Originally Posted by mike alexander

Warren wrote:


I would only say that this is where we may be using the same words to mean slightly different things. If we accept (just for the moment, no gotchas intended) that a coin flip is truly indeterminate, that is, unpredictable in advance, then the outcome of the flip is only precise in that it can result in one of only two states (heads or tails). The distribution of a large number of such flips is predictable, to any desired level of accuracy, depending on the total number of flips performed. The solution to the binomial distribution, predicated on equal outcomes of two states, offers the solution as well. (My sense of wonder at how this always works out is an emotional response. The rational side of my head understands this perfectly well, the kid in me still goes "Oooooh!")

The experimental verification of this is so strong that any significant deviation from the pattern in a large number of tests is a priori taken as evidence of experimental bias. And I do something like this many times every day.

Chromatography is based on the partitioning of a substance between two immiscible phases. As one phase passes over the other, individual molecules are distributed between the two (a dynamic equilibrium), based on the differential solubility bewteen the two phases. Even for the smallest sample the total number of molecules is on the order of 10^10 to 10^13. The shape of the chromatographic peak is Gaussian (the number of individual trials is so large as to move from the discrete distribution to the continuous), the result of ten to a thousand billion 'flips', each one completely unpredictable, results in a pattern so exact that any deviation form the peak shape is evidence of extra molecular interactions or a chromatographic column going bad.

I mention this because it is a more homely example of other indeterminate processes, such as nuclear decay, where the breakdown of a single nucleus is also unpredictable, but with millions or billions of them each second the decay rate is extremely predictable. It is so predictable that any deviations point to either experimental bias or new science.