Cultural evolution of material knot diversity

Abstract

In this thesis we discuss the cultural evolution of knot tying with an overview of the knots widely used and a multi-disciplinary analysis using mathematical knot theory and models exploring human learning and evolution.

In order to assess the knots commonly tied we analyse the knots appearing in the largest collection of material knots; the Ashley Book of Knots, using knot theory to assess their diversity. This analysis identifies 162 distinct mathematical knots appearing in the guise of over 500 different material knots, suggesting a selection for these particular knots.

To identify and explore the biases affecting the oblique transmission of knot tying we present a study comparing the successful replication of two of the simplest knots, the granny knot and the reef knot. The experimental results suggest a bias towards tying granny knots over reef knots through the identification of a bias towards the repetition of features previously tied, using a mathematical model and Approximate Bayesian Computation to fit the model to the experimental data.

With the aim of exploring the diversity in the Ashley Book of Knots, we use a model of social and asocial learning on knot types and a fitness analysis from an NK fitness landscape. Both models suggest highly accurate social learning and mutation through crossing changes is necessary to facilitate the diversity seen in the Ashley Book of Knots. Analysing the crossings present in the knots seen in the Ashley Book of Knots suggests a selection for knot features that increase the complexity of the knot and increase crossing number but also an introduction of redundant features, suggesting the knots used regularly are not optimal.