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In article <1940@uoregon.uoregon.edu>, markv@uoregon.uoregon.edu (Mark VandeWettering) writes:
> 	Mathematics suffers from exactly the same problems as
> 	programming languages: ideas get muddled in notation.

It's much worse than that.  The basic notation -- and therefore the thought
processes it fosters -- describes a system of "eternal truth", usually
shown by the equals sign ( = ).  It not only says stuff on each side is
equivalent; it implies it always has been, and always will be.  Whatever
process change is needed must be artificially imposed from outside.

At one time mathematicians honestly believed they were manipulating, and
discovering, basic truths about the universe. "God is a mathematician."
Truth was eternal (like the universe itself).

Unfortunately, Goedel smashed the first idea, Hubble the second.  Change
is far more universal than stasis.  Turing was, I think, the first to
realize the enormous power of the simple concept embedded in

    i <- i + 1

which is, confusingly, often written as 

    i = i + 1

but when it is, at least it negates the idea that truth cannot be changed.

-- 
Ed Nather
Astronomy Dept, U of Texas @ Austin
{allegra,ihnp4}!{noao,ut-sally}!utastro!nather
nather@astro.AS.UTEXAS.EDU