Log24

Tuesday, August 12, 2025

Tesseract Art . . . Continues.

Filed under: General — Tags: , , , — m759 @ 9:31 am

On magic hypercube  "slippabilities" —

As the crow flies  . . .

Or as the ant walks . . .

As usual, beware of the word "magic" —

Tuesday, March 15, 2022

Midnight Wrinkle

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

See as well the life of a real  astrophysicist.

Update of 12:26 PM ET March 15:
Vide  other posts now tagged The Rosenhain Symmetry.

Thursday, December 21, 2017

Wrinkles

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

TIME magazine, issue of December 25th, 2017 —

" In 2003, Hand worked with Disney to produce a made-for-TV movie.
Thanks to budget constraints, among other issues, the adaptation
turned out bland and uninspiring. It disappointed audiences,
L’Engle and Hand. 'This is not the dream,' Hand recalls telling herself.
'I’m sure there were people at Disney that wished I would go away.' "

Not the dream?  It was, however, the nightmare, presenting very well
the encounter in Camazotz of Charles Wallace with the Tempter.

From a trailer for the latest version —

Detail:

From the 1962 book —

"There's something phoney in the whole setup, Meg thought.
There is definitely something rotten in the state of Camazotz."

Song adapted from a 1960 musical —

"In short, there's simply not
A more congenial spot
For happy-ever-aftering
Than here in Camazotz!"

Monday, August 4, 2014

A Wrinkle in Space

Filed under: General,Geometry — Tags: , , — m759 @ 10:30 am

"There is  such a thing as a tesseract." — Madeleine L'Engle

An approach via the Omega Matrix:

http://www.log24.com/log/pix10A/100619-TesseractAnd4x4.gif

See, too, Rosenhain and Göpel as The Shadow Guests .

Thursday, May 8, 2014

Wrinkles in Time

Filed under: General — Tags: — m759 @ 2:25 pm

Rivka Galchen, in a piece mentioned here in June 2010

On Borges:  Imagining the Unwritten Book 

"Think of it this way: there is a vast unwritten book that the heart reacts to, that it races and skips in response to, that it believes in. But it’s the heart’s belief in that vast unwritten book that brought the book into existence; what appears to be exclusively a response (the heart responding to the book) is, in fact, also a conjuring (the heart inventing the book to which it so desperately wishes to respond)."

Related fictions

Galchen's "The Region of Unlikeness" (New Yorker , March 24, 2008)

Ted Chiang's "Story of Your Life." A film adaptation is to star Amy Adams.

… and non-fiction

"There is  such a thing as a 4-set." — January 31, 2012

Monday, June 19, 2023

The Original Portable Door

Filed under: General — Tags: , , — m759 @ 3:26 pm

"… a cardboard tube, more or less the same length as
the inner core of a toilet roll, but thicker. He frowned,
took the roll out, laid it on the desk and poked up it
with the butt end of a pencil. Something slid out.
It looked like a rolled-up black plastic dustbin liner;
but when he unfolded it, he recognised it as the funny
sheet thing he’d found in the strongroom and briefly
described as an Acme Portable Door, before losing
his nerve and changing it to something less facetious." 

— Holt, Tom. The Portable Door . Orbit. Kindle Edition. 

According to goodreads.com, the Holt book was
"first published March 6, 2003."

Compare and contrast the "portable door" as a literary device
with the "tesseract" in A Wrinkle in Time  (1962).

See also this  journal on March 6, 2003.

Thursday, February 17, 2022

Four Dots, Six Lines

Filed under: General — Tags: — m759 @ 1:46 am

"There is  such a thing  as  a tesseract." 

— Mrs. Whatsit in  A Wrinkle in Time  (1962)

"Simplify, simplify." — Henry David Thoreau in Walden  (1854)

Von Franz representation of the I Ching's Hexagram 2, The Receptive
 

A Jungian on this six-line figure:

“They are the same six lines that exist in the I Ching…. Now observe the square more closely: four of the lines are of equal length, the other two are longer…. For this reason symmetry cannot be statically produced and a dance results.”
 
— Marie-Louise von Franz,
   Number and Time  (1970)

Monday, July 13, 2020

Unpoetic License

Filed under: General — Tags: , , — m759 @ 6:21 am

The above novel uses extensively the term “inscape.”
The term’s originator, a 19th-century Jesuit poet,
is credited . . . sort of.  For other uses of the term,
search for Inscape in this journal. From that search —

A quote from a 1962 novel

“There’s something phoney
in the whole setup, Meg thought.
There is definitely something rotten
in the state of Camazotz.”

Addendum for the Church of Synchronology

The Joe Hill novel above was published (in hardcover)
on Walpurgisnacht —April 30, 2013.  See also this journal
on that date.

Monday, October 21, 2019

Algebra and Space… Illustrated.

Filed under: General — Tags: , — m759 @ 4:26 pm

Related entertainment —

Detail:

   George Steiner

"Perhaps an insane conceit."

 

Perhaps.

 

See Quantum Tesseract Theorem .

 

Perhaps Not.

 

 See Dirac and Geometry .

Monday, March 11, 2019

Ant-Man Meets Doctor Strange

Filed under: General — Tags: — m759 @ 1:22 pm

IMAGE- Concepts of Space

The 4×4 square may also be called the Galois Tesseract .
By analogy, the 4x4x4 cube may be called the Galois Hexeract .

"Think outside the tesseract.

Wednesday, December 12, 2018

An Inscape for Douthat

Some images, and a definition, suggested by my remarks here last night
on Apollo and Ross Douthat's remarks today on "The Return of Paganism" —

Detail of Feb. 20, 1986, note by Steven H. Cullinane on Weyl's 'relativity problem'

Kibler's 2008 'Variations on a theme' illustrated.

In finite geometry and combinatorics,
an inscape  is a 4×4 array of square figures,
each figure picturing a subset of the overall 4×4 array:


 

Related material — the phrase
"Quantum Tesseract Theorem" and  

A.  An image from the recent
      film "A Wrinkle in Time" — 

B.  A quote from the 1962 book —

"There's something phoney
in the whole setup, Meg thought.
There is definitely something rotten
in the state of Camazotz."

Tuesday, November 13, 2018

Blackboard Jungle Continues.

Filed under: G-Notes,General,Geometry — Tags: , , — m759 @ 6:19 pm

From the 1955 film "Blackboard Jungle" —

From a trailer for the recent film version of A Wrinkle in Time

Detail of the phrase "quantum tesseract theorem":

From the 1962 book —

"There's something phoney
in the whole setup, Meg thought.
There is definitely something rotten
in the state of Camazotz."

Related mathematics from Koen Thas that some might call a
"quantum tesseract theorem" —

Some background —

Koen Thas, 'Unextendible Mututally Unbiased Bases' (2016)

See also posts tagged Dirac and Geometry. For more
background on finite  geometry, see a web page
at Thas's institution, Ghent University.

Sunday, June 10, 2018

Pieces of April

Filed under: General — Tags: , , — m759 @ 12:25 am

This journal on April 16, 2018 —

Happy birthday to Pope Emeritus Benedict XVI.

Related material from another weblog in a post also dated April 16, 2018 —

"As I write this, it’s April 5, midway through the eight-day
festival of Passover. During this holiday, we Jews air our
grievances against the ancient Pharaoh who enslaved
and oppressed us, and celebrate the feats of strength
with which the Almighty delivered us from bondage —
wait a minute, I think I’m mixing up Passover with Festivus."
. . . .

"Next month: Time and Tesseracts."

From that next post, dated May 16, 2018 —

"The tesseract entered popular culture through
Madeleine L’Engle’s 'A Wrinkle in Time' . . . ."

The post's author, James Propp, notes that

" L’Engle caused some of her readers confusion
when one of the characters … the prodigy
Charles Wallace Murray [sic ] , declared 'Well, the fifth
dimension’s a tesseract.' "

Propp is not unfamiliar with prodigies:

"When I was a kid living in the Long Island suburbs,
I sometimes got called a math genius. I didn’t think
the label was apt, but I didn’t mind it; being put in
the genius box came with some pretty good perks."

— "The Genius Box," a post dated March 16, 2018

To me, Propp seems less like Charles Wallace
and more like the Prime Coordinator —

For further details, see the following synchronicity checks:

Propp March 16     Log24 March 16

Propp April 16        Log24 April 16

Propp May 16        Log24 May 16 .

Sunday, March 11, 2018

Blackboard Jungle Continues . . .

Filed under: General — m759 @ 10:28 am

. . . With intolerable disrespect for the word …
In particular, the word "theorem."
 

See also "Quantum Tesseract Theorem" in this  journal.

Thursday, March 8, 2018

Thanking the Academy…

Filed under: General,Geometry — Tags: — m759 @ 9:11 pm

Continues.

Monday, January 8, 2018

Raiders of the Lost Theorem

Filed under: General,Geometry — Tags: — m759 @ 11:15 pm
 

The Quantum Tesseract Theorem 

 


 

Raiders —

A Wrinkle in Time
starring Storm Reid,
Reese Witherspoon,
Oprah Winfrey &
Mindy Kaling

 

Time Magazine  December 25, 2017 – January 1, 2018

Saturday, April 16, 2016

Matinee (continued)

Filed under: General — m759 @ 2:15 pm

Today is Kelli O'Hara's last Saturday matinee in "The King and I."

A show that some may prefer —

Related to the plot of Dante's film

"…it would be quite a long walk
for him if he had to walk straight across."

The image “http://www.log24.com/log/pix07A/070831-Ant1.gif” cannot be displayed, because it contains errors.

Swiftly Mrs. Who brought her hands… together.

"Now, you see," Mrs. Whatsit said,
"he would be  there, without that long trip.
That is how we travel."

The image “http://www.log24.com/log/pix07A/070831-Ant2.gif” cannot be displayed, because it contains errors.

– A Wrinkle in Time , Chapter 5, "The Tesseract"

Friday, January 29, 2016

Excellent Adventure*

Filed under: General — Tags: — m759 @ 9:29 pm

(Continued from Dec. 9, 2013)

"…it would be quite a long walk
for him if he had to walk straight across."

The image “http://www.log24.com/log/pix07A/070831-Ant1.gif” cannot be displayed, because it contains errors.

Swiftly Mrs. Who brought her hands… together.

"Now, you see," Mrs. Whatsit said,
"he would be  there, without that long trip.
That is how we travel."

The image “http://www.log24.com/log/pix07A/070831-Ant2.gif” cannot be displayed, because it contains errors.

– A Wrinkle in Time 
Chapter 5, "The Tesseract"

From a media weblog yesterday, a quote from the video below —

"At 12:03 PM Eastern Standard Time, January 12th, 2016…."

This  weblog on the previous day (January 11th, 2016) —

"There is  such a thing as harmonic analysis of switching functions."

— Saying adapted from a young-adult novel

* For some backstory, see a Caltech page.

Friday, June 19, 2015

Footnote

Filed under: General,Geometry — m759 @ 9:29 pm

There is  such a thing as geometry.*

* Proposition adapted from A Wrinkle in Time , by Madeleine L'Engle.

Friday, March 14, 2014

The Search for Charles Wallace

Filed under: General — Tags: , — m759 @ 2:19 pm

The search in the previous post for the source of a quotation from Poincaré yielded, as a serendipitous benefit, information on an interesting psychoanalyst named Wilfred Bion (see the Poincaré  quotation at a webpage on Bion). This in turn suggested a search for the source of the name of author Madeleine L'Engle's son Bion, who may have partly inspired L'Engle's fictional character Charles Wallace.  Cynthia Zarin wrote about Bion in The New Yorker  of April 12, 2004 that

"According to the family, he is the person for whom L’Engle’s insistence on blurring fiction and reality had the most disastrous consequences."

Also from that article, material related to the name Bion and to what this journal has called "the Crosswicks Curse"*—

"Madeleine L’Engle Camp was born in 1918 in New York City, the only child of Madeleine Hall Barnett, of Jacksonville, Florida, and Charles Wadsworth Camp, a Princeton man and First World War veteran, whose family had a big country place in New Jersey, called Crosswicks. In Jacksonville society, the Barnett family was legendary: Madeleine’s grandfather, Bion Barnett, the chairman of the board of Jacksonville’s Barnett Bank, had run off with a woman to the South of France, leaving behind a note on the mantel. Her grandmother, Caroline Hallows L’Engle, never recovered from the blow. ….

… The summer after Hugh and Madeleine were married, they bought a dilapidated farmhouse in Goshen, in northwest Connecticut. Josephine, born in 1947, was three years old when they moved permanently to the house, which they called Crosswicks. Bion was born just over a year later."

* "There is  such a thing as a tesseract."

Monday, December 9, 2013

Being There

Filed under: General — Tags: — m759 @ 9:16 pm

Or: The Naked Blackboard Jungle

"…it would be quite a long walk
for him if he had to walk straight across."

The image “http://www.log24.com/log/pix07A/070831-Ant1.gif” cannot be displayed, because it contains errors.

Swiftly Mrs. Who brought her hands… together.

"Now, you see," Mrs. Whatsit said,
"he would be  there, without that long trip.
That is how we travel."

The image “http://www.log24.com/log/pix07A/070831-Ant2.gif” cannot be displayed, because it contains errors.

– A Wrinkle in Time 
Chapter 5, "The Tesseract"

Related material: Machete Math and

Starring the late Eleanor Parker as Swiftly Mrs. Who.

Saturday, March 16, 2013

The Crosswicks Curse

Filed under: General,Geometry — Tags: , — m759 @ 4:00 pm

Continues.

From the prologue to the new Joyce Carol Oates
novel Accursed

"This journey I undertake with such anticipation
is not one of geographical space but one of Time—
for it is the year 1905 that is my destination.

1905!—the very year of the Curse."

Today's previous post supplied a fanciful link
between the Crosswicks Curse of Oates and
the Crosswicks tesseract  of Madeleine L'Engle.

The Crosswicks Curse according to L'Engle
in her classic 1962 novel A Wrinkle in Time —

"There is  such a thing as a tesseract."

A tesseract is a 4-dimensional hypercube that
(as pointed out by Coxeter in 1950) may also 
be viewed as a 4×4 array (with opposite edges
identified).

Meanwhile, back in 1905

For more details, see how the Rosenhain and Göpel tetrads occur naturally
in the diamond theorem model of the 35 lines of the 15-point projective
Galois space PG(3,2).

See also Conwell in this journal and George Macfeely Conwell in the
honors list of the Princeton Class of 1905.

Friday, November 2, 2012

For All Souls’ Day

Filed under: General — m759 @ 9:48 am

From this journal yesterday (All Saints' Day)—

"But, I asked, is there a difference
between fiction and nonfiction?
'Not much,' she said, shrugging."

New Yorker  profile of tesseract
author Madeleine L'Engle

For a discussion of this issue in greater depth—

"Truth and fact are not the same thing."

— see a 1998 award acceptance speech by L'Engle.

See also a Log24 post of March 1st, 2008, on the soul.

Thursday, November 1, 2012

Theories of Truth

Filed under: General,Geometry — Tags: , — m759 @ 7:20 pm

A review of two theories of truth described
by a clergyman, Richard J. Trudeau, in
The Non-Euclidean Revolution

The Story Theory of Truth:

"But, I asked, is there a difference
between fiction and nonfiction?
'Not much,' she said, shrugging."

New Yorker  profile of tesseract
     author Madeleine L'Engle

The Diamond Theory of Truth:

(Click image for some background.)

Spaces as Hypercubes

See also the links on a webpage at finitegeometry.org.

Wednesday, October 31, 2012

The Malfunctioning TARDIS

Filed under: General,Geometry — m759 @ 11:01 am

(Continued from previous TARDIS posts)

Summary: A review of some  posts from last August is suggested by the death,
reportedly during the dark hours early on October 30, of artist Lebbeus Woods.

An (initially unauthorized) appearance of his work in the 1995 film
Twelve Monkeys 

 … suggests a review of three posts from last August.

Wednesday, August 1, 2012

Defining Form

Filed under: Uncategorized — m759 @ 11:01 AM 

Continued from July 29 in memory of filmmaker Chris Marker,
who reportedly* died on that date at 91 at his home in Paris.

See Slides and Chantingand Where Madness Lies.

See also Sherrill Grace on Malcolm Lowry.

Washington PostOther sources say Marker died on July 30.

 These notably occur in Marker's masterpiece
     La Jetée  (review with spoilers).

 

Wednesday, August 1, 2012

Triple Feature

Filed under: Uncategorized — m759 @ 11:11 PM

IMAGE- Triple Feature: 'Twelve Monkeys,' Reagan National Airport on July 31, 2012, and 'Die Hard 2'

For related material, see this morning's post Defining Form.

 

Sunday, August 12, 2012

Doctor Who

Filed under: Uncategorized — m759 @ 2:00 PM

On Robert A. Heinlein's novel Glory Road

"Glory Road  (1963) included the foldbox , a hyperdimensional packing case that was bigger inside than outside. It is unclear if Glory Road  was influenced by the debut of the science fiction television series Doctor Who  on the BBC that same year. In Doctor Who , the main character pilots a time machine called a TARDIS, which is built with technology which makes it 'dimensionally transcendental,' that is, bigger inside than out."

— Todd, Tesseract article at exampleproblems.com

From the same exampleproblems.com article—

"The connection pattern of the tesseract's vertices is the same as that of a 4×4 square array drawn on a torus; each cell (representing a vertex of the tesseract) is adjacent to exactly four other cells. See geometry of the 4×4 square."

For further details, see today's new page on vertex adjacency at finitegeometry.org.

 

"It was a dark and stormy night."— A Wrinkle in Time

Monday, January 30, 2012

Enda’s Game*

Filed under: General — Tags: , — m759 @ 7:00 pm

The following passage by Tolkien was suggested by a copy of next Sunday's New York Times Book Review  that arrived in the mail today. (See Orson Scott Card's remarks on page 26— "Uncle Orson"— and the Review 's concluding essay "Grand Allusion.")

"Lastly, tengwesta  [system or code of signs] has also become an impediment. It is in Incarnates clearer and more precise than their direct reception of thought. By it also they can communicate easily with others, when no strength is added to their thought: as, for example, when strangers first meet. And, as we have seen, the use of 'language' soon becomes habitual, so that the practice of ósanwe  (interchange of thought) is neglected and becomes more difficult. Thus we see that the Incarnate tend more and more to use or to endeavour to use ósanwe  only in great need and urgency, and especially when lambe  is unavailing. As when the voice cannot be heard, which comes most often because of distance. For distance in itself offers no impediment whatever to ósanwe . But those who by affinity might well use ósanwe  will use lambe  when in proximity, by habit or preference. Yet we may mark also how the 'affine' may more quickly understand the lambe  that they use between them, and indeed all that they would say is not put into words. With fewer words they come swifter to a better understanding. There can be no doubt that here ósanwe  is also often taking place; for the will to converse in lambe  is a will to communicate thought, and lays the minds open. It may be, of course, that the two that converse know already part of the matter and the thought of the other upon it, so that only allusions dark to the stranger need be made; but this is not always so. The affine** will reach an understanding more swiftly than strangers upon matters that neither have before discussed, and they will more quickly perceive the import of words that, however numerous, well-chosen, and precise, must remain inadequate."

* "If a poem catches a student's interest at all, he or she should damned well be able to look up an unfamiliar word in the dictionary…."

   — Elizabeth Bishop, quoted in the essay "Grand Allusion" mentioned above. For a brief dictionary of most of the unfamiliar words in this post's title and in the above passage, see Vinyar Tengwar  39 (July 1998). This is copyrighted but freely available on the Web.

** The word "affine" has connotations not intended by Tolkien. See that word in this journal. See also page 5 of next Sunday's Times Book Review , which contains a full-page ad for the 50th anniversary edition of A Wrinkle in Time . "There is  such a thing as a tesseract."

Thursday, November 3, 2011

Ockham’s Bubbles–

Filed under: General,Geometry — Tags: — m759 @ 10:30 am

Mathematics and Narrative, continued

"… a vision invisible, even ineffable, as ineffable as the Angels and the Universal Souls"

— Tom Wolfe, The Painted Word , 1975, quoted here on October 30th

"… our laughable abstractions, our wryly ironic po-mo angels dancing on the heads of so many mis-imagined quantum pins."

— Dan Conover on September 1st, 2011

"Recently I happened to be talking to a prominent California geologist, and she told me: 'When I first went into geology, we all thought that in science you create a solid layer of findings, through experiment and careful investigation, and then you add a second layer, like a second layer of bricks, all very carefully, and so on. Occasionally some adventurous scientist stacks the bricks up in towers, and these towers turn out to be insubstantial and they get torn down, and you proceed again with the careful layers. But we now realize that the very first layers aren't even resting on solid ground. They are balanced on bubbles, on concepts that are full of air, and those bubbles are being burst today, one after the other.'

I suddenly had a picture of the entire astonishing edifice collapsing and modern man plunging headlong back into the primordial ooze. He's floundering, sloshing about, gulping for air, frantically treading ooze, when he feels something huge and smooth swim beneath him and boost him up, like some almighty dolphin. He can't see it, but he's much impressed. He names it God."

— Tom Wolfe, "Sorry, but Your Soul Just Died," Forbes , 1996

"… Ockham's idea implies that we probably have the ability to do something now such that if we were to do it, then the past would have been different…"

Stanford Encyclopedia of Philosophy

"Today is February 28, 2008, and we are privileged to begin a conversation with Mr. Tom Wolfe."

— Interviewer for the National Association of Scholars

From that conversation—

Wolfe : "People in academia should start insisting on objective scholarship, insisting  on it, relentlessly, driving the point home, ramming it down the gullets of the politically correct, making noise! naming names! citing egregious examples! showing contempt to the brink of brutality!"

As for "mis-imagined quantum pins"…
This 
journal on the date of the above interview— February 28, 2008

http://www.log24.com/log/pix08/080228-Wooters2.jpg

Illustration from a Perimeter Institute talk given on July 20, 2005

The date of Conover's "quantum pins" remark above (together with Ockham's remark above and the above image) suggests a story by  Conover, "The Last Epiphany," and four posts from September 1st, 2011—

BoundaryHow It WorksFor Thor's Day,  and The Galois Tesseract.

Those four posts may be viewed as either an exploration or a parody of the boundary between mathematics and narrative.

"There is  such a thing as a tesseract." —A Wrinkle in Time

Sunday, September 11, 2011

First Lady

Filed under: General — m759 @ 7:59 am

Betty Skelton, "the First Lady of Firsts," died on the last day of August.

http://www.log24.com/log/pix11B/110911-NYTobitsSm.jpg

From this  journal on August thirty-first—

"The Tesseract was the jewel of Odin's treasure room."

http://www.log24.com/log/pix11B/110831-JohannSchmidt.jpg

Hugo Weaving also played Agent Smith
in The Matrix Trilogy .

For Cynthia Zarin, biographer of Madeleine L'Engle

"There is  such a thing as a tesseract."
A Wrinkle in Time

Thursday, September 1, 2011

Boundary (continued*)

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

It is now midnight. Yesterday was Odin's Day. Today is Thor's Day.

From a weblog post on Captain America and Thor

"While all this [Captain America] is happening an SS officer, Johann Schmidt (Hugo Weaving), has found a religious artefact called the Tesseract which Schmidt describes as 'the jewel of Odin’s treasure room,' linking it in with the Thor storyline."

That's Entertainment  weblog, August 14, 2011

From Wallace Stevens, "An Ordinary Evening in New Haven," Canto III—

The point of vision and desire are the same.
It is to the hero of midnight that we pray
On a hill of stones to make beau mont thereof.

Captain America opened in the United States on Friday, July 22, 2011.

Thor opened in the United States on Friday, May 6, 2011.

"There is  such a thing as a tesseract." —A Wrinkle in Time

* Continued from August 30.

Monday, June 21, 2010

Test

Filed under: General,Geometry — Tags: , — m759 @ 11:30 pm

From a post by Ivars Peterson, Director
of Publications and Communications at
the Mathematical Association of America,
at 19:19 UTC on June 19, 2010—

Exterior panels and detail of panel,
Michener Gallery at Blanton Museum
in Austin, Texas—

http://www.log24.com/log/pix10A/100621-MichenerGalleryPanel.jpg

Peterson associates the four-diamond figure
with the Pythagorean theorem.

A more relevant association is the
four-diamond view of a tesseract shown here
on June 19 (the same date as Peterson's post)
in the "Imago Creationis" post—

Image-- The Four-Diamond Tesseract

This figure is relevant because of a
tesseract sculpture by Peter Forakis—

http://www.log24.com/log/pix09A/091220-ForakisHypercube.jpg

This sculpture was apparently shown in the above
building— the Blanton Museum's Michener gallery—
as part of the "Reimagining Space" exhibition,
September 28, 2008-January 18, 2009.

The exhibition was organized by
Linda Dalrymple Henderson, Centennial Professor
in Art History at the University of Texas at Austin
and author of The Fourth Dimension and
Non-Euclidean Geometry in Modern Art

(Princeton University Press, 1983;
new ed., MIT Press, 2009).

For the sculptor Forakis in this journal,
see "The Test" (December 20, 2009).

"There is  such a thing
as a tesseract."
A Wrinkle in TIme   

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