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.)
Hans Aberg
* Email: Hans Aberg <mailto:[log in to unmask]>
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