# The Function Box

### The Big Picture

As told by Andy Long:

The "Function Box" was the brain child of my dad, Clifford Long, a mathematics professor at Bowling Green State University. He dreamed of a **function box**, a machine for
**dynamically** producing surfaces of functions of two variables. He was big
on what are now known as **manipulatives**: for example, he built a large
wooden hyperbolic paraboloid to use in multivariate calculus, because he knew
that lots of students have trouble visualizing surfaces (e.g. those projected
onto a screen). But this was an extremely time-consuming and energy-intensive
process: he wanted something computer-controlled, that would allow him to
dynamically produce such surfaces.

Years ago I bought him the toy **PinPressions**, which illustrates the
idea, only backwards:

Suppose we're interested in the function represented by
the height of Abe Lincoln's face above a table: you could take a
reading of the surface using pinpressions; if the pins were all wired,
we could read off the coordinates (as a matrix), and then create a
function to interpolate those values. This is an example of **rapid
prototyping**.

We want to operate in the reverse sense, however: suppose that we have a formula and seek a graphical representation of the surface corresponding to the function. We simply sample the function, and raise the pins to the corresponding heights, as a graphical representation of the function.