That ability to popularize is a gift, to be sure, although many great and good scientists lack it, so it is non a requirement for understanding. And something, some grasp of the contours of the subject matter, can be communicated to the innumerate, by a good teacher or popularizer. I do not deny that either. Feynman's book, which I am familiar with, is an example; I had John Wheeler's Physics For Poets as my first physics course in college with nary an equation in the class.
But, as I said, you can't even be in a position to know or say whether you understand mathematical science in nonmathemaetical terms unless you know the math or at the least have someone who does know the math approve your own nonmathematical statements.
I'm sorry if it sounds arrogant and elitist to say that a deep and practical, as opposed to a popular and superficial, understanding of mathematical science requires understanding the mathematics, but there's a reason they teach science mathematically in grad school and expect scientific papers to be set forth using mathematical techniques.
To head off the obviously forthcoming objection: of course impressive looking maths don't guarantee that there's good science going on -- witness most economics: in fact the greatest economics (e.g., Smith, Ricardo, Marx, Veblen, Keynes, Mises, Hayek, Robinson) has little or no math at all. Feynman has some biting remarks about "cargo cult science" -- the kind of science science that sets up the apparatus and waits for the science to fly in.
Nonetheless, the language of nature is mathematics, and while you can get it in translation, you lose a lot, just as the very best translations of Homer aren't the same as reading it in Greek, or the very best explanations of sculpture or painting leave out the crucial visual experience. If that's arrogant, well, to paraphrase Che's remark that "it's not _my_ fault that the world is Marxist," it's not my _my_ fault that God wrote the world in the language of numbers.
Btw, although I used to be on the understanding-maths side of this story, I'm not any more; my math, like like Latin, is all gone from disuse. So I am now with the most of us whose understanding of science is superficial and popular, nor deep and practical.
--- Andy F <andy274 at gmail.com> wrote:
> On 10/10/06, jthorn65 at sbcglobal.net
> <jthorn65 at sbcglobal.net> wrote:
>
> [...]
> > a brother with a Ph.D. in physics. I have had many
> conversations with them on this subject
> > and feel that if you can find someone who truly
> understands physics they can explain a great
> > deal of it to "non-math" people using almost no
> equations. People who cannot explain it well in
> > simplified language do not truly understand the
> subject in my opinion even if they do
> > understand the math.
>
> A frequently cited standard among the physics profs
> I've known is that
> if you really understand the subject, you should be
> able to explain it
> to nonspecialists.
>
> --
> Andy
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