Inspired by Shea Browne‘s recent post “Gaining Momentum” I decided to write an update but also a stab at a mathematical manifesto. What am I doing? Why am I doing it?

I’m easily pulled in many directions and have a number of projects brewing at any one time. Trying to juggle all of them is challenging. The more connected these projects are to a single goal the more likely I am to revisit them and keep them progressing.

I don’t have that goal quite yet but I do have a set of items I’m working on or want to work on.

(1) What are the assumptions and the consequences of such assumptions. This is one of the reasons I’m interested in topological physics. What can we do without a metric? How much physics is left? This physics seems, perhaps falsely, to be more fundamental.

(2) Information, entropy, black holes, quantum mechanics, computability, decidability, (which is why those various tilings and Turing machines are consistent with the grand plan).

(3) Transitions: classical mechanics to classical statistical mechanics (large dimensional phase space), classical mechanics to quantum mechanics (what happens to phase space?), thermodynamics to statistical mechanics (I know there’s a ton of really cool measure theory there just waiting to be gobbled up), Classical Mech to SR and then to GR. For some of these I’ve worked problems in the past, but I want a much deeper picture of the transition. For others there are commonly accepted ideas that are simply false, the prime example is the way in which quantum mechanics “reduces” to classical mechanics. While we can work example by example to see a classical limit, taking quantum mechanics as a whole and recapturing classical phase space is much much more difficult than letting .

(4) I want to see “beauty.” That sounds odd, I find many things beautiful. What I want is the opportunity to take something I look at and work all the details from my viewing of the phenomena all the way to the beautiful mathematics and physics which attempts to explain it. I want to look at a flower and think about groups, QED, and Hilbert spaces. Not instead of the flower but in addition to it.

(5) Group theory and physics, it’s not just for QFT, it’s all over the place and I suspect it’ll make connections easier to see.

(6) Education and Art: making toys and art that has superficial appeal coupled with deep ideas. This is coupled with my desire to bring narrative to teaching. A course should be a story, a collection of ideas built on each other that bring you somewhere. I have so many ideas in this category, summer camps, curricula, games, toys, children’s books, etc

Back to work…