Morwen thistlethwaite biography graphic organizer
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Their approach involved decomposing diagrams into prime tangles, analyzing flype operations as transformations preserving the Jones polynomial and other invariants, and using geometric arguments on 3-manifolds to show equivalence classes. The way the algorithm works is by restricting the positions of the cubes into a subgroup series of cube positions that can be solved using a certain set of moves.
[Singmaster p. 39]
As inventor of the Petrus method
In the second edition of his Notes on Rubik's "Magic Cube" (October 1979) David Singmaster mentions that Thistlethwaite had invented a novel strategy for restoring the cube in a maximum of 85 moves. Kauffman introduced the bracket polynomial, a state-sum model over crossings where each state contributes terms like Ai(−A2−A−2)s−1 (with i as the number of A-smoothings and s as Seifert circles), which specializes to the Jones polynomial via V(t)=f(A) with A=−t−1/4; this allowed him to show that non-alternating diagrams have higher crossing numbers and varying writhe compared to minimal alternating ones.
Once in group G1, quarter turns of the up and down faces are disallowed in the sequences of the look-up tables, and the tables are used to get to group G2, and so on, until the cube is solved.[4]
Dowker–Thistlethwaite notation
Thistlethwaite, along with Clifford Hugh Dowker, developed Dowker–Thistlethwaite notation, a knot notation suitable for computer use and derived from notations of Peter Guthrie Tait and Carl Friedrich Gauss.
A look up table of possible permutations is used that uses quarter turns of all faces to get the cube into group G1. He has made important contributions to both knot theory and Rubik's Cube group theory. His father, Bernard Thistlethwaite, was a chartered accountant employed by Cadbury's.[8] Thistlethwaite grew up in a family that included his mother, the artist Morwenna Thistlethwaite (née Brock), who joined the household after painting his father's portrait in 1944 and adopting the family surname by deed poll despite not being able to legally marry Bernard due to his prior marriage.[8] He had a sister, Felicity, born in 1947.[8] Details of his pre-university schooling and initial exposure to advanced mathematical topics are not publicly documented in available sources.
The method is too complex to be memorised by humans and so is only practical for computers. He devised this around July 1981. ISBN 0-89490-043-9
External links
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Recognition
Thistlethwaite was named a Fellow of the American Mathematical Society, in the 2022 class of fellows, "for contributions to low dimensional topology, especially for the resolution of classical knot theory conjectures of Tait and for knot tabulation".[5]
See also
- Optimal solutions for Rubik's Cube
References
External links
Morwen Thistlethwaite
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Morwen B.
Thistlethwaite is a British professor of mathematics at the University of Tennessee, USA. From 1978 to 1987 he taught at the Polytechnic of the South Bank in London.
Thistlethwaite and his collaborators used normal surface theory, originally developed by Wolfgang Haken, to analyze knot complements and verify irreducibility, ensuring that the enumerated knots were prime and non-equivalent under ambient isotopy.[29] Additionally, hyperbolic structures were computed using algorithms based on Epstein and Penner's work on ideal triangulations and Riley's methods for Dehn filling, allowing for the identification of knot complements' geometric invariants that distinguish non-hyperbolic cases and confirm hyperbolic ones.[29] These approaches, implemented computationally, enabled the processing of vast numbers of knot projections, often encoded via notation systems that facilitated efficient generation and comparison.[29]Thistlethwaite's contributions extended to the integration of these tabulated knots into key computational resources in low-dimensional topology.
The resulting dataset formed the basis for knot tables in KnotInfo, a comprehensive database of knot invariants maintained by researchers including Charles Livingston, which provides access to hyperbolic volumes, Jones polynomials, and other properties for knots up to 16 crossings. These diagrams played a central role in the work of Peter Guthrie Tait in the late 19th century, who proposed several conjectures regarding their properties to understand knot complexity and equivalence.[23]Tait's three classical conjectures concern the minimality and invariance of certain features in reduced alternating diagrams of alternating knots.
Biography
Morwen Thistlethwaite received his BA from the University of Cambridge in 1967, his MSc from the University of London in 1968, and his PhD from the University of Manchester in 1972 where his advisor was Michael Barratt. He taught at the North London Polytechnic from 1975 to 1978 and the Polytechnic of the South Bank, London from 1978 to 1987.
The resulting code is the sequence of these signed even integers j1,j2,…,jn, ordered by the odd labels. 39]
Thistlethwaite's algorithm
Thistlethwaite is famous for the Thistlethwaite Algorithm which allows a Rubik's Cube to be solved in a maximum of 52 moves. Similarly, the figure-eight knot (41) yields the code (4,−8,2,−6), illustrating how the sequence captures the over-under structure for quick diagram reconstruction.
He held a lecturing position at North London Polytechnic from 1975 to 1978, where he taught mathematics courses centered on advanced topics in topology.In 1978, Thistlethwaite joined the Polytechnic of the South Bank in London as a lecturer in the Department of Computing and Mathematics, a role he maintained until 1987.