Randomness Versus Explanation
Randomness is at its best when your knowledge is at its worst, making it a useful decision-making tool in complex situations. If you believe all lottery numbers are equally likely, you would act rationally to assume a “principle of indifference” when deciding which lottery ticket you should buy.
But you could hardly claim that anything about the actual outcome was particularly fundamental. In fact, if there was something that made the actual outcome more likely (say, a rigged machine), then the principle of indifference would have led you astray. Randomness can work for us, but only when there’s nothing fundamentally interesting that needs explaining.Now, it may be that the ultimate rules that govern our universe have randomness in them—perhaps the equivalent of little coin-flips that occur throughout space and time, buried in the microscopic dynamics. But even then, our best explanations would go through despite this randomness, rather than resulting from this randomness. Suppose it turned out that the time-asymmetry implied by the coin flips statistically cancelled out, averaging to what looked like larger-scale reversibility (yielding known time- symmetric dynamical rules). Certainly it wouldn’t be fair to say that the randomness “explained” the apparent large-scale time-symmetry, because this sort of random process would be time-asymmetric. Compatibility is not an explanation. Certainly, any interesting patterns in the larger scale laws would—if anything—be made less interesting by random noise.
Whatever one thinks about the validity of “random explanations”, it should be obvious that most events can have better, non-random explanations. In classical physics, if you know everything about the current state of the system, you can plug those values into dynamical equations and compute either the future state or an earlier state.
Given one state[37], therefore, we can explain other states at different times. When such “dynamical explanations” are available, they’re always more fundamental than random explanations. After all, they start with more inputs (and fewer unknowns) and so can always make better predictions.In practice, dynamical explanations usually don’t work as advertised. There’s always something we don’t know, and when those unknowns become important, our predictions are going to be uncertain. You could know the temperature, pressure, and volume of some gas, but that hardly tells you all the details of each molecule. Presented with such a vast number of unknowns, we’ve found that it’s useful to resort to the “equal a priori probability postulate” of statistical mechanics. We’ve found that adding randomness in this manner and then applying the dynamics works remarkably well—we’re often able to predict what happens next, even with our lack of knowledge. Viewed in this light, it seems that dynamical and random explanations work together to form an empirically successful package.
But this is simply not a correct reading of the situation. For known dynamical rules, if everything is known at some instant, accurate predictions can be made either forward or backward in time. In the partial-uncertainty case, on the other hand, predictions only work properly in the forward time direction. If you try to apply the same logic in reverse, you almost always get the wrong answer (unless you’re at thermodynamic equilibrium). Suppose you’re trying to use this technique to predict the past of a shattering egg. Even if your knowledge of the shattering egg was almost complete, you’d still find that the unknown parameters would conspire in unpredictable ways to throw off your dynamical predictions. In general, when analyzing time-reversed movies of physical phenomena, combining dynamic and random explanations fails entirely.
Given this, it should be evident that what is doing the explanatory work in the forward-time case isn’t the time-neutral assumption of randomness, but rather something that must necessarily be time-directed.
And that something is the Second Law of thermodynamics itself. When the Second Law is in play, there’s a nice provable reason why the unknown parameters usually don’t matter much. Of course, sometimes unknowns do matter—an unknown puff of wind can alter a thrown ball. But that’s a far cry from air-friction run in time-reverse, where the unknown microscopic details lead to coherent macroscopic effects which can accelerate balls without puffs of wind. Our empirical success at making predictions from imperfect data is therefore not due to “random explanations”, but rather “Second Law explanations”. If the randomness were doing the explanatory work, it would operate just as well in reverse.What really needs explaining, therefore, is the success of the Second Law. The next section will explore possible dynamical explanations and random explanations, finding that neither of these can do the job. A third type of explanation will then be needed.
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