between t and t1, someone swings a baseball bat at my head. What happens when it impacts? If there's enough force behind the swing, I'll die. Why is that? Well, when the bat hits my skull, it transfers a significant amount of kinetic energy through my skull and into my brain, which (among other things) randomizes[1] large swaths of my neural network, destroying the correlations that were previously in place, and making it impossible for the network to perform the kind of computation that it must perform to support the rest of my body. This is (I take it) relatively uncontroversial. However, it seems like we also want to say that my brain was more complex when it was capable of supporting both life and significant information processing than it was after it was randomized—we want to say that normal living human systems are more complex than corpses. But now we've got a problem: in randomizing the state of my brain, we've increased the Shannon entropy of the associated message encoding its state. A decrease in complexity here is associated with an increase in Shannon entropy. That looks like trouble, unless a system with minimal Shannon entropy is a system with maximal complexity (that is, unless the strict inverse correlation between entropy and complexity holds). But that's absurd: a system represented by a string of identical characters is certainly not going to be more complex than a system represented by a string of characters in which multiple nuanced patterns are manifest[2]. The correlation condition between entropy and complexity fails.
- ↑ The sense of “randomizes” here is a thermodynamic one. By introducing a large amount of kinetic energy into my brain, my assailant (among other things) makes it the case that the volume of the region of configuration space associated with my brain is wildly increased. That is, the state “Jon is conscious and trying to dodge that baseball bat” is compatible with far fewer microstates of my brain than is the state “Jon has been knocked out by a baseball bat to the face.” The bat’s impacting with my skull, then, results in a large amount of information loss about the system—the number of possible encodings for the new state is larger than the number of possible encodings for the old state. The Shannon entropy has thus increased.
- ↑ To see this point, think of two pieces of DNA—one of which codes for a normal organism (say, a human being) and one of similar length, but which consists only in cytosine-guanine pairs. Each DNA string can be encoded as a message consisting entirely of the letters A, C, G, and T. The piece of DNA that codes for a functional organism will be associated with a message with far higher Shannon entropy than the piece of DNA associated with a message that
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