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What Makes an Equation Beautiful?
New York Times ^

Posted on 10/25/2004 1:46:25 AM PDT by accipter

CONSIDER a verbal description of the effect of gravity: drop a ball, and it will fall.

That is a true enough fact, but fuzzy in the way that frustrates scientists. How fast does the ball fall? Does it fall at constant rate, or accelerate? Would a heavier ball fall faster? More words, more sentences could provide details, swelling into an unwieldy yet still incomplete paragraph.

The wonder of mathematics is that it captures precisely in a few symbols what can only be described clumsily with many words. Those symbols, strung together in meaningful order, make equations - which in turn constitute the world's most concise and reliable body of knowledge. And so it is that physics offers a very simple equation for calculating the speed of a falling ball.

Readers of Physics World magazine recently were asked an interesting question: Which equations are the greatest?

Dr. Robert P. Crease, a professor of philosophy at the State University of New York at Stony Brook and a historian at Brookhaven National Laboratory, posed the question in his Critical Point column and received 120 responses, nominating 50 different equations. Some were nominated for the sheer beauty of their simplicity, some for the breadth of knowledge they capture, others for historical importance. In general, Dr. Crease said, a great equation "reshapes perception of the universe."

(Excerpt) Read more at nytimes.com ...


TOPICS: Front Page News; Miscellaneous; Philosophy
KEYWORDS: 1plus1equals69; fun; india; math; thisisthis
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To: r9etb
" No. See, e.g., Quantum foam."

The pen exists. It's the same pen, regarless of whether, it's blue, foamy, stinks, dried up, or has any other particular quantification. It exists and is what it is, regardless of whether any sentient being exists to comprehend it.

161 posted on 10/26/2004 12:31:27 PM PDT by spunkets
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To: spunkets
The pen exists. It's the same pen, regarless of whether, it's blue, foamy, stinks, dried up, or has any other particular quantification. It exists and is what it is, regardless of whether any sentient being exists to comprehend it.

It's the "same pen" despite the fact that in reality its physical makeup is in a constant state of change?

You seem to be saying that the concept of "the same pen" has its basis in something other than physical reality -- it's an abstract concept of the sort that Plato talked about in his theory of "forms."

162 posted on 10/26/2004 12:39:12 PM PDT by r9etb
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To: r9etb
" You seem to be saying that the concept of "the same pen" has its basis in something other than physical reality"

No. The basis is in reality. I'm also the same person I was yesterday, even though I had some more coffee, took a few leaks and gobbled up a bag of candy bars.

163 posted on 10/26/2004 12:44:46 PM PDT by spunkets
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To: spunkets
... even though I had some more coffee ...

Aha! So you admit that A is NOT A. If fact, because nothing is even itself, as you yourself admit, then nothing is anything! QED
</bizarro mode>

164 posted on 10/26/2004 12:54:46 PM PDT by PatrickHenry (Hic amor, haec patria est.)
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To: spunkets
I'm also the same person I was yesterday, even though I had some more coffee, took a few leaks and gobbled up a bag of candy bars.

So you're "the same person" despite the fact that your physical state has changed considerably since yesterday. Clearly, then, physical reality is not the basis for what makes you "the same person."

If we grant that you are, nevertheless, the "same person," then the reality in which your claim is based must be something other than physical reality. Can you describe that reality? Again: you seem to need something akin to Plato's "forms." Or, perhaps, you may need to invoke the concept of a soul that exists independent of your corporeal body....

165 posted on 10/26/2004 1:05:26 PM PDT by r9etb
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To: r9etb
"Clearly, then, physical reality is not the basis for what makes you "the same person." "

Wrong, physical reality is what enables objects to exist. W/o physical reality, there is nothing.

"you seem to need something akin to Plato's "forms.""

Nope.

" perhaps, you may need to invoke the concept of a soul that exists independent of your corporeal body....

If it is not real, meaning not having a physical basis, or foundation, it doesn't exist. If the soul exists, it is real and is physical.

166 posted on 10/26/2004 1:26:00 PM PDT by spunkets
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To: spunkets
Right, that's the DeBroglie wavelength, which depends on the particle's kinetic E. The Compton wavelength depends on the particles rest mass only there can be no scattering of that wave, because it means the particle "came apart" and no longer exists with the same ID. It became other objects.

Well then, what does this wavelength do? Anything? It would be equivalent to the DeBroglie wavelength if the electron was moving at the speed of light. I think that neither the Compton "wavelength" nor E = hv represent physical objects. In the case of E = hv, it doesn't mean that radiation comes in "bundles" of energy but rather that the interaction of an electromagnetic wave and a charged particle results in the transfer of that amount of energy. The wave or "photon" doesn't contain that amount of energy, its that the electron only absorbs that amount from the wave.

What's interesting is that a full semiclassical analysis of the Compton experiment produces the Compton "wavelength" as part of the double Doppler shift. It also produces the E = hv equation, constant transfer of angular momentum (still haven't figured out the factor of 2 error yet), etc. Required field strengths are extreme but the theory works. It also leads to what I call the "Compton Catastrophe" where the energy in the wave goes up as the frequency cubed. Yikes.

If you're interested in this all at, see the paper I wrote on the topic (pdf format):

The Classical Photon: Absorption

It is mostly a review of what is already known and put in practice in ultrahigh intensity laser acceleration of particles. My only real contribution is the second paragraph of the Discussion section. I think it's significant because it turns quantum theory on its head.

167 posted on 10/26/2004 1:30:27 PM PDT by mikegi
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To: spunkets
You're talking in circles now. You claim that you're still "the same person," despite the fact that you also acknowledge that you have physically changed since yesterday. How is it that you can be physically different, and yet "the same person?" PH jokingly went off into bizarro mode on this, but I have to wonder whether he may have been right after all....

W/o physical reality, there is nothing.

Is mathematics "physical?"

168 posted on 10/26/2004 1:33:31 PM PDT by r9etb
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To: kevkrom

"Especially if he was a union guy endorsing Kerry"

I found the sandwich easier to swallow.


169 posted on 10/26/2004 8:25:00 PM PDT by PoorMuttly ("The right of the People to be Muttly shall not be infringed,")
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To: spunkets; longshadow

Like a dem voter, the thread is back from the dead.


170 posted on 10/27/2004 12:09:22 PM PDT by PatrickHenry (Hic amor, haec patria est.)
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To: PatrickHenry

I see dead voters.


171 posted on 10/27/2004 12:10:12 PM PDT by js1138 (D*mn, I Missed!)
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To: js1138
I see dead voters.

You're gonna see a whole lot more next Tuesday.

172 posted on 10/27/2004 12:16:01 PM PDT by PatrickHenry (Hic amor, haec patria est.)
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To: PatrickHenry

I see dead campaigns.


173 posted on 10/27/2004 12:18:25 PM PDT by js1138 (D*mn, I Missed!)
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To: Bandaneira
I think the Equator is very beautiful.

We can do very well without the Equator, thank you very much. After all, do we really need a stripe of toxic paint encircling Spaceship Earth?

174 posted on 10/27/2004 12:22:22 PM PDT by PeoplesRepublicOfWashington (Vote Kerry: The Space Needle is an eyesore anyway.)
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To: js1138; VadeRetro; jennyp; Junior; longshadow; RadioAstronomer
I just noticed. Tomorrow is the five-year anniversary of my registration on this website. Not counting the dozens of threads that were pulled during the anti-science crusades last year, I've posted 215 threads and 19,608 replies. And never suspended!

I know the banned whackos are still lurking. Eat your hearts out. Hee hee hee.

175 posted on 10/27/2004 12:28:59 PM PDT by PatrickHenry (Registered here for five years!!)
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To: PeoplesRepublicOfWashington

In four dimensions (as opposed to three) there are two orthogonal axes of rotation (as opposed to one.) If a hyphersphere is rotated about both axes at the same rate, all points on the surface have the same speed. Everywhere is an equator. (Not all points are on the same equator though.)

Isn't geometry fun?


176 posted on 10/27/2004 12:31:09 PM PDT by Doctor Stochastic (Vegetabilisch = chaotisch is der Charakter der Modernen. - Friedrich Schlegel)
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To: PatrickHenry
... never suspended!

What, never? </Pinafore_mode>

177 posted on 10/27/2004 12:31:36 PM PDT by VadeRetro (A self-reliant conservative citizenry is a better bet than the subjects of an overbearing state. -MS)
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To: PatrickHenry

I've been here longer and posted more replies, but you are about 5 to 1 ahead of me on threads.

Most of my replies are brief and pointless bad puns.


178 posted on 10/27/2004 12:32:56 PM PDT by js1138 (D*mn, I Missed!)
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To: PatrickHenry
Happy Anniversary!

BTW, how do you access those stats?

179 posted on 10/27/2004 1:10:09 PM PDT by Faraday
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To: Faraday
how do you access those stats?

They're at the top of your "personal menu" page, which you'll see as soon as you click on "more" at the top of your "my comments" page.

180 posted on 10/27/2004 1:26:40 PM PDT by PatrickHenry (Registered here for five years!!)
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