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From: beugnard@molene.enst-bretagne.fr (Antoine Beugnard)
Newsgroups: comp.ai.philosophy
Subject: Continuous vs discrete (Zenon)
Message-ID: <384@molene.enst-bretagne.fr>
Date: 19 Apr 91 14:43:48 GMT
Organization: enst-bretagne Brest, FRANCE
Lines: 67


The talk is about continuous vs discrete but despite some remarks, we don't
consider to waste the bandwidth. We have proposed an interpretation of an old
paradox (refered as Zeno's) to show that the world could be discrete.

Zeno's mind experiment leads to a mismatch between reality and its model.
That is: Achilles that runs faster than the Turtle never reaches her.

We have sent news to request advices or ideas...and we get 5 kinds of answer:

	1 - "ok, it seems to prove that either time is not infinitely divisible, or space
is not infinitively divisible"

	2 - "this model is nonsense, you should have used another one, such as,
	 Xa = N + Va*t and Xt = Vt*t"

	3 - "An inifinite sum is not necessary infinite"

	4 - "a limit is eventually reached" (Achilles never reaches the turtle 
until he does)

We, now, would like to discus the four last answers.

2 -> The problem was not to find a model that gives "wider" results, the problem 
was to explain why Zeno's modeling is not correct. Well, it is correct, because 
when you calculate limits, you obtain that Achilles *could* reach the turtle at 
time t = N / (Va-Vt), and at position ... which are the results obtained by more 
classical models. To decide that this model is partial (truncated), you have to 
assume that time and space are not limited and then you can complete your 
modeling. But you have to be *external* to your model. From the inside, your model
is definitivelly, for ever, correct, and Achilles cannot reach the Turtle.

3 -> We agree that an old Greek could not have thougth to that...but we are 
aware of that. The model is truncated. But we know it is truncated because we 
know time and space are not limited, the model doesn't. The calculus in the model 
never terminates, so, why would it be necessary to change the model...

4 -> take f(x) = 1 / x when x -> oo never reaches 0.

So, we reiterate the question: why Zeno's model is false?

We were advised to talk on a net about physics, sorry not to be connected to.

We would like to add a physicist remark. In our physics, we know 3 fundamental 
constants:
	G : gravitation attraction (Newton)
	h\: energy quantum (Planck)
	c : ligth velocity (Einstein)
These 3 constants may be expressed with 3 basic "units" T (in seconds), L (in meters) 
and M (in kilograms). As a system of 3 equations these units may be expressed with 
the 3 previous values (gravitation (G), velocity (v), energy (E)); we obtain:
	t = (EGv^-5)^(1/2)
And since c >= v and h\ < E then t >= 5.4E-44 s
Some physicist propose to call that quantity of time a Chronon.

This physicist deduction lies on our modern physics, that may be incorrect...
but Zeno's paradox is only a mind experiment...that is based only on our own
experience...and is, therefore, much more general...
Mind experiments lead Einstein to the theory of relativity... ; )
And they both (do they really?) conclude that time could be discontinuous.

Are you so troubled thinking time could be discrete?

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