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From: beugnard@batz.enst-bretagne.fr (Antoine Beugnard)
Newsgroups: comp.ai.philosophy
Subject: Continuous vs discrete
Message-ID: <382@batz.enst-bretagne.fr>
Date: 10 Apr 91 13:28:16 GMT
Organization: enst-bretagne Brest, FRANCE
Lines: 39


Some precisions about Zeno paradox...and our interpretation


>	T(n) denotes the successive locations of Turtle.
>	A(n) denotes the successive locations of Achilles.

n is certainly not the time.

If we try to express time as a sequence of numbers we obtain:

			 n
			---
	time(n)= (N/Va)	\    B^i	 We introduce B = (Vt/Va) with B < 1.
			/
			---
			i = 1

And it is very interresting pointing out that:

	lim time(n) = 1/(1-B) = N / (Va - Vt)
	n -> oo

Which is the time Achilles reaches the Turtle in the real world. This may be derived from another model, more classical:

	Xa = Va * t
	Xt = N + Vt * t

Why give a wrong (really wrong?) model as Zeno's one GOOD results, but troncated, both in time and space?

Is the model wrong, or are the hypotheses of continuity false?
Why the classical model works (matches our experience) while Zeno's one don't?

Our interpretation is that the world is by essence discontinuous.

	Antoine Beugnard and Didier Guy
	ENST de Bretagne, LIBr, Brest, France
	beugnard@enstb.enst-bretagne.fr
	guy@enstb.enst-bretagne.fr