Le 03-mai-06, à 16:34, Tom Caylor a écrit :

> I am beside myself  ;)  Perhaps the interactive step-by-step approach
> that you've used in the past would be easier for you and more
> profitable for us.

Thanks for the suggestion. I will give it a try asap.

>>> Speaking of "impasse with myself" and diagonalization, a thought
>>> occurred to me that an instruction that "erases information", like a
>>> Turing machine "goto" statement (e.g. Wei Dai's "go to the beginning 
>>> of
>>> the tape" instruction)
>> ? Why a goto should erase anything ?
> Actually, in reviewing the definition of Turing machine (it's been over
> 2 decades since I studied it) I agree with you.  The Turing machine
> leaves behind a memory of its past through its "writes" to the tape.
> Maybe I don't understand what Wei Dai was saying with his setting of
> the head back to the start of the tape.  In order to get back to the
> exact beginning *state* the Turing Machine would have to be instructed
> to do an inverse of all of the writes it has done and then go back to
> the start of the tape.

OK. Then it is not just a goto, it is a complete application of a 
reversible process. This will work only if you are using a reversible 
turing machine in the first place (like the one discover first by Hao 
Wang, Interesting work are those of Fredkin and Toffoli, and then the 
entire field of quantum computing).

> I believe that in the meta system, being "open" requires a paradigm
> shift in the meaning of understanding.

This is not entirely clear for me.

> If we just stick to our
> reductionist meaning of understanding, then we are still closed and we
> haven't really gone out of the system.  This new sense of understanding
> is what allows us to not go into an infinite or circular regress.  It
> is what allows us to assign *true* meaning in the first place.

I propose we come back on this after I (try to) explain a little bit 
more on diagonalization. I have a problem with the word "reductionism". 
For some people "number" or "machine" are reductionist concepts, but I 
think that this opinion stems from a reductionist conception of number 
or machine.
Surely some "new understanding" of machine or number is needed.

>> But now, I must confess (!) that I am discovering that if the Riemann
>> critical zeros really describe a spectrum related to a quasi (?)
>> classical chaotic regime---as it can be suspected from experimental
>> (but still purely mathematical!) evidences---then I could imagine that
>> the prime numbers could eventually describe not only a Universal Wave
>> Function (even if only by pieces but the first person doesn't care as
>> far as those pieces have a positive density) but would also describe a
>> sort of universal wave reduction like if an absolutely external
>> observer was included freely in the number's gift !
>> So, recursion theory (computer science) allows internal "metas", but
>> primes, by their so much irregular behavior could still provide an
>> apparent reduction justifying some external metas. Weird. I tend not 
>> to
>> believe in it, though.
>> Who did invite the primes to the banquet?
>> Just thinking aloud. Perhaps my Spring Riemann fever ...
> Wishful, but good, thinking in my view.  I take your "I tend not to
> believe in it, though" as saying that you don't think it's worth
> investing a lot of your resources in pursuing it.

I didn't say that. But we still don't know if Riemann hyp. is true and 
the field is technical. Clearly something happens there.

>  I tend to think that
> pursuing anything is worth it if it allows us to see in a new way why
> it is closer or further away from reality.  The theory is that we can
> use these experiences to formulate a viewpoint of reality that is
> closer and closer to reality.


>  Believing in this theory is actually an
> act of faith in the goodness of reality that goes beyond what evolution
> can explain.  I use the word "goodness" over and above
> "understandability".  If reality is understandable *by us* in any way
> close to the aspirations of the Everything List, then I feel pulled to
> express this as, "Someone out there is truly being good to us."

Plotinus says so but (from a 3 person point of view) I am not yet 
convinced. There are some evidences but we must try to be "cold" on 
this and to beware "wishful thinking", and then we should also not to 
exaggerate in the opposite direction.
We can have doubt when seeing kind people suffering a lot, and remember 
that the Platonists link evil with matter, and this question is not 
entirely clear from the comp or lobian discussion.
We will not answer all this today, for sure.



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