Failure to understand that in thermodynamics probabilities are not fixed entities has led to a misinterpretation that is responsible for the wide- spread and totally false belief that the second law of thermodynamics does not permit order to spontaneously arise from disorder. In fact, there are many examples in nature where order does arise spontaneously from disorder: Snowflakes with their six-sided crystalline symmetry are formed spontaneously from randomly moving water vapor molecules. Salts with precise planes of crystalline symmetry form spontaneously when water evaporates from a solution. Seeds sprout into flowering plants and eggs develop into chicks.
Thermodynamics is an exact science that is based on a limited number of specific mathematical concepts. It is not explainable in terms of qualitative metaphors. In order to understand the relationship between probability and the second law, the reader must be familiar with the relationship between probability and entropy. Entropy is a mathematically defined entity which is the fundamental basis of the second law of thermodynamics and all of its engineering and physical chemistry ramifications.
Creationists assume that a change characterized by a decrease in entropy can not occur under any circumstances. In fact, spontaneous entropy decreases can, and do, occur all the time, providing sufficient energy is available. The fact that the water wheel and pump are man-built contraptions has no bearing on the case: thermodynamics does not concern itself with the detailed description of a system; it deals only with the relationship between initial and final states of a given system (in this case, the water wheel and pump).
A favorite argument of creationists is that the probability of evolution occurring is about the same as the probability that a tornado blowing through a junkyard could form an airplane. They base this argument on their belief that changes in living things have a very low probability and could not occur without "intelligent design" which overcomes the laws of thermodynamics. This represents a fundamental contradiction in which (they say) evolution is inconsistent with thermodynamics because thermodynamics doesn't permit order to spontaneously arise from disorder, but creationism (in the guise of intelligent design) doesn't have to be consistent with the laws of thermodynamics.
A simpler analogy to the airplane/junkyard scenario would be the stacking of three blocks neatly on top of each other. To do this, intelligent design is required, but stacking does not violate the laws of
thermodynamics. The same relations hold for this activity as for any other activity involving thermodynamical energy changes. It is true that the blocks will not stack themselves, but as far as thermodynamics is concerned, all that is required is the energy to pick them up and place them one on top of the other. Thermodynamics merely correlates the energy relationships in going from state A to state B. If the energy relationships permit, the change may occur. If they don't permit it, the change can not occur. A ball will not spontaneously leap up from the floor, but if it is dropped, it will spontaneously bounce up from the floor. Whether the ball is lifted by intelligent design or just happens to fall makes no difference.
On the other hand, thermodynamics does not rule out the possibility of intelligent design; it is just simply not a factor with respect to the calculation of thermodynamic probability.
Considering the earth as a system, any change that is accompanied by an entropy decrease (and hence going back from higher probability to lower probability) is possible as long as sufficient energy is available. The ultimate source of most of that energy, is of course, the sun.
The numerical calculation of entropy changes accompanying physical and chemical changes are very well understood and are the basis of the mathematical determination of free energy, emf characteristics of voltaic cells, equilibrium constants, refrigeration cycles, steam turbine operating parameters, and a host of other parameters. The creationist position would necessarily discard the entire mathematical framework of thermodynamics and would provide no basis for the engineering design of turbines, refrigeration units, industrial pumps, etc. It would do away with the well-developed mathematical relationships of physical chemistry, including the effect of temperature and pressure on equilibrium constants and phase changes.
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