The following header lines retained to affect attribution:
Date: Tue, 3 Nov 1998 15:26:07 +0100
ReplyTo: Mailing list for the LaTeX3 project
From: Hans Aberg <[log in to unmask]>
Subject: Re: Quotes and punctuation
To: Multiple recipients of list LATEXL
At 07:56 0600 1998/11/03, Randolph J. Herber wrote:
>I disagree with your second pointwith sufficient encoding, any
>semantic can be preserved, possibly with a time penalty (which are
>ignored when discussing such equivalences). That is one of the
>points of Goedel's Incompleteness (Undecidability) Theorem.
 Provided the semantics that one wants to describe can be expressed by
binary numbers: For example, TeX proper cannot draw a nonstraight spline
curve no matter how you apply Turing theorems and Godel theorem, even
though you can define structures simulating that TeX can handle that  but
that has no practical significance unless you figure out a way to extend
TeX to print it. (In this example, even though the curve itself can be
described by binary numbers, the capacity of printing it cannot.)
1) TeX does not have to print it.
TeX only has to generate dvi that describes it.
Providing the necessry dvi semantics for necessary operations
is a problem for the dvi language providers.
2) Irrational numbers are not representable by rational numbers.
This is well known. But, irrational numbers can be
approximated, to any desired accuracy, by rational numbers.
TeX, disgarding memory issues, could generate rational numbers,
for some dvi encoding, to any desired precision. Therefore,
TeX could generate the output.
3) Goedel permits encoding with arbitary semantics. Therefore,
an encoding for ``nonstraight splines'' and for any specific
irrational numbers could be established.
 Hans Aberg
 * Email: Hans Aberg <mailto:[log in to unmask]>
 * Home Page: <http://www.matematik.su.se/~haberg/>
 * AMS member listing: <http://www.ams.org/cml/>
Back to the circus at hand.
Randolph J. Herber, [log in to unmask], +1 630 840 2966, CD/CDFTF PK149F,
Mail Stop 318, Fermilab, Kirk & Pine Rds., PO Box 500, Batavia, IL 605100500,
USA. (Speaking for myself and not for US, US DOE, FNAL nor URA.) (Product,
trade, or service marks herein belong to their respective owners.)
