This exercise that we have just sketched must qualify as one of
the greatest intellectual leaps ever taken by a man.
Essentially, it has taken us from dimensional analysis, some
non-trivial but still very accessible observations about objects
falling near the earth's surface, and some more exacting but
still very available *distant* observations of the motions
of planets and stars, and has correctly guessed an equation of
motion and the existence of a universal dimensionful constant
that are so close to a correct description that there are still
only three or four measurements precise enough to explicitly
expose any error in them. All of those measurements have been
triumphantly accounted for by Einstein with his later and more
universal theory of gravitation, which though very different in
spirit, is very close in predictions to Newton's law, discovered
three hundred years earlier, in almost every case that we are
yet able to measure. And, while Einstein's theory leads to new
equations of motion, and even to new ways to think about
equations of motion, it is built around precisely the same
fundamental dimensionful constant G as was Newtons, and does
nothing additional to express G as a derived quantity in terms
of anything ``more basic''.

In reaching it, we have been shown a way to reduce the
complexity of the natural world to something easily expressed in
a simple equation in very many cases (though often less easily
solved), we have been led to the concept of conservation of
momentum, which we will develop much further in the next
chapter, and we have found the next refinement of the *degree* of understanding beyond that of dimensional analysis, in
the form of the concept of an *equation of motion*, which
not only identifies the allowed from the disallowed paths, but
goes far beyond that to allow us to completely predict *which* allowed path will be taken, once we know only where it
starts and with what velocity.

This is a staggering legacy for the work of one man in a part of one lifetime, and we have not even mentioned the details of the calculus, which is the mathematical machinery enabling all of these equations to be solved, some of them nearly as easily as they can be stated.

And finally, we keep in mind, for perspective, that with this work, man inherited the first real possibility to change his disposition toward nature, from one of an inescapable superstition to one based, a piece at a time, on growing understanding.

Thu Aug 31 12:01:42 CDT 1995