Path: utzoo!utgpu!water!watmath!clyde!att!osu-cis!tut.cis.ohio-state.edu!bloom-beacon!hubcap.UUCP!steve
From: steve@hubcap.UUCP ("Steve" Stevenson)
Newsgroups: comp.ai.digest
Subject: Re: state and change/continuous actions
Message-ID: <3052@hubcap.UUCP>
Date: 26 Sep 88 12:18:24 GMT
References: <19880926060100.2.NICK@INTERLAKEN.LCS.MIT.EDU>
Sender: daemon@bloom-beacon.MIT.EDU
Organization: Clemson University, Clemson, SC
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From a previous article, by smryan@garth.UUCP (Steven Ryan):
> 
> Continuous systems are computably using calculus, but is this `effective
> computation?' Calculus uses a number of existent theorems which prove some
> point or set exists, but provide no method to effectively compute the value.


Clearly numerical analysis emulates continuous systems.  In the phil of
math, this is, of course, an issue.  For those denying reals but
allowing the actual infinity of integers, NA is as good as the Tm.

Not only are there existence theorems for point sets, but such theorems
as the Peano Kernel Theorem are effective computations.  At the point
set level, one uses things called ``simple functions''.

BTW, you're being too restrictive.  There are many ``continuous'' systems which
have a denumerable number of points of nondifferentiablity: there
are several ways to handle this (e.g., measure theory).  These are
not ``calculus'' in the usual sense.  Important applications are in diffusion
and probability.  So, is Riemann-Stiltjes the only true calculus? Nah.
There's one per view.


-- 
Steve (really "D. E.") Stevenson           steve@hubcap.clemson.edu
Department of Computer Science,            (803)656-5880.mabell
Clemson University, Clemson, SC 29634-1906