"Little emblems of eternity"
— Phrase by Oliver Sacks in today's
New York Times Sunday Review
Some other emblems —
Note the color-interchange
symmetry of each emblem
under 180-degree rotation.
Click an emblem for
some background.
"Little emblems of eternity"
— Phrase by Oliver Sacks in today's
New York Times Sunday Review
Some other emblems —
Note the color-interchange
symmetry of each emblem
under 180-degree rotation.
Click an emblem for
some background.
"Little emblems of eternity "
— Oliver Sacks, contemplating his own impending death,
in The New York Times Sunday Review section today.
Sacks's phrase refers to elements of the periodic table —
Another approach to "emblems of eternity" — The I Ching .
Hexagram 51:
"I woke last night to the sound of thunder,
How far off, I sat and wondered.
Started humming a song from 1962.
Ain't it funny how the night moves?"
From an explanation of the Web app IFTTT —
"IF This Then That" —
"If you are a programmer you can think of it as a loop*
that checks for a certain condition… to run one or
multiple actions if the condition is met."
After Completion (from Friday night, and 1989) —
Advertisement —
"On February 19, 2015, IFTTT renamed
their original application to IF…."
From Tuesday's post on the death of E. L. Doctorow —
“…right through hell
there is a path…”
— Malcolm Lowry
* More precisely, a conditional or conditional loop .
In memory of a talented frame-maker —
From July 4, the date of his reported death:
From the next day:
"Principles before personalities." — AA motto
For some personalities, see posts of November 23 last year.
This post was suggested by a book title in
the previous post: "Pieces of the Action."
A group action is a mathematical concept.
Related meditation:
"The number 9, that is to say, relates traditionally
to the Great Goddess of Many Names (Devi,
Inanna, Ishtar, Astarte, Artemis, Venus, etc.)
as matrix of the cosmic process, whether in the
macrocosm or in a microcosmic field of manifestation."
— Joseph Campbell,
The Inner Reaches of Outer Space
Examples:
It's Space Week at Camp Google.
“… the object sets up
a kind of frame or space or field
within which there can be epiphany.”
— Charles Taylor
“My little baby sister can do it with ease.
It’s easier to learn than those ABC’s.”
— Kylie Minogue
"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."
— Wittgenstein, Philosophical Investigations (1953), Section 109
Related material —
"… the common bond between chess, music, and mathematics
may, finally, be the absence of language."
— George Steiner, Fields of Force: Fischer and Spassky at Reykjavik ,
Viking hardcover, June 1974.
The New York Times this afternoon —
Professor Crone reportedly died at her home
in Princeton, N.J., on July 11, 2015.
See some posts, now with a new tag, that relate to that date.
Bloomberg.com —
July 21, 2015 — 3:51 PM EDT
Updated on July 21, 2015 — 6:04 PM EDT —
James Rothenberg of Capital Group
Dies at 69 of Heart Attack
"He was … chairman of Harvard Management Co.,
which invests the university’s $36.4 billion endowment."
See also …
The Harvard Crimson —
UPDATED: July 22, 2015, at 1:28 a.m.
"Rothenberg’s death, reportedly of a heart attack,
was unexpected."
He reportedly "chaired Harvard Management Company’s
board of directors from 2004 until his death."
“…right through hell
there is a path…”
— Malcolm Lowry
Buie reportedly died on Saturday, July 18, 2015.
Image from this journal on that date —
"In the cool of the evenin'
when everything is gettin'
kind of groovy
I call you up and ask you if
you'd like to go with me and
see a movie…."
Tom Stoppard, Jumpers —
“Heaven, how can I believe in Heaven?”
“To begin at the beginning: Is God?…” “Leave a space.” |
See as well a search for "Heaven.gif" in this journal.
For the more literate among us —
… and the modulation from algebra to space.
Detail from the Nov. 1998 cover of Mademoiselle —
Related meditation —
See as well "Intruders" in this journal.
CBS Sunday Morning today:
"On a warm summer night at the Greek Theatre
in Los Angeles last month, Brian Wilson — backed
by a band that included fellow former Beach Boy
Al Jardine — was running through his repertoire
of classics when a cake was wheeled out from
backstage by the extended Wilson family.
On this night, the man many regard as one of
America's greatest living songwriters turned 73.
Well, East coast girls are hip,
I really dig those styles they wear…"
Compare and contrast: Danny Collins.
See also last night's post.
The above passage was found in a search for thoughts of Heinz Pagels
on "perfect symmetry" (the title of one of his books). The "If all" part is,
however, apparently not by Pagels. That part seems to have been
online only in an NYU file that can no longer be accessed.
For perfect symmetry with structure, see (for instance)
Go Set a Structure (July 14, 2015) and Tombstone (July 16, 2015).
Robots pass "wise-men puzzle" to show a degree of self-awareness
New app … discourages self-awareness on social media —
"Self-awareness is a good thing.
Self-awareness is what tells us
'Hey, maybe just give us the highlights reel….'"
From this journal on July 13, Oslo artist Josefine Lyche —
Lyche's shirt honors the late Kurt Cobain.
"Here we are now, entertain us."
Dance scene from the 2015 film "Ex Machina"
Song from the 2015 film "Danny Collins" —
(More or less to the tune of "Sweet Caroline")
Hey, baby doll
What's goin' on?
Sweet baby doll
I'll sing my song!
For you!
You were strong when I was weak
With a kiss upon my cheek
We could fly so far away from here
My baby!
Baby!
Hey, baby doll!
What's goin' on?
Sweet baby doll
I'll sing my song for you!
Hey, baby doll!
What's goin' on…
Related material:
Robots pass 'wise-men puzzle' to show a degree of self-awareness
July 17, 2015 by Bob Yirka —
Or: Swan Boat for Kristen
In the recent film "Danny Collins," Al Pacino plays aging
rock star Danny and Christopher Plummer plays his agèd
agent-manager Frank …
"… when Danny tells Frank about his burgeoning relationship
with hotel manager Mary (Annette Bening), he declares happily,
'And she's age-appropriate!' 'Not really,' frowns Frank.
'Baby steps,' Danny replies."
The black rectangle at the end of Example 1.4
is known as the "end-of-proof symbol," "Halmos,"
or "tombstone."
"We have the answer to all your fears
It's short, it's simple, it's crystal clear"
See as well last night's Midnight Review.
Today's Huffington Post has a review of the
new book on John Horton Conway. The reviewer
is Colm Mulcahy. For some perspective, see
a search for Mulcahy in this journal.
(The title was suggested by the novel Weaveworld .)
Recent public selfie by Oslo artist Josefine Lyche —
Lyche's shirt honors the late Kurt Cobain.
Not-so-recent image of Hugo Weaving as
Agent Smith in "The Matrix" —
"Smells like teen spirit."
See also Weaving in the new film "Strangerland."
Omega is a Greek letter, Ω , used in
mathematics to denote a set on which
a group acts.
The Fano Plane —
"A balanced incomplete block design , or BIBD
with parameters b , v , r , k , and λ is an arrangement
of b blocks, taken from a set of v objects (known
for historical reasons as varieties ), such that every
variety appears in exactly r blocks, every block
contains exactly k varieties, and every pair of
varieties appears together in exactly λ blocks.
Such an arrangement is also called a
(b , v , r , k , λ ) design. Thus, (7, 3, 1) [the Fano plane]
is a (7, 7, 3, 3, 1) design."
— Ezra Brown, "The Many Names of (7, 3, 1),"
Mathematics Magazine , Vol. 75, No. 2, April 2002
W. Cherowitzo uses the notation (v, b, r, k, λ) instead of
Brown's (b , v , r , k , λ ). Cherowitzo has described,
without mentioning its close connection with the
Fano-plane design, the following —
"the (8,14,7,4,3)-design on the set
X = {1,2,3,4,5,6,7,8} with blocks:
{1,3,7,8} {1,2,4,8} {2,3,5,8} {3,4,6,8} {4,5,7,8}
{1,5,6,8} {2,6,7,8} {1,2,3,6} {1,2,5,7} {1,3,4,5}
{1,4,6,7} {2,3,4,7} {2,4,5,6} {3,5,6,7}."
We can arrange these 14 blocks in complementary pairs:
{1,2,3,6} {4,5,7,8}
{1,2,4,8} {3,5,6,7}
{1,2,5,7} {3,4,6,8}
{1,3,4,5} {2,6,7,8}
{1,3,7,8} {2,4,5,6}
{1,4,6,7} {2,3,5,8}
{1,5,6,8} {2,3,4,7}.
These pairs correspond to the seven natural slicings
of the following eightfold cube —
Another representation of these seven natural slicings —
These seven slicings represent the seven
planes through the origin in the vector
3-space over the two-element field GF(2).
In a standard construction, these seven
planes provide one way of defining the
seven projective lines of the Fano plane.
A more colorful illustration —
From Wikipedia —
"Many Leibniz scholars… seem to agree that he intended
his characteristica universalis … to be a form of …
ideographic language. This was to be based on a
rationalised version of the 'principles' of Chinese characters…."
See as well O Nine, Chinese Calligraphy, and Holy Field.
"Historically, the idea of a concept script
derives from the Leibnizian project of developing
a so-called 'universal characteristic'
(characteristica universalis )…."
— Dorothea Lotter, "Gottlob Frege: Language,"
in Internet Encyclopedia of Philosophy
Frege as quoted by Lotter —
"Arithmetical, geometrical and chemical symbols
can be regarded as realizations of the Leibnizian
conception in particular fields. The concept script
offered here adds a new one to these – indeed,
the one located in the middle, adjoining all the others."
Wittgenstein —
"Philosophy is a battle against the bewitchment
of our intelligence by means of our language."
"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."
— Philosophical Investigations (1953), Section 109
Frege, Preface to the Begriffsschrift —
"If it is one of the tasks of philosophy
to break the domination of words over the human spirit
by laying bare the misconceptions
that through the use of language
often almost unavoidably arise
concerning the relations between concepts
and by freeing thought from that with which only
the means of expression of ordinary language,
constituted as they are, saddle it,
then my ideography, further developed for these purposes,
can become a useful tool for the philosopher."
"Wenn es eine Aufgabe der Philosophie ist,
die Herrschaft des Wortes über den menschlichen Geist
zu brechen, indem sie die Täuschungen aufdeckt,
die durch den Sprachgebrauch über die Beziehungen der Begriffe
oft fast unvermeidlich entstehen,
indem sie den Gedanken von demjenigen befreit, womit ihn allein
die Beschaffenheit des sprachlichen Ausdrucksmittels behaftet,
so wird meine Begriffsschrift, für diese Zwecke weiter ausgebildet,
den Philosophen ein brauchbares Werkzeug werden können."
( A sequel to Friday’s post O Seven, O Eight )
In memory of opera singer Jon Vickers, who reportedly
died Friday at 88 —
“His deep faith — he was once dubbed ‘God’s voice’ —
saw him refuse to perform some roles on moral grounds,
specifically, Tannhäuser.” — BBC News
From Wolfram’s song to the evening star in Tannhäuser —
The soul, that longs for the highest grounds,
is fearful of the darkness before it takes flight.
There you are, oh loveliest star,
your soft light you send into the distance.
Der Seele, die nach jenen Höhn verlangt,
vor ihrem Flug durch Nacht und Grausen bangt.
Da scheinest du, o lieblichster der Sterne,
dein Sanftes Licht entsendest du der Ferne.
See as well a related meditation:
From Universals Revisited, Leap Day, 2012 —
A meditation from the date of death,
07/08/15,
of poet James Tate, 71 —
The previous post's Holy Field symbol,
with border removed, becomes the
Chinese character for "well."
See also The Lost Well.
A post of July 7, Haiku for DeLillo, had a link to posts tagged "Holy Field GF(3)."
As the smallest Galois field based on an odd prime, this structure
clearly is of fundamental importance.
It is, however, perhaps too small to be visually impressive.
A larger, closely related, field, GF(9), may be pictured as a 3×3 array…
… hence as the traditional Chinese Holy Field.
Marketing the Holy Field
The above illustration of China's Holy Field occurred in the context of
Log24 posts on Child Buyers. For more on child buyers, see an excellent
condemnation today by Diane Ravitch of the U. S. Secretary of Education.
Blaine Gibson, Designer of Lifelike Robots
at Disney Parks, Dies at 97
Log24 remarks on Sunday, July 5, the reported date of
Gibson's death:
Backstory for the previous post —
A Log24 post from the release date of the above Mat Zo album:
Remember, Remember the Fifth of November —
A scene suggested by today's 11:30 AM post —
The New York Times this afternoon on Nick Flynn —
This post was suggested in part by last night's post
of 11:14 PM ET, Southern Charm, and by a post
of 11/14 last year, Another Opening, Another Show.
See also Design Thinking at Wikipedia and the following
two quotations —
CHARLESTON COUNTY, SC (WCSC) (today) –
Dr. Gerrita Postlewait's contract for Superintendent
of Charleston County Schools was approved and
signed in a meeting with school board members
Wednesday morning, a school system official says….
From 2006 to 2013, she was the chief K-12 officer for
the Stupski Foundation, a San Francisco-based
education reform nonprofit. [See related page.]
PHILANTHROPY.COM (Aug. 2, 2012) –
Chris Tebben, executive director of Grantmakers for
Education, says the [Stupski] foundation was among
the first to consider how the problem-solving approach
known as “design thinking” could play a role in improving
education.
Related cinematic remarks: Robot Overlords (now on-demand).
A music video that opens with remarks by Lawrence Ferlinghetti
at the Last Waltz concert (Thanksgiving Day, Nov. 25, 1976):
"Our Father, whose art's in heaven…" —
For other religious remarks from the above upload date,
Sept. 9, 2011, see Holy Field GF(3).
Click the above "ripple" image for a Grateful Dead haiku
quoted here on Sunday, July 5, 2015.
For another meditation from the second upload date above,
March 19, 2012, see some thoughts on the word "field."
* For the title, see an excerpt from Point Omega .
"Throughout the years, weapons and targeting systems
were added to the aircraft without diminishing the F-16’s
agility, making it a true multirole aircraft."
— WCSC Television
Charleston, SC
* See yesterday's War Haiku.
It is false that "Mr. Shavitz sold his company… for about
$925 million." The New York Times seems to have
hired a Harvard unreliable reader. Also, following limited
prosperity, he no longer lived in a "converted turkey coop,"
though the coop remained on his property, according to
an Associated Press obit.
* For the title, see Weintraube in
a German-English dictionary.
This word was suggested by an
obituary in today's online Variety .
Remark by the director of "Project Almanac" on Feb. 10, 2015
about a proposed remake of "War Games":
"Israelite admitted that he was 'always very sceptical of remakes,
because the story's already been told,' but added that 'with this
particular title, I feel it's primed to say something new.'"
Related material: Log24 posts tagged Haiku.
A post suggested by today's news from
Calais, Maine (just across the St. Croix
river from St. Stephen in Canada) —
"Today’s operational environment presents situations so complex
that understanding them—let alone attempting to change them—
is beyond the ability of a single individual. Moreover, significant risk
occurs when assuming that commanders in the same campaign
understand an implicit design concept or that their design concepts
mutually support each other. The risks multiply…."
For the source, see June 6, 2014.
Some context for yesterday's post on a symplectic polarity —
This 1986 note may or may not have inspired some remarks
of Wolf Barth in his foreword to the 1990 reissue of Hudson's
1905 Kummer's Quartic Surface .
See also the diamond-theorem correlation.
A figure I prefer to the "Golden Tablet" of Night at the Museum —
The source — The Log24 post "Zero System" of July 31, 2014.
* For the title, see The New Yorker of Sept. 22, 2014.
Beloved professor dies unexpectedly
"Wesson also said Cottier had 'an encyclopedic
knowledge of everything historical and archaeological,'
and that he lectured straight from memory using
storytelling as a teaching method.
'He was absolutely the best lecturer that I've ever had,
spellbinding,' Wesson said. 'He would tell the most
amazing narratives, and the one thing that I could say,
that I've said to a couple of people today, is he was the
closest thing to a real Indiana Jones that there ever will be.
He lived an extraordinary life, just absolutely unusual
in every way and was unafraid of anything. He was the
most fearless person that I've ever met.'"
See also Pawn Sacrifice (June 28, 2015).
* For the title, see a search for Inside Man .
Related material: The co-editor of The Architecture of Modern Mathematics —
The title is that of a film which, according to Wikipedia,
"was promoted on the Oprah Winfrey Network, which
had the television premiere of the film on April 27, 2014."
See also this journal on that date.
Trailer for "Welcome to Me" published on Feb. 23, 2015 —
Related material: Manifest O (April 1, 2015).
A passage suggested by the 2006 Oxford University Press title
The Architecture of Modern Mathematics , edited by
José Ferreirós and Jeremy Gray —
Jeremy Gray, Plato's Ghost: The Modernist Transformation of Mathematics ,
Princeton, 2008 —
"Here, modernism is defined as an autonomous body of ideas,
having little or no outward reference, placing considerable emphasis
on formal aspects of the work and maintaining a complicated—
ndeed, anxious— rather than a naïve relationship with the day-to-day
world, which is the de facto view of a coherent group of people,
such as a professional or discipline-based group that has a high sense
of the seriousness and value of what it is trying to achieve.
This brisk definition…."
William Butler Yeats —
“Poets and Wits about him drew;
‘What then?’ sang Plato’s ghost.
‘What then?’
‘The work is done,’
grown old he thought,
‘According to my boyish plan;
Let the fools rage,
I swerved in naught,
Something to perfection brought’;
But louder sang that ghost,
‘What then?’“
(Continued from Friday, June 26, 2015)
In memory of an architect —
Donald Wexler, an architect whose innovative steel houses
and soaring glass-fronted terminal at the Palm Springs
International Airport helped make Palm Springs, Calif.,
a showcase for midcentury modernism, died on Friday
[June 26, 2015] at his home in Palm Desert. He was 89.
— William Grimes in this morning's New York Times
For a different sort of architecture in Palm Desert, see…
(A sequel to Expanding the Spielraum (Feb. 3, 2015))
"Knowledge, wisdom even, lies in depth, not extension."
— Tim Parks in The New York Review of Books ,
5 PM ET on June 26, 2015
See also Log24 posts on the following figure —
Chess
by Jorge Luis Borges, translated by I In their serious corner…. II Weak king, biased bishop ….
… they do not know Ajedrez I
En su grave rincón, los jugadores
Adentro irradian mágicos rigores
Cuando los jugadores se hayan ido,
En el Oriente se encendió esta guerra II
Tenue rey, sesgo alfil, encarnizada
No saben que la mano señalada
También el jugador es prisionero
Dios mueve al jugador, y éste, la pieza. |
As for "adamantine rigor," see the final link,
to "Windmill and Diamond," in the post on
the day of Bobby Fischer's death.
… de la Iglesia
See Jan. 16-18, 2008, on poetry in Spanish
and the death of chess champion Bobby Fischer.
Note also yesterday evening's post and the date
Jan. 18, 2008, in the following Google search sidebar:
The film of The Oxford Murders was first released on Jan. 18,
2008, in Spain. Its premiere was in Madrid on the preceding day,
which was also the day of Bobby Fischer's death.
Steen reportedly died on Sunday, June 21, 2015.
This was the day of the most recent post in
the "High White Noon" series.
(As opposed to the previous post.)
Today is the Feast of Saints Peter and Paul.
A reading from a parish named for them,
dated September 20, 2014 —
See also this journal on the above date — Sept. 20, 2014.
1985 — Church window in "Broken Wings" music video —
For Kristen Wiig, whose performances
give a new meaning to the phrase "flying fuck."
2015 — NASA video of June 28 Falcon 9 launch —
The title is that of a classic 1968 New Yorker essay
by George Steiner. See previous posts on this topic.
"It is as if one were to condense
all trends of present day mathematics
onto a single finite structure…."
— Gian-Carlo Rota, foreword to
A Source Book in Matroid Theory ,
Joseph P.S. Kung, Birkhäuser, 1986
"There is such a thing as a matroid."
— Saying adapted from a novel by Madeleine L'Engle
Related remarks from Mathematics Magazine in 2009 —
See also the eightfold cube —
For TD Arena …
See also Lincoln Alexander and posts in
this journal just before and on the date of
Alexander's death — Oct. 19, 2012.
* For the title, see Spielfeld posts.
Do you know where your watch is?
From a post of May 13, 2015 —
From the recent film "Interstellar" —
In keeping with the resurrection themes of the
previous post and of "Plan 9 from Outer Space,"
here is a link to the soundtrack of "Field of Dreams."
Related material:
A post of March 11, 2014, on
truth, cornfields, and Rebecca Goldstein —
Dark Fields of the Republic.
R.I.P., James Horner.
Rebecca Goldstein, the author mentioned in
the previous two posts, spoke at Santa Fe Institute
on Easter Monday, April 9, 2012.
This journal on that date:
The Santa Fe Institute logo, together with the previous post,
suggests a review of Whirligig and Quaternion for Goldstein.
The previous post's link to The Lindbergh Manifesto
and Thursday's post on Basel-born artist Wolf Barth
suggest the following —
See as well a June 14 New York Times
piece on Art Basel.
The logo of the University of Basel …
… suggests a review of The Holy Field —
There is such a thing as geometry.*
* Proposition adapted from A Wrinkle in Time , by Madeleine L'Engle.
The title of the previous post, "Slow Art," is a phrase
of the late art critic Robert Hughes.
Example from mathematics:
Click the Barth passage to see it with its surrounding text.
Related material:
Slowness is sometimes in the eye of the beholder.
See this journal on Slow Art Day 2015.
Related material: Epistemic States in this journal.
See that phrase in this journal.
See also last night's post.
The Greek letter Ω is customarily used to
denote a set that is acted upon by a group.
If the group is the affine group of 322,560
transformations of the four-dimensional
affine space over the two-element Galois
field, the appropriate Ω is the 4×4 grid above.
… 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.)
On a former LA Times editor who reportedly died today at 73 —
"Richard Masland, who grew up with Carroll, described
his friend as a mediocre student who enjoyed midnight
raids on auto junkyards and other mischief.
But, Masland noted, he 'was never the front man.
He let other people actually do the raising of hell.'"
( Continued )
Log24 on January 31, 2015 —Spellbound (continued)The New York Times this morning, in an “… the first known crossword puzzle appeared in See St. Nicholas magazine, November 1874, p. 59 : For the answer, see this journal on Aug. 29, 2002 |
On that same date …
The Seattle Times , Feb. 8, 2015, updated Feb. 12—
“… you begin by filling in the missing words Dice, yAhtzee, woN, yahTzee, twicE; The capital letters help to show what comes next, You take the first letter of the first inserted word, |
See also two other dates, June 3, 2015, and June 10, 2015,
in this journal and in the life of the puzzle author.
The date of the puzzle’s answer, Feb. 8, 2015, is also
not without interest.
“Click on fanciful .”
"And not all the king's men nor his horses
Will resurrect his corpus."
See as well Andy Weir's "The Egg" and Working Backward.
A version of the song in the previous post that I prefer:
A related meditation —
For a more abstract version of the
"matrix of the cosmic process,"
see "3×3 Grid" in this journal.
The online Los Angeles Times yesterday —
June 11, 2015
Robert Chartoff, an Oscar-winning Hollywood producer
who got a tantalizing peek into show business in the Catskills
and went on to make six "Rocky" films, "Raging Bull,"
"The Right Stuff" and nearly two dozen other movies,
has died at his home in Santa Monica. He was 81.
Chartoff, who died Wednesday, had been diagnosed with
pancreatic cancer two years ago, his son William said.
— Steve Chawkins
A fiction quoted here on the reported date of Chartoff's death —
“What… what happened?” you asked. “Where am I?”
“You died,” I said, matter-of-factly. No point in mincing words.
— Andy Weir, "The Egg"
“Was ist Raum, wie können wir ihn
erfassen und gestalten?”
The Theory and
Organization of the
Bauhaus (1923)
This post was suggested by the Bauhaus song
"Bela Lugosi's Dead" at the beginning of the
1983 Tony Scott classic "The Hunger."
"Now we're partners in crime" — Ace of Base, "The Golden Ratio"
Or not.
"The Hunger" (1983) was directed by Tony Scott.
See also Tony Scott in this journal.
" … yet the dread
Of dying, and being dead,
Flashes afresh to hold and horrify."
— Philip Larkin, "Aubade"
From tonight's New York Times obituaries —
See as well "Child Buyer" in this journal.
Omega is a Greek letter, Ω , used in mathematics to denote
a set on which a group acts.
For instance, the affine group AGL(3,2) is a group of 1,344
actions on the eight elements of the vector 3-space over the
two-element Galois field GF(2), or, if you prefer, on the Galois
field Ω = GF(8).
Related fiction: The Eight , by Katherine Neville.
Related non-fiction: A remark by Werner Heisenberg
in this journal on Saturday, June 6, 2015, the eightfold cube ,
and the illustrations below —
Mathematics
The Fano plane block design |
Magic
The Deathly Hallows symbol— |
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