Hal Ruhl wrote:
>I see it as a simple exercise to derive both quantum mechanics and
>relativity on a discrete physical system that is isomorphic to a recursive
>enumeration theorem cascade in an incomplete, finite, consistent Formal
>Axiomatic System [ifc-FAS]. A cellular automaton if you will. However,
>the incompleteness must be incrementally resolved which makes the system
>discontinuously computational - i. e. non deterministic. In this view
>information [relative] as measured by AIT program length [each such program
>being the proof of an individual member of the cascade] monotonically
>accumulates.
I basically agree with this. But don't confuse Axiomatic System and Formal
system.
(I answer it offline (by error ! Sorry Hal). I repeat my answer because
it still works for the last message by Hal Ruhl.)
>The universe I think is really quite simply described.
>
>Model at: http://www.connix.com/~hjr/model01.html
The same confusion everywhere! You are right when you say that Turing
shows
the equivalence of provability (in some rich system) with
computability, but this is only true from a computability point of view.
Godel and Turing result are better described as showing the abyssal
difference between provability (relative to a formal system) and
computabilility (which is a machine independent concept). I guess you know
that because your own approach is based on that difference, actually.
You should read the original paper by Godel and Turing
(instead of Casti who is not quite rigorous).
Buy Davis 1965. Read it, sleep with it!
Also, if you use the incompleteness for the (perhaps quantum)
indeterminacy,
then you should describe that indeterminacy as bifurcation in the
model 'trajectories', and then distinguish the possible type of discourses
of creature appearing in your model, ...
You seem also to presuppose an undefined part of classical mechanics, and
geometry.
Well your text is long and rather fuzzy. If you are on the right track,
which is not impossible for what I can judge, you should try to be
more pedagogical and learn
the minimal amount of proof theory/model theory to make your
use of incompleteness presentable for a (mathematical) logician ...
Do you know the book by Svozil ? He present some reasonable use of
Godel's incompleteness in physics (orthogonal to mine).
I think also that Girard linear logic could be genuine for your type
of interesting but very delicate mix of proof and dynamics.
Then Hal Ruhl wrote:
>I have been asked to compress my model so as to maximize its
>accessibility. The following is an attempt to do so. The result is rather
>cryptic and has little effort to "prove" anything. It is frequently just
>an application of Occam's Razor.
>
> BEGINNINGS
>
>Start with:
>
>1) Nothing - an empty finite consistent Formal Axiomatic System - an
> fc-FAS.
What do you mean ? A theory is intended for its models. If you take the
null theory you get ... every-models. That is our everything hypothesis.
>
>2) Nothing is incomplete because it can not address the meaningful question
>of its own stability - it is an ifc-FAS.
I don't understand.
>3) To address the incompleteness Nothing becomes Something.
I don't understand.
>4) To address the question of the stability of Nothing, Something must have
>a bifurcation to implement the concept of "Yes" vs "No", or "True" vs
>"False", or "Is" vs "Is Not", or affirmation vs negation. [As in "Nothing
>is unstable." is a well formed statement Yes or No.]
Honestly your shorter version seems completely not understandable, at
least to me. I'm afraid you don't realise the difficulty of the question
you are adressing. Try to imagine you must explain your theory
to a 14 years old student. Define your terms and make explicit your
primitive terms.
The incompleteness phenomena are notoriously misused. It is a reason
to be completely clear on it. Perhaps you should compare your approach
with those presented in the discussion list (Tegmark, Schmidhuber,
Russell,
George Levy, myself, etc.). That would help us.
I insist you should read the original paper on the incompleteness and
insolubility result (Davis 1965, ref in my thesis, URL below)
Bruno
Bruno MARCHAL Phone : +32 (0)2 650 27 11
Brussels University Fax : +32 (0)2 650 27 15
Avenue F.D. Roosevelt, 50 IRIDIA, CP 194/6
B-1050 BRUSSELS Email : marchal.domain.name.hidden
Belgium URL :
http://iridia.ulb.ac.be/~marchal
Received on Mon Nov 06 2000 - 02:52:59 PST