Wednesday, October 15, 2014

Diabolically Complex

Filed under: General,Geometry — Tags: , — m759 @ 12:00 PM

The title is from a Log24 post, "Diabolically Complex Riddle," of Sept. 27, 2014.

(See also a search for "Diabolic"  in this journal, which yields an application to
"magic" squares.)

From 'The Lost Theorem,' by Lee Sallows

Saturday, September 27, 2014

Diabolically Complex Riddle

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

Steve Chawkins in the Los Angeles Times
Friday, September 26, 2014, 12:09 PM LA time —

"Tom Tombrello, a Caltech physics professor for more than
50 years and an inspiration for freshmen who had to grapple
with diabolically complex riddles to enter his legendary class
on scientific thinking [Physics 11], has died. He was 78.

Tombrello collapsed Tuesday [Sept. 23, 2014] on a bus
between terminals at London's Heathrow airport, his wife,
Stephanie, said. The cause of his death has not yet been determined….

… Tombrello accepted only a handful of students for each year's
session of Physics 11."

How many students is a handful?

Related material from this journal on the day of the professor's death:

Tuesday, December 26, 2017

Raiders of the Lost Stone

Filed under: General,Geometry — m759 @ 8:48 PM



Two Students of Structure

A comment on Sean Kelly's Christmas Morning column on "aliveness"
in the New York Times  philosophy series The Stone  —

Diana Senechal's 1999 doctoral thesis at Yale was titled
"Diabolical Structures in the Poetics of Nikolai Gogol."

Her mother, Marjorie Senechal, has written extensively on symmetry
and served as editor-in-chief of The Mathematical Intelligencer .
From a 2013 memoir by Marjorie Senechal —

"While I was in Holland my enterprising student assistant at Smith had found, in Soviet Physics – Crystallography, an article by N. N. Sheftal' on tetrahedral penetration twins. She gave it to me on my return. It was just what I was looking for. The twins Sheftal' described had evidently begun as (111) contact twins, with the two crystallites rotated 60o with respect to one another. As they grew, he suggested, each crystal overgrew the edges of the other and proceeded to spread across the adjacent facet.  When all was said and done, they looked like they'd grown through each other, but the reality was over-and-around. Brilliant! I thought. Could I apply this to cubes? No, evidently not. Cube facets are all (100) planes. But . . . these crystals might not have been cubes in their earliest stages, when twinning occurred! I wrote a paper on "The mechanism of certain growth twins of the penetration type" and sent it to Martin Buerger, editor of Neues Jarbuch für Mineralogie. This was before the Wrinch symposium; I had never met him. Buerger rejected it by return mail, mostly on the grounds that I hadn't quoted any of Buerger's many papers on twinning. And so I learned about turf wars in twin domains. In fact I hadn't read his papers but I quickly did. I added a reference to one of them, the paper was published, and we became friends.[5]

After reading Professor Sheftal's paper I wrote to him in Moscow; a warm and encouraging correspondence ensued, and we wrote a paper together long distance.[6] Then I heard about the scientific exchanges between the Academies of Science of the USSR and USA. I applied to spend a year at the Shubnikov Institute for Crystallography, where Sheftal' worked. I would, I proposed, study crystal growth with him, and color symmetry with Koptsik. To my delight, I was accepted for an 11-month stay. Of course the children, now 11 and 14, would come too and attend Russian schools and learn Russian; they'd managed in Holland, hadn't they? Diana, my older daughter, was as delighted as I was. We had gone to Holland on a Russian boat, and she had fallen in love with the language. (Today she holds a Ph.D. in Slavic Languages and Literature from Yale.) . . . . 
. . .
 we spent the academic year 1978-79 in Moscow.

Philosophy professors and those whose only interest in mathematics
is as a path to the occult may consult the Log24 posts tagged Tsimtsum.

Saturday, July 30, 2016

Darkness Visible

Filed under: General — m759 @ 9:00 AM

Andrew O'Hehir on July 22 —

— and on July 27 —

"Unless th' Almighty Maker them ordain
His dark materials to create more Worlds
Into this wilde Abyss the warie fiend
Stood on the brink of Hell and look'd a while,
Pondering his Voyage…."

— John Milton, Paradise Lost , Book II

For Benedict Cumberbatch as a "warie fiend,"
see posts now tagged Both Hands.

Monday, October 26, 2015

Art and Theology

Filed under: General,Geometry — m759 @ 6:06 AM

Yesterday's nonsense from The New York Times  suggests
a better example of cultural criticism is needed.  Try this 

The opening paragraph of "The many faces of Pablo Picasso,"
by Peter Conrad, at theguardian.com on Saturday,
7 February, 2009, 19.01 EST* —

"Picasso," the surrealist poet Paul Eluard said,
"paints like God or the devil." Picasso favoured
the first option. "I am God," he was once heard
telling himself. He muttered the mantra three
times, boasting of his power to animate and
enliven the visible world. Any line drawn by
his hand pulsed with vitality; when he looked
at it, a bicycle seat and its handlebar could
suddenly turn into the horned head of a bull.
But he also took a diabolical pleasure in
warping appearances, deforming faces and
twisting bodies, subjecting reality to a
tormenting inquisition.

As noted here, yesterday was the birth date (in 1811) of Galois.
It was also the birth date (in 1881) of Picasso.

Related material from the 2009 date* of the Conrad article —
The Log24 post "Childish Things." For those who deeply
dislike Picasso, there is also an 1880 opening illustration 
to Hans Christian Andersen's The Snow Queen

Story the First,
Which Describes a Looking-Glass
and the Broken Fragments

"You must attend to the commencement
of this story, for when we get to the end
we shall know more than we do now about
a very wicked hobgoblin; he was one of the
very worst, for he was a real demon." 

Houghton Mifflin edition of 1880, Riverside Press, Cambridge

Click the above illustration for related posts in this journal.

* Also dated the following day, to correspond to the 00.01 GMT publication
  time of The Guardian 's Sunday version, The Observer , in which it appeared.

Tuesday, October 21, 2014

Art as a Tool

Filed under: General,Geometry — m759 @ 12:35 PM

Two news items on art as a tool:

Two Log24 posts related to the 3×3 grid, the underlying structure for China’s
ancient Lo Shu “magic” square:

Finally, leftist art theorist Rosalind Krauss in this journal
on Anti-Christmas, 2010:

Which is the tool here, the grid or Krauss?

Saturday, September 27, 2014

Sweet Sixteen

Filed under: General — Tags: — m759 @ 2:01 AM

Google celebrates its 16th birthday today.

Here are some family values found with its help.

The father-in-law of the late Thomas A. Tombrello
(previous post) was sociologist Robert K. Merton.
See a tribute to Merton by his daughter Stephanie,
Tombrello's widow. See also a Log24 post mentioning
Merton from Oct. 19, 2005. That post leads to a
post from the date of Merton's death, Feb. 23, 2003.

From that 2003 post:

“Her wall is filled with pictures,
She gets ‘em one by one.”

— “Sweet Little Sixteen,” by Chuck Berry
(Chess Records, January 1958)

Sunday, December 2, 2012

Knight’s Labyrinth

Filed under: General — Tags: , — m759 @ 9:29 AM

A magic— indeed, diabolic— square:

IMAGE- 5x5 magic- in fact, diabolic- square

For the construction, see a book
by W. W. Rouse Ball, founding president
of a Cambridge University magic society.

For some related religious remarks,
see Raiders of the Lost Matrix.

Thursday, October 14, 2010

Diamond Theory and Magic Squares

Filed under: General,Geometry — Tags: , — m759 @ 6:19 PM

"A world of made
is not a world of born— pity poor flesh
and trees, poor stars and stones, but never this
fine specimen of hypermagical

— e. e. cummings, 1944

For one such specimen, see The Matrix of Abraham
a 5×5 square that is hypermagical… indeed, diabolical.

Related material on the algebra and geometry underlying some smaller structures
that have also, unfortunately, become associated with the word "magic"—

  1. Finite Geometry of the Square and Cube
  2. Clifford Pickover on a 4×4 square
  3. Christopher J. Henrich on the geometry of 4×4 magic squares
    (without any mention of  [1] above or related work dating back to 1976)

" … listen: there's a hell
of a good universe next door; let's go"

— e. e. cummings

Happy birthday, e. e.

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