the shape of space

Jeff 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.

random day

I had lunch with John Clarke today. By this I mean, "I tagged along on an event intendend to help undergraduates schmooze with faculty," part of the Berkeley Physics Dept.'s efforts at self-improvement. I think it's an excellent idea, but I'm not so sure they got at their target audience: of the five of us excluding the emminent professor, two were grad students in the department, two were undergrads in other majors, and then there was me. So my schedule for the day was shaping up something like this:

08:00 Solid State Nap-Time
10:45 Coffee time at work
12:00 Lunch with Prof. Clarke
17:00 Birthday celebration for Chuck = beer and food at Jupiter

The lunch with John Clarke was good but a little strange. It was revealed that Diane was in 137A currently so then he asked me if I was also in 137A. I said, "Actually I took it a long time ago... with you!" I think he was kind of embarassed. I added, "And 137B and 7B and 7C." So pretty much the reason I went to the lunch thing was because, although I've taken nearly all the physics courses I've taken here from him, and he nods at me all the time, (his daughter was even in a couple of my classes!) we're hardly acquainted. I'm not sure that was really remedied.

At lunch (at Cafe Durant) somehow the first conversation topic that was launched into was the grad student girl ranting about how much she hated london. She had lived there for a semester or something and evidently hated every minute of it. She complained on and on about how dirty and expensive and polluted and crowded it was, how her lungs hurt and how her snot was black at the end of the day. Keep in mind that Prof. Clarke was born, raised, and educated in Cambridge. It was embarassing. I wished I had a button that would electrocute this girl so she'd get the message.

Then lunch was finished and Prof. Clarke invited us to coffee at Cafe Strada. On the way I talked to the girl who had been complaining about london about the CERN program — she had gone in 1998. "You know it's cancelled, " she said. Her theory was that it was because everyone who does the CERN REU subsequently "quits high-energy physics." That may be true, but it's probably only symptomatic...

At Strada I had an espresso, Prof. Clarke had a cappuccino, and the grad student guy had a regular coffee. Prof. Clarke said something like, "Now I'd like to ask you about what you think are big issues facing the department." Or something like that, that seemed to convey some higher-up interest in extracting opinions from current students, part of this whole departmental self-improvement scheme. I didn't have anything to add to the conversation.

So that was lunch with John Clarke.

---

Back at Donner Hall, I was feeling rather low in exactly the way I shouldn't, having just ingested an espresso; I think it was some kind of anticlimax from this lunch thing. I had to clean out my office, because its rightful owner is allegedly going to materialize any day now. Too bad. I felt so special having an office, even if I didn't use it too much.

At five I wandered down to Jupiter, a bar/restaraunt/microbrewery on Shattuck in downtown. It was Chuck's birthday and everyone from the lab was down there for occassion. It was a nice walk down there, and the sun came out on the way. Jupiter has a very nice, very relaxed back area that seems worlds apart from the downtown Berkeley that surrounds it. Drinking some tasty beer and enjoying the gormet pizza, it sort of felt like the summertime in Geneve.

But then I suddenly had the need to initiate this conversation, after some comedy in trying to get ahold of the server:

Tobin: Can you tell me the composition of your pesto?
Server: Well, let's see.. it's (mumble mumble) walnuts (mumble mumble) ..
Tobin: That is unfortunate. Do you happen to know the fraction of walnut?
Server: No.. why? Are you allergic? Is there something I can do?
Tobin: Do you happen to have any benedryl?
Server: Unfortunately I can't dispense medication...

But someone else had some funky antihistamine, saving me a trip to the nearby Wallgreens; and the walnut fraction must has been pretty low because I was able to power through the experience with not too much discomfort (although now, hours later, my stomach is all tied up in knots trying to process this poisoned pesto.. uuurgh).

It was supposedly a non-drowsy anti-histamine, but it wasn't entirely non-drowsy.. some hours after arriving back at the lab, I woke up with my head on my desk, the lights turned off, my arms asleep, all confused.. Sat up and the motion detector turned the lights on and I figured things out. Dragged myself home, lugging my now one-strapped backpack. Blaaaaah.

---

Then back at this house I collapsed into pseudo-slumber with weird half-dreams about the topology of the universe. Meanwhile Diane and Gina had a horrible conversation pertaining to flossing, and how you find all these horrible chunks of old rotten food matter, and it's all bloody and OH SO INCREDIBLY GROSS.

To advert nightmares I just had to try this whole flossing thing myself, and was quite relieved to not find any of this horribly disgusting junk they were talking about. So now I can sleep peacably again.

I just thought you needed to know that.