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narrator_time: 3h30m
narrator: pw
qa: km
client: lesswrong
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https://www.lesswrong.com/posts/REA49tL5jsh69X3aM/introduction-to-abstract-entropy

This post, and much of the following sequence, was greatly aided by feedback from the following people (among others): Lawrence Chan, Joanna Morningstar, John Wentworth, Samira Nedungadi, Aysja Johnson, Cody Wild, Jeremy Gillen, Ryan Kidd, Justis Mills and Jonathan Mustin. Illustrations by Anne Ore.

Introduction & motivation

In the course of researching optimization, I decided that I had to really understand what entropy is.[1] But there are a lot of other reasons why the concept is worth studying:

• Information theory:
  • Entropy tells you about the amount of information in something.
  • It tells us how to design optimal communication protocols.
  • It helps us understand strategies for (and limits on) file compression.
• Statistical mechanics:
  • Entropy tells us how macroscopic physical systems act in practice.
  • It gives us the heat equation.
  • We can use it to improve engine efficiency.
  • It tells us how hot things glow, which led to the discovery of quantum mechanics.
• Epistemics (an important application to me and many others on LessWrong):
  • The concept of entropy yields the maximum entropy principle, which is extremely helpful for doing general Bayesian reasoning.
• Entropy tells us how "unlikely" something is and how much we would have to fight against nature to get that outcome (i.e. optimize).
• It can be used to explain the arrow of time.
• It is relevant to the fate of the universe.
• And it's also a fun puzzle to figure out!

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