On 17 Jan 2013, at 14:49, Richard Ruquist wrote:

On Thu, Jan 17, 2013 at 6:02 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:



You are right.
But UDA shows that if comp is correct, and QM is correct, then the second
has to be a mathematical consequence of the first.


Agreed, just as I put it above.


So, let us derive the physics from comp,


I do believe that is primarily your concern.


Well it is the concern of anyone wanting to get a TOE which includes a
solution/explanation of the mind-body riddle.



I am too old to learn modal logic.

I would say that it is *far* simpler than string theory. (but anything new is hard after puberty!)

I have eventually realize that modal logic is simple, but only if you know well classical propositional calculus, and only professional logicians seems to know it. Logic is the hardest branch of math, as people needs to understand, at the start, when they should not understand strings of symbols, and this is hard to taught. This year I have taught the soundness and completeness proof of classical propositional logic, and I have realized that it is very difficult for the students. Logic is simply not taught anywhere, except as a graduate specialization for mathematicians.




So I will accept the results of arithmetics
in a systems analysis that includes as modules:
1. the CTM for a compactified-substance subspace that derives the MWI
Quantum Mind as well as
2. the physical world: Matter and Energy (that was created along with
Space and the Compact Manifold CM Subspace). According to string
theory the particles of fermionic matter are connected to membranes of
the Quantum Mind by strings, a theory verified by LHC measurements of
the viscosity of BEC quark/gluon plasma

Hmm... That includes far too much for a computationalist. It can be OK, temporarily.

If I am open for string theory, it is mainly because it already smells like number theory. I am already convinced that string theory will be a major tool for a general theory of diophantine polynomial equation, no matter what. I am even afraid that number theorist could find the TOE before the theologians, and that could mean some more millennia of hiding qualia and person from the picture.


Pratt and BEC duality connect the Physical to the Mind as well as strings.

The connection here is interesting but still too weak as to provide the clues needed to solve the mind body problem in the computationalist theory of mind.
This should follow from the paper I have referenced.
I know that some people dislike this, but with comp the mind reality is much bigger than the physical reality. Physical reality is the derivative of the mind reality, and you can picture the mind as a big volumic sphere, and the physical reality as its surface. The sphere can represent the universal dovetailing, or the (sigma_1) arithmetical truth, and the surface of the sphere as the "appearance seen from inside the sphere, taking into account that no machines can know on which particular universal system she run, or which computations support her.







and then we can compare with nature.


which I claim is best represented by quantum string theory


I am open to that hypothesis, but to get both the qualia and the quanta, we
must derive them from numbers and their self-referential abilities.
Again, that is the result of the UD Argument.

Agreed- both quantum mind and its qualia come from arithmetics

Everything should come from arithmetic (or Turing equivalent). Quanta, strings, qualia, suffering, taxes, death, ... even the gods, goddesses and "God" Itself.



If nature refutes comp, then we have learned something, but up to
now, thanks to QM, the two physics fits well.


Can you provide a reference for that claim? Is it your work?


Yes, it is the second part. I divide my work in two parts: UDA and AUDA, i.e. UDA = Universal Dovetailer Argument (or Universal Dovetailer Paradox, as I call it before defending this as a PhD thesis), and AUDA = Arithmetical UDA, it is the translation of the argument in arithmetic (or in any Turing Universal machine's language), and the answer of the machine (but also to its "guardian angel": the machine is mute on this, unless she too assume comp, and some amount of self-consistency (but not much so as to avoid the
consequence of Gödel's second theorem).

Bruno



I do not yet appreciate the intricacies of self-referential CTM or Godel.
How is your work different from Godel's, to ask a naive question?


Naive questions are the best questions. Now if I compare myself to Gödel, I *will* look like a crackpot ... (but that's not quite important).

Gödel's main contribution are the completeness (of predicate logic) in 1930 (his master thesis). Then his "famous" incompleteness theorem in 1931. But he has also many other contributions, notably in set theory (like the relative consistency of the continuum axiom, and the choice axiom), but also in general relativity (the rotating universe, solutions to Einstein's equation) which he did just to piss of Einstein when arguing about the notion of time, I think.

I have developed the main part of the UDA before knowing Gödel's existence, and I was about deciding to study biology when I found the little book by Nagel and Newman on "Gödel's proof", which changed my mind, so that I decided to study math instead. I was obsessed with one question, coming from my fondness toward amoeba and protozoans. "Does an amoeba duplicate itself, or are amoeba just duplicated *by* the universe?". What was the part of the self of the amoeba when biologist said that it duplicate itself?

I was lucky being born at the time when people like Watson and Crick unravelled the DNA structure, and people like Jacob and Monod discovered molecular genetic regulations, which convinced me that there was indeed a self, coded in the DNA, and implemented in the laws of chemistry.

But the role of chemistry was disturbing, and even more so when I tried to figure out what could be an atom.

Then by reading Nagel and Newman's book on Gödel's proof, I get a simple model of the self, which did not rely on atoms and chemistry at all. Indeed, it is in Gödel's work that I found the (Cantorian) Dx = "xx" trick to build self/referential machine/programs/numbers.

The main point will be made utterly clear, with Church thesis, by Stephen C. Kleene, whose book "Introduction to Metamathematics" will be my bible for years. With the work of Emil Post, Kleene is the founder of recursion theory, that is the study of the degree of non- computability or unsolvability. That will be my specialization in math. I intended to do a career in recursion theory, and to come back to foundational question at my retirement, but luckily or not, I did not get the funding to do recursion theory, and so I continue the foundational research as an hobby. I will use Gödel's work (and his many successor's work) as a tool to translate UDA in arithmetic (this will take about 20 years). Gödel's work will be polished through many other works, like Rosser, Löb, and eventually the modal completeness theorem of Solovay (the discovery of G and G*, which axiomatize the whole consequence of incompleteness, at some level).

So the relation with Gödel is that I am using his work to handle the translation of the comp mind-body problem in arithmetic (and/or in arithmetical terms). It is the AUDA part, and that will be defended (successfully!) as a Phd thesis in theoretical computer science.

Gödel did not address specifically the mind-body problem. In some text he seems open to comp, like when saying that mind can be emulated by self-developing machine, but he was also open to non comp, like when arguing that we might someday have evidence that evolution has been too quick to be purely mechanical. (an argument which fails in Everett QM, note). Also, Gödel took time to swallow Church thesis (which in my opinion means that he is just very serious, as that thesis is close to be unbelievable).

Thanks to Everett, I will eventually "understand" quantum mechanics, if I may say. Bizarre as it could seem, I found the many dreams in arithmetic well before realizing that the collapse of the quantum wave was just a trick to avoid the many-worlds. Up to my reading of Everett, I was still unsure about what makes an amoeba self- duplicating. After reading Everett I realize that QM, and thus chemistry, was the best ally of mechanism, and indeed QM-Everett can be seen as a confirmation of the most startling consequences of digital mechanism (indeterminacy, local apparent non locality, non cloning, many-worlds, etc.).

But the price of using comp is that the quantum wave must be eventually justified entirely in term of internal probabilities made by numbers relatively to the universal numbers "running" them. A big price, but even without the extraction, it does provide a model explaining where the laws of physics might come from (at least).

Well, I don't want to be too long, but I hope you get a bit of the idea. Gödel's work plays no role in UDA, but it plays the key role in AUDA.

Bruno



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



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