Poincaré
See just this Post & Comments / 0 Comments so far / Post a Comment / Home
Up, Down.
Actually Jules Henri Poincaré.
26/08/06, Siobhan Roberts, An equation for controversy, (Archive).
Sidetracked already ... first by the Google/Blogger servers which are playing silly buggers this morning, then by cute associations with 'Siobhan' - there was a woman with this name in St. John's running for the Liberals in the last election and the students then living with me decided to steal a couple of 4x8 foot plastic signs to decorate their rooms ... I don't quite know how to pronounce this name ... Siobhan ... ? no idea. A-and then she turns out to have an interest in H.S.M. Coxeter, the Geometer ... Harold Scott MacDonald "Donald" Coxeter, another like Northrop Frye that I failed to follow when the time was ripe, ai ai, and from the little I can glean, he had, like Frye, an abiding love in his life ... anyway, here is some bumph on the book and herself: King of Infinite Space - Donald Coxeter, The Man Who Saved Geometry, by Siobhan Roberts.
What caught me was this: "The Poincaré conjecture states that the three-dimensional sphere is the only three-dimensional space that does not go on forever, and does not have any walls, and in which you can shrink every loop to a point." It has been proven for higher dimensions: Stephen Smale, at the Toyota Technological Institute in Chicago, proved it for five or more dimensions in 1960. Michael Freedman, at Microsoft, proved it for four dimensions in 1983. And in the 1970s, William Thurston, now at Cornell, wrote the broader "geometrization conjecture" that encompassed Poincaré.
"Does not go on forever." - what could that mean?
Let's see if it has been stated correctly. The 'Poincaré conjecture' at Wikipedia does not quite match up: "If a closed three-dimensional manifold is sufficiently like a sphere in that each loop in the manifold can be tightened to a point, then it is really just a three-dimensional sphere." and I am lost.
Even getting just the shape of Grigory Perelman's proof is simply not on for me. First I guess you would have to understand what Richard Hamilton's concept of 'Ricci flow' is - "treating geometric manifolds in a manner that is analogous to the diffusion of heat" says the report - and I am lost again.
A-and that's it for now - I am lost ... oh well. I still have the damned signs and given the garbage situation in St. John's these days I guess I will have to cut them up into small pieces to get rid of them, maybe they can be recycled ...
Given what I learned from Anne Tyng about 3-dimensional consciousness, maybe that 3-space does not go on forever is another intimation of mortality?
I do admire Grigory Perelman (Grigori 'Grisha' Yakovlevich Perelman / Григорий Яковлевич Перельман) for not playing tic-tac-toe with the maggots; I hope he can afford his grand gestures. Maybe I can find a picture of him:
Coxeter's friend Escher; some of their collaboration; and Escher's wife Jetta:
Down.
Actually Jules Henri Poincaré.
26/08/06, Siobhan Roberts, An equation for controversy, (Archive).Sidetracked already ... first by the Google/Blogger servers which are playing silly buggers this morning, then by cute associations with 'Siobhan' - there was a woman with this name in St. John's running for the Liberals in the last election and the students then living with me decided to steal a couple of 4x8 foot plastic signs to decorate their rooms ... I don't quite know how to pronounce this name ... Siobhan ... ? no idea. A-and then she turns out to have an interest in H.S.M. Coxeter, the Geometer ... Harold Scott MacDonald "Donald" Coxeter, another like Northrop Frye that I failed to follow when the time was ripe, ai ai, and from the little I can glean, he had, like Frye, an abiding love in his life ... anyway, here is some bumph on the book and herself: King of Infinite Space - Donald Coxeter, The Man Who Saved Geometry, by Siobhan Roberts.
What caught me was this: "The Poincaré conjecture states that the three-dimensional sphere is the only three-dimensional space that does not go on forever, and does not have any walls, and in which you can shrink every loop to a point." It has been proven for higher dimensions: Stephen Smale, at the Toyota Technological Institute in Chicago, proved it for five or more dimensions in 1960. Michael Freedman, at Microsoft, proved it for four dimensions in 1983. And in the 1970s, William Thurston, now at Cornell, wrote the broader "geometrization conjecture" that encompassed Poincaré.
"Does not go on forever." - what could that mean?
Let's see if it has been stated correctly. The 'Poincaré conjecture' at Wikipedia does not quite match up: "If a closed three-dimensional manifold is sufficiently like a sphere in that each loop in the manifold can be tightened to a point, then it is really just a three-dimensional sphere." and I am lost.
Even getting just the shape of Grigory Perelman's proof is simply not on for me. First I guess you would have to understand what Richard Hamilton's concept of 'Ricci flow' is - "treating geometric manifolds in a manner that is analogous to the diffusion of heat" says the report - and I am lost again.
A-and that's it for now - I am lost ... oh well. I still have the damned signs and given the garbage situation in St. John's these days I guess I will have to cut them up into small pieces to get rid of them, maybe they can be recycled ...
Given what I learned from Anne Tyng about 3-dimensional consciousness, maybe that 3-space does not go on forever is another intimation of mortality?
I do admire Grigory Perelman (Grigori 'Grisha' Yakovlevich Perelman / Григорий Яковлевич Перельман) for not playing tic-tac-toe with the maggots; I hope he can afford his grand gestures. Maybe I can find a picture of him:
Coxeter's friend Escher; some of their collaboration; and Escher's wife Jetta:
Down.
