Cosmology and very theoretical physics are something we can judge from the outside because we can look at their implications in almost a philosophical way. But what that means is that the theories are so complete and so brilliant that they predict the physical behavior of the Universe from the smallest to the largest scale. But the math that was necessary to achieve those models is mind-bending.
Einstein didn't just say "E = MC2". That was the brilliant conclusion to a mathematical insight about very complicated mathematical propositions. Einstein played with the math first and then came to the physical conclusions.
Having ideas about how the Universe might work is not that hard. I personally "predicted" that cosmologists would come to observe that the Universe was not only expanding but accelerating. Indeed, in 1998, the accelerating Universe was observed and confirmed.
Of course my "prediction" was so much nonsense - an intuition based on a dilletante's observation. I "predicted" the acceleration by reading enough to know that cosmology theorists were uneasy with their results. These theorists themselves put forward a number of possibilities that might reconcile things and what kind of new results they would have to see to come to new conclusions - so let's say it was a dozen things. Of course I gave it all a lot of thought but what I really did was pick the thing it seemed most likely to have been ignored due to preconceived notions and about which there were the fewest solid observations.
I put the possibility of that change into my own, dilletante's "logical" model of the universe, chugged away (by drinking tea, wasting time and reading books, not doing math) and came to the conclusion that there seemed to be a pretty logical universe with the characteristic (acceleration) that the theorists were "ignoring". But of course they weren't ignoring it at all. They had all done even better speculation than I (after all, why were they looking for acceleration in the Universe at all?) but the implications of an accelerating Universe made them all tired because they would have to go back and re-do all that math to re-reconcile all the equations. What do I care about equations? I don't even understand them. But because they are actual, responsible scientists they don't want to go around throwing out big chunks of solid work that did a very good job of predicting things.
I was merely a dilletantish co-speculator. I don't even really understand how the results they've observed imply the acceleration that I speculated was there. The math is simply beyond me so I have to trust people who understand it. And I also have to trust that the math works - and it does.
For example, the guys who got the Nobel prize recently pointed out that the results they observed confirm the Big Bang theory predictions to a few parts per million. So, Joanna, there is a math Santa Claus and we can trust him.
Boddi
On 10/11/06, andie nachgeborenen <andie_nachgeborenen at yahoo.com> wrote:
> 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.
>
> 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
> > ___________________________________
> >
> http://mailman.lbo-talk.org/mailman/listinfo/lbo-talk
> >
>
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