> 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.
Successful popularization is a much rarer talent than explaining one-on-one, where the explainee can ask questions, request clarification, etc. And I don't think the test was meant to be without false negatives.
> 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.
True enough.
[...]
> 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.
While math often illuminates behaviors that don't reveal themselves well to intuition, such statements about the relationship between nature and math make me uneasy. Physics, in particular my current field of geophysical fluid dynamics, has made a hash of the math it uses: approximations of equations impervious to analysis, different systems at different scales and in different situations, finite difference modeling, the abandonment of determinism even in safely Newtonian systems. There is also the matter of various behaviors particularly in biological systems -- epiphenomena (at best) that appear quite irreducible. So talking of the language of math winds up begging the question of which dialect, and how is it selected for a particular case?
-- Andy