TURBULENCE AS THE CLASSICAL AMPLIFICATION OF QUANTUM RANDOMNESS:
Some have criticized my thoughts on Free Will by offering turbulence as an example of true randomness at the classical level but actually turbulence is one of the best examples of the differences between the classical level amplification of true quantum randomness and classical level non-computability. Turbulence is one of the least understood of all classical level phenomena even though there are are mathematical approaches that provide statistical, non exact, descriptions to a very limited accuracy of some aspects of this behavior.
Consider a river running over rapids. The volume of water flowing over the rapids can be considered constant in the short term. However the flow and pulse of the water over the rapids is seen to be continually changing in an exceedingly complex and ever changing dance. Though it stays within some larger scale limits, even it's moderate level details are never exactly the same.
If the physical world were actually completely deterministic the water flow over the rapids would stay exactly the same in every last detail. It would not dance. And I mean exactly in every detail, but of course it does dance. That is because the quantum level randomness of individual water molecules is in fact amplified by the the non homeogenity of the river bed. In a non quantum system, all turbulence would be constant and at most repetitive. In real life it continually varies in a never repeating dance. Classical turbulence theory does not explain how that could happen with constant inputs (boundary conditions). It can only happen because of the amplification of quantum randomness. There is no other source of such minute continual stochastic variation.
Some physical situations amplify the underlying quantum randomness and some submerge it into near macro homeogenity. A continuous large scale medium such as a gas in an insulated box tends to submerge quantum randomness because there is no structural variation for it to interact with; however a complex riverbed with rocks tends to amplify it. Human, and other biological, organisms are extremely complex non-homeogenous structures. Therefore they amplifly the underlying quantum randomness. That is why the action of humans is even freer in the sense of being less dependent on external causality than the river over rapids, and enormously freer than gas in an insulated box.
The suggestion by some that swimming fish might interject randomness into turbulent rapids just doesn't hold water. In any case these are not 'random' but 'circumstantial' events. But even so, a fish swimming here not there or a bird landing in the water produces only a trivial and unmeasurable effect on the every varying dance of a powerful rapids. The observations of such events clearly show no such effects - even when multiplied by the assumed number of fish in the river. The dance of turbulence occurs also in small streams with no fish or landing birds. Such effects are inconsequential and certainly not strong enough to cause the variability in the rapids that continues day and night in all weather, and even whether or not a herd of wildebeast are fording upstream.
The ever varying dance is also clearly evident in controlled situations such as large scale models of fluid dynamics of both water and air in which such circumstantial effects are purposely eliminated.
The only thing that can account for that in my opinion is the amplification of the quantum uncertainty of the uncountable trillions of H2O molecules banging into each other and rebounding on slightly random trajectories. When the flow is laminar rather than turbulent such quantum effects are much less amplified and tend to cancel out as they are all in the same general direction.
I hope that explains classical amplification of quantum randomness because its precisely this amplification of underlying quantum randomness that gives the world its wonderful living variability. Without it the world would be incredibly dull and uninteresting. Without it there would be no dancing of water, and none of the wonderful music of water flowing over rocks. It would just be the same monotonous sound over and over made by a completely non-variable uninteresting flow of water.
Likewise the widespread class of chaotic systems in general, systems in which very small changes become amplified to produce large system wide changes, are all cases in which those very small changes all must originate in quantum random effects.