Explaining is a difficult art. You can explain something so that your reader understands the words; [I try to] explain something so that the reader feels it in the marrow of his bones.

Richard Dawkins

My private school taught biology from the infamous creationist textbook Biology for Christian Schools, so my early understanding of evolution was a bit... confused. Lacking the curiosity to, say, check Altavista for a biologist’s explanation (faith is a virtue, don’t ya know), I remained confused about evolution for years.

Eventually I stumbled across an eloquent explanation of the fact that natural selection follows necessarily from heritability, variation, and selection.

Click. I got it.

Explaining is hard. Explainers need to pierce shields of misinformation (creationism), bridge vast inferential distances (probability theory), and cause readers to feel the truth of foreign concepts (quantum entanglement) in their bones. That isn’t easy. Those who do it well are rare and valuable.

Textbook writers are often skilled at explaining complex fields. That’s why I called on my fellow Less Wrongers to name their favorite textbooks (if they had read at least two other textbooks on those subjects). The Best Textbooks on Every Subject now gives 22 textbook recommendations, for fields as diverse as scientific self-help and representation theory.

Now I want to jump down a few levels in granularity. Let’s pool our knowledge to find great explanations for each important idea (in math, science, philosophy, etc.), whether or not there is equal value in the rest of the book or article in which each explanation is found.

Great explanations, in my meaning, have four traits:

1. A great explanation does more than report facts; it uses analogy and rhetoric and other tools to make readers feel the target idea in their bones.

2. A great explanation is not a single analogy nor a giant book. It is, roughly, between 2 and 100 pages in length.

3. A great explanation is comprehensible at best to a young teenager, or at least to a 75th percentile college graduate. (There may be no way to seriously explain string theory to an average 13-year-old.)

4. A great explanation is exciting to read.

By sharing great explanations we can more often experience that magical click.

List of Great Explanations

I’ve barely begun to assemble the list below. Please comment with your own additions!

(The list below is exclusive to written explanations, but feel free to share your favorite explanations from other media. My favorite explanation of BASIC programming is a piece of software from Interplay called Learn to Program BASIC, and of course many people love Khan Academy’s videos and The Teaching Company’s audio courses.)

Epistemology

• Aumann’s agreement theorem: Landsburg, The Big Questions, chapter 8.

• Occam’s razor: Yudkowsky, Occam’s razor.

Math and Logic

• Bayes’ Theorem: Yudkowsky, An Intuitive Explanation of Bayes’ Theorem.

Physics

• Special relativity: Wolfson, Simply Einstein, chapters 2–12.

• General relativity: Hawking, The Universe in a Nutshell, chapters 1–2.

• Infinite, flat universe: Greene, The Hidden Reality, chapters 1–3.

• Timeless reality / block universe: Greene, The Fabric of Reality, chapter 5.

• Inflationary cosmology: Greene, The Hidden Reality, chapter 3.

• Rainbows: Dawkins, The Magic of Reality, chapter 7.

Biology

• Tool use in animals: Zimmer, 50 Years of Animal Technology.

Psychology

• Anchoring: Kahneman, Thinking, Fast and Slow, chapter 11.

• Availability heuristic: Kahneman, Thinking, Fast and Slow, chapters 12–13.

• Prospect theory: Kahneman, Thinking, Fast and Slow, chapters 25–26.

• Modularity of mind: Kurzban, Why Everyone (Else) is a Hypocrite, chapters 1–4.

Economics

• The Pareto Principle: BetterExplained, Understanding the Pareto Principle.