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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.



Next: THE PRINCIPLE OF Up: NEWTON'S REVOLUTION: THE Previous: FREE-BODY DIAGRAMS


desmith@
Thu Aug 31 12:01:42 CDT 1995