Strange Loops: Capturing Knots With Powerful Notations
summary
Conway claims a compact notation lets him enumerate 54 six‑crossing knots in an afternoon versus six years previously; this talk actually compares Conway notation and Dowker notation, implements enumeration in code (Haskell), and generates diagrams for all knots ≤7 crossings. Rational tangles get tested by converting Conway strings into continued fractions so equivalence becomes a number check; Dowker is simpler to enumerate but produces more junk, while Conway captures many small knots compactly so the programic enumeration succeeds for low crossing counts.
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chapters (12)
- 0:00Start
- 3:16Alexander Briggs Notation
- 7:12Correspondences between Knots and Notations
- 12:08Enumerate Knots with Daggers
- 14:02History
- 15:58Energy for Enumeration
- 16:15Schools of Notation
- 18:12Zero Tangle
- 18:38Tangle Addition
- 24:22How To Enumerate Knots with Comma
- 33:59How Do Notations Correspond to Objects
- 35:54Summary
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