Comment by BB on The Second Law of Thermodynamics, and Engines of Cognition · 2008-03-02T05:35:59.000Z · LW · GW

I enjoyed this article. As several commenters have suggested, it seems not just counterintuitive but actually non-physical to say that the warm water has become colder just because I know more about it. The subjective nature of entropy that this seems to imply is absurd. As has been pointed out, a stationary thermometer in the water will show the same reading after my visit from Saint LaPlace as it did before.

I think the problem is resolved if we consider our system boundary to include not just the water, but the observer as well. The entropy of the water has not changed because I have more information, but the total entropy of the water-observer system can be considered to have decreased because of the mutual information that has been magically added (by Saint LaPlace).

To continue the analogy, it is as though my brain now contains negentropy that has been arranged to exactly cancel the entropy of the water, making our combined net entropy smaller. The entropy of the water itself has not changed and the effect is not subjective. It arises only if we consider me (the observer) with my magical cargo of negentropy as part of the system. Should I choose to put my knowledge to use as an avatar of Maxwell's Demon, then I can actually lower the entropy of the water (by taking it into myself). If, however, I walk away and do nothing to the water based on my knowledge then the entropy of the water itself remains just as it was. (I, however, have been lastingly changed by my encounter with LaPlace.)