Otto Piechowski
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Reged: 09/20/05
Loc: Lexington, KY

Beautiful, intriguing, elegant ideas
#5593614  12/29/12 12:12 AM

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I would like to know what scientific ideas you have found to be stunningly beautiful, breathtaking, elegant, intriguing, inspiring.
I'll start. Kepler's Second Law of Planetary Motion. This is the one which says if the orbit of a planet around a heavier body (i.e. sun) is an ellipse, and if one considers the distance the planet travels along the ellipse in the same amount of time, but at two different parts of the ellipse; one span being near perihelion and another near aphelion, the areas "covered" will be equal.
The idea I am trying to convey, which most of the readers here already know, is much more clearly stated with an accompanying diagram. Also, some of you probably know how to just use language better to express his seminal idea more simply and clearly.
Back to the point; I think this idea is stunning. The geometry of euclidean space is such, and the nature of gravity within that space is such, that it sweeps out equal areas. Who would have thought....!!

Pess
(Title)
Reged: 09/12/07
Loc: Toledo, Ohio

Re: Beautiful, intriguing, elegant ideas
[Re: Otto Piechowski]
#5593797  12/29/12 04:49 AM

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Pesse ( E=MC^2 ) Mist

FirstSight
Duke of Deneb
Reged: 12/26/05
Loc: Raleigh, NC

Re: Beautiful, intriguing, elegant ideas
[Re: Pess]
#5594096  12/29/12 10:28 AM

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relativistic mass:
m(r) = m(0)/sqrt(1  v^2/c^2)
Also very elegant is how e = mc^2 is directly derived from the above expression for relativistic mass; first restate the equation for relativistic mass as:
m(r) = m(o)*(1  v^2/c^2)^1/2
...using the binomial theorum to expand the above expression in a power series:
m(r) = m(0)(1 + 1/2(v^2/c^2) + 3/8(v^4/c^4) +....)
...which, when v is small, converges rapidly to:
m(r) = m(0) + 1/2 m(o)v^2(1/c^2)
...now, multiply both sides by c^2
m(r)c^2 = m(o)c^2 + 1/2m(0)v^2
...the last term on the right side is ordinary kinetic energy, the left term on the right side is the intrinsic energy of a body at rest. The term on the left is usually encapsulated as simply 'e', which incorporates both the intrinsic "rest" energy and kinetic energy expressions on the right.
*thanks to Feynman's "Lectures on Physics", pp 158 through 1511 for providing this clear, and surprisingly straightforward mathematical explanation.
Edited by FirstSight (12/29/12 11:50 PM)

scopethis
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Reged: 05/30/08
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Re: Beautiful, intriguing, elegant ideas
[Re: FirstSight]
#5594571  12/29/12 02:48 PM

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Og...inventing the wheel...

ColoHank
Carpal Tunnel
Reged: 06/07/07
Loc: western Colorado

Re: Beautiful, intriguing, elegant ideas
[Re: scopethis]
#5594697  12/29/12 04:31 PM

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The Mayan calendar...

mountain monk
Carpal Tunnel
Reged: 11/06/09
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Re: Beautiful, intriguing, elegant ideas
[Re: ColoHank]
#5595127  12/29/12 08:55 PM

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FirstSight:
I would say that the beauty of your example lies in the mathematics, not in the science, and that the line between the two is in itself interesting. I cannot think, offhand, of a scientific idea that is beautiful without it receiving a mathematical formulation. This is one of the main points of Penrose's The Road to Reality, section 34.2 (page 1014). I can think of beautiful experimentsNewton's prismbut scientific ideas...? On the other hand, mathematics is filled with beautyIMHO. Thanks for your example.
Dark skies.
Jack

Otto Piechowski
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Reged: 09/20/05
Loc: Lexington, KY

Re: Beautiful, intriguing, elegant ideas
[Re: Otto Piechowski]
#5595179  12/29/12 09:43 PM

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Making fire burn downwards.
In his Nicomachean Ethics, Aristotle asserted that persons are not born morally good or bad but are taught good behavior and bad behavior. This idea was the birth of all subsequent moral education in the western world. If good behavior could be learned, it could then be taught.
To make this point Aristotle contrasted moral values with things that happened "by nature". He pointed out that things which occurred "by nature" always happened the same way regardless of how many attempts were made to change their "way"; their "habit". One example he used was that although a person could be taught to be generous, a flame could never be taught to burn downwards.
However, in his 1869 Christmas lectures to children at the Royal Institution of Great Britain entitled The Chemical History of a Candle, Michael Faraday described and executed an experiment in which the fire of a candle was induced to burn downwards.
This novel idea, experiment and description in no way affect Aristotle's ethical ideas. However they do evidence an improvement of modern science compared to the more deductive methodology of ancient science; the importance of testing assumptions such as, fire always burns upwards.

Mike Casey
Reged: 11/11/04
Loc: El Pueblo de Nuestra SeĆ±ora l...

Re: Beautiful, intriguing, elegant ideas
[Re: Otto Piechowski]
#5595243  12/29/12 10:25 PM

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If true, the discovery of the Higgs boson.

Mister T
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Re: Beautiful, intriguing, elegant ideas
[Re: Mike Casey]
#5595625  12/30/12 07:02 AM

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NOBODY would be here discussing this if Ice didn't float....

Dave Mitsky
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Reged: 04/08/02
Loc: PA, USA, Planet Earth

Re: Beautiful, intriguing, elegant ideas
[Re: Mister T]
#5596190  12/30/12 01:39 PM

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Two equations from Sir Isaac certainly got the ball rolling: F=ma and F=Gm1m2/d^2
Dave Mitsky

Rick Woods
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Re: Beautiful, intriguing, elegant ideas
[Re: Dave Mitsky]
#5596377  12/30/12 03:31 PM

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Natural Selection is one.

star drop
Snowed In
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Re: Beautiful, intriguing, elegant ideas
[Re: Rick Woods]
#5596392  12/30/12 03:39 PM

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e^(i*pi) = 1

saxmaneagle
sage
Reged: 08/21/07
Loc: Saint Francis, MN

Re: Beautiful, intriguing, elegant ideas
[Re: star drop]
#5596650  12/30/12 06:03 PM

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http://www.space.com/17628warpdrivepossibleinterstellarspaceflight.html

Ravenous
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Reged: 11/14/09
Loc: UK

Re: Beautiful, intriguing, elegant ideas
[Re: star drop]
#5597708  12/31/12 10:41 AM

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Quote:
e^(i*pi) = 1
This is the one I was going to reply with too.
The Euler identity. A simple looking equation but it involves three fundamental constants  e, pi and i. (And 1 if you count that as a fundamental constant.)
I don't understand most of the maths behind it, but it's one of the most thoughtprovoking single lines of mathematics known...

deSitter
Still in Old School
Reged: 12/09/04

Re: Beautiful, intriguing, elegant ideas
[Re: star drop]
#5597989  12/31/12 01:34 PM

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Quote:
e^(i*pi) = 1
i^2 like
You can argue, this is the most important formula in all of science and engineering.
drl

Rick Woods
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Re: Beautiful, intriguing, elegant ideas
[Re: deSitter]
#5598111  12/31/12 02:44 PM

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Quote:
You can argue, this is the most important formula in all of science and engineering.
I always thought that honor belonged to the formula for beer...

scopethis
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Reged: 05/30/08
Loc: Kingman, Ks

Re: Beautiful, intriguing, elegant ideas
[Re: Rick Woods]
#5598284  12/31/12 04:12 PM

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the square root of a negative number..

EJN
Carpal Tunnel
Reged: 11/01/05
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Re: Beautiful, intriguing, elegant ideas
[Re: Otto Piechowski]
#5598461  12/31/12 05:53 PM Attachment (20 downloads)

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.

llanitedave
Humble Megalomaniac
Reged: 09/26/05
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Re: Beautiful, intriguing, elegant ideas
[Re: EJN]
#5598705  12/31/12 08:26 PM

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And there was light.

deSitter
Still in Old School
Reged: 12/09/04

Re: Beautiful, intriguing, elegant ideas
[Re: Rick Woods]
#5599912  01/01/13 04:24 PM

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Quote:
Quote:
You can argue, this is the most important formula in all of science and engineering.
I always thought that honor belonged to the formula for beer...
Zounds, I had forgot the beer.
drl
