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20: Sir Roger Penrose - Plotting the Twist of Einstein’s Legacy (edit)

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There’s also this diagram, which I found at a blog here: http://arkadiusz-jadczyk.eu/blog/tag/penrose/
There’s also this diagram, which I found at a blog here: http://arkadiusz-jadczyk.eu/blog/tag/penrose/
[[File:Penrose-Rindler-Clifford-parallels.jpg|thumb|none|alt=Penrose-Rindler-Clifford-parallels|Penrose-Rindler-Clifford parallels]]


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
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
[[File:Robinson.jpg|thumb|none|alt= A time-slice (t=0) of a Robinson congruence.| A time-slice (t=0) of a Robinson congruence.]]


[NOTE: these latter two might be Versions 1 and 2? Or later reproductions.]
[NOTE: these latter two might be Versions 1 and 2? Or later reproductions.]
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== Dirac’s Spinors ==
== Dirac’s Spinors ==
[[File:Paul Dirac, 1933.jpg|thumb|none|alt=Paul Dirac, 1933|Paul Dirac, 1933]]




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20:00 = PEN - "usually one talks about the Dirac Spinors, which are the 4 spinors, but they split into these 2 and 2 (WEIN - in even dimensions) Yes, that’s right.
20:00 = PEN - "usually one talks about the Dirac Spinors, which are the 4 spinors, but they split into these 2 and 2 (WEIN - in even dimensions) Yes, that’s right.
[[File:image_9.png|thumb|none|alt=image alt text|image alt text]]


Sir Roger Penrose’s favourite film is [https://en.wikipedia.org/wiki/2001:_A_Space_Odyssey_(film) 2001: A Space Odyssey]
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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“I had this picture of a flag. You have the flag-pole, goes along the light-cone (WEIN - that’s the vector-like piece of it) and then you have an extra piece of data which is this flag plane. You get a pretty good geometrical understanding. The one little catch is that if you rotate it through 360 degrees, so you might think just to where it started, it’s not the same as before, it’s changed its sign.”
“I had this picture of a flag. You have the flag-pole, goes along the light-cone (WEIN - that’s the vector-like piece of it) and then you have an extra piece of data which is this flag plane. You get a pretty good geometrical understanding. The one little catch is that if you rotate it through 360 degrees, so you might think just to where it started, it’s not the same as before, it’s changed its sign.”
[[File:Spinor.png|thumb|none|alt=A Spinor|A Spinor]]


Taken from Introduction to [https://arxiv.org/pdf/1312.3824.pdf Spinors - Andrew M Steane 2013] (pdf)
Taken from Introduction to [https://arxiv.org/pdf/1312.3824.pdf Spinors - Andrew M Steane 2013] (pdf)
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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 *
It also introduced me to [http://www2.memenet.or.jp/~keizo/index.html Keizo Ushio] who makes amazing toroidal sculptures, like this one *
[[File:NiihamaSculpture.jpg|thumb|none|alt=Niihama Sculpture|Niihama Sculpture]]


([http://www2.memenet.or.jp/~keizo/NiihamaSculptureProject.htm source])
([http://www2.memenet.or.jp/~keizo/NiihamaSculptureProject.htm source])
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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:
[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:
[[File:image_12.png|thumb|none|alt=image alt text|image alt text]]


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)
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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[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:
[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:
[[File:image_13.png|thumb|none|alt=image alt text|image alt text]]


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].
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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Faraday had clues that there were connections to light, but he didn’t have the equations.
Faraday had clues that there were connections to light, but he didn’t have the equations.
[[File:image_14.png|thumb|none|alt=image alt text|image alt text]]


Charles Darwin
Charles Darwin
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38:00 = [https://en.wikipedia.org/wiki/Ascending_and_Descending MC ESCHER - Ascending and Descending] (The Penrose Stairs)
38:00 = [https://en.wikipedia.org/wiki/Ascending_and_Descending MC ESCHER - Ascending and Descending] (The Penrose Stairs)
[[File:image_15.png|thumb|none|alt=image alt text|image alt text]]


Ascending and Descending - M.C. Escher
Ascending and Descending - M.C. Escher
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(I think) the print was [https://www.wikiart.org/en/m-c-escher/fishes-and-scales Fishes and Scales] *
(I think) the print was [https://www.wikiart.org/en/m-c-escher/fishes-and-scales Fishes and Scales] *
[[File:image_16.png|thumb|none|alt=image alt text|image alt text]]


43:00 =
43:00 =
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You think about the [https://en.wikipedia.org/wiki/Riemann_sphere Riemann Sphere]
You think about the [https://en.wikipedia.org/wiki/Riemann_sphere Riemann Sphere]
[[File:image_17.png|image alt text]][[File:image_18.png|image alt text]]


The Reimann Sphere and a Candy (or Toffee) Apple
The Reimann Sphere and a Candy (or Toffee) Apple
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== Resources ==
== Resources ==
<div data-type="resource" data-timestamp="00:14:00">
[[File:Penrose-Rindler-Clifford-parallels.jpg|thumb|Clifford parallels]]
</div>
<div data-type="resource" data-timestamp="00:38:00">
<div data-type="resource" data-timestamp="00:38:00">
[[File:Ascending and Descending.jpg|thumb|Ascending and Descending, by M. C. Escher. Lithograph, 1960.]]
[[File:Ascending and Descending.jpg|thumb|Ascending and Descending, by M. C. Escher. Lithograph, 1960.]]
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