Hi all,
I suddenly feel sorry putting too much burden on just one
correspondent in the list, and I would appreciate if someone else
could propose answers or any remarks to the exercises.
I am also a bit anxious about Kim, who is the one who suggested me the
initial explanations, but who seems to have disappear right now.
There is also some sort of burden onto me, because it is hard to
explain "the real thing" concerning the seventh step, without
explaining or just illustrating at least some relevant portion of the
mathematical reality: mainly the unexpected mathematical discovery of
the universal functions, sets, numbers, systems, language, machine ...
I don't mention the absence of drawing ability which does not help.
Given that the list raised from a critical approach toward Tegmark and
Schmidhuber, I was usually assuming some knowledge in math and
physics. What was harder for me in the beginning was to motivate the
use of "philosophy of mind" notions, notably the key distinction
between the first and third person point of view. Then UDA should make
you realize how non obvious the relation between the first person and
the third person can be once we assume comp (= work in the theory
comp). My original goal was to illustrate that once we assume digital
mechanism, we can build a "scientific formulation" of the mind-body
problem or the consciousness-reality problem. We probably depart from
Tegmark and Schmidhuber, or Wolfram, by taking into account that
making comp explicit entails a delocalisation of the 1-person
relatively to the third person computations, and makes the identity
thesis, a most complex equivalence relations.
The knowledge of most people participating to the discussion is very
varied, due to the extreme transdiciplinarity of the subject, and the
interest it can evidently have for the layman (and indeed, for any
universal machine).
Marty asked me to make an attempt toward a "journalistic" description
of "how physics has to become part of number theory". This is very
difficult, and risky due to inevitable misunderstanding.
And I feel like I have to explain in what deep sense the mathematical
discovery of the "universal machine", made by Post, Turing, ... is
already a quite utterly astonishing, yet subtle, discovery. Gödel
himself took time to swallow it and he described Church thesis as an
epistemological miracle.
My intention was to derive properly Cantor theorem, and then Kleene
theorem, which was the object of my old "diagonalization posts".
I feel important that people understand how unbelievable Church thesis
is, and why most startling propositions, including incompleteness, are
easy consequences of it.
Typically I am happy to share my enthusiasm about all theorems in
computer science which leads to the reversal, but knowing myself I
know that I could accelerate too much and makes too much burden for
the correspondent especially if he is alone.
So before becoming an harasser myself I invite Marty to let other
people trying to answer the exercises.
Marty has fully agreed to this proposal and is happy the pressure is
off him to represent all those who are following anonymously.
Eventually I can show the solution and proceed in addressing the post
to everyone.
Note that this is what I have done with the combinators, feedback were
made out-of-line, then. But this lead to difficulties too. I cannot
solve all the exercise out-of-line. By experience this ends up with
finding myself writing too many posts with almost the same info to
different people.
Yet I can imagine how much it is to be the only public target of what
could look like an perpetual exam, and I really want to proceed in a
cooler way.
Some people have encouraged me, out-of-line, to proceed, but now I
think they should participate a little bit, if only to witness they
are following the thread. I will probably stop to propose "easy" (a
quite relative notion) exercise, but then it is important to stop me
once anything is unclear. This is a problem with math, if you miss a
piece, everything becomes senseless.
Understanding implies some self-implication in the reasoning. So,
either someone else try to participate, or I continue impersonally and
eventually I will try some "non technical summary". I recall that one
of the goal consists in explaining the difference between a
computation and a description of a computation (beyond just doing the
step 7).
Any remark to improve the communication or to design a better
methodology is welcome,
Best regards to all of you, and thanks for letting me know your
interests,
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Fri Jul 10 2009 - 22:24:55 PDT