pragmatist comments on Great Explanations - Less Wrong

23 Post author: lukeprog 31 October 2011 11:58PM

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Comment author: Vladimir_M 01 November 2011 02:22:01AM *  33 points [-]

I see that the physics list consists of math-free pop-science books. I don't see how these can possibly count as "great explanations," since it's impossible to gain any real understanding of physics from such materials.

For example, a good explanation of relativity would first present the concepts of Minkowski spacetime and proper time, and then show how all those "relativistic effects" follow from these reasonably simple concepts. (This as opposed to a bad explanation of the traditional sort that confuses the reader with various "effects" and "paradoxes.") Then it would explain how a curved metric with a Minkowski signature can make the geodesic lines look like the free fall curves of Newtonian gravity, thus providing an intuitive grasp of the whole "gravity is geometry" business. Beyond that, you just have to get into the hairy tensor stuff, and even this minimum requires a solid knowledge of algebra, analytic geometry, and basic calculus. Anything less than that is just rambling that may have a lot of entertainment and signaling value, but won't move you one millimeter closer to any real insight.

Comment author: pragmatist 01 November 2011 03:00:04AM *  8 points [-]

Agreed. A good elementary exposition of relativity along these lines is Bob Geroch's General Relativity from A to B.

EDIT: Actually, I realize I'm only in partial agreement with Vladimir. While I do think that many pop-sci explanations of theoretical physics are fairly worthless and often actively misleading, I do not think that it is impossible to gain real insight into (say) the general theory of relativity without mastering differential geometry. Geroch's book presupposes only high school mathematics, but it provides a genuinely deep insight into relativity.

Comment author: Vladimir_M 01 November 2011 03:56:35AM *  9 points [-]

While I do think that many pop-sci explanations of theoretical physics are fairly worthless and often actively misleading, I do not think that it is impossible to gain real insight into (say) the general theory of relativity without mastering differential geometry. Geroch's book presupposes only high school mathematics, but it provides a genuinely deep insight into relativity.

I described the requirements as algebra, analytic geometry, and basic calculus, which is more or less within advanced high-school math. (Without calculus, I don't see how you could explain integrals along the world line, which are the very heart of the matter.)

However, note that just high-school algebra is already worlds apart from purely prose-based, general-audience pop-science. I would guess that for an average reader (let alone owner) of pop-science books, following a text using algebra would be far harder than it would be to figure out tensors for a reasonably math-savvy twelfth grade student.