Log24

Saturday, March 30, 2024

King Solomon’s Minecraft

Filed under: General — Tags: — m759 @ 11:34 am

See as well Aesthetics in Academia.

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."

Thursday, March 24, 2022

Mathematics and Narrative: Solomon vs. the Wicked Queen

Filed under: General — m759 @ 5:19 pm

"Solomon Golomb’s classic book Shift Register Sequences,
published in 1967—based on his work in the 1950s—
went out of print long ago. But its content lives on. . . ."

For part of that content, see Stencils .

A :Log24 post from the date of Golomb's death —

See as well other posts on Mathematics and Narrative.

Thursday, January 20, 2022

The Solomon Pill

Filed under: General — Tags: — m759 @ 1:26 pm

"Howard Solomon was building the pharmaceutical company
Forest Laboratories, not by manufacturing drugs but by
licensing them. In his search for deals in the United States and
Europe, he learned about citalopram, a Danish antidepressant."

Richard Sandomir, New York Times , Friday, Jan. 14, 2022

" '… he’d talk about Verdi writing "Falstaff" in his 80s,' Andrew Solomon
said. ' "Imagine that," he’d say, "in his 80s, he wrote some of the greatest
music ever written." That was the path he hoped to follow.' ”

Saturday, August 28, 2021

Solomon’s Super*  Cube…

Filed under: General — Tags: , , , , , — m759 @ 1:33 pm

Geometry for Jews  continues.

210828-Golomb-2x2x2-Super_Cube.jpg (500×373)

The conclusion of Solomon Golomb's
"Rubik's Cube and Quarks,"
American Scientist , May-June 1982 —

Related geometric meditation —
Archimedes at Hiroshima
in posts tagged Aitchison.

 

* As opposed to Solomon's Cube .

Tuesday, August 17, 2021

A Question for Solomon

Filed under: General — m759 @ 1:20 pm

The previous post, Mythical Figure, suggests a review of posts
tagged Solomon Marcus.

See as well . . .

Friday, March 1, 2019

Solomon and the Image

Filed under: General — Tags: , , , — m759 @ 2:27 am

"Maybe an image is too strong
Or maybe is not strong enough."

— "Solomon and the Witch,"
      by William Butler Yeats

Wednesday, September 14, 2016

The Fourth Solomon

Filed under: General — m759 @ 10:30 am

See the three dead Solomons in a Log24 post of May 8, 2016.

See also two posts from July on the day Solomon Feferman died —

A sample of the work of Feferman —

See also a tribute to Feferman respectively .

Sunday, May 8, 2016

The Three Solomons

Earlier posts have dealt with Solomon Marcus and Solomon Golomb,
both of whom died this year — Marcus on Saint Patrick's Day, and
Golomb on Orthodox Easter Sunday. This suggests a review of
Solomon LeWitt, who died on Catholic Easter Sunday, 2007.

A quote from LeWitt indicates the depth of the word "conceptual"
in his approach to "conceptual art."

From Sol LeWitt: A Retrospective , edited by Gary Garrels, Yale University Press, 2000, p. 376:

 

THE SQUARE AND THE CUBE
by Sol LeWitt

"The best that can be said for either the square or the cube is that they are relatively uninteresting in themselves. Being basic representations of two- and three-dimensional form, they lack the expressive force of other more interesting forms and shapes. They are standard and universally recognized, no initiation being required of the viewer; it is immediately evident that a square is a square and a cube a cube. Released from the necessity of being significant in themselves, they can be better used as grammatical devices from which the work may proceed."

"Reprinted from Lucy R. Lippard et al ., “Homage to the Square,” Art in America  55, No. 4 (July-August 1967): 54. (LeWitt’s contribution was originally untitled.)"

See also the Cullinane models of some small Galois spaces

Some small Galois spaces (the Cullinane models)

Thursday, May 5, 2016

Solomon’s Seal

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

Excerpt from a post of November 4, 2009

I. The structures in the Diamond Puzzle

Adam and God (Sistine Chapel), with Jungian Self-Symbol and Ojo de Dios (The Diamond Puzzle)

Click on image for Jungian background.

II: The structure on a recent cover of Semiotica

'Semiotica' cover and article by Solomon Marcus on Levi-Strauss's 'canonic formula' of myth

For some related material, see a search 
for Solomon Marcus in this  journal.

Wednesday, May 4, 2016

Solomon Golomb, 1932-2016

Filed under: General,Geometry — m759 @ 4:00 am

Material related to the previous post, "Symmetry" —

This is the group of "8 rigid motions
generated by reflections in midplanes"
of "Solomon's Cube."

Material from this journal on May 1, the date of Golomb's death —

"Weitere Informationen zu diesem Themenkreis
finden sich unter http://​www.​encyclopediaofma​th.​org/
​index.​php/​Cullinane_​diamond_​theorem
und
http://​finitegeometry.​org/​sc/​gen/​coord.​html ."

Friday, January 18, 2013

Solomon’s Rep-tiles

Filed under: General,Geometry — Tags: — m759 @ 1:04 pm

"Rep-tiles Revisited," by Viorel Nitica, in MASS Selecta: Teaching and Learning Advanced Undergraduate Mathematics ,  American Mathematical Society, 2003—

"The goal of this note is to take a new look at some of the most amazing objects discovered in recreational mathematics. These objects, having the curious property of making larger copies of themselves, were introduced in 1962 by Solomon W. Golomb [2], and soon afterwards were popularized by Martin Gardner [3] in Scientific American…."

2.  S. W. Golomb: "Replicating Figures in the Plane," Mathematical Gazette  48, 1964, 403-412

3.  M. Gardner: "On 'Rep-tiles,' Polygons That Can Make Larger and Smaller Copies of Themselves," Scientific American  208, 1963, 154-157

Two such "amazing objects"—

Triangle

Square

For a different approach to the replicating properties of these objects, see the square-triangle theorem.

For related earlier material citing Golomb, see Not Quite Obvious (July 8, 2012; scroll down to see the update of July 15.).

Golomb's 1964 Gazette  article may now be purchased at JSTOR for $14.

Thursday, July 26, 2012

Solomon’s Seal

Filed under: General,Geometry — Tags: , , , — m759 @ 12:00 pm

(Mathematics and Narrative, continued)

Narrative—

The Ring and The Stone from yesterday’s post, and…

“In Medieval Jewish, Christian and Islamic legends,
the Seal of Solomon was a magical signet ring
said to have been possessed by King Solomon….”

— Wikipedia article, Seal of Solomon

Mathematics—

IMAGE- Eric Temple Bell on the mathematics of 'Solomon's Seal' (in his 'Development of Mathematics')

A fact related to the mathematical
“Solomon’s seal” described above by Bell:

IMAGE- J.W.P. Hirschfeld on the mathematics of 'Solomon's Seal', with reference to Edge on the same topic

The reference to Edge is as follows—

[3] Edge, W. L., Quadrics over GF(2) and
their relevance for the cubic surface group
,
Canadian J. Maths. 11 (1959) ….

(This reference relates Hirschfeld’s remarks
quoted above to the 64-point affine space
illustrated below (via the associated
63-point projective  space PG (5, 2)).

As for the narrative’s Stone… 

See Solomon’s Cube.

IMAGE- 'Solomon's Cube'

Friday, August 26, 2011

Solomon’s Labyrinth

Filed under: General — m759 @ 1:20 pm

Some context for last night's post on group theorist Michael Aschbacher—

IMAGE- Ronald Solomon on the labyrinthine classification of finite simple groups

Tuesday, October 12, 2010

King Solomon’s Mind

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

"Always keep a diamond in your mind."

Tom Waits/Kathleen Brennan song performed by Solomon Burke at the Paradiso in Amsterdam

The Galois Quaternion

The Galois Quaternion

"The text is a two-way mirror
that allows me to look into
the life and times of the reader.
Who knows, someday i  may rise
to a text that will compel me
to push through to the other side."

The French Mathematician
   (Galois), by Tom Petsinis

 

http://www.log24.com/log/pix10B/101012-KingSolomonAlbum.jpg

Saturday, March 23, 2024

Alpha Bets

Filed under: General — Tags: , — m759 @ 6:31 am

"So you wanna play with magic?" — Katy Perry

Wednesday, November 22, 2023

For E. Lily Yu* — Devs Setting

Filed under: General — Tags: , , — m759 @ 12:49 pm
 

Friday, July 11, 2014

Spiegel-Spiel des Gevierts

Filed under: Uncategorized — m759 @ 12:00 PM

See Cube Symbology.

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

Da hats ein Eck 

* Author of Jewel Box: Stories  ( Erewhon Books, Oct. 24, 2023).

Sunday, November 19, 2023

Six Dimensions

Filed under: General — Tags: , — m759 @ 9:59 am

Heinlein:

"Sharpie, we have condensed six dimensions into four,
then we either work by analogy into six, or we have to use math
that apparently nobody but Jake and my cousin Ed understands.
Unless you can think of some way to project six dimensions into three–
you seem to be smart at such projections."

I closed my eyes and thought hard. "Zebbie, I don't think it can be done.
Maybe Escher could have done it."

Image-- Escher's 'Verbum'

Escher’s Verbum

Image-- Solomon's Cube

Solomon’s Cube

Friday, November 17, 2023

Classicism Continued: An Apotheosis of Modernity

Filed under: General — Tags: — m759 @ 12:34 pm
 

From Chapter 23, "Poetry," by Adam Parkes, in
A Companion to Modernist Literature and Culture,
edited by David Bradshaw and Kevin J. H. Dettmar,
Blackwell Companions to Literature and Culture,
© 2006 by Blackwell Publishing Ltd.

Writing in 1910–11, the English poet and critic T. E. Hulme claimed that the two major traditions in poetry, romanticism and classicism, were as different as a well and a bucket. According to the romantic party, Hulme explained, humankind is “intrinsically good, spoilt by circumstance”; that is, our nature is “a well, a reservoir full of possibilities.” For the classical party, however, human nature is “like a bucket”; it is “intrinsically limited, but disciplined by order and tradition to something fairly decent” (Hulme 1987: 117). But it was not only that romanticism and classicism were as dissimilar as a well and a bucket; their contents were different, too. To draw water from the well of romanticism was, in effect, to pour a “pot of treacle over the dinner table,” while the classical bucket was more likely to be full of little stones – or jewels, perhaps. Romanticism, in Hulme’s view, was the result of displaced religious fervor; it represented the return of religious instincts that the “perverted rhetoric of Rationalism” had suppressed, so that “concepts that are right and proper in their own sphere are spread over, and so mess up, falsify and blur the clear outlines of human experience” (Hulme 1987: 118). Classicism, by contrast, traded in dry goods – dry, hard goods, to be precise.

Hulme left little doubt as to which side he was on. “It is essential to prove,” he argued, “that beauty may be in small, dry things. The great aim is accurate, precise and definite description. . . . I prophesy that a period of dry, hard, classical verse is coming” (Hulme 1987: 131–3). If by “dry, hard, classical verse” Hulme meant poems looking like the fragments of Sappho, he didn’t have to wait long to see his prophecy fulfilled.

The hard sand breaks,
and the grains of it
are clear as wine.

Far off over the leagues of it,
the wind,

228

playing on the wide shore,
piles little ridges,
and the great waves
break over it.

So wrote Hilda Doolittle in “Hermes of the Ways,” the first poem that she signed “H. D., Imagiste” at the behest of her fellow American expatriate Ezra Pound. From Pound’s perspective, the Imagist movement that he co-founded in 1912 with H. D. and the English poet Richard Aldington was finished well before the First World War began in August 1914; throughout this war-torn decade, however, Imagism continued to spawn the poetry of “small, dry things” whose coming Hulme had predicted a few years before.

Indeed, modernist poets weren’t content merely to break down the extended heroic narratives – the “spilt religion,” as Hulme put it – of their treacly nineteenthcentury predecessors; they insisted on breaking down small things into ever-smaller particles and subparticles. This logic of disintegration is clearly at work in poems like “Hermes of the Ways,” where each line is metrically unique, creating a sense of perpetual freshness – an apotheosis of modernity, as it were.

REFERENCE

Hulme, T. E. (1987). Speculations: Essays on Humanism and the Philosophy of Art, ed. Herbert Read. London and New York: Routledge and Kegan Paul. First published 1924.

Compare and contrast:

Jeremy Gray,
Plato's Ghost: The Modernist Transformation of Mathematics,
Princeton University Press, first edition Sept. 22, 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—
indeed, 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…."

(Quoted at the webpage Solomon's Cube.)

Friday, November 10, 2023

Cube Mine

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

In memory of a former president of Boston University
Other posts now tagged Cube Mine.

Related entertainment —

Friday, October 13, 2023

Hungarian Puzzle

Filed under: General — Tags: — m759 @ 8:25 pm

See "Cube Space" + Lovasz.

This search was suggested by . . .

The conclusion of Solomon Golomb's
"Rubik's Cube and Quarks,"
American Scientist , May-June 1982 —

Artbox.group

Filed under: General — Tags: — m759 @ 2:03 pm

This new URL will forward to http://m759.net/wordpress/?s=Solomon+Cube.

Monday, May 15, 2023

Boolean Functions Review

Filed under: General — Tags: , — m759 @ 1:25 pm

The previous post included an illustration by Solomon Golomb
from his 1959 paper "On the Classification of Boolean Functions."

This suggests a review of some later work in this area —

This post was suggested by the word "Boolean" in a May 10
ChatGPT response —

In the above, "Boolean algebras" should be "Boolean functions,"
as indicated by Harrison's 1964 remarks.

Wednesday, May 10, 2023

Saving the Appearances

Filed under: General — Tags: , — m759 @ 2:18 pm

Douglas Hofstadter —

“… I realized that to me,
Gödel and Escher and Bach
were only shadows
cast in different directions by
some central solid essence.
I tried to reconstruct
the central object, and
came up with this book.”

Goedel Escher Bach cover

Related images —

Image-- Escher's 'Verbum'

Escher’s Verbum

Image-- Solomon's Cube

Solomon’s Cube

Thursday, April 20, 2023

Alphabet Meets Gestalt . . .

Filed under: General — Tags: , , — m759 @ 2:25 pm

Continued from April 18 .

"Working with words to create art
and working with your hands to create art
seem like two separate activities to me."

Cover artist, The New Yorker , on April 17

See also Alphabet Blocks in this  journal
as well as Escher's Verbum.

Image-- Escher's 'Verbum'

Escher’s Verbum

Image-- Solomon's Cube

Solomon’s Cube

Saturday, February 11, 2023

Zwei Seelen

Filed under: General — Tags: — m759 @ 7:39 pm

"Zwei Seelen wohnen, ach! in meiner Brust,
die eine will sich von der andern trennen:
Die eine hält in derber Liebeslust
sich an die Welt mit klammernden Organen;
die andre hebt gewaltsam sich vom Dust
zu den Gefilden hoher Ahnen."

— Faust 1, Vers 1112 – 1117; Vor dem Tor. (Faust),
according to www.gutzitiert.de.

A version in English "In me there are two souls."

This post was suggested by  a New York Times  obituary today.

Monday, January 16, 2023

Ready When You Are, C. B.

Filed under: General — m759 @ 12:23 pm

Monday, January 9, 2023

Theology and Narrative

Filed under: General — m759 @ 1:16 pm

The tortoise of the previous post suggests . . .

"Is it the good turtle soup
 or merely the mock?" 

Related material from the above
Toronto premiere date —

Solomon and the Ring.

Monday, November 28, 2022

Groups, Spaces, and Ripoffs

Filed under: General — Tags: — m759 @ 8:21 pm

"Rubik's Cube, and the simpler [2x2x2] Super Cube, represent
one form of mathematical and physical reality."

— Solomon W. Golomb, "Rubik's Cube and Quarks:
Twists on the eight corner cells of Rubik's Cube
provide a model for many aspects of quark behavior
,"
American Scientist , Vol. 70, No. 3 (May-June 1982), pp. 257-259 

From the last (Nov. 14, 2022) of the Log24 posts now tagged Groups and Spaces

From the first (June 21, 2010) of the Log24 posts now tagged Groups and Spaces

Thursday, November 10, 2022

For Students of the Forked Tongue

Filed under: General — Tags: , , , — m759 @ 11:42 am

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

The above 1975 book by Robert Greer Cohn, Modes of Art, is
Volume I of a planned three-volume work.

The passage below is from a review of Cohn's Vol. II, Ways of Art — 

Franklin, Ursula (1987) "Book Review: A Critical Work II.
Ways of Art: Literature. Music, Painting in France 
,"
Grand Valley Review : Vol. 3: Iss. 1, Article 19. Available at: http://scholarworks.gvsu.edu/gvr/vol3/iss1/19 .

. . . .

Those not familiar with the author's epistemology should begin with Appendix A of Ways of Art , a schematic demonstration of his tetrapolar-polypolar-dialectic, especially as it concerns the development of the French novel within the European tradition. But this dialectic, which has antecedents in Kierkegaard, Mallarme and Joyce, underlies all art, because: "this dimensional pulsation, or tetrapolar (and polypolar) higher vibrancy is, in short, the stuff of life: life is vibrant in this more complex way as well as in the more bipolar sense" (7). Cohn shows that "far out enough" the male or linear and the female or circular, the male vertical and the female horizontal dimensions "tend to merge as in relativity theory" (19). Ways of Art  shows us the way through a historical becoming of art in its complex dialectic in which the metonymic (horizontal) axis constantly interrelates with the metaphoric (vertical). "Life is the mother, art the father" (vii); hence Cohn's quarrel with most contemporary Feminism, which is pronounced throughout the volume. Firmly grounded in its author's tetra-polypolar epistemology, this beautiful book becomes, however, at no point dryly abstract; it is the mature work of a true humanist who stands in clear and open opposition to the dehumanizing trend of "the quasi-scientific reductionism and abstract gimmickry of a great deal of current academic literary study, bellwethered by the structuralists, post-structuralists, and deconstructionists" (vi). Abundant footnotes constitute a substantial part of Ways of Art , on occasion developing insights almost into essays demonstrating crucial points along the general flow of the tradition from "Obscure Beginnings;' the opening chapter, to our "Contemporaries;' the last.

Cohn reminds us that "In the Beginning was the Word;' for the Judaeo-Christian tradition at least, which his study fervently embraces; thus, for example, in Appendix 0 on "The Dance of the Sexes;' he censures "those who live by slogans, camps, and peer-opinion, the countless little bastard cults which characterize an era which has massively veered away from our free and beautiful Greco-Judaeo-Christian tradition" (332). Cohn traces man's way and that of his myths and rituals culminating in his art from that beginning along the lines of Freud, Neumann and Cassirer, and many others, always demonstrating the underlying polypolar dialectical rhythm. Thus in "From Barbarism to Young Culture;' we follow the Celts to Druidic ritual, Hebrew beginnings to the Psalms, Dionysian ritual to Greek tragedy, and thence to the beginnings of French dramatic literature originating in the Quem quaeritis sequence of the medieval Mass. Along the way arises artistic symbolism, for Cohn synonymous with "effective poetry;' to finally "ripen in France as never before" (99). Table I (134) graphs this development from the twelfth to the late nineteenth and early twentieth centuries. The author traces the rise of the artistic vocation from its antecedents in the double function of bard and priest, with the figure of Ronsard at the crossroads of that dying institution and the nascent concept of personal glory. "The Enlightenment Vocation" is exemplified in Montaigne, who humanizes the French cultural elite and points the way to French classicism and, farther down the road, after the moral collapse with the outgoing reign of Louis XIV, toward the Age of Reason. Clearly the most significant figure of the French Enlightenment for all of Western civilization is Rousseau, and Cohn beautifully shows us why this is so. Subsequently, "the nineteenth-century stage of the writer's journey will lead, starting from the crossroads of Rousseau, primarily in these two directions: the imperialistic and visionary prose of Balzac, the equally ambitious poetry of Mallarme", brothers under the skin" (199). And these two paths will then be reconciled in Proust's monumental A la recherche du temps perdu .

. . . .

Monday, October 31, 2022

Folklore vs. Mathematics

Filed under: General — Tags: , , , — m759 @ 5:59 pm


Folklore —
 

Earlier in that same journal . . .

The 1955 Levi-Strauss 'canonic formula' in its original context of permutation groups


Mathematics —
 

Webpage demonstrating symmetries of 'Solomon's Cube'

Saturday, June 25, 2022

Gödel, Escher, Bach

Filed under: General — Tags: , — m759 @ 12:31 pm

Image-- Escher's 'Verbum'

Escher’s Verbum

Image-- Solomon's Cube

Solomon’s Cube

Tuesday, June 21, 2022

For the Church of Synchronology*

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

'The Klein Correspondence' at Cambridge University Press, in a 2009 book on Twistor Geometry

See also this journal on the above Cambridge U. Press date.

"There are many places one can read about twistors
and the mathematics that underlies them. One that
I can especially recommend is the book Twistor Geometry
and Field Theory
, by Ward and Wells."

— Peter Woit, "Not Even Wrong" weblog post, March 6, 2020.

* A fictional entity. See Synchronology in this journal.

Friday, May 6, 2022

Interality and the Bead Game

Filed under: General — Tags: , , — m759 @ 3:00 pm

WIkipedia on the URL suffix ".io" —

"In computer science, "IO" or "I/O" is commonly used
as an abbreviation for input/output, which makes the
.io domain desirable for services that want to be
associated with technology. .io domains are often used
for open source projects, application programming
interfaces ("APIs"), startup companiesbrowser games,
and other online services."

An association with the Bead Game from a post of April 7, 2018

IMAGE- 'Solomon's Cube'

Glasperlenspiel  passage quoted here in Summa Mythologica 

“"I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”

A less poetic meditation on the above 4x4x4 design cube —

"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."

See also a related remark by Lévi-Strauss in 1955

"…three different readings become possible:
left to right, top to bottom, front to back."

The recent use by a startup company of the URL "interality.io" suggests
a fourth  reading for the 1955 list of Lévi-Strauss — in and out
i.e., inner and outer group automorphisms —  from a 2011 post
on the birthday of T. S. Eliot :

A transformation:

Inner and outer group automorphisms

Click on the picture for details.

Interality and the I Ching

Filed under: General — Tags: , , — m759 @ 12:57 am

See "Flusser and the I Ching," by Peter Zhang.

Zhang has written extensively on the concept of "interality,"
a term coined by his colleague Geling Shang.

For interality as the mathematics underlying the natural
automorphism group of the I Ching, see my own work.

Sunday, April 24, 2022

Structuralism: Three Betweens

Filed under: General — Tags: , , , — m759 @ 10:44 am
 

Tuesday, November 3, 2009

Summa Mythologica

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

Book review by Jadran Mimica in Oceania, Vol. 74, 2003:

"In his classic essay of 1955 'The Structural Study of Myth' Levi-Strauss came up with a universal formula of mythopoeic dynamics

[fx(a) : fy(b) :: fx(b) : fa-1(y)]

that he called canonical 'for it can represent any mythic transformation'. This formulation received its consummation in the four massive Mythologiques volumes, the last of which crystallises the fundamental dialectics of mythopoeic thought: that there is 'one myth only' and the primal ground of this 'one' is 'nothing'. The elucidation of the generative matrix of the myth-work is thus completed as is the self-totalisation of both the thinker and his object."

So there.

At least one mathematician has claimed that the Levi-Strauss formula makes sense. (Jack Morava, arXiv pdf, 2003.)

I prefer the earlier (1943) remarks of Hermann Hesse on transformations of myth:

"…in the spirit of the Glass Bead Game, everything actually was all-meaningful, that every symbol and combination of symbols led not hither and yon, not to single examples, experiments, and proofs, but into the center, the mystery and innermost heart of the world, into primal knowledge. Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created."

Saturday, March 26, 2022

Box Geometry: Space, Group, Art  (Work in Progress)

Filed under: General — Tags: — m759 @ 2:06 am

Many structures of finite geometry can be modeled by
rectangular or cubical arrays ("boxes") —
of subsquares or subcubes (also "boxes").

Here is a draft for a table of related material, arranged
as internet URL labels.

Finite Geometry Notes — Summary Chart
 

Name Tag .Space .Group .Art
Box4

2×2 square representing the four-point finite affine geometry AG(2,2).

(Box4.space)

S4 = AGL(2,2)

(Box4.group)

 

(Box4.art)

Box6 3×2 (3-row, 2-column) rectangular array
representing the elements of an arbitrary 6-set.
S6  
Box8 2x2x2 cube or  4×2 (4-row, 2-column) array. S8 or Aor  AGL(3,2) of order 1344, or  GL(3,2) of order 168  
Box9 The 3×3 square. AGL(2,3) or  GL(2,3)  
Box12 The 12 edges of a cube, or  a 4×3  array for picturing the actions of the Mathieu group M12. Symmetries of the cube or  elements of the group M12  
Box13 The 13 symmetry axes of the cube. Symmetries of the cube.  
Box15 The 15 points of PG(3,2), the projective geometry
of 3 dimensions over the 2-element Galois field.
Collineations of PG(3,2)  
Box16 The 16 points of AG(4,2), the affine geometry
of 4 dimensions over the 2-element Galois field.

AGL(4,2), the affine group of 
322,560 permutations of the parts
of a 4×4 array (a Galois tesseract)

 
Box20 The configuration representing Desargues's theorem.    
Box21 The 21 points and 21 lines of PG(2,4).    
Box24 The 24 points of the Steiner system S(5, 8, 24).    
Box25 A 5×5 array representing PG(2,5).    
Box27 The 3-dimensional Galois affine space over the
3-element Galois field GF(3).
   
Box28 The 28 bitangents of a plane quartic curve.    
Box32 Pair of 4×4 arrays representing orthogonal 
Latin squares.
Used to represent
elements of AGL(4,2)
 
Box35 A 5-row-by-7-column array representing the 35
lines in the finite projective space PG(3,2)
PGL(3,2), order 20,160  
Box36 Eurler's 36-officer problem.    
Box45 The 45 Pascal points of the Pascal configuration.    
Box48 The 48 elements of the group  AGL(2,3). AGL(2,3).  
Box56

The 56 three-sets within an 8-set or
56 triangles in a model of Klein's quartic surface or
the 56 spreads in PG(3,2).

   
Box60 The Klein configuration.    
Box64 Solomon's cube.    

— Steven H. Cullinane, March 26-27, 2022

Wednesday, March 9, 2022

Supercube Space

Filed under: General — Tags: , — m759 @ 12:31 am

The new URL supercube.space forwards to http://box759.wordpress.com/.

The term supercube  is from a 1982 article by Solomon W. Golomb.

The related new URL supercube.group forwards to a page that
describes how the 2x2x2 (or eightfold, or "super") cube's natural
underlying automorphism group is Klein's simple group of order 168.

For further context, see the new URL supercube.art.

For some background, see the phrase Cube Space in this journal. 

Friday, December 31, 2021

Aesthetics in Academia

Filed under: General — Tags: — m759 @ 9:33 am

Related art — The non-Rubik 3x3x3 cube —

The above structure illustrates the affine space of three dimensions
over the three-element finite (i.e., Galois) field, GF(3). Enthusiasts
of Judith Brown's nihilistic philosophy may note the "radiance" of the
13 axes of symmetry within the "central, structuring" subcube.

I prefer the radiance  (in the sense of Aquinas) of the central, structuring 
eightfold cube at the center of the affine space of six dimensions over
the two-element field GF(2).

Thursday, November 25, 2021

Fire

Filed under: General — m759 @ 1:28 pm

"Faced with a larger surface than he had ever provided with facets,
in his desperation he had divided the diamond with imaginary lines,
treating each section as if it were a single small stone and arranging
the clusters of facets so they would interact with one another, as if they
were single facets in a smaller stone.  What if the final result lacked fire?"

— Novel* by Noah Gordon, who reportedly died on Monday, Nov. 22.

*

Novel by Noah Gordon, 'The Diamond of Solomon' (in German translation)

German translation of an April 1, 1979, novel.

Thursday, November 4, 2021

Socrates — “One, Two, Three … But where is the Fourth?”

Filed under: General — m759 @ 9:14 am

   See "Empty Quarter."

Tuesday, October 26, 2021

Katz! — The Musical…

Filed under: General — m759 @ 8:17 am

From a post of June 28, 2020 —

"David Solomon Katz was born in Brooklyn to Jewish immigrant parents from
Eastern Europe on Oct. 23, 1916, and grew up in a neighborhood famous for
the gangsters of Murder Inc. …."

Further context —

"His early movie credits include 'The Lusty Men' (1952), a western, directed by
Nicholas Ray and starring Susan Hayward and Robert Mitchum…."

—  Bruce Weber in The New York Times , Sept. 9, 2010

Not His First Rodeo

Wednesday, July 7, 2021

In Memoriam

Filed under: General — Tags: — m759 @ 2:36 am

Related material —

Monday, June 21, 2021

The Bauhaus Dance

Filed under: General — Tags: — m759 @ 10:04 pm

"If you have built castles in the air,
your work need not be lost;
that is where they should be.
Now put the foundations under them.”
— Henry David Thoreau

http://www.log24.com/log/pix11B/110714-BauhausRoof.jpg

Wednesday, March 3, 2021

Ink

Filed under: General — Tags: — m759 @ 3:09 pm

From this journal on Nov. 9-12, 2004:

Fade to Black

“…that ineffable constellation of talents that makes the player of rank: a gift for conceiving abstract schematic possibilities; a sense of mathematical poetry in the light of which the infinite chaos of probability and permutation is crystallized under the pressure of intense concentration into geometric blossoms; the ruthless focus of force on the subtlest weakness of an opponent.”

— Trevanian, Shibumi

“‘Haven’t there been splendidly elegant colors in Japan since ancient times?’

‘Even black has various subtle shades,’ Sosuke nodded.”

— Yasunari Kawabata, The Old Capital

The image “http://www.log24.com/log/pix05A/050619-AdReinhardt.gif” cannot be displayed, because it contains errors.
Ad Reinhardt

An Ad Reinhardt painting described in the entry of
noon, November 9, 2004, is illustrated below.

Ad Reinhardt,  Greek Cross

Ad Reinhardt, Abstract Painting, 1960-66.
Oil on canvas, 60 x 60 inches.  Solomon R. Guggenheim Museum

The viewer may need to tilt the screen to see that
this painting is not uniformly black, but is instead
a picture of a Greek cross, as described below.

“The grid is a staircase to the Universal…. We could think about Ad Reinhardt, who, despite his repeated insistence that ‘Art is art,’ ended up by painting a series of… nine-square grids in which the motif that inescapably emerges is a Greek cross.

Greek Cross

There is no painter in the West who can be unaware of the symbolic power of the cruciform shape and the Pandora’s box of spiritual reference that is opened once one uses it.”

— “Grids,” by Rosalind Krauss,
Meyer Schapiro Professor of Modern Art and Theory
at Columbia University
(Ph.D., Harvard U., 1969).

Related material from The New York Times  today —

Monday, November 9, 2020

Geometric Logic

Filed under: General — Tags: , — m759 @ 11:31 am

“Strawberry Fields Forever” — Song title

“Let me take you down
’Cause I’m going to Strawberry Fields
Nothing is real
And nothing to get hung about… ”  More

“Ah, but the strawberries, that’s, that’s where I had them,
they laughed at me and made jokes, but I proved
beyond the shadow of a doubt, and with geometric logic,
that a duplicate key to the wardroom icebox did exist,
and I’ve had produced that key if they hadn’t pulled
the Caine out of action.  I, I know now they were only
trying to protect some fellow officer. … Naturally, I can
only cover these things from memory. If I left anything out,
why, just ask me specific questions and I’ll be glad to
answer them, one by one.” — monologuedb.com

See also The Solomon Key .

Sunday, November 1, 2020

Art Theory

Filed under: General — Tags: , — m759 @ 2:37 pm

“If you have built castles in the air, your work need not be lost;
that is where they should be. Now put the foundations under them.”
— Henry David Thoreau

Between, or:  Interality Illustrated   (according to Sherald)

“We live in between the lines;
in between the cracks . . . .
That’s where the bonds are formed. ”

Amy Sherald

Sunday, June 28, 2020

Mystic Cristal Revelation

Filed under: General — Tags: — m759 @ 11:26 pm

In memory of actress Linda Cristal — The New York Times  today —

“After a modest film career, followed by guest roles on television,
Ms. Cristal auditioned for ‘The High Chaparral,’ a western
developed by David Dortort, the creator and producer of ‘Bonanza.’
In her telling, it was a memorable occasion.”

Judy Carne and Hoss in NBC’s “Bonanza,”  a nemesis of
CBS Sunday programming.

The New York Times  on “Bonanza” in 2010

“Mr. Dortort oversaw production of the show for most of its run. In addition
to telling stories based on historical events involving the Comstock Lode and
the oncoming Civil War, the show dealt with themes like racial prejudice and
religious tolerance. Mostly, though, its drama, and its popularity, were because
of its focus on the Cartwrights and their tightknit bond.

‘What is the message?’ Mr. Dortort said. ‘Love is the message.’

David Solomon Katz was born in Brooklyn to Jewish immigrant parents from
Eastern Europe on Oct. 23, 1916, and grew up in a neighborhood famous for
the gangsters of Murder Inc. …”

Wednesday, June 10, 2020

Count to X

Filed under: General — m759 @ 12:00 am

“X marks the spot” — Indiana Jones.

Indiana Jones’s love interest in “The Last Crusade” was Alison Doody.

See as well . . .

Patrick Swayze in 'King Solomon's Mines'

  Howdy, Doody.

Sunday, May 3, 2020

Into the Westworld

Filed under: General — Tags: , — m759 @ 2:03 pm

He beomes aware of something else… some other presence.
“Anybody here?” he says.
I am here.
He almost jumps, it is so loud. Or it seems loud. Then he wonders if
he has heard anything at all.
“Did you speak?”
No.
How are we communicating? he wonders.
The way everything communicates with everything else.
Which way is that?
Why do you ask if you already know the answer?

— Sphere   by Michael Crichton, Harvard ’64

Tuesday, March 24, 2020

No Ordinary Venue

Filed under: General — Tags: , — m759 @ 4:24 am

See the above title in this journal.  See also the Paradiso in Amsterdam.

 

Thursday, March 19, 2020

Class

Filed under: General — m759 @ 11:58 pm

In memory of Stephen Schwartz, a member of
the Harvard College class of 1963 —

Synchronology check —

Thursday, March 5, 2020

Pythagorean Letter Meets Box of Chocolates

Filed under: General — Tags: , , , , — m759 @ 10:30 am

Friday, July 11, 2014

Spiegel-Spiel des Gevierts

Filed under: Uncategorized — m759 @ 12:00 PM

See Cube Symbology.

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

Da hats ein Eck 

Monday, November 11, 2019

Time and Chance

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

http://www.log24.com/log/pix10B/101202-DreidelAndStone.jpg

The misleading image at right above is from the cover of
an edition of Charles Williams's classic 1931 novel 
Many Dimensions  published in 1993 by Wm. B. Eerdmans.

Compare and constrast —

Goedel Escher Bach cover

Cover of a book by Douglas Hofstadter

IMAGE- 'Solomon's Cube'

An Invariance of Symmetry

Monday, September 9, 2019

ART WARS at Harvard: The Wertham Professorship

Filed under: General — Tags: , — m759 @ 8:38 pm

See as well an obituary for Mrs. Wertham from 1987.

Related art —

Friday, July 11, 2014

Spiegel-Spiel des Gevierts

Filed under: Uncategorized — m759 @ 12:00 PM 

See Cube Symbology.

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

Da hats ein Eck 

For further details, search the Web for "Wertham Professor" + Eck.

Sunday, September 1, 2019

Verhexung

Filed under: General — Tags: — m759 @ 5:50 pm

Illustration from other posts now tagged
Cervantes Meets Pascal.

See as well Verhexung  in this journal.

This  post was suggested by . . .

Tuesday, August 6, 2019

The Final Page

Filed under: General — m759 @ 8:36 pm


Thursday, June 27, 2019

Group Actions on the 4x4x4 Cube

Filed under: General — Tags: — m759 @ 6:23 am

For affine  group actions, see Ex Fano Appollinis  (June 24)
and Solomon's Cube.

For one approach to Mathieu  group actions on a 24-cube subset
of the 4x4x4 cube, see . . .

For a different sort of Mathieu cube, see Aitchison.

Sunday, May 26, 2019

Sunday Shul: Connecting the Dots

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

"It's very easy to say, 'Well, Jeff couldn't quite connect these dots,'"
director Jeff Nichols told BuzzFeed News. "Well, I wasn't actually
looking at the dots you were looking at."

— Posted on March 21, 2016, at 1:11 p.m,
Adam B. Vary, BuzzFeed News Reporter

"Magical arrays of numbers have been the talismans of mathematicians and mystics since the time of Pythagoras in the sixth century B.C. And in the 16th century, Rabbi Isaac ben Solomon Luria devised a cosmological world view that seems to have prefigured superstring theory, at least superficially. Rabbi Luria was a sage of the Jewish cabalist movement — a school of mystics that drew inspiration from the arcane oral tradition of the Torah.

According to Rabbi Luria's cosmology, the soul and inner life of the hidden God were expressed by 10 primordial numbers [sic ], known as the sefirot. [Link added.]"

— "Things Are Stranger Than We Can Imagine,"
by Malcolm W. BrowneNew York Times Book Review ,
Sunday, March 20, 1994

Monday, May 13, 2019

Doris Day at the Hudson Rock

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

" 'My public image is unshakably that of
America’s wholesome virgin, the girl next door,
carefree and brimming with happiness,' 
she said in Doris Day: Her Own Story
a 1976 book . . . ."

From "Angels & Demons Meet Hudson Hawk" (March 19, 2013) —

From the March 1 post "Solomon and the Image," a related figure —

Tuesday, October 16, 2018

QDOS

Filed under: General — Tags: , — m759 @ 9:11 pm

For the title, see the Wikipedia article on the late Paul Allen.

See also . . .

Related material — the late Patrick Swayze in Ghost and King Solomon's Mines.


"Please wait as your operating system is initiated."

Her

Sunday, July 15, 2018

Jewish Oases

Filed under: General,Geometry — Tags: , — m759 @ 10:06 pm

"… Lincoln Plaza Cinemas, the Juilliard String Quartet,
and the Strand Book Store remained  oases
for cultural and intellectual stimulation."

John S. Friedman in The Forward , Jan. 21, 2018

Read more: 

https://forward.com/culture/392483/
how-fred-bass-dan-talbot-robert-mann
-shaped-new-york-culture/

From  the Oasis  in Steven Spielberg's "Ready Player One" (2018) —

I prefer, from a Log24 search for Flux Capacitor

Symbologist Robert Langdon views a corner of Solomon's Cube

From "Raiders of the Lost Images" —

"The cube shape of the lost Mother Box,
also known as the Change Engine,
is shared by the Stone in a novel by
Charles Williams, Many Dimensions .
See the Solomon's Cube webpage."

Sunday, July 8, 2018

Sixers*

Filed under: General,Geometry — m759 @ 12:00 pm

Eric Temple Bell, 'The Development of Mathematics'

See also Solomon's  cube.

* Title suggested by a 2011 dystopian novel.

Thursday, June 7, 2018

For Dan Brown

Filed under: General,Geometry — Tags: , , , — m759 @ 1:09 pm

See also Eightfold Trinity in this  journal.

Symbologist Robert Langdon views a corner of Solomon's Cube

Thursday, May 24, 2018

Bucharest Semiotics

Filed under: General — m759 @ 11:00 pm

See Solomon Marcus in this journal.

Related art —

 

Related fictions: The Seventh Function of Language  (2017)
and Lexicon  (2013).  I prefer Lexicon .

Saturday, May 19, 2018

Flux Capacitor

Filed under: General,Geometry — Tags: , , , — m759 @ 4:13 pm

For Tom Hanks and Dan Brown —

Symbologist Robert Langdon views a corner of Solomon's Cube

From "Raiders of the Lost Images" —

"The cube shape of the lost Mother Box,
also known as the Change Engine,
is shared by the Stone in a novel by
Charles Williams, Many Dimensions .
See the Solomon's Cube webpage."

See as well a Google search for flux philosophy
https://www.google.com/search?q=flux+philosophy.

Uh-Oh.

Filed under: General — Tags: — m759 @ 2:27 am

From the linked website —

The circle-in-a-triangle symbol is known as "the triangle of art" —

See as well a post of Feb. 27, 2018:  Raiders of the Lost Images.

Saturday, April 7, 2018

Sides

The FBI holding cube in "The Blacklist" —

" 'The Front' is not the whole story . . . ."

— Vincent Canby, New York Times  film review, 1976,
     as quoted in Wikipedia.

See also Solomon's Cube in this  journal.

IMAGE- 'Solomon's Cube'

Webpage demonstrating symmetries of 'Solomon's Cube'

Some may view the above web page as illustrating the
Glasperlenspiel  passage quoted here in Summa Mythologica 

“"I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”

A less poetic meditation on the above 4x4x4 design cube —

"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."

See also a related remark by Lévi-Strauss in 1955

"…three different readings become possible:
left to right, top to bottom, front to back."

Monday, March 12, 2018

Stein

Filed under: General,Geometry — m759 @ 9:55 pm

Stein reportedly died at 100 last Friday (March 9).

Related material —

Textiles by Stein arranged on the six faces of a cube —

Ethel Stein, "Circus & Slapstick," 1996

See also a less amusing approach to
patterns on the faces of a cube.

Monday, March 5, 2018

Sacramento Legend

Filed under: General — m759 @ 7:00 pm

"Russell M. Solomon’s story was a Sacramento legend . . . ."

Tuesday, February 27, 2018

Raiders of the Lost Images

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

On the recent film "Justice League" —

From DC Extended Universe Wiki, "Mother Box" —

"However, during World War I, the British rediscovered
mankind's lost Mother Box. They conducted numerous studies
but were unable to date it due to its age. The Box was then
shelved in an archive, up until the night Superman died,
where it was then sent to Doctor Silas Stone, who
recognized it as a perpetual energy matrix. . . ." [Link added.]

The cube shape of the lost Mother Box, also known as the
Change Engine, is shared by the Stone in a novel by Charles Williams,
Many Dimensions . See the Solomon's Cube webpage.

See too the matrix of Claude Lévi-Strauss in posts tagged
Verwandlungslehre .

Some literary background:

Who speaks in primordial images speaks to us
as with a thousand trumpets, he grips and overpowers,
and at the same time he elevates that which he treats
out of the individual and transitory into the sphere of
the eternal. 
— C. G. JUNG

"In the conscious use of primordial images—
the archetypes of thought—
one modern novelist stands out as adept and
grand master: Charles Williams.
In The Place of the Lion  he incarnates Plato’s
celestial archetypes with hair-raising plausibility.
In Many Dimensions  he brings a flock of ordinary
mortals face to face with the stone bearing
the Tetragrammaton, the Divine Name, the sign of Four.
Whether we understand every line of a Williams novel
or not, we feel something deep inside us quicken
as Williams tells the tale.

Here, in The Greater Trumps , he has turned to
one of the prime mysteries of earth . . . ."

— William Lindsay Gresham, Preface (1950) to
Charles Williams's The Greater Trumps  (1932)

For fans of what the recent series Westworld  called "bulk apperception" —

Saturday, February 10, 2018

Into the Upside Down

Filed under: General — m759 @ 10:45 am

(Title suggested by the TV series Stranger Things )

" 'Untitled' (2016) is the most recent painting in the show
and includes one of Mr. Johns’s recurring images of a ruler."

— Image caption in an article by Deborah Solomon
     in The New York Times  online, Feb. 7, 2018
 

From a Log24 search for "Ruler"

Related art —

See also, in this journal, Magic Mountain and Davos.

Einstein and Thomas Mann, Princeton, 1938

Tuesday, January 16, 2018

The Pentagram Papers

Filed under: General,Geometry — Tags: , , — m759 @ 9:16 am

Other intersection-points-counting material —

The Finkelstein Talisman:

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

See also Hanks + Cube in this journal —

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube.

Thursday, December 21, 2017

For Winter Solstice 2017

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 10:30 am

A review —

Some context —

Webpage demonstrating symmetries of 'Solomon's Cube'

Tuesday, October 24, 2017

Visual Insight

Filed under: G-Notes,General,Geometry — m759 @ 1:00 pm

The most recent post in the "Visual Insight" blog of the
American Mathematical Society was by John Baez on Jan. 1, 2017


A visually  related concept — See Solomon's Cube in this  journal.
Chronologically  related — Posts now tagged New Year's Day 2017.
Solomon's cube is the 4x4x4 case of the diamond theorem — 

Tuesday, October 10, 2017

The 35-Year Wait

Filed under: G-Notes,General,Geometry — m759 @ 11:17 am

From the Web this morning —

A different 35-year wait:

A monograph of August 1976 —

Thirty-five years later, in a post of August 2011, "Coordinated Steps" —

'The Seven Dwarfs and their Diamond Mine

"SEE HEAR READ" — Walt Disney Productions

Some other diamond-mine productions —

 Image -- The cast of 1937's 'King Solomon's Mines' goes back to the future

Sunday, July 30, 2017

Sermon: MS R I

Filed under: General,Geometry — Tags: — m759 @ 9:57 am

From Solomon's Cube

"Here MSRI, an acronym for Mathematical Sciences Research Institute,
is pronounced 'Misery.' See Stephen King [and] K.C. Cole . . . ."

From a manuscript by Mikhail Gromov cited yesterday in MSRI Program —

Quotes from a founder of geometric group theory

Monday, July 24, 2017

Penguin Classics Deluxe Edition

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

The above title was suggested by a film trailer quoted here Saturday

" Jeremy Irons' dry Alfred Pennyworth:
'One misses the days when one's biggest concerns
were exploding wind-up penguins.' "

"Penguin Classics Deluxe Edition" describes, among other books,
an edition of the I Ching  published on December 1, 2015.

Excerpt from this journal on that date

Tuesday, December 1, 2015

Verhexung

Filed under: Uncategorized — m759 @ 9:00 PM 

(Continued)

"The positional meaning of a symbol derives from
its relationship to other symbols in a totality, a Gestalt,
whose elements acquire their significance from the
system as a whole."

— Victor Turner, The Forest of Symbols , Ithaca, NY,
Cornell University Press, 1967, p. 51, quoted by
Beth Barrie in "Victor Turner."

(Turner pioneered the use of the term "symbology,"
a term later applied by Dan Brown to a fictional
scholarly pursuit at Harvard.)

. . . .

Related material —

IMAGE by Cullinane- 'Solomon's Cube' with 64 identical, but variously oriented, subcubes, and six partitions of these 64 subcubes

The I Ching's underlying group has 1,290,157,424,640 permutations.

Thursday, June 22, 2017

Face Henge

Filed under: General,Geometry — Tags: , , — m759 @ 3:07 pm

With a hat tip to Vinnie Mancuso

Wednesday, June 21, 2017

Concept and Realization

Filed under: General,Geometry — Tags: , , — m759 @ 1:12 pm

Remark on conceptual art quoted in the previous post

"…he’s giving the concept but not the realization."

A concept See a note from this date in 1983:

IMAGE- 'Solomon's Cube'

A realization  

Webpage demonstrating symmetries of 'Solomon's Cube'

Not the best possible realization, but enough for proof of concept .

Tuesday, May 2, 2017

Image Albums

Filed under: General,Geometry — Tags: , , , , , — m759 @ 1:05 pm

Pinterest boards uploaded to the new m759.net/piwigo

Diamond Theorem 

Diamond Theorem Correlation

Miracle Octad Generator

The Eightfold Cube

Six-Set Geometry

Diamond Theory Cover

Update of May 2 —

Four-Color Decomposition

Binary Galois Spaces

The Galois Tesseract

Update of May 3 —

Desargues via Galois

The Tetrahedral Model

Solomon's Cube

Update of May 8 —

Art Space board created at Pinterest

Saturday, April 1, 2017

Beyond All Recognition

Filed under: General,Geometry — m759 @ 10:45 am

Prequel —

Cube symmetry subgroup of order 8 from 'Geometry and Symmetry,' Paul B. Yale, 1968, p.21

Note that Yale's die design and use of the phrase "rigid motions"
differ from those in the webpage "Solomon's Cube."

Wednesday, March 29, 2017

Art Space Illustrated

Another view of the previous post's art space  —

IMAGE by Cullinane- 'Solomon's Cube' with 64 identical, but variously oriented, subcubes, and six partitions of these 64 subcubes

More generally, see Solomon's Cube in Log24.

See also a remark from Stack Exchange in yesterday's post Backstory,
and the Stack Exchange math logo below, which recalls the above 
cube arrangement from "Affine groups on small binary spaces" (1984).

IMAGE- Current math.stackexchange.com logo and a 1984 figure from 'Notes on Groups and Geometry, 1978-1986'

Friday, March 10, 2017

Transformers

Filed under: General,Geometry — Tags: , — m759 @ 1:00 pm

Or:  Y  for Yale  continued

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

See also Transformers in this journal and Y for Yale.

Thursday, March 2, 2017

Stories

Filed under: General,Geometry — Tags: , , — m759 @ 12:48 pm

"We tell ourselves stories in order to live." — Joan Didion

The New York Times Magazine  online today —

"As a former believer and now a nonbeliever, Carrère,
seeking answers, sets out, in The Kingdom , to tell
the story of the storytellers. He is trying to understand
what it takes to be able to tell a story, any story.
And what he finds, once again, is that you have to find
your role in it."

Wyatt Mason in The New York Times Magazine ,
     online March 2, 2017 

Like Tom Hanks?

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

Click image for related posts.

Sunday, February 26, 2017

Poetic Order

Filed under: General,Geometry — Tags: , — m759 @ 1:06 pm

Transformations acting on Solomon's Cube
furnish a model of poetic order.

Some backstory for Hollywood —

Hollywood analogue to Solomon's Cube in 'Transformers'

Saturday, February 18, 2017

Solid Symmetry (continued)

Filed under: General,Geometry — Tags: , , — m759 @ 12:00 pm

See Hanks + Cube in this journal For instance

Friday, July 11, 2014

Spiegel-Spiel des Gevierts

Filed under: Uncategorized — m759 @ 12:00 PM 

See Cube Symbology.

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

Da hats ein Eck 

Verbum

Filed under: General,Geometry — Tags: , , — m759 @ 3:00 am

The Log24 version  (Nov. 9, 2005, and later posts) —

VERBUM
SAT
SAPIENTI

 

Escher's 'Verbum'

Escher's Verbum


Solomon's Cube

Solomon's Cube
 

I Ching hexagrams as parts of 4x4x4 cube

Geometry of the I Ching

The Warner Brothers version

The Paramount version

See also related material in the previous post, Transformers.

Thursday, January 12, 2017

The Cherished Gift

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

From "Solomon's Cube" —

Related material —

"Is this a dagger I see before me?

"No." (A line suggested by Polanski's 2010 "The Ghost Writer")

Saturday, December 3, 2016

SIAM Publication

Filed under: General — m759 @ 10:01 am

For "the Trojan family" —

Related material on the late Solomon W. Golomb —

"While at JPL, Sol had also been teaching some classes
at the nearby universities: Caltech, USC and UCLA. In
the fall of 1962, following some changes at JPL—and
perhaps because he wanted to spend more time with
his young children— he decided to become a full-time
professor. He got offers from all three schools. He
wanted to go somewhere where he could 'make
a difference'. He was told that at Caltech 'no one has
any influence if they don’t at least have a Nobel Prize',
while at UCLA 'the UC bureaucracy is such that no one
ever has any ability to affect anything'. The result was
that—despite its much-inferior reputation at the time—
Sol chose USC. He went there in the spring of 1963 as
a Professor of Electrical Engineering—and ended up
staying for 53 years." — Stephen Wolfram, 5/25/16

See also Priority (Nov. 25) and "What's in a Name" (Dec. 1).

Monday, November 14, 2016

Flashback

Filed under: General,Geometry — Tags: — m759 @ 10:12 am

See also Solomon Marcus in this journal.

"Look out, kid, they keep it all hid." — Bob Dylan

Monday, October 3, 2016

Ein Eck

Filed under: General,Geometry — Tags: , — m759 @ 5:05 pm
 

Friday, July 11, 2014

Spiegel-Spiel des Gevierts

Filed under: Uncategorized — m759 @ 12:00 PM 

See Cube Symbology.

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

Da hats ein Eck 

Friday, September 9, 2016

There IS such a thing …

Filed under: General,Geometry — Tags: — m759 @ 12:00 pm

http://gregegan.customer.netspace.net.au/APPLETS/29/NonSimple4E.gif

See also Dueling Formulas,  Sinner or Saint?,  and The Zero Obit.

Friday, August 5, 2016

Sleight of Post

Filed under: General,Geometry — Tags: , , — m759 @ 1:00 pm

From an earlier Log24 post —

Friday, July 11, 2014

Spiegel-Spiel des Gevierts

Filed under: Uncategorized — m759 @ 12:00 PM 

See Cube Symbology.

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

Da hats ein Eck 

From a post of the next day, July 12, 2014 —

"So there are several different genres and tones
jostling for prominence within Lexicon :
a conspiracy thriller, an almost abstract debate
about what language can do, and an ironic
questioning of some of the things it’s currently used for."

Graham Sleight in The Washington Post 
     a year earlier, on July 15, 2013

For the Church of Synchronology, from Log24 on the next day — 

From a post titled Circles on the date of Marc Simont's death —

See as well Verhexung  in this journal.

Thursday, July 14, 2016

Symmetries and Correspondences

Filed under: General,Geometry — Tags: , , — m759 @ 7:30 pm

The title is that of a large-scale British research project
in mathematics. On a more modest scale

"Hanks + Cube" in this journal —

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

Block That Metaphor

Sunday, June 26, 2016

Common Core versus Central Structure

Filed under: General,Geometry — Tags: , — m759 @ 2:56 pm

Rubik's Cube Core Assembly — Swarthmore Cube Project, 2008 —

"Children of the Common Core" —

There is also a central structure within Solomon's  Cube

'Children of the Central Structure,' adapted from 'Children of the Damned'

For a more elaborate entertainment along these lines, see the recent film

"Midnight Special" —

Tuesday, June 21, 2016

The Central Structure

Filed under: General,Geometry — Tags: , , — m759 @ 8:00 am

“The central poem is the poem of the whole,
The poem of the composition of the whole”

— Wallace Stevens, “A Primitive like an Orb”

The symmetries of the central four squares in any pattern
from the 4×4 version of the diamond theorem  extend to
symmetries of the entire pattern.  This is true also of the
central eight cubes in the 4×4×4  Solomon’s cube .

Saturday, May 28, 2016

Plan 4

Filed under: General — Tags: , — m759 @ 2:45 am

See a search in this journal for "As Is."

Thursday, May 19, 2016

Kulturkampf

Filed under: General,Geometry — Tags: — m759 @ 2:27 am

From a check tonight of The New York Review of Books

These NYRB  stories from May 15 and May 13 suggest a
review of images on Ratner's Star  and on the Eye of God.

IMAGE- 'Ratner's Star,' by Don DeLillo (1976)

Above image reposted from Jan. 10, 2014

I. The structures in the Diamond Puzzle

Adam and God (Sistine Chapel), with Jungian Self-Symbol and Ojo de Dios (The Diamond Puzzle)

Click on image for Jungian background.

II: The structure on a recent cover of Semiotica

'Semiotica' cover and article by Solomon Marcus on Levi-Strauss's 'canonic formula' of myth

Above images reposted from May 5, 2016

Related material:  The previous post, Dueling Formulas.

Tuesday, May 17, 2016

Bullshit Studies

The originator of the phrase 'Fab Four' reportedly
died at 80 on Saturday, May 14, 2016.

This suggests a review of another noted four-set.

The above image is from a study of Lévi-Strauss's "Canonical Formula"

Midrash —

Log24 post titled 'As Is'

[Above photo of Lévi-Strauss and formula added June 6, 2016.]

Monday, May 9, 2016

Search for the Lost Theorem

Filed under: General,Geometry — Tags: — m759 @ 12:00 pm

The three Solomons of the previous post (LeWitt,
Marcus, and Golomb) suggest the three figures
-1, 0, and 1  symbols for the three elements
of the Galois field GF(3).  This in turn suggests a
Search for The Lost Theorem. Some cross-cultural
context:  The First of May, 2010.

Wednesday, May 4, 2016

Golomb and Symmetry

Filed under: General,Geometry — Tags: — m759 @ 12:00 pm

From the webpage Diamond Theory Bibliography

Golomb, Solomon W. 
Shift register sequences  (Revised edition)
Aegean Park Press, Laguna Hills, CA, 1982
   The fifteen "stencils" in Golomb's Fig. VIII-8, page 219,
   are the same as the fifteen affine hyperplanes that
   account for patterns' symmetry in diamond theory.
   This figure occurs in a discussion of Rademacher-
   Walsh functions.

Elsewhere

Tuesday, May 3, 2016

Symmetry

A note related to the diamond theorem and to the site
Finite Geometry of the Square and Cube —

The last link in the previous post leads to a post of last October whose
final link leads, in turn, to a 2009 post titled Summa Mythologica .

Webpage demonstrating symmetries of 'Solomon's Cube'

Some may view the above web page as illustrating the
Glasperlenspiel  passage quoted here in Summa Mythologica 

“"I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”

A less poetic meditation on the above web page* —

"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."

Update of Sept. 5, 2016 — See also a related remark
by Lévi-Strauss in 1955:  "…three different readings
become possible: left to right, top to bottom, front
to back."

* For the underlying mathematics, see a June 21, 1983, research note.

Wednesday, April 20, 2016

Symmetric Generation of a Simple Group

The reference in the previous post to the work of Guitart and
The Road to Universal Logic  suggests a fiction involving
the symmetric generation of the simple group of order 168.

See The Diamond Archetype and a fictional account of the road to Hell 

'PyrE' in Bester's 'The Stars My Destination'

The cover illustration below has been adapted to
replace the flames of PyrE with the eightfold cube.

IMAGE- 'The Stars My Destination' (with cover slightly changed)

For related symmetric generation of a much larger group, see Solomon’s Cube.

Tuesday, April 12, 2016

Slow Art

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

(Continued)

The American Mathematical Society today got around to
publishing an obituary for Solomon Marcus, a Bucharest
mathematician who died on St. Patrick's Day, March 17.

See as well this  journal on March 22.

Tuesday, March 22, 2016

The Zero Obit

Filed under: General,Geometry — Tags: — m759 @ 9:00 pm

From St. Patrick's Day 2016 —

Solomon Marcus obituary

See also posts mentioning
Terry Gilliam's film "The Zero Theorem."

Wednesday, January 13, 2016

Geometry for Jews

Filed under: General,Geometry — Tags: — m759 @ 7:45 am

(Continued from previous episodes)

'Games Played by Boole and Galois'

Boole and Galois also figure in the mathematics of space
i.e. , geometry.  See Boole + Galois in this journal.

Related material, according to Jung’s notion of synchronicity —

Saturday, January 2, 2016

The Beethoven Midrash

Filed under: General — m759 @ 3:33 am

From Commentary  magazine on Dec. 14, 2015

"Three significant American magazines started life in the 1920s.
The American Mercury , founded in 1924, met with the greatest
initial success, in large part because of the formidable reputations
of its editors, H.L. Mencken and George Jean Nathan, and it soon
became the country’s leading journal of opinion."

— Terry Teachout, article on the history of The New Yorker  

A search for "American Mercury" in this  journal yields a reference from 2003
to a book containing the following passage —

As Webern stated in "The Path to Twelve-Note Composition":

"An example: Beethoven's 'Six easy variations on a Swiss song.'
Theme: C-F-G-A-F-C-G-F, then backwards! You won't notice this
when the piece is played, and perhaps it isn't at all important,
but it is unity ." 

— Larry J. Solomon, Symmetry as a Compositional Determinant ,
     Chapter 8, "Quadrate Transformations"

This is the Beethoven piece uploaded to YouTube by "Music and such…"
on Dec. 12, 2009. See as well this journal on that same date.

Wednesday, December 2, 2015

Symbology

Filed under: General,Geometry — Tags: , — m759 @ 12:00 pm

Symbologist Robert Langdon views a corner of Solomon's Cube

Click image to search Log24
for Solomon + Stone.

Sunday, November 15, 2015

The Diamond and the Cube

Filed under: General,Geometry — Tags: — m759 @ 8:00 pm

Anyone who clicked on the Dirac search at the end of
the previous post, "Dirac's Diamond," may wonder why the
"Solomon's Cube" post of 11 AM Sunday, March 1, 2009,
appeared in the Dirac search results, since there is no
apparent mention of Dirac in that Sunday post.

Use the source

<!– See also "a linear transformation of V6… which preserves
the Klein quadric; in this way we arrive at the isomorphism of
Sym(8) withthe full orthogonal group O+(6; 2)." in "The
Classification of Flats in PG(9,2) which are External to the
Grassmannian G1,4,2 Authors: Shaw, Ron;
&#160;Maks, Johannes;&#160;Gordon, Neil; Source: Designs,
Codes and Cryptography, Volume 34, Numbers 2-3, February
2005 , pp. 203-227; Publisher: Springer.&#160; For more details,
see "Finite Geometry, Dirac Groups and the Table of Real
Clifford Algebras," by R. Shaw (U. of Hull), pp. 59-99 in
Clifford Algebras and Spinor Structures, by By Albert
Crumeyrolle, Rafa&#322; Ab&#322;amowicz, Pertti Lounesto,
published by Springer, 1995. –>

Tuesday, September 29, 2015

Quotes for Michaelmas

Filed under: General — Tags: — m759 @ 9:48 pm

A search in this journal for material related to the previous post
on theta characteristics yields

"The Solomon Key  is the working title of an unreleased
novel in progress by American author Dan Brown. 
The Solomon Key  will be the third book involving the
character of the Harvard professor Robert Langdon,
of which the first two were Angels & Demons  (2000) and 
The Da Vinci Code  (2003)." — Wikipedia

"One has O+(6) ≅ S8, the symmetric group of order 8! …."
 — "Siegel Modular Forms and Finite Symplectic Groups,"
by Francesco Dalla Piazza and Bert van Geemen, 
May 5, 2008, preprint.

"It was only in retrospect
that the silliness
became profound."

— Review of   
Faust in Copenhagen

"The page numbers
are generally reliable."

— Michaelmas 2007 

For further backstory, click the above link "May 5, 2008," 
which now leads to all posts tagged on080505

Saturday, April 25, 2015

Ghosts and Shadows

Filed under: General,Geometry — Tags: , , — m759 @ 5:31 pm

For Poetry Month

From the home page of Alexandre Borovik:

Book in progress: Shadows of the Truth

This book (to be published soon) can be viewed
as a sequel to Mathematics under the Microscope ,
but with focus shifted on mathematics as it was
experienced by children (well, by children who
became mathematicians). The cover is designed
by Edmund Harriss.

See also Harriss's weblog post of Dec. 27, 2008, on the death
of Harold Pinter: "The Search for the Truth Can Never Stop."

This suggests a review of my own post of Dec. 3, 2012,
"The Revisiting." A figure from that post:

The image “http://www.log24.com/theory/images/GEB.jpg” cannot be displayed, because it contains errors.

Thursday, February 26, 2015

Brit Award

Filed under: General,Geometry — m759 @ 1:06 am

"The Brit Awards are the British equivalent
of the American Grammy Awards." — Wikipedia 

Detail of an image from yesterday's 5:30 PM ET post:

Related material:

From a review: "Imagine 'Raiders of the Lost Ark'
set in 20th-century London, and then imagine it
written by a man steeped not in Hollywood movies
but in Dante and the things of the spirit, and you
might begin to get a picture of Charles Williams's
novel Many Dimensions ."

See also Solomon's Seal (July 26, 2012).

Monday, January 5, 2015

Gitterkrieg*

Filed under: General,Geometry — Tags: , — m759 @ 2:00 pm
 

Wednesday, March 13, 2013

Blackboard Jungle

Filed under: Uncategorized — m759 @ 8:00 AM 

From a review in the April 2013 issue of
Notices of the American Mathematical Society

"The author clearly is passionate about mathematics
as an art, as a creative process. In reading this book,
one can easily get the impression that mathematics
instruction should be more like an unfettered journey
into a jungle where an individual can make his or her
own way through that terrain."

From the book under review—

"Every morning you take your machete into the jungle
and explore and make observations, and every day
you fall more in love with the richness and splendor 
of the place."

— Lockhart, Paul (2009-04-01). 
A Mathematician's Lament:
How School Cheats Us Out of Our Most Fascinating
and Imaginative Art Form 
 (p. 92).
Bellevue Literary Press. Kindle Edition. 

Related material: Blackboard Jungle in this journal.

See also Galois Space and Solomon's Mines.

"I pondered deeply, then, over the
adventures of the jungle. And after
some work with a colored pencil
I succeeded in making my first drawing.
My Drawing Number One.
It looked something like this:

I showed my masterpiece to the
grown-ups, and asked them whether
the drawing frightened them.

But they answered: 'Why should
anyone be frightened by a hat?'"

The Little Prince

* For the title, see Plato Thanks the Academy (Jan. 3).

Wednesday, September 17, 2014

Raiders of the Lost Articulation

Tom Hanks as Indiana Langdon in Raiders of the Lost Articulation :

An unarticulated (but colored) cube:

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

A 2x2x2 articulated cube:

IMAGE- Eightfold cube with detail of triskelion structure

A 4x4x4 articulated cube built from subcubes like
the one viewed by Tom Hanks above:

Image-- Solomon's Cube

Solomon’s Cube

Saturday, July 12, 2014

Mars Package

Filed under: General,Geometry — Tags: , — m759 @ 8:00 pm

For Ursula K. Le Guin

“For me it is a sign that we have fundamentally different
conceptions of the work of the intelligence services.”

— Germany’s Chancellor Angela Merkel in
theguardian.com, Saturday, 12 July 2014, 14.32 EDT

Another sort of service, thanks to Dan Brown and Tom Hanks:

Friday, July 11, 2014

Spiegel-Spiel des Gevierts

Filed under: Uncategorized — m759 @ 12:00 PM 

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

Sequel

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

A sequel to the 1974 film
Thunderbolt and Lightfoot :

Contingent and Fluky

Some variations on a thunderbolt  theme:

Design Cube 2x2x2 for demonstrating Galois geometry

These variations also exemplify the larger
Verbum  theme:

Image-- Escher's 'Verbum'

Escher’s Verbum

Image-- Solomon's Cube

Solomon’s Cube

A search today for Verbum  in this journal yielded
a Georgetown 
University Chomskyite, Professor
David W. Lightfoot.

"Dr. Lightfoot writes mainly on syntactic theory,
language acquisition and historical change, which
he views as intimately related. He argues that
internal language change is contingent and fluky,
takes place in a sequence of bursts, and is best
viewed as the cumulative effect of changes in
individual grammars, where a grammar is a
'language organ' represented in a person's
mind/brain and embodying his/her language
faculty."

Some syntactic work by another contingent and fluky author
is related to the visual patterns illustrated above.

See Tecumseh Fitch  in this journal.

For other material related to the large Verbum  cube,
see posts for the 18th birthday of Harry Potter.

That birthday was also the upload date for the following:

See esp. the comments section.

Friday, July 11, 2014

Spiegel-Spiel des Gevierts

Filed under: General,Geometry — Tags: , — m759 @ 12:00 pm

See Cube Symbology.

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

Da hats ein Eck 

Friday, May 9, 2014

Models of Everything

Filed under: General,Geometry — Tags: , — m759 @ 11:16 am

“The About page contains detailed descriptions of the project….”

The Illustris project on constructing a model of the universe

For the mathematics of a simpler traditional Chinese model
of everything, see

Thursday, March 27, 2014

Diamond Space

Filed under: General,Geometry — Tags: , , , — m759 @ 2:28 pm

(Continued)

Definition:  A diamond space  — informal phrase denoting
a subspace of AG(6, 2), the six-dimensional affine space
over the two-element Galois field.

The reason for the name:

IMAGE - The Diamond Theorem, including the 4x4x4 'Solomon's Cube' case

Click to enlarge.

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