[Numpy-discussion] [Python-3000] PEP 31XX: A Type Hierarchy for Numbers (and other algebraic entities)

[David Goldsmith]

Bill Janssen wrote:
>> Jeffrey, is there any way you can drop the top of the tree and going
>> straight from Number to Complex -> Real -> Rational -> Integer? These
>> are the things that everyone with high school math will know.
>>     
>
> I think knowledge of the concepts of group, ring, and field is
> supposed to be standard knowledge for any high-school senior -- isn't
> this what the "new math" was all about?.  
Nah, AFAIK, not really.  Of course, for those who remember Tom Lehrer, 
New Math was about learning that one could base number representation on 
bases other than 10 (even more fundamental to CS, no?), but I think it 
was rather more about broadening the standard curriculum to include more 
than just arithmetic drill, i.e., to more prominently include things 
like problem solving skills, (somewhat) more abstraction, etc.  Along 
the latter lines, I do remember learning (and tutoring), by name, things 
like the symmetric, reflexive, transitive, associative, commutative, and 
distributive properties, but I didn't hear/see the words group, ring, or 
field (in a math context) 'til I got to college and was formally 
introduced to the subject of Linear Algebra (and lest you think my HS 
math curriculum was deficient and/or non-standard, I don't want to go in 
that direction, but trust me, it was more than sufficient and it was 
non-standard, but in the positive direction, not in the negative, and I 
graduated 1st in my class in math).  As far as the scientific 
disciplines which one might reasonably expect a college major therein to 
have at least a "nodding acquaintance" w/ the classes of Abstract 
Algebra, certainly Math (and hopefully Appl. Math and Stats), probably 
Physics, perhaps Chemistry, CS if you say so, but even Engineering I'd 
say you're beginning to tread in uncertain territory, and Biology, etc., 
unless taken with a large dose of formal mathematics, fuhget-about-it.

DG
> But they're pretty
> fundamental to computer science; anyone trying to do serious work in
> the field (that is, anyone with a reason to read the PEP) should have
> a nodding acquaintance with them.
>
> Bill
>
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