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From: maxwebb@moe.cse.ogi.edu (Max G. Webb)
Newsgroups: comp.ai.philosophy
Subject: Re: Continuous vs discrete
Message-ID: <19984@ogicse.ogi.edu>
Date: 13 Apr 91 00:11:09 GMT
References: <382@batz.enst-bretagne.fr> <1991Apr10.182036.29916@beaver.cs.washington.edu> <383@zeus.enst-bretagne.fr>
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In article <383@zeus.enst-bretagne.fr> beugnard@zeus.enst-bretagne.fr (Antoine Beugnard) writes:
>We are aware of that. The problem is that **a limit is NEVER
>reached**. Zeno's model never becomes wrong...and Achilles never
>reaches the Turtle because the limit cannot be reached. The model
>is actually troncated both in time and space, that is T(n) and
>time(n) have limits that are never reached...

Just because you represent a finite duration with an approximation
which is infinite in the number of computation steps doesn't
mean that the finite duration is infinitely long.
It is if you are assuming reality has to sequentially compute
each term of *your* limit before it is to be allowed to go on.

After all, there is another expression for the time til
catch up which is closed, computable in one step.

	PositionA = SpeedA * t
	PositionT = SpeedT * t + 50

	catchUp = 50 / (SpeedA - SpeedT)


You are being amazingly dense. If you still don't understand,
ask in sci.math, or sci.physics. Waste no more bandwidth.

>Our experience shows it is wrong, but why?
>
>In a discreet world and with a reasonning and modelling
>similar to Zeno's one. The calculus terminates *claiming* the end
>of the model validity...

This makes no sense at all.

>	Antoine Beugnard and Didier Guy
>	ENST de Bretagne, LIBr, Brest, France
>	beugnard@enstb.enst-bretagne.fr
>	guy@enstb.enst-bretagne.fr
>
>
>Ps: We do not call into question mathematics and its powerfull use.
>Even continuous mathematics!!. It works...but it may just be an
>abstraction of the reality, a usefull tool that has not to be
>related to the essence of world...

You have failed to demonstrate any discrepancy between the
prediction of the continuous, limit based math and reality.

>The question is not only philosophical, people thinking discreet
>machines cannot become "intelligent" assumes the world is
>continuous ... which is not so obvious ...

This point has already been addressed (better) several times 
by people pointing out the limited precision of NN's, and the
existence of noise.

	Max