A space where author Madeleine L'Engle worked as a librarian —
A more abstract space —
"If you have built castles in the air, your work need not be lost;
that is where they should be. Now put the foundations under them.”
— Henry David Thoreau
260731-Fano-1892-PG(3,2)…AI_Overview.jpg
...AI_Overview.jpg)
260731-Square_Model_of_PG(3,2)-by-Cullinane…AI_Overview.jpg
-by-Cullinane...AI_Overview.jpg)
* See Kirkman's schoolgirl problem in Wikipedia, esp.
the sections "Galois Geometry" and "Spreads and Packing."
The geometry of what might be called "Schoolgirl Space"
is, as the above image "Geometry of the Six Element Set"
indicates, the same as the geometry of the "Hexastigm"
described by Richmond (King's College, Cambridge,
March 30, 1899) —
"On the Figure of Six Points in Space of Four Dimensions,"
by H. W. Richmond, Quarterly Journal of Pure and Applied
Mathematics, Vol. 31 (1900), pp. 125-160.
This is available on the Web at Scribd.com . . .
https://www.scribd.com/document/424182244/
Richmond-QuarterlyJournal-1900-SixPoints .
Richmond's excellent historical survey, together with the Cullinane
square model of PG(3,2), provide the connection of finite geometry
to earlier, non-finite geometry that is lacking in some later treatments
of the subject . . . in particular, the connection to finite geometry of
studies of the classical sixty Pascal lines of the Hexagrammum.
From posts tagged Schoolgirl Space —
"Old men ought to be explorers." — T. S. Eliot.
Rose the Hat in her younger days.
See as well Barsotti in this journal.
The exercise in the previous post was suggested by a passage
purporting to "use standard block design theory" that was written
by some anonymous author at Wikipedia on March 1, 2019:
Here "rm OR" apparently means "remove original research."
Before the March 1 revision . . .
The "original research" objected to and removed was the paragraph
beginning "To explain this further." That paragraph was put into the
article earlier on Feb. 28 by yet another anonymous author (not by me).
An account of my own (1976 and later) original research on this subject
is pictured below, in a note from Feb. 20, 1986 —
The Square "Inscape" Model of
the Generalized Quadrangle W(2)
Click image to enlarge.
-embedding-in-PG(3,2)-Planat-Saniga-1000w.jpg)
* The title refers to the role of PG (3,2) in Kirkman's schoolgirl problem.
For some backstory, see my post Anticommuting Dirac Matrices as Skew Lines
and, more generally, posts tagged Dirac and Geometry.
From Dan Brown's novel Angels & Demons (2000)—
Cube Bricks 1984 —
From "Tomorrowland" (2015) —
From John Baez (2018) —
See also this morning's post Perception of Space
and yesterday's Exploring Schoolgirl Space.
See also "Quantum Tesseract Theorem" and "The Crosswicks Curse."
A song whose melody was used in
Westworld, Season 4, Episode 1 —
"Singin' in the old bars
Swingin' with the old stars
Livin' for the fame
Kissin' in the blue dark
Playin' pool and wild darts
Video games"
In memory of a video game executive
who reportedly died on June 22, 2022 —
* Adapted from a book title.
Mathematics: See Tetrahedron vs. Square in this journal
(Notes on two different models of schoolgirl space ).
Narrative: Replacing the square from the above posts by
a related cube …
… yields a merchandising inspiration —
Dueling Holocrons:
Jedi Cube vs. Sith Tetrahedron —
* See also earlier posts on Mathematics and Narrative.
Usage example —
(Click to enlarge.)
See also the previous post as well as PG(3,2),
Schoolgirl Space, and Tetrahedron vs. Square.
Representing Schoolgirl Space
From a book reviewed in the April 1923
Bulletin of the American Mathematical Society —
From a later book —
"Her wall is filled with pictures" — Chuck Berry
The 15 points of the finite projective 3-space PG(3,2)
arranged in tetrahedral form:
The letter labels, but not the tetrahedral form,
are from The Axioms of Projective Geometry , by
Alfred North Whitehead (Cambridge U. Press, 1906).
The above space PG(3,2), because of its close association with
Kirkman's schoolgirl problem, might be called "schoolgirl space."
Screen Rant on July 31, 2019:
A Google Search sidebar this morning:
Apocalypse Soon! —
Screen Rant on July 31, 2019 —
The above space PG(3,2), because of its close association with
Kirkman's schoolgirl problem, might be called "schoolgirl space."
See as well a Log24 post from the above Screen Rant date —
The title is from the post "Child's Play" of May 21, 2012 . . .
"It seems that only one course is open to the philosopher
who values knowledge and truth above all else. He must
refuse to accept from the champions of the forms the
doctrine that all reality is changeless [and exclusively
immaterial], and he must turn a deaf ear to the other party
who represent reality as everywhere changing [and as only
material]. Like a child begging for 'both', he must declare
that reality or the sum of things is both at once [το όν τε και
το παν συναμφότερα] (Sophist 246a-249d)."
Related material —
"Schoolgirl Space: 1984 Revisited" (July 9, 2019) and
posts tagged Tetrahedron vs. Square.
A revision of the above diagram showing
the Galois-addition-table structure —
Related tables from August 10 —
See "Schoolgirl Space Revisited."
American Songwriters (the Petrusich versions)
The New Yorker Culture Desk online yesterday —
The New Yorker Culture Desk onine July 16 —
Related aesthetic meditation from this journal on July 16 —
(From the post "Schoolgirl Space for Quantum Mystics")
The geometry of the 15 point-pairs in the previous post suggests a review:
From "Exploring Schoolgirl Space," July 8 —
The date in the previous post — Oct. 9, 2018 — also suggests a review
of posts from that date now tagged Gen-Z:
… and Schoolgirl Space
"This poem contrasts the prosaic and sensual world of the here and now
with the transcendent and timeless world of beauty in art, and the first line,
'That is no country for old men,' refers to an artless world of impermanence
and sensual pleasure."
— "Yeats' 'Sailing to Byzantium' and McCarthy's No Country for Old Men :
Art and Artifice in the New Novel,"
Steven Frye in The Cormac McCarthy Journal ,
Vol. 5, No. 1 (Spring 2005), pp. 14-20.
See also Schoolgirl Space in this journal.
* See, for instance, Lewis Hyde on the word "artifice" and . . .
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