Edge.org has collaborated with the Serpentine Gallery in London on a fun kind of artistic event: a collections of formulas, equations, and algorithms scribbled (or typeset) on pieces of paper and hung from the gallery walls like honest-to-goodness pieces of art. I was one of the people asked to contribute, along with another blogger or two. You can check out the entries online.
Some of the entries are straightforwardly hard-core mathematical, such as the one from J. Doyne Farmer or this from Shing-Tung Yau:
Mathematical truths have a uniquely austere beauty in their own right, but the visual presentation of such results in the form of equations can be striking even if the concepts being expressed aren’t immediately accessible. (Yau is talking about Ricci Flow, a crucial element in the recent proof of the Poincare Conjecture.) Meanwhile, many of the entries take the form of metaphorical pseudo-equations, using the symbols of mathematics to express a fundamentally non-quantitative opinion (Jonathan Haidt, Linda Stone). Some of the entries are dryly LaTeXed up (David Deutsch), some are hastily scribbled (Rudy Rucker), some tell fun little stories (George Dyson), and some are painstakingly elaborate constructions (Brian Eno). Several aren’t equations at all, but take the form of flowcharts or other representations of processes, such as this from Irene Pepperberg:
My favorites are the ones that look formidably mathematical, but upon closer inspection aren’t any more rigorous than your typical sonnet, like this one by Rem Koolhaas:
Or the ones that are completely minimalistic, a la James Watson or Lenny Susskind. Note that the more dramatic your result, the more minimal you are allowed to be.
The big challenge, of course, is to choose just one equation. There are a lot of good ones out there.
I think yours is very nice! A real air of mystery to it.
Yours is one of the most colorful, Sean!
Yick. I’ve gone through only four so far (by clicking the “next” button after yours, Sean), and so far two people have announced how ennamored they are with the Drake equation.
Sorry, it looks like Max’s beats Sean’s for colorfulnes.
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just for a practical joke, if i were offered, i’d probably submit the “women are evil” equation.
The equation is right (-e^(i pi)=1), but I’m not sure Dean Kamen’s proof works out exactly.
http://www.edge.org/3rd_culture/serpentine07/Kamen.html
Respectfully, I feel compelled to say that we should not get confused about the aesthetics of mathematics, science and the aesthetics of art … they are completely different yet equally beautiful things however, they are not the same. Why present science as art when you can use mathematical equations to write your own poetry and make your own art.
Again respectfully yours,
Kaz
http://mathematicalpoetry.blogspot.com
I didn’t know Freeman J. Dyson was also called George!
George = Dyson jr.
A pretty minimalistic equation, but my favorite one is
this, because I discovered it (more precisely, the c_2 term) 🙂
For Alex F
I think this is how it’s supposed to be:
– e^(i pi) = – ( cos pi + i sin pi ) = – ( – 1 + 0 i ) = 1
Right?
Pi is approximately equal to:
Log[(15*23*29*64)^3 + 24*31]/sqrt[163]
How about E = c^2m? Yes, that’s the way I think it should look. IIUC, the constants are supposed to be in front, like for f = Gm1m2/r^2, E = hbar*omega, etc. What really determines the order symbols should be in, other than some obvious things like actual numbers first? Some try it according to numbers*constants*variables, others in terms of low powers first, etc. BTW, by now there should be a relatively easy way to show good equations on comment screens like this. I am not picking on Sean, it is like this everywhere that I know.
I like George Church’s submission of exponential function. It’s simple, and he is right that exponential growth (or decline) as a great propensity to muck up the works.
I like indexed better:
http://indexed.blogspot.com/
The beta function equation in string theory, relating spacetime Einstein equation with conformal invariance on the worldsheet. Elementary as it is, still pretty much a mysterious statement for me.
I’m very surprised that neither
delta S = 0
nor
Delta S geq 0
made it. Those would be my top two choices, for sure.
I think the point was not “the best equation ever,” but your equation — either one you have actually come up with, or failing that, the one that you are thinking about most obsessively these days.
OK, here’s my equation:
Delta S = 2 n hbar (A^2 – B^2)
Here, Delta S is the change in the rotational angular momentum (or as transferred by axle etc.) of a half-wave plate through which n photons pass of a given “circularity” (expectation value of angular momentum, derived from the wave function A |R> + B e^(i theta) |L> using newer standard of handness. That is pretty straightforward, since transiting a HWP inverts the rotation of CP light while maintaining “form” (ellipse shape, but axis may change) and has a corresponding effect on photon wave function. (Sometimes circularity is called or confused with ellipticity, but I prefer the former.)
However, there’s another meaning for the equation: Instead of passing n photons through once each, try a return circuit for a single photon. We can re-invert the spin flip with another HWP, and use mirrors to bring the photon back through the first HWP over and over. Indistinguishability says, the plate can’t tell the difference between these two cases. Hence, the plate should build up the same change in AM as shown by the equation, but then n means transits of a photon not “number of photons” (with all due respect for the ambiguity of n for the latter, the uncertainty in n is usually relatively small.)
Well: that would allow finding the circularity of a single photon, which is the projection postulate says we can’t do. Yet the argument (cascading of a known process) seems straightforward. Any thoughts?
Surprised Maxwell’s Equations not mentioned.
The heat kernel equation
Two more favorites:
The Newton-Witten equation:
F = ma.
The Beatle identity:
1 + 1 + 1 = 3
“We haven’t figured out what it has to do with physics yet, but the mathematical relation is so profound there must be some application.”
Also:
“Amplitudes can then be expressed in terms of the two-dimensional Green function
G (?, ?) = ? d ? I?(?) R(?, ?; ?),
where I = ? J is the Imbessel function, R is the retarded potential, and ? is a dummy variable.” 🙂
Scribbled on a church bulletin to keep me awake one Easter sunday:
At risk of a blasphemy towards one or the other, here’s a diagrammatic mashup of the BigBang and Genesis.
That was really well done, Jim.