Log24

Friday, April 16, 2021

Schoolgirl Problem (Kirkman’s, not Epstein’s)

Filed under: General — m759 @ 2:30 PM

As for Epstein’s problem . . .

Thursday, November 19, 2020

Set Design and the Schoolgirl Problem

Filed under: General — Tags: — m759 @ 9:36 AM

Underlying Structure of the Design —

Schoolgirl Problem

Sunday, July 7, 2019

Schoolgirl Problem

Filed under: General — Tags: , , — m759 @ 11:18 PM

Anonymous remarks on the schoolgirl problem at Wikipedia —

"This solution has a geometric interpretation in connection with
Galois geometry and PG(3,2). Take a tetrahedron and label its
vertices as 0001, 0010, 0100 and 1000. Label its six edge centers
as the XOR of the vertices of that edge. Label the four face centers
as the XOR of the three vertices of that face, and the body center
gets the label 1111. Then the 35 triads of the XOR solution correspond
exactly to the 35 lines of PG(3,2). Each day corresponds to a spread
and each week to a packing
."

There is a different "geometric interpretation in connection with
Galois geometry and PG(3,2)" that uses a square  model rather
than a tetrahedral  model. The square  model of PG(3,2) last
appeared in the schoolgirl-problem article on Feb. 11, 2017, just
before a revision that removed it.

Saturday, August 25, 2018

Schoolgirl Problem

Filed under: General — Tags: , — m759 @ 5:40 PM

For Pagan Moore

Sunday, July 15, 2018

Schoolgirl Problems

Filed under: General — Tags: — m759 @ 12:00 PM

A Warren, Pennsylvania, newspaper article from May 12, 2018,
“A terrorist among them,” quotes Ann Creal of Warren on
schooldays of the late 1950’s and on a German exchange student,
Gudrun Ensslin, who later became famous for her violent political
activities:

“She said Ensslin dated while here (the man
she identified as Ensslin’s date told the Times Observer
he had no recollection of her).”

I am the man that was identified as Ensslin’s date, and I still
have no recollection of her.

Ann Creal is the former Ann Fuellhart, who was a college freshman
in the fall of 1959, when I was a high school senior —

Ann Creal apparently confused me with Scott Mohr, who
graduated from Warren High School in 1958. See the Log24
posts Crux and Doppelgänger.

Tuesday, November 29, 2016

Schoolgirl Problem

Filed under: General — m759 @ 2:14 AM

Thursday, August 4, 2016

Schoolgirl Problems

Filed under: General — m759 @ 12:00 PM

Compare and contrast the recent films
"The Diary of a Teenage Girl" and "Strangerland."

(This post was suggested by yesterday's
"How Deep the Rabbit Hole Goes.")

Monday, February 22, 2016

Schoolgirl Problems…

Filed under: General — m759 @ 10:10 AM

and versions of "Both Sides Now"

See a New York Times  version of "Both Sides Now."

I prefer a version by Umberto Eco.

Related material for storytellers and the Church of Synchronology

This journal on the date of the above shooting script, 03/19/15.

Tuesday, September 15, 2015

Schoolgirl Problem

Filed under: General,Geometry — m759 @ 2:00 PM

Or: Ten Years and a Day

In memory of film director Robert Wise,
who died ten years ago yesterday.

A search in this journal for "Schoolgirl" ends with a post
from Sept. 10, 2002, The Sound of Hanging Rock.

See as well a Log24 search for "Strangerland"
(a 2015 film about a search for a schoolgirl) and
a Log24 search for "Weaving."

Related mathematics:  Symplectic.

Some related images (click to enlarge) —

Friday, August 14, 2015

Schoolgirl Problem

Filed under: General,Geometry — m759 @ 6:00 PM

But first, a word from our sponsa*

Sir Laurence Olivier in "Term of Trial" (1962),
a film starring Sarah Miles as a schoolgirl

a phrase from mathematical pedagogy.

Friday, June 19, 2015

Schoolgirl Problem

Filed under: General — m759 @ 12:30 PM

The star of the new film "Chappie" is on tour.

Thursday, January 23, 2020

Exploring Schoolgirl Space…

Filed under: General — Tags: , , — m759 @ 11:59 PM

"Old men ought to be explorers." — T. S. Eliot.

Rose the Hat in her younger days.

See as well Barsotti in this journal.

Friday, September 27, 2019

Algebra for Schoolgirls

Filed under: General — Tags: , , — m759 @ 8:37 AM

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!

Saturday, September 21, 2019

Exploring Egypt: The Sequel to Exploring Schoolgirl Space*

Filed under: General — Tags: — m759 @ 9:02 AM

* See Schoolgirl Space in this journal.

Friday, September 13, 2019

Schoolgirl Space…

Filed under: General — Tags: , — m759 @ 4:56 AM

Thursday, August 15, 2019

Schoolgirl Space — Tetrahedron or Square?

Filed under: General — Tags: , , — m759 @ 9:03 PM

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 —

Saturday, August 10, 2019

Schoolgirl Space* Revisited:

Filed under: General — Tags: , , — m759 @ 10:51 PM

The Square "Inscape" Model of

Click image to enlarge.

* 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.

Tuesday, July 16, 2019

Schoolgirl Space for Quantum Mystics

Filed under: General — Tags: , , — m759 @ 2:16 PM

From a post on St. Andrew's Day, 2017

Schoolgirl Space Continues.

Filed under: General — Tags: , — m759 @ 10:59 AM

Monday, July 15, 2019

Arche’s Schoolgirl Space

Filed under: General — Tags: — m759 @ 2:30 PM

From Dan Brown's novel Angels & Demons  (2000)—

Tuesday, July 9, 2019

Schoolgirl Space: 1984 Revisited

Filed under: General — Tags: , , , , — m759 @ 9:24 PM

Cube Bricks 1984 —

From "Tomorrowland" (2015) —

From John Baez (2018) —

and yesterday's Exploring Schoolgirl Space.

Sunday, February 17, 2019

For the Schoolgirls of 1959

Filed under: General — Tags: — m759 @ 1:35 PM

The dies natalis  of St. Buddy Holly was Feb. 3, 1959.

This  year on Feb. 3, a geometric illustration of the well-known
schoolgirl problem was added to a brand-new Wikipedia article
on the finite geometry PG(3,2).

Friday, July 28, 2017

Prize Problem

Filed under: General — Tags: — m759 @ 9:57 PM

The last page of a novel published on Sept. 2, 2014 —

Related material —

The 2017 film Gifted  presents a different approach to the Navier-Stokes
problem.

The figure below perhaps represents the above novel 's Millennium Prize
winner reacting, in the afterlife, to the film 's approach in Gifted .

Bustle  online magazine last April  —

By JOHNNY BRAYSON Apr 11 2017

See also other news from the above Bustle  date — April 11, 2017.

Thursday, February 16, 2017

Filed under: General,Geometry — m759 @ 11:32 AM

A Feb. 12 note in the "talk" section of the Wikipedia article
"Kirkman's schoolgirl problem" —

The illustration above was replaced by a new section in the article,
titled "Galois geometry."

The new section improves the article by giving it greater depth.
For related material, see Conwell Heptads in this journal
(or, more generally, Conwell) and a 1985 note citing Conwell's work.

Friday, February 21, 2014

Raumproblem*

Filed under: General,Geometry — Tags: , , — m759 @ 7:01 PM

Despite the blocking of Doodles on my Google Search
screen, some messages get through.

Today, for instance —

"Your idea just might change the world.

Clicking the link yields a page with the following image—

Clearly there is a problem here analogous to
the square-triangle coordinatization problem,
but with the 4×6 rectangle of the R. T. Curtis
Miracle Octad Generator playing the role of
the square.

I once studied this 24-triangle-hexagon
coordinatization problem, but was unable to
obtain any results of interest. Perhaps
someone else will have better luck.

* For a rather different use of this word,
see Hermann Weyl in the Stanford
Encyclopedia of Philosophy.

Wednesday, September 18, 2019

Powers of X

Filed under: General — Tags: , — m759 @ 11:45 AM

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 —

Tuesday, April 30, 2019

Heraldry for Walpurgisnacht

Filed under: General — m759 @ 11:05 AM

A problem not only at Harvard.

For instance… A Hollywood anticlerical classic:

Schoolgirl Problem

Tuesday, January 2, 2018

Filed under: General — Tags: — m759 @ 3:15 PM

Or:  Schoolgirl Problems

The above images were suggested in part by the birthdays
on Sept. 21, 2011, of Bill Murray and Stephen King.

More seriously, also in this journal on that date, from a post
titled Symmetric Generation —

Sunday, November 12, 2017

Review

Filed under: General,Geometry — m759 @ 7:04 PM

Sunday, October 29, 2017

File System… Unlocked

Filed under: Uncategorized — m759 @ 2:16 PM

. . . .

"Wikipedia's first true logo . . . . included a quote from the preface
of Euclid and His Modern Rivals  by Lewis Carroll . . . ."

. . . .

Related dialogue from the new film "Unlocked" —

1057
01:31:59,926 –> 01:32:01,301
Nice to have you back, Alice.

1058
01:32:04,009 –> 01:32:05,467
Don't be a stranger.

See as well Chloë Grace Moretz portraying  a schoolgirl problem.

Thursday, November 2, 2017

History of Mathematics for All Souls’ Day

Filed under: General — m759 @ 9:00 AM

Schoolgirl Problem

"Buy this image" . . . Or not.

Related material from the date of the above photo —

For related drama, see "Child's Play" in this journal.

Thursday, October 12, 2017

Filed under: General — m759 @ 10:00 AM

Related material — See Gifted in this journal.

See as well Tulips.

Yesterday was the International Day of the Girl Child . . .
A related archived Wikipedia article on Kirkman's schoolgirl problem:

Wednesday, July 5, 2017

Imaginarium of a Different Kind

Filed under: General,Geometry — m759 @ 9:00 PM

The title refers to that of the previous post, "The Imaginarium."

In memory of a translator who reportedly died on May  22, 2017,
a passage quoted here on that date —

Related material — A paragraph added on March 15, 2017,
to the Wikipedia article on Galois geometry

 George Conwell gave an early demonstration of Galois geometry in 1910 when he characterized a solution of Kirkman's schoolgirl problem as a partition of sets of skew lines in PG(3,2), the three-dimensional projective geometry over the Galois field GF(2).[3] Similar to methods of line geometry in space over a field of characteristic 0, Conwell used Plücker coordinates in PG(5,2) and identified the points representing lines in PG(3,2) as those on the Klein quadric. — User Rgdboer

Wednesday, June 1, 2016

Mathematics and Narrative

Filed under: General — m759 @ 12:06 PM

Principles before Personalities — AA  Saying .

Principles —

See Schoolgirl Problem in Wikipedia.

Personalities —

See Alexandra Alter in the May 26 online New York Times :

"With the proliferation of 'girl' titles,
there are signs that the trend may have peaked;
it already seems ripe for parody."

Update of 12:40 PM ET on Wednesday, June 1, 2016 —

A note for the Church of Synchronology
See a post from this  journal on the date of the Alter piece, May 26:

(Click image for the rest of the post .)

Monday, May 30, 2016

Perfect Universe

Filed under: General,Geometry — Tags: — m759 @ 7:00 PM

(A sequel to the previous post, Perfect Number)

Since antiquity,  six has been known as
"the smallest perfect number." The word "perfect"
here means that a number is the sum of its
proper divisors — in the case of six: 1, 2, and 3.

The properties of a six-element set (a "6-set")
divided into three 2-sets and divided into two 3-sets
are those of what Burkard Polster, using the same
adjective in a different sense, has called
"the smallest perfect universe" — PG(3,2), the projective
3-dimensional space over the 2-element Galois field.

A Google search for the phrase "smallest perfect universe"
suggests a turnaround in meaning , if not in finance,
that might please Yahoo CEO Marissa Mayer on her birthday —

The semantic  turnaround here in the meaning  of "perfect"
is accompanied by a model  turnaround in the picture  of PG(3,2) as
Polster's tetrahedral  model is replaced by Cullinane's square  model.

Further background from the previous post —

Sunday, August 1, 2021

The Savage Sixteens

Filed under: General — Tags: — m759 @ 3:51 PM

"Savage ('wild,' 'undomesticated') modes of thought are primary
in human mentality. They are what we all have in common."

— "The Cerebral Savage: On the Work of Claude Lévi-Strauss,"
by Clifford Geertz (Encounter, vol. 28 no. 4, April 1967, pp. 25-32)

For more Geertz and some related art, see The Kaleidoscope Puzzle
which lets you picture twin sixteens .

"Can you imagine the mathematical possibilities?"

— Line from "Annie Hall" (1977)

Monday, March 16, 2020

Mathematics and Narrative* Continues:

Filed under: General — Tags: — m759 @ 1:27 AM

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:

Wednesday, February 26, 2020

“Perfect”

Filed under: General — Tags: — m759 @ 9:59 PM

Usage example —

(Click to enlarge.)

Schoolgirl Space, and Tetrahedron vs. Square.

Friday, November 22, 2019

The Virgin Field:

Filed under: General — Tags: — m759 @ 8:45 AM

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

Monday, August 19, 2019

A Couple of Tots

Filed under: General — Tags: , — m759 @ 10:15 PM

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.

Friday, August 16, 2019

Nocciolo

Filed under: General — Tags: , , , — m759 @ 10:45 AM

A revision of the above diagram showing

Related tables from August 10

See "Schoolgirl Space Revisited."

Wednesday, July 31, 2019

The Epstein Chronicles, or:  Z is for Zorro

Filed under: General — Tags: , , , — m759 @ 8:54 PM

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:

Wednesday, July 17, 2019

The Artsy Quantum Realm

Filed under: General — Tags: — m759 @ 6:38 PM

 Quantum Physics Placing Kirkman's Schoolgirls and Quantum Spin Pairs on the Fano Plane: A Rainbow of Four Primary Colors, A Harmony of Fifteen Tones J. P. Marceaux, A. R. P. Rau (Submitted on 14 May 2019) A recreational problem from nearly two centuries ago has featured prominently in recent times in the mathematics of designs, codes, and signal processing. The number 15 that is central to the problem coincidentally features in areas of physics, especially in today's field of quantum information, as the number of basic operators of two quantum spins ("qubits"). This affords a 1:1 correspondence that we exploit to use the well-known Pauli spin or Lie-Clifford algebra of those fifteen operators to provide specific constructions as posed in the recreational problem. An algorithm is set up that, working with four basic objects, generates alternative solutions or designs. The choice of four base colors or four basic chords can thus lead to color diagrams or acoustic patterns that correspond to realizations of each design. The Fano Plane of finite projective geometry involving seven points and lines and the tetrahedral three-dimensional simplex of 15 points are key objects that feature in this study. Comments:16 pages, 10 figures Subjects:Quantum Physics (quant-ph) Cite as:arXiv:1905.06914 [quant-ph]  (or arXiv:1905.06914v1 [quant-ph] for this version) Submission history From: A. R. P. Rau [view email]  [v1] Tue, 14 May 2019 19:11:49 UTC (263 KB)

Wednesday, July 10, 2019

Artifice* of Eternity …

Filed under: General — Tags: , , , — m759 @ 10:54 AM

… 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, for instance, Lewis Hyde on the word "artifice" and . . .

Thursday, May 9, 2019

The Birdseye Requiem

Filed under: General — Tags: — m759 @ 9:10 AM

From The Boston Globe  yesterday evening —

she understood you and she loved you. She was a true friend —
a true generous, generous friend. This is the kind of person

'And she had such a great sense of humor,' Birdseye said.
“She would always have the last laugh. She wasn’t always
the loudest, but she was always the funniest, and in the
smartest way.' "

"Ms. Adams, who lived in Waltham, was 55 when she died April 9 . . . ."

See as well April 9 in the post Math Death and a post from April 8,
also now tagged "Berlekamp's Game" — Horses of a Dream.

"When logic and proportion have fallen sloppy dead
And the white knight is talking backwards . . . ."

— Grace Slick in a song from yesterday's post "When the Men"

Friday, February 22, 2019

Desperately Seeking Comedy

Filed under: General — m759 @ 1:24 PM

"I need a photo opportunity . . ." — Paul Simon

Sunday, October 29, 2017

File System… Unlocked

Filed under: General,Geometry — Tags: — m759 @ 2:16 PM

Logo from the above webpage

Related dialogue from the new film "Unlocked"

1057
01:31:59,926 –> 01:32:01,301
Nice to have you back, Alice.

1058
01:32:04,009 –> 01:32:05,467
Don't be a stranger.

Wednesday, October 11, 2017

IPFS Version

Filed under: General,Geometry — m759 @ 9:00 PM

Friday, August 4, 2017

Clay

Filed under: General — Tags: — m759 @ 4:08 PM

Landon T. Clay, founder of the Clay Mathematics Institute,
reportedly died on Saturday, July 29, 2017.

See related Log24 posts, now tagged Prize Problem,
from the date of Clay's death and the day before.

Update of 9 PM ET on August 4, 2017 —

Other mathematics discussed here on the date of Clay's death —

MSRI Program. Here MSRI is pronounced "Misery."

Update of 9:45 PM ET on August 4, 2017 —

Saturday, July 29, 2017

Science News

Filed under: General — Tags: , — m759 @ 10:29 AM

Continued from the post Aesthetic Distance of July 28, 2017.

Friday, July 28, 2017

Creeds

Filed under: General — Tags: — m759 @ 12:21 PM

From a novel featuring the Navier-Stokes problem —

A search for "Creed" in this journal yields
a different sort of Shiva —

For further reviews, click on the Penguin below.

Aesthetic Distance

Filed under: General,Geometry — Tags: , — m759 @ 11:23 AM

In memory of a Disney "imagineer" who reportedly died yesterday.

From the opening scene  of a 2017 film, "Gifted":

Frank calls his niece Mary to breakfast on the morning she is
to enter first grade. She is dressed, for the first time, for school —

 - Hey! Come on. Let's move! - No! - Let me see. - No. - Come on, I made you special breakfast. - You can't cook. - Hey, Mary, open up. (She opens her door and walks out.) - You look beautiful. - I look like a Disney character. Where's the special? - What? - You said you made me special breakfast. Read more: http://www.springfieldspringfield.co.uk/ movie_script.php?movie=gifted

Saturday, May 20, 2017

van Lint and Wilson Meet the Galois Tesseract*

Filed under: General,Geometry — Tags: — m759 @ 12:12 AM

Click image to enlarge.

The above 35 projective lines, within a 4×4 array —

The above 15 projective planes, within a 4×4 array (in white) —

* See Galois Tesseract  in this journal.

Wednesday, February 15, 2017

Warp and Woof

Filed under: General,Geometry — m759 @ 3:00 PM

Space —

Space structure —

From Gotay and Isenberg, “The Symplectization of Science,”
Gazette des Mathématiciens  54, 59-79 (1992):

“… what is the origin of the unusual name ‘symplectic’? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure ‘line complex group’ the ‘symplectic group.’
… the adjective ‘symplectic’ means ‘plaited together’ or ‘woven.’
This is wonderfully apt….”

The above symplectic  figure appears in remarks on
the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2).

Space shuttle —

Related ethnic remarks —

As opposed to Michael  Larsen —

Funny, you don't look  Danish.

Monday, September 28, 2015

Cracker Jack Prize

Filed under: General,Geometry — Tags: — m759 @ 11:00 PM

A review —

“The story, involving the Knights Templar, the Vatican, sunken treasure,
the fate of Christianity and a decoding device that looks as if it came out of
a really big box of medieval Cracker Jack, is the latest attempt to combine
Indiana Jones derring-do with ‘Da Vinci Code’ mysticism.”

A feeble attempt at a purely mathematical "decoding device"
from this journal earlier this month

For some background, see a question by John Baez at Math Overflow
on Aug. 20, 2015.

The nonexistence of a 24-cycle in the large Mathieu group
might discourage anyone hoping for deep new insights from
the above figure.

See Marston Conder's "Symmetric Genus of the Mathieu Groups" —

Saturday, September 19, 2015

Geometry of the 24-Point Circle

Filed under: General,Geometry — Tags: — m759 @ 1:13 AM

The latest Visual Insight  post at the American Mathematical
Society website discusses group actions on the McGee graph,
pictured as 24 points arranged in a circle that are connected
by 36 symmetrically arranged edges.

Wikipedia remarks that

"The automorphism group of the McGee graph
is of order 32 and doesn't act transitively upon
its vertices: there are two vertex orbits of lengths
8 and 16."

The partition into 8 and 16 points suggests, for those familiar
with the Miracle Octad Generator and the Mathieu group M24,
the following exercise:

Arrange the 24 points of the projective line
over GF(23) in a circle in the natural cyclic order
, 1, 2, 3,  , 22, 0 ).  Can the McGee graph be
modeled by constructing edges in any natural way?

In other words, if the above set of edges has no
"natural" connection with the 24 points of the
projective line over GF(23), does some other
set of edges in an isomorphic McGee graph
have such a connection?

Update of 9:20 PM ET Sept. 20, 2015:

Backstory: A related question by John Baez
at Math Overflow on August 20.

Sunday, June 14, 2015

New Image of PG(3,2)

Filed under: General,Geometry — m759 @ 11:02 PM

was added to the Wikipedia article Finite geometry.

(Shown above is a slightly newer image, changed to reflect
the Wikipedia article's remarks on the schoolgirl problem.)

Tuesday, June 17, 2014

Finite Relativity

Filed under: General,Geometry — Tags: , — m759 @ 11:00 AM

Anyone tackling the Raumproblem  described here
on Feb. 21, 2014 should know the history of coordinatizations
of the 4×6 Miracle Octad Generator (MOG) array by R. T. Curtis
and J. H. Conway. Some documentation:

The above two images seem to contradict a statement by R. T. Curtis
in a 1989 paper.  Curtis seemed in that paper to be saying, falsely, that
his original 1973 and 1976 MOG coordinates were those in array M below—

This seemingly false statement involved John H. Conway's supposedly
definitive and natural canonical coordinatization of the 4×6 MOG
array by the symbols for the 24 points of the projective line over GF(23)—
{∞, 0, 1, 2, 3… , 21, 22}:

An explanation of the apparent falsity in Curtis's 1989 paper:

By "two versions of the MOG" Curtis seems to have meant merely that the
octads , and not the projective-line coordinates , in his earlier papers were
mirror images of the octads  that resulted later from the Conway coordinates,
as in the images below.

Tuesday, July 9, 2013

Vril Chick

Filed under: General,Geometry — m759 @ 4:30 AM

Profile picture of "Jo Lyxe" (Josefine Lyche) at Vimeo

Compare to an image of Vril muse Maria Orsitsch.

From the catalog of a current art exhibition
(25 May – 31 August, 2013) in Norway,
I DE LANGE NÆTTER —

 Josefine Lyche Born in 1973 in Bergen, Norway. Lives and works in Oslo and Berlin. Keywords (to help place my artwork in the proper context): Aliens, affine geometry, affine planes, affine spaces, automorphisms, binary codes, block designs, classical groups, codes, coding theory, collineations, combinatorial, combinatorics, conjugacy classes, the Conwell correspondence, correlations, Cullinane, R. T. Curtis, design theory, the diamond theorem, diamond theory, duads, duality, error correcting codes, esoteric, exceptional groups, extraterrestrials, finite fields, finite geometry, finite groups, finite rings, Galois fields, generalized quadrangles, generators, geometry, GF(2), GF(4), the (24,12) Golay code, group actions, group theory, Hadamard matrices, hypercube, hyperplanes, hyperspace, incidence structures, invariance, Karnaugh maps, Kirkman’s schoolgirls problem, Latin squares, Leech lattice, linear groups, linear spaces, linear transformations, Magick, Mathieu groups, matrix theory, Meno, Miracle Octad Generator, MOG, multiply transitive groups, occultism, octahedron, the octahedral group, Orsic, orthogonal arrays, outer automorphisms, parallelisms, partial geometries, permutation groups, PG(3,2), Plato, Platonic solids, polarities, Polya-Burnside theorem, projective geometry, projective planes, projective spaces, projectivities, Pythagoras, reincarnation, Reed-Muller codes, the relativity problem, reverse engineering, sacred geometry, Singer cycle, skew lines, Socrates, sporadic simple groups, Steiner systems, Sylvester, symmetric, symmetry, symplectic, synthemes, synthematic, Theosophical Society tesseract, Tessla, transvections, Venn diagrams, Vril society, Walsh functions, Witt designs. (See also the original catalog page.)

Clearly most of this (the non-highlighted parts) was taken
from my webpage Diamond Theory. I suppose I should be
flattered, but I am not thrilled to be associated with the
(apparently fictional) Vril Society.

For some background, see (for instance)
Conspiracy Theories and Secret Societies for Dummies .

Wednesday, March 11, 2009

Wednesday March 11, 2009

Filed under: General,Geometry — Tags: — m759 @ 9:00 AM
Sein Feld
in Translation
(continued from
May 15, 1998)

The New York Times March 10–
"Paris | A Show About Nothing"–

The Times describes one of the empty rooms on exhibit as…

"… Yves Klein’s 'La spécialisation de la sensibilité à l’état matière première en sensibilité picturale stabilisée, Le Vide' ('The Specialization of Sensibility in the Raw Material State Into Stabilized Pictorial Sensibility, the Void')"

This is a mistranslation. See "An Aesthetics of Matter" (pdf), by Kiyohiko Kitamura and Tomoyuki Kitamura, pp. 85-101 in International Yearbook of Aesthetics, Volume 6, 2002

"The exhibition «La spécialisation de la sensibilité à l’état matière-première en sensibilité picturale stabilisée», better known as «Le Vide» (The Void) was held at the Gallery Iris Clert in Paris from April 28th till May 5th, 1955." –p. 94

"… «Sensibility in the state of prime matter»… filled the emptiness." –p. 95

Kitamura and Kitamura translate matière première correctly as "prime matter" (the prima materia of the scholastic philosophers) rather than "raw material." (The phrase in French can mean either.)

Related material:
The Diamond Archetype and
The Illuminati Diamond.

prima materia
is to an 1876 review
by Cardinal Manning of
a work on philosophy
by T. P. Kirkman, whose
"schoolgirl problem" is
closely related to the
finite space of the
diamond theorem.

Friday, January 18, 2008

Friday January 18, 2008

Filed under: General — Tags: — m759 @ 12:00 PM

Friday January 18, 2008

Filed under: General — Tags: — m759 @ 4:00 AM

Rubén Darío,
born January 18, 1867

Thursday, January 17, 2008

Thursday January 17, 2008

Filed under: General — Tags: , — m759 @ 5:24 PM
Well, she was
just seventeen…

(continued)

"Mazur introduced the topic of prime numbers with a story from Don Quixote in which Quixote asked a poet to write a poem with 17 lines. Because 17 is prime, the poet couldn't find a length for the poem's stanzas and was thus stymied."

— Undated American Mathematical Society news item about a Nov. 1, 2007, event

Related material:

Desconvencida,
Jueves, Enero 17, 2008

Horses of a Dream
(Log24, Sept. 12, 2003)

Knight Moves
(Log24 yesterday–
anniversary of the
Jan. 16 publication
of Don Quixote)

Windmill and Diamond
(St. Cecilia's Day 2006)

Wednesday, January 16, 2008

Wednesday January 16, 2008

Filed under: General,Geometry — Tags: , , , , — m759 @ 12:25 PM
Knight Moves:
Geometry of the
Eightfold Cube

Click on the image for a larger version
and an expansion of some remarks
quoted here on Christmas 2005.

Tuesday, October 3, 2006

Tuesday October 3, 2006

Filed under: General,Geometry — Tags: — m759 @ 9:26 AM

Serious

"I don't think the 'diamond theorem' is anything serious, so I started with blitzing that."

Charles Matthews at Wikipedia, Oct. 2, 2006

"The 'seriousness' of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. We may say, roughly, that a mathematical idea is 'significant' if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas."

— G. H. Hardy, A Mathematician's Apology

Matthews yesterday deleted references to the diamond theorem and related material in the following Wikipedia articles:

Affine group‎
Reflection group‎
Symmetry in mathematics‎
Incidence structure‎
Invariant (mathematics)‎
Symmetry‎
Finite geometry‎
Group action‎
History of geometry‎

This would appear to be a fairly large complex of mathematical ideas.

See also the following "large complex" cited, following the above words of Hardy, in Diamond Theory:

Affine geometry, affine planes, affine spaces, automorphisms, binary codes, block designs, classical groups, codes, coding theory, collineations, combinatorial, combinatorics, conjugacy classes, the Conwell correspondence, correlations, design theory, duads, duality, error correcting codes, exceptional groups, finite fields, finite geometry, finite groups, finite rings, Galois fields, generalized quadrangles, generators, geometry, GF(2), GF(4), the (24,12) Golay code, group actions, group theory, Hadamard matrices, hypercube, hyperplanes, hyperspace, incidence structures, invariance, Karnaugh maps, Kirkman's schoolgirl problem, Latin squares, Leech lattice, linear groups, linear spaces, linear transformations, Mathieu groups, matrix theory, Meno, Miracle Octad Generator, MOG, multiply transitive groups, octads, the octahedral group, orthogonal arrays, outer automorphisms, parallelisms, partial geometries, permutation groups, PG(3,2), polarities, Polya-Burnside theorem, projective geometry, projective planes, projective spaces, projectivities, Reed-Muller codes, the relativity problem, Singer cycle, skew lines,  sporadic simple groups, Steiner systems, symmetric, symmetry, symplectic, synthemes, synthematic, tesseract, transvections, Walsh functions, Witt designs.