Now that I know that I am providing endless amusement to the grad students, faculty, and (dare-I-say) postdocs in OCIAM, here's a little survey that I have been meaning to do for a while.
Basically, I want to write (or co-write, if anybody else is interested) an article for a venue like the AMS Notices or American Mathematical Monthly that discusses the "top 10 differential equations of all time" (a la David Letterman). The thing is that I need some sort of survey first, so if I just choose 10 that I like, it would be geared too much towards specific subjects. So, if anybody wants to pipe in here, by e-mail, or by any other venue, I would be greatly appreciative. (List of differential equations written on napkins are particularly encouraged, but toilet paper is right out.)
I'd like to get enough lists from people so that I can take the 10 most popular choices from that list and write the article. For each equation, I'd include some (reasonably brief) discussion of where it comes from and why it's important.
Here is a list that partially reflects my opinion but also reflects how little time I'm going to spend typing up the rest of this entry:
10. Lorentz equations
9. the Nesterenko equation*
8. the Klausmeier equation (because it's named after a former colleague who made a great Thanksgiving turkey)
7. Duffing's equation
6. Einstein's field equations (if for no other reason than because it made a guest appearance in The Triplets of Bellevile, and I got a free book out of that)
5. Navier-Stokes equations
4. the linear Schrodinger equation
3. the complex Ginzburg-Landau equation
2. the cubic nonlinear Schrodinger equation (aka, the Gross-Pitaevskii equation) [notice the correlations from 2-4; that's why I need help writing this list]
1. x' = 0
Honorable mention: That equation I "derived" on my AMa 95b final back in the day. (Actually, I could have mentioned any number of courses here, and I think 95b is one of the few in which I didn't develop my own equation of one sort or another with some misplaced derivation. But it amuses me to attribute this to AMa 95, so I won't let the truth get in the way of a good story.)
* This is the "unnamed" equation in a recent paper of mine (and several upcoming ones!) that my collaborators and I decided to name after the person who first derived it because it makes citing his results less cumbersome for the exposition. I wonder if this is how other equations have gotten named?
I swear I'm going to write my review for Avenue Q in the relatively near future.
Why do the Oxforders find you so very amusing? I'm not saying you aren't, it's just not generally as pervasive an opinion as you make it out to be here... :-)
ReplyDeleteAs for your actual question, I notice that Maxwell's equations are conspicuously absent. And although x'=0 is good (I like that kind of thinking on this type of question), x'=x seems better to me.
The collisionless Boltzmann equation is rather important in astronomy, if you're looking for more specific content.
I might also suggest emailing Chad Orzel (Uncertain Principles, over at Scienceblogs) since he has a regular series of Dorky Polls. And a bigger readership than you, even now. :-D
Justin: I think perhaps the Oxonians may be developing the kind of relationship with me as Jane Goodall had with her chimps (where I'm playing the role of the chimp).
ReplyDeleteI don't remember claiming that the Pasadenans found me particularly amusing. I think a fair share of them did but that others thought that I was a complete asshole. I don't think there was much middle ground. Anyway, a very nontrivial number of people from back home actually like me (for better or worse), so that's good enough for me. And I would think that a reasonable subset of those folks are also amused by me.
The absence of Maxwell's equation isn't actually conspicuous. It's more a matter of my being lazy and wanting to put equations that I deal with. (Now, if you think about Maxwell's equations in a problem that has random cracks in it, then that's a different story entirely.)
Chad Orzel is way out of my league. I am not even trying to compete with the likes of him. The only comparison I'm really making is the number of readers I have now versus the number I had before. Egocentric as I am, I figure I should just compare me to myself. (Also, I would also claim that AG still has a lot more readers than I do, though it would be nice if he would give us a little more to read. :P Why bother with your thesis when you can pay attention to your blog instead!) The short version is that it's less an issue of bragging (especially if you compare to the readership others have, which basically says that I have no right to brag) and more an issue of my being happy that people are actually reading what I write.
Passing along the idea to Chad is a good one, though I'd be happy with a collection of thoughts applied mathematicians --- as they would be the target audience of the intended paper anyway. I figure if they're looking here anyway, I can put this here, because I don't feel comfortable sending out a spam e-mail with that kind of question.
Maxwell's should be on there, and you can go suck on a scratched missile, Mason.
ReplyDeleteTo be fair though, the whole random cracks thing did, perhaps, help get the attention of someone who has some very interesting, very specific cracks, that make for challenging (but probably doable) problems with interesting applications.
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ReplyDeletePasadenans with whom I associated nearly uniformly considered you amusing, though not all for the same reasons.
ReplyDeleteMaxwell's equations need to be there, even I know that. Come on. And it's not just about electromagnetics, you know... use controls and dynamics folk build our models around modal variants of the wave equation.
And I think x'=x and x'=0 should be #2 and #1, respectively. Both merit thought and a nod.
GFreak: I'm not going to even ask what the various reasons are, though I have a natural preference for those who are laughing with me rather than laughing at me.
ReplyDeleteIt seems that Maxwell's equations are a popular choice among this crowd. I didn't find any napkins under my door with other equations that I dissed, but we'll see if I see any of those eventually.
Lemming: I am going to find excuses to bring up random cracks until I get bored of it. :) Actually, I want to invite Cat to give a talk here and then ask him about random cracks. The ensuing rant alone might be worth the cost of flying him over here (ok, well maybe not, but I do plan on being amused by it).