Log24

Tuesday, March 26, 2024

Kindergarten Report on Fröbel’s Third Gift:
“Behaves well under group action.”

Filed under: General — Tags: — m759 @ 8:02 am

From the above:  "electronically published on October 6. 2023."

See as well that date in other Log24 posts tagged The Prize Shining.

A co-author of the book reviewed has appeared here previously.

Monday, August 1, 2022

Review

Filed under: General — Tags: , — m759 @ 5:12 am

From Log24 posts tagged Art Space —

From a paper on Kummer varieties,
arXiv:1208.1229v3 [math.AG] 12 Jun 2013,
The Universal Kummer Threefold,” by
Qingchun Ren, Steven V Sam, Gus Schrader,
and Bernd Sturmfels —

IMAGE- 'Consider the 6-dimensional vector space over the 2-element field,' from 'The Universal Kummer Threefold'

Two such considerations —

IMAGE- 'American Hustle' and Art Cube

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman 

Friday, August 20, 2021

Space Note

Filed under: General — Tags: — m759 @ 7:50 pm

"Consider the six-dimensional vector space ( 𝔽2 )6
over the two-element field 𝔽2 ."

— Page 23 of "The Universal Kummer Threefold,"
arXiv:1208.1229v3, 12 June 2013, by Qingchun Ren,
Steven V. Sam, Gus Schrader, and Bernd Sturmfels.

An illustration of that space from 1981 —

IMAGE- 'Solid Symmetry' by Steven H. Cullinane, Dec. 24, 1981

The above recollection of the Kummer Threefold  remark was suggested by
recent posts now tagged Smallfield . . .

"Third Man – an elderly American railway bum,
a schizophrenic, speaks with a Southern drawl"

"Art to which I fix my celebrated signature."

— "Third Man" in Victor Snaith's play "Changing Stations"

If we read the above "art" as  a scythe blade to which the "signature" —
Snaith ("the crooked handle or shaft of a scythe") — is attached,
an image of the late art critic Robert Hughes comes to mind:

That image of Hughes appeared here in a post of June 17, 2015 —
"Slow Art, Continued" — that also referenced the Kummer Threefold
paper above.

Wednesday, November 22, 2017

The Prize

Filed under: General,Geometry — m759 @ 2:45 pm

Bernd Sturmfels to Receive 2018
George David Birkhoff Prize in Applied Mathematics
 

— American Mathematical Society on
     Monday, November 20th, 2017

See also Sturmfels and Birkhoff + Geometry in this  journal.

Wednesday, March 29, 2017

Art Space, Continued

Filed under: General — Tags: , , — m759 @ 4:35 am

"And as the characters in the meme twitch into the abyss
that is the sky, this meme will disappear into whatever
internet abyss swallowed MySpace."

—Staff writer Kamila Czachorowski, Harvard Crimson  today

From Log24 posts tagged Art Space

From a recent paper on Kummer varieties,
arXiv:1208.1229v3 [math.AG] 12 Jun 2013,
The Universal Kummer Threefold,” by
Qingchun Ren, Steven V Sam, Gus Schrader, and
Bernd Sturmfels —

IMAGE- 'Consider the 6-dimensional vector space over the 2-element field,' from 'The Universal Kummer Threefold'

Two such considerations —

IMAGE- 'American Hustle' and Art Cube

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman 

Wednesday, June 15, 2016

Rubik’s Deathtrap

Filed under: General — Tags: — m759 @ 7:20 pm

The previous post suggests a search in this journal
for "Deathtrap."

"Rubik’s Cube® used by permission
Rubik’s Brand Ltd. www.rubiks.com."

— Bernd Sturmfels, June-July 2016 Notices
of the American Mathematical Society
,
Volume 63, Number 6, page 605

"Tenser, said the Tensor …." — The Demolished Man
 

Max von Sydow in Branded  (2012)

Expanding the Spielraum …

Filed under: General — Tags: — m759 @ 2:40 pm

Continues

Rubik cube in the heading of the homepage of the Notices of the American Mathematical Society

"My AMS invited address at the SIAM Annual Meeting July 11–15
in Boston discusses the extension of eigenvectors and singular
vectors from matrices to higher order tensors."

Bernd Sturmfels in the June-July 2016 AMS Notices

See also Sturmfels in this  journal — for instance, in
"Expanding the Spielraum," a post of Feb. 3, 2015 —

Tuesday, February 3, 2015

Expanding the Spielraum

Filed under: General — Tags: , — m759 @ 11:00 am

A short poem by several authors:

"The role of
the 16 singular points
on the Kummer surface
is now played by
the 64 singular points
on the Kummer threefold."

— From Remark 2.4 on page 9 of
"The Universal Kummer Threefold,"
by Qingchun Ren, Steven V Sam,
Gus Schrader, and Bernd Sturmfels,
http://arxiv.org/abs/1208.1229v3,
August 6, 2012 — June 12, 2013.

See also "Expanded Field" in this journal.

IMAGE- Concepts of Space

Illustration from "Sunday School," July 20, 2014.

Other Log24 background:  Kummer, Spielraum, Art Space.

Sunday, March 9, 2014

Hesse’s Table

Filed under: General,Geometry — Tags: , , , — m759 @ 9:00 pm

From “Quartic Curves and Their Bitangents,” by
Daniel Plaumann, Bernd Sturmfels, and Cynthia Vinzant,
arXiv:1008.4104v2  [math.AG] 10 Jan 2011 —

The table mentioned (from 1855) is…

Exercise: Discuss the relationship, if any, to
the Miracle Octad Generator of R. T. Curtis.

Friday, March 7, 2014

Kummer Varieties

Filed under: General,Geometry — Tags: , , — m759 @ 11:20 am

The Dream of the Expanded Field continues

Image-- The Dream of the Expanded Field

From Klein's 1893 Lectures on Mathematics —

"The varieties introduced by Wirtinger may be called Kummer varieties…."
E. Spanier, 1956

From this journal on March 10, 2013 —

From a recent paper on Kummer varieties,
arXiv:1208.1229v3 [math.AG] 12 Jun 2013,
"The Universal Kummer Threefold," by
Qingchun Ren, Steven V Sam, Gus Schrader, and Bernd Sturmfels —

IMAGE- 'Consider the 6-dimensional vector space over the 2-element field,' from 'The Universal Kummer Threefold'

Two such considerations —

IMAGE- 'American Hustle' and Art Cube

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman 

Update of 10 PM ET March 7, 2014 —

The following slides by one of the "Kummer Threefold" authors give
some background related to the above 64-point vector space and
to the Weyl group of type E7(E7):

The Cayley reference is to "Algorithm for the characteristics of the
triple ϑ-functions," Journal für die Reine und Angewandte
Mathematik  87 (1879): 165-169. <http://eudml.org/doc/148412>.
To read this in the context of Cayley's other work, see pp. 441-445
of Volume 10 of his Collected Mathematical Papers .

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