Log24

Monday, September 19, 2022

Mosaic Kaleidoscope

Filed under: General — Tags: — m759 @ 12:04 am

"The kaleidoscope of peoples, parties and religions…."

— Description of Vienna in the early 20th century from
"Black Gold and Yellow Star" by Jerome Segal (PDF, 16 pp.) 

See as well Mosaic and Kaleidoscope in this  journal.

Sunday, September 18, 2022

Requiem for a Tin Man

Filed under: General — m759 @ 11:49 am

— "Heisenberg group modulo 2" from Wikipedia.   Click to enlarge.

For a related tune, click the Heisenberg link.

Culture Notes from All Over

Filed under: General — m759 @ 10:56 am

Sunday Morning Lockscreen

Filed under: General — m759 @ 9:42 am

Chamonix. Photo credit: Luca Gino, Sime.

"Dimensión de Arco"

Friday, September 16, 2022

Symmetric Generation

Filed under: General — Tags: , — m759 @ 2:20 pm

Symmetric Generation of a Linear Code

The above is about a subspace of the
24-dimensional vector space over GF(2) 
. . . "An entire world of just 24 squares,"
to adapt a phrase from other Log24
posts tagged "Promises."

 

Update of 1:45 AM ET Sept. 18, 2022 —

It seems* from a Magma calculation that
the resemblance of the above extended
cube-motif code to the Golay code is only
superficial.

 

Without  the highly symmetric generating codewords that were added
to extend its dimension from 8 to 12, the cube-motifs code apparently
does , like the Golay code, have nonzero weights of only 8, 12, 16, and 24 —

Perhaps someone can prove there is no  way that adding more generating
codewords can turn the cube-motif code into the Golay code.

* The "seems" is because I have not yet encountered any of these
relatively rare (42 out of 4096) purported weight-4 codewords. Their
apparent existence may be due to an error in my typing of 0's and 1's.

Thursday, September 15, 2022

Requiem for a Sleuth

Filed under: General — Tags: , — m759 @ 10:22 pm

A Grid for Agent Smith*

Filed under: General — Tags: — m759 @ 3:23 pm

* See Hugo Weaving in "The Matrix" and "V for Vendetta."

“R We D8ing?”

Filed under: General — Tags: , — m759 @ 1:43 pm

See also "R We D8ing?" and related posts.

Krysten Ritter narrates a podcast that asks 'R We D8ting?'

Literary Symbolism: Math for Roundheads

Filed under: General — Tags: , , — m759 @ 5:47 am

"The Virginia Cavalier is a concept that attaches the qualities
of chivalry and honor to the aristocratic class in Virginia history
and literature. Its origin lies in the seventeenth century, when
leading Virginians began to associate themselves with the
Royalists, or Cavaliers, who fought for and remained loyal to
King Charles I during the English Civil Wars (1642–1648)."

— https://encyclopediavirginia.org/entries/virginia-cavalier-the/

Wednesday, September 14, 2022

Not Safe for Work?

Filed under: General — Tags: — m759 @ 11:51 pm

      

A Line for Woody

Filed under: General — Tags: , — m759 @ 8:04 pm

 

"Here’s Looking at You, Grid"

Counting symmetries with the orbit-stabilizer theorem

Starr 80: A Barbie for Ken

Filed under: General — Tags: , , — m759 @ 7:27 pm

Related comedy lines:

A Late Quartet

01:13:08.25,01:13:12.35
(STRING QUARTET PLAYING
SLOW, LUSH MELODY)

01:13:22.59,01:13:26.23
"They’re fucking sixteenths,
Steve, stop milking them."

01:13:26.36,01:13:29.78
"Folks, disagree,
but do it nicely, and please…

01:13:30.47,01:13:33.38
…try not to get caught up in mistakes."

A Linear Code with 4×6 Symmetry

Filed under: General — Tags: — m759 @ 12:03 pm

The exercise of 9/11 continues . . .

From 'A Linear Code with 4x6 Symmetry,' a weblog post on 14 Sept. 2022.

As noted in an update at the end of the 9/11 post,
these 24 motifs, along with 3 bricks and 4 half-arrays,
generate a linear code of 12 dimensions. I have not
yet checked the code's minimum weight. 

For Odd Jean-Luc: Alpha Alpha Double Feature

Filed under: General — Tags: — m759 @ 7:16 am

. . . as well as starring in Alpha Dog and in . . .

Tuesday, September 13, 2022

A Helpful Survey of the Literature

Filed under: General — Tags: — m759 @ 9:39 pm

Some background for the exercise of 9/11

Vera Pless, "More on the uniqueness of the Golay codes,"
Discrete Mathematics 106/107 (1992) 391-398 —

"Several people [1-2,6] have shown that
any set of 212 binary vectors of length 24,
distance ≥ 8, containing 0, must be the
unique (up to equivalence) [24,12,8] Golay code." 

[1] P. Delsarte and J.M. Goethals, "Unrestricted codes
with the Golay parameters are unique
,"
Discrete Math. 12 (1975) 211-224.

[2] A. Neumeier, private communication, 1990.

[6] S.L. Snover, "The uniqueness of the
Nordstrom-Robinson and the Golay binary codes
,"
Ph.D. Thesis, Dept. of Mathematics, 
Michigan State Univ., 1973.

Related images —

"Before time began, there was the Cube."

              — Optimus Prime in 2007

      

"Remember, remember the fifth of November"

  — Hugo Weaving in 2005

Cinema News

Filed under: General — Tags: , — m759 @ 6:18 am

From a search in this  journal for Godard —

"I perceived . . . cinema is that which is between things,
not things [themselves] but between one and another."

— Jean-Luc Godard, "Introduction à une véritable histoire
du cinéma
," Albatros , Paris, 1980, p. 145

“We Got This Covered”

Filed under: General — Tags: — m759 @ 3:45 am

The previous post's quotation of the word "leitmotif" suggests a review:

      

See as well Sunday's post "Raiders of the Lost Space."

The Return of Krankheit and Dubious

Filed under: General — m759 @ 2:39 am

In memory of Ramsey Lewis, famed for his recording
of "The In Crowd" —

An old vaudeville routine, slightly adapted :

— Are you a doctor?
— I'm a doctor.
— I'm dubious.
— I'm glad to know you, Miss Dubious.

"The In Crowd" was a leitmotif in the 2015 film "Irrational Man."

Joaquin Phoenix as Dr. Krankheit,
Emma Stone as Miss Dubious —

Monday, September 12, 2022

“Hard Boiled” (Action Movie Title, Hong Kong, 1992)

Filed under: General — Tags: — m759 @ 4:55 pm

The "all-time great actioner" of the above news story is "Hard Boiled,"
a 1992 Hong Kong action film by John Woo. Related art —

Revised New Yorker cover from 5/21/07
Revised version of the
New Yorker  cover of 5/21/07

Sunday, September 11, 2022

Raiders of the Lost Space

Filed under: General — Tags: , — m759 @ 2:29 pm

From 1981 —

From today —

Update —

A Magma check of the motif-generated space shows that
its dimension is only 8, not 12 as with the MOG space.
Four more basis vectors can be added to the 24 motifs to
bring the generated space up to 12 dimensions: the left
brick, the middle brick, the top half (2×6), the left half (4×3).
I have not yet checked the minimum weight in the resulting
12-dimensional 4×6 bit-space.

— SHC 4 PM ET, Sept. 12, 2022.

Saturday, September 10, 2022

Solomon’s Mental Health Month

Filed under: General — Tags: , , — m759 @ 12:21 pm

May 2003 was "Solomon's Mental Health Month" in this journal.

An essay linked to on the 9th of May in that month —

"Taking the Veil," by Jessica Kardon

https://web.archive.org/web/20021102182519/
http://www.thespleen.com/otherorgans/otherorgans/
index.php?artID=724

James Hillman, writing in The Soul's Code, argues for his "acorn theory" of human individual identity, and suggests that "each person bears a uniqueness that asks to be lived and that is already present before it can be lived." He insists we are born with a given character, a daimon, the carrier of destiny. This theory is closely linked to the beautiful myth described by Plato in his Republic, when the soul stands before Lachesis and receives his specific soul guardian. Hillman maintains that the daimon will always emerge somehow, even if thwarted or unrecognized.

I never had ambitions that reached fruition in the adult world. I have had only two career interests in my life – both formed precognitively. I wanted to be a mermaid or a nun. By the time I learned – shockingly late – that I could not be a mermaid, I had realized I would not be a nun. I concur with Hillman's emphasis on the persistence of early disposition, and I like to imagine that my dreamy, watery, Victorian and self-righteous psyche has held aspects of both of these early interests, throughout my life.

I was adopted one month after my birth. I was tended by nuns during the first four weeks of my life. Thereafter, I spent my whole educational life in convent schools. It was the sisters of Saint Vincent de Paul that gave me my favorite musical and my early distortions about romantic love and the gender plans of Our Lord. My misconceptions about love and marriage were culled from the Lerner Loewe musical Gigi, a wonderful film based loosely on a Colette novel. I was summoned along with my whole class to the gymnasium to view the movie under the edgy eye of Sister Bernadette.

Sister Bernadette was a large, mesomorphic nun famed for the beatings she gave to boys and girls alike, and feared for the mean zest with which she bestowed her favors upon many of us. I was not beaten – but once, believing I was wearing lipstick, she held my head in a sink and scrubbed my lips until they bled, then slapped me. I recall this with a mild, rueful whimsy. We were all manhandled. In memory, Bernadette seems more like an angry and troubled older sibling than a true figure of authority.

Anyway, I loved Gigi. It fed directly into my Francophilia. I was convinced that at some future date, I, like Gigi, would be trained as a courtesan. I, too, would cause some hard case, experienced roué to abandon his chill and irony. I saw myself strolling down the Champs Elysee with Louis Jordan in rapt attendance, pushing a baby carriage, wearing a hat the size of a manhole cover, hoisting a parasol above that to assure the longevity of my adorable pallor.

The gender plans of Our Lord had recently been revealed to me too. Sister B. had drawn a ladder on the blackboard, a ladder with three rungs. At the top, she explained, were the priests, the nuns, and the monks. These souls had surrendered their lives to God. All would be taken directly to heaven upon their passing from this vale of tears, as we all referred to the world in those lean emotional times. On the middle rung stood the married. If you married and kept the law – which meant leaving every act of marital congress open to the reception of a child, you would be eligible for heaven. If you were foul in marriage, seeking your pleasure, you were going to be damned. On the bottom rung were those selfish souls who had remained single and had imagined their lives their own. This group had never given themselves to Our Lord. They were headed to hell in a sort of preternatural laundry chute.

So we little ladies had two viable options: marry and breed without ceasing – or take the veil.

Despite my hat and perambulator fantasies, once given the sorry news of the ladder, the veil became the clear romantic favorite. Therefore I began my research. I obtained a catalogue of nunnery. It offered photographs of each order, describing the duties of the specific order, and displaying the garb of that order. I was looking for two things – a great looking veil and gown, and a contemplative order. I had no desire to sully my glorious vision of myself with a life in the outer world. It was apparent to me that the teaching of children was going to involve a whole range of miseries – making them cry, telling them the bad news about the ladder, and so forth. This was not for me. I saw myself kneeling on the floor of my pristine little cell, serene and untouched by human hands. Teaching would be certain to interfere with the proper lighting. Yoked to a bunch of messy children, I could not possibly have the opalescent illumination of heaven falling reliably on my upturned visage.

What divided me from my dream of rebirth as a mermaid was the force of what was real: I could not morph. What divided me from my dream of life as a nun was the force of the erotic: I would not abstain.

Now, long years later, I am still underwater, and I am still bending the knee. I live in the blue shadows of hidden grottoes, and I am swimming, too, in the gold of my drifting prayers.

September 7th, this dream. I am standing in a dimly lit room, gazing at a group of heavy, antique silk burqas that look weirdly like Fortuny gowns. A holy woman approaches me, and tells me that my soul will leave my body, and enter these garments. She turns and points at a young girl standing nearby, a child with close-cropped hair and a solemn look. My heart knows her, but my eyes don't.

For a moment I am thinking, exactly as I did in the seventies when holding a joint: "This isn't working." Suddenly, these things: I feel the shape of flame, then I am the shape. I am released into the air, and as pure essence I enter other forms, dissolving in them, gathering my energy back into myself, and flying out again. This was a sensation so exquisite that my dreaming brain woke up and announced to me: "This is a dream about death."

I saw that child again as I flew. This time my eyes knew her. I flew to her, but the flame of my soul would not cohere with hers, this child who was, of course, my own self.

In the shadows alone, I heard myself whisper: "I'm in the wind. I'm in the water."

This lovely dream, which gave me the sublime gift of a little visceral preview of the soul in the death process, also showed me my guardian spirit; divided, but viable.

I pass through my life swimming in one self, kneeling in the other. I thought of Rilke's 29th Sonnet to Orpheus and realized this was what I had been dreaming about all my life, moving between them.

Silent friend of many distances, feel
how your breath enlarges all of space.
Let your presence ring out like a bell
into the night. What feeds upon your face

grows mighty from the nourishment thus offered.
Move through transformation, out and in.
What is the deepest loss that you have suffered?
If drinking is bitter, change yourself to wine.

In this immeasurable darkness, be the power
that rounds your senses in their magic ring,
the sense of their mysterious encounter.

And if the earthly no longer knows your name,
whisper to the silent earth: I'm flowing.
To the flashing water say: I am.

– Stephen Mitchell, translating Rainer Marie Rilke.

by jessica kardon
iowa city, iowa
2002-09-23

See as well yesterday's post "At a Still Point."

Orthogonal Latin Triangles

Filed under: General — Tags: , — m759 @ 1:38 am

From a 1964 recreational-mathematics essay —

Note that the first two triangle-dissections above are analogous to
mutually orthogonal Latin squares . This implies a connection to
affine transformations within Galois geometry. See triangle graphics
in this  journal.

Affine transformation of 'magic' squares and triangles: the triangle Lo Shu 

Update of 4:40 AM ET —

Other mystical figures —

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

"Before time began, there was the Cube."

— Optimus Prime in "Transformers" (Paramount, 2007)

Friday, September 9, 2022

Pillars of Wisdom . . . Count ’Em!

Filed under: General — m759 @ 11:19 pm

Related reading — Program or Be Programmed — 

At a Still Point

Filed under: General — m759 @ 4:43 pm

"The music was as formal as
Job's argument with God.
Her dance was God's reply."

— "A Rose for Ecclesiastes"

Relentless Exploitation Flick

Filed under: General — Tags: — m759 @ 12:19 pm

A New York Times  obituary today reports a death
from the Feast of St. Louis, 2022 —

"Dr. Gottfried said at the time that the world was
undergoing a transformative revolution driven by
'the relentless exploitation of scientific knowledge.'”

Also on that date . . .

Thursday, September 8, 2022

Analogy in Mathematics: Chevron Variations

André Weil in 1940 on analogy in mathematics —

. "Once it is possible to translate any particular proof from one theory to another, then the analogy has ceased to be productive for this purpose; it would cease to be at all productive if at one point we had a meaningful and natural way of deriving both theories from a single one. In this sense, around 1820, mathematicians (Gauss, Abel, Galois, Jacobi) permitted themselves, with anguish and delight, to be guided by the analogy between the division of the circle (Gauss’s problem) and the division of elliptic functions. Today, we can easily show that both problems have a place in the theory of abelian equations; we have the theory (I am speaking of a purely algebraic theory, so it is not a matter of number theory in this case) of abelian extensions. Gone is the analogy: gone are the two theories, their conflicts and their delicious reciprocal reflections, their furtive caresses, their inexplicable quarrels; alas, all is just one theory, whose majestic beauty can no longer excite us. Nothing is more fecund than these slightly adulterous relationships; nothing gives greater pleasure to the connoisseur, whether he participates in it, or even if he is an historian contemplating it retrospectively, accompanied, nevertheless, by a touch of melancholy. The pleasure comes from the illusion and the far from clear meaning; once the illusion is dissipated, and knowledge obtained, one becomes indifferent at the same time; at least in the Gitâ there is a slew of prayers (slokas) on the subject, each one more final than the previous ones."

"The pleasure comes from the illusion" . . .

Exercise:

Compare and contrast the following structure with the three
"bricks" of the R. T. Curtis Miracle Octad Generator (MOG).

http://www.log24.com/log/pix11B/110805-The24.jpg

Note that the 4-row-2-column "brick" at left is quite 
different from the other two bricks, which together
show chevron variations within a Galois tesseract —

Tuesday, September 6, 2022

Literary Master

Filed under: General — Tags: — m759 @ 4:56 pm

Update at 11:19 PM ET —

"We all float down here." — Pennywise the Clown

A comparison of Peter Straub's novel Floating Dragon  (1982)
with Stephen King's novel It  (1986)

"Many people have cited some distinct similarities between Stephen King’s It  and Floating Dragon .  An ancient evil that awakes every thirty years, several main male characters and a single female character who come together to confront that evil, a number of asides around the small town as bystanders are picked off, even a number of scenes and themes in common."

— https://www.fantasybookreview.co.uk/
Peter-Straub/Floating-Dragon.html

From the same webpage —

"As the book rockets towards its ending, Straub really does pull out all the stops. A late chapter is entitled 'through the looking glass' and that really is how the book begins to feel, more like a surreal and disturbing fantasy world than a book set in late twentieth century America. Usually in horror novels the point when reality seriously starts to crumble, whether its visions of grandmothers turning into fish or angel shaped biscuits turning evil, there is always the sense that this must be just a dream and the main characters will wake up. Well not here, the weirder things seem, the deadlier they are, indeed one comment late on in the book by Graham that just because something isn’t real doesn’t mean it can’t kill you seemed almost like Straub’s mission statement."

Tata Note

Filed under: General — m759 @ 3:00 pm

"This volume is the first of three in a series surveying
the theory of theta functions. Based on lectures given by
the author at the Tata Institute of Fundamental Research
in Bombay, these volumes constitute a systematic exposition
of theta functions, beginning with their historical roots as
analytic functions in one variable (Volume I), touching on
some of the beautiful ways they can be used to describe
moduli spaces (Volume II), and culminating in a methodical
comparison of theta functions in analysis, algebraic geometry,
and representation theory (Volume III)."

Digits of August

Filed under: General — Tags: , — m759 @ 1:14 pm

See as well Kipnis on the separatrix, and a notation
that represents a date in September, not August:
 

9/6.


Too clever by half ?

Gell-Mann Meets Bosch* at Hiroshima

Filed under: General — Tags: — m759 @ 3:18 am

Gell-Mann Meets Bosch . . .

At Hiroshima . . .

Iain Aitchison's 'dice-labelled' cuboctahedron at Hiroshima, March 2018

* The Bosch  cuboctahedron is from an exhibition at Napoli in 2021.

See also, from that exhibition's starting date,
the Log24 post Desperately Seeking Symmetry.

Monday, September 5, 2022

Annals of Science: Cognitive Testing

Filed under: General — m759 @ 6:03 pm

See also http://m759.net/wordpress/?s="Block+Design"

2001: A Time Odyssey

Filed under: General — m759 @ 4:15 pm

See as well a search for intelligent life at Santa Cruz —

Related art —

Sunday, September 4, 2022

Dice and the Eightfold Cube

Filed under: General — Tags: , , , , — m759 @ 4:47 pm

At Hiroshima on March 9, 2018, Aitchison discussed another 
"hexagonal array" with two added points… not at the center, but
rather at the ends  of a cube's diagonal axis of symmetry.

See some related illustrations below. 

Fans of the fictional "Transfiguration College" in the play
"Heroes of the Fourth Turning" may recall that August 6,
another Hiroshima date, was the Feast of the Transfiguration.

Iain Aitchison's 'dice-labelled' cuboctahedron at Hiroshima, March 2018

The exceptional role of  0 and  in Aitchison's diagram is echoed
by the occurence of these symbols in the "knight" labeling of a 
Miracle Octad Generator octad —

Transposition of  0 and  in the knight coordinatization 
induces the symplectic polarity of PG(3,2) discussed by 
(for instance) Anne Duncan in 1968.

Saturday, September 3, 2022

1984 Revisited

Filed under: General — m759 @ 2:46 pm

Cube Bricks 1984 —

An Approach to Symmetric Generation of the Simple Group of Order 168

Related material

Note the three quadruplets of parallel edges  in the 1984 figure above.

Further Reading

The above Gates article appeared earlier, in the June 2010 issue of
Physics World , with bigger illustrations. For instance —

Exercise: Describe, without seeing the rest of the article,
the rule used for connecting the balls above.

Wikipedia offers a much clearer picture of a (non-adinkra) tesseract —

      And then, more simply, there is the Galois tesseract

For parts of my own  world in June 2010, see this journal for that month.

The above Galois tesseract appears there as follows:

Image-- The Dream of the Expanded Field

See also the Klein correspondence in a paper from 1968
in yesterday's 2:54 PM ET post

Friday, September 2, 2022

Kyoto Prize

Filed under: General — Tags: — m759 @ 9:43 pm

Related material —

Wittgenstein and Fly from Fly-Bottle

Fly from Fly Bottle

History of Mathematics

Filed under: General — m759 @ 2:54 pm

Anne Duncan in 1968 on a 1960 paper by Robert Steinberg —


_______________________________________________________________________________

Related remarks in this  journal — Steinberg + Chevalley.

Related illustrations in this journal — 4×4.

Related biographical remarksSteinberg Deathdate.

Independence

Filed under: General — m759 @ 11:22 am

On the wife of the fictional billionaire Byron Gogol

Continuing the theme of independence, a less fictional Byron . . .

Thursday, September 1, 2022

Plan 9: A Recurring Theme

Filed under: General — m759 @ 7:23 pm

September Morn Concludes

Filed under: General — Tags: , — m759 @ 11:56 am

"This is the worst trip I've ever been on"

Sloop John B lyrics.  

That song was played at the end of the TV series
"The Resort," which concluded today.

Wednesday, August 31, 2022

Release Dates: The Iceman Goeth

Filed under: General — Tags: — m759 @ 1:41 pm

Part I —

Also in May 1986 —

86-05-08… A linear complex related to M24 .

Anatomy of the polarity pictured in the 86-04-26 note.

86-05-26… The 2-subsets of a 6-set are the points of a PG(3,2).

Beutelspacher's model of the 15 points of PG(3,2)
compared with a 15-line complex in PG(3,2).


Part II — (36 years later)

Tuesday, August 30, 2022

Geometry d’Or

Filed under: General — Tags: — m759 @ 8:20 pm

On the director of "The Square" —

For Gaynil

Filed under: General — m759 @ 7:19 pm

Related material — The Hunt for Blue August.

http://www.log24.com/log10/saved/100813-Contact.jpg

Space Notes

Filed under: General — Tags: — m759 @ 11:09 am

Also on January 17, 2022 . . .

Related space remarks:  Overarching.space.

Quartets.space

Filed under: General — Tags: — m759 @ 3:22 am

Four Quartets

Monday, August 29, 2022

Euphoria High Meets Dragonrider School

Filed under: General — Tags: — m759 @ 2:19 pm

A literary  prequel to the new HBO series "House of the Dragon" —

Sunday, August 28, 2022

Upriver

Filed under: General — Tags: — m759 @ 12:30 pm

From http://usuarios.lycos.es/jabizanda/album/miscelanea/tn/Apocal.jpg.index.html

The Turning

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

For fans of the fictional Transfiguration College, an institution
in the play "Heroes of the Fourth Turning" — now reportedly
featuring Sophia Lillis in an upcoming Washington, D.C., production

See "theatrical Hiroshimas" and "Jolt" in this journal.

Related philosophy — Taiji.

Saturday, August 27, 2022

Lullaby 86

Filed under: General — Tags: — m759 @ 10:18 pm

In memory of a founder of MCC Theater:

A musical rendition of the ending of the classic
1947  E. B. White short story
"The Second Tree from the Corner."

Endings

Filed under: General — Tags: — m759 @ 1:23 pm

"In my beginning is my end." — T. S. Eliot

Two readings from December 7, 2008 —

  • A column on Eliot's remark that reportedly "originally appeared in 
    the December 7, 2008, edition of Our Sunday Visitor  newspaper"
  • "Space and the Soul," a Log24 post, also from December 7, 2008.

A related quotation, suggested by the now-deceased professor David Lavery
of Middle Tennessee State University —

Lavery, a professor of English, was born in 1949 in Oil CIty, Pa.

Friday, August 26, 2022

“A Room Somewhere” — Song Lyric

Filed under: General — Tags: , , — m759 @ 7:59 pm

The Peacock series "The Resort" yesterday presented its concept
of "a room outside of time" (the Pasaje ) as a hole in the ground.

A concept I prefer

The 'High Life' concept of 'Room' (cf. German 'Raum')

Thursday, August 25, 2022

Affine I Ching

Filed under: General — Tags: — m759 @ 10:45 pm

'Affine I Ching' image search

Affine Lo Shu

Filed under: General — Tags: , — m759 @ 5:37 pm

'Affine Lo Shu' Google search

Meditation on a Song Lyric

Filed under: General — Tags: , , — m759 @ 12:25 am

"I saw a werewolf with a Chinese menu in his hand
Walking through the streets of Soho in the rain"

— Warren Zevon

See other posts now tagged Structure Character.

Wednesday, August 24, 2022

Metaphor

Filed under: General — m759 @ 2:53 pm

The Wondertale Tag

Filed under: General — m759 @ 1:19 am

See as well the Tolkien  release date in Wondertale posts.

Tuesday, August 23, 2022

Pasaje:  Raiders of the Lost Chord

Filed under: General — m759 @ 1:17 pm

Season 1 of "The Resort" will end as "The Lord of the Rings:
The Rings of Power
" begins.

For seekers of the Pasaje — "The Room Outside of Time" —

"The Vision is of what the transliteration of their collaborative
Great Music into a material reality would be like. They are
shown that the Music has a point, has a result and effect
beyond its composition and singing: it amounts to no less
than a highly detailed template commensurate with the entire
history – beginning to end – of a material, 'physical' Universe
that could exist inside 'time'." 

— https://lotr.fandom.com/wiki/Ainulindal%C3%AB

Chair

Filed under: General — m759 @ 2:40 am

"Where fashion sits" — Song lyric

Monday, August 22, 2022

Tokens/Totems

Filed under: General — Tags: , , — m759 @ 7:23 pm

See Ballet Blanc  and Black Art in this journal.

From the former:

"A blank underlies the trials of device."

— Wallace Stevens

From the latter:

IMAGE- 'Inception' totems: red die and chess bishop, with Inception 'Point Man' poster

La Chair et l’Esprit

Filed under: General — m759 @ 2:17 pm

Lilyjcollins, https://www.instagram.com/p/ChiBYx2PsaO/

Sunday, August 21, 2022

Ophelia’s Song

Filed under: General — m759 @ 3:27 pm

Lilyjcollins, https://www.instagram.com/p/ChiBYx2PsaO/

Or: Verbum Sat .

Saturday, August 20, 2022

Recent Configuration Geometry

Filed under: General — Tags: — m759 @ 3:37 pm

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))

Friday, August 19, 2022

The Guy Embedding

Filed under: General — Tags: , , — m759 @ 3:43 pm

M. J. T. Guy discovered that the lexicographic  version
of the Golay code contains, embedded within it, the
Miracle Octad Generator  (MOG)  of R. T. Curtis.

For 12 basis vectors of the lexicographic version, see below.

Basis vectors for the lexicographic version of the binary Golay code

For some context, click the embedded guy.

For a closely related, but simpler, mathematical
structure, see posts tagged The Omega Matrix.

Mathematical Evolution

Filed under: General — Tags: , — m759 @ 2:49 am

From the Stillwell remembrance, a Shenitzer quote —

"An English major may or may not be a novelist or a poet,
but would undoubtedly be expected to be able to evaluate
a novel or a poem. The term 'English major' implies some
historical, philosophical, and evaluative training and
competence. It is sad but true that the term 'mathematician'
does not imply corresponding training and competence."

Related material — The previous post, and posts tagged Super-8.

Cut  Geometry

Filed under: General — Tags: , — m759 @ 12:15 am

"… the new geometries … provide the best example of
the power of the human mind, for the mind had to defy
and overcome habit, intuition, and sense perceptions
to produce these geometries."

— Morris Kline, Mathematics in Western Culture ,
Oxford University Press, 1953, page 430.
 

Points  as Cuts

Points as Cuts: Some Small Finite Spaces

Thursday, August 18, 2022

The Razr’s Edge

Filed under: General — Tags: , — m759 @ 2:42 pm

A view from Hollywood

A view from Silicon Valley

A view from the Holiday Hotel

'The Resort' S1E1 - The 2007 Razr

Wednesday, August 17, 2022

Carnival Knowledge

Filed under: General — Tags: — m759 @ 8:03 pm
 

"This discussion, intended to define the nature and the largest common denominator of all games, has at the same time the advantage of placing their diversity in relief and enlarging very meaningfully the universe ordinarily explored when games are studied. In particular, these remarks tend to add two new domains to this universe: that of wagers and games of chance, and that of mimicry and interpretation. Yet there remain a number of games and entertainments that still have imperfectly defined characteristics— for example, kite-flying and top-spinning, puzzles such as crossword puzzles, the game of patience, horsemanship, seesaws, and certain carnival attractions."

Caillois, Roger. 1913-1978, in
Man, Play and Games, Chapter 1, "The Definition of Play."

Translated by Meyer Barash from Les jeux et les hommes .
French original © 1958 by Librairie Gallimard, Paris.
English translation © 1961 by The Free Press of Glencoe, Inc.

See also Caillois in the previous post.

The Holiday Hotel

Filed under: General — Tags: — m759 @ 6:01 pm

'Desperate Games' cover

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

Cold Comfort Dam

Filed under: General — Tags: , — m759 @ 10:50 am

"And, as with all retold tales that are in people's hearts,
there are only good and bad things and black and white
things and good and evil things and no in-between anywhere."

— John Steinbeck, author's epigraph to The Pearl

From the Season 4 finale of Westworld :
uploading Dolores's pearl at Hoover Dam —

For those who prefer greater theological simplicity . . .

Optimus Prime on a different Hoover Dam figure, that of 
the AllSpark: "Before time began, there was the Cube."

Simplifying even more . . .

“A set having three members is a single thing
wholly constituted by its members but distinct from them.
After this, the theological doctrine of the Trinity as
‘three in one’ should be child’s play.”

– Max Black, Caveats and Critiques: Philosophical Essays
in Language, Logic, and Art
 , Cornell U. Press, 1975

IMAGE- The Trinity of Max Black (a 3-set, with its eight subsets arranged in a Hasse diagram that is also a cube)

As above, Black's theology forms a cube.

Cold Comfort

Filed under: General — Tags: , — m759 @ 9:32 am

Some will prefer Leonard  Bernstein.

From a search in this  journal for Bernstein + Mahler

IMAGE- 'Bernstein conducts Mahler 9th ending'

Tuesday, August 16, 2022

The Central Forum

Filed under: General — m759 @ 10:11 am

A Web search shows that the above 2014 photo is, specifically,
from June 26, 2014, when the guest speaker was Jules Feiffer.

See as well this  journal on June 26, 2014.

The Pristine Edge of Darkness

 

Westworld Season 4 Episode 8 (Finale)

Christina: Where am I? 
Maya: You're nowhere. Unplugged from the rest of the world. (Wind swooshing)
Christina: I'm alone again. In the walled garden. 
Maya: You're scared. So you brought me back. Talk to me, Chrissie. 
Christina: Everything is destroyed. Everyone is dying. I don't know. (Wind whooshing) (Leaves rustling) But I think it may be my fault. (Melancholic music playing) 
Maya: You know, people think they know what a tree is. They have no idea. What we see, it's only part of the story. But beneath the ground… everything's connected and working together. There's violence and chaos everywhere. And you can choose to focus on all of that. And that's all you'll see. But if you sit still… (Leaves rustling) …long enough… you'll sense an ancient order. A deep peace. (Breathes deeply) And that's what I choose to see. (Inhales) I see the beauty in this world. 
Christina: Yes. (Chuckles softly) I know the feeling. 
Maya: I thought you might. (Melancholic music concludes)

Read more at
https://tvshowtranscripts.ourboard.org/
viewtopic.php?f=738&t=55566

From a college botany laboratory in the 1915
D. H. Lawrence novel The Rainbow

"Suddenly she had passed away into
an intensely-gleaming light of knowledge."

A later passage in the same novel, under
a metaphorical Tree of Life —

"She passed away as on a dark wind, far, far away,
into the pristine darkness of paradise, into the original
immortality. She entered the dark fields of immortality."

Some will prefer . . .

For further context, see posts tagged Screw Theory.

Monday, August 15, 2022

Holding the Center: A Study in Composition

Filed under: General — Tags: — m759 @ 1:58 pm

Earlier . . .

The Dark Fields… Continues.

Filed under: General — Tags: , — m759 @ 1:36 pm

See also Dark Fields in this journal.

Pyramid Song

Filed under: General — m759 @ 3:55 am

Sunday, August 14, 2022

The Fourth Poet*

Filed under: General — Tags: — m759 @ 10:00 am

* See the previous post.

Saturday, August 13, 2022

Summer Reading

Filed under: General — Tags: , — m759 @ 11:28 am

At the End

Filed under: General — m759 @ 10:44 am

See as well the above eight-ray star in Damnation Morning posts.

For the Late Zoltan Dienes (and Charles Kinbote)*

Filed under: General — m759 @ 4:56 am

[Shortly after 4 p.m. in Cetinje would have been shortly after 10 a.m. ET.]

* See Dienes and Kinbote in this journal.

Friday, August 12, 2022

The Representation Stage

Filed under: General — Tags: — m759 @ 6:40 pm

See also "Abstract Signature" in this journal.

Line of Action

Filed under: General — Tags: , — m759 @ 10:39 am

The art-school phrase "line of action" has a mathematical counterpart.

Some background . . .

In memoriam —

For those who prefer bullshit . . .

https://www.forbes.com/sites/chadorzel/2016/11/21/
the-physics-that-got-left-out-of-arrival/?sh=40db87855a0a
.

Mathematical Games: The Common Core

Filed under: General — Tags: — m759 @ 8:17 am

'The Resort' S1E5 - Shapes Puzzle

“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.

Thursday, August 11, 2022

“Enhance your line of action”

Filed under: General — Tags: , , — m759 @ 6:55 pm

Space X

Filed under: General — Tags: — m759 @ 11:18 am

"Leave a space." — Tom Stoppard, "Jumpers"

See also Lily Collins's recent ice-cream-cone post.

The number 105 displayed in that post may suggest,
to sufferers from apophenia, the date  1/05.

See that date in this journal. For the color  of Collins's
ice cream — lavender — see posts now tagged Space X.

Wednesday, August 10, 2022

Hollywood Reality Check

Filed under: General — m759 @ 11:39 am

For Jeff Bridges and John Lithgow

(as well as Old Man creators Steinberg and Levine) —

A Space

Filed under: General — Tags: — m759 @ 9:20 am

"Snowman author Raymond Briggs dies aged 88"

See as well a Log24 search Stoppard + "Leave a space" .

Related literary notes:

Tuesday, August 9, 2022

Book Lovers Day

Filed under: General — Tags: , — m759 @ 11:43 am

Click El Catalejo  below for some book-related remarks.

Nihilism for Science Groupies

Filed under: General — Tags: — m759 @ 10:21 am

Related, but only poetically —

The Pure Mathematics of Power Sets.

The Yosemite Six

Filed under: General — Tags: — m759 @ 9:39 am

"Jurassic World: Maisie Lockwood Adventures 2: The Yosemite Six ​​​​
will be released on September 27, 2022."

Thanks for the warning.

Of greater interest to some: The Number  Six.

Mirror, Mirror

Filed under: General — Tags: — m759 @ 3:04 am

A phrase from the above scene: "the metaphysics of identity."

I prefer a May 1986 looking-glass from pure mathermatics.

Story Line

Filed under: General — Tags: — m759 @ 12:44 am

"Down the arches of the years"

The above phrase was quoted in a novel by Joan Didion.

Monday, August 8, 2022

“An Air of Freedom”

Filed under: General — Tags: , — m759 @ 4:10 pm

Update of 4:50 PM ET the same day —

Summer Camp: De Bas* en Haut**

Filed under: General — Tags: — m759 @ 12:25 pm

See more? Yes, Yes!


* See this morning's Rimshot Muse.

** See Lillian Roth in Madam Satan (1930, pre-Code).

Centro Linden

Filed under: General — m759 @ 6:52 am

The centrolinden.com address in the previous post
suggests a search for Navarre  in this journal that yields

“D’exterieur en l’interieur entre
Qui va par moi, et au milieu du centre
Me trouvera, qui suis le point unique,
La fin, le but de la mathematique;
Le cercle suis dont toute chose vient,
Le point ou tout retourne et se maintient.”

— Marguerite de Navarre

The Rimshot Muse

Filed under: General — Tags: — m759 @ 6:11 am

Related philosophical reflections . . .

Waxing poetic . . .

"In the Garden of Adding live Even and Odd" — E. L. Doctorow

To wit:

1/2 + 1/3 = 5/6, since the LCM of 2 and 3 is 6.

See as well . . .

Sunday, August 7, 2022

For the Church of the Wicked Stepmother:

Filed under: General — Tags: — m759 @ 9:00 am

Progressive Matrices

A sample Raven's Progressive Matrices  test item —

IMAGE- Raven's Progressive Matrices item with symbols from Cullinane's box-style I Ching

IMAGE- Charlize Theron as Ravenna with raven in poster for 'Snow White and the Huntsman'

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.

From Coxeter’s Nutshell: Points and Marks

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

Saturday, August 6, 2022

Atman

Filed under: General — Tags: — m759 @ 2:29 pm

Bob and Carol

… And then there is the Jack Carr version of Snuggles.

Myth Space Date Note

Filed under: General — Tags: , — m759 @ 11:54 am

The above obituary reports a death that happened on July 23.
Also on that date . . . Myth Space and Date Note.

Metadata

Filed under: General — Tags: , — m759 @ 6:29 am

Also on Aug. 2, 2019 —

Later that August —

Also on Aug. 6, 2019 —

The Story of Q:  Quantity/Quality

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

"“Quantity has a quality all its own.”
James Stavridis, quoted on Aug. 5, 2022.

Friday, August 5, 2022

A Lockscreen for Sunrise

Filed under: General — Tags: — m759 @ 5:13 am

Thursday, August 4, 2022

Motif

Filed under: General — Tags: , , — m759 @ 7:34 pm

The New York Times  today reports a July 18 death —

Skully*

Filed under: General — Tags: — m759 @ 5:44 am

Click image to enlarge.

* An instance of ambiguation, as opposed to dis   ambiguation.

Wednesday, August 3, 2022

From the “Shifting Phantasmagoria” of Joan Didion

Filed under: General — Tags: , — m759 @ 12:45 pm

Also on July 30 . . .

Scully Disambiguation

Filed under: General — Tags: , — m759 @ 5:41 am

In order, approximately, of increasing popularity:

Sean Scully, artist, whose work is the subject of 
the recent book and exhibition, "The Shape of Ideas."

Vincent Scully, architectural historian at Yale.

Vincent Edward ("Vin") Scully, "Voice of the Dodgers"

Tuesday, August 2, 2022

Recent Reading List

Filed under: General — m759 @ 11:33 am

A Separatrix for Kipnis*

Filed under: General — Tags: , — m759 @ 12:00 am
 

8/2 

 

* See Kipnis in this journal. For instance . . .

The trait  of Derrida is mentioned also in
the paper from yesterday's Gefüge  post.

Monday, August 1, 2022

Enowning

Filed under: General — Tags: — m759 @ 3:26 pm

Related material — The Eightfold Cube.

See also . . .

"… Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to 
explain how art fits into our subject and what we mean by beauty."

— Sir Michael Atiyah, “The Art of Mathematics”
in the AMS Notices , January 2010

Interality Again: The Art of the Gefüge

Filed under: General — Tags: , , — m759 @ 2:52 pm

"Schufreider shows that a network of linguistic relations
is set up between Gestalt, Ge-stell,  and Gefüge, on the
one hand, and Streit, Riß,  and Fuge, on the other . . . ."

— From p. 14 of French Interpretations of Heidegger ,
edited by David Pettigrew and François Raffoul.
State U. of New York Press, Albany, 2008. (Links added.)

One such "network of linguistic relations" might arise from
a non-mathematician's attempt to describe the diamond theorem.

(The phrase "network of linguistic relations" appears also in 
Derrida's remarks on Husserl's Origin of Geometry .)

For more about "a system of slots," see interality in this journal.

The source of the above prefatory remarks by editors Pettigrew and Raffoul —

"If there is a specific network that is set up in 'The Origin of the Work of Art,'
a set of structural relations framed in linguistic terms, it is between
Gestalt, Ge-stell and Gefüge, on the one hand, and Streit, Riß and Fuge
on the other; between (as we might try to translate it)  
configuration, frame-work and structure (system), on the one hand, and
strife, split (slit) and slot, on the other. On our view, these two sets go
hand in hand; which means, to connect them to one another, we will
have to think of the configuration of the rift (Gestalt/Riß) as taking place
in a frame-work of strife (Ge-stell/Streit) that is composed through a system
of slots (Gefüge/Fuge) or structured openings." 

— Quotation from page 197 of Schufreider, Gregory (2008):
"Sticking Heidegger with a Stela: Lacoue-Labarthe, art and politics."
Pp. 187-214 in David Pettigrew & François Raffoul (eds.), 
French Interpretations of Heidegger: An Exceptional Reception.
State University of New York Press, 2008.

Update at 5:14 AM ET Wednesday, August 3, 2022 —

See also "six-set" in this journal.

"There is  such a thing as a six-set."
— Saying adapted from a 1962 young-adult novel.

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 

Sunday, July 31, 2022

The Space Joker: A Shiva for Star Trek

Filed under: General — m759 @ 9:12 pm

"Show me all  the Natalie Portmans!"

Domingo for Ramos*

Filed under: General — m759 @ 10:31 am

The reference to Vallega-Neu in posts that last night were tagged
The Ereignis Sanction leads to . . .

Heidegger’s ‘Contributions to Philosophy.’ An Introduction
(Indiana University Press, 2003).

That book is about . . .

Martin Heidegger, Contributions to Philosophy (From Enowning) ,
trans. Parvis Emad and Kenneth Maly (Bloomington:
Indiana University Press, 1999). German edition:
Beiträge zur Philosophie (vom Ereignis) ,
ed. F.-W. von Herrmann, Gesamtausgabe, vol. 65
(Frankfurt a. M.: Klostermann, 1989).

* See today's news and a Log24 search for "Philippine."

For Camp Sontag*

Filed under: General — Tags: , — m759 @ 4:21 am
 

"We need the word 'metaphor' for the whole double unit, and to use it sometimes for one of the two components in separation from the other is as injudicious as that other trick by which we use 'the meaning' here sometimes for the work that the whole double unit does and sometimes for the other component–the tenor, as I am calling it–the underlying idea or principal subject which the vehicle or figure means. It is not surprising that the detailed analysis of metaphors, if we attempt it with such slippery terms as these, sometimes feels like extracting cube-roots in the head."​

— I. A. Richards, The Philosophy of Rhetoric .
Oxford University Press, 1936.

The above quotation was appropriated  from
https://www.thoughtco.com/tenor-metaphors-1692531 .

* See yesterday's post Summer Camp.

The Ereignis Sanction: Traumlogik Continued.

Filed under: General — m759 @ 3:36 am

The posts of February 1, 2, and 3, 2020, have now 
been tagged "The Ereignis Sanction."

Saturday, July 30, 2022

Literary Figures

Filed under: General — m759 @ 7:48 pm

"… the tesseract, identified with a figure too inclusive,
contradictory, and all-pervasive to be seen as a character,
connects multiple dimensions in a manner counter to
ordinary thought…."

— Catherine Flynn, "From Dowel to Tesseract" (2016)

As does the I Ching .

Modal Diamond Box

Filed under: General — m759 @ 10:54 am
 

A  mnemonic  from a course titled
Galois Connections and Modal Logics“—

“Traditionally, there are two modalities, namely,
possibility and necessity. The basic modal operators
are usually written box (square) for necessarily
and diamond (diamond) for possibly.
Then, for example, diamondP  can be read as
‘it is possibly the case that P .'”

See also Intensional Semantics , lecture notes
by Kai von Fintel and Irene Heim, MIT,
Spring 2007 edition—

“The diamond  symbol for possibility is due to C.I. Lewis, first introduced in Lewis & Langford (1932), but he made no use of a symbol for the dual combination ¬¬. The dual symbol  was later devised by F.B. Fitch and first appeared in print in 1946 in a paper by his doctoral student Barcan (1946). See footnote 425 of Hughes & Cresswell (1968). Another notation one finds is L for necessity and M for possibility, the latter from the German möglich  ‘possible.’”

Barcan, Ruth C.: 1946. “A Functional Calculus of First Order Based on Strict Implication.” Journal of Symbolic Logic, 11(1): 1–16. URL http://www.jstor.org/pss/2269159.

Hughes, G.E. & Cresswell, M.J.: 1968. An Introduction to Modal Logic. London: Methuen.

Lewis, Clarence Irving & Langford, Cooper Harold: 1932. Symbolic Logic. New York: Century.

For less rigorous remarks, search Log24 for Modal Diamond Box.

Summer Camp

Filed under: General — Tags: — m759 @ 1:07 am

Or: The Sontag Puzzlement

Wikipedia on "Heavenly Creatures"

"Juliet introduces Pauline to the idea of 'the Fourth World',
a Heaven without Christians where music and art are
celebrated. Juliet believes she will go there when she dies.
Certain actors and musicians have the status of saints in
this afterlife, such as singer Mario Lanza, with whom
both girls are obsessed."

   Related material — Sontag + Camp .

Friday, July 29, 2022

… From the Stadium

Filed under: General — Tags: — m759 @ 12:05 pm

(A sequel to the previous post — "To the Lighthouse")

From that same date . . .

Log24 on August 5, 2002 —

"To really know a subject you've got to learn a bit of its history."

— John Baez, August 4, 2002

"We both know what memories can bring;
They bring diamonds and rust."

—  Joan Baez, April 1975 

"Venn considered three discs R, S, and T as typical subsets of a set U. The intersections of these discs and their complements divide U into 8 nonoverlapping regions."

— History of Mathematics at St. Andrews

"Who would not be rapt by the thought of such marvels?"

— Saint Bonaventure on the Trinity

"Who would not be rapt?" . . . Cristin Milioti? —

'The Resort' S1E1 - The 2007 Razr

To the Lighthouse Continues.

Filed under: General — Tags: — m759 @ 9:18 am

Midrash on Woolf for Reiner —

Illustrated! —

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