Re: Bijections (was OM = SIGMA1)

From: Bruno Marchal <marchal.domain.name.hidden>
Date: Mon, 4 Feb 2008 15:21:36 +0100

Le 30-janv.-08, 13:43, Mirek Dobsicek wrote (in different posts):




> 2\ Bruno, you recently wrote that you do not agree with Wolfram's
> Principle of Computational Equivalence. As I understand to that
> principle, Wolfram says that universe is a big cellular automata. What
> is the evidence that it is unlikely this way?



Wolfram is very vague about his Principle of Comp Equiv (PCE):
http://www.wolframscience.com/nksonline/page-6-text

The problem is that Wolfram seems to take a "natural world" for
granted, and does not seem to be aware that each of us (us = Lobian
machine or even just Lobian entity) cannot discern about 2^ALEPH_0
locally equivalent computations.
So Wolfram is either not aware of the consequence of the
computationalist hypothesis, or not aware about what we can expect
nature to be after knowing that Bell's inequality are violated, quantum
measurement "problem" and its MW "solution", etc.

Wolfram's idea is inconsistent for the same reason that , "as a TOE"
Schmidhuber's constructive approach is inadequate or at least
incomplete.
Such theories entails COMP. But COMP entails the physical world cannot
be entirely a constructive structure. Physics or physicalness emerges
from an infinite sum (the nature of which is still under scrutiny) of
computational histories, observed in relative perspectives (points of
view). There is no reason to believe this leads to a constructive
universe. On the contrary, its "geographical and local aspects" could
have verifiable non computational feature (like when we repeat spin
measurements for example).
The problem is that, like many, not only Wolfram and Schmidhuber, seem
to take a physical universe for granted, but they take also a sort of
identity thesis (brain/mind) for granted. The Universal Dovetailer
sequence of thought experiences is supposed to explain in all details
why such an identity thesis just can't go through ...

Now, Mirek, I don't know if you really want to dig on the UDA and the
"philosophy-of-mind/theology" issue, because you can enjoy the math per
se. Many people dislike or get stuck in front of the idea that comp
makes us duplicable, or by the same token that QM makes us 100%
duplicable too, although not 100% clonable. But the UDA does explain
why we have to take into account the different points of view (first
singular, first plural, third, zeroth, ... ).

The UDA, in english, can be found here:
   The Origin of Physical Laws and Sensations, (Invited Talk SANE 2004).
Click on that title, or copy the following in your browser:
http://iridia.ulb.ac.be/~marchal/publications/
SANE2004MARCHALAbstract.html
(if you study it I would suggest you print the slider too, so that you
could perhaps tell me which step you would find hard to go through
....).


> Uu, reading about cardinals and ordinals on Wikipeadia did not helped
> me
> at this point.
>
> Could you please elaborate more on this? Of course, only relatively to
> its importance towards CT ...


I will. Slowly because I will be more and more busy, and also I should
write papers, I should extend a bit the Plotinus' one, correct the typo
error, submit, etc. I still don't know if it is the physicists, the
logicians, or the theologians who will grasp the UDA/AUDA highly
interdisciplinary or trans-disciplinary reasoning ... Got not enough
feed-back ...
I will also solve the combinator "crashing" problem: it does illustrate
another form of use of the diagonalization idea ... (this is a hint)
...

Best,

Bruno

http://iridia.ulb.ac.be/~marchal/

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Received on Mon Feb 04 2008 - 09:22:21 PST

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