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Took a deep breath and decided to download and read this paper. Surprise, surprise: it's super approachable and the reasoning for using log is explained on the first page.
As many other commentators has mentioned, it is impressive that such an approachable paper would lay the foundations for a whole field. I actually find that many subsequent textbooks seem to obfuscate the simplicity of the idea of entropy.
Two examples from the paper really stuck with me. In one, he discusses the importance of spaces for encoding language, something which I had never really considered before. In the second, he discusses how it is the redundancy of language that allows for crosswords, and that a less redundant language would make it harder to design these (unless we started making them 3D!). It made me think more deeply about communication as a whole.
* https://en.wikipedia.org/wiki/A_Symbolic_Analysis_of_Relay_a...