Re: MN and the Principia

Bill Hamilton (
Fri, 27 Mar 1998 17:03:55 -0500

Paul Nelson quoted Newton

> This most beautiful system of the sun, planets, and comets,
> could only proceed from the counsel and dominion of an
> intelligent and powerful Being. And if the fixed stars are the
> centres of other like systems, these, being formed by the
> like wise counsel, must be all subject to the dominion of
> One; especially since the light of the fixed stars is of the
> same nature with the light of the sun, and from every system
> light passes into all other systems: and lest the systems of
> the fixed stars should, by their gravity, fall on each other, he
> hath placed those systems at immense distances from each
> other. (General Scholium)
Newton gets criticized for this statement, and those who criticize him hold
up LaPlace -- who told Napoleon "I had no need of that assumption (God)" --
as an example of a "more scientific" attitude. But it seems to me that
later developments would make LaPlace less confident. Poincare (I believe
it was Poincare) tried for years to solve the three body problem and
finally gave up saying it couldn't be done. Orbital dynamics problems
involve many more than three bodies. (Providentially, they can usually be
modeled as two body problems with perturbation terms to handle the
anomalies due to the presence of other bodies. But there is no law of
nonlinear dynamics that says that that is the situation that must occur)
Well into the twentieth century we began to realize that most nontrivial
dynamical systems -- especially many-body systems like the solar system --
are nonlinear and subject to chaotic behavior -- also known as sensitive
dependence on initial conditions. The upshot of all this is that perhaps
it is only possible for a wise, omniscient God to set the planets in their
orbits in such a way that their behavior is predictable. Newton looks
better all the time.
Bill Hamilton
Staff Research Engineer
Chassis and Vehicle Systems
GM R&D Center
Warren, MI