Le 21-juil.-06, à 22:52, John M a écrit :

> Could we talk 'topics' without going into trivialities what every child
> knows after the first visit to the grocery store?


But the cute thing (in my perhaps naive lobianity) here is that you 
don't need more than the trivialities every child knows after the first 
visit to the grocery store, to understand that, once we assume comp, 
Numbers protects the free mind against a *vast* class of reductionism.
I should perhaps not insist on that because, sometimes I ask myself, 
humanity could be not mature enough, but there are many reason to 
believe that eventually all universal machines sufficiently correct to 
survive will converge toward a state of being universal dissident, a 
typical allergy to authoritative arguments.

> As long as we cannot identify what a 'number' is, it does not 
> contribute to
> an understanding of reason.

Could we identify what a human is?



> What is '3' without monitoring something?

With the Fi I tried to explain how far can numbers can monitors 
numbers, including partially themselves.
Also,  I would get the feeling of lying to myself if I was not 
acknowledging that I understand better the number 3 than an electron or 
a theory about electrons.



> (This is not a personal attack on you or YOUR theory, it is a common 
> belief
> and I question its usability -  not by opposing, just curious to find 
> a way
> to accept it and experience the happiness of the mathematicians).


Do you know the proof that the square root of 2 is irrational. It is an 
impossibility theorem. Godel's incompletness and Turing's 
insolubilities are very deep impossibility theorem concerning machine, 
and us (assuming comp). The happiness of the mathematician is of many 
type: barock, romantic, jazz, mystery-inspired, esthetic ....




> As you can see, I have no idea about number theory. Whenever I tried 
> to read
> into it, I found myself  (the text) inside the mindset which I wanted 
> to
> approach from the outside. Nobody offered so far a way to "get in" if 
> you
> are "outside" of it


I can offer my help, but I don't want to insist.


> It is a magic and I do not like magic.

I like true magic. I hate magic+ marmelade.



> Next time when I ask "how can you describe the taste of vanilla by
> manipulating ordinary numbers"?  TRY IT.


You asked me more difficult problems in the past, John.
*assuming comp*, there is an easy answer.  Go to Numberplatonia, use 
Goedel's technic to write a little program with the instruction "help 
yourself". Pray each day your little program develop itself convenably, 
perhaps with the help of the heaven.  When sufficiently developed, 
maybe after billions of years, invite e to the next grocery and buy er 
a vanilla candy, and then ask er. E will give you the best description 
you can ever hope of a taste of vanilla, corresponding to a billion 
years of ordinary number manipulations and you can look at them if you 
have print the execution of the program.

If comp is true, nobody will know for sure which numbers are 
responsible for the vanilla qualia, although empirical theories will 
progress up to the point of buying "qualia". Successes there will be 
serendipitous, and unproved scientifically, but most of us will not 
care ... only for bugs ... and protection of privacy (an explosively 
daunting task of the future which will be made tractable through 
quantum information practice I think).

Bruno

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


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