Emergent rewrites in knot theory and logic

I explain in what sense new graph rewrite systems emerge from given ones, with two examples:

(1) the emergence of the R3 (Reidemeister 3) rewrite from R1, R2 and some uniform continuity assumptions, and relations to curvature,

(2) the emergence of the beta rewrite in lambda calculus from the shuffle rewrite and relations to the commutativity of the addition of vectors in the tangent space of a manifold.

This is a pdf version of the slides used in the talk "Emergent rewrites in knot theory and logic", presented at the Knots2020 conference.