[Edu-sig] Queens, NY - PYTHON Programming for Kids
Kirby Urner
pdx4d@teleport.com
Thu, 13 Jul 2000 15:13:06 -0700
Howdy Dirk --
This might be a bit off-topic for Python, but I agree with you
that metaphors are often the key to unlocking esoterica in=20
mathematics, the simplex algorithm included.[1]
I had the good fortune to study linear programming (the math
sub-specialty in which this algorithm shows up), with one of
the originators of the discipline: Kuhn I think the name
was, then a professor at Princeton U (I'm Class of 1980).
What gets confusing sometimes is that people lose sight of=20
what's metaphoric and what's literal. In science fiction,=20
this is deliberate -- we want to take advantage of hyper-
dimensional timespace worm holes and such. But I wish we
had more humanities people willing to help deconstruct=20
"dimension" in ways that subtract "hype" rather than add
to it. It's hard to think of a concept more deeply embedded=20
in a morass of semantic confusions than "dimension".
This is why Coxeter has to waste time in 'Regular Polytopes'
trying to disentangle what's been deliberately mixed, i.e.
his brand of hyperdimensional geometry from the Einsteinian
stuff, in which "4D" resonates with "time as the fourth
dimension" -- no such resonance exists in extrapolated=20
Euclideanism (where the simplex algorithm lives [2] --=20
simplex also means "tetrahedron" BTW, in the 3D case),=20
where we're just making the tuples wider i.e. if it works=20
for (1,0,0), it'll work for (1,0,0,0,0,0,0,0,0) [overlap
with Python's "tuple" in this neighborhood, i.e. it's
just a data structure, an object, nothing mysterious or
"hard to visualize"].
You'd think mathematicians could be trusted to fight these
confusions, but I think (a) a good mathematician isn't=20
necessarily a trained philosopher, and many a math head
hasn't sufficiently appreciated Wittgensteins 'Philosophical=20
Investigations' into the foundations of mathematics and=20
(b) math, like physics, tends to gain in the public eye=20
in proportion to it's "gee whiz" capabilities, and being=20
able to truck out some chatter about n-dimensional manifolds=20
is always a sure-fire way to get laypersons to see stars,=20
and maybe fatten the budget for next year's circus.
My approach has been to offer some polemical critiques,=20
e.g. my 'Synergetics Versus Hypercross Dogmatics' at
http://www.teleport.com/~pdx4d/hypercross.html, designed
to signal my disdain for those charlatans who would hoodwink=20
the lay public by milking the hyperdimensional cow. Too=20
much math chatter sounds like Federation Science e.g.=20
gibberish designed to artificially inflate its own=20
significance (or support plot development with pseudo-
science, in the case of 'Star Trek'). That's not to=20
say it's purely nonsensical, but I think too few mathe-
maticians are ready to own up to the fact that the=20
"fractional dimensions" lingo, for example, isn't a=20
requirement for moving ahead with dynamical systems theory. =20
We _could_ be doing the same algorithms and getting the=20
same pretty pictures, without buying a jargon in which=20
"dimensions exist in fractional parts" (I file that=20
innovation under "clever marketing hype" -- hats off to=20
Mandelbrot & Co.).[3]
In sum, I think kids should be instilled with some=20
healthy skepticism when it comes to these various brands=20
of high flying academese. There's nothing "wrong" or=20
"incorrect" about these ways of talking, and I'm not=20
trying to win points by ruling them out of bounds (a=20
hopeless battle). More to the point, I'm willing to=20
undermine and subvert any creeping dogmatism, which you=20
find around teachers who say "it MUST be this way". For=20
example, how'd you like to see a "four dimensional geometry"=20
that is neither Coxeter's nor Einstein's, yet is internally=20
self-consistent enough to merit the terminology. I've got=20
one of those on tap, in Python no less (ah, here's the=20
tie in): http://www.inetarena.com/~pdx4d/ocn/pyqvectors.html.
Kirby
4D Solutions http://www.teleport.com/~pdx4d/
^^
no, _not_ "3D + Time"
Linear Programming References
[1] http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html
http://www.alliance-computer.com/linearp.htm
[2] http://www.ece.purdue.edu/~echong/book/toc.html
4 Concepts from Geometry=20
4.1 Line Segments=20
4.2 Hyperplanes and Linear Varieties=20
4.3 Convex Sets=20
4.4 Neighborhoods=20
4.5 Polytopes and Polyhedra=20
[3] http://www.cribx1.u-bordeaux.fr/fractals/history.html
At 09:59 PM 07/13/2000 +0200, Dirk-Ulrich Heise wrote:
>-----Urspr=FCngliche Nachricht-----
>Von: "Thomas A. Williams" <Thomas_A._Williams@NEWYORKLIFE.COM>
>An: <edu-sig@python.org>
>Gesendet: Donnerstag, 13. Juli 2000 18:58
>Betreff: Re: [Edu-sig] Queens, NY - PYTHON Programming for Kids
>> Hi Kirby,
>> Thanks Much for the info. Methaphorics - using metaphors to teach
>> subject material. I've not used metaphors that often in teaching.
>
>Here's a metaphor that made me understand the Simplex
>algorithm (finding an optimal solution for a set of unequations):
>
>The (multidimensional) problem space is divided by hyper-planes,
>each unequation defining one hyperplane, and each hyperplane
>has a side that falls into the "non-solution" area, and the other
>side falls into the "solution" area. This way, all hyperplanes
>together form a diamond-like shape.
>
>The Simplex algorithm travels all vertices of the diamond to
>find the one that is optimal (minimizes one of the coordinates
>or a combination of several of them).
>
>I never understood Simplex until i read this metaphor. I think
>i read it in Sedgewicks "Algorithms" book. (Don't remember
>the exact title, and it wasn't Edie Sedgewick but a professor)
>
>And i think, this explanation would make the Simplex algorithm
>even feasible for 17-years-old :-)
>
>Dipl.Inform. Dirk-Ulrich Heise
>hei@adtranzsig.de
>dheise@debitel.net