Thursday, January 26, 2012
Thermodynamics and information theory are often grouped with classical dynamics. This is especially true where theory space is cleaved with quantum dynamics and other quote/unquote "non-deterministic" or "non-linear" theories on one side. But such classifications are problematic for several important reasons. Traditionally, the criteria of inclusion within the rubric "classical" has leaned heavily upon the concept of computation from knowledge of initial conditions. in Newtonian (and Relativistic) dynamics, knowing the initial state of a system allows one to calculate and thus predict the state of that system at any time in the future. Accuracy in prediction, from a classical perspective, is gated only by accuracy of knowledge of the original conditions of that system. Enter now, the strange world of quantum dynamics, where indeterminacy and sensitivity to observation turn classical calculations on their head. Non-clasical systems are systems in which determinism actually works against accuracy of prediction. The more you try to increase your knowledge of the initial conditions of a quantum situation, the less accurately you can predict that system's future. Much is made of the philosophical implications of observer "relativity" in an Einsteinium space/time model, but vantage-sensitivity is absolutely classical – the more you know about the initial conditions, the more accurate will be your relativistic predictions. In the quantum world, knowledge is itself, a cost of business attribute. In the quantum world, knowledge perturbs. In the quantum world, a system that seeks to know itself, is a system that is changed. In the quantum world, there are two types of systems, systems that are statistically perturbed, and systems that are locally perturbed. Meaning, you can measure (observe) aspects of a whole system without messing with that system, but should you want discrete knowledge of individual particles within that system, you must pay the price of a system that is forever thereafter disturbed. It is interesting how closely the empirically observed quantum world mimics the limits Kurt Godel placed on absolute knowledge. OK, let us now contrast thermodynamics, specifically the second law of thermodynamics, against both classical or deterministic dynamics and quantum indeterminacy. If one accepts that purpose of knowledge is prediction, is fidelity of calculation to actual future states, than both classical and non-linear theory are self-limitiing. Classical prediction is hampered by limits to the accuracy of observation of the initial state. Quantum prediction is limited by the way systems are perturbed by measurement, the more you know, the more you must include yourself into to prediction calculations, and the more said act is limited by Godel's caps on self-knowledge. One could say that classical prediction is dependent at base upon naiveté, and that quantum prediction is limited by knowledge itself. But what of the second law? The second law allows for absolute knowledge of the end state, of "heat death" or complete dissipation. Unlike all other forms of theoretical abstraction, the second law is absolutely agnostic to initial condition(s). You can use Newton's laws to look into the immediate future of a gravitationally bound system, but the same laws are meaningless in a system perturbed by other forces. Thermodynamic theory doesn't care what forces or materials are at play, it only cares about difference. In fact, thermodynamics doesn't know for the difference between material and force. The second law says that difference will always be less after any change in any system. The second law says that a change in any system will always result in the greatest possible reduction in difference. And importantly, the second law flips determinism on its head by providing perfect knowledge of the final state and doing so absolutely independent of any knowledge of initial conditions. Well that is certainly interesting, a theory that can predict the ultimate future independent of any past or present configuration, or, for that matter, any knowledge what so ever. What can be said of the quality or quantity of action that can be taken as result of this strange sort of knowledge? If success in competition can be linked to accuracy and capacity to predict, than what can be said of competitive success as a function of range of prediction? Imagine one could make and than order all possible predictions from most immediate to most long term. Comparing short-term against long-term predictions, which have the greatest impact on competitive advantage? If someone came into your office today and said, "I can say with absolute confidence that you will die as an artist in Copenhagen", how would such knowledge effect your future decisions and actions? How would absolute knowledge of your ultimate future effect your behavior? What if we were to compare the influence of such knowledge to short term knowledge of the same certainty? What if that same person came into your office and instead declared, "I have no knowledge of your ultimate fate, but I do know that you will not be able to fall asleep tonight". Would you be more (or less) likely to change or conform your plans or to take action based on short term predictions? There might be a tendency to ignore predictions that are far removed in time. One might reasonably think, "Even if I know that I will become an artist and eventually die in Copenhagen, I have a life to live until then, concentrating on long term eventualities interferes with my ability to successfully negotiate success in the short term, in the here and now. But it might also be reasonable to try to conform local goals to long term eventualities. One might eliminate actions that one feels will make it harder to plot a path towards know eventualities. Or, one might take risks they would not otherwise have taken. If I know I will die in Copenhagen, I might as well go base jumping in the Andes or climb Everest sans bottled oxygen. Surely, the heat death of the universe is an eventuality of much greater philosophical remove. What's more, evolution, as a process, seems to work just fine in the absence of any knowledge of eventualities. Can one make an argument that knowledge of universal eventuality gains its owner any special form of evolutionary advantage? Lets pit two entities against each other, one knows of heat death, the other doesn't. Which has the evolutionary advantage?
Randall Lee Reetz, January 26, 2012