nothing.
I think we are left with numbers' dreams. Third person realness
*feelings* develops from or in bunches of very long histories, which
are relatively so numerous and entangled that we can share them. No
doubt we share a very long (cosmic) history. But, assuming the comp
hyp, we have no ways to distinguish "real" from "virtual", nor
"virtual" from arithmetical. We cannot know if we are in a block-mind
or a block-universe. (But they cannot both be computable)
The fact that we cannot make such a distinction is the result of the
"movie-graph" argument. Latter Tim Maudlin has found independently an
argument which shows basically the same thing, and put a serious doubt
to the identity thesis in the computationalist philosophy of mind.
Note that the identity thesis is already in difficult position in most
"Everett-like interpretation" of QM.
> According to http://en.wikipedia.org/wiki/Mechanism_(philosophy) :
> >In <http://en.wikipedia.org/wiki/Philosophy>philosophy, mechanism is
> >a theory that all natural
> >phenomena can be explained by physical causes.
To be short I will say Wikipedia is wrong: the idea that all natural
phenomena can be explained by physical laws is physicalism (or
materialism, or naturalism. Not mechanism).
Mechanism is an assumption in the philosophy of mind, or in cognitive
science. It is the assumption that "I" am a machine. And digital
mechanism (in the weak sense I am most of the time using) is that my
consciousness is "Turing emulable". It means that my consciousness can
be processed through a computer program execution.
For the reason above, the computer execution does not have to be real
or virtual. It can be purely arithmetical. From the point of view of
the program which is executed, there is no possible difference.
Actually the program is "statically" executed almost everywhere in the
block-mind structure.
I am aware that mechanism is the usual theory of mind of the
naturalist/physicalist. And indeed physicalism implies reasonably
mechanism (unless you believe in the wave packet reduction or some
other "collective hallucinations" (Feynman). This explains probably
the confusion between mechanism and physicalism.
But you better should not confuse them, because *digital* mechanism
entails the falsity of physicalism. Or equivalently, physicalism
entails the falsity of digital mechanism, or equivalently digital
mechanism and physicalism are incompatible. By logic alone "I" or "the
universe" cannot be completely described in term of a digital machine.
This shows also that physicalism cannot really entails digital
mechanism, without being inconsistent.
I am not pretending at all that this is completely obvious. It *is* a
bit work demanding of course.
>
> So mechanism implies physical causes, which implies material. And yet
> you deny material. So it doesn't seem comp is a form of mechanism.
OK, but digital mechanism implies only arithmetical causes (like 4
divides n implies that 2 divides n).
Physical causes emerge in the mind of the arithmetical observers, in
some sense.
This emergence is not a purely statistical emergence, but a mixture of
statistical emergence (due to the first person (plural) indeterminacy
bearing on the universal dovetailing or on any block-mind structure),
and of an emergence from that "block-mind structure" which is
constrained non trivially by computer science. See below for
Mandelbrot Set videos. They are probable block-mind structure.
Everett Deutch Zurek explanation of bit (mind) from qubit (matter)
remains correct, but if we take mechanism seriously enough we can see
that such an explanation has a reverse, i.e. an explanation of qubit
(matter) from bit (mind). But the reverse makes the explanation richer
by "explaining" consciousness, "free-will", "infinities" ... and this
by the fact, that computer science can explain how and why universal
machine can be "aware" of the presence of something they cannot be
entirely aware of, and other things of that kind. This has been
already well understood mathematically by Emil Post, Gödel at the very
beginning (but he will forget later) and Judson Webb. Thist is missed
by Lucas and Penrose, for example. Universal Machine can prove their
own incompleteness theorem. When consistent, it is easy
(computationally) for them to infer correctly their intrinsical
ignorance, indeterminacy, etc. For them universe(s) are first of all
big unknown thing(s).
This is an important FOR topics, imo, if a bit critical certainly, in
the sense that it shows that David has not pushed the Turing thread as
far as taking the comp hyp seriously *enough*. No physicists does
that, actually, but David is the closer, well, after J.A. Wheeler.
Digitalism provides also an explanation why, if we look at ourselves
close enough, we should have indirect evidence of many computations/
histories/worlds. Indeed, up to now, the comp hyp is still a priory
too much many-wordly. But QM fits better than Newton in that regard.
Digital Mechanism could be wrong, of course, but the "easy white
rabbit refutation" is blocked by the non triviality of mathematical
computer science. It is a priori too much many-wordly, but no more
easily prove to be so.
*I* could be wrong too, of course. That why I have submit this work as
a thesis, or as papers, and although there are few people courageous
enough to study such an extreme interdisciplinary subject, (which
traverses cognitive science/philosophy of mind, physics, computer
science, mathematical logic), those who have done so either get the
point, or get the idea that it could be interesting to find precisely
where an error could be.
As a possible help for having some idea or image of the "block-mind"
or Universal Deployment, and its non triviality, you could perhaps
take a look on the Mandelbrot Set.
Penrose has conjectured that the Mandelbrot set in undecidable (in a
sense close to Turing), and this has been proved by Blum, Smale and
Shub. Well, much before Penrose I have made a stronger assumption
which is that the Mandelbrot set is "creative" in the sense of Post.
That means mainly "Turing-Universal". I am still conjecturing this.
If that is true, the Mandelbrot set would give a compact and connexe
plane representation of the "block-mind", or of the Universal
Deployment.
So you could contemplate those beautiful movies below, bearing in mind
they give only a third person view of the block-mind.
Unlike the Universe of Sets, or even the possible physical universe
(in most current theories), the block-mind *does* contain itself or
versions of itself, indeed with all possible variations.
You will see that this is indeed the case for the Mandelbrot Set.
Indeed, the Mandelbrot Set contains itself everywhere. Note that each
of the following are generated by a very simple program (mainly an
interation of z := z^2 + C, for each C in the complex plane and
deciding if it goes to infinity or not) + zooming on the result. The
border of the set is infinitely intricate and "complex" (sorry for the
pun). The color measures the quickness of the way you go to infinity
in that iteration, and it measures in that way how close you are to
the Mandelbrot set.
http://www.youtube.com/watch?v=a1MQGVFxN64
http://www.youtube.com/watch?v=CsUq4qVi_Mg
Look at those instructive little musical pieces of art:
http://www.youtube.com/watch?v=BUhFLpC2EfU
http://www.youtube.com/watch?v=G0nmVUU_7IQ&feature=related
http://www.youtube.com/watch?v=1l9N5a0nxuQ
I hope this could help in this highly difficult subject.
Bruno
-------------------------------
2) Message to Charles:
On 29 Sep 2008, at 23:40, Charles Goodwin wrote:
> > From: Fabric-of-Reality.domain.name.hidden [mailto:Fabric-of-
> > Reality.domain.name.hidden] On Behalf Of Henry Sturman
> >
> > And how do natural laws arise from numbers? How do h, c and other
> > physical constants arise out of numbers? Would not many different
> > worlds with different laws be consistent with numbers? Or is that
> > what you are arguing? A sort of plentitude? But in any case, can you
> > give an example of how a physical process arises from integers? It
> > seems integers is just a list of numbers increasing 1 at a time.
> > That's not very complicated. How do we get from something as simple
> > as counting numbers to, say, the law of Gravity? Or a molecule? Your
> > theory seems rather abstract, and it would be more helpful if your
> > explanations were more specific. And how does the mere existence of
> > numbers create reality? If I write 1, 2, 3, 4 etc. on a piece of
> > paper, surely that doesn't create a reality? Again I come back the
> > the issue, there must be some kind of hardware, matter, physical
> > stuff, some sort of stuff, which actually *runs* the processes which
> > are hapening in reality?
>
> I too would love to hear an answer to this. Of course I believe we are
> dealing with numbers so large that they couldn't even be written
> down - even
> a formula to generate them couldn't be, in fact. Perhaps those sorts
> of
> numbers look like reality when seen from inside...?
I would say it is more due to the fact that little numbers can
generate complex gigantic realities.
The big numbers are more in the generation steps than in the original
seed. Stable realities should be filtered from inside.
Digitalness prevents the need of time, the digital notion of step (a
cousin of the function n+1) is enough.
It is also more in the many relations between numbers than in the
numbers themselves.
See my hopefully not too much lengthy answer to Henry. It is a
delicate point.
Bruno
---------------
3) Message to Peter
On 30 Sep 2008, at 19:08, Peter D Jones wrote:
> No form of arithmetic proves Platonism.
In the premisses I am using platonism, not Platonism. In the
conclusion something akin to some text of Plato appears, but in the
conclusion only.
platonism (with a little "p") is just that we accept the principle of
excluded middle in arithmetic. It is the usual platonism of the
working mathematician.
> Here's the error: substitutible doesn't mean substituted,
> and here is no first-peson inderminacy wihout actual substitution.
Once comp is assumed, it can be shown that "substituted" means
"substitutible from inside". Like "real" means "possible from inside".
Like "now" means "sometime from inside". It is an indexical and
relative notion. I don't say that this is obviously so. It come from
the fact, that, as I said to Henry, machine cannot distinguish "real"
from "virtual", from "arithmetical". See my url for detailed
explanations.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Sun Oct 05 2008 - 11:36:16 PDT