I'm still not sure what you mean by "real understanding," but all I'm trying to claim in the post above is that readable but non-technical explanations of scientific concepts and theories from people like Brian Greene and Richard Dawkins can be helpful.
My original point was only about physics, not about evolution, and I have already written that there is an important difference between the accessibility of these two for lay readers. So by dragging evolution into the discussion again, you are obscuring the issue.
They have improved not just my ability to guess the teacher's password, but also my ability to have more accurate anticipations in ways that help me achieve my goals. Is that something you actually think is "impossible"?
Yes, I do think that math-free popular books about modern physics (by which I mean QM, relativity, and the more advanced fields that use them) cannot give the reader any such ability.
A physicist with good writing skills could easily write a book full of completely nonsensical pop-scientific "explanations" of relativity and QM (let alone cosmology etc.), and there would be no way for non-expert readers to notice that something's wrong (unless they noticed that it's explicitly contradicting something they previously read elsewhere). In contrast, someone who studies with full understanding from a real textbook will notice the errors of the author purely from internal evidence, since these errors will stick out blatantly in the otherwise smooth and clear logical flow of exposition. There we see the fundamental difference between real explanations and fake explanations.
If so, what is your response to the examples wedrifid and I gave?
Some of these examples are about using classical physics to improve on folk-physical intuitions or gain insight that can be based on folk physics or simple Newtonian physics. Such insights can indeed be gained without much (or even any) math, so I admit my claims should be qualified to exempt such cases. Note however that the original context was about advanced non-classical fields of physics, which are the subject of the overwhelming majority of pop-scientific texts, some of which you originally cited as supposedly "great explanations."
As for the example of the limited speed of light, it's a completely isolated rule that stands outside of any systematic understanding. It's as if you claimed that you can understand Maxwell's electromagnetic theory without knowing vector calculus, and then supported it by arguing that your non-mathematical understanding enables you to predict that bad things will happen if you touch uninsulated high-voltage lines. Yes, it is a correct rule that makes correct and practically useful predictions, but it's completely isolated and learned by heart -- and there is no way to connect it with some more general framework for understanding physical phenomena without learning real (i.e mathy) physics. [*] Similarly, unless you have real mathy knowledge of relativity, your knowledge of this particular fact about the limited speed of light is just an isolated fact, which is not integrated with any broader and deeper understanding of physics.
[] -- *Edit: Thinking about this a bit more, I would say that there are in fact such ways. Some people manage to develop amazing intuitive understanding of electromagnetic phenomena without any math or formalism at all, and sometimes their intuitions will be more accurate than the products of laborious number-crunching by experts. However, such understanding is about hands-on technical practice, and it's radically different from anything that can result from reading pop-science.
My original point was only about physics, not about evolution, and I have already written that there is an important difference between the accessibility of these two for lay readers. So by dragging evolution into the discussion again, you are obscuring the issue.
Huh? I didn't bring up evolution again. I mentioned Richard Dawkins, but not evolution, and the 'great explanation' from Dawkins that I list above is in physics (rainbows), not biology.
BTW, are the physics ones the only ones you object to? Are you still mostly on board with the project of track...
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:
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.
A great explanation is not a single analogy nor a giant book. It is, roughly, between 2 and 100 pages in length.
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.)
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
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
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