Where have I been? What have I been up to?

These questions were posed to me yesterday, and my blogging absence was pointed out, so I thought I would jump back into it this morning!  In answer, I have been spending my time, as ever, with math. In Spectral Theory, we're talking about crazy beasts called 'Ultrafilters' (honestly, the names for things in math just get sillier and sillier as we go on. We proved a theorem in Algebraic Topology called the 'Hedgehog Theorem', and I know that a certain mathematical object called a 'Super Algebra' also exists. Good grief!)

But some of the rest of the time, I've been getting to know people - having potlucks and get togethers, and encountering things like this most magnificent pie:

This pie (which is a good 3.5 inches deep) sparked a lively discussion at this potluck, about how cruel it is that cakes are always allowed to be as tall as they please, yet pies are reduced to tiny heights by design. So, my friends threw the design away and made an enormous pie.

I've also been wandering around Budapest and finding lovely little markets that are popping up in this cold weather. The last one I was at had several antiques booths where old Hungarian money, ancient bottles and tools, aged china and silver, and a whole manner of old photographs and paintings could be found. I strolled around with a friend, each of us with a glass of mulled wine, and had a lovely Saturday.

My friends from back in California have been in communication lately as well, including the lovely Matilda and Kamaji, as you might remember from my summer adventures in Berkeley.

Is there anything more lovable?

Have you ever seen such wise, knowing eyes??

Receiving those pictures from my old friends made me miss that life there. Somebody asked me what I had done over the summer and before I knew it, I was back with the chickens and the lemon tree, work in downtown SF and walks in the Berkeley hills with the dogs and my friends. It really was a great summer.

And things are winding down here for the semester. If I'm not mistaken, there are only four more full weeks of the semester! Then I'll be dashing quickly to Pennsylvania, to finally see my mom and sister and MY lovely dog again (I'd having her living with me here if I could), then to Washington, DC to see the rest of the family, and then some time with friends in Germany and Scotland over New Years.

And speaking of Scotland, my good friend Erin is coming here for Thanksgiving, which means I'll see her in less than two weeks! I can't wait to wander around the city with her - it's such a marvelous thing to have become an expert within the place that you live, so that you can show it to others. So much fun. :)

Alas, ultrafilters and ultralimits await. I was talking to a friend about my Algebraic Topology course the other day and how our professor doesn't really lean towards the incredibly rigorous proofs (I'm talking variables with several layers of indices on them, etc) because so much in the subject can be easily shown by a picture, but that would take ages to write out precisely. (If you think about it, this makes sense - think about drawing a plane perpendicular to a line in three dimensions. You can see just how perpendicular it is, but expressing that mathematically takes some crunchy numbers and variables. Now, imagine that we're talking about manifolds in n-dimensions... Yeah. Pretty hairy stuff.) However, understandably, some students don't like the lack of rigor in our proofs, because it makes them feel a bit afloat and not as in charge of the material. It can seem a bit 'hand-wave-y', as the phrase goes. And I was thinking about it during our conversation because my friend was particularly opposed to this kind of hand-waving (imagine someone waving a hand at a picture on a blackboard, saying "can't you see this this, if you pinch the corners together, looks like this??" - that's what I mean) and I couldn't help but compare her to Hermione talking about Divination, and then I had to compare my professor to Trelawney, and then my Algebraic Topology lectures became very amusing for a few days.