[Phys-L] Re: Calculators a Distraction?

[John Denker <jsd@AV8N.COM>]

Edmiston, Mike wrote:
> I did enough assembly-language programming in the 1970s to know that
> iterative subtraction was the easiest way to do division.

1) When you're doing it on paper -- which is appropriate
to the current context i.e. grade school math concepts --
it is conceptually equivalent and operationally easier to
do division by iterated *addition*.  Try it sometime.

The argument that division is just iterated subtraction
could equally well be used to "prove" that division is
just iterated addition!  IMHO the conceptual point is
mostly wrong, and even if it's not _entirely_ wrong it
serves no pedagogical purpose.

My conceptual point is this:

  ==> the iteration of an inverse is not
      the inverse of an iteration <==

2) The binary version of long division is remarkably easy
to code.  Is iterated subtraction really easier?  I'll
bet it's not much easier ... and it runs a whole lot less
efficiently.  YMMV, but I was doing real-time interactive
applications, and we were planning on selling lots of
copies, so the cost of coding the long division algorithm
was trivial compared to the cost of upgrading the hardware
to run an inefficient algoritm like iterated subtraction.