The knowledge of knots: an interdisciplinary literature review |
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Authors: | Paulo E Santos Pedro Cabalar Roberto Casati |
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Institution: | 1. Electrical Engineering Department, Centro Universitário da FEI, S?o Paulo, Brazil;2. College of Science and Engineering, Flinders University, Adelaide, Australiapsantos@fei.edu.brhttps://orcid.org/0000-0001-8484-0354;4. CITIC Research Center, University of A Coru?a, A Coru?a, Spainhttps://orcid.org/0000-0001-7440-0953;5. Institut Jean Nicod, Ecole Normale Supérieure, Paris, France;6. Ecole des Hautes Etudes en Sciences Sociales, Paris, Francehttps://orcid.org/0000-0001-8215-6428 |
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Abstract: | ABSTRACTKnots 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. |
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Keywords: | Artificial intelligence (AI) common sense and qualitative models of space qualitative reasoning robotics topology |
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