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| = episode 20 experimental markup dump =
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| == Experimental Markup for player ==
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| <div data-type="note" data-timestamp="0:00:01">
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| Eric Weinstein interviews Sir Roger Penrose, Episode 20 of The Portal
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| </div>
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| <div data-type="note" data-timestamp="0:00:01">
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| Player by Demp
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| Annotations by R1chard5mith
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| </div>
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| <div data-type="resource" data-timestamp="0:00:01">
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| [[File:Eric weinstein.png|thumb]]
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| <div data-type="resource" data-timestamp="0:00:02">
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| [[File:Roger penrose.jpg|thumb]]
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| <div data-type="resource" data-timestamp="0:11:05">
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| https://upload.wikimedia.org/wikipedia/en/thumb/f/f9/Sciama2.jpg/200px-Sciama2.jpg
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| [https://en.wikipedia.org/wiki/Dennis_W._Sciama Dennis Sciama]
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| </div>
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| <div data-type="resource" data-timestamp="0:11:10">
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| https://static.scientificamerican.com/blogs/cache/file/7DAF801B-9AED-4B63-B7EAD43F5E9B1B2D_source.jpg
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| </div>
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| <div data-type="note" data-timestamp="0:11:17">
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| [https://en.wikipedia.org/wiki/Physics Physics]
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| </div>
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| <div data-type="resource" data-timestamp="0:11:31">
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| https://upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Stephen_Hawking.StarChild.jpg/220px-Stephen_Hawking.StarChild.jpg
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| </div>
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| <div data-type="note" data-timestamp="0:11:31">
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| [https://en.wikipedia.org/wiki/Stephen_Hawking Stephen Hawking]
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| </div>
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| <div data-type="resource" data-timestamp="0:11:40">
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| https://upload.wikimedia.org/wikipedia/commons/thumb/5/50/Paul_Dirac%2C_1933.jpg/220px-Paul_Dirac%2C_1933.jpg
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| </div>
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| <div data-type="note" data-timestamp="0:11:40">
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| [https://en.wikipedia.org/wiki/Paul_Dirac Paul Dirac]
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| </div>
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| <div data-type="note" data-timestamp="0:11:50">
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| Book: [https://www.amazon.com/Strangest-Man-Hidden-Dirac-Mystic/dp/0465022103 The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom] by [https://en.wikipedia.org/wiki/Graham_Farmelo Graham Farmelo]
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| </div>
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| <div data-type="note" data-timestamp="0:12:22">
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| [https://en.wikipedia.org/wiki/Albert_Einstein Albert Einstein]
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| <div>
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| <div data-type="note" data-timestamp="0:12:35">
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| Eric imputes that Dirac’s hair was not as good as Einstein’s.
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| </div>
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| <div data-type="resource" data-timestamp="0:12:34">
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| https://vignette.wikia.nocookie.net/wildcards/images/c/c7/Einstein.jpg
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| </div>
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| <div data-type="note" data-timestamp="0:12:42">
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| [https://en.wikipedia.org/wiki/Quantum_mechanics Quantum mechanics]
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| </div>
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| <div data-type="resource" data-timestamp="0:12:42">
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| https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Hydrogen_Density_Plots.png/290px-Hydrogen_Density_Plots.png
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| </div>
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| <div data-type="resource" data-timestamp="0:13:00">
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| http://arkadiusz-jadczyk.eu/blog/wp-content/uploads/2017/01/Penrose-Rindler-Clifford-parallels.jpg
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| </div>
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| <div data-type="note" data-timestamp="0:13:08">
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| NB:Roger Penrose and Eric Weinstein are friends with the guy who does the commentary for the cage fighting. What a time to be alive.
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| [https://www.youtube.com/channel/UCzQUP1qoWDoEbmsQxvdjxgQ Joe Rogan Experience]
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| </div>
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| <div data-type="resource" data-timestamp="0:13:08">
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| https://i.kym-cdn.com/entries/icons/original/000/027/944/everdonedmt.jpg
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| </div>
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| <div data-type="resource" data-timestamp="0:13:11">
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| https://thumbs.gfycat.com/GrotesqueApprehensiveCusimanse-mobile.mp4
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| </div>
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| <div data-type="note" data-timestamp="0:13:11">
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| The [https://en.wikipedia.org/wiki/Hopf_fibration Hopf Fibration] is the only non-trivial principal bundle that can be visually seen
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| </div>
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| <div data-type="resource" data-timestamp="0:13:11">
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| https://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Hopf_Fibration.png/250px-Hopf_Fibration.png
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| </div>
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| <div data-type="note" data-timestamp="0:13:13">
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| [https://en.wikipedia.org/wiki/Fiber_bundle Fibre Bundles]
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| </div>
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| <div data-type="note" data-timestamp="0:13:13">
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| The “[https://en.wikipedia.org/wiki/Hopf_fibration Hopf fibration]”, or the “[https://en.wikipedia.org/wiki/Clifford_parallel Clifford Parallels]” was instrumental in the subject of Twistor Theory.
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| </div>
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| <div data-type="note" data-timestamp="0:13:20">
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| There’s also this diagram, which I found at a blog here: http://arkadiusz-jadczyk.eu/blog/tag/penrose/
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| </div>
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| <div data-type="resource" data-timestamp="0:13:20">
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| http://arkadiusz-jadczyk.eu/blog/wp-content/uploads/2017/01/Penrose-Rindler-Clifford-parallels.jpg
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| </div>
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| <div data-type="note" data-timestamp="0:13:22">
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| And there’s this diagram, which I found at this link ( http://users.ox.ac.uk/~tweb/00001/ ) which is an HTML presentation of “On the Origins of Twistor Theory” - Roger Penrose, 1987
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| </div>
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| <div data-type="resource" data-timestamp="0:13:22">
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| http://users.ox.ac.uk/~tweb/00001/robinson.jpg
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| </div>
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| <div data-type="resource" data-timestamp="0:14:17">
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| [[File:Road to reality hopf.jpg|thumb]]
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| </div>
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| <div data-type="note" data-timestamp="0:14:39">
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| [https://en.wikipedia.org/wiki/Spinor Spinors] (Wikipedia)
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| [https://arxiv.org/pdf/1312.3824.pdf An introduction to spinors by Andrew M Steane] (pdf)
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| [https://www.youtube.com/playlist?list=PLJHszsWbB6hoOo_wMb0b6T44KM_ABZtBs Spinors for Beginners by Eigenchris] (YouTube course)
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| </div>
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| <div data-type="resource" data-timestamp="0:14:39">
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| [[File:Spinors flag.png|thumb]]
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| </div>
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| <div data-type="note" data-timestamp="0:14:43">
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| [https://en.wikipedia.org/wiki/Twistor_theory Twistor Theory]
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| </div>
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| <div data-type="note" data-timestamp="0:14:54">
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| quantum mechanics and the first course
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| </div>
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| <div data-type="note" data-timestamp="0:14:59">
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| Dirac gave a course (2 courses) of lectures on Quantum Mechanics
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| Course 1 - Basic [https://en.wikipedia.org/wiki/Quantum_mechanics Quantum Mechanics]
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| Course 2 - [https://en.wikipedia.org/wiki/Quantum_field_theory Quantum Field Theory] but also Spinors
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| </div>
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| <div data-type="resource" data-timestamp="0:15:00">
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| https://upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Spinor_on_the_circle.png/330px-Spinor_on_the_circle.png
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| </div>
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| <div data-type="note" data-timestamp="0:15:02">
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| In the second course (when Penrose took the course) Dirac deviated from his normal course of lectures to give two or three lectures on [https://en.wikipedia.org/wiki/Spinor#Component_spinors Two Component Spinors]. ([https://arxiv.org/abs/1312.3824 Spinors])
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| </div>
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| <div data-type="note" data-timestamp="0:16:06">
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| [https://en.wikipedia.org/wiki/Quark Quarks]
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| </div>
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| <div data-type="resource" data-timestamp="0:16:06">
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| https://upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Proton_quark_structure.svg/225px-Proton_quark_structure.svg.png
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| </div>
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| <div data-type="note" data-timestamp="0:16:12">
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| General phenomenon of [https://en.wikipedia.org/wiki/Wave Waves]
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| </div>
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| <div data-type="resource" data-timestamp="0:16:12">
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| https://upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Superpositionprinciple.gif/220px-Superpositionprinciple.gif
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| </div>
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| <div data-type="resource" data-timestamp="0:16:39">
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| [[File:Cordon spinors book.png|thumb]]
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| </div>
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| <div data-type="note" data-timestamp="0:16:39">
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| Denis recommended to Roger a book by Corson (presumably this one: [https://www.amazon.com/Introduction-Tensors-Spinors-Relativistic-Wave-Equations/dp/B0000CIMO7 Introduction to Tensors, Spinors, and Relativistic Wave-Equations], 1953 by [https://www.ias.edu/scholars/edward-michael-corson E.M. Corson] *
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| </div>
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| <div data-type="note" data-timestamp="0:17:39">
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| [https://en.wikipedia.org/wiki/Quantum_field_theory Quantum Field Theory]
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| </div>
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| <div data-type="resource" data-timestamp="0:17:39">
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| https://upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Feynmann_Diagram_Gluon_Radiation.svg/211px-Feynmann_Diagram_Gluon_Radiation.svg.png
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| </div>
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| <div data-type="resource" data-timestamp="0:18:00">
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| https://www.chu.cam.ac.uk/media/assets/8c/c2317c444c70a04633e4fd29095ef1adda7d8f.jpg
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| </div>
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| <div data-type="note" data-timestamp="0:18:26">
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| Other people said that Dirac’s course was just like his book but Roger hadn’t read the book.
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| (I assume this one? Dirac - [https://www.amazon.com/Principles-Quantum-Mechanics-P-Dirac/dp/1607965607 Principles of Quantum Mechanics])
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| </div>
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| <div data-type="note" data-timestamp="0:18:55">
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| Mention of Mathematicians:
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| * [https://en.wikipedia.org/wiki/Wilhelm_Killing Wilhelm Killing]
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| * “Lee”? - this Lee https://en.wikipedia.org/wiki/John_M._Lee was in Differential Geometry but was born in 1950. Maybe his father?
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| * [https://en.wikipedia.org/wiki/%C3%89lie_Cartan Élie Cartan]
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| </div>
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| <div data-type="resource" data-timestamp="0:18:55">
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| https://upload.wikimedia.org/wikipedia/commons/thumb/5/57/Wilhelm_Karl_Joseph_Killing.jpeg/220px-Wilhelm_Karl_Joseph_Killing.jpeg
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| Wilhelm Killing
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| </div>
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| <div data-type="resource" data-timestamp="0:18:55">
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| https://upload.wikimedia.org/wikipedia/en/thumb/e/e8/Elie_Cartan.jpg/220px-Elie_Cartan.jpg
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| Elie Cartan
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| </div>
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| <div data-type="resource" data-timestamp="0:19:00">
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| [[File:Eric gesticulating.png|thumb]]
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| </div>
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| <div data-type="note" data-timestamp="0:19:17">
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| Sir Roger Penrose’s favourite film is [https://en.wikipedia.org/wiki/2001:_A_Space_Odyssey_(film) 2001: A Space Odyssey]
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| </div>
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| <div data-type="resource" data-timestamp="0:19:15">
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| https://upload.wikimedia.org/wikipedia/en/thumb/1/11/2001_A_Space_Odyssey_%281968%29.png/220px-2001_A_Space_Odyssey_%281968%29.png
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| </div>
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| <div data-type="resource" data-timestamp="0:19:20">
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| [[File:2001 monolith.png|thumb]]
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| </div>
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| <div data-type="resource" data-timestamp="0:19:25">
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| https://vignette.wikia.nocookie.net/optical-illusions/images/6/62/Note.gif
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| </div>
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| %%%%%%%
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| <!--
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| [NOTE: I’m not sure if he ever gets back to saying what this proposal is. It looks like it might be “Conformal Cyclic Cosmology”, see eg; [https://physicsworld.com/a/new-evidence-for-cyclic-universe-claimed-by-roger-penrose-and-colleagues/ Physics World], [https://physicsworld.com/a/inside-penroses-universe/ ibid], his own book, [https://en.wikipedia.org/wiki/Cycles_of_Time Cycles of Time]]
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| 8:00 = Talking to his brother in the Kingswood Restaurant, Cambridge *, Roger expressed his doubts and was referred to Dennis.
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| [NOTE: I tried to find a link for this restaurant, which appears to no longer exist, and came across this really interesting paper by Professor Penrose and [https://en.wikipedia.org/wiki/George_F._R._Ellis George Ellis], which is a kind of “scientific eulogy”* for Dennis Sciama, in which the same anecdote is recalled, amongst others: https://royalsocietypublishing.org/doi/pdf/10.1098/rsbm.2009.0023 (pdf) ]
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| <<<There’s probably a better term for this, right?
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| <<<When I search for ‘“the kingswood restaurant” cambridge’ I don’t turn up anything that seems relevant and when I add the word “remember” to that search I start to turn up links to Sir Roger himself.Possibly it was called by a different name. Also possible that no trace of it has made it onto the internet other than his telling.
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| Penrose’s supervisor was Hodge - [https://en.wikipedia.org/wiki/W._V._D._Hodge W.V.D Hodge]
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| But later he threw Roger out and Todd became his supervisor - [https://en.wikipedia.org/wiki/J._A._Todd J.A Todd] *
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| <<<The links I’ve added to Hodge and Todd both seem right but I’m not personally familiar
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| The Hopf Fibration ([https://en.wikipedia.org/wiki/Hopf_fibration#/media/File:Hopf_Fibration.png source],[https://nilesjohnson.net/hopf.html gif])
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| PEN - The “[https://en.wikipedia.org/wiki/Hopf_fibration Hopf fibration]”, or the “[https://en.wikipedia.org/wiki/Clifford_parallel Clifford Parallels]” was instrumental in the subject of Twistor Theory.
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| 14:00 = Penrose’s diagram
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| There were three versions. The third version is in The Road to Reality. He thinks the second version is probably the best.
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| (I think they are talking about the diagram of the Hopf Fibration ?? as seen at the link above )
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| I '''think''' this is the one from “The Road to Reality”, which would make it Version 3: * **
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| please correct this if you know better
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| There’s also this diagram, which I found at a blog here: http://arkadiusz-jadczyk.eu/blog/tag/penrose/
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|
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| And there’s this diagram, which I found at this link ( http://users.ox.ac.uk/~tweb/00001/ ) which is an HTML presentation of “On the Origins of Twistor Theory” - Roger Penrose, 1987
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| [NOTE: these latter two might be Versions 1 and 2? Or later reproductions.]
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| Penrose thinks Version 2 was the best.
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| In the second course (when Penrose took the course) Dirac deviated from his normal course of lectures to give two or three lectures on [https://en.wikipedia.org/wiki/Spinor#Component_spinors Two Component Spinors]. ([https://arxiv.org/abs/1312.3824 Spinors])
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| Denis recommended to Roger a book by Corson (presumably this one: [https://www.amazon.com/Introduction-Tensors-Spinors-Relativistic-Wave-Equations/dp/B0000CIMO7 Introduction to Tensors, Spinors, and Relativistic Wave-Equations], 1953 by [https://www.ias.edu/scholars/edward-michael-corson E.M. Corson] *
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| The book was reviewed by [https://en.wikipedia.org/wiki/Abdus_Salam Abdus Salam] in 1955 (https://www.nature.com/articles/175831b0 )
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| (I assume this one? Dirac - [https://www.amazon.com/Principles-Quantum-Mechanics-P-Dirac/dp/1607965607 Principles of Quantum Mechanics])
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| Taken from Introduction to [https://arxiv.org/pdf/1312.3824.pdf Spinors - Andrew M Steane 2013] (pdf)
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| WEIN: [https://en.wikipedia.org/wiki/Klein_bottle Klein Bottle]:
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|
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| == Interlude: Klein Bottles ==
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| Get your Klein Bottle today from our friends at [https://www.kleinbottle.com/ Acme Klein Bottles]
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| Here’s a good [https://www.youtube.com/watch?v=AAsICMPwGPY video about Klein Bottles]
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| (the presenter is [https://en.wikipedia.org/wiki/Clifford_Stoll Clifford Stoll], Astronomer and proprietor of [https://www.kleinbottle.com/ Acme Klein Bottles] )
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|
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| * The Klein Bottle is “two [https://en.wikipedia.org/wiki/M%C3%B6bius_strip Möbius Strips] stitched together” (after [https://en.wikipedia.org/wiki/August_Ferdinand_M%C3%B6bius August Ferdinand Möbius])
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| * The Klein Bottle is named after [https://en.wikipedia.org/wiki/Felix_Klein Felix Klein]
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| * The Klein Bottle only has one side
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| * Klein bottles is 3D Universes must have a self-intersection
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| * Klein hats are continuously deformable back to themselves
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| * Clifford’s friend, [https://en.wikipedia.org/wiki/Robert_J._Lang Robert Lang], made an [https://langorigami.com/crease-pattern/klein-bottle-opus-444/ Origami Klein Bottle] *
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|
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| Here is another, related video, also from Numberphile, about the [https://www.youtube.com/watch?v=3_VydFQmtZ8&list=PLt5AfwLFPxWIpgtcFs_7fHGUedGEKu73p&index=8&t=0s Topology of a Twisted Torus]
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|
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| <<<NB: This is a link to the actual pattern so that you can make your very own Origami Klein bottle.
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| This video is about slicing up toroids. The presenter is [https://en.wikipedia.org/wiki/Carlo_H._S%C3%A9quin Carlo H. Séquin]. Later in the podcast, Roger talks about the [https://en.wikipedia.org/wiki/Clifford_parallel Clifford Parallels] dividing up space in a similar way. This helped me to visualise that.
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|
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| <<<One of his sculptures is not far from where I live. May have to make a visit.
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| It also introduced me to [http://www2.memenet.or.jp/~keizo/index.html Keizo Ushio] who makes amazing toroidal sculptures, like this one *
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| ([http://www2.memenet.or.jp/~keizo/NiihamaSculptureProject.htm source])
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| Here is an interview with [https://www.youtube.com/watch?v=bkInMmWcblI Keizo Ushio].
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| In [https://www.youtube.com/watch?v=_w1qkiRHQ4E this video] he can be heard speaking in English.
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| There are some more interesting (if somewhat amateur) visualisations in [https://www.youtube.com/watch?v=sRTKSzAOBr4 this Youtube video], from which I learned:
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| * The Klein Bottle is a [http://mathworld.wolfram.com/NonorientableSurface.html non-orientable], [https://www2.cs.duke.edu/courses/fall06/cps296.1/Lectures/sec-II-1.pdf 2-dimensional manifold].
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| * It can be “[https://en.wikipedia.org/wiki/Immersion_(mathematics) immersed]” into [https://en.wikipedia.org/wiki/Three-dimensional_space Euclidean 3-dimensional space] with a [https://en.wikipedia.org/wiki/Intersection_theory self-intersection].
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| * Non-orientable means “there exists no continuous normal unit vector field”
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| [Note: googling for “the square root of the Klein Bottle” didn’t get me far but searching for “[https://en.wikipedia.org/wiki/Double_cover double cover]” I got useful things like [https://math.stackexchange.com/questions/1073425/two-sheeted-covering-of-the-klein-bottle-by-the-torus this question on math Stackexchange], where someone has drawn this:
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|
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| And the top respondent says “Most topologists would be happy just drawing the diagram you’ve drawn” (to prove that there is a two-sheeted covering of the Klein bottle by the Torus)
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| Reading that answer and then this one: https://math.stackexchange.com/questions/140439/torus-as-double-cover-of-the-klein-bottle gave me a pretty good idea of what’s going on.]
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| Dirac gave a demonstration due to [https://en.wikipedia.org/wiki/Hermann_Weyl Hermann Weyl] of rolling one [https://en.wikipedia.org/wiki/Cone cone] on another
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| Here is a google-books link to Penrose describing the same model in the [https://books.google.com.au/books?id=Qk5Q74166qcC&pg=PA41&lpg=PA41#v=onepage&q&f=false Hermann Weyl Centenary Lectures].
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|
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| [http://www.weylmann.com This site] also has a description of the model (http://www.weylmann.com/2010archive.shtml - you need to search for the word “cone” to find the right article) and lots of other information about Weyl himself. It includes this diagram to illustrate the model:
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| The author of the site is William O. Straub and he has written other papers about Spinors, including eg; [http://www.weylmann.com/weyldirac.pdf Weyl Spinors and Dirac’s Electron Equation].
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| This [https://www.youtube.com/watch?v=yLH4l_SoIy0 video on Youtube] is a visualisation of rolling one coin around another.
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| Dirac’s scissors, aka the [https://en.wikipedia.org/wiki/Plate_trick Plate Trick], (related to?) the [https://www.youtube.com/watch?v=JaIR-cWk_-o&feature=youtu.be Belt Trick]
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| Air on a Dirac String: https://www.youtube.com/watch?v=CYBqIRM8GiY
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| 34:00 = [https://en.wikipedia.org/wiki/Phlogiston_theory Phlogiston]
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| [NOTE: Phlogiston was the supposed substance that inhered in bodies capable of combustio
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| Book: [https://en.wikipedia.org/wiki/Charles_Darwin Darwin] - ON THE VARIOUS CONTRIVANCES BY WHICH BRITISH AND FOREIGN ORCHIDS ARE FERTILISED BY INSECTS, AND ON THE GOOD EFFECTS OF INTERCROSSING. BY CHARLES DARWIN, M.A., F.R.S., &c. WITH ILLUSTRATIONS.
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| ([http://darwin-online.org.uk/content/frameset?itemID=F800&viewtype=text&pageseq=1 full text as HTML])
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| 38:00 = [https://en.wikipedia.org/wiki/Ascending_and_Descending MC ESCHER - Ascending and Descending] (The Penrose Stairs)
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| Ascending and Descending - M.C. Escher
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| 39:00 = PEN - anecdote about visiting Amsterdam. Mentions [https://en.wikipedia.org/wiki/Shaun_Wylie Shaun Wyile] *
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| 41:00 = “I played around with this and whittled it down to the triangle which people refer to as a ‘tribar’.” NB: He’s being modest and we actually call it a [https://en.wikipedia.org/wiki/Penrose_triangle Penrose Triangle]. ([http://mathworld.wolfram.com/PenroseTriangle.html Penrose Triangle on Wolfram])
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| I’m pretty sure this is the paper: [https://onlinelibrary.wiley.com/doi/abs/10.1111/j.2044-8295.1958.tb00634.x impossible objects a special type of visual illusion] - L.S. Penrose and R. Penrose *
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| <<<NB: Wiley want $7 to rent this 62 year old paper for 48 hours (!) or $42 (!!) to buy it as a PDF. It is on SciHub and is 3 pages long. If you had to buy Penrose’s (paperback) book (tRtR) for the same per-page price, it would cost $14,000 a copy
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| Escher gave Penrose a print and it is in the [https://en.wikipedia.org/wiki/Ashmolean_Museum Ashmolean Museum]
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| <<<I can’t read this article: https://www.thetimes.co.uk/article/roger-penrose-on-his-friend-mc-escher-the-genius-that-galleries-ignored-90nhp8gsd0l because it’s behind a paywall, but the google link-summary says “… and he chose Fish and Scales, now on loan to the Ashmolean in Oxford”
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| (I think) the print was [https://www.wikiart.org/en/m-c-escher/fishes-and-scales Fishes and Scales] *
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| [https://en.wikipedia.org/wiki/Roman_Jackiw Roman Jackiw] - “when we talked to the geometers, we started to learn new things”
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| Jakiw is interviewed [https://www.aip.org/history-programs/niels-bohr-library/oral-histories/34449 here at aip] *
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| [https://people.maths.ox.ac.uk/lmason/Tn/ Twistor Newsletter]
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| * [https://en.wikipedia.org/wiki/Sheldon_Lee_Glashow Sheldon Lee Glashow]
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| * [https://en.wikipedia.org/wiki/Howard_Georgi Howard Georgi]
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| * [https://en.wikipedia.org/wiki/Jean-Pierre_Petit Jean-Pierre Petit] *
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| * [https://en.wikipedia.org/wiki/Abdus_Salam Abdus Salam]
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| * [https://en.wikipedia.org/wiki/Engelbert_Sch%C3%BCcking Engelbert Schücking]
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| * [https://en.wikipedia.org/wiki/Roy_Kerr Roy Kerr]
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| * [https://en.wikipedia.org/wiki/Rainer_K._Sachs Rainer K. Sachs]
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| He travelled back with [https://www.researchgate.net/scientific-contributions/2038878487_Istvan_Ozsvath István Ozsváth] * who didn’t speak much and started to think about
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| I visited (Bruno) [https://en.wikipedia.org/wiki/Bruno_Zumino Zumino]
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| Deep supersymmetric model (the [[https://en.wikipedia.org/wiki/Wess–Zumino_model|Wess-Zumino model]])
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| * [https://en.wikipedia.org/wiki/Nigel_Hitchin Nigel Hitchin]
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| * Mason - possibly [https://www.maths.ox.ac.uk/people/lionel.mason Lionel Mason]?
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| * [https://www.maths.ox.ac.uk/people/philip.candelas Philip Candelas]
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