silber@voodoo.ucsb.edu (08/06/89)
-Message-Text-Follows- Intelligence and its instantiation as reasoning must be conditioned by the initial conditions of the universe; if the universe had started as a continuous distribution of matter, there would have been no discrete sets (?), hence no numbers. if the initial conditions had decreed a different set of discrete elementary particles, there would have been a different number theory, different primes, or perhaps no primes at all (?)
garym@cognos.UUCP (Gary Murphy) (08/06/89)
In article <2182@hub.UUCP> silber@voodoo.ucsb.edu writes: > >Intelligence and its instantiation as reasoning must be conditioned by >the initial conditions of the universe; if the universe had started as >a continuous distribution of matter, there would have been no discrete >sets (?), hence no numbers. if the initial conditions had decreed a different >set of discrete elementary particles, there would have been a different >number theory, different primes, or perhaps no primes at all (?) What a curious posting; a provocation perhaps? I wonder about this first premise, since recent talk here does not neccessarily predicate Reason as an instance of Intelligence (some might say Reason is, in Humans, a client or even the operator of intelligence, most would call both terms fuzzy). The second step is even more odd, given the all-but-certain quantized nature of JAE (Just About Everything). Given Hawking, Guth & al, One could restate the conclusion as "IN a Universe started as...", replace Silber's romantic-but-unsupportable 'continuous' with something more plausible, such as a different ratio of matter vs light vs anti-matter, or more simply 'different Laws', and the conclusion (ignoring the ?) might hold. Including the ?, it becomes anthropic: all other configurations are too unstable to permit our evolution. Is this what Silber meant? Does Silber know? -- | Gary Murphy - Cognos Incorporated - (613) 738-1338 x5537 | |3755 Riverside Dr - P.O. Box 9707 - Ottawa Ont - CANADA K1G 3N3| | e-mail: decvax!utzoo!dciem!nrcaer!cognos!garym | |Cosmic Irreversibility: 1 pot T -> 1 pot P, 1 pot P /-> 1 pot T|
cik@l.cc.purdue.edu (Herman Rubin) (08/08/89)
In article <2182@hub.UUCP>, silber@voodoo.ucsb.edu writes: > Intelligence and its instantiation as reasoning must be conditioned by > the initial conditions of the universe; if the universe had started as > a continuous distribution of matter, there would have been no discrete > sets (?), hence no numbers. if the initial conditions had decreed a different > set of discrete elementary particles, there would have been a different > number theory, different primes, or perhaps no primes at all (?) It is not necessary for the fundamental structure of the universe to be discrete to have observed discreteness. If we have discrete planets or stars, or rocks, or plants, or animals, or intelligences, we have the notion of discreteness. We use mathematics to describe the universe. The mathematics is independent of the universe. How it is used to describe it is not. -- Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907 Phone: (317)494-6054 hrubin@l.cc.purdue.edu (Internet, bitnet, UUCP)
rwex@IDA.ORG (Richard Wexelblat) (08/11/89)
In article <2182@hub.UUCP> silber@voodoo.ucsb.edu writes: >Intelligence and its instantiation as reasoning must be conditioned by >the initial conditions of the universe; if the universe had started as >a continuous distribution of matter, there would have been no discrete >sets (?), hence no numbers. if the initial conditions had decreed a different >set of discrete elementary particles, there would have been a different >number theory, different primes, or perhaps no primes at all (?) Reminds me of the line from a recent SF novel: If the TV News were on and no one was watching, would anything have happened? -- --Dick Wexelblat |I must create a System or be enslav'd by another Man's; | (rwex@ida.org) |I will not Reason and Compare: my business is to Create.| 703 824 5511 | -Blake, Jerusalem |
rwex@IDA.ORG (Richard Wexelblat) (08/11/89)
In article <1490@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes: > The mathematics is independent >of the universe. You beg the question. How do you know this is so? -- --Dick Wexelblat |I must create a System or be enslav'd by another Man's; | (rwex@ida.org) |I will not Reason and Compare: my business is to Create.| 703 824 5511 | -Blake, Jerusalem |
jk3k+@andrew.cmu.edu (Joe Keane) (08/13/89)
In article 1989Aug11.114022.481@IDA.ORG> rwex@IDA.ORG (Richard Wexelblat) writes: >In article <1490@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes: >> The mathematics is independent >>of the universe. > >You beg the question. How do you know this is so? Because we state in advance what assumptions (axioms) we're using. Everything else can be derived from them. If you prove 2+2=3 (in your universe) either you're using different axioms or you're using the same ones and have found a contradiction in them. In either case, Herman's statement is still true.
lee@uhccux.uhcc.hawaii.edu (Greg Lee) (08/13/89)
From article <0YtCI7a00V4G40XHNL@andrew.cmu.edu>, by jk3k+@andrew.cmu.edu (Joe Keane): \In article 1989Aug11.114022.481@IDA.ORG> rwex@IDA.ORG (Richard Wexelblat) \writes: \>In article <1490@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes: \>> The mathematics is independent of the universe. \> \>You beg the question. How do you know this is so? \ \Because we state in advance what assumptions (axioms) we're using. Everything \else can be derived from them. ... In advance of doing the mathematics? But that's not so, in general. Axioms have usually been discovered after some significant mathematics has been done. If there were no interesting or useful mathematics in some area, why would anyone bother to axiomatize it? It is also not true that axioms have a logical priority. The theorems that follow from a set of axioms are also sufficient to deduce the axioms. Besides, if axioms _were_ stated in advance, how would that show that mathematics is independent of the universe? And besides _that_, where did you get the idea that only mathematics can be axiomatized? Greg, lee@uhccux.uhcc.hawaii.edu
kung@mips.COM (Kung Hsu) (08/15/89)
In article <4558@uhccux.uhcc.hawaii.edu>, lee@uhccux.uhcc.hawaii.edu (Greg Lee) writes: > From article <0YtCI7a00V4G40XHNL@andrew.cmu.edu>, by jk3k+@andrew.cmu.edu (Joe Keane): > \In article 1989Aug11.114022.481@IDA.ORG> rwex@IDA.ORG (Richard Wexelblat) > \writes: > \>In article <1490@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes: > \>> The mathematics is independent of the universe. > \> > \>You beg the question. How do you know this is so? > \ > \Because we state in advance what assumptions (axioms) we're using. Everything > \else can be derived from them. ... > > In advance of doing the mathematics? But that's not so, in general. > Axioms have usually been discovered after some significant mathematics > has been done. If there were no interesting or useful mathematics in > some area, why would anyone bother to axiomatize it? It is also not > true that axioms have a logical priority. The theorems that follow from > a set of axioms are also sufficient to deduce the axioms. Besides, if > axioms _were_ stated in advance, how would that show that mathematics is > independent of the universe? And besides _that_, where did you get > the idea that only mathematics can be axiomatized? > > Greg, lee@uhccux.uhcc.hawaii.edu Mathematics, as what we know right now, has little to do with the essense (or initial condition) of universe. From knowledge point of view, number theory, Topology, Hilbert Space,... are just a partial models to explain certain facets of the world, not even universe, because something are man made. The reason I call then partial is that from Godel incomplete theorem, it is pretty easy to find contraditions within itself, even though they serve the purpose of explain the space partially very well. Also, look at the lack of any connection among these Mathematical fields, to me, it is like complicated deduction games. It barely covers its own field, never talking about universe. When you say Mathematics have something to do with universe is like saying automobile has something to do with the essense of universe. From meta level point of view, if Mathematics knowledge is of no signaficance, how about the logic? It seems to me logic is just a language that everybody use to describe or reason about the complicated Math phenomenon. As to why everybody believes logic, I don't really know, but seems to have something to do with how information is organized. e.g. deduction is relinking of information. Human intelligence has a lot to do with mastering techniques in this level(not just Mathematical Logic). What kind of calculus in human brain is still in research. From this point of view, things like number theory, prime numbers in the original posting is first level knowledge which is the product of second level logics/intelligence. They are not the core of intelligence. What is the essense of universe then? Today, majority of physicist probably believe Big Bang theory and contructed the Unifying Field Theory alone it. Theoretical Physicist try to describe the universe 10 to the -30th second after Big Bang when all the four fundamental forces are unified. The universe, at that time, is indeed not discrete, it does not even have proton, neutron, atom,...etc. This theory is roughly in place. The question is what is before Big Bang? Some physicist postulate that is Emptiness. This is the postulation, after formulating the situation at a fragment of a second after Big Bang, it is intuitive. However, it may be an *appropriate* description. Three thousand years ago, a Chinese, LaoSze, father of Taoism, writes in his book very similar description about the initial condition of universe. Another analogy is that there is a pond, when there is no breeze, the surface of the water is so tranquil, and Big Bang is like throwing a stone in the middle of the pond. Thers is an execellent series of film on PBS couple months ago, talks a lot about state of the art study in this area. Given all this, the initial condition of universe, right now is sur-experiential, sur-logical, is of yet higher level and should not internixed with intelligence/logic level, nor knowledge/experience level.
rwex@IDA.ORG (Richard Wexelblat) (08/16/89)
In article <0YtCI7a00V4G40XHNL@andrew.cmu.edu> jk3k+@andrew.cmu.edu (Joe Keane) writes: >In article 1989Aug11.114022.481@IDA.ORG> rwex@IDA.ORG (Richard Wexelblat) >writes: >>In article <1490@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes: >>> The mathematics is independent >>>of the universe. >> >>You beg the question. How do you know this is so? > >Because we state in advance what assumptions (axioms) we're using. Everything >else can be derived from them. If you prove 2+2=3 (in your universe) either >you're using different axioms or you're using the same ones and have found a >contradiction in them. In either case, Herman's statement is still true. Sorry, I don't see what the assumptions have to do with the universe. If you mean that the axioms are ASSUMED to be independent of the universe, then that confirms my statement that the original poster is begging the question. If you mean that the axioms can be PROVEN independent of the universe that I'd like to see the proof. Classical math is just the opposite. Your example comes from that trivial(:-) part of mathematics* wherein one can prove things by demonstration. Let's go on to geometry. Does the same argument hold for the law of parallels? Going back to Riemann's dissertation (in translation, of course) Space is only a special-case of of a three-fold extensive magnitude. From this, however, it follows of necessity that the propositions of geometry cannot be deduced from magnitude-ideas but that these peculiarities through which space distinguishes itself from other thinkable three-fold extended magnitudes can only be gotten from experience. I.e. the mathematics is conditioned by experience or observation. Look at Lobachevski's Theory of Parallels. I think the excellent 1914 translation by G. B. Halstead is still in print. *Here is my argument that number theory is trivial: Computers are very good at number theory (Lenat, etc.) Anything a computer can do is only a step or so away from trivial Ergo, number theory is next to trivial. -- --Dick Wexelblat |I must create a System or be enslav'd by another Man's; | (rwex@ida.org) |I will not Reason and Compare: my business is to Create.| 703 824 5511 | -Blake, Jerusalem |
lee@uhccux.uhcc.hawaii.edu (Greg Lee) (08/16/89)
From article <25445@batman.mips.COM>, by kung@mips.COM (Kung Hsu): " ... Topology, Hilbert Space,... Godel incomplete theorem, ... " logic ... Big Bang theory ... the Unifying Field Theory ... " Emptiness ... Taoism ... But where does Chaos Theory fit in to all this? Greg, lee@uhccux.uhcc.hawaii.edu
jl3j+@andrew.cmu.edu (John Robert Leavitt) (08/16/89)
I believe that chaos fits in somewhere between emptiness and Taosim...
Seriously, though, just because something is overhyped does not mean that there
is not something to it (just because you're paranoid doesn't mean they're not
out to get you). "Chaos: The Making of a New Science" is an interesting book
that can get your mind looking into a bunch of dark nooks and crannies you
may have ignored before... Chaos has not yet been nicely theorized, true. But
that should not be the ultimate criteria for whether something is useful.
Newtonian physics is incomplete since it does not account for relativity.
But, Newtonian physics was still useful... An even better metaphor is in
astronomy... primitive cultures explained the movements of the stars with Gods
and the like. They did not have the motion of heavenly bodies nicely theorized
into a neat tidy bundle... but they were still able to use that motion to
plan crop plantings and harvests, etc. Engineering CAN be useful without a
science to back it up.... it is more useful WITH the science, but the science
is not necessary...
-John.
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+------------------------------------------+----------------------------------+news@sramha.sra.JUNET (USENET News) (08/21/89)
In article <2182@hub.UUCP>, silber@voodoo.ucsb.edu writes: >-Message-Text-Follows- > > >Intelligence and its instantiation as reasoning must be conditioned by >the initial conditions of the universe; if the universe had started as >a continuous distribution of matter, there would have been no discrete >sets (?), hence no numbers. if the initial conditions had decreed a different >set of discrete elementary particles, there would have been a different >number theory, different primes, or perhaps no primes at all (?)