By Walter J. Meyer

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Vol. 3, p. 122, 1936. This is the first published work on the manufacturing progress curve. 3 APPROXIMATE AND LIMITED MODELS—GRAVITY, ROCKETS, AND RAINDROPS Abstract Mathematical models usually describe only very limited aspects of the world around us and, even then, only give approximately correct answers. Often the limitations and approximations are acceptable for our purposes. If they are not, we can sometimes build a new and better model by adding certain refinements. In this section, we illustrate these points by examining the limitations of Galileo’s model of gravity.

While the arguments raged about how many fluids there were and their nature, some men (notably Henry Cavendish, Charles de Coulomb, and George Ohm) were doing experiments and devising instruments that measured electricity precisely and provided the beginnings of a mathematical theory. However, this did not occur until the end of the eighteenth century, and it wasn’t till many years later that the nonmathematical fluid model became entirely obsolete among researchers. Those of us who deal with electricity only on a practical level have never quite given it up.

Our examples show that mathematical models are often, but not always, better; that nonmathematical models may evolve into mathematical ones; and that experimental work may be needed to provide data for mathematical models. Prerequisites None. No human investigation can claim to be scientific if it doesn’t pass the test of mathematical proof. Leonardo Da Vinci Mathematical modeling is an attempt to describe some part of the real world in mathematical terms. It is an endeavor as old as antiquity but as modern as tomorrow’s newspaper.