building in the center

I continue to try to figure out how to work in this area of the interface between the electron beam and the photon beam. I see that there is a close parallel between my personal life story of trying to figure out how to live with both my mom's family and dad's family.

How to create space and build something substantial between two different things?
Perhaps the key is that secretly one gets help from a third thing. With my life in Santa Cruz, I think the key was to have good friends. It was within this context that I came closer to finding a common ground out of which I could exist in between both parents' houses and not feel like I was having to change myself so dramatically that there would be no continuity.

So, one claims a bit of ground somewhere in between this and that. Both this and that each think you belong to them. Or perhaps I myself think I belong to each of them, periodically. At one moment I am this. At the next, I am that. And while I am in the space that I am creating and building between the two, I try to make something that relates to the other two.

The title of this blog "adiabatic invariants", expressed a hope that I could find a space of more stability without the dramatic shifts. Perhaps I might also use a double well potential as a physics model for the kind of dynamics I am trying to deal with. And, for yet a third image, I have often thought of building a bridge between this and that. Building a bridge, however, is helpful for traveling in between, but does not in itself constitute a place of residency. One does not live on a bridge. And the imagery suggests a deep chasm. Perhaps it is not a chasm, but simply forest. And thus, instead of building a bridge, all that is needed is a path, and perhaps a map.

The task of life, then, is to inhabit the in-between territory, or if uninhabitable, to go elsewhere, but perhaps to keep the paths back alive. What are some topics where one must do this? Food is certainly one area. At my mom's house, we cooked and shopped ourselves. At my dad's, we were cooked for. Food meant something different. Meals had a different feel. So, today, I still do not have a way of shopping and eating that feels comfortable. Perhaps by continuing to think and write about this topic, I will make more progress. Creating a personal space which is comfortable is another area where I have a hard time. Choices feel political and charged, and what I actually create is often not very coherent. The same applies to how I dress and how I clean, and how I organize my projects and papers and other belongings. I have made progress, but the result is still not so coherent. I am trying to build in the center, between this and that. And the result is not always as satisfying as I might like.

adiabatic invariants

Research, research, research. Trying to find the right definition of action.

So, what's an adiabatic invariant?
Its something that stays constant as the environment changes.
For my undergrad thesis, I tried to figure out what happens to simple systems as they are transported from here to there. So this research provided an answer to the question: which part of Boaz is unchanged by his weekly transitions from A to B, from mom to dad. Adiabatic invariants. Just find them and I will know what to count on.

Ok, still working on these metaphors. Does it say something about isolation and self-containment that I focus on the single particle case? Does it take away the fun to give away the punchline... that I'm trying to find my own adiabatic invariants? When does one transcend the personal and create something of interest to others? Perhaps this dynamic is healthy? Continually reinterpretting in terms of trenchant metaphors?

Let me give a concrete example of an adiabatic invariant: the classic example is a pendulum which has a string the length of which is slowly shortening. As the environment changes so does the motion. The frequency of the pendulum increases as the length decreases (f~sqrt(g/l)). But the energy of the pendulum divided by the frequency stays constant. This is an adiabatic invariant.

Are there fluid dynamicists out there that think of themselves as scale models of the world and wonder what their true Reynolds number is? Are there quantum field theorists who renormalize away their existential concerns, find that the infinite difference between self and God can be swept under the rug if one cares only about practical solutions? What about economists who see all interactions as a game and try to make the market of human kindness as free as possible?

But I will be an adiabatic invariant. I will search for that which remains the same in me and allows for equilibrium. I can only be so many things at the same time. A 2n dimensional integrable Hamiltonian system has only n adiabatic invariants.
Right. right.