Log24

"The nightingale sings his fairy tale . . . ." — "Stardust"

From "A special configuration of 12 conics and generalized Kummer surfaces,"
by David Kohel, Xavier Roulleau, and Alessandra Sarti.
(arXiv:2004.11421 (math), submitted on 23 Apr 2020 (v1),
last revised 17 May 2021 (this version, v2)) —

"… we study the set C₁₂ of conics that contain at least 6 points in P₉.  One has

Theorem 1. The set C₁₂ has cardinality 12. Each conic in C₁₂ contains exactly
6 points in P₉ and through each point in P₉ there are 8 conics. The sets (P₉, C₁₂)
form therefore a (9₈, 12₆)-configuration.

The configuration (P₉, C₁₂) has interesting symmetries, e.g. there are 8 conics
among the 12 passing through a fixed point q in P₉ and the 8 points in P₉ \ {q},
which form a 8₅ point-conic configuration. The freeness of the arrangement of
curves C₁₂ is studied in [19], where we learned that this configuration has been
also independently discovered in [11]."

[11] Dolgachev I., Laface A., Persson U., Urzúa G.,
"Chilean configuration of conics, lines and points," preprint.
(arXiv:2008.09627 (math), submitted on 21 Aug 2020)

[19] Pokora P., Szemberg T.,
"Conic-line arrangements in the complex projective plane," preprint
(arXiv:2002.01760 (math), submitted on 5 Feb 2020 (v1),
last revised 10 Feb 2022 (this version, v3))

See also Caillois in the previous post.

See as well the discussion of 

"the flag of the nude above the holiday hotel,"

on pages 108-109 in 

Leon Surette, “Wallace Stevens, Roger Caillois and
‘The Pure Good of Theory',” Paideuma , Vol. 32, 
Nos. 1-2-3 (Spring, Fall and Winter 2003), pp. 95-122

See also "Abstract Signature" in this journal.

“There comes a time when the learner has identified
the abstract content of a number of different games
and is practically crying out for some sort of picture
by means of which to represent that which has been
gleaned as the common core of the various activities.”

— Article  at Zoltan Dienes’s website

This quote is from a Log24 post of Feb. 6, 2014,
The Representation of Minus One.

Progressive Matrices

A sample Raven's Progressive Matrices  test item —

Update of 10 AM ET Sunday, August 7, 2022 —

See as well Siobhan Roberts on geometry in The New York Times
on March 22, 2022, and a Log24 post on geometry on that date.

Finesse —

Geometrie —