Log24

Monday, January 16, 2017

The Magic Valley*

Filed under: Uncategorized — m759 @ 1:25 PM

An alternative to Davos

From a professor at Grand Valley

* Title suggested by Thomas Mann's 1924 novel about Davos

Friday, May 22, 2015

Mathmagic Land

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

Donald Duck with Pythagorean pentagram on hand

Donald in Mathmagic Land

Manly P. Hall

Friday, July 25, 2014

Magic for Jews

Filed under: Uncategorized — Tags: — m759 @ 8:00 PM

(Continued from April 8, 2013.)

See Two Blocks Short of a Design (May 5, 2011).

Magic in the Moonshine

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

“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

Filed under: Uncategorized — Tags: , , — m759 @ 11:29 AM

(Continued from May 14, 2014.)

See also consciousness growth and the previous post.

Wednesday, May 14, 2014

Death in Mathmagic Land

Filed under: Uncategorized — Tags: , — m759 @ 3:28 PM

"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

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

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

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

Two Blocks Short of a Design:

A sequel to this morning's post on Douglas Hofstadter

http://www.log24.com/log/pix11A/110505-ThemeAndVariations-Hofstadter.jpg

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 —

http://www.log24.com/log/pix11A/110505-BlockDesignTheory.jpg

Mathematics

http://www.log24.com/log/pix11A/110505-WikipediaFanoPlane.jpg

The Fano plane block design

Magic

http://www.log24.com/log/pix11A/110505-DeathlyHallows.jpg

The Deathly Hallows  symbol—
Two blocks short of  a design.

Saturday, February 10, 2018

Into the Upside Down

Filed under: Uncategorized — 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

Wednesday, January 14, 2015

Kulturkampf for Princeton*

Filed under: Uncategorized — Tags: — m759 @ 2:01 PM

Einstein and Thomas Mann (author of 'The Magic Mountain') at 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

Filed under: Uncategorized — m759 @ 2:01 AM

"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.

Tuesday, April 3, 2018

The Cage Country

Filed under: Uncategorized — Tags: — m759 @ 1:04 PM

See also "Black Mountain Meets Blue Ridge" (Log24, Feb. 22, 2018).

Wednesday, October 18, 2017

Dürer for St. Luke’s Day

Filed under: Geometry — Tags: — m759 @ 1:00 PM

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

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

See also Holy Field in this journal.

Some related mathematics —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

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

Filed under: Geometry — Tags: , — m759 @ 10:13 AM

"God said to Abraham …." — Bob Dylan, "Highway 61 Revisited"

Related material — 

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):

"Ultra Super Magic Square"

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

Filed under: Uncategorized — Tags: , , — m759 @ 4:24 PM

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 —

Donald Duck with pentagram

Tuesday, July 29, 2014

Radio Days

Filed under: Uncategorized — Tags: — m759 @ 11:29 AM

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

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

See…

"Numbers themselves are fictions, abstractions humans invented
to gain more control over the world." — Keith Devlin

Related material:

Friday, July 11, 2014

Thanks for having me on.

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

See also this  journal on April 12, 2014.

Wednesday, January 22, 2014

A Riddle for Davos

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

Hexagonale Unwesen

Einstein and Thomas Mann, Princeton, 1938


IMAGE- Redefining the cube's symmetry planes: 13 planes, not 9.


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

Filed under: Uncategorized — Tags: — m759 @ 1:00 PM
Random Walk with
X's and O's

Part I: Random Walk

NY Lottery June 23, 2008: Mid-day 322, Evening 000

Part II: X's

3/22:

Actor contemplating the Chi-rho Page of the Book of Kells

"Shakespeare, Rilke, Joyce,
Beckett and Levi-Strauss are
instances of authors for whom
chiasmus and chiastic thinking
are of central importance,
for whom chiasmus is a
generator of meaning,
tool of discovery and
  philosophical template."
 
— Chiasmus in the
Drama of Life

Part III: O's —

A Cartoon Graveyard
in honor of the late
Gene Persson

Today's Garfield

Garfield cartoon of June 24, 2008

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:

5x5 ultra super magic square

"The Moslems thought of the
central 1 as being symbolic
of the unity of Allah.
"

Thursday, March 27, 2008

Thursday March 27, 2008

Filed under: Uncategorized — Tags: — m759 @ 3:29 PM

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…"

    — Ken Kesey  

Related material:

The Beauty Test, 5/23/07–
 
H.S.M. Coxeter's classic
Introduction to Geometry (2nd ed.):

The image “http://www.log24.com/log/pix07/070523-Coxeter62.jpg” cannot be displayed, because it contains errors.

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

Filed under: Uncategorized — m759 @ 5:01 PM
Fairy Tales

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:

       The image “http://www.log24.com/log/pix05B/051209-Cin.gif” cannot be displayed, because it contains errors.

  “Brokeback Mountain” and

“The Chronicles of Narnia.”

  by ANTHONY LANE

Brokeback Mountain:

“This slow and stoic movie, hailed as a gay Western, feels neither gay nor especially Western….”

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

Filed under: Uncategorized — m759 @ 11:07 AM
Windmills
 
The image “http://www.log24.com/log/pix05B/051115-StarRocks1.jpg” cannot be displayed, because it contains errors.

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:

“This magical place, according to Navajo Legend, was the home of Spider Woman, who gave the gift of weaving to the Dineh’ People.  Today’s Navajos trace the excellence of their finest textiles to this time of legends, when their patron, Changing Woman, met Spider Woman, the first Weaver.”

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.”

Related material–

A figure from
last night’s entry,
Spider Woman:

Fritz Leiber's 'Spider' symbol

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     

See also the windmill figure

The image “http://www.log24.com/theory/images/Whirl3.gif” cannot be displayed, because it contains errors.

in Time and Eternity
(Log 24, Feb. 1, 2003)

and

a review
of Fritz Leiber’s
The Big Time,

The image “http://www.log24.com/log/pix05B/051115-BigTimePic.jpg” cannot be displayed, because it contains errors.

a story that works.”

Sunday, October 9, 2005

Sunday October 9, 2005

Filed under: Uncategorized — m759 @ 11:00 AM
Today’s Sermon:
Magical Thinking

On this date– “In 1936,
the first generator at Boulder
(later Hoover) Dam began
transmitting electricity to Los Angeles.”
— Today in History, Associated Press

“Brightness doubled
   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:

The image “http://www.log24.com/log/pix04A/040715-Pit2.jpg” cannot be displayed, because it contains errors.

A quotation that somehow
seems relevant:

O the mind, mind has mountains,
   cliffs of fall
Frightful, sheer, no-man fathomed.
   Hold them cheap
May who ne’er hung there.

Gerard Manley Hopkins

Thursday, October 17, 2002

Thursday October 17, 2002

Filed under: Uncategorized — m759 @ 8:42 AM

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

Gods and Fighting Men
The Story of the Tuatha De Danaan
and of the Fianna of Ireland,
arranged and put into English
by Lady Augusta Gregory
with a preface by W. B. Yeats
[1904]

“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….”

Finn, again!James Joyce

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