[Edu-sig] From my Mathematics Classroom: Re: Python's advantages

[kirby urner]

FYI, here's me replying to myself on the Math Forum.  Feedback welcome.

A lot of this will go over the heads of my target audience, especially
advantage (c), which is all about avoiding unwanted intellectual
purity when it comes to enforcing a "one data structure" regime. 
That's just not Python's paradigm, and that's OK.

http://mathforum.org/kb/message.jspa?messageID=4623827&tstart=0#reply-tree

Kirby

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For those few who don't know, maybe just joined this list, Pythonic
Mathematics involves a hands-on, shop-like approach, per Popular
Mechanics or more recently Make: (O'Reilly) i.e. using some computer
language as an apparatus to build actual "math objects" such as
polynomials and rational numbers, polyhedra, vectors, integers with a
modulus,
quaternions, whatever.

The advantages of Python are several, but among the top few would be:

a. an interactive evaluation loop
b. a strong OO paradigm, and
c. simple but not too simple syntax.

Let me say a few words about each of these features...

<topic = "Python's positive features">

a. An interactive evaluation loop

Many languages come with an implied development cycle that includes
the step of compilation, perhaps to be followed by a separate linking
step, whereby "source code" is translated to a faster, stripped-down
machine or assembly language (not to be confused with .NET
assemblies). The compiled and linked executables are then usually
platform specific, fast, and efficient. The Python engine itself is
just such an executable (different binaries work on different
operating systems).

However, Python source, like Java source, compiles to a byte code
language implemented atop a VM (a virtual machine). Transporting
Python across platforms means reimplementing the VM in various brands
of C (or whatever), while keeping the language itself essentially
unchanged at the top level.

Yes, some subtle differences in core Python may be felt (perhaps in
the frequency of garbage collection), plus the shared libraries will
only partially overlap (the GUI widgets on your Nokia cell phone won't
match the GUI widgets in Gnome), but still, the high level of
cross-platform compatibility means we can't be accused of fostering
servile obedience to any one particular operating system and/or
business model and/or corporate regime.

As users jump from one computer to another, perhaps between operating
systems, the Pythonic VM presents a fairly constant command line
environment to the student, maintaining continuity and allowing the
swift learning cycle associated with "immediate feedback" i.e., in
being interpreted to byte codes, Python is able to accomplish
line-at-a-time translation to executable code, meaning the student has
full access to an interactive command line experience, as well as a
scripting mode.

Note: Python is one of many languages to host its own interactive
shell sessions, some others being Logo, Scheme, APL, J, ISETL, and
xBase (the various dBases and FoxPros).

b. A strong OO paradigm

Many teachers don't seem to realize that OO is valuable for its
connections to everyday experience, in terms of shared metaphors, not
because it's the superior paradigm for all programming or anything
like that.

OOP is simply very accessible to neophytes, provides a bridge, in the
form of a simple yet sophisticated set of concepts, easy enough to
grasp: blueprints (templates), a class hierarchy, objects as
instances, ready for business, presenting methods and properties to
their users. Just like in real life: the bus door opens, passengers
get on, paying or flashing passes -- now draw that in OO.

Python is very consistent in its OOness. Primitive objects like 1,
2e-5, 'b', 3j are immutable objects, with callable methods. 1 + 1 is
equivalent to 1 .__add__(1), i.e. we're passing the right-of-operator
argument to the polymorphously definable __add__ method, in this case
the version associated with the integer class or type. The __add__
method characteristic of vector objects, as in vA.__add__(vb), as in
vA + vB, would be somewhat different, but with commonalities (e.g. per
the group theoretic properties of 'addition' (the existence of an
additive identity, inverse and so on)).

Through the lense of an OO language, the apparatus of ordinary K-12
level mathematics becomes surveyable as an extensible type system, not
just in practical terms, but somewhat formally and theoretically as
well (yet just the practical advantages alone would be enough to
motivate the change-over, at least out here, in our Silicon Forest
economy).

c. Simple but not too simple syntax

The "batteries included" aspect of Python is in part its Standard
Library, but more primitively its rich set of built-in data
structures.

It shares this feature with other so-called P languages (Perl and PHP
-- remember LAMP?), with Ruby, with myriad others.

There's less of a compulsion to regard data structures as atomic, such
that one lucky devil must be ultimately cast as the root form of all
other data structures.

Yes, there's satisfying intellectual purity in pursuing the "holy
grail" of data structures, but other pursuits deserve their own
shining knights. Python's quest is not to turn everything into lists,
but everything into objects. That's the atom (the object). Our goal
has already been attained. We're entitled to preach our little OO
gospel without too much guff from the functionalists or whomever.

A richness of built-in data types is not an embarrassment, but simply
an intelligent-enough design, a workable set of primitive tools. We
have the punctuation on every ASCII-compatible keyboard ({}, (), [])
so why not use what we've got? Dictionaries, tuples and lists, oh my.

</topic>

However, much of what I intend to talk about in London won't be all
that language-specific. You won't have to know Python to understand my
proposal: that we phase out such heavy reliance on calculators and
give students more opportunities to tune in what the computer
scientists have been up to in these last few decades. It could no
kidding even help with their math skills and boost their level of
understanding. In any case, it's worth trying, and trials are
currently underway, with more planned.

Kirby