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A while back I peered into the code of SICM and was confused to find a scheme for computing derivatives that works by passing ordered pairs (x,Dx) around. I put it on my figure-this-out-sometime list and forgot about it until I saw Will Farr's blog entry yesterday, ``Automatic Differentiation'' in OCaml. Apparently "Automatic" or "Algorithmic Differentiation" is a long-known technique for computing the derivative of an arbitrary function as implemented in a algorithmic language.
life in ROC
Aug. 25th, 2005 09:41 pm1. Bicycled down south plymouth avenue to north plymouth avenue.. Tucked into church street to visit City Hall for the Neighborhood Associations Presidents' Meeting. I hadn't even known where it was located. It's a smaller place than you think, but in grand style--what I'd call "Upstate Gothic," if that makes any sense at all. I locked up my bike to the flagpole bearing the Rochester flag. It was all very anti-climactic, though. First I couldn't figure out how to get in the building (the front door is locked after hours). And then it turned out that the meeting had been mysteriously cancelled. I guess I'll have to wait a little longer to meet John Borek.
2. Having some free time, I biked out State to check out Flat Iron Cafe, which is located where State, Lake, Smith, and Lyell streets and avenues come together. There were just two guys there, a well-dressed middle-aged man and an older man sitting at a wrought-iron table outside, enjoying espresso. The younger one, Tom, turned out to be the owner; the older one spoke with a thick Italian accent. I sat and talked with them for a while. It's a good place— I plan to return one night with a backgammon set and my officemate Stefanos. Some review I read of the place suggested it as a place to read Kerouac. I read Spivak's Calculus on Manifolds.
At one point while there, cops suddenly descended on the place. Three officers on foot from one side, and a car with lights from the other. But the car with lights was a total coincidence, and the cops on foot were there as customers.
Tom and partners are also opening up a comic book store behind the cafe.
3. Riding home through downtown, I chatted with![[livejournal.com profile]](https://www.dreamwidth.org/img/external/lj-userinfo.gif)
hypostatization on the phone, he currently on the road in South Carolina. At some point out on West Main, a bunch of kids approached me. "Get off that bicycle!" one of them yelled, apparently wanting to steal it. I've been approached by kids maybe two or three times this summer and threatened in some way, but this was the only time it was at all serious. Still—I never know how serious these would-be muggers are and my first response to muggings is apparently indignation. "I don't think so!" I yelled back. "Give me that bike, I'm serious!" "What the hell?" It occurs to me that I should flee—I know this kid could beat me up pretty bad, and there's a half-dozen of his cronies closing in. I ride out into traffic. He runs after and grabs my backpack. Some older black man leans out of an SUV and yells "Don't do it, man!" and the kid lets go briefly, I ride off.
A couple blocks later, I called Rob back.
"Was that a mugging?" he asked.
Then out in South Carolina there was something like a gunshot and he had to go. Weird night, huh?
4. Back at the co-op we're moving into an exciting transitionary phase—Summer residents Mike, Leland, Lewis, Jon McVay, and Andrew are leaving, moving back into the dorms. And Jon P., Nicole, Kastan, Bree, and Zach are moving into the house. Doug, Becky, and Jeremy are moving into an additional house across the street. Exciting times. We're going to have an orientation of some kind next weekend. Perhaps to involve wine and cheese. My twister suggestion may have been vetoed.
5. Critical Mass tomorrow!
2. Having some free time, I biked out State to check out Flat Iron Cafe, which is located where State, Lake, Smith, and Lyell streets and avenues come together. There were just two guys there, a well-dressed middle-aged man and an older man sitting at a wrought-iron table outside, enjoying espresso. The younger one, Tom, turned out to be the owner; the older one spoke with a thick Italian accent. I sat and talked with them for a while. It's a good place— I plan to return one night with a backgammon set and my officemate Stefanos. Some review I read of the place suggested it as a place to read Kerouac. I read Spivak's Calculus on Manifolds.
At one point while there, cops suddenly descended on the place. Three officers on foot from one side, and a car with lights from the other. But the car with lights was a total coincidence, and the cops on foot were there as customers.
Tom and partners are also opening up a comic book store behind the cafe.
3. Riding home through downtown, I chatted with
hypostatization on the phone, he currently on the road in South Carolina. At some point out on West Main, a bunch of kids approached me. "Get off that bicycle!" one of them yelled, apparently wanting to steal it. I've been approached by kids maybe two or three times this summer and threatened in some way, but this was the only time it was at all serious. Still—I never know how serious these would-be muggers are and my first response to muggings is apparently indignation. "I don't think so!" I yelled back. "Give me that bike, I'm serious!" "What the hell?" It occurs to me that I should flee—I know this kid could beat me up pretty bad, and there's a half-dozen of his cronies closing in. I ride out into traffic. He runs after and grabs my backpack. Some older black man leans out of an SUV and yells "Don't do it, man!" and the kid lets go briefly, I ride off.A couple blocks later, I called Rob back.
"Was that a mugging?" he asked.
Then out in South Carolina there was something like a gunshot and he had to go. Weird night, huh?
4. Back at the co-op we're moving into an exciting transitionary phase—Summer residents Mike, Leland, Lewis, Jon McVay, and Andrew are leaving, moving back into the dorms. And Jon P., Nicole, Kastan, Bree, and Zach are moving into the house. Doug, Becky, and Jeremy are moving into an additional house across the street. Exciting times. We're going to have an orientation of some kind next weekend. Perhaps to involve wine and cheese. My twister suggestion may have been vetoed.
5. Critical Mass tomorrow!
the shape of space
Apr. 20th, 2004 11:47 amJeff Weeks' MSRI-Evans talk yesterday was quite different than the usual MSRI talks "for grad students and Mathematicians" — much of the talk was illustrated by a fly-through ("first person shooter" for you silly gamers) of the universe given many different possibly topologies. It's easy to think of a spherical surface or a hyperbolic surface or a planar surface when you're talking about embedding a two dimensional surface in a three dimensional world — but when you start talking about three dimensional manifolds with various "shapes" (spherical, etc), things get a little weird.
For instance, if you look straight ahead on a spherical surface, you will see yourself from behind. But the weirder thing is that perspective is nonlinear — if you're standing at the pole, then things get smaller as you head towards the equator, but things further than the equator get bigger and bigger! Something directly opposite you on the sphere will occupy your whole field of view — in the background! The universe might really have such topology, but the reason we don't see ourselves in the distance has to do with the horizon, which is set by the speed of light (?).
But the key thing that was sort of an "ah-ha!" moment was when he made the connection between topologies of space and lattice symmetries. Actually, in the talk it was one of those things that was assumed to be obvious. And it is obvious, but I hadn't thought of it before! Say you live in a surface with toroidal symmetry — then you can meet yourself again if you translate a certain distance either horizontally or vertically. In other words, the toroidal space corresponds to a rectangular lattice! (But there's got to be a difference.. after all, you have curvature to worry about, as you "go around the donut.") Likewise, a klein bottle surface is like a lattice with one line of mirror symmetry — go off in one direction and you'll encounter a reversed copy of yourself, then keep going and you'll find an identical copy.
In the talk he also managed to explain the microwave background radiation and how it is used to determine Ω (which is related to the shape of the universe — "open," "flat," or "closed") in an understandable and accessible way. Anyway, it was an amusing talk — not particularly deep, but a good introduction to concepts I think will be quite useful to me.
Another awesome thing about Jeff Weeks is that he is a freelance mathematician. His web site includes the program that was rendering curved spaces.
For instance, if you look straight ahead on a spherical surface, you will see yourself from behind. But the weirder thing is that perspective is nonlinear — if you're standing at the pole, then things get smaller as you head towards the equator, but things further than the equator get bigger and bigger! Something directly opposite you on the sphere will occupy your whole field of view — in the background! The universe might really have such topology, but the reason we don't see ourselves in the distance has to do with the horizon, which is set by the speed of light (?).
But the key thing that was sort of an "ah-ha!" moment was when he made the connection between topologies of space and lattice symmetries. Actually, in the talk it was one of those things that was assumed to be obvious. And it is obvious, but I hadn't thought of it before! Say you live in a surface with toroidal symmetry — then you can meet yourself again if you translate a certain distance either horizontally or vertically. In other words, the toroidal space corresponds to a rectangular lattice! (But there's got to be a difference.. after all, you have curvature to worry about, as you "go around the donut.") Likewise, a klein bottle surface is like a lattice with one line of mirror symmetry — go off in one direction and you'll encounter a reversed copy of yourself, then keep going and you'll find an identical copy.
In the talk he also managed to explain the microwave background radiation and how it is used to determine Ω (which is related to the shape of the universe — "open," "flat," or "closed") in an understandable and accessible way. Anyway, it was an amusing talk — not particularly deep, but a good introduction to concepts I think will be quite useful to me.
Another awesome thing about Jeff Weeks is that he is a freelance mathematician. His web site includes the program that was rendering curved spaces.
differential geometry
Apr. 12th, 2004 12:25 amBlah. Covariant derivative. Parallel transport. What's the story?
"a geodesic is a curve whose parametrization, when viewed from within the surface, appears to have zero acceleration" (i.e., all of the acceleration is normal to the surface)
The phrase "objects not experiencing external forces follow geodesics" is more of a tautology than I thought.
If gravity is actually a warping of space-time — so that there's not actually any 'force' of gravity, but rather falling objects travel in "straight lines" along geodesics in space time — why is there still the occasional mention of graviton messenger particles for the gravitational force?
sleepy time.
"a geodesic is a curve whose parametrization, when viewed from within the surface, appears to have zero acceleration" (i.e., all of the acceleration is normal to the surface)
The phrase "objects not experiencing external forces follow geodesics" is more of a tautology than I thought.
If gravity is actually a warping of space-time — so that there's not actually any 'force' of gravity, but rather falling objects travel in "straight lines" along geodesics in space time — why is there still the occasional mention of graviton messenger particles for the gravitational force?
sleepy time.
I was in Birge to get some form signed (yay! I might be a legitimate student soon!) this afternoon, and there was a physics faculty meeting starting in 375 LeConte. It was funny, because it just made me realize how familiar all the profs are to me. John Clarke gave me a nod, George Smoot said "What's up, Tobin?", etc, and Alessandra Lanzara found out that my real name is not "Nicky Hamilton." (-: Renews my feeling that I should just hold out and try to get into the physics department here. (-:
I actually went to Office Hours today for more or less the first time. It was by accident. I went to get the aforementioned form signed by Bjorn Poonen (my prof for metric differential geometry), and he was having office hours, so I stayed. He was addressing a question from our first homework that I didn't find particularly interesting, but then we started talking about turning surfaces into metric spaces, and then about geodesics and gravitational lensing, which was cool.
(no subject)
Feb. 16th, 2003 12:38 amI have `liberated' this new icon from the CERN website.
The sound of rain on my room's roof is quite pleasant.
Isn't it cheating to require a new axiom (the ``Infinity Axiom'') in order to construct the natural numbers, and still call it ``constructive'' (versus axiomatic)? The Infinity Axiom (
∃A:(∅∈A)&(∀a∈A, a+∈A)) seems tailor made for the construction of the naturals.vmwareis amazing. I can run Windows 2000 and Linux and Plan9 simultaneously, just as if this little computer were actually three. With Mozilla and OpenOffice running on both Win2K and Linux; and with Mindterm SSH running in a Java VM; and connected to my mailboxes via IMAP, it's clear to me that the future of computers isn't with platform independence, it's with platform irrelevancy.(nonetheless, it's still impossible to get any work done in Windows without somehow connecting to or emulating a Unix environment :-)
multivariate valentine
Feb. 9th, 2003 11:23 pm``How ironic that a day reserved for the celebration of love (with compliments paid to sisters, infatuation, and lust) is also the source of such singlehood sadness, dating disasters, and marital mischief. Lest any of you have fallen victim to a lover's lascivious lures or enjoyed excruciating experiences, take refuge now in the romantic tale of our dear topologist, Monsieur Topologie, a story not about the other side of Fortune's coin but rather the same side of Cupid's Möbius, with his arrow slung in the opposite direction. ...''
Continue reading this tale (the best written Math 53 homework assignment I've yet seen) written by Matthew J. Rodriguez
