[Tutor] [Edu-sig] school physics/math courses

[bob gailer]

Edward Cherlin wrote:
> [snip]
>
> As a teacher, I know very well what it means. Some representations are
> easier to understand, or easier to work with, or easier to learn from.
> Various thinkers, including Babbage, Whitehead, and Iverson, have
> commented on the effects of the way we represent problems on our
> ability to think about them, and not only they but luminaries from
> Fibonacci to Einstein have labored to invent or teach new notations
> and representations.
>   
I'm glad to see Iverson amongst Babbage and Whitehead. In 1974 I was 
introduced to his invention: APL. That transformed how I thought about 
problems and expressed algorithms. I still wish for some way to bring 
some of that magic into Python.

I found it interesting to hear (in the migration to Python 3) that the 
Python reduce function was not used a lot or well understood. I 
certainly use and understand it.

A brief tutorial for any who have read this far and are curious: In 
Python one may combine the elements of a list using sum() (if the sum is 
desired). For other functions one uses reduce. To get the product of the 
elements of a list Y: reduce(operator.mul, Y). In APL reduce is / and 
multiply is x so one writes x/Y. (Classic APL had only upper case for 
names).

I can write and comprehend x/Y much faster than the wordy equivalent.

And Y can  be an array of 0 or more dimensions. +/Y computes the "row 
sum" giving an array of one less dimensions*. So if Y were:
1 2 3
4 5 6
the row sum is 6 15.
* if the number of dimensions is 0 (a "scalar" value) the result is the 
scalar value unchanged.

-- 
Bob Gailer
Chapel Hill NC 
919-636-4239

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