Entropy and Watermelons


What is the entropy of a watermelon? This question is not entirely fair, because living things are singularities swimming upstream against the tide of entropy. We can’t merely count the ways the invisible molecules in a watermelon can be rearranged and still be a watermelon. We don’t even know all of the molecules in a watermelon.

We do know that a watermelon is usually over 90% water. We can weigh the watermelon and calculate the number of water molecules with 90% accuracy. We can then take the ideal gas constant and divide it by Avogadro’s number (this is the Boltzmann constant), multiply this by the log of the enormous number of ways we could exchange water molecules throughout the watermelon without changing its appearance, and derive a number for the entropy of 90% of the watermelon. This would be foolishness, because the reason a watermelon can swim upstream against the tide of entropy to exist at all is a result of information; the information in its DNA. Information can create singularities of negative entropy.

A watermelon is not a gas. Most gasses are invisible to us even at the macroscopic levels we chunk their molecules up, like pressure, temperature, and wind. Our conceptions of thermodynamics were really developed for steam engines, machines designed to extract work from the disequilibrium of pressurized gas. The molecules in a gas want to spread out. The molecules in a watermelon do not, at least not as quickly. The watermelon seems content, as if it has reached some (temporary) quantum of negative entropy equilibrium.

Steam is the gas phase of 90% of a watermelon. Not the steam we think we can see, that is actually liquid water that has condensed from the invisible gas phase. Most of the water in a watermelon is liquid or bound up in solid organic molecules. Solids, by definition, do now want to spread out as much as liquids or gasses.  The very property of being solid constrains the spread. The information coding for particularly the solid rind of the watermelon temporarily defeats the tendency to spread out.

Boltzmann entropy was the intellectual beginning of the notion that a probability field extends through the universe from the point human perception fails. The existence of the watermelon in negative probability phase space makes the value of W (the number of ways the invisible components can be rearranged without perceptible difference) negative. The fundamental reason for this negative entropy is information. Information implies purpose.

Entropy is perplexing because while we easily understand why it increases toward the future, since all the fundamental laws of physics seem reversible, entropy should also increase toward the past. Boltzmann wrote this off to probability, simply maintaining as a brute fact that probability flows to the future. Yet probability fails to explain why an entire universe should evolve with billions of galaxies each containing billions of stars, just to get to a human brain. It is far more likely that a human brain, whose perceptions reputedly define the line between the classical and the probabilistic, would randomly fluctuate into existence.

So while we can derive a number for the entropy of a watermelon based on the statistical mechanical properties of the high proportion of water it contains, we really have no way to evaluate the probability of the information it contains. In some sense all living things are watermelons. In some sense our planet is a watermelon.

 

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