The phrase “Chaos Magic” in the conclusion of last week’s
WandaVision episode suggests . . .
Tuesday, March 2, 2021
For Fans of Chaos Magic
Friday, February 26, 2021
Non-Chaos Non-Magic
For fans of “WandaVision” —
“1978 was perhaps the seminal year in the origin of chaos magic. . . .”
— Wikipedia article on Chaos Magic
Non-Chaos Non-Magic from Halloween 1978 —
Related material —
A doctoral student of a different Peter Cameron —
( Not to be confused with The Tin Man’s Hat. )
Monday, January 16, 2017
The Magic Valley*
An alternative to Davos —
From a professor at Grand Valley —
* Title suggested by Thomas Mann's 1924 novel about Davos
Friday, May 22, 2015
Friday, July 25, 2014
Magic for Jews
(Continued from April 8, 2013.)
See Two Blocks Short of a Design (May 5, 2011).
Magic in the Moonshine
“The yarns of seamen have a direct simplicity, the whole meaning
of which lies within the shell of a cracked nut. But Marlow was not
typical (if his propensity to spin yarns be excepted), and to him the
meaning of an episode was not inside like a kernel but outside,
enveloping the tale which brought it out only as a glow brings out a
haze, in the likeness of one of these misty halos that sometimes
are made visible by the spectral illumination of moonshine.”
— Joseph Conrad in Heart of Darkness
“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
“Spectral evidence is a form of evidence
based upon dreams and visions.” —Wikipedia
See also Moonshine (May 15, 2014) and, from the date of the above
New York Times item, two posts tagged Wunderkammer .
Related material: From the Spectrum program of the Mathematical
Association of America, some non-spectral evidence.
Thursday, July 24, 2014
Death in Mathmagic Land
Wednesday, May 14, 2014
Death in Mathmagic Land
"It was our old friend Pythagoras who discovered
that the pentagram was full of mathematics."
— Narrator, "Donald in Mathmagic Land," Disney, 1959
… and it was Peter J. Cameron who discovered that
mathematics was full of pentagrams.
From Log24 on May 3: Gray Space —
Robert J. Stewart (left) and a pentagram photo posted May 2
by Oslo artist Josefine Lyche. See also Lyche in this journal.
From Log24 on May 13: An Artist's Memorial —
The death mentioned in the above May 13 post occurred on
May 12, the date of a scheduled Black Mass at Harvard.
Related material:
Monday, April 8, 2013
Magic for Jews
A commenter on Saturday's "Seize the Dia" has
suggested a look at the work of one Mark Collins.
Here is such a look (click to enlarge):
I find attempts to associate pure mathematics with the words
"magic" or "mystic" rather nauseating. (H. F. Baker's work
on Pascal's mystic hexagram is no exception; Baker was
stuck with Pascal's obnoxious adjective, but had no truck
with any mystic aspects of the hexagram.)
The remarks above by Clifford Pickover on Collins, Dürer, and
binary representations may interest some non-mathematicians,
who should not be encouraged to waste their time on this topic.
For the mathematics underlying the binary representation of
Dürer's square, see, for instance, my 1984 article "Binary
Coordinate Systems."
Those without the background to understand that article
may enjoy, instead of Pickover's abortive attempts above at
mathematical vulgarization, his impressively awful 2009 novel
Jews in Hyperspace .
Pickover's 2002 book on magic squares was, unfortunately,
published by the formerly reputable Princeton University Press.
Related material from today's Daily Princetonian :
See also Nash + Princeton in this journal.
Thursday, May 5, 2011
On Art and Magic
Two Blocks Short of a Design:
A sequel to this morning’s post on Douglas Hofstadter
![]() Photo of Hofstadter by Mike McGrath taken May 13, 2006 |
Related material — See Lyche’s “Theme and Variations” in this journal
and Hofstadter’s “Variations on a Theme as the Essence of Imagination”
— Scientific American October 1982
A quotation from a 1985 book by Hofstadter—
“… we need to entice people with the beauties of clarity, simplicity, precision,
elegance, balance, symmetry, and so on.
Those artistic qualities… are the things that I have tried to explore and even
to celebrate in Metamagical Themas . (It is not for nothing that the word
‘magic’ appears inside the title!)”
The artistic qualities Hofstadter lists are best sought in mathematics, not in magic.
An example from Wikipedia —
Mathematics The Fano plane block design |
Magic The Deathly Hallows symbol— |
Saturday, February 10, 2018
Into the Upside Down
(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.
Wednesday, January 14, 2015
Kulturkampf for Princeton*
Einstein and Thomas Mann, Princeton, 1938
A sequel to Princeton Requiem,
Gesamtkunstwerk , and Serial Box —
Fearful Symmetry, Princeton Style:
* See as well other instances of Kulturkampf in this journal.
Tuesday, February 26, 2013
Snow
"Hans Castorp is a searcher after the Holy Grail.
You would never have thought it when you read
his story—if I did myself, it was both more and
less than thinking. Perhaps you will read the
book again from this point of view. And perhaps
you will find out what the Grail is: the knowledge
and the wisdom, the consecration, the highest
reward, for which not only the foolish hero but
the book itself is seeking. You will find it in the
chapter called 'Snow'…."
— Thomas Mann, "The Making of
The Magic Mountain "
In related entertainment news…
Click image for some backstory.
Mann's tale is set in Davos, Switzerland.
See also Mayer at Davos.
Thursday, March 4, 2021
Continuity
Actually, Dirac “bridged math and physics” much earlier —
“Spinors, which are a kind of square root of vectors, had been introduced
in algebra and also in physics as part of Paul Dirac’s theory of the electron.
A spin structure on a manifold allows such square roots to exist.”
— Quanta Magazine today, article by Daniel S. Freed
See The Eddington Song and . . .
Poetic paraphrase —
“How can we tell the singer from the song?”
Teaching the Academy to See
“Art bears the same relationship to society
that the dream bears to mental life. . . .
Like art, the dream mediates between order
and chaos. So, it is half chaos. That is why
it is not comprehensible. It is a vision, not
a fully fledged articulated production.
Those who actualize those half-born visions
into artistic productions are those who begin
to transform what we do not understand into
what we can at least start to see.”
— A book published on March 2, 2021:
Beyond Order , by Jordan Peterson
The inarticulate, in this case, is Rosalind Krauss:
A “raid on the inarticulate” published in Notices of the
American Mathematical Society in the February 1979 issue —
Wednesday, March 3, 2021
Out on the Cutting Edge*
That edge, where artists are always transforming chaos into order, can be a very rough and dangerous place. Living there, an artist constantly risks falling fully into the chaos, instead of transforming it. But artists have always lived there, on the border of human understanding. Art bears the same relationship to society that the dream bears to mental life. You are very creative when you are dreaming. That is why, when you remember a dream, you think, “Where in the world did that come from?” It is very strange and incomprehensible that something can happen in your head, and you have no idea how it got there or what it means. It is a miracle: nature’s voice manifesting itself in your psyche. And it happens every night. Like art, the dream mediates between order and chaos. So, it is half chaos. That is why it is not comprehensible. It is a vision, not a fully fledged articulated production. Those who actualize those half-born visions into artistic productions are those who begin to transform what we do not understand into what we can at least start to see. That is the role of the artist, occupying the vanguard. That is their biological niche. They are the initial civilizing agents.
— Peterson, Jordan B., Beyond Order (p. 215), |
See also . . .
* Title credit —
Click for a clearer version —
Tuesday, December 17, 2019
A Singular Eye
Heyman reportedly died on Dec. 10, 2019.
See this journal on that date.
Wednesday, October 2, 2019
A Long Literary Tradition
"There's a long literary tradition associating
certain kinds of geometry with horror."
— American Mathematical Society yesterday:
See also yesterday's Log24 post "Transylvania Revisited."
A related post —
Friday, July 5, 2019
Tuesday, April 3, 2018
The Cage Country
Saturday, January 20, 2018
The Chaos Symbol of Dan Brown
In the following passage, Dan Brown claims that an eight-ray star
with arrowheads at the rays’ ends is “the mathematical symbol for
entropy.” Brown may have first encountered this symbol at a
questionable “Sacred Science” website. Wikipedia discusses
some even less respectable uses of the symbol.
Related news —
Related symbolism —
A star figure and the Galois quaternion.
The square root of the former is the latter.
Wednesday, October 18, 2017
Dürer for St. Luke’s Day
Structure of the Dürer magic square
16 3 2 13
5 10 11 8 decreased by 1 is …
9 6 7 12
4 15 14 1
15 2 1 12
4 9 10 7
8 5 6 11
3 14 13 0 .
Base 4 —
33 02 01 30
10 21 22 13
20 11 12 23
03 32 31 00 .
Two-part decomposition of base-4 array
as two (non-Latin) orthogonal arrays —
3 0 0 3 3 2 1 0
1 2 2 1 0 1 2 3
2 1 1 2 0 1 2 3
0 3 3 0 3 2 1 0 .
Base 2 –
1111 0010 0001 1100
0100 1001 1010 0111
1000 0101 0110 1011
0011 1110 1101 0000 .
Four-part decomposition of base-2 array
as four affine hyperplanes over GF(2) —
1001 1001 1100 1010
0110 1001 0011 0101
1001 0110 0011 0101
0110 0110 1100 1010 .
— Steven H. Cullinane,
October 18, 2017
See also recent related analyses of
noted 3×3 and 5×5 magic squares.
Tuesday, October 17, 2017
Plan 9 Continues
See also Holy Field in this journal.
Some related mathematics —
Analysis of the Lo Shu structure —
Structure of the 3×3 magic square:
4 9 2
3 5 7 decreased by 1 is …
8 1 6
3 8 1
2 4 6
7 0 5
In base 3 —
10 22 01
02 11 20
21 00 12
As orthogonal Latin squares
(a well-known construction) —
1 2 0 0 2 1
0 1 2 2 1 0
2 0 1 1 0 2 .
— Steven H. Cullinane,
October 17, 2017
Monday, October 16, 2017
Highway 61 Revisited
"God said to Abraham …." — Bob Dylan, "Highway 61 Revisited"
Related material —
-
"Inner Truth" in this journal
-
"On Linguistic Creation," June 25, 1999
-
"Ultra Super Magic Squares of 5×5" at
http://mathsforeurope.digibel.be/magic.htm .
See as well Charles Small, Harvard '64,
"Magic Squares over Fields" —
— and Conway-Norton-Ryba in this journal.
Some remarks on an order-five magic square over GF(52):
on the numbers 0 to 24:
22 5 18 1 14
3 11 24 7 15
9 17 0 13 21
10 23 6 19 2
16 4 12 20 8
Base-5:
42 10 33 01 24
03 21 44 12 30
14 32 00 23 41
20 43 11 34 02
31 04 22 40 13
Regarding the above digits as representing
elements of the vector 2-space over GF(5)
(or the vector 1-space over GF(52)) …
All vector row sums = (0, 0) (or 0, over GF(52)).
All vector column sums = same.
Above array as two
orthogonal Latin squares:
4 1 3 0 2 2 0 3 1 4
0 2 4 1 3 3 1 4 2 0
1 3 0 2 4 4 2 0 3 1
2 4 1 3 0 0 3 1 4 2
3 0 2 4 1 1 4 2 0 3
— Steven H. Cullinane,
October 16, 2017
Tuesday, April 5, 2016
Spring Play
The spring play this March at Princeton's McCarter Theatre Center
was Agatha Christie's "The Mousetrap."
In related news —
See as well, in this journal, a post from the date pictured above,
that of the Disneyland Diamond Celebration on May 22, 2015 —
Tuesday, July 29, 2014
Radio Days
In memoriam :
“Margot Adler, an iconic NPR correspondent and Wiccan priestess,
died on Monday July 28 from endometrial cancer at the age of 68.”
— Huffington Post 07/28/2014 5:39 pm EDT
See also Log24 posts tagged NPR Magic.
Sunday, July 13, 2014
Useful Princeton
See…
- An Apple for Devlin (July 2)
- Thanks for having me on (July 11)
- Useful Idiot (Wikipedia article)
-
Useful Fictions (a Princeton mathematics
department Spring 2014 course)
"Numbers themselves are fictions, abstractions humans invented
to gain more control over the world." — Keith Devlin
Related material:
-
From today's New York Times Sunday Review ,
The World According to Maxwell Smart, Part 1
- Madonna, "Get Stupid," a political video from 2008
Friday, July 11, 2014
Thanks for having me on.
Wednesday, January 22, 2014
A Riddle for Davos
Einstein and Thomas Mann, Princeton, 1938
See also the life of Diogenes Allen, a professor at Princeton
Theological Seminary, a life that reportedly ended on the date—
January 13, 2013— of the above Log24 post.
January 13 was also the dies natalis of St. James Joyce.
Some related reflections —
"Praeterit figura huius mundi " — I Corinthians 7:31 —
Conclusion of of "The Dead," by James Joyce— The air of the room chilled his shoulders. He stretched himself cautiously along under the sheets and lay down beside his wife. One by one, they were all becoming shades. Better pass boldly into that other world, in the full glory of some passion, than fade and wither dismally with age. He thought of how she who lay beside him had locked in her heart for so many years that image of her lover's eyes when he had told her that he did not wish to live. Generous tears filled Gabriel's eyes. He had never felt like that himself towards any woman, but he knew that such a feeling must be love. The tears gathered more thickly in his eyes and in the partial darkness he imagined he saw the form of a young man standing under a dripping tree. Other forms were near. His soul had approached that region where dwell the vast hosts of the dead. He was conscious of, but could not apprehend, their wayward and flickering existence. His own identity was fading out into a grey impalpable world: the solid world itself, which these dead had one time reared and lived in, was dissolving and dwindling. A few light taps upon the pane made him turn to the window. It had begun to snow again. He watched sleepily the flakes, silver and dark, falling obliquely against the lamplight. The time had come for him to set out on his journey westward. Yes, the newspapers were right: snow was general all over Ireland. It was falling on every part of the dark central plain, on the treeless hills, falling softly upon the Bog of Allen and, farther westward, softly falling into the dark mutinous Shannon waves. It was falling, too, upon every part of the lonely churchyard on the hill where Michael Furey lay buried. It lay thickly drifted on the crooked crosses and headstones, on the spears of the little gate, on the barren thorns. His soul swooned slowly as he heard the snow falling faintly through the universe and faintly falling, like the descent of their last end, upon all the living and the dead. |
Tuesday, June 24, 2008
Tuesday June 24, 2008
X's and O's
Part I: Random Walk
Part II: X's
3/22:
Beckett and Levi-Strauss are
instances of authors for whom
chiasmus and chiastic thinking
for whom chiasmus is a
generator of meaning,
tool of discovery and
philosophical template."
Drama of Life
Part III: O's —
A Cartoon Graveyard
in honor of the late
Gene Persson †
Today's Garfield —
See also
Midsummer Eve's Dream:
"The meeting is closed
with the lord's‡ prayer
and refreshments are served."
† Producer of plays and musicals
including Album and
The Ruling Class
‡ Lower case in honor of
Peter O'Toole, star of
the film version of
The Ruling Class.
(This film, together with
O'Toole's My Favorite Year,
may be regarded as epitomizing
Hollywood's Jesus for Jews.)
Those who prefer
less randomness
in their religion
may consult O'Toole's
more famous film work
involving Islam,
as well as
the following structure
discussed here on
the date of Persson's death:
"The Moslems thought of the
central 1 as being symbolic
of the unity of Allah."
Thursday, March 27, 2008
Thursday March 27, 2008
Back to the Garden
Film star Richard Widmark
died on Monday, March 24.
From Log24 on that date:
"Hanging from the highest limb
of the apple tree are
the three God's Eyes…"
Related material:
The Beauty Test, 5/23/07–
H.S.M. Coxeter's classic
Introduction to Geometry (2nd ed.):
Note the resemblance of
the central part to
a magical counterpart–
the Ojo de Dios
of Mexico's Sierra Madre.
From a Richard Widmark film festival:
GARDEN OF EVIL
Henry Hathaway, 1954
"A severely underrated Scope western, shot in breathtaking mountain locations near Cuernavaca. Widmark, Gary Cooper and Cameron Mitchell are a trio of fortune hunters stranded in Mexico, when they are approached by Susan Hayward to rescue her husband (Hugh Marlowe) from a caved-in gold mine in Indian country. When they arrive at the 'Garden of Evil,' they must first battle with one another before they have to stave off their bloodthirsty Indian attackers. Widmark gives a tough, moving performance as Fiske, the one who sacrifices himself to save his friends. 'Every day it goes, and somebody goes with it,' he says as he watches the setting sun. 'Today it's me.' This was one of the best of Hollywood veteran Henry Hathaway's later films. With a brilliant score by Bernard Herrmann."
See also
the apple-tree
entries from Monday
(the date of Widmark's death)
and Tuesday, as well as
today's previous entry and
previous Log24
entries on Cuernavaca.
Friday, December 9, 2005
Friday December 9, 2005
“It’s all in Plato.”
— C. S. Lewis
Talking Narnia to Your Neighbors
ChristianityToday.com
by Keri Wyatt Kent
“The summer Lindy Lowry was 20,
she rejected the Christian faith
she’d had since childhood–
dismissing it as a fairy tale
that made no sense
in a world full of evil.”
Tales from
The New Yorker:
“Brokeback Mountain” and
by ANTHONY LANE
The Chronicles of Narnia:
“If the movie has to forgo Lewis’s narrative tone, with its grimly Oxonian blend of the bluff and the twee (‘And now we come to one of the nastiest things in this story’), that is fine by me. And, if there is Deep Magic, as Lewis called it, in his tale, it resides not in the springlike coming of Aslan but in the dreamlike, compacted poetry of Lewis’s initial inspiration—the sight of a faun….”
Concluding Unscientific Postscript
From The Circle is Unbroken,
a web page in memory of
June Carter Cash:
Sir Arthur Quiller-Couch (“Q”), quoting Socrates–
“By Hera,” says Socrates, “a fair resting-place, full of summer sounds and scents! This clearing, with the agnus castus in high bloom and fragrant, and the stream beneath the tree so gratefully cool to our feet! Judging from the ornaments and statues, I think this spot must be sacred to Acheloüs and the Nymphs.”
See, too, Q’s quoting of Socrates’s prayer to Pan, as well as the cover of the May 19, 2003, New Yorker:
For a discussion of the music that
Pan is playing (today’s site music),
see my entry of Sept. 10, 2002,
“The Sound of Hanging Rock.”
Tuesday, November 15, 2005
Tuesday November 15, 2005

Upper part of above picture–
From today’s New York Times,
Seeing Mountains in
Starry Clouds of Creation.
Lower part of above picture–
Pilgrimage to Spider Rock:
Vine Deloria Jr.,
Evolution, Creationism,
and Other Modern Myths:
“The continuing struggle between evolutionists and creationists, a hot political topic for the past four decades, took a new turn in the summer of 1999 when the Kansas Board of Education voted to omit the mention of evolution in its newly approved curriculum, setting off outraged cries of foul by the scientific establishment. Don Quixotes on both sides mounted their chargers and went searching for windmills.”
A figure from
last night’s entry,
Spider Woman:
From Sunday, the day
of Vine Deloria’s death,
a picture that might be
called Changing Woman:
Kaleidoscope turning…
Shifting pattern
within unalterable structure…
— Roger Zelazny, Eye of Cat
in Time and Eternity
(Log 24, Feb. 1, 2003)
and
a review
of Fritz Leiber’s
The Big Time,
Sunday, October 9, 2005
Sunday October 9, 2005
Magical Thinking
the first generator at Boulder
(later Hoover) Dam began
transmitting electricity to Los Angeles.”
— Today in History, Associated Press
generates radiance.”
— Hexagram 30
“I know what nothing means.”
— Maria Wyeth in Play It As It Lays
“Nothing is random.”
— Mark Helprin in Winter’s Tale
Maria Wyeth in Las Vegas:
“… She thought about nothing. Her mind was a blank tape, imprinted daily with snatches of things overheard, fragments of dealers’ patter, the beginnings of jokes and odd lines of song lyrics. When she finally lay down nights in the purple room she would play back the day’s tape, a girl singing into a microphone and a fat man dropping a glass, cards fanned on a table and a dealer’s rake in closeup and a woman in slacks crying and the opaque blue eyes of the guard at some baccarat table. A child in the harsh light of a crosswalk on the Strip. A sign on Fremont Street. A light blinking. In her half sleep the point was ten, the jackpot was on eighteen, the only man that could ever reach her was the son of a preacher man, someone was down sixty, someone was up, Daddy wants a popper and she rode a painted pony let the spinning wheel spin.
By the end of a week she was thinking constantly about where her body stopped and the air began, about the exact point in space and time that was the difference between Maria and other. She had the sense that if she could get that in her mind and hold it for even one micro-second she would have what she had come to get. As if she had fever, her skin burned and crackled with a pinpoint sensitivity. She could feel smoke against her skin. She could feel voice waves. She was beginning to feel color, light intensities, and she imagined that she could be put blindfolded in front of the signs at the Thunderbird and the Flamingo and know which was which. ‘Maria,’ she felt someone whisper one night, but when she turned there was nobody.
She began to feel the pressure of Hoover Dam, there on the desert, began to feel the pressure and pull of the water. When the pressure got great enough she drove out there. All that day she felt the power surging through her own body. All day she was faint with vertigo, sunk in a world where great power grids converged, throbbing lines plunged finally into the shallow canyon below the dam’s face, elevators like coffins dropped into the bowels of the earth itself. With a guide and a handful of children Maria walked through the chambers, stared at the turbines in the vast glittering gallery, at the deep still water with the hidden intakes sucking all the while, even as she watched, clung to the railings, leaned out, stood finally on a platform over the pipe that carried the river beneath the dam. The platform quivered. Her ears roared. She wanted to stay in the dam, lie on the great pipe itself, but reticence saved her from asking.
‘Just how long have you been here now,’ Freddy Chaikin asked when she ran into him in Caesar’s. ‘You planning on making a year of it? Or what?'”
Related material
The front page of today’s
New York Times Book Review
and Log24, July 15, 2004:
A quotation that somehow
seems relevant: O the mind, mind has mountains, |
Thursday, October 17, 2002
Thursday October 17, 2002
Slieve na mBan
The view in the entry below is from Slievenamon or Slieve/Sliabh na mBan, a mountain in County Tipperary.
From an interview with Dr. Mary McAuliffe, an historian who specializes in women’s history of the medieval period in Ireland:
“It seems that there were no witchcraft trials in the Gaelic Irish areas. There isn’t a tradition of witchcraft in the Gaelic Irish communities because people believed in magical women…. Another interesting thing about the… case was that it happened in Slieve na mBan, where the barrier between this world and the next is thinnest. Slieve na mBan means the ‘mountain of women.'”
From Finn’s Household in Part II Book I of
and of the Fianna of Ireland,
“Where do you come from, little one, yourself and your sweet music?” said Finn. “I am come,” he said, “out of the place of the Sidhe in Slieve-nam-ban….”