About

Holonomy Digital is an independent software studio. It makes a small number of apps, each built to do one job well.

How the studio works

Projects start small and get used early, by real people, before they grow. Each release is a loop: ship it, watch how it's used, come back and adjust. Apps are designed to collect as little as they need and to say plainly what they keep.

The name

Holonomy is what you find when you carry something around a closed loop and come back to the start: in curved space, it doesn’t return the way it left.

The word, said ho-LON-uh-mee, is from the Greek holos, whole, and nomos, law.

Walk an arrow from the North Pole down to the equator, a quarter of the way around, and back up. Keep it as straight as the surface allows the whole way, and it still ends up turned by 90°. That turn is the holonomy of the loop, and it equals the curvature the loop encloses:

θ = ∬ K dA = 4π/8 = π/2

Where it turns up

• A Foucault pendulum's swing slowly rotates over the day, because Earth's surface is curved.
• The Berry phase is the quantum version: a system taken slowly round a loop of conditions comes back with a phase it didn't have.
• In the Aharonov–Bohm effect, an electron picks one up circling a magnetic field it never touches.
• In gauge theory, Wilson loops are holonomies, and loop quantum gravity is built out of them.
• The Calabi–Yau spaces of string theory are defined by their holonomy.

It seemed the right idea to build a studio around: you go round, you come back, and something has changed.