This book is Matter in Motion: The Spirit and Evolution of Physics, by Ernest S. Abers and Charles F. Kennel, two UCLA professors. I was a students in Abers's quantum mechanics classes, and Kennel was in the plasma physics group, so I knew them both, although I hadn't known that they had written a book in 1977 for their "Physics for Non-Science Majors" class. I discovered the book while perusing the July 1977 issue of Physics Today while looking for another article (but that is another story, perhaps to be written about in a future post).
The review praised the book for not trying to do too much, and successfully dispelling "the widely held misapprehension that science consists of little more than a vast collection of uncontestable facts meticulously gathered and catalogued by individuals distinguished primarily by their ability to repress their emotions completely." They extend their discussion of the history of physics to the pre-Galileo period, where "Greek and medieval science finally get their day in court." That is, Abers and Kennel show how the Greeks obtained their results, rather than simply telling you.
My two favorites (that I have come across so far) are a simple proof of the Pythagorean theorem (one that they claim is essentially the same as the original) and a neat proof that there are only five regular solids. I've already posted about Euler's formula
F + V - E = 2
in August 2014 when I discussed Zometools. I mentioned then that there were at least 20 different proofs. Now, I don't have a classical math background. In fact, I'm one of the physicists that avoid as much math as possible, not because I don't love it, but because I like to use it rather than play around with it for its own sake. However, the latter is sometimes lots of fun. Back in 2014 I learned one of those proofs. And Abers & Kennel use Euler's formula to prove that there are only 5 regular solids (also known as Platonic solids: tetrahedron, cube, octahedron, dodecahedron, icosahedron).
So, now that I can prove some things, does that make me a mathematician?
Nope. (In response to your question at the end.) In fact, you say so yourself: "I like to use [mathematics] rather than play around with [mathematics] for its own sake." Another litmus-test is whether one is interested in the claim of a theorem and its utility or the method of proof. However—as with lots of other things—the choice is not binary but continuous. So, yes: there's "a smidgeon" of a mathematician in you. :-)
ReplyDeleteOne of the things that got me into physics, and I suspect other physicists who came to the game late (i.e., not on the common track of playing with chemistry sets or building radios at age 10), is the fun of solving mathematical puzzles. So in that sense I have my "inner mathematician," but I keep him locked up while I work on physics. :)
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