Hi John,

On 15 Jun 2010, at 13:41, John Mikes wrote:

Bruno, I don't claim to follow your discussion with Colin in 'good' understanding, but there was a sentence to which I ask some explanation:

"I study just the hypothesis that the brain is Turing emulable."

Do you mean 'brain' as the physical tissue-mass (not likely), or the brainfunction as 'mentality' into the summation of what we try to use?

The brain is whatever is needed to be Turing emulated for my consciousness to persist. It may be the whole Milky galaxy, described at the level of the Heisenberg matrix or Schroedinger wave with a fine graining up to the superstring, quantum fields or elementary particles (if that exist). I just don't know.

If digital mechanism is true, not only I cannot know that, but such a fine graining hides a finer graining ad infinitum, which play a role in matter, but no more in consciousness (below that level).

If I am dying, and that my doctor believes that my brain is constituted of some wet machinery (glials cells and neurons), and that an emulation at the level of molecules is enough, I may as well trust him, like doing some Pascal Gambit. I will cross my fingers, and assuming mechanism, I 'know' why I have to cross my fingers.



Do you mean 'Turing' as the presently used embryonic binary adding machine, or the universal machine - what we (us) try to emulate?

It is the same. Roughly speaking Turing discovered that Universal Computability, although non trivial at all, is very cheap. To be sure binary adding machine are not universal, but if they can add *and* multiply, they become universal. This is not obvious at all, but we know this since Gödel, Church, Kleene's works around 1930.

The universality of addition and multiplication is the main reason we can say today, about arithmetical truth: we know almost nothing. Assuming comp, we can add, and we will never know. It is too big, too complex, too much transcendental.



I do not think the 1st part of the 1st Q gets a yes, just as the 2nd Q is also likely to be anchored in the 2nd part.

In which case instead of saying something, like "AI is digitally computable" I may paraphrase the idea in my primitive wording:

"We may suppose to be able to compute (~understand) whatever is in store to be understood"


Computing is quite different from understanding. There is more in (just) the computing store than what we can ever understand.

When a universal machine begins to try to understand herself, she grows indefinitely, and her ignorance grows indefinitely, and even more quickly than herself. There is a threshold, though, at which point she will *understand* that very phenomenon. She will understand she will never understand, even just herself, still less any of her possible universal neighborhoods. She may become wise, or modest, (Löbian) at that point.





What I would hold a bit exaggerated considering that our 'universal database' (the wholeness of the existence (~nature) ) MAY(?) include lots of domains so far not absorbed into our working personal mental capabilities (beyond Colin's mini solipsism, D.Bohm's explicate, R. Rosen's system-model?) and so our 'computing' is far from being able to match the universal machine's.

May be. I make explicit that I identify "our computing" with the computing power of the universal machine. This statement is equivalent with Church's thesis. Church's thesis is very plausible, both empirically and conceptually. I recall that the universal "Turing" machine, or the set of what such a machine can compute, is close for the Cantor Diagonal procedure. This is an utterly incredible fact, that Gödel disbelieved until his reading of Turing, and then called a 'miracle'.



Unless, of course, you may include into the 'emulable' the acceptance of such hiatus.

Absolutely.
Like Hofstadter illustrated, anyone can emulate the brain of Einstein, for example when doing an oral presentation on GR, even without the knowledge of German, or of general relativity (and without understanding anything).

For the same reason we will probably copy brains well before understanding the brain, and when we will understand brains, it will be too late, we will be more complex than brain.

Computing, or emulating, IS not equivalent with understanding, or even just with proving-in-a-theory.

The ultra-weak theory ROBINSON-ARITHMETIC is already universal (in the sense of computer science), yet quite dumb and without capacity to prove any non trivial generalizations. Yet ROBINSON-ARITHMETIC, by computing universality, can already emulate all the richer, and Löbian, effective theories or machines.

ROBINSON-ARITHMETIC cannot prove the consistency of ROBINSON- ARITHMETIC, still less of the consistency of the richer ZERMELO- FRAENKEL set theory-machine. But ROBINSON-ARITHMETIC *can* prove that ZERMELO-FRAENKEL set theory proves the consistency of ROBINSON- ARITHMETIC. This will not really help ROBINSON-ARITHMETIC!


Or: if you apply the words "theoretically" : WE (~universal machines) have - theoretically- the capability of applying omniscience.

I don't think so. WE (universal machine), as far as we are self- referentially correct (and thus Löbian), are cured from the idea of omniscience. We cannot be omniscient, still less apply that concept to anything.

In the frame of the digital mechanist hypothesis, even "God" is NOT omniscient, nor omnipotent.




Excuse my asking into what you say you ARE still studying.

The subject is infinite and infinitely fascinating. Here I try more to share my enthusiasm and befuddling than to convince anyone of any truth. It is always a pleasure to answer (or to try to answer) questions. Feel always free to ask any questions, I love *all* questions.

Best,

Bruno

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



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