Xah's Edu Corner: The importance of syntax & notations.

John Nagle nagle at animats.com
Sun Aug 16 23:58:40 CEST 2009


Xah Lee wrote:
> Xah's Edu Corner: The importance of syntax & notations.
> 
> http://www.stephenwolfram.com/publications/recent/mathml/mathml_abstract.html
> 
> this article should teach the coding sophomorons and computer
> “science” idiotic authors who harbor the notion that syntax is not
> important, picked up by all the elite i-reddit & twittering &  hacker
> news am-hip dunces.

    Definitely read Wolfram's paper.  He and his people actually had
to solve the problem.

    Wolfram had to face up to the big problem - how do we input traditional
mathematics into a computer unambiguously.  Version 1 was Mathematica
FullForm, which is very wordy but clear, like Ada.  This worked, but
was too clunky.  After a few redesigns, they came up with what he
calls StandardForm, which is Mathematica's variant on what he calls
"TraditionalForm", or mathematics as currently written in textbooks.
The differences are subtle; the main one is that precedence is more
explicit, and a "double strike" convention is used to disambiguate
certain meta-symbols, like the "d" used in derivatives and "i" used
as sqrt(-1).

StandardForm is unambiguous.  TraditionalForm is not, as anyone who
spends too much time reading other people's math publications realizes.
Cleverly, the Mathematica people have been able to produce a set of
heuristics which, Wolfram claims, allows converting traditional form
into the unambiguous StandardForm, getting it right most of the time.
(I've been struggling to read a paper on machine learning which has some
non-standard operator precedence problems, and I wish the paper was in
StandardForm.)

    Wolfram would, I think, like to make "StandardForm" the standard for
publication, and in time, something like that will probably happen.
It's useful to be able to get math in and out of symbolic manipulation
systems.

    Anyway, read the paper.

				John Nagle



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