Last night on the way to Cambridge, I had a small panic attack whereby I form a plan of attack on the rest of my immediate life lest it overtake me and I black-out in public. [It has never come to that, but I’m sure that’s what would happen.] In case you are wondering — if you’re not, you should stop reading now — I have organized my life into three hour days. Each day I must do the following:

Calculus of Variations. (1 hour) First I’ll work through Fomin’s translation of Gelfands lectures. They work out variational problems in flat space with a few examples from field theory, classical mechanics, and geometry. Mostly it’s a journey into analysis. Once I’m done with that, I’ll move on to Jost’s book and learn about minimal surfaces properly. If at some point I make it through Jost, I’ll hit up Morrey, but he’s a long ways off.

General Relativity. (1 hour) For this I’ve chosen an obscure but very good book by Barret O’Neill called Riemannian Geometry with Applications to General Relativity. The whole point of the book is to give a proof of the Penrose-Hawking singularity theorems: given some very weak causality assumptions, there needs be a black hole or a big bang. Along the way he fleshes out symmetric spaces, Lie algebras, and other good and fundemental stuff. He also takes on variational problems, mostly that of geodesics. Hawking and Penrose all but force him to. It’ll be good to visit the calculus of variations from two very different points of view.

Cognitive Theory. (1 hour) Now this is less straight-forward. It’s very difficult to make a good curriculum if you don’t know the material already. Even still, my [general] plan is this: Piaget’s Psychology of Intelligence to learn about assimilation and adaptation. Then to learn why he’s wrong, I’ll read the boldly titled Getting it wrong from the beginning: Our progressivist inheritance from Herbert Spencer, John Dewey, and Jean Piaget by Egan. It was written in 2003, so it must be righter than Piaget who wrote the Psychology back in 1950. Afterwards, it’s time for Vygotsky and situated learning in the Mind in Society and some other stuff about activity theory. There are a number of journal articles I’ll read, but I’m not sure which ones just yet. And there’s this book called Cognition in the Wild and I should reread stuff by Papert. Why can’t all disciplines write textbooks like math textbooks?

And math education! Gelfand wrote a number of books on algebra and trigonometry and arithmetic designed specifically elementary school students. I should check them out. I know next to nothing about elementary school math education. And then Paul Sally wrote those nice geometry books for little kid teachers, too. And if I’m not mistaken, Schmidt is big into math education, too. I wonder if he’d talk to me. And Judah Schwartz! and Andrea diSessa. There are a lot of people I should read.

Also, each day I must either do two hundred push-ups or go swimming. Last night I swam with Laura Chapman at Blodgett. It was the first time I’d been in the water since I had to cut off my jammers with a Swiss Army knife to avoid an extended, wet, and naked wriggle in the locker room. It was also the first time since I had thrown six-year old Robert on his head, landing myself on my knees. It took several days for them to bruise. That’s how you can tell it was really bad. Despite these physical and emotional trauma, I was able to pull along nicely. I cut my work-out in half, swimming only sets of 250 yards rather than the full 500. Laura tried to teach me the breast stroke, something I find rather unnatural. I kept defaulting to the dolphin kick, so eventually I just switched to butterfly. [Not for long, of course. I went 25 yards; she went 25 yards. Not to be outdone, I went another 25 yards. By this time we were sufficiently tired and left.]