The thing with popular science books about maths and physics is that they always try to cover modern stuff, presumably on the grounds that it's what most people would be interested in. And yes, it's all very good to go off and write books about cat's in boxes, twins on spaceships and franticly flapping butterflies which will blow people's minds, but personally I think that even elementary maths and physics are absolutely fascinating.

Take your basic, bog standard trigonometric functions. Study them at school, and they're as dull as dishwater, because you spend hour after hour staring at ever more implausible arrangements of triangles, being asked to repeat the same calculation over and over again. Dull. Dull. Dull. On the other hand, put a right triangle into a unit circle and play around with that a bit, and it doesn't take long to intuitively derive sin

^{2}x + cos

^{2}x = 1. Or you can then think of circular motion, or take a one dimensional projection of it and then go off into differential equations. And so on and so forth.

Or think about Newtonian mechanics. A lot of mechanics can be derived and shown to be equivalent with fairly straightforward thought experiments, but nobody ever seems to take the time to do that. Even the equivalence of Newton's third law and the principle of conservation of momentum is something that's rarely stated at an elementary level. Newton's laws are something that we can fairly easily call on intuition and instinct to demonstrate, and from there comes pretty much all of classical mechanics. You can go so far just by thinking about it, and not having to do any maths at all, other than the bits where it all just falls into place.

To me, this is all really interesting. The best book I've come across for explaining things in that sort of way is the Feynman lectures on physics. They're rather constrained though, by the fact that they aren't a book at all, but an undergraduate physics course, which has been turned into book form. What I would like to do is to write a book which a casual reader could pick up and could take in some of the joy at maths and physics, and get a glimpse of how things work; but which a different reader could use as a sort of "alternative" text book, explaining things in detail, but coming at it from a totally different angle to conventional textbooks so as to avoid draining all life from the subject. Or possibly trying to achieve both goals would be too much and I should settle for just one.

Of course, I lack the resources, know-how, motivation, time, and other such things that would be necessary to actually write this book, but still. It's not a bad goal to have, I feel.

madcaptenorI should read the Feynman lectures at some point. I keep saying I will, but I never get around to it. I think last time I thought of it, I was stopped by the fact that at MIT's libraries the Feynman lectures cannot be checked out, and I didn't want to sit around the library reading them.

bunnykpthalogreendave_t_lurkerI'd like to write the text book I'd have loved back in A-level and at the start of my undergrad degree.

Too many of the books I've used have been of the type that show the derivation of one equation / principle then set a dozen or so questions just plugging in numbers. You need to do some practise, but in that form it gets rapidly boring.

The new Roger Penrose book - The Road to Reality, is pretty good. Not exactly popular science, not exactly a textbook. Penrose covers a lot of the interesting derivations and theories, giving pointers to the capable reader on how to continue from there.

(Deleted comment)memevector