[plt-scheme] Scheme contradictions

On Wed, 2006-05-03 at 01:05 +0000, Glenn Ambrose wrote:
   . . .
> Here now is the contradiction. A programming language called Scheme yet 
> there seems little scheme as a term refering to a goal there. I look around

Suppose the goal is to provide an excellent language with which to
implement the programs that further a wide variety of goals?  A
meta-level goal is still a goal.
   . . .
> Compare this to Logo, you start out drawing little pictures and writing 
> small conversations you can have with the computer. Fun and interesting. 
> Netlogo, make a landscape with a hundred little turtles that will run up the 
> nearest hill, all in one sitting. Fun and interesting. Visual Basic, make a 
> simple calculator, that looks like a calculator. Interesting. Scheme, write 
> a series of fibbonacci numbers. Unless your name is Fibbonacci this isn't 
> interesting. People would be willing to put up with a lot of boredom if

I can still remember myself at sixteen -- I was reading Newman &
Kasner's "Mathematics and the Imagination", Dantzg's "Number - the
Language of Science", Gamow's "One, Two, Three ... Infinity".  I would
have *loved* a tool like Scheme where I could explore Fibonacci numbers!
Think of it: A few lines of code and I could see as many as I wanted; a
few more and I could *see* the ratio Fn+1/Fn converge to tau.
Change a few lines and Presto! Lucas numbers.  Some experimentation and
Holy hailstones, Batman! the Collatz sequences (3n+1 problem).  It
wouldn't be long before continued fractions are in hand.  In fact, much
of recreational mathematics is available for experimentation and play
with a tool like Scheme around.

I wasn't alone in High School and I believe there are kids like me to be
found in any High School today.  I and my cohorts and like-minded
students today would find deep interest in the *content* in a tool like
Scheme, and not in the glitz of pointless games.  Of course, we would
all need a teacher/parent/friend who recognized that our minds were
starting to develop in a somewhat unusual way, perhaps, and who could
figure out a way to engage them.
   . . .
> People seem to learn best when they are persuing a goal. As web-programming 

Such as the goal of playing with, experimenting with, exploring
elementary mathematics?  Scheme is ideal for that.

I've seen several introductory number theory texts that use programming
to foster exploration.  They use Pascal or C or Basic, and they all
spend time talking about the limits of machine numbers and how that
restricts the ranges over which the student can play.  All their
exercises and problems can be implemented *at least* as easily in PLT
Scheme, and under-the-hood multiple-precision integers and rationals
makes the all mumblage about machines superfluous.  Time enough for the
grodie details later; right now, let's play!

Just a note from a slightly different perspective,

 -- Bill Wood