Log24

Friday, November 1, 2019

Rules of Magic

Filed under: General — m759 @ 12:21 PM

From Director's Cut (Saturday morning, Oct. 26) —

A related death on Saturday, Oct. 26  —

Tuesday, July 23, 2019

Word Magic

Filed under: General — m759 @ 1:52 PM

"Business-wise, Magic is working—Bloomberg reported 
that the game brought in $500 million in revenue last year.
Hasbro owns Monopoly and Scrabble, but Magic  is its top
game brand. . . . 

The idea of using a card mechanic to generate story has
precedent—the Italian postmodern writer Italo Calvino
generated an entire novel based on drawing from a
tarot card deck. Games provide frameworks that miniaturize
and represent idealized realities; so do narratives."

— Adam Rogers, Sunday, July 21, 2019, at Wired

"The Esper party began . . ." —

Life of the Party

    From Stephen King's Dreamcatcher :

The 'Dreamcatcher' warning

    From Alfred Bester's The Demolished Man :

Alfred Bester— 'The Esper party began.'

    From Anne McCaffrey's To Ride Pegasus :

"… it's going to be accomplished in steps, this
establishment of the Talented in the scheme of things."

Adam Rogers at Wired  as quoted above —

"The idea of using a card mechanic to generate story
has precedent. . . ."

See The Greater Trumps .

Friday, April 13, 2018

Mathmagic Land

Filed under: General — Tags: — m759 @ 5:45 PM

Continued from yesterday.

From Log24 on July 24, 2014

Later . . .

"Button, Button, Who's Got the Button?"

Manil Suri?

See also The Abacus Conundrum.

Monday, June 5, 2017

Magic in Mexico

Filed under: General — m759 @ 11:59 AM

This post's title is that of a book in the 1958 film
"Bell Book and Candle." 

See also

Monday, January 16, 2017

The Magic Valley*

Filed under: General — m759 @ 1:25 PM

An alternative to Davos

From a professor at Grand Valley

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

Monday, July 18, 2016

ART WARS: Magic Circles

Filed under: General — m759 @ 2:01 AM

An artist mentioned in  a NY Times  obituary  this morning —

(Click for the source.)

I prefer some not-so-magic circles —

Primitive roots modulo 17 and a related figure

Click for related posts tagged root circle.

Friday, May 22, 2015

Mathmagic Land

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

Donald Duck with Pythagorean pentagram on hand

Donald in Mathmagic Land

Manly P. Hall

Wednesday, February 18, 2015

Magical and Seductive

Filed under: General — m759 @ 9:45 AM

"I am trying to introduce a narrative,
something magical and seductive…."

— Oslo artist Josefine Lyche, translated
from the Norwegian by Google

Perhaps something like Arcade Fire or
Taylor Swift? (Click links for related posts.)

Friday, July 25, 2014

Magic for Jews

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

(Continued from May 14, 2014.)

See also consciousness growth and the previous post.

Thursday, June 12, 2014

Magic

Filed under: General — Tags: — m759 @ 10:00 AM

Wikipedia article on mathematician Herbert Wilf:

“One of Wilf’s former students is Richard Garfield,
the creator of the collectible card game
Magic: The Gathering .”

For more about Garfield, see yesterday’s post House of Cards.

Related material:  This journal on the date of Wilf’s death—

See also 2/02, 2014.

Wednesday, May 14, 2014

Death in Mathmagic Land

Filed under: General — 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: General,Geometry — 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, December 6, 2012

Magic Square

Filed under: General — m759 @ 10:18 PM

This post was suggested by the December 4th death
of modernist composer Jonathan Harvey, 73,
and by Harvey's reflections on his 2007 opera
Wagner Dream .

For related reflections, see the Oct. 10 post on
the Dürer magic square in Mann's Doctor Faustus .

See also a December 2nd post on the Nov. 18 death of
chess grandmaster Elena Akhmilovskaya Donaldson.

IMAGE- Chess grandmaster and Dürer's angel with magic square
 

Thursday, July 28, 2011

Magical Realism Revisited

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

http://www.log24.com/log/pix11B/110728-RogerCohen-MagicalRealism.jpg

http://www.log24.com/log/pix11B/110727-ProtoZone-Quilters500w.jpg

http://www.log24.com/log/pix11B/110727-LICM-QuiltMaker500w.jpg

The magical part— Synchronicity—

See Roger Cohen in this journal on January 15, 2009 and, on the
same date, Jesse Jarnow on Bob Dylan in  The Jewish Daily Forward .

The realism part— Cohen's "smart power" and IQ tests involving pattern blocks.

The above quilt pattern software (both versions) is by Jarnow's father Al.
For a realistic approach to such patterns, see Blockheads in this journal.

Friday, July 15, 2011

The Magic of Numbers*

Filed under: General — Tags: — m759 @ 2:29 PM

NY Lottery this afternoon:

http://www.log24.com/log/pix11B/110715-NYlotteryMidday.jpg

See Post 757— "Release Date"— and The-Numbers.com
on a film with the release date 7/3/85.

* Title of a course at Harvard. See (for instance)
the Harvard page on The Numerology of the Beast

"Now in math the magic is not in special numbers
like 7 or 28, but in the fabric of number systems…."

Sure it is.

Thursday, June 23, 2011

Script Magic

Filed under: General — m759 @ 3:33 AM

In a Jewish Cathedral

From The New York Times Magazine  of Sunday, April 6, 1986—

"David Rayfiel's Script Magic" by Alex Ward

WHEN THE CALL came last year to revise ''The Morning After,'' Rayfiel was working on a screenplay about the 1911 Triangle Shirtwaist Company fire for Barbra Streisand and Jane Fonda. He has now resumed work— as the principal writer, not the reviser— on that script. But chances are good that he will have further interruptions. Pollack will probably call and say, as he usually does, ''David, I need access to your brain.'' And Rayfiel will probably say, as he usually does, ''That's O.K., I'm not using it.'' He will revise another script, and be reluctant about taking credit for it.

''I guess it's like the medieval stonecutters who worked on the cathedrals,'' he says. ''There's all that elaborate work. The saints were carved by one guy, the cherubs by someone else. They didn't care about getting credit, they knew what they'd done. I'm like that. I'm the guy who does the cherubs.''

Related material:

Proginoskes in this journal and Abracadabra from the midnight of June 18-19.

See also Rayfiel's obituary in today"s Times .

For some quite different work, also  from April 1986, see—

Oslo: Points and Hyperplanes.

Thursday, May 5, 2011

On Art and Magic

Filed under: General,Geometry — 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.

Thursday, October 14, 2010

Diamond Theory and Magic Squares

Filed under: General,Geometry — Tags: , — m759 @ 6:19 PM

"A world of made
is not a world of born— pity poor flesh
and trees, poor stars and stones, but never this
fine specimen of hypermagical
ultraomnipotence."

— e. e. cummings, 1944

For one such specimen, see The Matrix of Abraham
a 5×5 square that is hypermagical… indeed, diabolical.

Related material on the algebra and geometry underlying some smaller structures
that have also, unfortunately, become associated with the word "magic"—

  1. Finite Geometry of the Square and Cube
  2. Clifford Pickover on a 4×4 square
  3. Christopher J. Henrich on the geometry of 4×4 magic squares
    (without any mention of  [1] above or related work dating back to 1976)

" … listen: there's a hell
of a good universe next door; let's go"

— e. e. cummings

Happy birthday, e. e.

Tuesday, November 12, 2019

Exercise

Filed under: General — m759 @ 2:26 AM

Wednesday, October 2, 2019

A Long Literary Tradition

Filed under: General — Tags: — m759 @ 12:38 PM

"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 —

Harvard Showbiz.

Sunday, September 29, 2019

Spiritual Kin

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

"The 15 Puzzle and the Magic Cube
are spiritual kin …."

"Metamagical Themas"  column,
Douglas R. Hofstadter, Scientific American ,
Vol. 244, No. 3 (March 1981), pp. 20-39

As are the 15 Schoolgirls and the Eightfold Cube.

Stage Direction: “Comments Off.”

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

The previous post dealt with "magic" cubes, so called because of the
analogous "magic" squares. Douglas Hofstadter has written about a 
different, physical , object, promoted as "the  Magic Cube," that Hofstadter
felt embodied "a deep invariant":

Saturday, August 24, 2019

Sophia in Storyville*

Filed under: General — m759 @ 12:54 PM

* See the previous post.  Related material:
The Lolita Express  and Magic Carpet Ride.

Tuesday, August 13, 2019

The Central Myth

Filed under: General — Tags: — m759 @ 12:12 PM

Wikipedia on film producer Lorenzo di Bonaventura
(Harvard AB (1980) in Intellectual History*) —

"His tenure at Warner Bros. included discovering and
shepherding The Matrix  into production, and the
purchase of the rights to the Harry Potter  books by 
J. K. Rowling."

From the previous post

"But he enters into the central myth of
this book at another, higher level as well;
for he is an artist, a potter . . . ."

— Wendy Doniger O'Flaherty on 
Claude Lévi-Strauss, author of 
The Jealous Potter

* See as well "What is Intellectual History?" and
   Magic for Liars .

Friday, August 9, 2019

For Wright State University

Filed under: General — m759 @ 12:31 AM

That university, in Dayton, Ohio, appeared in the previous post.

A curious recent wardrobe choice in Dayton suggests a review
of posts tagged Mathmagic Land.

Wednesday, July 24, 2019

Frameworks

Filed under: General — m759 @ 7:50 PM

"Games provide frameworks that miniaturize
and represent idealized realities; so do narratives."

— Adam Rogers, Sunday, July 21, 2019, at Wired

Reviewing yesterday's post Word Magic

See also a technological framework (the microwave at left) vs. a
purely mathematical framework (the pattern on the towel at right)
in the image below:

170703-The_Forger-Christopher_Plummer-2015-500w.jpg (500×336)

For some backstory about the purely mathematical framework, 
see Octad Generator in this journal.

Monday, July 22, 2019

Space, Time, Form

Filed under: General — Tags: — m759 @ 3:33 AM

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

Click the image for some remarks on a related novel.

Monday, July 15, 2019

Social Prism

Filed under: General — Tags: — m759 @ 4:19 PM

"Douglas Crimp, Who Saw Art Through a Social Prism*,
Is Dead at 74
" — The online New York Times  today

Crimp reportedly died on July 5. This  journal on that date —

* Update of 11:35-11:59 PM the same day — The Times  headline has
been changed, but the phrase "social prism" can still be found in the article's
source code, and the earlier headline found in a Google search —

Another prism note — "Magic in the Moonshine."

Tuesday, July 9, 2019

Perception of Space

Filed under: General — Tags: , — m759 @ 10:45 AM

(Continued)

The three previous posts have now been tagged . . .

Tetrahedron vs. Square  and  Triangle vs. Cube.

Related material —

Tetrahedron vs. Square:

Labeling the Tetrahedral Model  (Click to enlarge) —

Triangle vs. Cube:

and, from the date of the above John Baez remark —

Friday, July 5, 2019

“Darkly Enchanting”

Filed under: General — m759 @ 11:05 PM

For the Church of Synchronology

Thursday, July 4, 2019

From Devil’s Night 2014

Filed under: General — m759 @ 7:59 AM

And now, General, time presses; and America is in a hurry.
Have you realized that though you may occupy towns and win battles,
you cannot conquer a nation? — The Devil's Disciple

A figure related to Dürer's "magic" square posted during Devil's Night —

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, April 1, 2019

Indiana Jones and the Temple of High Life

Filed under: General — m759 @ 5:12 AM

Posts now tagged Spaceman include an image . . .

From March 9

Meanwhile . . .

Related material —

Friday, March 29, 2019

The Blazon World*

Filed under: General — m759 @ 4:59 PM

“At that instant he saw, in one blaze of light,
an image of unutterable conviction,
the reason why the artist works and lives
and has his being — the reward he seeks —
the only reward he really cares about,
without which there is nothing. It is to snare
the spirits of mankind in nets of magic,
to make his life prevail through his creation,
to wreak the vision of his life, the rude and painful
substance of his own experience, into the congruence
of blazing and enchanted images that are themselves
the core of life, the essential pattern whence
all other things proceed, the kernel of eternity.”

— Thomas Wolfe, Of Time and the River

* Title suggested by that of a Siri Hustvedt novel.
   See also Blazon in this journal.

Saturday, March 23, 2019

Plan 9 Manifesto

Filed under: General — m759 @ 7:11 PM

"Arnheim was a particularly important source
for Norway's principal architectural theorist,
Christian Norberg-Schulz."

— Andrew Peter Steen, University of Queensland
doctoral thesis, 2015

See

"Nine is a very powerful Nordic number."

— Katherine Neville, The Magic Circle

Thursday, February 28, 2019

Fooling

Filed under: General — m759 @ 10:12 AM

Galois (i.e., finite) fields described as 'deep modern algebra'

IMAGE- History of Mathematics in a Nutshell

The two books pictured above are From Discrete to Continuous ,
by Katherine Neal, and Geometrical Landscapes , by Amir Alexander.

Note: There is no Galois (i.e., finite) field with six elements, but
the theory  of finite fields underlies applications of six-set geometry.

Tuesday, December 18, 2018

Shadowhunter Tales

Filed under: General — Tags: , — m759 @ 12:59 PM

The recent post "Tales from Story Space," about the 18th birthday
of the protagonist in the TV series "Shadowhunters" (2016-),
suggests a review of the actual  18th birthday of actress Lily Collins.

Collins is shown below warding off evil with a magical rune as
a shadowhunter in the 2013 film "City of Bones" —

She turned 18 on March 18, 2007.  A paper on symmetry and logic
referenced here on that date displays the following "runes" of 
philosopher Charles Sanders Peirce

See also Adamantine Meditation  (Log24, Oct. 3, 2018)
and the webpage Geometry of the I Ching.

Wednesday, December 5, 2018

The Hassenfeld Legacy

Filed under: General — m759 @ 11:30 AM

The Finkelstein Talisman —

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

"Before time began, there was the Cube."

— Optimus Prime in "Transformers" (Paramount, 2007)
 

Wikipedia on Hasbro

Three American Jewish brothers,[6] Herman, Hillel, and Henry Hassenfeld[7] 
founded Hassenfeld Brothers in Providence, Rhode Island in 1923 . . . .
 

The Hassenfeld Auction — 

Also on September 16, 2015 —


 

The Hindman Image —

The Hood Warenkorb —

Under the Hood —

Megan Fox in "Transformers" (2007) —


 

This Way to the Egress —

Sunday, November 25, 2018

Ricky Jay

Filed under: General — m759 @ 2:05 AM

See also Ricky Jay in this  journal.

Wednesday, October 24, 2018

Raiders of the Lost Crucible Continues

Filed under: General — Tags: , , — m759 @ 10:22 PM

Wednesday, October 17, 2018

Aesthetics

Filed under: General,Geometry — Tags: — m759 @ 11:22 AM
 

From "The Phenomenology of Mathematical Beauty,"
by Gian-Carlo Rota —

The Lightbulb Mistake

. . . . Despite the fact that most proofs are long, and despite our need for extensive background, we think back to instances of appreciating mathematical beauty as if they had been perceived in a moment of bliss, in a sudden flash like a lightbulb suddenly being lit. The effort put into understanding the proof, the background material, the difficulties encountered in unraveling an intricate sequence of inferences fade and magically disappear the moment we become aware of the beauty of a theorem. The painful process of learning fades from memory, and only the flash of insight remains.

We would like  mathematical beauty to consist of this flash; mathematical beauty should  be appreciated with the instantaneousness of a lightbulb being lit. However, it would be an error to pretend that the appreciation of mathematical beauty is what we vaingloriously feel it should be, namely, an instantaneous flash. Yet this very denial of the truth occurs much too frequently.

The lightbulb mistake is often taken as a paradigm in teaching mathematics. Forgetful of our learning pains, we demand that our students display a flash of understanding with every argument we present. Worse yet, we mislead our students by trying to convince them that such flashes of understanding are the core of mathematical appreciation.

Attempts have been made to string together beautiful mathematical results and to present them in books bearing such attractive titles as The One Hundred Most Beautiful Theorems of Mathematics . Such anthologies are seldom found on a mathematician’s bookshelf. The beauty of a theorem is best observed when the theorem is presented as the crown jewel within the context of a theory. But when mathematical theorems from disparate areas are strung together and presented as “pearls,” they are likely to be appreciated only by those who are already familiar with them.

The Concept of Mathematical Beauty

The lightbulb mistake is our clue to understanding the hidden sense of mathematical beauty. The stark contrast between the effort required for the appreciation of mathematical beauty and the imaginary view mathematicians cherish of a flashlike perception of beauty is the Leitfaden  that leads us to discover what mathematical beauty is.

Mathematicians are concerned with the truth. In mathematics, however, there is an ambiguity in the use of the word “truth.” This ambiguity can be observed whenever mathematicians claim that beauty is the raison d’être of mathematics, or that mathematical beauty is what gives mathematics a unique standing among the sciences. These claims are as old as mathematics and lead us to suspect that mathematical truth and mathematical beauty may be related.

Mathematical beauty and mathematical truth share one important property. Neither of them admits degrees. Mathematicians are annoyed by the graded truth they observe in other sciences.

Mathematicians ask “What is this good for?” when they are puzzled by some mathematical assertion, not because they are unable to follow the proof or the applications. Quite the contrary. Mathematicians have been able to verify its truth in the logical sense of the term, but something is still missing. The mathematician who is baffled and asks “What is this good for?” is missing the sense  of the statement that has been verified to be true. Verification alone does not give us a clue as to the role of a statement within the theory; it does not explain the relevance  of the statement. In short, the logical truth of a statement does not enlighten us as to the sense of the statement. Enlightenment , not truth, is what the mathematician seeks when asking, “What is this good for?” Enlightenment is a feature of mathematics about which very little has been written.

The property of being enlightening is objectively attributed to certain mathematical statements and denied to others. Whether a mathematical statement is enlightening or not may be the subject of discussion among mathematicians. Every teacher of mathematics knows that students will not learn by merely grasping the formal truth of a statement. Students must be given some enlightenment as to the sense  of the statement or they will quit. Enlightenment is a quality of mathematical statements that one sometimes gets and sometimes misses, like truth. A mathematical theorem may be enlightening or not, just as it may be true or false.

If the statements of mathematics were formally true but in no way enlightening, mathematics would be a curious game played by weird people. Enlightenment is what keeps the mathematical enterprise alive and what gives mathematics a high standing among scientific disciplines.

Mathematics seldom explicitly acknowledges the phenomenon of enlightenment for at least two reasons. First, unlike truth, enlightenment is not easily formalized. Second, enlightenment admits degrees: some statements are more enlightening than others. Mathematicians dislike concepts admitting degrees and will go to any length to deny the logical role of any such concept. Mathematical beauty is the expression mathematicians have invented in order to admit obliquely the phenomenon of enlightenment while avoiding acknowledgment of the fuzziness of this phenomenon. They say that a theorem is beautiful when they mean to say that the theorem is enlightening. We acknowledge a theorem’s beauty when we see how the theorem “fits” in its place, how it sheds light around itself, like Lichtung — a clearing in the woods. We say that a proof is beautiful when it gives away the secret of the theorem, when it leads us to perceive the inevitability of the statement being proved. The term “mathematical beauty,” together with the lightbulb mistake, is a trick mathematicians have devised to avoid facing up to the messy phenomenon of enlightenment. The comfortable one-shot idea of mathematical beauty saves us from having to deal with a concept that comes in degrees. Talk of mathematical beauty is a cop-out to avoid confronting enlightenment, a cop-out intended to keep our description of mathematics as close as possible to the description of a mechanism. This cop-out is one step in a cherished activity of mathematicians, that of building a perfect world immune to the messiness of the ordinary world, a world where what we think should be true turns out to be true, a world that is free from the disappointments, ambiguities, and failures of that other world in which we live.

How many mathematicians does  it take to screw in a lightbulb?

Monday, September 24, 2018

Mathematics as Art

Filed under: General — m759 @ 8:45 AM

[Revised throughout the day on Sept. 24, 2018.]

"Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to explain
how art fits into our subject and what we mean by beauty."

— Sir Michael Atiyah, quoted here on April 4, 2016

Atiyah's remarks today on the Riemann hypothesis, based on his earlier
remarks on "arithmetic physics" and α, the fine-structure constant,
seem to exemplify the "magic and mystery" approach.

From some previous Log24 posts

AMS on 'mathematics, magic, and mystery,' April 2014

MAA on 'mathematics, magic, and mystery,' April 2014

Update of 6:06 PM ET the same day —

https://twitter.com/mpoessel/status/1044131977950109696

For related magic and mystery, see Log24 posts tagged on090405.

Wednesday, July 4, 2018

Raiders of the Lost Spell

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

From The New York Review of Books ,
issue dated July 19, 2018 —

"The only useful thing about The Seventh Function of Language 
is the idea that one would need some magical means to persuade
through language, some secret spell. Useful, because perfectly
ridiculous. The spell, we know, exists . . . ."

— "Imagining the Real," by Wyatt Mason

Some nineteenth-century thoughts along these lines:

See also Declarations.

Monday, May 7, 2018

Fish Babel

Filed under: General,Geometry — Tags: , , — m759 @ 10:00 AM

Stanley Fish in the online New York Times  today —

". . . Because it is an article of their faith that politics are bad
and the unmediated encounter with data is good,
internet prophets will fail to see the political implications
of what they are trying to do, for in their eyes political implications
are what they are doing away with.

Indeed, their deepest claim — so deep that they are largely
unaware of it — is that politics can be eliminated. They don’t
regard politics as an unavoidable feature of mortal life but as
an unhappy consequence of the secular equivalent of the
Tower of Babel: too many languages, too many points of view.
Politics (faction and difference) will just wither away when
the defect that generates it (distorted communication) has
been eliminated by unmodified data circulated freely among
free and equal consumers; everyone will be on the same page,
reading from the same script and apprehending the same
universal meanings. Back to Eden!"

The final page, 759, of the Harry Potter saga —

"Talk about magical thinking!" — Fish, ibidem .

See also the above Harry Potter page 
in this  journal Sunday morning.

Friday, April 13, 2018

Strahlenkreis*

Filed under: General — Tags: , — m759 @ 11:23 PM

Or:  A Magic Circle for Penny 

The subtitle was suggested by the character Penny
in today's post on Mathmagic Land.

* Ray-circle. See an image search.

Thursday, April 12, 2018

Play

Filed under: General — Tags: — m759 @ 1:51 PM

Continued from Monday morning, for Lev Grossman —

Sunday, April 8, 2018

Raiders of the Lost Circle

Filed under: General — Tags: — m759 @ 10:10 AM

Today is Orthodox Easter.

From a search in this journal for "Magic Circle" —

Saturday, April 7, 2018

Dot

Filed under: General — Tags: — m759 @ 10:41 PM

The late Philip J. Davis in his 2004 essay 

"A Brief Look at Mathematics and Theology,"
Humanistic Mathematics Network Journal ,
Issue 27, Article 14. Available at:
http://scholarship.claremont.edu/hmnj/vol1/iss27/14/ 

wrote —

"In my childhood, the circle persisted as a potent magic figure
in the playtime doggerel 'Make a magic circle and sign it with a dot.'
The interested reader will find thousands of allusions to the phrase
'magic circle' on the Web."

There are fewer allusions to "magic circle" + "sign it with a dot."

One such allusion (click to enlarge) is . . .

Davis died on Pi Day .

Tuesday, April 3, 2018

The Cage Country

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

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

Entertainment Overload

Filed under: General — Tags: — m759 @ 1:00 AM

From a May 13, 2010, New York Times  theater review

From a link in a post from yesterday evening —

"Why don't you come with me, little girl,
on a magic carpet ride?" — Steppenwolf lyrics

These lyrics are heard in  Star Trek: First Contact  (1996).

Related entertainment —

The production of "Passion Play" reviewed above opened May 12, 2010.

See also this journal on that date.

Saturday, February 24, 2018

The Ugly Duck

Filed under: General,Geometry — m759 @ 7:11 PM

"What of the night
That lights and dims the stars?
Do you know, Hans Christian,
Now that you see the night?"

— The concluding lines of
"Sonatina to Hans Christian,"
by Wallace Stevens
(in Harmonium  (second edition, 1931))

From "Mathmagic Land" (May 22, 2015)

Donald Duck with Pythagorean pentagram on hand

Donald in Mathmagic Land

From "The Trials of Device" (April 24, 2017)

Wittgenstein's pentagram and 4x4 'counting-pattern'

Pentagon with pentagram    

Sunday, February 11, 2018

Visions of Hell

Filed under: General — m759 @ 9:45 PM

In memory of  a Manhattan art figure
who reportedly died on
Wednesday, February Seventh, 2018 —

ABOUT 'ASCENSION VARIATIONS'

Ascension Variations is a magical adventure
woven from grand and pedestrian touches, and
in the end the space itself is the star
or Ms. Monk's transformation of it.
For an hour, we've lived in a spiral,
where up is down and down is up.
It's a sacred place.”

— Gia Kourlas, The New York Times , March 6, 2009

See also the previous post — yesterday's Into the Upside Down
and two posts of February Seventh:

Conceptual Art  and  Conceptual Minimalism.

For some related artistic remarks, see this  journal on March 6-7, 2009.

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

Sunday, January 21, 2018

Spiritual Memoir

Filed under: General — m759 @ 9:09 AM

In her new spiritual memoir . . . .

Armies of the Night —

Armies of the Day —

Cole Porter —

Night and Day —

Wednesday, January 17, 2018

At Heaven’s Gate

Filed under: General — Tags: — m759 @ 7:30 AM

(Continued from September 12, 2005)

The previous post contrasted the number-triple 11-7-8 below
with number triples 12-9-5 and 12-5-9.

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

A perhaps more logical counterpart of the triple 11-7-8, based
on opposite  locations of star-points or cube-edges, is
the triple 9-12-5. For a theological interpretation, see 9/12/05.

Tuesday, January 16, 2018

An Orison for Ha-Why

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

'Cloud Atlas' book cover illustrating the film

Lines from characters played in the film by Tom Hanks and Halle Berry —

— Cloud Atlas , by David Mitchell (2004).

An orison of sorts from a post on Martin Scorsese's
birthday, Sunday, Nov. 18, 2007 —

BlackBerry with pictures from Log24

Displayed on the BlackBerry are parts
of Log24 posts from October 25, 2007,
and October 24, 2007.

Related pattern geometry 

From a Log24 search for Angleton + Brotherhood:
A photo of Angleton in a post from 12/9/5

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

From a post of 11/7/8

http://www.log24.com/log/pix08A/081107-Tilespuzzle.jpg

A cryptic note for Dan Brown:

The above dates 11/7/8 and 12/9/5 correspond to the corner-labels
(read clockwise and counter-clockwise) of the two large triangles
in the Finkelstein Talisman

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

Above: More symbology for Tom Hanks from
this morning's post The Pentagram Papers.

The above symbology is perhaps better suited to Hanks in his
role as Forrest Gump than in his current role as Ben Bradlee.

The image “http://www.log24.com/log/pix05B/051211-gump.jpg” cannot be displayed, because it contains errors.

For Hanks as Dan Brown's Harvard symbologist 
Robert Langdon, see the interpretation 12/5/9, rather
than 12/9/5, of the above triangle/cube-corner label.

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.

Sunday, January 7, 2018

Clueless:

Filed under: General — Tags: — m759 @ 11:00 AM

Peter Zhang and Eric McLuhan on Interality

Saturday, December 9, 2017

Lackaday Quotation

Filed under: General — m759 @ 9:45 AM

The previous post discussed an alleged description by
William H. Gass of his fellow author Malcolm Lowry as 
"a black magician."

In defense of Gass, it seems that quote is inaccurate:

Friday, December 8, 2017

Mythos and Logos

Filed under: General,Geometry — m759 @ 9:48 PM

Part I:  Black Magician

"Schools of criticism create their own canons, elevating certain texts,
discarding others. Yet some works – Malcolm Lowry’s Under the Volcano
is one of them – lend themselves readily to all critical approaches."

— Joan Givner, review of 
A Darkness That Murmured: Essays on Malcolm Lowry and the Twentieth Century
by Frederick Asals and Paul Tiessen, eds.

The Asals-Tiessen book (U. of Toronto Press, 2000) was cited today
by Margaret Soltan (in the link below) as the source of this quotation —

"When one thinks of the general sort of snacky
under-earnest writers whose works like wind-chimes
rattle in our heads now, it is easier to forgive Lowry
his pretentious seriousness, his old-fashioned ambitions,
his Proustian plans, [his efforts] to replace the reader’s
consciousness wholly with a black magician’s."

A possible source, Perle Epstein, for the view of Lowry as black magician

Part II:  Mythos  and Logos

Part I above suggests a review of Adam Gopnik as black magician
(a figure from Mythos ) —

Tuesday, November 7, 2017

Polarities and Correlation

Filed under: Uncategorized — Tags:  
— m759 @ 11:00 PM 

— and of an opposing figure from Logos
     Paul B. Yale, in the references below:

Thursday, November 2, 2017

The Trojan Pony

Filed under: G-Notes,General,Geometry — m759 @ 7:31 PM

From a search in this journal for Springer Knight

     Binary coordinates for a 4x2 array  Chess knight formed by a Singer 7-cycle

Related material from Academia —

Nash and Needleman, 'On Magic Finite Projective Space,' Dec. 4, 2014

See also Log24 posts from the above "magic" date,
December 4, 2014, now tagged The Pony Argument.

Thursday, October 19, 2017

Design Grammar***

Filed under: G-Notes,General,Geometry — m759 @ 10:22 PM

The elementary shapes at the top of the figure below mirror
the looking-glass property  of the classical Lo Shu square.

The nine shapes at top left* and their looking-glass reflection
illustrate the looking-glass reflection relating two orthogonal
Latin squares over the three digits of modulo-three arithmetic.

Combining these two orthogonal Latin squares,** we have a
representation in base three of the numbers from 0 to 8.

Adding 1 to each of these numbers yields the Lo Shu square.

* The array at top left is from the cover of
Wonder Years:
Werkplaats Typografie 1998-2008
.

** A well-known construction.

*** For other instances of what might be
called "design grammar" in combinatorics,
see a slide presentation by Robin Wilson.
No reference to the work of Chomsky is
intended.

Wednesday, October 18, 2017

Three Small Grids

Filed under: General,Geometry — m759 @ 8:48 PM

An earlier post today, now tagged "Three Small Magic Squares,"
suggests a review of a post from October 25 three years ago
that contains the following figure —

Fans of the October Revolution may enjoy a passage
by Rosalind Krauss on grids:

Dürer for St. Luke’s Day

Filed under: G-Notes,General,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: General,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

Halloween Meditation

Filed under: General — Tags: — m759 @ 7:27 PM

Box Office Report —

"Only a peculiar can enter a time loop."

'Only a peculiar can enter a time loop' — Nov. 21, 2016

A post from Halloween season seven years ago last Saturday

Related material — This morning's "Highway 61 Revisited."

Highway 61 Revisited

Filed under: G-Notes,General,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, September 5, 2017

Florence 2001

Filed under: General,Geometry — Tags: — m759 @ 4:44 AM

Or:  Coordinatization for Physicists

This post was suggested by the link on the word "coordinatized"
in the previous post.

I regret that Weyl's term "coordinatization" perhaps has
too many syllables for the readers of recreational mathematics —
for example, of an article on 4×4 magic squares by Conway, Norton,
and Ryba to be published today by Princeton University Press.

Insight into the deeper properties of such squares unfortunately
requires both the ability to learn what a "Galois field" is and the
ability to comprehend seven-syllable words.

Thursday, August 31, 2017

A Conway-Norton-Ryba Theorem

Filed under: General,Geometry — m759 @ 1:40 PM

In a book to be published Sept. 5 by Princeton University Press,
John Conway, Simon Norton,  and Alex Ryba present the following
result on order-four magic squares —

A monograph published in 1976, "Diamond Theory," deals with 
more general 4×4 squares containing entries from the Galois fields
GF(2), GF(4), or GF(16).  These squares have remarkable, if not 
"magic," symmetry properties.  See excerpts in a 1977 article.

See also Magic Square and Diamond Theorem in this  journal.

Tuesday, August 29, 2017

The Finkelstein Talisman

Filed under: General — m759 @ 8:38 PM

An image in memory of a publisher* who reportedly died
on Saturday, August 26, 2017.  

He and his wife wrote a novel, The Twelve , that has been compared to
the classic film "Village of the Damned." (See a sequel in this journal.)

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

For more on the image, see posts now tagged The Finkelstein Talisman.

*
 

Saturday, August 26, 2017

The Seventh Door Meets the Seventh Function

Filed under: General — m759 @ 10:21 AM
 

The Seventh Function
of Language
 
A novel by Laurent Binet

The New York Times  
online Aug. 16, 2017, 
in a book review —

"What if . . . Barthes was murdered? . . . in order to
procure a document that Barthes possessed . . . .
That document explained that, beyond the six
functions of language proposed by the Russian
linguist Roman Jakobson, there was a seventh
secret one:  an occult kind of language-use
guaranteed to persuade, a 'magic' power of
control over a listener."

Schorske mentioned hopefully "the fresh light of
the present" in 1971.

Some later light from Brian Aldiss in his novel
Frankenstein Unbound , first published in 1973

Wednesday, August 16, 2017

Punctum

Filed under: General — Tags: — m759 @ 9:00 AM

Or:  Every Picture Tells a Story  (Continued)

Related material —

The New York Times  online today, in a book review

"What if . . . Barthes was murdered? . . . in order to
procure a document that Barthes possessed . . . .
That document explained that, beyond the six
functions of language proposed by the Russian
linguist Roman Jakobson, there was a seventh
secret one:  an occult kind of language-use
guaranteed to persuade, a 'magic' power of
control over a listener."

See also Barthes in this  journal.

"Down in the Jungle Room" — Marc Cohn

Wednesday, July 5, 2017

The Imaginarium

Filed under: General — m759 @ 1:45 PM

"The heart of the doctor's show is a magic mirror that allows
those who go through it to experience another dimension of
their own minds. Once inside, people choose for good or evil,
opting for — to give one example — either the difficult but
rewarding heights of Mt. Parnassus or the easy pleasures of
Mr. Nick's Lounge Bar. As the doctor angrily puts it when asked
what he's playing at, 'We don't play, what we do is deadly serious,' 
which means nothing less than the eternal battle with the devil
for the spirit of man."

— Kenneth Turan, Los Angeles Times  film critic, Christmas Day 2009,
reviewing "The Imaginarium of Doctor Parnassus."

In terms that might interest the late museum director of the previous post

Quoted here from The New Criterion  on June 2, 2017 —

Quoted here from The New York Times  on June 1, 2017 —

MoMA’s Makeover Rethinks the Presentation of Art

"The new design calls for more gallery space and a transformed
main lobby, physical changes that, along with the re-examination
of art collections and diversity, represent an effort to open up MoMA
and break down the boundaries defined by its founder, Alfred Barr.

'It’s a rethinking of how we were originally conceived,' Glenn D. Lowry,
the museum’s director, said in an interview at MoMA. 'We had created
a narrative for ourselves that didn’t allow for a more expansive reading
of our own collection, to include generously artists from very different
backgrounds.'"

Saturday, April 8, 2017

Eye

Filed under: General — m759 @ 7:24 PM

"I guess I found my future through Billy Name’s eye.
I saw his pictures of the Warhol Factory when I was
in college and thought, 'Oh that’s the place to get to.
Everyone is so beautiful and it looks brilliant and
complicated – art, music, film, but most of all a kind
of wild life.' It looked like the future as I imagined it."

The late Glenn O'Brien in The Guardian
     
on November 8, 2014.  O'Brien reportedly
     died at 70 yesterday, Friday (April 7) morning,
     in Manhattan.

"… through Billy Name's eye …."
Then there is Kurt Seligmann's eye

The above-mentioned Billy Name appeared in this journal
in July 2016  in the post "Coterie (for Philip Rieff)." Also
featured in that post was artist Kurt Seligmann.

A Google Search sidebar on Seligmann today:

Synchronology check of this  journal on the above Guardian  date:

Saturday, November 8, 2014

At 11:59*

Filed under: Uncategorized — m759 @ 11:59 PM 

Fantasy and the Buffered Self.”

*For the title, see Enormous Changes.

See also an 11:59 PM ET post on Thursday, April 6, titled
"Where Entertainment Is God (continues)."

Some related entertainment:

I do not recommend any of the above entertainments,
but they do supply some background for the article
"Fantasy and the Buffered Self" (which is  recommended.)

Monday, February 27, 2017

Tricky Business*

Filed under: General — m759 @ 12:45 AM

* For the title, see Sunday morning.

Wednesday, February 1, 2017

Faust and the Media

Filed under: General — m759 @ 2:00 PM

Announcement of a Harvard event:

"The Future of News: Journalism in a Post-Truth Era,"
 Tuesday, January 31, 4 – 6 pm., Sanders Theatre,
 Harvard University, Cambridge, Mass."

The event as reported by The Harvard Crimson

Related material — This  journal at 12:31 PM ET Tuesday —
"The Devil's Arithmetic," a post with title taken from a 1988
fiction by Jane Yolen.

From the Jan. 28 post Cranking It Up —

"We are rooted in yoga and love the magic
that happens when that practice is
cranked up to eleven." — The late Trevor Tice

Saturday, January 28, 2017

Cranking It Up

Filed under: General — m759 @ 12:17 PM

From "Core," a post of St. Lucia's Day, Dec. 13, 2016 —

'We are rooted in yoga and love the magic that happens when that practice is cranked up to eleven.'

In related news yesterday —

California yoga mogul’s mysterious death:
Trevor Tice’s drunken last hours detailed

"Police found Tice dead on the floor in his home office,
blood puddled around his head. They also found blood
on walls, furniture, on a sofa and on sheets in a nearby
bedroom, where there was a large bottle of Grey Goose
vodka under several blood-stained pillows on the floor."

See as well an image from "The Stone," a post of March 18, 2016 —

Some backstory —

“Lord Arglay had a suspicion that the Stone would be
purely logical.  Yes, he thought, but what, in that sense,
were the rules of its pure logic?”

Many Dimensions  (1931), by Charles Williams

Friday, January 27, 2017

In Memory of Actor John Hurt

Filed under: General,Geometry — m759 @ 11:00 PM

Hurt, who reportedly died today, played a purveyor
of magic wands
in the Harry Potter series and also
Control in "Tinker Tailor Soldier Spy."

"In the original screenplay for the film adaptation 
of Tinker Tailor Soldier Spy, Smiley muses that
Control had once told him that Howard Staunton 
was the greatest chess master Britain had ever
produced. 'Staunton' later turns out to be the name
that Control used for the rental of his flat."

— Wikipedia, Control (fictional character)

Related images —

Happy Chinese New Year.

Monday, January 2, 2017

Sitcom Theology

Filed under: General,Geometry — Tags: — m759 @ 1:20 PM

The Hollywood Reporter

"William Christopher, best known for playing Father Mulcahy
on the hit sitcom M*A*S*H , died Saturday [Dec. 31, 2016] of
lung cancer, his agent confirmed to The Hollywood Reporter.
He was 84.

Christopher died at his home in Pasadena, with his wife by
his bedside, at 5:10 a.m. on New Year's Eve, according to a
statement from his agent."

— 5:59 PM PST 12/31/2016 by Meena Jang

Image reshown in this journal on the midnight (Eastern time)
preceding Christopher's death —

IMAGE- Triangular models of the 4-point affine plane A and 7-point projective plane PA

Related material —

From a Log24 search for "Deathly Hallows" —

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.

Those who prefer Latin with their theology
may search this journal for "In Nomine Patris."

Sunday, December 11, 2016

Stark to Parker in New Trailer

Filed under: General — m759 @ 9:28 AM

Literature marches on

"Don't do anything I would  do.
And definitely don't do anything I wouldn't do.
There's a little gray area in there
and that's where you operate."

See as well "Spirit and Space" (Nov. 25, 2016) —

Friday, December 2, 2016

Smoke from the Sacred Wood

Filed under: General — Tags: , — m759 @ 11:00 PM

The beginning of an essay by Emily Witt that is to appear on Sunday,
Dec. 4, 2016, in the T Magazine  of The New York Times

"Palo santo, which means 'holy stick' in Spanish, is a tree indigenous to the Caribbean and South America. When burned, it emits a fragrance of pine and citrus. Lighting a stick of palo santo, like burning a bundle of sage or sweetgrass, is believed to chase away misfortune. Amazonian shamans use it in ayahuasca ceremonies to cleanse a ceremonial space of bad spirits. Given its mystical connotations, it’s not a scent associated with the secular world, but lately I have noticed its distinctive smoke wafting over more earthly settings, from Brooklyn dive bars to blue-chip art openings."

The ending of an essay by T. S. Eliot that appeared in his 1921 book
titled The Sacred Wood

Those who prefer ayahuasca ceremonies may consult
a Sept. 10 post, Cocktail of the Damned.

A Small Witt Design*

Filed under: General — Tags: — m759 @ 2:00 PM

The New York Times 's  online T Magazine  yesterday —

"A version of this article appears in print on December 4, 2016, on page
M263 of T Magazine with the headline: The Year of Magical Thinking."

* Thanks to Emily Witt for inadvertently publicizing the
   Miracle Octad Generator  of R. T. Curtis, which
   summarizes the 759 octads found in the large Witt design.

Friday, November 25, 2016

Spirit and Space

Filed under: General — Tags: , — m759 @ 11:07 AM

For those who prefer stories

Friday, October 21, 2016

CV

Filed under: General — m759 @ 9:25 AM

A sequel to last night's Chess Problem

See as well a related CV .

Saturday, October 15, 2016

Twelve and Twelve

Filed under: General — m759 @ 1:12 PM

See All Saints 2014 in this journal and listen to 
the new Stevie Nicks reissue of Bella Donna.

Related religious imagery —

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points (The 6 cube faces are mapped to the 6 hexagram lines.)

Saturday, September 10, 2016

Annals of Psychopharmacology

Filed under: General — m759 @ 3:45 PM

The New Yorker , issue dated Feb. 9, 2015

"After trying magic mushrooms in Cuernavaca, in 1960,
Leary conceived the Harvard Psilocybin Project, to study
the therapeutic potential of hallucinogens. His involvement
with LSD came a few years later."

Related viewing —

Friday, September 2, 2016

Raiders of the Lost Birthday

Filed under: General — Tags: , — m759 @ 10:00 AM

Some images from the posts of last July 13
(Harrison Ford's birthday) may serve as funeral
ornaments for the late Prof. David Lavery.

IMAGE- Massimo Vignelli, his wife Lella, and cube

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

See as well posts on "Silent Snow" and "Starlight Like Intuition."

Sunday, August 7, 2016

A Talisman for Finkelstein

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

The late physicist David Ritz Finkelstein on the magic square
in Dürer's "Melencolia I" —

"As a child I wondered why such a square was called magic.
The Occult Philosophy  [of Agrippa] answers this question
at least. They were used as magical talismans."

The correspondence  in the previous post between
Figures A and B may serve as a devotional talisman
in memory of Finkelstein, a physicist who, in the sort of
magical thinking enjoyed by traditional Catholics, might
still be lingering in Purgatory.

See also this journal on the date of Finkelstein's death —

Saturday, August 6, 2016

Mystic Correspondence:

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

The Cube and the Hexagram

The above illustration, by the late Harvey D. Heinz,
shows a magic cube* and a corresponding magic 
hexagram, or Star of David, with the six cube faces 
mapped to the six hexagram lines and the twelve  
cube edges mapped to the twelve hexagram points.
The eight cube vertices correspond to eight triangles
in the hexagram (six small and two large). 

Exercise:  Is this noteworthy mapping** of faces to lines, 
edges to points, and vertices to triangles an isolated 
phenomenon, or can it be viewed in a larger context?

* See the discussion at magic-squares.net of
   "perimeter-magic cubes"

** Apparently derived from the Cube + Hexagon figure
    discussed here in various earlier posts. See also
    "Diamonds and Whirls," a note from 1984.

Wednesday, July 27, 2016

Deathly Hallows

Filed under: General — Tags: — m759 @ 7:00 AM

The previous post, on the July 13 death of computer scientist Robert Fano,
suggests a review of "Deathly Hallows" posts in this journal. From that review —

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.

For further information, click the image below —

 .

Friday, July 15, 2016

Autistic Enchantment*

Filed under: General,Geometry — m759 @ 10:29 AM

Robert Nye, author of the novel Falstaffreportedly died
at 77 on July 2, 2016.

Harvey D. Heinz, expert on magic squares, cubes,
tesseracts, etc., reportedly died at 82 on July 6, 2013.

In memoriam —

From the date of Nye's death:

From Nye's book:

From the date of Heinz's death:

* See also a search for the title in this journal.

Thursday, July 14, 2016

Midnight Special

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

(Continued)

"Poincaré said that science is no more a collection of facts than a house is a collection of bricks. The facts have to be ordered or structured, they have to fit a theory, a construct (often mathematical) in the human mind.

… Mathematics may be art, but to the general public it is a black art, more akin to magic and mystery. This presents a constant challenge to the mathematical community: to explain how art fits into our subject and what we mean by beauty.

In attempting to bridge this divide I have always found that architecture is the best of the arts to compare with mathematics. The analogy between the two subjects is not hard to describe and enables abstract ideas to be exemplified by bricks and mortar, in the spirit of the Poincaré quotation I used earlier."

— Sir Michael Atiyah, "The Art of Mathematics"
     in the AMS Notices , January 2010

A post  from this  journal later in 2010 —

The above post's date — May 20, 2010 — was
the date of death for mathematician Walter Rudin.

The above post from that date has a link to the
Heinlein story "And He Built a Crooked House."
A not-so-crooked house —

Wednesday, July 13, 2016

Block That Metaphor

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

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points (The 6 cube faces are mapped to the 6 hexagram lines.)

Happy dies natalis  to the late Frida Kahlo.

Tuesday, June 14, 2016

Hamiltonian Philosophy

Filed under: General — m759 @ 2:40 PM

For some philosophical background, see (for instance) Jeremy Butterfield,
"Some Aspects of Modality in Analytical Mechanics," and

 .

For those who prefer entertainment —

Monday, April 18, 2016

A Problem

Filed under: General — m759 @ 12:00 PM

(Continued, in memory of the late meteorologist William Gray,
from August 10, 2010, and from April 16, 2016.)

For some backstory, see Huàn, the Flood and Impact Award.

"… Mathematics may be art, but to the general public
it is a black art, more akin to magic and mystery."

— Sir Michael Atiyah, "The Art of Mathematics"
     in the AMS Notices , January 2010, quoted in
     Log24 on April 4, 2016.

Related material:  Gray Space and

Tuesday, April 5, 2016

Spring Play

Filed under: General — 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

Monday, April 4, 2016

Cube for Berlin

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

Foreword by Sir Michael Atiyah —

"Poincaré said that science is no more a collection of facts
than a house is a collection of bricks. The facts have to be
ordered or structured, they have to fit a theory, a construct
(often mathematical) in the human mind. . . . 

 Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to
explain how art fits into our subject and what we mean by beauty.

In attempting to bridge this divide I have always found that
architecture is the best of the arts to compare with mathematics.
The analogy between the two subjects is not hard to describe
and enables abstract ideas to be exemplified by bricks and mortar,
in the spirit of the Poincaré quotation I used earlier."

— Sir Michael Atiyah, "The Art of Mathematics"
     in the AMS Notices , January 2010

Judy Bass, Los Angeles Times , March 12, 1989 —

"Like Rubik's Cube, The Eight  demands to be pondered."

As does a figure from 1984, Cullinane's Cube —

The Eightfold Cube

For natural group actions on the Cullinane cube, 
see "The Eightfold Cube" and
"A Simple Reflection Group of Order 168."

See also the recent post Cube Bricks 1984

An Approach to Symmetric Generation of the Simple Group of Order 168

Related remark from the literature —

http://www.log24.com/log/pix11B/110918-Felsner.jpg

Note that only the static structure is described by Felsner, not the
168 group actions discussed by Cullinane. For remarks on such
group actions in the literature, see "Cube Space, 1984-2003."

(From Anatomy of a Cube, Sept. 18, 2011.)

Friday, March 4, 2016

Cube Bricks 1984

Filed under: General,Geometry — Tags: , — m759 @ 12:06 PM

An Approach to Symmetric Generation of the Simple Group of Order 168

Related aesthetics —

"Poincaré said that science is no more a collection of facts
than a house is a collection of bricks. The facts have to be
ordered or structured, they have to fit a theory, a construct
(often mathematical) in the human mind. . . . 

Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to
explain how art fits into our subject and what we mean by beauty.

In attempting to bridge this divide I have always found that
architecture is the best of the arts to compare with mathematics.
The analogy between the two subjects is not hard to describe
and enables abstract ideas to be exemplified by bricks and mortar,
in the spirit of the Poincaré quotation I used earlier."

— Sir Michael Atiyah, "The Art of Mathematics"
     in the AMS Notices , January 2010

Friday, February 19, 2016

Marissa Mayer News

Filed under: General — m759 @ 10:45 AM

"Have you ever thought about
 the properties of numbers?"

 — "The Maiden" in Shaw's
 Back to Methuselah , quoted in
 the Fritz Leiber Changewar  story
“No Great Magic” (1963), Part V

Sunday, January 24, 2016

The Magpie

Filed under: General — m759 @ 10:45 AM

"Once upon a midnight dreary, while I pondered, weak and weary,
Over many a quaint and curious volume of forgotten lore…."

— Edgar Allan Poe, 1845 (link added)

"The infamous pseudohistorian Eric Temple Bell
begins his book 'The Magic of Numbers' as follows:

The hero of our story is Pythagoras…."

John Baez, June 20, 2006

Related material —

See also "Temple Bell" in this  journal.

Monday, December 28, 2015

Fuse

Filed under: General — m759 @ 10:30 PM

"Tell me the news, something I can use
Something red hot to light my fuse"

— Motörhead, "Bad Magic" album

Illustration from Oct. 25, 2013.

Tuesday, December 22, 2015

Bell de Jour

Filed under: General — m759 @ 7:00 PM

This journal on Saturday, Dec. 19

“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

In memory of Madame Claude, who
reportedly died in Nice December 19:

"There were fairies and spirits."

Amen.

Monday, December 21, 2015

Slouching Towards Christmas (continued)

Filed under: General — m759 @ 11:00 AM

Under the Volcano:
A Bottle, a Door, a Box

Katherine Neville, 'The Magic Circle' excerpt

See also Glory Season (Nov. 12, 2005) and Unique Figure (April 12, 2011).

Update of 11:22 AM —

Today in History —

"On December 21, 1937, 'Snow White and the Seven Dwarfs'
premiered to a record-breaking audience at the Carthay Circle
Theatre in Los Angeles."

Related material:  The Red Book.

Saturday, December 19, 2015

Nunc Stans

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

On conductor Kurt Masur, who reportedly died at 88
in Greenwich, Connecticut, today, Saturday, Dec.19, 2015 —

"Rehearsal conductor at Halle State Theater,
Saxony, East Germany, conductor at Erfurt City Theater
and Leipzig Opera, and guest conductor with Leipzig
and Dresden Radio orchestras, 1951-53…."

Motifs from yesterday's 9 PM post

Design from 1697

— and from a novel by Thomas Mann:

Design from 1514

Related text —

Friday, December 11, 2015

Charm School

Filed under: General — m759 @ 3:31 PM

Continued from November 26.

“She was absolutely magical.”

The above quote is from the obituary of a British actress.

Her birth date was July 19.  Her death date was November 25.

Saturday, November 7, 2015

Clarifying Dyson

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

The previous post quoted a passage from Turing's Cathedral ,
a 2012 book by George Dyson —

A passage in 'Turing's Cathedral' that recalls the Go chip in 'Wild Palms'

It should be noted that Dyson's remarks on "two species of
bits," space, time, "structure and sequence" and logic gates
are from his own idiosyncratic attempt to create a philosophy
based on the workings of computers.  These concepts are not,
so far as I can tell, part of anyone else's approach to the subject.

For a more standard introduction to how computers work, see
(for instance) a book by an author Dyson admires:

The Pattern on the Stone , by W. Daniel Hillis (Basic Books, 1998).

PREFACE: MAGIC IN THE STONE

I etch a pattern of geometric shapes onto a stone.
To the uninitiated, the shapes look mysterious and
complex, but I know that when arranged correctly
they will give the stone a special power, enabling it
to respond to incantations in a language no human
being has ever spoken. I will ask the stone questions
in this language, and it will answer by showing me a
vision: a world created by my spell, a world imagined
within the pattern on the stone.

A few hundred years ago in my native New England,
an accurate description of my occupation would have
gotten me burned at the stake. Yet my work involves
no witchcraft; I design and program computers. The
stone is a wafer of silicon, and the incantations are
software. The patterns etched on the chip and the
programs that instruct the computer may look
complicated and mysterious, but they are generated
according to a few basic principles that are easily
explained. . . . .

Hillis's title suggests some remarks unrelated to computers —

See Philosopher + Stone in this journal.

Saturday, September 26, 2015

Posthumous Man

Filed under: General — m759 @ 3:45 PM

The above book, a tribute by admirers of the late Michael Weinstein
(not, as a campus obituary states, by Weinstein himself),
was reportedly published by Routledge on December 19, 2014.

This journal on that date had a post on an early Greek philosopher who
supposedly was killed because he discovered irrational numbers.

A later approach to academic life —

Emma Stone being directed by Woody Allen in the recent "Irrational Man":

Fans of Allen and Stone may also enjoy Magic in the Moonlight.

Friday, September 25, 2015

“May I aid you, travelers?”

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

A file photo of Mark and Debby Constantino on Oct. 24, 2011.

The couple, who worked as paranormal investigators, were often
featured in the Travel Channel series Ghost Adventures .

As the above screenshot shows, this post's title is from
"Might and Magic II: Gates to Another World" (1988).

Related material, quoted here on Oct. 24, 2011

"Deja vu all over again." — Yogi Berra

Saturday, September 19, 2015

The Observatory Mystery

Filed under: General — m759 @ 11:00 AM

Part I:        Magic Moonlight

Part II:    To Walk the Night 

Cover from a 1944 edition of
the 1937 novel by William Sloane


Part III:   Sept. 18, 2015, review by Stephen King
                of the works of William Sloane 

Friday, September 4, 2015

“Tell it to the hand.”

Filed under: General — m759 @ 11:12 AM

A followup to the previous post, Delft Speaks  —

Manohla Dargis, film reviewer, on illusionist Penn Jillette:

“It’s as if Vermeer,” Mr. Jillette says, “were
some unfathomable genius who could just
walk up to a canvas and magically paint
with light.” And everyone knows — perhaps
professional illusionists most of all — that
magic doesn’t exist.

"Tell it to the hand."

Sunday, August 30, 2015

Lines

Filed under: General,Geometry — Tags: , — m759 @ 11:01 AM

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

A post from St. Augustine's day, 2015, may serve to
illustrate this.

The post started with a look at a painting by Swiss artist
Wolf Barth, "Spielfeld." The painting portrays two
rectangular arrays, of four and of twelve subsquares, 
that sit atop a square array of sixteen subsquares.

To one familiar with Euclid's "bride's chair" proof of the
Pythagorean theorem, "Spielfeld" suggests a right triangle
with squares on its sides of areas 4, 12, and 16.

That image in turn suggests a diagram illustrating the fact
that a triangle suitably inscribed in a half-circle is a right 
triangle… in this case, a right triangle with angles of 30, 60,
and 90 degrees… Thus —

In memory of screenwriter John Gregory Dunne (husband
of Joan Didion and author of, among other things, The Studio
here is a cinematric approach to the above figure.

The half-circle at top suggests the dome of an observatory.
This in turn suggests a scene from the 2014 film "Magic in
the Moonlight."  

As she gazes at the silent universe above
through an opening in the dome, the silent
Emma Stone is perhaps thinking, 
prompted by her work with Spider-Man

"Drop me a line."

As he  gazes at the crack in the dome,
Stone's costar Colin Firth contrasts the vastness 
of the Universe with the smallness of Man, citing 

"the tiny field F2 with two elements."

In conclusion, recall the words of author Norman Mailer
that summarized his Harvard education —

"At times, bullshit can only be countered
with superior bullshit."

Friday, August 28, 2015

Art and Space

Filed under: General,Geometry — Tags: , — m759 @ 10:00 AM

IMAGE- Spielfeld (1982-83), by Wolf Barth
 

            Observatory scene from "Magic in the Moonlight"

"The sixteen nodes… can be parametrized
by the sixteen points in affine four-space
over the tiny field F2 with two elements."

Wolf Barth

Wednesday, August 26, 2015

Ride

Filed under: General — Tags: , — m759 @ 3:01 PM

"Why don't you come with me, little girl,
on a magic carpet ride?" — Steppenwolf lyrics

Related material for fans of Christopher Alexander
(see previous post) — "The 'Life' of a Carpet."

Saturday, July 4, 2015

Multiple Storylines

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

Another one of them —

Commentary — 

Thursday, June 11, 2015

Omega

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

Omega is a Greek letter, Ω , used in mathematics to denote
a set on which a group acts. 

For instance, the affine group AGL(3,2) is a group of 1,344
actions on the eight elements of the vector 3-space over the
two-element Galois field GF(2), or, if you prefer, on the Galois
field  Ω = GF(8).

Related fiction:  The Eight , by Katherine Neville.

Related non-fiction:  A remark by Werner Heisenberg
in this journal on Saturday, June 6, 2015, the eightfold cube ,
and the illustrations below —

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.

Tuesday, May 26, 2015

Colorful Tales

Filed under: General — Tags: , — m759 @ 9:50 PM

See also the Log24 post from May 18,
the date of Eric Caidin's reported death,
as well as Hexagram 50 and May 14, 2014—
Death in Mathmagic Land.

Monday, April 13, 2015

Deutsche Schule

Filed under: General — m759 @ 12:00 PM

Continued from December 5, 2002 —

Braucht´s noch Text?

Un-magical realism for Montevideo.

Unorthodox Easter

Filed under: General — Tags: — m759 @ 11:00 AM

(A sequel to yesterday's Orthodox Easter posts)

This morning's Google News —

The New York Times  on the late Günter Grass —

"Many of Mr. Grass’s books are phantasmagorical
mixtures of fact and fantasy, some of them inviting
comparison with the Latin American style known as
magical realism. His own name for this style was
'broadened reality.'"

From p. xii of the 2005 second edition of a book discussed
in yesterday's Orthodox Easter posts —

(Click image to enlarge.)

Early editions of The Heart of Mathematics  include 
Gary Larson's legendary Hell's Library "Far Side" cartoon. 
Books in Hell's Library include Big Book of Story Problems ,
More Story Problems , and Even More Story Problems .

— Adapted from a review of the 2000 first edition

See also Mathematics and Narrative in this journal.

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