Comments on: What is Your Equation?

By: Sean

Sean — Fri, 19 Oct 2007 19:19:56 +0000

That was really well done, Jim.

By: Jim Clarage

Jim Clarage — Fri, 19 Oct 2007 18:27:40 +0000

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.

By: Count Iblis

Count Iblis — Thu, 18 Oct 2007 17:50:07 +0000

Also:

“Amplitudes can then be expressed in terms of the two-dimensional Green function

G (σ, τ) = ∫ d ν Iν(σ) R(σ, τ; ν),

where I = ℑ J is the Imbessel function, R is the retarded potential, and ν is a dummy variable.”

By: Thomas Larsson

Thomas Larsson — Thu, 18 Oct 2007 11:40:43 +0000

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.”

By: Haelfix

Haelfix — Thu, 18 Oct 2007 07:37:13 +0000

The heat kernel equation

By: Stu Savory

Stu Savory — Thu, 18 Oct 2007 03:15:10 +0000

Surprised Maxwell’s Equations not mentioned.

By: Neil B.

Neil B. — Thu, 18 Oct 2007 01:46:08 +0000

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?

By: Sean

Sean — Wed, 17 Oct 2007 20:52:14 +0000

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.

By: noname

noname — Wed, 17 Oct 2007 20:36:22 +0000

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.

By: Moshe

Moshe — Wed, 17 Oct 2007 16:48:18 +0000

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.

By: Philip Downey

Philip Downey — Tue, 16 Oct 2007 20:02:10 +0000

I like indexed better:
http://indexed.blogspot.com/

By: Babbler

Babbler — Tue, 16 Oct 2007 03:18:54 +0000

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.

By: Neil B.

Neil B. — Tue, 16 Oct 2007 00:56:41 +0000

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.

By: Count Iblis

Count Iblis — Mon, 15 Oct 2007 20:10:14 +0000

Pi is approximately equal to:

Log[(15*23*29*64)^3 + 24*31]/sqrt[163]

By: Freiddie

Freiddie — Mon, 15 Oct 2007 14:21:46 +0000

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?

By: Thomas Larsson

Thomas Larsson — Mon, 15 Oct 2007 06:46:48 +0000

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)

By: Amitabha

Amitabha — Mon, 15 Oct 2007 06:41:42 +0000

I didn’t know Freeman J. Dyson was also called George!

By: Kaz Maslanka

Kaz Maslanka — Mon, 15 Oct 2007 04:22:50 +0000

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

By: Alex F

Alex F — Mon, 15 Oct 2007 04:18:30 +0000

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

By: Chris

Chris — Mon, 15 Oct 2007 03:58:07 +0000

just for a practical joke, if i were offered, i’d probably submit the “women are evil” equation.