Mathematics, as currently taught, consists of the manipulation
of abstract symbols. For most people, the level of abstraction
makes math unpleasant or unusable as a practical tool for
exploring the problems of their lives. I believe that software
makes possible a new form of practical mathematics, based on
concrete modeling, simulation, and visualization. I believe it
is possible to design a tool that enables people to pose and
answer their mathematical questions in an entirely concrete
domain, without having to invoke abstractions, symbols, or
arcane rules. This tool would eventually displace many symbolic
forms of math, in the same way that the pocket calculator has
displaced manual arithmetic methods. This interactive essay is
an early step towards justifying and motivating the development
of such a tool. I take a typical school problem which is
intended to be solved with equations and geometric reasoning,
and present a solution using physical modeling and simulation.
This inspires the posing and solving o