In memory of Jane Russell —
H.S.M. Coxeter's classic
Introduction to Geometry (2nd ed.):
Note the resemblance of the central part to
a magical counterpart— the Ojo de Dios
of Mexico's Sierra Madre.
Related material— page 55 of Polly and the Aunt ,
by Mary E. Blatchford.
"What is your original face before you were born?"
See also yesterday's sermon, the birth date of William Faulkner, and Of Time and the River.
A Meditation on Harvard, Pi, and Rhetoric
Recall that pi equals 3.14159… "Et cetera, et cetera, et cetera." —The King and I
Related material—
"It's hard for thee to kick against the pricks."
Happy birthday from Samuel Beckett to Johnny Cash.
Last night's post was about a talk last year at the annual student symposium of the ACCA (Associated Colleges of the Chicago Area), a group of largely Christian colleges.
The fact that the talk was by a student from Benedictine University suggests a review of the Urbi et Orbi speech by Pope Benedict XVI on Christmas 2010.
“The Word became flesh”. The light of this truth is revealed to those who receive it in faith, for it is a mystery of love. Only those who are open to love are enveloped in the light of Christmas. So it was on that night in Bethlehem, and so it is today. The Incarnation of the Son of God is an event which occurred within history, while at the same time transcending history. In the night of the world a new light was kindled, one which lets itself be seen by the simple eyes of faith, by the meek and humble hearts of those who await the Saviour. If the truth were a mere mathematical formula, in some sense it would impose itself by its own power. But if Truth is Love, it calls for faith, for the “yes” of our hearts.
And what do our hearts, in effect, seek, if not a Truth which is also Love? Children seek it with their questions, so disarming and stimulating; young people seek it in their eagerness to discover the deepest meaning of their life; adults seek it in order to guide and sustain their commitments in the family and the workplace; the elderly seek it in order to grant completion to their earthly existence.
The above excerpt from the Pope's speech may be regarded as part of a continuing commentary on the following remark—
There is a pleasantly discursive treatment of Pontius Pilate's unanswered question "What is truth?" — H. S. M. Coxeter, 1987
"THE DIAMOND THEOREM AND QUILT PATTERNS
Victoria Blumen, Mathematics, Junior, Benedictine University
Tim Comar, Benedictine University
Mathematics
Secondary Source Research
Let D be a 4 by 4 block quilt shape, where each of the 16 square blocks is consists of [sic ] two triangles, one of which is colored red and the other of which is colored blue. Let G: D -> D_g be a mapping of D that interchanges a pair of columns, rows, or quadrants of D. The diamond theorem states that G(D) = D_g has either ordinary or color-interchange symmetry. In this talk, we will prove the diamond theorem and explore symmetries of quilt patterns of the form G(D)."
Exercise— Correct the above statement of the theorem.
Background— This is from a Google search result at about 10:55 PM ET Feb. 25, 2011—
[DOC] THE DIAMOND THEOREM AND QUILT PATTERNS – acca.elmhurst.edu
File Format: Microsoft Word – 14 hours ago –
Let G: D -> D_g be a mapping of D that interchanges a pair of columns, rows, or quadrants of D. The diamond theorem states that G(D) = D_g has either …
acca.elmhurst.edu/…/victoria_blumen9607_
THE%20DIAMOND%20THEOREM%20AND%20QUILT%20PATTERNS…
The document is from a list of mathematics abstracts for the annual student symposium of the ACCA (Associated Colleges of the Chicago Area) held on April 10, 2010.
Update of Feb. 26— For a related remark quoted here on the date of the student symposium, see Geometry for Generations.
"…the farther back we manage to wiggle
the more we need the loan of a lens…." —Finnegans Wake
For some background on the lens below, see the sermon on February 20th, 2011.
“The quad gospellers may own the targum but any of the Zingari shoolerim
may pick a peck of kindlings yet from the sack of auld hensyne.”
The above "Zingari shoolerim" passage was quoted here in Frame Tales (November 10th, 2008).
That post concerned the Heinrich Zimmer tale "The King and the Corpse." Some related material—
For seven — Two poems: Lord Shiva and somewhere i have never travelled
Incidentally… " 'Posh' is a word in Romany, the language of Gypsies, meaning 'half.' According to poet and etymologist John Ciardi, the word originally entered the argot of England's underworld in the 17th century in such compounds as 'posh-houri,' meaning 'half-pence,' and soon became a slang term for money in general. From there it was a short hop to meaning 'expensive' or 'fancy.' … the Gypsies… came originally from Northern India…."
Word detectives who are too clever by half may enjoy some context —
From www.4to40.com/poems/
* Suggested by yesterday's post on a Martin Harris Centre production of "Posh,"
by last night's remarks on horseness and Guild Awards, and
by last year's February Mysteries of Faith.
In memory of Pete Postlethwaite, who played father figures in
"In the Name of the Father" and in "Inception."
He died on January 2, 2011.
"And I looked and behold: a pale horse" — Johnny Cash
This journal on the day of Postlethwaite's death—
For somewhat deeper discussions see "Blackburn+universals" in this journal.
"It is arguable that this is always the deepest, most profound problem of philosophy.”
– Simon Blackburn, Think (Oxford, 1999)
Quotes from the new film "Unknown" —
Related fantasia —
Ad for Posh — Click to enlarge —
From May 11, 2010, an image—
See also the same date in 2005 in light of
Christchurch Philosophy. See also today's news.
The sequel to Another Manic Monday and The Abacus Conundrum —
You'll glitter and gleam so
Make somebody dream so that
Some day he may buy you a ring, ringa-linga
I've heard that's where it leads…
Related material — Janet's Tea Party
From Das Glasperlenspiel (Hermann Hesse, 1943) —
“Bastian Perrot… constructed a frame, modeled on a child’s abacus, a frame with several dozen wires on which could be strung glass beads of various sizes, shapes, and colors. The wires corresponded to the lines of the musical staff, the beads to the time values of the notes, and so on. In this way he could represent with beads musical quotations or invented themes, could alter, transpose, and develop them, change them and set them in counterpoint to one another. In technical terms this was a mere plaything, but the pupils liked it.… …what later evolved out of that students’ sport and Perrot’s bead-strung wires bears to this day the name by which it became popularly known, the Glass Bead Game.”
From “Mimsy Were the Borogoves” (Lewis Padgett, 1943)—
…”Paradine looked up. He frowned, staring. What in—
…”Is that an abacus?” he asked. “Let’s see it, please.”
…Somewhat unwillingly Scott brought the gadget across to his father’s chair. Paradine blinked. The “abacus,” unfolded, was more than a foot square, composed of thin, rigid wires that interlocked here and there. On the wires the colored beads were strung. They could be slid back and forth, and from one support to another, even at the points of jointure. But— a pierced bead couldn’t cross interlocking wires—
…So, apparently, they weren’t pierced. Paradine looked closer. Each small sphere had a deep groove running around it, so that it could be revolved and slid along the wire at the same time. Paradine tried to pull one free. It clung as though magnetically. Iron? It looked more like plastic.
…The framework itself— Paradine wasn’t a mathematician. But the angles formed by the wires were vaguely shocking, in their ridiculous lack of Euclidean logic. They were a maze. Perhaps that’s what the gadget was— a puzzle.
…”Where’d you get this?”
…”Uncle Harry gave it to me,” Scott said on the spur of the moment. “Last Sunday, when he came over.” Uncle Harry was out of town, a circumstance Scott well knew. At the age of seven, a boy soon learns that the vagaries of adults follow a certain definite pattern, and that they are fussy about the donors of gifts. Moreover, Uncle Harry would not return for several weeks; the expiration of that period was unimaginable to Scott, or, at least, the fact that his lie would ultimately be discovered meant less to him than the advantages of being allowed to keep the toy.
…Paradine found himself growing slightly confused as he attempted to manipulate the beads. The angles were vaguely illogical. It was like a puzzle. This red bead, if slid along this wire to that junction, should reach there— but it didn’t. A maze, odd, but no doubt instructive. Paradine had a well-founded feeling that he’d have no patience with the thing himself.
…Scott did, however, retiring to a corner and sliding beads around with much fumbling and grunting. The beads did sting, when Scott chose the wrong ones or tried to slide them in the wrong direction. At last he crowed exultantly.
…”I did it, dad!”
…””Eh? What? Let’s see.” The device looked exactly the same to Paradine, but Scott pointed and beamed.
…”I made it disappear.”
…”It’s still there.”
…”That blue bead. It’s gone now.”
…Paradine didn’t believe that, so he merely snorted. Scott puzzled over the framework again. He experimented. This time there were no shocks, even slight. The abacus had showed him the correct method. Now it was up to him to do it on his own. The bizarre angles of the wires seemed a little less confusing now, somehow.
…It was a most instructive toy—
…It worked, Scott thought, rather like the crystal cube.
* Title thanks to Saturday Night Live (Dec. 4-5, 2010).
"The curriculum begins with a game called Winding Around Positions.
There are twelve stations that could represent hours on a clock
or the Chinese years zodiac."
— The current (March 2011) Notices of the American Mathematical Society
Background — "Winding Games" (pdf, 1.43 MB)—
For the not-too-tightly wound —
“Always with a little humor.” – Dr. Yen Lo (See The China Candidate and Humorism)
We are now at the Year of the Rabbit —
(Click images for sources.)
 |
 |
 |
|
Judith Shulevitz at The New York Times
on Sunday, July 18, 2010 —
"What would an organic Christian Sabbath look like today?
For James Carroll, an ex-priest and dissenting Catholic
in Boston (he is the author of Practicing Catholic ,
published in 2009), it would look like the Sunday dinners
of his childhood. These were big formal meals,
held at 2 p.m. every Sunday….
'If Jesus were to visit us, it would have been
the Sunday dinner he would have insisted on
being a part of, not the worship service at the church.'"
Possible Table Topics
|
Arts & Letters Daily (20 Feb 2011) Sat Feb 19, 2011 23:00
Nobody likes a grammar scold, but it must be said:
How did the armies of Mordor cope with defeat?
Is philosophy of science an obsolete |
Some background for the discussion —
A book said to have received 15,480 reviews—
From Galleri MGM in Oslo —
Josefine Lyche "Why do we remember the past, but not the future?" "If you want a vision of the future, imagine a boot stamping on a human face – forever." Galleri MGM is pleased to present the second solo exhibition by Josefine Lyche (b.1973). Lyche presents a body of work consisting of sculptures and a wall painting, as well as a series of new paperwork, all using geometrical abstractions and light as a medium. Her work dissolves boundaries between fiction and documentation, depicting how fantasies and dreams collide with and yet help determine the shape of reality. Theme and variations is a term most commonly used in the music genre as a musical form in which the fundamental musical idea, or theme, is repeated in altered form or accompanied in a different manner. The exhibition explores geometric shapes and solids and revisits work of artists like Robert Morris and Ellsworth Kelly, giving it a disco treatment of glitter, neon and gloss. The mathematical, science-fiction and new age references incorporated in the works comments on the ambivalent foretelling of utopian hope and dystopian vision of a near, yet unknown future. The transmission between past and future is shown in the sculpture "The Omega Point" a portal that leads in or out of time and space. … |
A connection to today's earlier post, Sunday School— The Oslo Version, from Friday, May 21, 2010.
Lyche's "Omega Point" portal, together with her last name, suggested three posts from the following Saturday morning— which later proved to be the date of Martin Gardner's death—
Art Space, Through the Lyche Gate and The Lyche Gate Asterisk.
For some further religious remarks, see November 9th, 2010— A Theory of Pure Design.
From Epiphany Revisited —
A star figure and the Galois quaternion.
The square root of the former is the latter.
… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.
Harvard Science Review (Winter 1997) on Thomas Kuhn's
The Structure of Scientific Revolutions —
"…his language often portrays paradigms as cults
and the battle between paradigms as quasi-religious wars."
Related material: This journal's "Paradigms" on February 17th
and the following notes—
From this journal yesterday—
|
American Spectator – Ben Stein's Diary: Watch … A vertiginous occlusion opened at my feet… |
From The New York Times today—
"Isn’t it true that every great comedian operates on the edge of an abyss?"
"These passages suggest that the Form is a character or set of characters
common to a number of things, i.e. the feature in reality which corresponds
to a general word. But Plato also uses language which suggests not only
that the forms exist separately (χωριστά ) from all the particulars, but also
that each form is a peculiarly accurate or good particular of its own kind,
i.e. the standard particular of the kind in question or the model (παράδειγμα )
[i.e. paradigm ] to which other particulars approximate….
… Both in the Republic and in the Sophist there is a strong suggestion
that correct thinking is following out the connexions between Forms.
The model is mathematical thinking, e.g. the proof given in the Meno
that the square on the diagonal is double the original square in area."
— William and Martha Kneale, The Development of Logic,
Oxford University Press paperback, 1985
Plato's paradigm in the Meno —
Changed paradigm in the diamond theorem (2×2 case) —
Aspects of the paradigm change* —
Monochrome figures to
colored figures
Areas to
transformations
Continuous transformations to
non-continuous transformations
Euclidean geometry to
finite geometry
Euclidean quantities to
finite fields
Some pedagogues may find handling all of these
conceptual changes simultaneously somewhat difficult.
* "Paradigm shift " is a phrase that, as John Baez has rightly pointed out,
should be used with caution. The related phrase here was suggested by Plato's
term παράδειγμα above, along with the commentators' specific reference to
the Meno figure that serves as a model. (For "model" in a different sense,
see Burkard Polster.) But note that Baez's own beloved category theory
has been called a paradigm shift.
The White Album – Google Books Result
Joan Didion – 1990 – Fiction – 222 pages
… a slippage, a certain vertiginous occlusion of the imagined and the real, and this slippage was particularly acute the last time I arrived in Honolulu,…
books.google.com/books?isbn=0374522219…
American Spectator – Ben Stein's Diary: Watch …
A vertiginous occlusion opened at my feet… …He had so much time to spend with me it was hard to believe… …The food was ghastly, simply horrible,…
search.opinionarchives.com/Summary/…/V30I10P52-1.htm – Cached
"Why don't you come with me, little girl,
On a magic carpet ride?"
– Steppenwolf lyrics
"I like to fold my magic carpet, after use,
in such a way as to superimpose
one part of the pattern upon another."
– Vladimir Nabokov in Speak, Memory
See also Nabokov at Harvard in today's Crimson
and the Russian boxes of Henry James.
"… Only by the form, the pattern,
Can words or music reach
The stillness…."
— T. S. Eliot,
Four Quartets
For further details, see Time Fold.
From this evening's online New York Times—
Flock Around ‘The Clock’
By RANDY KENNEDY Benjamin Norman for The New York Times “The Clock,” a video work by Christian Marclay, uses thousands of film and television clips of timepieces to create, minute by minute, a 24-hour montage that unfolds in real time. “The Clock,” a 24-hour video work by Christian Marclay, draws crowds at the Paula Cooper Gallery in Chelsea. Critic’s NotebookThe Musical Rhythms in Images Out of Time By BEN RATLIFFTime is a kind of music, music is a kind of time, and Christian Marclay seems to understand this implicitly. |
See also Don DeLillo's Point Omega , a novel published on Groundhog Day, 2010.
Powered by WordPress
