First of all, a big THANKS for all the interesting ideas. I've been
trying to get my brain around all this for quite some time. And I
think its time I sit down and start writing on the divide between
Math and Computing.
One of the more interesting discussions on this topic comes from the
APL/Ken Iverson world. APL (A Programming Language) used a concise
mathematical notation for its syntax. It was quite a hit at Xerox in
the early to mid '70s and indeed was considered a great rapid
prototyping language.
One of Iverson's ideas was that mathematical notation was flawed and
could easily be fixed by focusing on making it more parseable and
less ambiguous. His 1979 Turing Award lecture was a wonderful
summary of these ideas:
Notation as a Tool of Thought (1979 Turing Award Lecture)
by Kenneth E. Iverson, Communications of the ACM,
Volume 23, Number 8, August 1980.
http://elliscave.com/APL_J/tool.pdf
In a sense, Ken was the one of the pioneers poking at the topic we're
discussing. I suspect Turing, Von Neuman, and others were there too.
Ken's APL work has been carried on by Ken's son Eric and Roger Hui,
both of whom worked closely with Ken. APL has been morphed into the
J Programming Language:
http://en.wikipedia.org/wiki/J_programming_language
I've taken a run at J with some success. Its reasonably cross
platform. But boy, the learning curve is steep! The power of J,
however, is considerable. If any FRIAMers start in on J, let me
know. These sites are representative of the leaders of the J community:
http://olegykj.sourceforge.net/
.. and all the External links at the end of the Wikipedia article.
-- Owen
Owen Densmore http://backspaces.net
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