"Kevin Aylward"  wrote in 
news:br7nsr$1nas$1{at}darwin.ediacara.org:

> Paul P. Budnik Jr. wrote:
>> "Kevin Aylward"
 wrote in

>>> Your claim that it is not always possible to predict the
>>> consequences of an otherwise deterministic system is a claim I have
>>> not seen related to goedal, or otherwise. If this were so, this
>>> notion would have cropped up in many areas. It would be a
>>> fundamental issue of classical physics. You are claiming that given
>>> Newton's laws, and a ball in a box, than all of its future motion
>>> cannot be predicted, in priniple. This is such an astounding
>>> statement that it would have surly been noticed before now.

>> Not all of its motions but it has been well known for a long time
>> that the three body probem is recursively unsolvable. There is no
>> general method to determine if three masses orbiting each other will
>> ultimately collide. [snip]
 
> But this notion is not relevant to the general question of 
deterministic
> systems. We can write down the differential equations for the 3 body
> system and simply solve them numerically. In principle, from a 
classical
> perspective, all of its motion can be absolutly predicted for as long
> into the future as required. This is what is meant by a deterministic
> system. Whether or not the bodies will collide will indeed be predicted
> if the equations are solved for the appropiate time. A non 
deterministic
> system by *definition* is *only* when an action can be taken, which in
> *principle*, can not be predicted.

Poincare proved in the nineteenth century that in *principle* you cannot 
solve the three body problem - you cannot absolutely predict the future 
motions of a 3 body system. So yes, given Newton's laws, and three balls 
in a box, you cannot predict all of their future motion. It has been 
noticed before now, but was not well recognized until chaos theory became 
fashionable. 

Yours,

Bill Morse
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