Lesson 7.2 · Chapter 7: Sources and questions
Open questions
What could select a geometry, supply dynamics, handle infinite limits, or admit competition?
From John Cullen’s knotlab guide
- Space from a law. Logic allows every shape. Which uniform, local law, not written on a space in advance, gives a shape that looks like a space of low dimension? One necessary condition is known: a law keeps a lasting record of its loops only if its contacts act as group elements (lessons 4.4 and 4.5).
- Dynamics. Are loops better modelled as processes whose outputs over time are the data, and does the static test survive that change?
- Limits. No set of finite clauses binds infinitely many loops into one contact (by compactness). Does the program need a limit rule that does?
- Competition. If least-violation states count as allowed, frustrated pairs make knots (lesson 4.3). Should they count?