The Center
Anonymous Woman
Adapted from Harvard Crimson
March 2008 photo by Isabella N. Lai
at the Harvard Women's Center
See also …
Yeats –
“the centre cannot hold,”
Stevens –
“the center of resemblance,”
and Zelazny –
“center loosens,
forms again elsewhere.”
From last night's note on finite geometry—
"The (83, 83) Möbius-Kantor configuration here described by Coxeter is of course part of the larger (94, 123) Hesse configuration. Simply add the center point of the 3×3 Galois affine plane and the four lines (1 horizontal, 1 vertical, 2 diagonal) through the center point." An illustration—
This suggests a search for "diamond+star."
See the new note Configurations and Squares at finitegeometry.org/sc/.
Part I: Naturalized Epistemology
Part II: Peter Cameron
"Desire, hearing the calendar hymn, repudiates the negativity of the mind of winter…."
Related material: Appalachian Spring at Harvard and Reba.com.
On this date 106 years ago…
Prefatory note from Hudson's classic Kummer's Quartic Surface ,
Cambridge University Press, 1905—
RONALD WILLIAM HENRY TURNBULL HUDSON would have
been twenty-nine years old in July of this year; educated at
St Paul's School, London, and at St John's College, Cambridge,
he obtained the highest honours in the public examinations of the
University, in 1898, 1899, 1900; was elected a Fellow of St John's
College in 1900; became a Lecturer in Mathematics at University
College, Liverpool, in 1902; was D.Sc. in the University of London
in 1903; and died, as the result of a fall while climbing in Wales,
in the early autumn of 1904….
A many-sided theory such as that of this volume is
generally to be won only by the work of many lives;
one who held so firmly the faith that the time is well spent
could ill be spared.
— H. F. Baker, 27 March 1905
For some more recent remarks related to the theory, see
Defining Configurations and its updates, March 20-27, 2011.
| Crazy Arms Ray Price Chart position: No. 1, 1956 (written by Ralph E. Mooney) Now blue ain't the word for the way that I feel And a storm is brewing in this heart of mine This ain't no crazy dream I know that it's real You're someone else's love now, you're not mine Crazy arms that reach to hold somebody new But my yearning heart keeps saying you're not mine My troubled mind knows soon to another you'll be wed That's why I'm lonely all the time Please take these treasured dreams I had for you and me And take all the love I thought was mine Someday my crazy arms will hold somebody new But right now I'm so lonesome I could die Crazy arms that reach to hold somebody new But my yearning heart keeps saying you're not mine My troubled mind knows soon to another you'll be wed You're someone else's love now, you're not mine Well you're someone else's love now, you're not mine ~~~~~~~~~~~~~~~~~~~~ Portions of this work contain the intellectual property |
| … All her nubied |
| companions were asleeping with the squirrels. Their mivver, |
| Mrs Moonan, was off in the Fuerst quarter scrubbing the back- |
| steps of Number 28. Fuvver, that Skand, he was up in Norwood's |
| sokaparlour, eating oceans of Voking's Blemish. Nuvoletta lis- |
| tened as she reflected herself, though the heavenly one with his |
| constellatria and his emanations stood between…. |
* See The Black Queen.
"I just seemed to have more frames per second than other kids."
— Mary Karr, "Facing Altars: Poetry and Prayer"
See also "Signs and Symbols."
See Margaret Atwood in this journal.
This link was suggested by the phrase "combinatorial* delight" in last night's quote from Nabokov, which also appears in Douglas Glover's review essay, "Her Life Entire," in Books in Canada , Volume 17, Number 7, October 1988—
Cat's Eye is Atwood's seventh novel. It is dense, intricate, and superb, as thematically diverse and complex as anything she has written. It is what you might expect from a writer at mid-career, mid-life: a portrait of the artist, a summation of what she knows about art and people. It is also an Atwoodian Under the Volcano , a vision of Toronto as Hell.
See also Under the Volcano and Toronto in this journal.
"Right through hell there is a path." –Under the Volcano
* Update: Corrected on Dec. 13, 2014, to "combinational delight."
" … I feel I understand
Existence, or at least a minute part
Of my existence, only through my art,
In terms of combinational delight;
And if my private universe scans right,
So does the verse of galaxies divine
Which I suspect is an iambic line.
I'm reasonably sure that we survive
And that my darling somewhere is alive…."
— Vladimir Nabokov, Pale Fire
"When Death tells a story,
you really have to listen."
— Cover, The Book Thief
An image from a post linked to in Tuesday's Koan for Larsson—
An image from today's New York Times obituaries—
Wikipedia on singer Loleatta Holloway, who died Monday—
[Her] "Like a Prayer," a Madonna cover, was a track on the Madonna tribute album Virgin Voices.
New York Times on actress Helen Stenborg, who died Tuesday—
A Minnesotan of Swedish descent, she naturally brought to all her roles the kind of reserve that reflected her upbringing.
From The New York Times on February 27th, 1949— the day Elizabeth Taylor turned 17—
"Tragedy enlightens-and it must, in that it points the heroic finger at the enemy of man's freedom."
— Arthur Miller, "Tragedy and the Common Man"
For an illustration, see the link in last Saturday's Night of the Supermoon to July 2005.
"On the one-ton temple bell
a moon-moth, folded into sleep,
sits still." — Haiku by Buson
From the day author Stieg Larsson died—
The Nine (November 9th, 2004).
See also Pandora's Box (September 16th, 2006).
"a sort of… Dr. Strangelove" —Review of Point Omega
Context— From March 13— The Counter and Twenty-Four.
Readings for tonight, the Night of the Supermoon—
In memory of David Rumelhart, who "explored the possibility of formulating a formal grammar to capture the structure of stories." (Wikipedia)
Rumelhart died on Sunday, March 13, 2011.*
I've got a little schema you oughta know….
So make it one for my baby and one more for the road.
* From that date: The Counter and Twenty-Four.
The On-Line Encyclopedia of Integer Sequences has an article titled "Number of combinatorial configurations of type (n_3)," by N.J.A. Sloane and D. Glynn.
From that article:
The following corrects the word "unique" in the example.
* This post corrects an earlier post, also numbered 14660 and dated 7 PM March 18, 2011, that was in error.
The correction was made at about 11:50 AM on March 20, 2011.
_____________________________________________________________
Update of March 21
The problem here is of course with the definition. Sloane and Glynn failed to include in their definition a condition that is common in other definitions of configurations, even abstract or purely "combinatorial" configurations. See, for instance, Configurations of Points and Lines , by Branko Grunbaum (American Mathematical Society, 2009), p. 17—
In the most general sense we shall consider combinatorial (or abstract) configurations; we shall use the term set-configurations as well. In this setting "points" are interpreted as any symbols (usually letters or integers), and "lines" are families of such symbols; "incidence" means that a "point" is an element of a "line". It follows that combinatorial configurations are special kinds of general incidence structures. Occasionally, in order to simplify and clarify the language, for "points" we shall use the term marks, and for "lines" we shall use blocks. The main property of geometric configurations that is preserved in the generalization to set-configurations (and that characterizes such configurations) is that two marks are incident with at most one block, and two blocks with at most one mark.
Whether or not omitting this "at most one" condition from the definition is aesthetically the best choice, it dramatically changes the number of configurations in the resulting theory, as the above (8_3) examples show.
Update of March 22 (itself updated on March 25)
For further background on configurations, see Dolgachev—
Note that the two examples Dolgachev mentions here, with 16 points and 9 points, are not unrelated to the geometry of 4×4 and 3×3 square arrays. For the Kummer and related 16-point configurations, see section 10.3, "The Three Biplanes of Order 4," in Burkard Polster's A Geometrical Picture Book (Springer, 1998). See also the 4×4 array described by Gordon Royle in an undated web page and in 1980 by Assmus and Sardi. For the Hesse configuration, see (for instance) the passage from Coxeter quoted in Quaternions in an Affine Galois Plane.
Update of March 27
See the above link to the (16,6) 4×4 array and the (16,6) exercises using this array in R.D. Carmichael's classic Introduction to the Theory of Groups of Finite Order (1937), pp. 42-43. For a connection of this sort of 4×4 geometry to the geometry of the diamond theorem, read "The 2-subsets of a 6-set are the points of a PG(3,2)" (a note from 1986) in light of R.W.H.T. Hudson's 1905 classic Kummer's Quartic Surface , pages 8-9, 16-17, 44-45, 76-77, 78-79, and 80.
A phrase from yesterday evening's post "Time Travel Poem"—
"what Joe Public is thinking."
An expert on Joe Public delivers his opinion on time travel—
"The time is now."
Source: NY Times obituaries—
From “This Week’s Hype II,” a post at Peter Woit’s physics weblog this afternoon, a comment—
TedUnger says:
March 17, 2011 at 5:34 pm
“… there’s been nothing from these CERN scientists
except some lousy boring data on physics!
They better at least give us some time travel or else!
You know that is what Joe Public is thinking.”
The commenter’s identity is not clear. Even less clear is the identity of his subject, Joe Public.
For some remarks on time travel from literature rather than science, see “Damnation Morning” in this journal.
Erin O’Connor’s St. Patrick’s Day post this morning says,
“[Roddy] Doyle’s take on the Irish struggle for independence,
A Star Called Henry , has a lovely touch of magical realism.”
Note that the remarks by Henry Baker in this morning’s post here were dated Thursday, 11 September 1913.
Related material—
Yet they were of a different kind
The names that stilled your childish play,
They have gone about the world like wind,
But little time had they to pray
For whom the hangman’s rope was spun,
And what, God help us, could they save:
Romantic Ireland’s dead and gone,
It’s with O’Leary in the grave.
William Butler Yeats, “September 1913“
Conclusion of “The Place of Pure Mathematics” —
“Dogmas and philosophies, it would seem, rise and fall. But gradually accumulating throughout the ages, from the earliest dawn of history, there is a body of doctrine, a reasoned insight into the relations of exact ideas, painfully won and often tested. And this remains the main heritage of man; his little beacon of light amidst the solitudes and darknesses of infinite space; or, if you prefer, like the shout of children at play together in the cultivated valleys, which continues from generation to generation.
Yes, and continues for ever! A universe which has the potentiality of becoming thus conscious of itself is not without something of which that which we call memory is but an image. Somewhere, somehow, in ways we dream not of, when you and I have merged again into the illimitable whole, when all that is material has ceased, the faculty in which we now have some share, shall surely endure; the conceptions we now dimly struggle to grasp, the joy we have in the effort, these are but part of a greater whole. Some may fear, and some may hope, that they and theirs shall not endure for ever. But he must have studied Nature in vain who does not see that our spiritual activities are inherent in the mighty process of which we are part; who can doubt of their persistence.
And, on the intellectual side, of all that is best ascertained, and surest, and most definite, of these; of all that is oldest and most universal; of all that is most fundamental and far-reaching, of these activities, Pure Mathematics is the symbol and the sum.”
— From a 1913 address by geometry saint Henry Frederick Baker, who died on this date in 1956
The feast of another saint, Patrick, also falls on 3/17. The date itself is related, if only by chance, to the following remark—
“317 is a prime, not because we think so,
or because our minds are shaped in one way
rather than another, but because it is so,
because mathematical reality is built that way.”
— From a 1940 book by the somewhat less saintly number theorist G. H. Hardy
Accidental Time and Space
New York Lottery today— midday 987, evening 522.
Time
The midday 987 may be interpreted as "…nine, eight, seven, …."—
"The countdown as we know it, 10-9-8-u.s.w.,
was invented by Fritz Lang in 1929 for
the Ufa film Die Frau im Mond . He put it into
the launch scene to heighten the suspense.
'It is another of my damned "touches,"' Fritz Lang said."
Space
The evening 522 suggests the date 5/22. From that date last year—
Art Space (2:02 AM EDT)
|
Pictorial version |
|
“Space: what you damn well have to see.”
– James Joyce, Ulysses
Related material:
See a search for the author of
Venus on the Half-Shell .
"For every kind of vampire,
there is a kind of cross."
— Gravity's Rainbow
"Hang a shining star upon the highest bough."
— Hugh Martin. Martin died on March 11th, 2011.
"The shaping of a work of art means, paradoxically, preserving some space for ambiguity."
— Rebecca Newberger Goldstein in The Wall Street Journal , December 11th, 2010
From January 16th—
Here are links to the source posts: December 3, 2010 and December 4, 2010.
A comment yesterday at Peter Woit's weblog—
Glenn says:
March 14, 2011 at 8:49 pm
Perhaps John G. Cramer’s prediction will come true after all?
http://en.wikipedia.org/wiki/Einstein%27s_Bridge_(book)
Of course, in that case, the proof would exist on a world-line
inaccessible to any living observer.
New York Lottery—
Related material:
From the weblog of Cramer's daughter Kathryn on Feb. 28—
For 928. see the two posts from last year's 9/28 in this journal—
From "Mathematicians and Poets," by Cai Tianxin, in the April 2011 AMS Notices—
Gauss, “the prince of mathematics”, wrote to tell a
friend, after solving a problem (symbols of Gaussian
summation) that had been bothering him for
years, “Finally, two days ago, I succeeded—not on
account of my hard efforts, but by the grace of the
Lord. Like a sudden flash of lightning, the riddle
was solved. I am unable to say what the conducting
thread was that connected what I previously knew
with what made my success possible.”
Gauss appears also in the results of the search for the phrase "only connect"
in this morning's Ides of Art post.
See as well the Grateful Dead logo in that post, and the following ad
shown today at Secret Blogging Seminar's Oct. 11, 2008, post
"The Sign of the Gauss Sum"—
Part I: A search in this journal for Cuernavaca+garden
Part II: This life can be very strange –Steely Dan, 1976
Part III: Owsley Stanley Dies at 76
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