Jforum: Absolute beginner question...

Tue Mar 19 00:09:30 HKT 2002

Dr. Sastry -
take a look at the J Help/Help/Computers and Mathematical
Notation - Kenneth E. Iverson
for an exposition by Dr. Iverson on mathematical
notation. This reflects his ongoing interest which
I believe was motivated at least in part by the
ad-hoc, inconsistent nature of traditional math
notation.
Traditional notation has been cobbled together over
the years by many different people thus it is utterly
lacking in consistency. Consider the
traditional notations for numerical negation (e.g. -x),
factorial (n!) and absolute value (|x|). Looking
at the positioning of the symbol for the function in
each case, what would be the general rule if I were
inventing a new function? Obviously, there is no
such rule.
Consider also the widely-accepted notion of order of
execution: this is a concept which does not scale well.
It works fine when we first learn arithmetic
and know only the 4 or 5 most basic functions. 
However, it becomes increasingly arbitrary and 
complex to apply when we know of 10 or 20 or more 
functions. Take a look at a C programming manual's
section on order of execution - you'll see something 
like a table with 15 or so rows divided into 2 
columns (for right and left associativity). This is
30 or more things to remember instead of one simple 
rule of positional precedence.
These are but a couple of the issues we seldom 
consider when learning traditional mathematical
notation. Dr. Iverson has attempted to provide
a consistent, extensible framework in the form
of a grammar, to help us organize this most
important facet of mathematics.
Devon H. McCormick, CFA
devon at acm.org
--- Venkat V S S Sastry <sastry at rmcs.cranfield.ac.uk> wrote:
> Dear Members,
>> I have recently came across J from friends and one student(!)
> about J.
> Curiosity got better of me, and downloaded the software.
>> From my initial explorations, I couldn't find any articles as
> to WHY J
> is developed. I would appreciate if some one could point me
> to such an
> article.
>> Venkat.
>> --
> Dr. Venkat V S S Sastry
> Applied Mathematics and Operational Research,
> Engineering Systems Department,
> Cranfield University, RMCS Shrivenham,
> Swindon, Wilts, SN6 8LA, UK
> Tel: 01793 785315
> Fax: 01793 784196
> Email: mailto:sastry at rmcs.cranfield.ac.uk
>>>
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