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To: jim black who wrote (18235)	4/16/2002 2:24:32 PM
From: marcos	Respond to of 74559

Eccentrics sure, why not, but not mathematicians, dammit -g- .... you might type out all the words, that doesn't mean you get all the meanings, the nuances, the glorious spin ... take, for example, the term 'is' ... can't be finite until it has borders, and the human mind was built to jump those, maths notwithstanding Even to get all the words you'll need all the diacríticos [and never mind that you lack cyrillic, kanji, and kwakiutl petroglyph keys] .... to get o with two dots on top, hold down your Alt key and put 148 into the numberpad, release Alt key and poof - ö ... using 129, you get ü, 225 ß

To: jim black who wrote (18235)	4/16/2002 2:35:51 PM
From: S. maltophilia	Respond to of 74559

More OT Another take on the tireless typewriter, by Borges: thecore.nus.edu.sg

To: jim black who wrote (18235)	4/16/2002 3:29:16 PM
From: smolejv@gmx.net	Respond to of 74559

Hey, JB, this watering hole has rather interesting visitors - must be the water composition, but my conjecture is unprovable. Re Gödel's work of 1965, I for one meant his work of 1931. good refs ((off the top of google scoop of cc 6810 hits) ltn.lv users.ox.ac.uk

To: jim black who wrote (18235)	4/16/2002 5:49:15 PM
From: AC Flyer	Read Replies (3) \| Respond to of 74559

>>The conclusion is inescapable. Human knowledge in so far as it can be written down (and presumsably translated from there to any other human language, is FINITE! There is a theoretical limit to what we are ABLE to know.<< There are two problems with your proof, Jim. First, 36 to the 75th power (the finite number of sets) is a very large number - a very, very large number. Far larger than the number of grains of sand on all the beaches on Earth, far larger than the number of stars in the known Universe. To most folks, 36 to the 75th is a good approximation of infinity. Second, while to a pure mathematician 36th to the 75th is very definitely NOT infinity, you have designed your proof to yield the "not infinite" result by limiting the size of each set to 75 elements. Any number that is factorable (as in a finite number of finite sets) is not infinity. Remove the limit from the set size and you get "an infinite number of infinite sets" yielding the "infinite" result. Contemporary quantum physics provides the strongest support for the "infinite" result, imo, as the old ideas of matter consisting of a finite number of indivisible particles is being replaced by the idea that every particle is composed of smaller particles, which require higher and higher energy experiments to reveal. Fractal mathematics is a variation on this theme. I'm in the infinite camp. Good day today, huh? Mr. Market doesn't need much of an excuse to ramp. Dumb old Mr. Market just refuses to do what it's "supposed" to do.

To: jim black who wrote (18235)	4/16/2002 7:57:30 PM
From: Terry Maloney	Read Replies (1) \| Respond to of 74559

Hi, jim. I see your post has garnered a number of responses already, so I'll be brief, being a lousy typist in the first place, and somewhat befuddled by painkillers (for a twisted back) in the second ... but: 1) I don't think anything is truly off-topic on this or any other thread worth reading ... butterfly wings and all that. <g> 2) Abstract, philosophical math is indeed fascinating ... unfortunately, I abandoned that path years ago, and so can't really hold up my end in any meaningful way ... dj, on the other hand, seems to be familiar with this particular kind of music. 3) Notwithstanding the above, the extent to which modern physics/math corroborates the teachings of ancient mystics always intrigues me ... paradox ... whether it's Goeden or Heisenberg, the question remains the same: if g*d didn't create the universe, wtf did? <g> 4) ACF, as always, presumes to know, but I tend to side with you, Horatio, and Shakespeare. Best, Terry

To: jim black who wrote (18235)	4/16/2002 11:28:31 PM
From: LLCF	Respond to of 74559

<< Simply ( very simply!) put, his conclusions were disturbing and their implications far reaching. He showed in a brilliant indirect proof that in any! axiom system sufficient to deal with something as simple as ordinary numbers and arithmetic it is in and of itself absolutely impossible to prove internal consistency. In other words despite our impressive advancements in science and mathematics we can never know if the axioms systems even of the simplest, non-trivial nature have in them internal inconsistencies that have simply not yet been discovered.>> And I thought I was a ludite for such suggestions! :) Nothing off topic here,and besides its bin Laden that's Jesus -VBG- DAK

To: jim black who wrote (18235)	4/17/2002 5:02:51 AM
From: Maurice Winn	Read Replies (2) \| Respond to of 74559

Jim, re: <He showed in a brilliant indirect proof that in any! axiom system sufficient to deal with something as simple as ordinary numbers and arithmetic it is in and of itself absolutely impossible to prove internal consistency. In other words despite our impressive advancements in science and mathematics we can never know if the axioms systems even of the simplest, non-trivial nature have in them internal inconsistencies that have simply not yet been discovered. > How did he prove that idea since it is locked up in it's own little Shrodinger box, going around in circles, but with no externality to observe the internal inconsistencies of his proof? English as it exists right now is finite, but English is infinite in that anything which we can perceive, directly or indirectly or via imagination can have a neologism ascribed to it and there is no limit to the number of neologisms we can create [though we would need to also extend the alphabet some more]. English is merely a hopelessly inadequate way of representing reality as perceived by somebody and with that perception being shared by somebody else so that they can match the words with the reality described, using symbols to identify the selected reality. Mathematics is just another kind of symbolic representation of reality. By saying that English is finite is another way of saying that reality is finite. Since we all exist with a probability of 1, it's quite reasonable to say that reality is very finite and in fact is in a single state. By probability of 1, I mean that if we go back up through our ancestors, over millions and billions of years, not a single one of our ancestors died before we were conceived. What is the probability of every single ancestor not dying before they became our progenitor? It is infinitely improbable given the number of things which could have gone wrong for any one of them. But it happened, for every single living thing alive right now. At the beginning, one would say that the probability of the situation of everything existing as it is right now would be infinitely unlikely, or, 0.000000000000000...75 times....00001. BUT, here you are, right here, right now, reading these pixels. You lucky, lucky, lucky, ... 75..., lucky, probability = 1 man! I don't buy all that quantum bunk, with all states existing until brought into reality by an observer, as though anything could be and it's all a matter of luck. I reckon there are no dice [or die for the pedants]. As Jay is fond of saying, we are reading a script. We just disagree on what the script says. A more likely limit to human knowledge than the English language is the form of our brains - little grapefruit-sized alcohol-sodden misfits of protoplasm with limited data input, processing methods and dodgy neuron connections. It doesn't have such a limit. With graviton.com inputs, It will seem remarkably akin to a supernatural being to people. Already, Google has better knowledge and memory than anyone - although not yet very good at doing tricks with that vast and quickly recalled knowledge. We've had our day mate! Mqurice