The knowledge of knots: an interdisciplinary literature review

Paulo E. Santos, Pedro Cabalar, Roberto Casati

Research output: Contribution to journalReview article

Abstract

Knots can be found and used in a variety of situations in the 3D world, such as in vines, in the DNA, polymer chains, electrical wires, in mountaineering, seamanship and when ropes or other flexible objects are involved for exerting forces and holding objects in place. Research on knots as topological entities has contributed with a number of findings, not only of interest to pure mathematics, but also to statistical mechanics, quantum physics, genetics, and chemistry. Yet, the cognitive (or algorithmic) aspects involved in the act of tying a knot are a largely uncharted territory. This paper presents a review of the literature related to the investigation of knots from the topological, physical, cognitive and computational (including robotics) standpoints, aiming at bridging the gap between pure mathematical work on knot theory and macroscopic physical knots, with an eye to applications and modeling.

Original languageEnglish
Pages (from-to)334-358
Number of pages25
JournalSpatial Cognition and Computation
Volume19
Issue number4
DOIs
Publication statusPublished - 30 Sep 2019

Keywords

  • Artificial intelligence (AI)
  • common sense and qualitative models of space
  • qualitative reasoning
  • robotics
  • topology

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