*or*a math methods class, just sort of picked them up on my own), so it should keep me on my toes and fill in a few gaps.

Today we made liquid nitrogen icecream again, our best batch ever! yummm... we put eggs in it this time, which made it much creamier and taste delicious. I think that was the secret ingredient we were missing before.

I officially got the word back that I passed all my quals, but I feel an odd combination of outrage, disappointment, and relief because my statmech score was far below what I projected, and I barely passed E&M at all. Apparently, I'm not nearly as good as I thought at self-assessment. (That's the

*last*time I put errorbars on my projections!) I have yet to figure out what the hell the extra points they took off are for, since my answer agrees with the book and as far as I can see I didn't skip any steps or make any leaps in reasoning. But then again, it's said and done with. I narrowly escaped certain death by a closer margin than I thought possible, but I suppose it matters little now. :) I'm on the other side of the gateway, awaiting the next challenge.

What else? Oh, I never knew we had this here, but I was invited to join "journal club" today. I signed up for the email list and plan to attend (and hopefully) present at some point. Looks interesting:

Dear physics grads, To promote a broader knowledge of physics, we have started a journal club which was very successful last spring. We wish to continue this and invite (encourage) all interested grads to attend (and maybe present). Basically, we just get together on fridays at 11:30am and have lunch and talk about a specific article that the presenter has read and found worth sharing. Unlike fight club, you can talk about it. Our first meeting is friday, Oct 1. (old JCers, note new time). we meet at the picnic tables outside ISB. Prime Directives: 1) Go where no physicist has gone before by communicating complex subject matter in a comprehensible way to a reasonably intelligent sentient beings. 2) No extra work; present articles that you've already read and feel is interesting.

## Comments

dankamongmenlucentspoonlessexcellent question!

There are some properties of spaces which work like your time example... you can't measure them unless the space is embedded in a higher dimensional space. For instance, a piece of paper is a two-dimensional space. From inside that space, there's no way to tell if it is folded up or crumpled or what direction it's turned in. These are meaningless questions to ask unless it's sitting in some larger-dimensional space such as the 3D world we're used to moving around in. But there are other properties, such as curvature, which are intrinsic to a space. You can measure the curvature at any point in space from inside, without reference to any larger space.

Notice that even though you can fold a piece of paper without changing its internal geometry, you cannot wrap a piece of paper smoothly around a baseball without warping it. In order to deform a flat piece of paper into a curved (warped) piece of paper you'd need it to be made out of rubber or something which stretches. As long as there is no stretching allowed, the paper has an intrinsically "flat geometry" to it.

One of the easiest ways to tell if a space is locally curved is to measure the sum of the angles in a small triangle. If it adds up to 180, then it is flat. If it adds up to more than 180 then it has positive curvature. If it adds up to less than 180, it has negative curvature. The surface of the earth is an example of a 2D surface which has positive curvature. Another consequence of positive curvature is that parallel lines will always eventually intersect. For instance, take two meridians on the earth which are parallel at the equator (both form 90-degree angles with the equator). Follow them up and they will intersect at the north pole.

A 3D (or 4D, in the case of spacetime) curved space works the same way; you can tell from inside that triangles sum up to more than 180 degrees, and parallel lines can intersect if you follow them far enough. Even if you can't see the whole space or if it isn't embedded in any higher dimensional space. Such is the case for spacetime. The mathematical study of these kinds of spaces is called "Non-Euclidean Geometry" because it violates many of Euclid's original postulates about geometry (such as parallel lines never intersecting). When you do calculus on such spaces it's called "differential geometry", one of the coolest classes I got to take as an undergrad.

Hope that helps!

lucentspoonlessYou could also ask on

physics; I usually try to answer any questions on there if I have a good answer and nobody else has said it yet. Although be aware that some people there will give partially correct (or even incorrect) answers, and others might give correct answers that aren't very illuminating. You have to learn "who you can trust" to some extent. But if anyone istoofar off base, someone will usually point it out.