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*To*: occam-com@xxxxxxxxx*Subject*: Complexity change in top-down design*From*: Øyvind Teig <Oyvind.Teig@xxxxxxxxxxxx>*Date*: Mon, 22 Jun 1998 14:44:58 +0200*Alternate-recipient*: Allowed*X400-mts-identifier*: [/PRMD=autronica/ADMD=TELEMAX/C=NO/;5262 98/06/22 14:44]*X400-originator*: Oyvind.Teig@xxxxxxxxxxxx*X400-received*: by mta mail.autronica.no in /PRMD=autronica/ADMD=TELEMAX/C=NO/; Relayed; Mon, 22 Jun 1998 14:44:58 +0200*X400-recipients*: non-disclosure:;

Dear all 22Jun98 Complexity change in top-down design ==================================== In "Is "the therory of everything" merely the ultimate ensemble theory" Max Tegmark writes on page 22.: We noted that if one keeps adding additional axioms to a formal system in attempt to increase its complexity; one generically reaches point where the ballon bursts: the formal system becomes inconsistent, all WFFs become theorems, and the mathematical structure becomes trivial and looses all its complexity. (p22) He continues: In Section IV, we replaced this "top-down" approach with a "bottom-up" approach, making an overview of our local neighbourhood in "mathematical space". (p22) In the paper of which I understand one ppm, he describes an example of top-down approach, and I started thinking about what we do every day: both top-down and bottom-up approaches are used for software design. Even if this isn't what he has in mind, it is interesting to see if it fits into my world as well. I can understand that we "attempt to increase complexity" in top-down (see New Scientist excerpt). But 1) when does our balloon burst, 2) what becomes theorems (WFFs: I'm not sure what it is, not the least I cannot see what it is that in our case becomes theorems) and, 3) which mathematical structure in our case becomes trivial and loses its complexity? In other words, please explain, anyone! "Anything goes" in New Scientist, June 6 excerpt: Another difficulty with the ultimate ensemble theory is that it appears very wasteful. However, Tegmark has an extraordinary argument with which to counter his critics. He says there is actually less information in the multiverse than in an individual universe. To illustrate his argument, Tegmark gives the example of the numbers between 0 and 1. A useful definition of something's complexity is the length of a computer program needed to generate it. Imagine trying to generate a single number between 0 and 1, specified by an infinite number of decimal places. Expressing it would take an infinitely long computer program. But to generate all numbers between 0 and 1, all you would have to do is start at 0, step through 0·1, 0·2 and so on, then 0·01, 0·11, 0·21 and so on--an easy program to write. In other words, creating all possibilities is much simpler than creating one very specific one. References New Scientist: http://www.newscientist.com/ns/980606/features.html Max Tegmark's abstract: http://www.sns.ias.edu/~max/toe.tml ------ Cheers, Oyvind Teig, Autronica, Trondheim, Norway Oyvind.Teig@xxxxxxxxxxxx Tel.: +47 73 58 12 68 Fax.: +47 73 91 93 20

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