 
                         20060106.00

              The Computer Program as Knowledge

     Comparisons between the computer and the human brain
have always seemed naive to me, and I have considered efforts
to create artificial intelligence as overtly simplistic, no
less than the presumption to implement the very limited
available information about brain function in computer
structures grandiosely referred to as neural networks.

     Yet extrapolating from my own (admittedly) very limited
ability to write, to read, to interpret computer programs,
as distinct from using them, I see an analogy between the
computer program as an expression of symbolic (mathematical)
skills, and as such, as an expression of symbolic
(mathematical) knowledge, and those discovery-inventions of
the mathematician which are exhibited, and which are
comprehensible only in the obscure symbolism of mathematical
notation.  In the case of "pure" mathematics, validation is
obtainable only by those processes of thought that demonstrate
the consistency and congruity of the processes of calculation. 
One adds the result of subtraction to the subtrahend and
compares the sum of that addition with the minuend.  It is
their agreement which validates both the processes of
subtraction and addition. As one proceeds to more complex
areas of mathematics, this process of validation remains the
same, even where it becomes more obscure, and more difficult,
much more difficult to follow.

     Computer programming is a species of mathematics, with
the difference that the validation of computing algorithms
is not internal; one does nothing like adding a result to a
minuend in order to determine and demonstrate the correctness
of of a computer program; the validation is external. One
"runs", one executes the program, and the computer's function,
or lack thereof, is the criterion and the index of the program's
correctness.  Such externalization of what is essentially a
mathematical proof makes the invention of computer programs
not only more enjoyable but also more accessible to me.  The
opportunity to execute a program to establish its validity
constitutes a feedback mechanism for finding and correcting
mistakes.cw That mechanism makes computer mathematics self-
validating and self-correcting. Hence opening to someone
otherwise so hopelessly incompetent in mathematics as myself,
the door to this most fundamental of intellectual exercises.


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Copyright 2006, Ernst Jochen Meyer
