Log24

Saturday, February 17, 2018

The Binary Revolution

Filed under: Uncategorized — m759 @ 5:00 PM

Michael Atiyah on the late Ron Shaw

Phrases by Atiyah related to the importance in mathematics
of the two-element Galois field GF(2) —

  • "The digital revolution based on the 2 symbols (0,1)"
  • "The algebra of George Boole"
  • "Binary codes"
  • "Dirac's spinors, with their up/down dichotomy"

These remarks are from the year-end review of Trinity College,
Cambridge, Trinity Annual Record 2017 .

I prefer other, purely geometric, reasons for the importance of GF(2) —

  • The 2×2 square
  • The 2x2x2 cube
  • The 4×4 square
  • The 4x4x4 cube

See Finite Geometry of the Square and Cube.

See also today's earlier post God's Dice and Atiyah on the theology of 
(Boolean) algebra vs. (Galois) geometry:

Frosties: A Sequel to “Frozen”

Filed under: Uncategorized — m759 @ 11:48 AM

See as well a search in this  journal for Frost at Wanganui.

God’s Dice

Filed under: Uncategorized — m759 @ 10:45 AM

On a Trinity classmate of Ian Macdonald (see previous post)—

Atiyah's eulogy of Shaw in Trinity Annual Record 2017 
is on pages 137 through 146.  The conclusion —

 

Friday, February 16, 2018

Two Kinds of Symmetry

Filed under: Uncategorized — m759 @ 11:29 PM

The Institute for Advanced Study (IAS) at Princeton in its Fall 2015 Letter 
revived "Beautiful Mathematics" as a title:

This ugly phrase was earlier used by Truman State University
professor Martin Erickson as a book title. See below. 

In the same IAS Fall 2015 Letter appear the following remarks
by Freeman Dyson —

". . . a special case of a much deeper connection that Ian Macdonald 
discovered between two kinds of symmetry which we call modular and affine.
The two kinds of symmetry were originally found in separate parts of science,
modular in pure mathematics and affine in physics. Modular symmetry is
displayed for everyone to see in the drawings of flying angels and devils
by the artist Maurits Escher. Escher understood the mathematics and got the
details right. Affine symmetry is displayed in the peculiar groupings of particles
created by physicists with high-energy accelerators. The mathematician
Robert Langlands was the first to conjecture a connection between these and
other kinds of symmetry. . . ." (Wikipedia link added.)

The adjective "modular"  might aptly be applied to . . .

The adjective "affine"  might aptly be applied to . . .

From 'Beautiful Mathematics,' by Martin Erickson, an excerpt on the Cullinane diamond theorem (with source not mentioned)

The geometry of the 4×4 square combines modular symmetry
(i.e., related to theta functions) with the affine symmetry above.

Hudson's 1905 discussion of modular symmetry (that of Rosenhain
tetrads and Göpel tetrads) in the 4×4 square used a parametrization
of that square by the digit 0 and the fifteen 2-subsets of a 6-set, but 
did not discuss the 4×4 square as an affine space.

For the connection of the 15 Kummer modular 2-subsets with the 16-
element affine space over the two-element Galois field GF(2), see my note
of May 26, 1986, "The 2-subsets of a 6-set are the points of a PG(3,2)" —

— and the affine structure in the 1979 AMS abstract
"Symmetry invariance in a diamond ring" —

For some historical background on the symmetry investigations by
Dyson and Macdonald, see Dyson's 1972 article "MIssed Opportunities."

For Macdonald's own  use of the words "modular" and "affine," see
Macdonald, I. G., "Affine Lie algebras and modular forms," 
Séminaire N. Bourbaki , Vol. 23 (1980-1981), Talk no. 577, pp. 258-276.

Nicht Spielerei

Filed under: Uncategorized — m759 @ 2:19 PM

"What of the night
That lights and dims the stars?
Do you know, Hans Christian,
Now that you see the night?"

— The concluding lines of
"Sonatina to Hans Christian,"
by Wallace Stevens
(in Harmonium  (second edition, 1931))

". . . in the end the space itself is the star. . . ."

Related material — The death Tuesday night
of Prince Consort Henrik of Denmark, and the
New Year's Eve speech on Dec. 31, 2015, of
Queen Margrethe II of Denmark.

Distantly  related material — Yesterday morning's
post The Search for Child's Play.

Thursday, February 15, 2018

The Search for Child’s Play

Filed under: Uncategorized — m759 @ 8:00 AM

Yesterday morning's post "Child's  Play" suggests . . .

"Jinx! Jinx again!"

— "Love is an Open Door," from Disney's "Frozen"

Wednesday, February 14, 2018

Child’s Play

Filed under: Uncategorized — m759 @ 11:19 AM

From a search for Child's Play in this journal —

See also the previous post.

"In pascuis herbarum adclinavit me."

Tuesday, February 13, 2018

Babble On

Filed under: Uncategorized — m759 @ 9:00 PM

Symbology for Tom Hanks and for a Latin teacher
who reportedly died on Saturday, Feb. 10, 2018 —

Click the image below to search Log24 for "green fields."

See also Space Cross.

Attention Must Be Paid

Filed under: Uncategorized — m759 @ 7:06 PM

For the late Anne M. Treisman, who reportedly died Friday, Feb. 9:

From "A Feature-Integration Theory of Attention" —

"The controversy between analytic and synthetic theories
of perception goes back many years: the Associationists
asserted that the experience of complex wholes is built
by combining more elementary sensations, while the
Gestalt psychologists claimed that the whole precedes
its parts, that we initially register unitary objects and
relationships, and only later, if necessary, analyze these
objects into their component parts or properties. This view 
is still active now . . . ."

— Anne M. Treisman, University of British Columbia,
and Garry Gelade, Oxford University, in
Cognitive Psychology  12, 97-136 (1980)

"Before time began, there was the Cube." — Optimus Prime

A Titan of the Field

Filed under: Uncategorized — Tags: — m759 @ 9:45 AM
 

On the late Cambridge astronomer Donald Lynden-Bell —

"As an academic at a time when students listened and lecturers lectured, he had the disconcerting habit of instead picking on a random undergraduate and testing them on the topic. One former student, now a professor, remembered how he would 'ask on-the-spot questions while announcing that his daughter would solve these problems at the breakfast table'.

He got away with it because he was genuinely interested in the work of his colleagues and students, and came to be viewed with great affection by them. He also got away with it because he was well established as a titan of the field."

The London Times  on Feb. 8, 2018, at 5 PM (British time)

Related material —

Two Log24 posts from yesteday, Art Wars and The Void.

See as well the field GF(9)

http://www.log24.com/log/pix12/120220-CoxeterFig10.jpg

and the 3×3 grid as a symbol of Apollo
    (an Olympian rather than a Titan) —

 .

Monday, February 12, 2018

The Void

Filed under: Uncategorized — Tags: — m759 @ 11:46 AM

In memory of Professor Donald Lynden-Bell,
Emeritus Professor of Astrophysics at the University of Cambridge

Lynden-Bell with colleagues at Meteor Crater, Arizona, reportedly in 1960 —

Lynden-Bell was one of the subjects of the 2015 film "Star Men."

Related material —

"After peering into the void from a perch 
outside the visitor center, young Henry, 9, 
said he liked the rugged landscape. 
'It’s a good place to film a space movie,' he said.

Funny he should mention that — 
the crater was the setting for the climactic scenes 
of the 1984 sci-fi film 'Starman,' with Jeff Bridges 
and Karen Allen arriving for a rendezvous with 
an alien mother ship."

— Henry Fountain in The New York Times , Jan. 22, 2009

Lynden-Bell reportedly died at 82 on Feb. 5, 2018 (British time).

See as well this  journal on that date.

Art Wars

Filed under: Uncategorized — Tags: — m759 @ 8:55 AM

'In the end the space itself is the star'— Gia Kourlas

See also Krauss Cross.

Sunday, February 11, 2018

Visions of Hell

Filed under: Uncategorized — m759 @ 9:45 PM

In memory of  a Manhattan art figure
who reportedly died on
Wednesday, February Seventh, 2018 —

ABOUT 'ASCENSION VARIATIONS'

Ascension Variations is a magical adventure
woven from grand and pedestrian touches, and
in the end the space itself is the star
or Ms. Monk's transformation of it.
For an hour, we've lived in a spiral,
where up is down and down is up.
It's a sacred place.”

— Gia Kourlas, The New York Times , March 6, 2009

See also the previous post — yesterday's Into the Upside Down
and two posts of February Seventh:

Conceptual Art  and  Conceptual Minimalism.

For some related artistic remarks, see this  journal on March 6-7, 2009.

Saturday, February 10, 2018

Into the Upside Down

Filed under: Uncategorized — m759 @ 10:45 AM

(Title suggested by the TV series Stranger Things )

" 'Untitled' (2016) is the most recent painting in the show
and includes one of Mr. Johns’s recurring images of a ruler."

— Image caption in an article by Deborah Solomon
     in The New York Times  online, Feb. 7, 2018
 

From a Log24 search for "Ruler"

Related art —

See also, in this journal, Magic Mountain and Davos.

Einstein and Thomas Mann, Princeton, 1938

Wednesday, February 7, 2018

Village Voices

Filed under: Uncategorized — m759 @ 12:01 PM

It Takes a Village 

Cutting-Edge Research

See as well The Prisoner of the Village

IMAGE- Patrick McGoohan as 'The Prisoner,' with lapel button that says '6.'

Conceptual Minimalism

Filed under: Uncategorized — m759 @ 10:08 AM

 

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by Helen Lane 

See also AS IS.

Conceptual Art

Filed under: Uncategorized — m759 @ 9:17 AM

Related conceptual  art —

Tom Wolfe in The Painted Word :

Click the automat image above to enlarge.

See as well a new retrospective at Facebook.

Tuesday, February 6, 2018

For Times Square Church*

Filed under: Uncategorized — m759 @ 1:01 AM

http://www.log24.com/log/pix10A/100506-Hcube_fold.gif

Image--Chess game from 'The 
Seventh Seal'

The metaphor for metamorphosis no keys unlock.
— Steven H. Cullinane, "Endgame"

* See Times Square Church in this journal and
   the posts of July 2010.  Related material:

   A Monday night death —

Monday, February 5, 2018

Stranger Things than Pulp Fiction

Filed under: Uncategorized — m759 @ 12:30 PM

Diamond Theory cover, said to resemble Proginoskes in 'A Wind in the Door'

Click on the image for a
relevant Wallace Stevens poem.

A new Facebook page will describe
some background for the above image.

Sunday, February 4, 2018

Picture at Eleven

Filed under: Uncategorized — m759 @ 11:00 AM

Logos for Sunday, February 4

Filed under: Uncategorized — m759 @ 10:00 AM

"The walls in the back of the room show geometric shapes
that remind us of the logos on a space shuttle. "

Web page on an Oslo art installation by Josefine Lyche.

See also Subway Art posts.

The translation above was obtained via Google.

The Norwegian original —

"På veggene bakerst i rommer vises geometriske former
som kan minne om logoene på en romferge."

Related logos — Modal Diamond Box in this journal:

Nietzsche, 'law in becoming' and 'play in necessity'

Logos for Philosophers
(Suggested by Modal Logic) —

Nietzsche, 'law in becoming' and 'play in necessity'

Friday, February 2, 2018

For Plato’s Cave

Filed under: Uncategorized — Tags: , — m759 @ 12:06 PM

"Plato's allegory of the cave describes prisoners,
inhabiting the cave since childhood, immobile,
facing an interior wall. A large fire burns behind
the prisoners, and as people pass this fire their
shadows are cast upon the cave's wall, and
these shadows of the activity being played out
behind the prisoner become the only version of
reality that the prisoner knows."

— From the Occupy Space gallery in Ireland

IMAGE- Patrick McGoohan as 'The Prisoner,' with lapel button that says '6.'

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