Reading about mutual information between amino acids in protein-protein interaction pairs, and got distracted:

Although not particularly obvious from this equation, has a very concrete interpretation: Suppose is chosen randomly from the distribution , and someone who knows the distribution is asked to guess which was chosen by asking only yes/no questions. If the guesser uses the optimal question-asking strategy, which is to divide the probability in half on each guess by asking questions like “is greater than ?”, then the average number of yes/no questions it takes to guess lies between and (Cover and Thomas, 1991). This gives quantitative meaning to “uncertainty”: it is the number of yes/no questions it takes to guess a random variables, given knowledge of the underlying distribution and taking the optimal question-asking strategy.

Scholarpedia: Mutual information

For some reason, reading and re-reading this reminded me of this Farside comic from back in the day. The search terms to actually find this image on Google probably like between H(x) and H(x)+1 as well.

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