> A great many people have weighed in against my remark
> that to understand mathematical science at a deep
> level you have to know mathematics. The main theme is
> that someone who knows mathematics and understands the
> science ought to be explain it non-mathematically to
> the innumerate.
If your remark had been that to deeply understand you need the math I doubt anyone have objected. You said that "In my opinion, someone without the math can understand the physics (pop biolog, etc.) only as well as a blind person can understand painting." That is to say they do not understand it at all, not that they do not understand it deeply. A blind person cannot appreciate a painting at any level. A person well read in popular titles of physics will understand the larger issues at a superficial level.
> 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.
I am not alone in believing that unless a scientist can explain his subject to non-scientists in an understandable manner then they do not deeply understand it even if they can do the math. They only understand the subject in a mathmetically superficial level. You are not alone in believing this is not so. We will simply disagree on this point.
> 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.
I must have missed any posts that disagreed with this idea.
> 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.
Which explains how a scientist can do the math but still not deeply understand the subject and not be able to explain it to non-scientists.
> 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.
The language of nature is math? How about the best way humans can deeply understand nature is through mathematical representations of reality. Mankind wrote the mathematics that we use to explain things, not god.
John Thornton