Thursday, February 28, 2019

Where Fashion Sits

Filed under: General — Tags: — m759 @ 8:33 PM

The above reported death was on Sunday, Feb. 24.
See that date in other posts now tagged Hexengown.

Previn’s Wake

Filed under: General — Tags: , — m759 @ 1:19 PM

A search for Previn in this  journal yields . . . 

"whyse Salmonson set his seel on a hexengown,"
Finnegans Wake Book II, Episode 2, pp. 296-297

Wikipedia Scholarship

Filed under: General — Tags: , , — m759 @ 12:31 PM

Cullinane's Square Model of PG(3,2)

Besides omitting the name Cullinane, the anonymous Wikipedia author
also omitted the step of representing the hypercube by a 4×4 array —
an array called in this  journal a Galois  tesseract.


Filed under: General — m759 @ 10:12 AM

Galois (i.e., finite) fields described as 'deep modern algebra'

IMAGE- History of Mathematics in a Nutshell

The two books pictured above are From Discrete to Continuous ,
by Katherine Neal, and Geometrical Landscapes , by Amir Alexander.

Note: There is no Galois (i.e., finite) field with six elements, but
the theory  of finite fields underlies applications of six-set geometry.

Wednesday, February 27, 2019

Construction of PG(3,2) from K6

Filed under: General,Geometry — Tags: , , — m759 @ 11:38 AM

From this journal on April 23, 2013

IMAGE- Geometry of the Six-Set, Steven H. Cullinane, April 23, 2013

From this journal in 2003

From Wikipedia on Groundhog Day, 2019

Tuesday, February 26, 2019

Annals of Philology

Filed under: General — Tags: — m759 @ 11:05 PM

"What kind of person bokehs an inscape?"

— Question adapted from the weblog Barefooted Philologists

An illustration (click to enlarge) —

Axis of Anti-Evil?

Filed under: General — m759 @ 3:16 PM


Wolff reportedly did on Sunday, Feb. 17.

For the Church of Synchronology

Log24 posts on the reported date of Wolff's death.

Related Log24 post — Good News and Bad News.

Wolff himself, in a weblog post of Oct. 16, 2017,*
had some trenchant comments on religion . . .
See "How Odd of God." (See as well today's midnight
post in this  journal, "Ghost in the Shell.")

* "Broomsday." See also Log24 posts on that date.


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

Some related material in this journal — See a search for k6.gif.

Some related material from Harvard —

Elkies's  "15 simple transpositions" clearly correspond to the 15 edges of
the complete graph K6 and to the 15  2-subsets of a 6-set.

For the connection to PG(3,2), see Finite Geometry of the Square and Cube.

The following "manifestation" of the 2-subsets of a 6-set might serve as
the desired Wikipedia citation —

See also the above 1986 construction of PG(3,2) from a 6-set
in the work of other authors in 1994 and 2002 . . .

IMAGE- Dolgachev and Keum, coordinatization of the 4x4 array in 'Birational Automorphisms of Quartic Hessian Surfaces,' AMS Transactions, 2002

Ghost in the Shell

Filed under: General — m759 @ 12:00 AM

Monday, February 25, 2019

A Nervy Makeover is Born

Filed under: General — m759 @ 6:08 PM

The previous post suggests a review

Karaoke Specials

Filed under: General — m759 @ 5:30 PM

From 1988


See as well . . .

From a 2003 film

Social Networks

Filed under: General — Tags: — m759 @ 4:24 PM

CCA as a fictional Communications Corporation of America —

CCA as a non-fictional Centre for Contemporary Art —

Attention Must Be Paid

Filed under: General — Tags: — m759 @ 3:28 PM

The Sartwell Illusion

Filed under: General — Tags: — m759 @ 2:56 PM

See Sartwell in this journal and . . .

"Read something that means something." — New Yorker  motto.

From a search for Alperin in this  journal —


Why PSL(2,7) is isomorphic to GL(3.2)

The Deep Six

Filed under: General,Geometry — Tags: , , , , — m759 @ 11:00 AM

". . . this notion of ‘depth’ is an elusive one
even for a mathematician who can recognize it. . . ."

— G. H. Hardy, A Mathematician's Apology

See Six-Set in this journal.

“Far from the shallow now”

Filed under: General,Geometry — Tags: , , , — m759 @ 12:06 AM

See posts tagged depth.

See as well Eddington Song and the previous post.

Sunday, February 24, 2019

Exceeding His Grasp

Filed under: General,Geometry — Tags: , , , — m759 @ 4:09 PM

See also Hudson Hawk in this  journal.

Lost in Rashomon

Filed under: General — Tags: — m759 @ 10:01 AM

" What this research implies is that we are not just hearing different 'stories' 
about the electron, one of which may be true. Rather, there is one true story,
but it has many facets, seemingly in contradiction, just like in 'Rashomon.' "

Edward Frenkel on "the Rashomon effect"

"Program or be programmed." — The Rushkoff Maxim

Saturday, February 23, 2019

Code Rain

Filed under: General — Tags: — m759 @ 11:30 PM

See 031105-code in this journal, the Wachowskis
at Wikipedia, and The Omega Matrix in this journal.

Austrian Wins Kyoto Prize (Revisited)

Filed under: General — Tags: — m759 @ 3:29 PM

For the title, see Schwarzenegger and "Clockwork Orange"
in the June 2005 post "All in the Timing."

Related music — Taps for Donen

Donen reportedly died on Thursday.
See this journal on that day for a related
New York Times  meditation.

Déjà Vu All Over Again

Filed under: General — m759 @ 2:00 PM

From 2004

From 2013

Eye-Popping Imagery and Consciousness as a Whole

Filed under: General — m759 @ 12:54 PM

'Front and Center'— affinity groups and space in the Harvard Crimson

Related material — Yesterday's post "Desperately Seeking Comedy."

Hello Darkness*

Filed under: General — m759 @ 12:24 PM

* For the title, see yesterday's "Happy Birthday, George Washington."

Friday, February 22, 2019

Back Issues of AMS Notices

Filed under: General — m759 @ 3:04 PM

From the online home page of the new March issue —

Feb. 22, 2019 — AMS Notices back issues now available.

For instance . . .

The Cullinane diamond theorem, AMS Notices, Feb. 1979, pp. A-193-194

Related material now at Wikipedia

The Miracle Octad Generator (MOG), the affine 4-space over GF(2), and the Cullinane diamond theorem

Desperately Seeking Comedy

Filed under: General — m759 @ 1:24 PM

"I need a photo opportunity . . ." — Paul Simon

Space Force

Filed under: General — m759 @ 12:35 PM

See also this  journal on the above date — Feb. 28, 2018.

This post was suggested by a Crimson  piece from yesterday —

Happy Birthday, George Washington

Filed under: General — m759 @ 12:01 PM

The Manchurian Song —

Annals of Entertainment

Filed under: General — m759 @ 12:54 AM

See also a post of August 8, 2018, "Annals of Phenomenology."

Thursday, February 21, 2019

Gaslighting America

Filed under: General — m759 @ 11:28 PM

From The Atlantic  September 2017 issue — "How America Lost Its Mind,"
by former Harvard Lampoon  writer Kurt Andersen —

Note the accusing phrase "a suspicion of science and reason."

Related material by Andersen received in today's mail —

Note the accusing phrase "the cyanide in Donald Trump's Kool-Aid."

Related graphic design —

The source of the above cover art —

A Tale of Eight Building Blocks*

Filed under: General — Tags: , — m759 @ 4:53 PM

* For another such tale, see Eightfold Cube in this  journal.

The Believer’s Fist

Filed under: General — m759 @ 3:12 PM

(Sequel to "The Monkey's Paw")


Frenkel on “the Rashomon Effect”

Filed under: General — Tags: , , — m759 @ 1:44 PM

Earlier in Frenkel's above opinion piece —

"What this research implies is that we are not just hearing
different 'stories' about the electron, one of which may be
true. Rather, there is one true story, but it has many facets,
seemingly in contradiction, just like in 'Rashomon.' 
There is really no escape from the mysterious — some
might say, mystical — nature of the quantum world."

See also a recent New Yorker  version of the fashionable cocktail-party
phrase "the Rashomon effect."

For a different approach to the dictum "there is one true story, but
it has many facets," see . . .

"Read something that means something."
New Yorker  motto

Wednesday, February 20, 2019

Wordsworth at the Academy

Filed under: General — m759 @ 10:42 AM

On this date four years ago . . .

Today . . .

In 2016 . . .

Tuesday, February 19, 2019

The Big Kiss-Off

Filed under: General — m759 @ 10:46 AM

Monday, February 18, 2019

For Times Square…

Filed under: General — m759 @ 3:45 PM

and the Church of Synchronology

The date of the Urban Dictionary "Joy of Six"
article in this afternoon's previous post was Oct. 15, 2016.

A check of that date in this journal yielded a post titled "Word and Object"
that featured an image of a sailor in Times Square.

Related material encountered later this afternoon —

From the "Word and Object" post

The Joy of Six

Filed under: General,Geometry — Tags: , , — m759 @ 3:00 PM


See also the previous post.

I prefer the work of Josefine Lyche on the smallest perfect number/universe.

Context —

Lyche's Lynx760 installations and Vigeland's nearby Norwegian  clusterfuck.

Quantum Choreography

Filed under: General — Tags: — m759 @ 1:06 PM

In the beginning of the 1954 film "Seven Brides for Seven Brothers,"
Adam, oldest of the brothers, is paired with Milly. The problem then is
to find brides for Adam's six brothers.

Above is a video illustration, published on Aug. 12, 2016, of the six couples. 
Matching them involves some choreography.

See also this  journal on Aug. 12, 2016 — "Dustbucket Physics" —

" through the proposition machine of quantum mechanics
comes pregeometry; pregeometry makes geometry;
geometry gives rise to matter and the physical laws
and constants of the universe." 

— Harvard professor Peter Galison, 
     defender of the faith of Scientism

For a different sort of quantum "proposition machine," see posts tagged
Dirac and Geometry.

Sacerdotal K6, Continued

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

From yesterday's post on sacerdotal jargon

A related note from May 1986 —

Sunday, February 17, 2019

Sacerdotal K6

Filed under: General,Geometry — Tags: , — m759 @ 7:35 PM

From a recently created Wikipedia article —

See also Sacerdotal Jargon (Log24, Dec. 5, 2002).

For the Schoolgirls of 1959

Filed under: General — Tags: — m759 @ 1:35 PM

The dies natalis  of St. Buddy Holly was Feb. 3, 1959.

This  year on Feb. 3, a geometric illustration of the well-known
schoolgirl problem was added to a brand-new Wikipedia article
on the finite geometry PG(3,2).

See Also …

Filed under: General — Tags: — m759 @ 12:31 PM

"And the Führer digs for trinkets in the desert."

"See also Acht "
— Cambridge German-English Dictionary, article on "Elf "

Dictionary Time

Filed under: General — Tags: — m759 @ 11:00 AM

Saturday, February 16, 2019

Campaign Style

Filed under: General — m759 @ 8:49 PM

See also "Ready Player One" in this journal.

“Always with a little humor” — Dr. Yen Lo

Filed under: General — m759 @ 7:50 PM

Welcome to the Garden Club, Pilgrim


"Program or be programmed."

Bunker Bingo Continues.

Filed under: General — Tags: , — m759 @ 2:27 PM

From a post of October 16, 2017, "Halloween Meditation" —

Melancholy for Dürer

Filed under: General — Tags: — m759 @ 11:53 AM

The title refers to a 1514 engraving.

See also Angel Particle in this  journal.

Friday, February 15, 2019

The Gifts Reserved for Age

Filed under: General — m759 @ 3:30 PM

"But, as the passage now presents no hindrance
     To the spirit unappeased and peregrine
     Between two worlds become much like each other…."

T. S. Eliot, Four Quartets

Related obituary:


Related date:

"as of Feb. 6, 2019" (from a post at 12 AM ET Feb. 7) —

"There is  such a thing as a four-dimensional finite affine space."
— Saying adapted from a 1962 young-adult novel by Madeleine L'Engle

A Simple Interlacing

Filed under: General — m759 @ 1:07 PM

Paul Valéry, "Introduction to the Method of Leonardo da Vinci,"
La Nouvelle Revue , Paris, Vol. 95 (1895)—

"Regarded thus, the ornamental conception is to the individual arts
what mathematics is to the other sciences. …the objects chosen
and arranged with a view to a particular effect seem as if disengaged
from most of their properties and only reassume them in the effect,
in, that is to say, the mind of the detached spectator. It is thus
by means of an abstraction that the work of art can be constructed,
and is more or less easy to define according as the elements borrowed
from reality for it are more or less complex. Inversely it is by a sort of
induction, by the production of mental images, that all works of art are
appreciated, and this production must equally be more or less active,
more or less tiring, according as it is set in motion by a simple interlacing
on a vase or a broken phrase by Pascal."

— Translated by Thomas McGreevy (Valéry's Selected Writings,
     New Directions, 1950)

Related art —

New Services

Filed under: General — m759 @ 10:41 AM

From today's online Boston Globe


See also Wechsler + Siri in this  journal and a post from
the date of Dr. Gunderson's death, January 11, 2019 —

Thursday, February 14, 2019


Filed under: General — m759 @ 10:16 AM

See D8ing in this journal.

Wednesday, February 13, 2019

April 18, 2003 (Good Friday), Continued

Filed under: General,Geometry — Tags: , — m759 @ 11:03 AM

"The purpose of mathematics cannot be derived from an activity 
inferior to it but from a higher sphere of human activity, namely,

Igor Shafarevitch, 1973 remark published as above in 1982.


— Steven H. Cullinane, February 13, 2019

From Log24 on Good Friday, April 18, 2003

. . . What, indeed, is truth?  I doubt that the best answer can be learned from either the Communist sympathizers of MIT or the “Red Mass” leftists of Georgetown.  For a better starting point than either of these institutions, see my note of April 6, 2001, Wag the Dogma.

See, too, In Principio Erat Verbum , which notes that “numbers go to heaven who know no more of God on earth than, as it were, of sun in forest gloom.”

Since today is the anniversary of the death of MIT mathematics professor Gian-Carlo Rota, an example of “sun in forest gloom” seems the best answer to Pilate’s question on this holy day.  See

The Shining of May 29.

“Examples are the stained glass windows
of knowledge.” — Vladimir Nabokov


Motto of Plato’s Academy

 The Exorcist, 1973

Detail from an image linked to in the above footnote —

"And the darkness comprehended it not."

Id est :

A Good Friday, 2003, article by 
a student of Shafarevitch

" there are 25 planes in W . . . . Of course,
replacing {a,b,c} by the complementary set
does not change the plane. . . ."

Of course.

See. however, Six-Set Geometry in this  journal.

Tuesday, February 12, 2019

A Long Time

Filed under: General — Tags: , — m759 @ 2:01 PM

This  journal on the above date, October 17, 2008

“Every musician wants to do something of lasting quality,
something which will hold up for a long time, and
I guess we did it with ‘Stairway.'”

— Jimmy Page on “Stairway to Heaven

Scholium —

"Kummer " in German means "sorrow."

Related material —

Other posts now tagged Dolmen.

A Dolmen for Ungerer

Filed under: General — Tags: — m759 @ 12:26 PM

See also The Dolmen of the Sorrows (atlasobscura.com) —

Monday, February 11, 2019

Better Call Saul

Filed under: General — m759 @ 10:36 AM

"Christmas in February!" — SNL cold open, Feb. 9

Detail, online New York Times  front page,
Saint Bridget's Day (Feb. 1), 2013 —

IMAGE- NY Times market quotes, American Express Gold Card ad, Kevin Spacey in 'House of Cards' ad

See also Nietzsche and modal logic.

Sunday, February 10, 2019

Cold Open

Filed under: General — m759 @ 12:25 PM

The previous post, on the Bauhaus 100th anniversary, suggests a review . . .

"Congratulations to the leaders of both parties:
The past 20 years you’ve taken us far.
We’re entering Weimar, baby."

Peggy Noonan in The Wall Street Journal
   on August 13, 2015

Image from yesterday's Log24 search Bauhaus Space.

Saturday, February 9, 2019


Filed under: General — m759 @ 4:48 PM

See also posts in the Log24 search Bauhaus Space.


Filed under: General — Tags: — m759 @ 9:00 AM

In memory of Albert Finney's role as an architect
in "Two for the Road," see Lintel in this journal.

Related material:  Finney in "The Green Man" and
RIP: The Peace of Pi.

Friday, February 8, 2019

RIP Albert Finney

Filed under: General — m759 @ 10:15 AM

Thursday, February 7, 2019

Geometry of the 4×4 Square: The Kummer Configuration

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

From the series of posts tagged Kummerhenge

A Wikipedia article relating the above 4×4 square to the work of Kummer —

A somewhat more interesting aspect of the geometry of the 4×4 square
is its relationship to the 4×6 grid underlying the Miracle Octad Generator
(MOG) of R. T. Curtis.  Hudson's 1905 classic Kummer's Quartic Surface
deals with the Kummer properties above and also foreshadows, without
explicitly describing, the finite-geometry properties of the 4×4 square as
a finite affine 4-space — properties that are of use in studying the Mathieu
group M24  with the aid of the MOG.

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