Three body problem such as the interaction between say, the sun, Earth and Jupiter. At the end of the nineteenth century Poincare' showed mathematically that the positions cannot be precisely predicted.
The solar system is not like a piece of clockwork however much the early modern scientists, mixing observation with mediaeval idealism about perfect spheres, hoped this was so.
The location of the asteroid belt is better understood as lying in a position in the solar system that would otherwise probably have been occupied by another planet. For reasons we cannot yet explain, on the boundary between the smaller planets and the larger ones, this band of debris did not form a planet. It almost certainly represents a "multipe-body" problem between the sun, Jupiter, and the other planets, that still defies the power of our best computers to resolve.
I agree very much about what you say about biological systems. But as Prigone argues in his optimistic book "The End of Certainty", Newtonian mechanics too was a simplification. I.E non linear dynamics apply to the inanimate realm as well as the realm of living things. Machines are merely temporary, relatively-stable man-made objects, and no analogy for the workings of society, or human minds.
Murders will not stop just because murderers can themselves be killed with the most efficient scientific method known to the richest society on this planet, with the throw of a switch or the press of a button. Nor by changing the DNA of the potential murders.
This form of thinking represents a sort of impiety to the natural order and our possibility of living together with dignity.
Chris Burford
London