Pornography, calculus, cinema, metaphor

[Glenn Scheper]

> The Greek letter "delta" in math is used to indicate change, 
> or "difference" and T stands for time.

My first encounter with Delta was with "first differences".

In high school on the IBM 1620, I would type in a list of
numbers, and the Fortran or Newtran program I had written
would type back (Literally: Solenoids pulled down the keys
of the tallish office machine type of typewriter console.)
it would type back a list of numbers gotten by subtracting
adjacent input values, the "first difference".

Then of course, the differences of all the adjacent first
differences became the second differences. Then the third,
etc., each list of discrete differences becoming shorter
by one, until the triangle peters out, whereupon no more
differences are needed to fully describe or recompute the
original list of data. These are also, "The Derivatives".

Suppose i concoct a few lists:

2 4 6 8 10...

 2 2 2 2 ....

  0 0 0 0 ...

If the top line represents samples one unit apart on an
X axis, and the values their plotted height on a Y axis;
which are the dX or "change in X value", and the dY, or
"change in Y value", then the ratio of dy/dx represents
the slope of the graphed function at any given point X.

In this case, it is a straight line, and the slope at any
point has the constant value of 2: Two rise per one run.

If the X axis represented Time, t, and the Y axis were
distance, then dy/dt would mean "the change in distance
for a given change in time", that is, the "speed".
And the second derivative would mean the "change in speed
for a given change in time", that is, the "acceleration".


Some input data never settles down like the list above.
Consider this input data:

 0 +1  0 -1  0 +1  0 -1  0 ...

  +1 -1 -1 +1 +1 -1 -1 +1 ...

    -2  0 +2  0 -2  0 +2  ...

Well, I expected to show you that the first line
was like a SINE function, and the second line its
derivative, which I thought would be the COSINE,
and alternating on down. But I never did too well
with all the odd constants like 2 that would pop
out of calculus' integration and differentiation.

So I'd better quit before reduced to sputtering.

Gee. I didn't mention pornography. Okay, there.

Yours truly,
Glenn Scheper
http://home.earthlink.net/~glenn_scheper/
glenn_scheper + at + earthlink.net
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