John Armstrong has a short and sweet post on popularizing mathematics and physics which is worth reading in its entirety. I don’t want to quote the whole thing, so just go read it.
Incidentally, he says he was inspired to write the post by the movie Mindwalk (1990). I had only ever heard of this flick because they’d stuck a preview for it on the Brief History of Time video I rented sometime in the late nineties. I then managed to forget about it until a few weeks ago, when I was poking through Wikipedia for articles containing pseudoscience. Somehow, in the tangled thicket of pages growing like weeds upon quantum mysticism and Choprawoo, I found Mindwalk. “Aha! I remember seeing a preview for that movie.”
I think that the notion of “popularizing” mathematics is a bit different than what we would think of as “popularizing” physics. To be perfectly honest, most concepts in the higher mathematics are extremely difficult to approximate for someone completely unfamiliar with the field, while the concepts in physics are a tad bit more accessible to the non-specialist via such an approximation. On a professional level the dynamic is different, of course, but I think it’s easier to “visualize” physically real things than abstract syntax.
Tyler, that’s really the problem with popularizing physics. Roger Penrose noted specifically in his introduction to The Road To Reality that modern physics is no longer accessible to anyone — specialists included — except through the mathematics. We understand quantum field theory as well as we do because we understand the mathematics. To avoid the mathematics in its entirely cuts the legs out from under any popularization of physics, and risks becoming The Tao of Physics or The Dancing Wu Li Masters.
I think that a large proportion of popular physics books do more harm than good. As you point out the understanding is in the mathematics. A book about quantum mechanics with out any mathematics doesn’t really give any understanding. What it does do is give some people the illusion that they understand the subject. This pseudo-understanding can be more dangerous than complete ignorance. The ultimate result is all the quantum-woo that has infiltrated popular culture.