At 10:53 0600 1998/11/03, Randolph J. Herber wrote:
> 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.
The main point is that with the original setup whatsoever, it is not
possible to print such a curve, no matter how you apply the Godel theorem.
> 2) Irrational numbers are not representable by rational numbers.
Anything that can be described in mathematics can of course be
represented in the computer: Just put the math paper into the computer.
This does not work with a physics paper because QM is not logical, so what
it describes may have no logical representation, even though the
description itself has a logical representation (the paper) of course.
> 3) Goedel permits encoding with arbitary semantics.
I think this line should read:
Goedel permits encoding with arbitary logical semantics.
> Therefore,
> an encoding for ``nonstraight splines'' and for any specific
> irrational numbers could be established.
Encoding for splines, or Bezier curves, are of course used by PS, PDF and
such formats.
So summing it up, even though reasoning with Turing machines and Godel
theorems may be of theoretical interest, it has no practical value when
dealing with a computer system that should perform a particular task.
Returning to TeX and LaTeX, I think that we will have to wait for
suitable extensions of TeX instead of hoping for an implementation via the
Godel theorem. :)
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/>
