Log24

Thursday, August 16, 2012

Raiders of the Lost Tesseract

Filed under: General,Geometry — Tags: — m759 @ 8:00 PM

(Continued from August 13. See also Coxeter Graveyard.)

Coxeter exhuming Geometry

Here the tombstone says
"GEOMETRY… 600 BC — 1900 AD… R.I.P."

In the geometry of Plato illustrated below,
"the figure of eight [square] feet" is not , at this point
in the dialogue, the diamond in Jowett's picture.

An 1892 figure by Jowett illustrating Plato's Meno

Jowett's picture is nonetheless of interest for
its resemblance to a figure drawn some decades later
by the Toronto geometer H. S. M. Coxeter.

A similar 1950 figure by Coxeter illustrating a tesseract

For a less scholarly, but equally confusing, view of the number 8,
see The Eight , a novel by Katherine Neville.

Thursday, October 20, 2011

The Thing Itself

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

Suggested by an Oct. 18 piece in the Book Bench section
of the online New Yorker  magazine—

http://www.log24.com/log/pix11C/111020-Derrida.GIF

http://www.log24.com/log/pix11C/111020-Topia122.GIF

Related material suggested by the "Shouts and Murmurs" piece
in The New Yorker , issue dated Oct. 24, 2011—

"a series of e-mails from a preschool teacher planning to celebrate
the Day of the Dead instead of Halloween…"

A search for Coxeter + Graveyard in this journal yields…

Coxeter exhuming Geometry

Here the tombstone says "GEOMETRY… 600 BC — 1900 AD… R.I.P."

A related search for Plato + Tombstone yields an image from July 6, 2007…

The image “http://www.log24.com/log/pix06A/061019-Tombstones.jpg” cannot be displayed, because it contains errors.

Here Plato's poems to Aster suggested
the "Star and Diamond" tombstone.

The eight-rayed star is an ancient symbol of Venus
and the diamond is from Plato's Meno .

The star and diamond are combined in a figure from
12 AM on September 6th, 2011—

The Diamond Star

http://www.log24.com/log/pix11B/110905-StellaOctangulaView.jpg

See Configurations and Squares.

That webpage explains how Coxeter
united the diamond and the star.

Those who prefer narrative to mathematics may consult
a definition of the Spanish word lucero  from March 28, 2003.

Saturday, November 8, 2008

Saturday November 8, 2008

Filed under: General,Geometry — m759 @ 8:28 AM
From a
Cartoon Graveyard

 “That corpse you planted
          last year in your garden,
  Has it begun to sprout?
          Will it bloom this year? 
  Or has the sudden frost
          disturbed its bed?”

— T. S. Eliot, “The Waste Land

Wikipedia:

“In the Roman Catholic tradition, the term ‘Body of Christ’ refers not only to the body of Christ in the spiritual realm, but also to two distinct though related things: the Church and the reality of the transubstantiated bread of the Eucharist….

According to the Catechism of the Catholic Church, ‘the comparison of the Church with the body casts light on the intimate bond between Christ and his Church. Not only is she gathered around him; she is united in him, in his body….’

….To distinguish the Body of Christ in this sense from his physical body, the term ‘Mystical Body of Christ’ is often used. This term was used as the first words, and so as the title, of the encyclical Mystici Corporis Christi of Pope Pius XII.”

Pope Pius XII
:

“83. The Sacrament of the Eucharist is itself a striking and wonderful figure of the unity of the Church, if we consider how in the bread to be consecrated many grains go to form one whole, and that in it the very Author of supernatural grace is given to us, so that through Him we may receive the spirit of charity in which we are bidden to live now no longer our own life but the life of Christ, and to love the Redeemer Himself in all the members of His social Body.”

Related material:

Log24 on this date in 2002:

Religious Symbolism
at Princeton

as well as

King of Infinite Space

Coxeter exhuming Geometry

and a
“striking and wonderful figure”
 from this morning’s newspaper–

Garfield brings to the fridge a birthday cupcake for the leftover meatloaf. Nov. 8, 2008.

Friday, September 5, 2008

Friday September 5, 2008

Filed under: General — Tags: — m759 @ 2:45 AM

For Mike Hammer

Block That Metaphor

“Michael Hammer, an engineer and author on management who helped popularize the ‘re-engineering’ movement in the 1990s, died Thursday [Sept. 4, 2008].

A spokesman for Mr. Hammer’s consulting firm, Hammer and Co., said Mr. Hammer died from cranial bleeding that began Aug. 22 while he was vacationing in Massachusetts. He was 60 years old.

Mr. Hammer was the co-author of the bestselling management book Reengineering the Corporation and founder and president of Hammer and Co., Cambridge, Mass.”

The Wall Street Journal

“An engineer by training, Hammer focused on the operational nuts and bolts of business.

Hammer’s relentless pursuit of ‘why?’ drove his entire career. ‘My modus operandi is simple,’ he once wrote, ‘though not always easy to carry out. I take nothing at face value. I approach all business issues and practices with the same skepticism: Why?’

A funeral will be held at 9:30 a.m. Friday, Sept. 5 in Stanetsky Memorial Chapel, 1668 Beacon St., Brookline. Interment will follow at the Shaarei Tefillah Section of the Chevra Shaas Cemetery at Baker Street Jewish Cemeteries in West Roxbury.”

web.mit.edu

Related material:

From Feb. 12:

Shoe: 'Mort's Mortuary,' Sunday, Feb. 10, 2008

From today:Outside the Box

The late Michael Hammer, engineer: 'Outside the Box'

“I need a photo opportunity,
I want a shot at redemption.
Don’t want to end up a cartoon
In a cartoon graveyard…”

Paul Simon

Bill Melendez, Peanuts animator, in NYT obituaries Friday, Sept. 5, 2008

Friday, July 4, 2008

Friday July 4, 2008

Filed under: General,Geometry — m759 @ 8:00 AM
REDEMPTION

“I need a photo-opportunity,
I want a shot at redemption.
Don’t want to end up a cartoon
In a cartoon graveyard.”
— Paul Simon

From Log24 on June 27, 2008,
the day that comic-book artist
Michael Turner died at 37 —

Van Gogh (by Ed Arno) in
The Paradise of Childhood
(by Edward Wiebé):

'Dear Theo' cartoon of van Gogh by Ed Arno, adapted to illustrate the eightfold cube


Two tomb raiders: Lara Croft and H.S.M. Coxeter

For Turner’s photo-opportunity,
click on Lara.

Sunday, June 1, 2008

Sunday June 1, 2008

Filed under: General,Geometry — Tags: — m759 @ 2:14 PM
Yet Another
Cartoon Graveyard

The conclusion of yesterday’s commentary on the May 30-31 Pennsylvania Lottery numbers:

Thomas Pynchon, Gravity’s Rainbow:

“The fear balloons again inside his brain. It will not be kept down with a simple Fuck You…. A smell, a forbidden room, at the bottom edge of his memory. He can’t see it, can’t make it out. Doesn’t want to. It is allied with the Worst Thing.

He knows what the smell has to be: though according to these papers it would have been too early for it, though he has never come across any of the stuff among the daytime coordinates of his life, still, down here, back here in the warm dark, among early shapes where the clocks and calendars don’t mean too much, he knows that’s what haunting him now will prove to be the smell of Imipolex G.

Then there’s this recent dream he is afraid of having again. He was in his old room, back home. A summer afternoon of lilacs and bees and

286”

What are we to make of this enigmatic 286? (No fair peeking at page 287.)

One possible meaning, given The Archivists claim that “existence is infinitely cross-referenced”–

Page 286 of Ernest G. Schachtel, Metamorphosis: On the Conflict of Human Development and the Psychology of Creativity (first published in 1959), Hillsdale NJ and London, The Analytic Press, 2001 (chapter– “On Memory and Childhood Amnesia”):

“Both Freud and Proust speak of the autobiographical [my italics] memory, and it is only with regard to this memory that the striking phenomenon of childhood amnesia and the less obvious difficulty of recovering any past experience may be observed.”

The concluding “summer afternoon of lilacs and bees” suggests that 286 may also be a chance allusion to the golden afternoon of Disney’s Alice in Wonderland. (Cf. St. Sarah’s Day, 2008)

Some may find the Disney afternoon charming; others may see it as yet another of Paul Simon’s dreaded cartoon graveyards.

More tastefully, there is poem 286 in the 1919 Oxford Book of English Verse– “Love.”

For a midrash on this poem, see Simone Weil, who became acquainted with the poem by chance:

“I always prefer saying chance rather than Providence.”

— Simone Weil, letter of about May 15, 1942

Weil’s brother André might prefer Providence (source of the Bulletin of the American Mathematical Society.)

Andre Weil and his sister Simone, summer of 1922(Photo from Providence)

 

Related material:


Log24, December 20, 2003–
White, Geometric, and Eternal

A description in Gravity’s Rainbow of prewar Berlin as “white and geometric”  suggested, in combination with a reference elsewhere to “the eternal,” a citation of the following illustration of the concept “white, geometric, and eternal”–

For more on the mathematical significance of this figure, see (for instance) Happy Birthday, Hassler Whitney, and Combinatorics of Coxeter Groups, by Anders Björner and Francesco Brenti, Graduate Texts in Mathematics, vol. 231, Springer, New York, 2005.

This book is reviewed in the current issue (July 2008) of the above-mentioned Providence Bulletin.

The review in the Bulletin discusses reflection groups in continuous spaces.

For a more elementary approach, see Reflection Groups in Finite Geometry and Knight Moves: The Relativity Theory of Kindergarten Blocks.

See also a commentary on
the phrase “as a little child.”

Sunday, May 18, 2008

Sunday May 18, 2008

Filed under: General,Geometry — Tags: — m759 @ 2:02 PM

From the Grave

DENNIS OVERBYE

in yesterday's New York Times:

"From the grave, Albert Einstein
poured gasoline on the culture wars
between science and religion this week…."

An announcement of a
colloquium at Princeton:

Cartoon of Coxedter exhuming Geometry

Above: a cartoon,
"Coxeter exhuming Geometry,"
with the latter's tombstone inscribed

"GEOMETRY

  600 B.C. —
1900 A.D.
R.I.P."

Page from 'The Paradise of Childhood,' 1906 edition

The above is from
The Paradise of Childhood,
a work first published in 1869.

"I need a photo-opportunity,
I want a shot at redemption.
Don't want to end up a cartoon
In a cartoon graveyard."

— Paul Simon

Einstein on TIME cover as 'Man of the Century'

Albert Einstein,
1879-1955:

"It is quite clear to me that the religious paradise of youth, which was thus lost, was a first attempt to free myself from the chains of the 'merely-personal,' from an existence which is dominated by wishes, hopes and primitive feelings.  Out yonder there was this huge world, which exists independently of us human beings and which stands before us like a great, eternal riddle, at least partially accessible to our inspection and thinking.  The contemplation of this world beckoned like a liberation…."

Autobiographical Notes, 1949

Related material:

A commentary on Tom Wolfe's
"Sorry, but Your Soul Just Died"–

"The Neural Buddhists," by David Brooks,
 in the May 13 New York Times:

"The mind seems to have
the ability to transcend itself
and merge with a larger
presence that feels more real."

A New Yorker commentary on
a new translation of the Psalms:

"Suddenly, in a world without
Heaven, Hell, the soul, and
eternal salvation or redemption,
the theological stakes seem
more local and temporal:
'So teach us to number our days.'"

and a May 13 Log24 commentary
on Thomas Wolfe's
"Only the Dead Know Brooklyn"–

"… all good things — trout as well as
eternal salvation — come by grace
and grace comes by art
and art does not come easy."

A River Runs Through It

"Art isn't easy."
— Stephen Sondheim,
quoted in
Solomon's Cube.

For further religious remarks,
consult Indiana Jones and the
Kingdom of the Crystal Skull
and The Librarian:
Return to King Solomon's Mines.

Tuesday, February 12, 2008

Tuesday February 12, 2008

Filed under: General — Tags: — m759 @ 5:01 PM

Centerpiece

“Kirk Browning… television director of ‘Live* From Lincoln Center,’ died on Sunday [Feb. 10, 2008] in Manhattan. He was 86.

The cause was a heart attack, his son, David, said.
Kirk Browning, TV director of 'Live from Lincoln Center'

… In addition to his ‘Live From Lincoln Center’ programs, 10 of which won Emmy Awards, Mr. Browning… directed, among other productions… the first TV show with Frank Sinatra as host (1957); and ‘Hallmark Hall of Fame’ music and drama specials (1951 to 1958).”

The New York Times

In Memoriam:

Shoe: 'Mort's Mortuary,' Sunday, Feb. 10, 2008

* The timestamp of this entry is, however, not live. The entry was actually produced at about 5:55 AM on Feb. 13.  The timestamp of the entry, 5:01 PM on Lincoln’s Birthday, is a veiled reference to Cemetery Ridge, to the meadow in “Readings for Candlemas” (see also the previous two entries) and to a Gettysburg address.

Powered by WordPress