Curvature and coordinates.
Why the firm is named after a gauge field, and what we mean when we say we look for structure that survives a change of description.
F = dA + A ∧ A
parallel transport around a closed loopΔθ = 0.0°
In geometry, you cannot compare two vectors that live at different points without some additional structure telling you how to carry one to the other. That structure is called a connection. Write it down in coordinates and you get a set of numbers, but the numbers are partly about the space and partly about the coordinates you chose. Change the description and the numbers change with it.
Now carry a vector around a closed loop, keeping it as parallel to itself as the connection allows, and bring it back to where it started. If the space is flat, it returns unchanged. If the space is curved, it returns rotated, and the angle of that rotation — the holonomy — is the same for every observer, in every coordinate system. Curvature is the part of the structure that does not depend on how you describe it. Physicists write it as F = dA + A ∧ A; the figure above simply draws it.
We find this a useful way to think about research. A result is a vector expressed in coordinates: a sample, a period, a universe, a set of parameters, a cost model, a way of handling the awkward cases. Change any of those and the numbers move. A great deal of what passes for signal in financial data is coordinates — a feature of one particular description that vanishes under another. It is not that the finding was false, exactly; it is that it was never about the world.
The discipline, then, is to carry a finding around the loop. Different sample, different period, different assumptions, different implementation — and see what comes back. Whatever returns unchanged is the part worth keeping. Whatever returns rotated tells you, precisely, how much of what you thought you knew was your own choice of coordinates.
None of this is a new idea. It is the ordinary discipline of out-of-sample thinking, restated in the language we happen to think in. But names matter, because names are what you say to yourself when you are tempted. We named the firm after the field whose curvature is the invariant, as a standing reminder that the goal is not a better description of the market. It is the part that does not depend on the description.
This note is about how we think. It is not investment advice, and it describes no strategy, position, or product.