Le 05-juil.-06, à 19:17, Norman Samish a écrit :

Dear Bruno,

You have, more than once, referred to something I (jokingly) said a month ago:

"I've endured this thread long enough! Let's get back to something I can understand!"

I said this because I am hungry for more informed speculation on "Why does anything exist?" and related questions.

All right. Thanks for your kind reply.

Most recently you have very kindly offered to help me understand some of the foundation concepts you are so proficient at.

I have spent years doing scientific Fortran programming, and am already familiar with elementary math concepts such as trig, number bases, statistics, differential equations and the like. It even makes sense to me that natural numbers are countable and real numbers are not.

OK.

However my aged brain is unable, or perhaps unwilling, to exert the time and effort it would take for me to learn concepts such as eigenvalues, diagonalization, Godel's incompleteness theorem, Turing's proof that no algorithm can solve the halting problem, the Universal Dovetailer Argument, etc.

I respect this. Perhaps in time .... ;-)

If you just remember what a fortran program is, you would be astonished how simple the diagonalization are. I wish you just remain open to get it one day or another. (Two years ago I succeed in explaining the diag trick to a 98 years student, who made a carrier in the human sciences. It just take times, but it is worth of it).

I did react perhaps a little bit strongly, and this is probably related to, well, let us say a future thread, because there is one point where I am, well I mean where comp is closer to Jesus than to Pythagoras, which is that the "theological message" of the universal machine is really universal, all lobian machine can get it: no elitism, no Homo Superior. Some person can be more efficient, more competent, more rapid, ... but no universal machine display behavior unreachable by any other (universal) machine. Pythagorean sectary friendship leads to elitism if not really just corporatism ...

I accept those and many other concepts on faith - enough respected experts (such as yourself) affirm their truth that I have no doubt that they are correct.

Computationalism makes sense to me, and I do not accept this quote from a recent book: "… human cognition is too rich to be simulated by computer programs" (Horgan and Tienson 1996, p. 1).

Reductionist conception of numbers and machines are alas widespread. Incredibly enough, from Pythagoras to Proclus, the greek intellectuals were aware that numbers could have some non reductionist (indeed theological) interpretations. Plotinus (+/- 250 after JC) is almost two millenia in advance in his treatise on "Number". Since Post, Turing, Markov, ... mathematician *knows* that very weak form of computationalist philosophy entails the complete and fatal breakdown of any reductionist conception of numbers, machine, ... Somehow we know that we will never really know what numbers are and what is possible for them.

Thanks again for your offer, but I do not want you to spend your valuable time attempting to get blood from a turnip.

No problem, you are welcome, in any case feel free to ask any questions, or to make any remark.

You know, to understand the result I got, people must understand something in a first stage, and then, in a second stage, they must understand that a lobian machine can understand "in some precise (and a bit technical) sense" that same something, this leads to an arithmetical interpretation of Plotinus hypostases including a "complete" theory of the platonician notion of matter/evil.

Bruno

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

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