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