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Neatness in Nature | 15 comments (15 topical, editorial, 0 pending)
Neatness: all in your mind ( 5.00 / 1 ) (#1)
by Axel Harvey on Sun Jun 9th, 2002 at 13:31:14 EDT
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Shortly afterwards I found out about the inverse square law in relation to the intensity of light at certain distances and noticed the obvious connection between the varying intensity of light at certain distances and the mean periods of planets cycles.... "How could 'Nature' know about square roots of numbers and organise many things according to precise mathematical rules?"

Nature doesn't need to know, Nature does. Of course that's a type of knowledge, like the spider knowing how to spin a web. As for your other question, "How do they do it?", in the case of inverse-square laws (which apply both to light and to gravity, as you have already figured out) it's really simple. Imagine light emanating from a point behind a square hole in a sheet of aluminium foil. The resulting square beam of light fans out through the aperture to a sheet of paper 1 meter away from the point. The square of light on the paper has a certain area. Now move the sheet back to 2 meters, 3 m, 4 m. How much bigger than the original square of light are the new squares at these other distances? Keep in mind that the amount of light doesn't change, only the area on which it shines gets bigger; what does that say about the relationship between the distance to the source of light and the amount of light per area falling on that paper? If you are a gnat on that sheet of paper, what does it say about the amount of light you will perceive at each distance?

There is no way of knowing if Nature has chosen "neat rules." We can only ask ourselves, how would it make sense for such-and-such a thing to behave? - for example, light at a distance - build a model, and then see how it matches our perceptions. The neatness is all in our minds. In fact light doesn't quite behave the way we thought it should when the distances are cosmic; so we go back and think a little more sophisticatedly.

For an idea of a mathematical tool greatly favoured in Nature (that is to say, in the way human beings think about their perceptions of Nature), see Ron Knott's marvellous pages about Fibonacci numbers and especially his notes on how Fibonacci numbers are used by honeybees, pine trees, and molluscs.

As for the fancy numbers you have obtained for the Great Year, they lack an essential step. You are multiplying your first number (days per year) by the factor 70.71067811865475244... (100 divided by the square root of 2). The result comes out as years. Therefore the magic factor must be in units of years squared. Why?

Note that if instead of dividing 100 by the square root of 2 you had taken the famous number pi and multiplied it by 22.5, which is related to an important harmonic (if you believe that the number 360 has some kind of natural relationship to the circle), then you would have gotten a very similar result, namely 70.6858347... Does any of this make sense? Why?


unreasonable nature of mathematics ( 4.00 / 1 ) (#14)
by Bill Sheeran on Tue Oct 8th, 2002 at 22:52:01 EDT
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from: The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner (joint Nobel Prize Winner, Quantum Physics, 1963) http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

THERE IS A story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former classmate. The reprint started, as usual, with the Gaussian distribution and the statistician explained to his former classmate the meaning of the symbols for the actual population, for the average population, and so on. His classmate was a bit incredulous and was not quite sure whether the statistician was pulling his leg. "How can you know that?" was his query. "And what is this symbol here?" "Oh," said the statistician, "this is pi." "What is that?" "The ratio of the circumference of the circle to its diameter." "Well, now you are pushing your joke too far," said the classmate, "surely the population has nothing to do with the circumference of the circle."

*

... the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it.

*

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.

Bill



no mystery, really ( 3.00 / 1 ) (#13)
by Anonymous Hero on Tue Oct 8th, 2002 at 18:34:07 EDT

Actually, you have it almost backwards.  To slightly oversimplify, physicists and mathematicians observed the patterns of Nature, and gave simple names (like "square root") to the patterns they saw most frequently.

I.e., there's no mystery to why Nature follows physical and mathematical laws, because those laws were derived by observing the very Nature that is being described.


Neatness in Nature ( 3.00 / 1 ) (#6)
by LSmerillo (kajamanu@rdn.it) on Thu Jun 6th, 2002 at 21:01:21 EDT
(User Info)

maybe this interests someone:

http://the-light.com/misc/

feliciter,

Lorenzo Smerillo


test - ignore comment ( 1.00 / 1 ) (#9)
by johnnyc (johnnyc@urania-dott-info) on Fri Jun 7th, 2002 at 18:02:45 EDT
(User Info) http://www.livejournal.com/users/johnnycampbell

test...


Neatness in Nature | 15 comments (15 topical, 0 editorial, 0 pending)

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