idealistic theory that the arrow of time is a subjective illusion, and because the fight against this theory has taken up much of my thought in recent years.


36.

THE SUBJECTIVIST THEORY OF ENTROPY

What I mean here by the subjectivist theory of entropy 265 is not Boltzmann's theory, in which the arrow of time is subjective but entropy objective. I mean rather a theory, originally due to Leo Szilard, 266 according to which the entropy of a system increases whenever our information about it decreases, and vice versa. According to Szilard's theory, any gain of information or knowledge must be interpreted as a decrease in entropy: in accordance with the second law it must somehow be paid for by an at least equal increase in entropy. 267

I admit that there is something intuitively satisfying in this thesis-especially, of course, for a subjectivist. Undoubtedly, information (or “informative content”) can be measured by improbability, as in fact I pointed out in 1934 in my Logik der Forschung. 268 Entropy, on the other hand, can be equated with the probability of the state of the system in question. Thus the following equations appear to be valid:

information = negentropy;

entropy = lack of information = nescience.

These equations, however, should be used with the greatest caution: all that has been shown is that entropy and lack of information can be measured by probabilities, or interpreted as probabilities. It has not been shown that they are probabilities of the same attributes of the same system.

Let us consider one of the simplest possible cases of entropy

-189-

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