The passage from Lewis Carroll's Euclid and His Modern Rivals
in the previous post suggests two illustrations —
Click the Trudeau book for related Log24 posts.
The passage from Lewis Carroll's Euclid and His Modern Rivals
in the previous post suggests two illustrations —
Click the Trudeau book for related Log24 posts.
These are Rothko's Swamps .
See a Log24 search for related meditations.
For all three topics combined, see Coxeter —
" There is a pleasantly discursive treatment
of Pontius Pilate’s unanswered question
‘What is truth?’ "
— Coxeter, 1987, introduction to Trudeau’s
The NonEuclidean Revolution
Update of 10 AM ET — Related material, with an elementary example:
Posts tagged "Defining Form." The example —
John Updike on Don DeLillo's thirteenth novel, Cosmopolis —
" DeLillo’s postChristian search for 'an order at some deep level'
has brought him to global computerization:
'the zerooneness of the world, the digital imperative . . . . ' "
— The New Yorker , issue dated March 31, 2003
On that date ….
Related remark —
" There is a pleasantly discursive treatment
of Pontius Pilate’s unanswered question
‘What is truth?’ "
— Coxeter, 1987, introduction to Trudeau’s
The NonEuclidean Revolution
"Again, in spite of that, we call this Friday good."
— T. S. Eliot, Four Quartets
From this journal on Orthodox Good Friday, 2016,
an image from New Scientist on St. Andrew's Day, 2015 —
From an old Dick Tracy strip —
See also meditations from this year's un Orthodox Good Friday
in a Tennessee weblog and in this journal —
" There is a pleasantly discursive treatment
of Pontius Pilate’s unanswered question
‘What is truth?’ ”
— Coxeter, 1987, introduction to Trudeau’s
The NonEuclidean Revolution
Toronto geometer H.S.M. Coxeter, introducing a book by Unitarian minister
Richard J. Trudeau —
"There is a pleasantly discursive treatment of Pontius Pilate’s
unanswered question ‘What is truth?’”
— Coxeter, 1987, introduction to Trudeau’s
The NonEuclidean Revolution
Another such treatment …
"Of course, it will surprise no one to find low standards
of intellectual honesty on the Tonight Show.
But we find a less trivial example if we enter the
hallowed halls of Harvard University. . . ."
— Neal Koblitz, "Mathematics as Propaganda"
Less pleasantly and less discursively —
"Funny how annoying a little prick can be."
— The late Garry Shandling
Material related to the title:
"Euclid's edifice loomed in my consciousness
as a marvel among sciences, unique in its clarity
and unquestionable validity."
—Richard J. Trudeau in
The NonEuclidean Revolution (1986)
"Euclid's edifice loomed in my consciousness as a marvel among
sciences, unique in its clarity and unquestionable validity."
—Richard J. Trudeau in The NonEuclidean Revolution (1986)
See also Edifice in this journal and last night's architectural post.
A post in honor of Évariste Galois (25 October 1811 – 31 May 1832)
From a book by Richard J. Trudeau titled The NonEuclidean Revolution —
See also “nonEuclidean” in this journal.
One might argue that Galois geometry, a field ignored by Trudeau,
is also “nonEuclidean,” and (for those who like rhetoric) revolutionary.
New! Improved!
"Euclid's edifice loomed in my consciousness
as a marvel among sciences, unique in its
clarity and unquestionable validity."
—Richard J. Trudeau in
The NonEuclidean Revolution (First published in 1986)
Readers of this journal will be aware that Springer's new page
advertising Trudeau's book, pictured above, is a baitandswitch
operation. In the chapter advertised, Trudeau promotes what he
calls "the Diamond Theory of Truth" as a setup for his real goal,
which he calls "the Story Theory of Truth."
For an earlier use of the phrase "Diamond Theory" in
connection with geometry, see a publication from 1977.
A review of two theories of truth described
by a clergyman, Richard J. Trudeau, in
The NonEuclidean Revolution—
"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
(Click image for some background.)
See also the links on a webpage at finitegeometry.org.
Weblog posts of two prominent mathematicians today discussed
what appears to be a revolution inspired by the business practices
of some commercial publishers of mathematics.
My own concern is more with the socalled "NonEuclidean Revolution"
described by Richard Trudeau in a book of that title (Birkhäuser, 1987).
A 1976 document relevant to the concerns in the Trudeau book—
Though not as well known as another document discussing
"selfevident" truths, Cameron's remarks are also of some
philosophical interest.
They apply to finite geometry, a topic unknown to Euclid,
but nevertheless of considerable significance for the foundations
of mathematics.
"The hand of the creative artist, laid upon the major premise,
rocks the foundations of the world." — Dorothy Sayers
From math16.com—
Quotations on Realism

The story of the diamond mine continues
(see Coordinated Steps and Organizing the Mine Workers)—
From The Search for Invariants (June 20, 2011):
The conclusion of Maja Lovrenov's
"The Role of Invariance in Cassirer’s Interpretation of the Theory of Relativity"—
"… physical theories prove to be theories of invariants
with regard to certain groups of transformations and
it is exactly the invariance that secures the objectivity
of a physical theory."
— SYNTHESIS PHILOSOPHICA 42 (2/2006), pp. 233–241
Related material from Sunday's New York Times travel section—
Richard J. Trudeau, a mathematics professor and Unitarian minister, published in 1987 a book, The NonEuclidean Revolution , that opposes what he calls the Story Theory of truth [i.e., Quine, nominalism, postmodernism] to what he calls the traditional Diamond Theory of truth [i.e., Plato, realism, the Roman Catholic Church]. This opposition goes back to the medieval "problem of universals" debated by scholastic philosophers.
(Trudeau may never have heard of, and at any rate did not mention, an earlier 1976 monograph on geometry, "Diamond Theory," whose subject and title are relevant.)
From yesterday's Sunday morning New York Times—
"Stories were the primary way our ancestors transmitted knowledge and values. Today we seek movies, novels and 'news stories' that put the events of the day in a form that our brains evolved to find compelling and memorable. Children crave bedtime stories…."
— Drew Westen, professor at Emory University
From May 22, 2009—
The above ad is by Diamond from last night’s

For further details, see Saturday's correspondences 
For the title, see Palm Sunday.
"There is a pleasantly discursive treatment of
Pontius Pilate's unanswered question 'What is truth?'" — H. S. M. Coxeter, 1987
From this date (April 22) last year—
Richard J. Trudeau in The NonEuclidean Revolution , chapter on "Geometry and the Diamond Theory of Truth"– "… Plato and Kant, and most of the philosophers and scientists in the 2200year interval between them, did share the following general presumptions: (1) Diamonds– informative, certain truths about the world– exist. Presumption (1) is what I referred to earlier as the 'Diamond Theory' of truth. It is far, far older than deductive geometry." Trudeau's book was published in 1987. The nonEuclidean* figures above illustrate concepts from a 1976 monograph, also called "Diamond Theory." Although nonEuclidean,* the theorems of the 1976 "Diamond Theory" are also, in Trudeau's terminology, diamonds. * "NonEuclidean" here means merely "other than Euclidean." No violation of Euclid's parallel postulate is implied. 
Trudeau comes to reject what he calls the "Diamond Theory" of truth. The trouble with his argument is the phrase "about the world."
Geometry, a part of pure mathematics, is not about the world. See G. H. Hardy, A Mathematician's Apology .
“Nuvoletta in her lightdress, spunn of sisteen shimmers,
was looking down on them, leaning over the bannistars….
Fuvver, that Skand, he was up in Norwood’s sokaparlour….”
— Finnegans Wake
To counteract the darkness of today’s 2:01 AM entry—
Part I— Artist Josefine Lyche describes her methods—
A— “Internet and hard work”
B— “Books, both fiction and theory”
Part II— I, too, now rely mostly on the Internet for material. However, like Lyche, I have Plan B— books.
Where I happen to be now, there are piles of them. Here is the pile nearest to hand, from top to bottom.
(The books are in no particular order, and put in the same pile for no particular reason.)
Lyche probably could easily make her own list of what Joyce might call “sisteen shimmers.”
Stanford Encyclopedia of Philosophy —
“Mereology (from the Greek μερος, ‘part’) is the theory of parthood relations: of the relations of part to whole and the relations of part to part within a whole. Its roots can be traced back to the early days of philosophy, beginning with the Presocratics….”
A nonEuclidean* approach to parts–
Corresponding nonEuclidean*
projective points —
Richard J. Trudeau in The NonEuclidean Revolution, chapter on “Geometry and the Diamond Theory of Truth”–
“… Plato and Kant, and most of the philosophers and scientists in the 2200year interval between them, did share the following general presumptions:
(1) Diamonds– informative, certain truths about the world– exist.
(2) The theorems of Euclidean geometry are diamonds.
Presumption (1) is what I referred to earlier as the ‘Diamond Theory’ of truth. It is far, far older than deductive geometry.”
Trudeau’s book was published in 1987. The nonEuclidean* figures above illustrate concepts from a 1976 monograph, also called “Diamond Theory.”
Although nonEuclidean,* the theorems of the 1976 “Diamond Theory” are also, in Trudeau’s terminology, diamonds.
* “NonEuclidean” here means merely “other than Euclidean.” No violation of Euclid’s parallel postulate is implied.
Truth, Geometry, Algebra
The following notes are related to A Simple Reflection Group of Order 168.
1. According to H.S.M. Coxeter and Richard J. Trudeau
“There is a pleasantly discursive treatment of Pontius Pilate’s unanswered question ‘What is truth?’.”
— Coxeter, 1987, introduction to Trudeau’s The NonEuclidean Revolution
1.1 Trudeau’s Diamond Theory of Truth
1.2 Trudeau’s Story Theory of Truth
2. According to Alexandre Borovik and Steven H. Cullinane
2.1 Coxeter Theory according to Borovik
2.1.1 The Geometry–
Mirror Systems in Coxeter Theory
2.1.2 The Algebra–
Coxeter Languages in Coxeter Theory
2.2 Diamond Theory according to Cullinane
2.2.1 The Geometry–
Examples: Eightfold Cube and Solomon’s Cube
2.2.2 The Algebra–
Examples: Cullinane and (rather indirectly related) Gerhard Grams
Summary of the story thus far:
Diamond theory and Coxeter theory are to some extent analogous– both deal with reflection groups and both have a visual (i.e., geometric) side and a verbal (i.e., algebraic) side. Coxeter theory is of course highly developed on both sides. Diamond theory is, on the geometric side, currently restricted to examples in at most three Euclidean (and six binary) dimensions. On the algebraic side, it is woefully underdeveloped. For material related to the algebraic side, search the Web for generators+relations+”characteristic two” (or “2“) and for generators+relations+”GF(2)”. (This last search is the source of the Grams reference in 2.2.2 above.)
Unitarian Universalist Origins: Our Historic Faith—
“In sixteenthcentury Transylvania, Unitarian congregations were established for the first time in history.”
Gravity’s Rainbow–
“For every kind of vampire, there is a kind of cross.”
Unitarian minister Richard Trudeau—
“… I called the belief that
(1) Diamonds– informative, certain truths about the world– exist
the ‘Diamond Theory’ of truth. I said that for 2200 years the strongest evidence for the Diamond Theory was the widespread perception that
(2) The theorems of Euclidean geometry are diamonds….
As the news about nonEuclidean geometry spread– first among mathematicians, then among scientists and philosophers– the Diamond Theory began a long decline that continues today.
Factors outside mathematics have contributed to this decline. Euclidean geometry had never been the Diamond Theory’s only ally. In the eighteenth century other fields had seemed to possess diamonds, too; when many of these turned out to be manmade, the Diamond Theory was undercut. And unlike earlier periods in history, when intellectual shocks came only occasionally, received truths have, since the eighteenth century, been found wanting at a dizzying rate, creating an impression that perhaps no knowledge is stable.
Other factors notwithstanding, nonEuclidean geometry remains, I think, for those who have heard of it, the single most powerful argument against the Diamond Theory*– first, because it overthrows what had always been the strongest argument in favor of the Diamond Theory, the objective truth of Euclidean geometry; and second, because it does so not by showing Euclidean geometry to be false, but by showing it to be merely uncertain.” —The NonEuclidean Revolution, p. 255
H. S. M. Coxeter, 1987, introduction to Trudeau’s book—
“There is a pleasantly discursive treatment of Pontius Pilate’s unanswered question ‘What is truth?’.”
As noted here on Oct. 8, 2008 (A Yom Kippur Meditation), Coxeter was aware in 1987 of a more technical use of the phrase “diamond theory” that is closely related to…
Pilate Goes
to Kindergarten
“There is a pleasantly discursive
treatment of Pontius Pilate’s
unanswered question
‘What is truth?’.”
— H. S. M. Coxeter, 1987,
introduction to Trudeau’s
remarks on the “Story Theory“
of truth as opposed to the
“Diamond Theory” of truth in
The NonEuclidean Revolution
Consider the following question in a paper cited by V. S. Varadarajan:
E. G. Beltrametti, “Can a finite geometry describe physical spacetime?” Universita degli studi di Perugia, Atti del convegno di geometria combinatoria e sue applicazioni, Perugia 1971, 57–62.
Simplifying:
“Can a finite geometry describe physical space?”
Simplifying further:
“Yes. Vide ‘The Eightfold Cube.'”
This journal on October 8, 2008, at noon: “There is a pleasantly discursive treatment of Pontius Pilate’s unanswered question ‘What is truth?'” Trudeau’s 1987 book uses the phrase “diamond theory” to denote the philosophical theory, common since Plato and Euclid, that there exist truths (which Trudeau calls “diamonds”) that are certain and eternal– for instance, the truth in Euclidean geometry that the sum of a triangle’s angles is 180 degrees. Insidehighered.com on “Future readers may consider Updike our era’s Mozart; Mozart was once written off as a tooprolific composer of ‘charming nothings,’ and some speak of Updike that way.” — Comment by BPJ 
Updike died on January 27.
On the same date,
Mozart was born.
Requiem
Mr. Best entered, tall, young, mild, light. He bore in his hand with grace a notebook, new, large, clean, bright. — James Joyce, Ulysses, 
Serious Numbers
A Yom Kippur
Meditation
"When times are mysterious
Serious numbers
Will always be heard."
— Paul Simon,
"When Numbers Get Serious"
"There is a pleasantly discursive treatment of Pontius Pilate's unanswered question 'What is truth?'"
— H. S. M. Coxeter, introduction to Richard J. Trudeau's remarks on the "story theory" of truth as opposed to the "diamond theory" of truth in The NonEuclidean Revolution
Trudeau's 1987 book uses the phrase "diamond theory" to denote the philosophical theory, common since Plato and Euclid, that there exist truths (which Trudeau calls "diamonds") that are certain and eternal– for instance, the truth in Euclidean geometry that the sum of a triangle's angles is 180 degrees. As the excerpt below shows, Trudeau prefers what he calls the "story theory" of truth–
"There are no diamonds. People make up stories about what they experience. Stories that catch on are called 'true.'"
(By the way, the phrase "diamond theory" was used earlier, in 1976, as the title of a monograph on geometry of which Coxeter was aware.)
What does this have to do with numbers?
Pilate's skeptical tone suggests he may have shared a certain confusion about geometric truth with thinkers like Trudeau and the slave boy in Plato's Meno. Truth in a different part of mathematics– elementary arithmetic– is perhaps more easily understood, although even there, the existence of what might be called "nonEuclidean number theory"– i.e., arithmetic over finite fields, in which 1+1 can equal zero– might prove baffling to thinkers like Trudeau.
Trudeau's book exhibits, though it does not discuss, a less confusing use of numbers– to mark the location of pages. For some philosophical background on this version of numerical truth that may be of interest to devotees of the Semitic religions on this evening's High Holiday, see Zen and Language Games.
For uses of numbers that are more confusing, see– for instance– the new website The Daily Beast and the old website Story Theory and the Number of the Beast.
“There is a pleasantly discursive treatment
of Pontius Pilate’s unanswered question
‘What is truth?'”
— H. S. M. Coxeter, 1987, introduction to
Richard J. Trudeau’s remarks on
the “Story Theory” of truth
as opposed to
the “Diamond Theory” of truth
in The NonEuclidean Revolution
A Serious Position
“‘Teitelbaum,’ in German,
is ‘date palm.'”
— Generations, Jan. 2003
“In Hasidism, a mystical brand
of Orthodox Judaism, the grand rabbi
is revered as a kinglike link to God….”
— Today’s New York Times obituary
of Rabbi Moses Teitelbaum,
who died on April 24, 2006
(Easter Monday in the
Orthodox Church)
From Wikipedia, an unsigned story:
“In 1923 Alfred Teitelbaum and his brother Wacław changed their surnames to Tarski, a name they invented because it sounded very Polish, was simple to spell and pronounce, and was unused. (Years later, he met another Alfred Tarski in northern California.) The Tarski brothers also converted to Roman Catholicism, the national religion of the Poles. Alfred did so, even though he was an avowed atheist, because he was about to finish his Ph.D. and correctly anticipated that it would be difficult for a Jew to obtain a serious position in the new Polish university system.”
Adapted from
illustration below:
“There is a pleasantly discursive treatment of Pontius Pilate’s unanswered question ‘What is truth?'”
— H. S. M. Coxeter, 1987, introduction to Richard J. Trudeau’s remarks on the “Story Theory” of truth as opposed to the “Diamond Theory” of truth in The NonEuclidean Revolution
“A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the ‘Story Theory’ of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called ‘true.’ The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes*….”
— Richard J. Trudeau in
The NonEuclidean Revolution
“‘Deniers’ of truth… insist that each of us is trapped in his own point of view; we make up stories about the world and, in an exercise of power, try to impose them on others.”
— Jim Holt in The New Yorker.
Exercise of Power:
Show that a white horse–
a figure not unlike the
symbol of the mathematics
publisher Springer–
is traced, within a naturally
arranged rectangular array of
polynomials, by the powers of x
modulo a polynomial
irreducible over a Galois field.
This horse, or chess knight–
“Springer,” in German–
plays a role in “Diamond Theory”
(a phrase used in finite geometry
in 1976, some years before its use
by Trudeau in the above book).
Related material
On this date:
In 1490, The White Knight
(Tirant lo Blanc )–
a major influence on Cervantes–
was published, and in 1910
the Mexican Revolution began.
Illustration:
Zapata by Diego Rivera,
Museum of Modern Art,
New York
“First published in the Catalan language in Valencia in 1490…. Reviewing the first modern Spanish translation in 1969 (Franco had ruthlessly suppressed the Catalan language and literature), Mario Vargas Llosa hailed the epic’s author as ‘the first of that lineage of Godsupplanters– Fielding, Balzac, Dickens, Flaubert, Tolstoy, Joyce, Faulkner– who try to create in their novels an allencompassing reality.'”
— H. S. M. Coxeter, introduction to
Richard J. Trudeau’s
The NonEuclidean Revolution
“People have always longed for truths about the world — not logical truths, for all their utility; or even probable truths, without which daily life would be impossible; but informative, certain truths, the only ‘truths’ strictly worthy of the name. Such truths I will call ‘diamonds’; they are highly desirable but hard to find….The happy metaphor is Morris Kline’s in Mathematics in Western Culture (Oxford, 1953), p. 430.”
— Richard J. Trudeau,
The NonEuclidean Revolution,
Birkhauser Boston,
1987, pages 114 and 117
“A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the ‘Story Theory’ of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called ‘true.’ The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes…. My own viewpoint is the Story Theory…. I concluded long ago that each enterprise contains only stories (which the scientists call ‘models of reality’). I had started by hunting diamonds; I did find dazzlingly beautiful jewels, but always of human manufacture.”
— Richard J. Trudeau,
The NonEuclidean Revolution,
Birkhauser Boston,
1987, pages 256 and 259
An example of
the story theory of truth:
Actress Gwyneth Paltrow (“Proof”) was apparently born on either Sept. 27, 1972, or Sept. 28, 1972. Google searches yield “about 193” results for the 27th and “about 610” for the 28th.
Those who believe in the “story theory” of truth may therefore want to wish her a happy birthday today. Those who do not may prefer the contents of yesterday’s entry, from Paltrow’s other birthday.
Mathematics and Narrative
continued
"There is a pleasantly discursive treatment of Pontius Pilate's unanswered question 'What is truth?'"
— H. S. M. Coxeter, 1987, introduction to Richard J. Trudeau's remarks on the "Story Theory" of truth as opposed to the "Diamond Theory" of truth " in The NonEuclidean Revolution
"I had an epiphany: I thought 'Oh my God, this is it! People are talking about elliptic curves and of course they think they are talking mathematics. But are they really? Or are they talking about stories?'"
— An organizer of last month's "Mathematics and Narrative" conference
"A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the 'Story Theory' of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called 'true.' The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes*…."
— Richard J. Trudeau in The NonEuclidean Revolution
"'Deniers' of truth… insist that each of us is trapped in his own point of view; we make up stories about the world and, in an exercise of power, try to impose them on others."
— Jim Holt in this week's New Yorker magazine. Click on the box below.
* Many stripes —
"What disciplines were represented at the meeting?"
"Apart from historians, you mean? Oh, many: writers, artists, philosophers, semioticians, cognitive psychologists – you name it."
— An organizer of last month's "Mathematics and Narrative" conference
Indiana Jones 
In memory of Bernard Williams,
Oxford philosopher, who died Tuesday, June 10, 2003.
“…in… Truth and Truthfulness [September, 2002], he sought to speak plainly, and took on the postmodern, politically correct notion that truth is merely relative…”
“People have always longed for truths about the world — not logical truths, for all their utility; or even probable truths, without which daily life would be impossible; but informative, certain truths, the only ‘truths’ strictly worthy of the name. Such truths I will call ‘diamonds’; they are highly desirable but hard to find….
A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the ‘Story Theory’ of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called ‘true.’ The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes…. My own viewpoint is the Story Theory….”
— Richard J. Trudeau, The NonEuclidean Revolution, Birkhauser Boston, 1987
Today is the feast day of Saint Jorge Luis Borges (b. Buenos Aires, August 24, 1899 – d. Geneva, June 14, 1986).
From Borges’s “The Aleph“:
“The Faithful who gather at the mosque of Amr, in Cairo, are acquainted with the fact that the entire universe lies inside one of the stone pillars that ring its central court…. The mosque dates from the seventh century; the pillars come from other temples of preIslamic religions…. Does this Aleph exist in the heart of a stone?”
(“Los fieles que concurren a la mezquita de Amr, en el Cairo, saben muy bien que el universo está en el interior de una de las columnas de piedra que rodean el patio central…. la mezquita data del siglo VII; las columnas proceden de otros templos de religiones anteislámicas…. ¿Existe ese Aleph en lo íntimo de una piedra?”)
From The Hunchback of Notre Dame:
Un cofre de gran riqueza
Hallaron dentro un pilar,
Dentro del, nuevas banderas
Con figuras de espantar.*
* A coffer of great richness
In a pillar’s heart they found,
Within it lay new banners,
With figures to astound.See also the figures obtained by coloring and permuting parts of the above religious symbol.
Lena Olin and Harrison Ford
in “Hollywood Homicide“
ART WARS:
Toward Eternity
April is Poetry Month, according to the Academy of American Poets. It is also Mathematics Awareness Month, funded by the National Security Agency; this year's theme is "Mathematics and Art."
Some previous journal entries for this month seem to be summarized by Emily Dickinson's remarks:
"Because I could not stop for Death–
He kindly stopped for me–
The Carriage held but just Ourselves–
And Immortality.
Math Awareness Month April is Math Awareness Month.

An Offer He Couldn't Refuse Today's birthday: Francis Ford Coppola is 64.
From a note on geometry of April 28, 1985: 
The Eight Today, the fourth day of the fourth month, plays an important part in Katherine Neville's The Eight. Let us honor this work, perhaps the greatest bad novel of the twentieth century, by reflecting on some properties of the number eight. Consider eight rectangular cells arranged in an array of four rows and two columns. Let us label these cells with coordinates, then apply a permutation.
The resulting set of arrows that indicate the movement of cells in a permutation (known as a Singer 7cycle) outlines rather neatly, in view of the chess theme of The Eight, a knight. This makes as much sense as anything in Neville's fiction, and has the merit of being based on fact. It also, albeit rather crudely, illustrates the "Mathematics and Art" theme of this year's Mathematics Awareness Month. The visual appearance of the "knight" permutation is less important than the fact that it leads to a construction (due to R. T. Curtis) of the Mathieu group M_{24} (via the Curtis Miracle Octad Generator), which in turn leads logically to the Monster group and to related "moonshine" investigations in the theory of modular functions. See also "Pieces of Eight," by Robert L. Griess. 
An Offer He Couldn't Refuse
Today's birthday: Francis Ford Coppola is 64.
"There is a pleasantly discursive treatment
of Pontius Pilate's unanswered question
'What is truth?'."
— H. S. M. Coxeter, 1987, introduction to Richard J. Trudeau's remarks on the "Story Theory" of truth as opposed to the "Diamond Theory" of truth in The NonEuclidean Revolution
"Then came From Here to Eternity. Sinatra lobbied hard for the role, practically getting on his knees to secure the role of the street smart punk G.I. Maggio. He sensed this was a role that could revive his career, and his instincts were right. There are lots of stories about how Columbia Studio head Harry Cohn was convinced to give the role to Sinatra, the most famous of which is expanded upon in the horse's head sequence in The Godfather. Maybe no one will know the truth about that. The one truth we do know is that the feisty New Jersey actor won the Academy Award as Best Supporting Actor for his work in From Here to Eternity. It was no looking back from then on."
From a note on geometry of April 28, 1985:
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