MATHEMATICS AND REALITY
Copyright 1984 to 2005 Allen C. Goodrich

Newton's equation for gravitational force
F = Gm^2/L^2 is only true for particular values of L
, m and G.
And it provides the value of a force that does not exist
in the real world. Force of gravity is an illusion which
is created by the equation and which Newton assumed
to exist.
What does this tell us about mathematics and reality?
We must be very careful to define all of the terms of the
equation because it will be only these terms that are
related by the equation.
We must be very careful in drawing conclusions from
the equation, Equations represent reality only if they
are proven to be true by exhaustive experimentation
and experience. And then, only to the limit of our
present knowledge.
This is probably the most important lesson that
scientists and engineers must learn from experience.