Tuesday, September 19, 2017

Time and Chance

Filed under: Uncategorized — Tags: — m759 @ 5:55 AM

(For Qohen Leth)

Friday, July 27, 2012

Raiders of the Lost Ring

Filed under: Uncategorized — Tags: , — m759 @ 11:30 AM

Wikipedia on a magical ring

IMAGE- Wikipedia article, 'Seal of Solomon'

Background—  The Ring and the Stone, a story linked to here Wednesday.

"By then he was familiar with the work of the Vienna Actionists….
He once said that he had his first taste of the movement
when he heard the screams of his mother’s dental patients
from her office next door to the family’s apartment."

Obituary of a Viennese artist who reportedly died Wednesday

"Is it safe?"

Thursday, July 26, 2012

Solomon’s Seal

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

(Mathematics and Narrative, continued)


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


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'

Saturday, April 21, 2012

Finding a Form

Filed under: Uncategorized — Tags: , — m759 @ 11:30 PM

In "Contact," Dr. Arroway  is shown the key to the Primer

In this journal, fictional symbologist Robert Langdon is shown a cube

Symbologist Robert Langdon views a corner of Solomon's Cube

"Confusion is nothing new." — Song lyric

Thursday, April 5, 2012

Meanwhile, back in 1950…

Filed under: Uncategorized — Tags: — m759 @ 10:30 AM

See also Solomon's Cube.

Friday, January 6, 2012

Defining Form

Filed under: Uncategorized — Tags: , — m759 @ 10:10 AM

IMAGE- MLA session, 'Defining Form,' chaired by Colleen Rosenfeld of Pomona College

Some related resources from Malcolm Lowry

"…his eyes ranged the Consul's books disposed quite neatly… on high shelves around the walls: Dogme et Ritual de la Haute Magie , Serpent and Siva Worship in Central America , there were two long shelves of this, together with the rusty leather bindings and frayed edges of the numerous cabbalistic and alchemical books, though some of them looked fairly new, like the Goetia of the Lemegaton of Solomon the King , probably they were treasures, but the rest were a heterogeneous collection…."

Under the Volcano , Chapter VI

— and from Matilde Marcolli

Seven books on analytical psychology

See also Marcolli in this morning's previous post, The Garden Path.

For the relevance of alchemy to form, see Alchemy in this journal.

Saturday, August 20, 2011

Castles in the Air

Filed under: Uncategorized — Tags: , — m759 @ 12:00 PM

"… the Jews have discovered a way to access a fourth spatial dimension."
— Clifford Pickover, description of his novel Jews in Hyperspace

"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

"King Solomon's Mines," 1937—

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

The image above is an illustration from  "Romancing the Hyperspace," May 4, 2010.

Happy birthday to the late Salomon Bochner.

Thursday, January 6, 2011

Epiphany Riddle

Filed under: Uncategorized — Tags: — m759 @ 11:32 AM

"Spaces and geometries, those which we perceive,
which we can’t perceive, or which only some of us perceive,
are a recurring theme in Against  the Day ."

Michael White

"大哉大哉  宇宙之谜
 美哉美哉  真理之源"

"Great indeed is the riddle of the universe.
 Beautiful indeed is the source of truth."

— Shing-Tung Yau, Chairman,
Department of Mathematics, Harvard University

"Always keep a diamond in your mind."

King Solomon at the Paradiso

IMAGE-- Imaginary movie poster- 'The Galois Connection'- from stoneship.org

Image from stoneship.org

Tuesday, December 7, 2010

The Tiffany Puzzle

Filed under: Uncategorized — Tags: — m759 @ 5:00 AM

Suggested by Dan Brown's remarks in today's Science Times  special section on puzzles—


For a fanciful linkage of the dreidel 's concept of chance
to The Stone 's concept of invariant law, note that the
New York Lottery evening number on Dec. 1 (the
beginning of Hanukkah) was 840. See also the number
840 in the final post (July 20, 2002) of a search for
Solomon's Cube.


Wednesday, June 16, 2010

Brightness at Noon

Filed under: Uncategorized — Tags: , — m759 @ 12:00 PM

David Levine's portrait of Arthur Koestler (see Dec. 30, 2009) —

Image-- Arthur Koestler by David Levine, NY Review of Books, Dec. 17, 1964, review of 'The Act of Creation'

Image-- Escher's 'Verbum'

Escher’s Verbum

Image-- Solomon's Cube

Solomon’s Cube

Image-- The 64 I Ching hexagrams in the 4 layers of the Cullinane cube

Geometry of the I Ching

See also this morning's post as well as
Monday's post quoting George David Birkhoff

"If I were a Leibnizian mystic… I would say that…
God thinks multi-dimensionally — that is,
uses multi-dimensional symbols beyond our grasp."

Tuesday, January 26, 2010


Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

From this journal:

Friday December 5, 2008

m759 @ 1:06 PM
Mirror-Play of
the Fourfold

For an excellent commentary
 on this concept of Heidegger,

View selected pages
from the book

Dionysus Reborn:

Play and the Aesthetic Dimension
in Modern Philosophical and
Scientific Discourse

(Mihai I. Spariosu,
Cornell U. Press, 1989)

Related material:
the logo for a
web page

Logo for 'Elements of Finite Geometry'

– and Theme and Variations.

Transition to the
Garden of Forking Paths–

(See For Baron Samedi)–

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

and Dissemination, by Jacques Derrida,
translated by Barbara Johnson,
London, Athlone Press, 1981–

Pages 354-355
On the mirror-play of the fourfold

Pages 356-357
Shaking up a whole culture

Pages 358-359
Cornerstone and crossroads

Pages 360-361
A deep impression embedded in stone

Pages 362-363
A certain Y, a certain V

Pages 364-365
The world is Zeus's play

Page 366
It was necessary to begin again


Sunday, March 1, 2009

Sunday March 1, 2009

Filed under: Uncategorized — Tags: , — m759 @ 11:00 AM

Solomon's Cube

"There is a book… called A Fellow of Trinity, one of series dealing with what is supposed to be Cambridge college life…. There are two heroes, a primary hero called Flowers, who is almost wholly good, and a secondary hero, a much weaker vessel, called Brown. Flowers and Brown find many dangers in university life, but the worst is a gambling saloon in Chesterton run by the Misses Bellenden, two fascinating but extremely wicked young ladies. Flowers survives all these troubles, is Second Wrangler and Senior Classic, and succeeds automatically to a Fellowship (as I suppose he would have done then). Brown succumbs, ruins his parents, takes to drink, is saved from delirium tremens during a thunderstorm only by the prayers of the Junior Dean, has much difficulty in obtaining even an Ordinary Degree, and ultimately becomes a missionary. The friendship is not shattered by these unhappy events, and Flowers's thoughts stray to Brown, with affectionate pity, as he drinks port and eats walnuts for the first time in Senior Combination Room."

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

"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.

"The complete projective group of collineations and dualities of the [projective] 3-space is shown to be of order [in modern notation] 8! …. To every transformation of the 3-space there corresponds a transformation of the [projective] 5-space. In the 5-space, there are determined 8 sets of 7 points each, 'heptads' …."

— George M. Conwell, "The 3-space PG(3, 2) and Its Group," The Annals of Mathematics, Second Series, Vol. 11, No. 2 (Jan., 1910), pp. 60-76

"It must be remarked that these 8 heptads are the key to an elegant proof…."

— Philippe Cara, "RWPRI Geometries for the Alternating Group A8," in Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference (July 16-21, 2000), Kluwer Academic Publishers, 2001, ed. Aart Blokhuis, James W. P. Hirschfeld, Dieter Jungnickel, and Joseph A. Thas, pp. 61-97

Tuesday, February 17, 2009

Tuesday February 17, 2009

Filed under: Uncategorized — Tags: , , — m759 @ 1:06 PM

of the Rock

A discussion of Stevens's late poem "The Rock" (1954) in Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 120:

For Stevens, the poem "makes meanings of the rock." In the mind, "its barrenness becomes a thousand things/And so exists no more." In fact, in a peculiar irony that only a poet with Stevens's particular notion of the imagination's function could develop, the rock becomes the mind itself, shattered into such diamond-faceted brilliance that it encompasses all possibilities for human thought:

The rock is the gray particular of man's life,
The stone from which he rises, up—and—ho,
The step to the bleaker depths of his descents ...

The rock is the stern particular of the air,
The mirror of the planets, one by one,
But through man's eye, their silent rhapsodist,

Turquoise the rock, at odious evening bright
With redness that sticks fast to evil dreams;
The difficult rightness of half-risen day.

The rock is the habitation of the whole,
Its strength and measure, that which is near,
     point A
In a perspective that begins again

At B: the origin of the mango's rind.

                    (Collected Poems, 528)

A mathematical version of
this poetic concept appears
in a rather cryptic note
from 1981 written with
Stevens's poem in mind:


For some explanation of the
groups of 8 and 24
motions referred to in the note,
see an earlier note from 1981.

For the Perlis "diamond facets,"
see the Diamond 16 Puzzle.

For a much larger group
of motions, see
Solomon's Cube.

As for "the mind itself"
and "possibilities for
human thought," see
Geometry of the I Ching.

Sunday, May 18, 2008

Sunday May 18, 2008

Filed under: Uncategorized — Tags: — m759 @ 2:02 PM

From the Grave


in yesterday's New York Times:

"From the grave, Albert Einstein
poured gasoline on the culture wars
between science and religion this week…."

An announcement of a
colloquium at Princeton:

Cartoon of Coxedter exhuming Geometry

Above: a cartoon,
"Coxeter exhuming Geometry,"
with the latter's tombstone inscribed


  600 B.C. —
1900 A.D.

Page from 'The Paradise of Childhood,' 1906 edition

The above is from
The Paradise of Childhood,
a work first published in 1869.

"I need a photo-opportunity,
I want a shot at redemption.
Don't want to end up a cartoon
In a cartoon graveyard."

— Paul Simon

Einstein on TIME cover as 'Man of the Century'

Albert Einstein,

"It is quite clear to me that the religious paradise of youth, which was thus lost, was a first attempt to free myself from the chains of the 'merely-personal,' from an existence which is dominated by wishes, hopes and primitive feelings.  Out yonder there was this huge world, which exists independently of us human beings and which stands before us like a great, eternal riddle, at least partially accessible to our inspection and thinking.  The contemplation of this world beckoned like a liberation…."

Autobiographical Notes, 1949

Related material:

A commentary on Tom Wolfe's
"Sorry, but Your Soul Just Died"–

"The Neural Buddhists," by David Brooks,
 in the May 13 New York Times:

"The mind seems to have
the ability to transcend itself
and merge with a larger
presence that feels more real."

A New Yorker commentary on
a new translation of the Psalms:

"Suddenly, in a world without
Heaven, Hell, the soul, and
eternal salvation or redemption,
the theological stakes seem
more local and temporal:
'So teach us to number our days.'"

and a May 13 Log24 commentary
on Thomas Wolfe's
"Only the Dead Know Brooklyn"–

"… all good things — trout as well as
eternal salvation — come by grace
and grace comes by art
and art does not come easy."

A River Runs Through It

"Art isn't easy."
— Stephen Sondheim,
quoted in
Solomon's Cube.

For further religious remarks,
consult Indiana Jones and the
Kingdom of the Crystal Skull
and The Librarian:
Return to King Solomon's Mines.

Saturday, May 10, 2008

Saturday May 10, 2008

Filed under: Uncategorized — Tags: , , — m759 @ 8:00 AM
MoMA Goes to

"… the startling thesis of Mr. Brosterman's new book, 'Inventing Kindergarten' (Harry N. Abrams, $39.95): that everything the giants of modern art and architecture knew about abstraction they learned in kindergarten, thanks to building blocks and other educational toys designed by Friedrich Froebel, a German educator, who coined the term 'kindergarten' in the 1830's."

— "Was Modernism Born
     in Toddler Toolboxes?"
     by Trip Gabriel, New York Times,
     April 10, 1997



Figure 1 —
Concept from 1819:

Cubic crystal system
(Footnotes 1 and 2)

Figure 2 —
The Third Gift, 1837:

Froebel's third gift

Froebel's Third Gift

Froebel, the inventor of
kindergarten, worked as
an assistant to the
crystallographer Weiss
mentioned in Fig. 1.

(Footnote 3)

Figure 3 —
The Third Gift, 1906:

Seven partitions of the eightfold cube in a book from 1906

Figure 4 —
Solomon's Cube,
1981 and 1983:

Solomon's Cube - A 1981 design by Steven H. Cullinane

Figure 5 —
Design Cube, 2006:

Design Cube 4x4x4 by Steven H. Cullinane


The above screenshot shows a
moveable JavaScript display
of a space of six dimensions
(over the two-element field).

(To see how the display works,
try the Kaleidoscope Puzzle first.)


For some mathematical background, see




1. Image said to be after Holden and Morrison, Crystals and Crystal Growing, 1982
2. Curtis Schuh, "The Library: Biobibliography of Mineralogy," article on Mohs
3. Bart Kahr, "Crystal Engineering in Kindergarten" (pdf), Crystal Growth & Design, Vol. 4 No. 1, 2004, 3-9

Powered by WordPress