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Friday, December 25, 2020

Change Arises: Mathematical Examples

Filed under: General — Tags: — m759 @ 12:59 AM

From old posts tagged Change Arises

From Christmas 2005:

The Eightfold Cube: The Beauty of Klein's Simple Group
Click on image for details.

For the eightfold cube
as it relates to Klein’s
simple group, see
A Reflection Group
of Order 168
.”

For an rather more
complicated theory of
Klein’s simple group, see

Cover of 'The Eightfold Way: The Beauty of Klein's Quartic Curve'

Click on image for details.

The phrase “change arises” is from Arkani-Hamed in 2013, describing
calculations in physics related to properties of the positive Grassmannian

 

A related recent illustration from Quanta Magazine —

The above illustration of seven cells is not unrelated to
the eightfold-cube model of the seven projective points in
the Fano plane.

Thursday, December 24, 2020

Change Arises: A Literary Example

Filed under: General — Tags: — m759 @ 12:12 PM

The “Change Arises” part of the title refers to the previous post.
The 1905 “geometric object” there, a 4×4 square, appeared earlier,
in 1869, in a paper by Camille Jordan. For that paper, and the
“literary example” of the title, see “Ici vient M. Jordan .”

This  post was suggested by the appearance of Jordan in today’s
memorial post for Peter M. Neumann by Peter J. Cameron.

Related remarks on Jordan and “geometrical objects” from 2016 —

These reflections are available from their author as a postprint.

Change Arises

Filed under: General — Tags: — m759 @ 1:44 AM

See posts so tagged.

“Change arises from the structure of the object.” — Arkani-Hamed

Related material from 1936 —

Related material from 1905, with the “object” a 4×4 array —

Related material from 1976, with the “object”
a 4×6 array — See Curtis.

Related material from 2018, with the “object”
a cuboctahedron — See Aitchison.

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