**Ben Goertzel** (*ben@goertzel.org*)

*Sun, 04 Apr 1999 16:38:27 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Ben Goertzel: "[time 166] Philosophy of science and other distractions ;)"**Previous message:**Ben Goertzel: "[time 164] Question"**In reply to:**Stephen P. King: "[time 158] An idea for particle modeling"**Next in thread:**Matti Pitkanen: "[time 171] Re: [time 165] Prime numbers in pregeometry"

Thinking about the possible pregeometric meaning of prime numbers...

In my pregeometric explorations with Tony Smith/Kent Palmer/Onar Aam, I

made the following

philosophical observations...

ADDITION = COEXISTENCE

MULTIPLICATION = INTERPENETRATION

Suppose we take two sets, e.g.

X = {a,b}

Y = {c,d,e}

Then

X + Y = {a,b,c,d,e} with a cardinality of 5

this represents drawing a common boundary around X and Y,

considering X and Y to live in the same "local system" so to speak

X * Y = {a*c,a*d,a*e,b*c,b*d,b*e} with a cardinality of 6

this represents X interpenetrated through Y, each

element of X allowed to transform (occupy the same local space as)

each element of Y

The idea is that coexistence and interpenetration are basic philosophical

operations, reflected in the quantitative domain by + and *

Prime numbers enter in in an obvious way: a set with a prime number of elements

can ~never~ be obtained by interpenetrating two sets different from itself..

Pregeometrically, prime numbers seem to correspond to "minimal systems"

in some sense.

These are obviously just some half-formed ideas. However they are the

first inkling I have

had as to what could form a philosophical foundation for Matti's elaborate

mathematical improvisations on the theme of p-adicity and physics

ben

**Next message:**Ben Goertzel: "[time 166] Philosophy of science and other distractions ;)"**Previous message:**Ben Goertzel: "[time 164] Question"**In reply to:**Stephen P. King: "[time 158] An idea for particle modeling"**Next in thread:**Matti Pitkanen: "[time 171] Re: [time 165] Prime numbers in pregeometry"

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