Tuesday, February 17, 2026
A Game of Tags: All Saints Mythspace
From “The Crimson Passion: A Drama at Mardi Gras”
From "The Practice of Mathematics, Part 1" by Robert P. Langlands —
|
My feeling for the Greeks as mathematicians is every bit as inadequate as that for the youthful Gauss. I do not know whence came their curiosity and depth. Perhaps no-one does. We live in a highly structured environment dedicated to research. We earn our living by it and we pin our hopes of recognition on it, but the questions we ask and the problems we solve are determined more by tradition, more by our colleagues than by our own natural and spontaneous curiosity. We are seldom playful; our efforts are never simply for our own amusement. A brief romp with Greek mathematics in which we examine the construction of the pentagon at length may be an occasion to capture briefly the ludible spirit of the Greeks An hour is also not enough for an adequate understanding of analytic geometric and complex numbers nor for a presentation of the algebra required for Gauss’s construction [of the 17-sided regular polygon]. The complex numbers are an enormously effective tool that swallows the geometry, but it will be good to ask ourselves how. Moreover the four-fold or sixteen-fold algebraic symmetry is far more subtle than the five-fold or seventeen-fold geometric symmetry. Since it will reappear again and in spades when, and if, we discuss Galois and Kummer, it is best to get used to it now. |
Wednesday, September 11, 2024
Roots for St. Rose of Lima
Sunday, April 2, 2023
Roots
"I’ve been heavily influenced by American 'roots' music."
— Natalie Merchant in a New Yorker piece dated April 2, 2023.
"Roots" non-music —
See other "Root Circle" posts.
Saturday, April 1, 2023
For this weekend’s Bombay Beach Biennale
Friday, June 17, 2022
Just 17 : Circle in the Square
Sunday, July 19, 2020
Thursday, June 25, 2020
After Gauss
Wednesday, June 24, 2020
Iconic Form
“I appreciate simple, iconic and timeless forms —
things that can adapt or serve multiple purposes
and avoid being easily labelled. At the same time,
I love parts and fragments that reveal how things
move or work. Mostly, anything that tells its
own story and isn’t generalized or clad in some
sort of ornamental icing.”
— Charlottesville, VA, architect Fred Wolf, who seems
to have been associated with the business name
“Gauss LLC ” in Charlottesville.
Posts tagged Space Writer include —
Friday, July 12, 2019
Instrumental
The title is from a New York Times correction in the previous post.
Piano roll for "I am sixteen going on seventeen" —
Backstory: Posts tagged Root Circle.
Thursday, May 17, 2018
May 17
"Well, she was just 17 …" — Song lyric
See as well, from last Christmas Eve, Piano Roll.
Tuesday, August 29, 2017
Midnight Special
From a Log24 search for "Midnight Special."
Update of 12:45 AM the same night —
"I appreciate simple, iconic and timeless forms —
things that can adapt or serve multiple purposes
and avoid being easily labelled. At the same time,
I love parts and fragments that reveal how things
move or work. Mostly, anything that tells its
own story and isn’t generalized or clad in some
sort of ornamental icing."
— Charlottesville, VA, architect Fred Wolf, who seems
to have been associated with the business name
"Gauss LLC " in Charlottesville.
And I appreciate bulk apperception.
Friday, August 5, 2016
Sleight of Post
From an earlier Log24 post —
Friday, July 11, 2014
|
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.
Monday, July 18, 2016
ART WARS: Magic Circles
An artist mentioned in a NY Times obituary this morning —
(Click for the source.)
I prefer some not-so-magic circles —
Click for related posts tagged root circle.
Friday, October 17, 2014
Mathematics and Narrative, continued:
Raiders of the Lost Archetype
“… an unexpected development: the discovery of a lost archetype….”
— “The Lost Theorem,” by Lee Sallows, Mathematical Intelligencer, Fall 1997
Related material:
A scene from the 1954 film:
A check of this journal on the above MetaFilter date — Jan. 24, 2012 —
yields a post tagged “in1954.” From another post with that tag:

Backstory: Posts tagged Root Circle.
Monday, May 26, 2014
Springtime for Vishnu
… Continues.
A post by Margaret Soltan this morning:
Links (in blue) from the above post:
Cane and Mondo Cane.
Bagger Vance — “Time for you to see the field.”
From Pictures for Kurosawa (Sept. 6, 2003) —
“As these flowing rivers that go towards the ocean,
when they have reached the ocean, sink into it,
their name and form are broken, and people speak of
the ocean only, exactly thus these sixteen parts
of the spectator that go towards the person (purusha),
when they have reached the person, sink into him,
their name and form are broken, and people speak of
the person only, and he becomes without parts and
immortal. On this there is this verse:
‘That person who is to be known, he in whom these parts
rest, like spokes in the nave of a wheel, you know him,
lest death should hurt you.’ “
— Prasna Upanishad
Related material — Heaven’s Gate images from Xmas 2012:

“This could be heaven or this could be hell.” — Hotel California
Those who prefer mathematics to narrative may consult Root Circle.
Sunday, January 19, 2014
Deep Beauty
Old punchline: “Spell chrysanthemum.”
Variation: “Spell coordinatization.”
Related test: Chrysanthemum Coordinatization —

Context: Root circle.
Monday, July 15, 2013
Tag
Some recent posts have been added to the Root Circle saga.
Update of 12:13 AM July 16, 2013:
Click the above image for further details. This "every other term"
strategy may be illustrated as in the July 12, 2013, post "Ein Bild "—
This image was originally posted on June 5, 2006 at 12:06 AM ET.
Saturday, July 13, 2013
Circles
A sort of poem
by Gauss and Weyl —
Click the circle for the context in Weyl's Symmetry .
For related remarks, see the previous post.
A literary excursus—
|
Brad Leithauser in a New Yorker post of July 11, 2013: If a poet determines that a poem should begin at point A and conclude at point D, say, the mystery of how to get there—how to pass felicitously through points B and C—strikes me as an artistic task both genuine and enlivening. There are fertile mysteries of transition, no less than of termination. And I’d like to suppose that Frost himself would recognize that any ingress into a poem is better than being locked out entirely. His little two-liner, “The Secret,” suggests as much: “We dance round in a ring and suppose / But the Secret sits in the middle and knows.” Most truly good poems might be said to contain a secret: the little sacramental miracle by which you connect, intimately, with the words of a total stranger. And whether you come at the poem frontward, or backward, or inside out—whether you approach it deliberately, word by word and line by line, or you parachute into it borne on a sudden breeze from the island of Serendip—surely isn’t the important thing. What matters is whether you achieve entrance into its inner ring, and there repose companionably beside the Secret. |
One should try, of course, to avoid repose in an inner circle of Hell .
Friday, July 12, 2013
Ein Bild
A rhetorical question from this journal—
"Und was für ein Bild des Christentums
ist dabei herausgekommen?"
A rhetorical answer from this journal (June 5, 2006)—
Material closely related to the above rhetorical answer—
(Click for clearer image.)
Wednesday, July 10, 2013
Nachthexen
From a Telegraph obituary about a death on July 8, 2013:
"The pilots’ tactic was to fly to within a certain distance of the target, and cut their engines. They would then glide in silently, release their bombs, then restart their engines and fly home. The Germans called them the 'Nachthexen' (the Night Witches) due to the whooshing sound they made— 'like a witch’s broomstick in the night'— as they flew past. There was, supposedly, a promise to award an Iron Cross to any Luftwaffe pilot who actually managed to bring down a Night Witch."
In memoriam:
Wednesday, December 26, 2012
Roots
This journal on June 24, 2006—
Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance , 1974:
"But what's happening is that each year our old flat earth of
conventional reason becomes less and less adequate to handle
the experiences we have and this is creating widespread feelings
of topsy-turviness. As a result we're getting more and more people
in irrational areas of thought… occultism, mysticism, drug changes
and the like… because they feel the inadequacy of classical reason
to handle what they know are real experiences."
"I'm not sure what you mean by classical reason."
"Analytic reason, dialectic reason. Reason which at the University
is sometimes considered to be the whole of understanding. You've
never had to understand it really. It's always been completely
bankrupt with regard to abstract art. Nonrepresentative art is one of
the root experiences I'm talking about. Some people still condemn it
because it doesn’t make 'sense.' But what's really wrong is not
the art but the 'sense,' the classical reason, which can't grasp it.
People keep looking for branch extensions of reason that will cover
art's more recent occurrences, but the answers aren't in the
branches, they're at the roots."
See also an exhibition at the Museum of Modern Art that opened Dec. 23—
— and an exhibition in this journal of the image "Root Circle."
Sunday, September 26, 2010
Where Credit Is Due…
The Dick Medal
Review of the film "Knowing" from 2009—
Nicolas Cage's character, an astrophysicist, looks at a chart (written 50 years earlier by a child) with a colleague and points out a chronologically correct prediction of the date and number of dead in world wide tragedies over the last fifty years, and his colleague's response is "Systems that find meaning in numbers are a dime a dozen. Why? Because people see what they want to see." Well that would be a pretty neat trick. You could build a career on that in a Vegas showroom.
Film Title: Next
Based on the 1954 short story
"The Golden Man" by Philip K. Dick
Release Date:
April 27, 2007
About the Film:
Nicolas Cage stars as Cris Johnson, a Las Vegas magician with a secret gift that is both a blessing and a curse: He has the uncanny ability to tell you what happens next.
Related material from this journal on the release date of "Next"— April 27, 2007—
|
Production Credits: Thanks to the
– and to
|
"It’s almost enough to make you think that time present and time past might both be present in time future. As someone may have said."
— David Orr, "The Age of Citation"
Saturday, May 22, 2010
In the Details
Today's New York Times—
|
"…there were fresh questions about whether the intelligence overhaul that created the post of national intelligence director was fatally flawed, and whether Mr. Obama would move gradually to further weaken the authorities granted to the director and give additional power to individual spy agencies like the . Mr. Blair and each of his predecessors have lamented openly that the intelligence director does not have enough power to deliver the intended shock therapy to America’s byzantine spying apparatus." |
Catch-22 in Doonesbury today—

From Log24 on Jan. 5, 2010—
Artifice of Eternity—
A Medal
In memory of Byzantine scholar Ihor Sevcenko,
who died at 87 on St. Stephen's Day, 2009–
Thie above image results from a Byzantine
meditation based on a detail in the previous post—

"This might be a good time to
call it a day." –Today's Doonesbury
"TOMORROW ALWAYS BELONGS TO US"
Title of an exhibition by young Nordic artists
in Sweden during the summer of 2008.
The exhibition included, notably, Josefine Lyche.
Tuesday, January 5, 2010
Artifice of Eternity
A Medal
In memory of Byzantine scholar Ihor Sevcenko,
who died at 87 on St. Stephen's Day, 2009–
| William Grimes on Sevcenko in this morning's New York Times:
"Perhaps his most fascinating, if uncharacteristic, literary contribution came shortly after World War II, when he worked with Ukrainians stranded in camps in Germany for displaced persons. In April 1946 he sent a letter to Orwell, asking his permission to translate 'Animal Farm' into Ukrainian for distribution in the camps. The idea instantly appealed to Orwell, who not only refused to accept any royalties but later agreed to write a preface for the edition. It remains his most detailed, searching discussion of the book." |
See also a rather different medal discussed
here in the context of an Orwellian headline from
The New York Times on Christmas morning,
the day before Sevcenko died.
That headline, at the top of the online front page,
was "Arthur Koestler, Man of Darkness."

The medal, offered as an example of brightness
to counteract the darkness of the Times, was designed
by Leibniz in honor of his discovery of binary arithmetic.
See Brightness at Noon and Brightness continued.
"By groping toward the light we are made to realize
how deep the darkness is around us."
— Arthur Koestler, The Call Girls: A Tragi-Comedy,
Random House, 1973, page 118
Saturday, June 14, 2008
Saturday June 14, 2008
An online tribute to Tim Russert
this morning had a song by a
Russert favorite, Bruce Springsteen:
Hard Lessons

and the
five Log24 entries
ending on July 20, 2006,
which contain the following
example of what might be
caled "sacred order"
(see yesterday's entries)–

See also "Grave Matters" here
on November 8, 2006, and
the same date four years earlier,
as well as
"O Grave, Where Is Thy Victory?"
(pdf), a lecture by Jack Miles
at Clark Art Institute
(see Oct. 7-9, 2002)
on November 9, 2002.
The Miles lecture may be of
more comfort to Russert's
mourners than the
cross/wheel symbolism,
which has its dark side.
The cross, the wheel,
the Catholic faith, and
Russert's field of expertise,
politics, are of course
notably combined in the
crux gammata, discussed
here in a 2002 entry on
the Triumph of the Cross
and the Death of Grace
(Princess of Monaco).
Sunday, May 25, 2008
Sunday May 25, 2008
— Song lyric, Cyndi Lauper
Magister Ludi
Hermann Hesse's 1943 The Glass Bead Game (Picador paperback, Dec. 6, 2002, pp. 139-140)–
"For the present, the Master showed him a bulky memorandum, a proposal he had received from an organist– one of the innumerable proposals which the directorate of the Game regularly had to examine. Usually these were suggestions for the admission of new material to the Archives. One man, for example, had made a meticulous study of the history of the madrigal and discovered in the development of the style a curved that he had expressed both musically and mathematically, so that it could be included in the vocabulary of the Game. Another had examined the rhythmic structure of Julius Caesar's Latin and discovered the most striking congruences with the results of well-known studies of the intervals in Byzantine hymns. Or again some fanatic had once more unearthed some new cabala hidden in the musical notation of the fifteenth century. Then there were the tempestuous letters from abstruse experimenters who could arrive at the most astounding conclusions from, say, a comparison of the horoscopes of Goethe and Spinoza; such letters often included pretty and seemingly enlightening geometric drawings in several colors."
A Bulky Memorandum
From Siri Hustvedt, author of Mysteries of the Rectangle: Essays on Painting (Princeton Architectural Press, 2005)– What I Loved: A Novel (Picador paperback, March 1, 2004, page 168)–
A description of the work of Bill Wechsler, a fictional artist:
"Bill worked long hours on a series of autonomous pieces about numbers. Like O's Journey, the works took place inside glass cubes, but these were twice as large– about two feet square. He drew his inspiration from sources as varied as the Cabbala, physics, baseball box scores, and stock market reports. He painted, cut, sculpted, distorted, and broke the numerical signs in each work until they became unrecognizable. He included figures, objects, books, windows, and always the written word for the number. It was rambunctious art, thick with allusion– to voids, blanks, holes, to monotheism and the individual, the the dialectic and yin-yang, to the Trinity, the three fates, and three wishes, to the golden rectangle, to seven heavens, the seven lower orders of the sephiroth, the nine Muses, the nine circles of Hell, the nine worlds of Norse mythology, but also to popular references like A Better Marriage in Five Easy Lessons and Thinner Thighs in Seven Days. Twelve-step programs were referred to in both cube one and cube two. A miniature copy of a book called The Six Mistakes Parents Make Most Often lay at the bottom of cube six. Puns appeared, usually well disguised– one, won; two, too, and Tuesday; four, for, forth; ate, eight. Bill was partial to rhymes as well, both in images and words. In cube nine, the geometric figure for a line had been painted on one glass wall. In cube three, a tiny man wearing the black-and-white prison garb of cartoons and dragging a leg iron has
— End of page 168 —
opened the door to his cell. The hidden rhyme is "free." Looking closely through the walls of the cube, one can see the parallel rhyme in another language: the German word drei is scratched into one glass wall. Lying at the bottom of the same box is a tiny black-and-white photograph cut from a book that shows the entrance to Auschwitz: ARBEIT MACHT FREI. With every number, the arbitrary dance of associations worked togethere to create a tiny mental landscape that ranged in tone from wish-fulfillment dream to nightmare. Although dense, the effect of the cubes wasn't visually disorienting. Each object, painting, drawing, bit of text, or sculpted figure found its rightful place under the glass according to the necessary, if mad, logic of numerical, pictorial, and verbal connection– and the colors of each were startling. Every number had been given a thematic hue. Bill had been interested in Goethe's color wheel and in Alfred Jensen's use of it in his thick, hallucinatory paintings of numbers. He had assigned each number a color. Like Goethe, he included black and white, although he didn't bother with the poet's meanings. Zero and one were white. Two was blue. Three was red, four was yellow, and he mixed colors: pale blue for five, purples in six, oranges in seven, greens in eight, and blacks and grays in nine. Although other colors and omnipresent newsprint always intruded on the basic scheme, the myriad shades of a single color dominated each cube.
The number pieces were the work of a man at the top of his form. An organic extension of everything Bill had done before, these knots of symbols had an explosive effect. The longer I looked at them, the more the miniature constructions seemed on the brink of bursting from internal pressure. They were tightly orchestrated semantic bombs through which Bill laid bare the arbitrary roots of meaning itself– that peculiar social contract generated by little squiggles, dashes, lines, and loops on a page."
(named not for
Bill Wechsler, the
fictional artist above,
but for the non-fictional
David Wechsler) –
|
From 2002:
Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale "block design" subtest. |
A Magic Gallery
|
ZZ
Figures from the
Poem by Eugen Jost:
Mit Zeichen und Zahlen
Numbers and Names,
With numbers and names
English translation A related poem:
Alphabets
From time to time
But if a savage
— Hermann Hesse (1943), |
Sunday, June 24, 2007
Sunday June 24, 2007
in the Garden
of Good and Evil

"I Put a Spell on You"
— Nina Simone,
title of autobiograpy
— Glenna Whitley, "Voodoo Justice," The New York Times, March 20, 1994
"But what's happening is that each year our old flat earth of conventional reason becomes less and less adequate to handle the experiences we have and this is creating widespread feelings of topsy-turviness. As a result we're getting more and more people in irrational areas of thought… occultism, mysticism, drug changes and the like… because they feel the inadequacy of classical reason to handle what they know are real experiences."
"I'm not sure what you mean by classical reason."
"Analytic reason, dialectic reason. Reason which at the University is sometimes considered to be the whole of understanding. You've never had to understand it really. It's always been completely bankrupt with regard to abstract art. Nonrepresentative art is one of the root experiences I'm talking about. Some people still condemn it because it doesn’t make 'sense.' But what's really wrong is not the art but the 'sense,' the classical reason, which can't grasp it. People keep looking for branch extensions of reason that will cover art's more recent occurrences, but the answers aren't in the branches, they're at the roots."
Related material:
D-Day Morning,
Figures of Speech,
Ursprache Revisited.
See also
the midnight entry
of June 23-24, 2006:
"Let the midnight special
shine her light on me."

Friday, April 27, 2007
Friday April 27, 2007
Thanks to the
Pennsylvania Lottery for
today's suggestion of links
to the dates 9/15 and 6/06–

— and to
Hermann Weyl
for the illustration
from 6/06 (D-Day)
underlying the
following "gold medal"
from 9/15, 2006:

.
Tuesday, April 3, 2007
Tuesday April 3, 2007
Our Judeo-Christian
Heritage –
Lottery
Hermeneutics
Part I: Judeo
| The Lottery 12/9/06 | Mid-day | Evening |
| New York | 036
See |
331
See 3/31— “square crystal” and “the symbolism could not have been more perfect.” |
| Pennsylvania | 602
See 6/02— Walter Benjamin |
111
See 1/11— “Related material:
|
Part II: Christian
| The Lottery 4/3/07 | Mid-day | Evening |
| New York | 115
See 1/15— |
017
See |
| Pennsylvania | 604
See |
714
See |
Related material:
It is perhaps relevant to
this Holy Week that the
date 6/04 (2006) above
refers to both the Christian
holy day of Pentecost and
to the day of the
facetious baccalaureate
of the Class of 2006 in
the University Chapel
at Princeton.
For further context for the
Log24 remarks of that same
date, see June 1-15, 2006.


























