Friday, December 25, 2020

Design Theory

Filed under: General — m759 @ 3:33 PM


The Fano plane block design



The Deathly Hallows symbol—
Two blocks short of  a design.

Another name for the Fano plane design — The Ghostly  Hallows.
From a search in this journal  for Ghostly  —

Thursday, November 19, 2020

Set Design and the Schoolgirl Problem

Filed under: General — Tags: — m759 @ 9:36 AM

Underlying Structure of the Design

Schoolgirl Problem —

Monday, October 26, 2020

Set + Design

Filed under: General — Tags: — m759 @ 9:41 PM

In memoriam . . .

http://m759.net/wordpress/?s=Set+Design .

Tuesday, September 8, 2020


Filed under: General — m759 @ 1:46 PM

Illustration by Pietro Corraini

Corraini design lecture on June 29, 2016 —

This journal on the same day —


Wednesday, August 12, 2020

Hidden Figure: Type Design at the East Village Other

Filed under: General — Tags: , — m759 @ 12:59 PM

    I.e.  . . . 

Monday, March 30, 2020

Annals of Ugly Design

Filed under: General — m759 @ 5:33 PM

The Boston Globe  Saturday on Friday’s death of one of
the two architects of Boston City Hall

A gifted storyteller, Mr. McKinnell liked to recount
the response of renowned architect Philip Johnson to
City Hall. “ ‘Absolutely marvelous. … I think it’s wonderful.
… And it’s so ugly!’ ” Mr. McKinnell told Pasnik, adding:
“We thought that was the greatest praise we could get.”

See more ugliness from this  journal on Friday

See also this journal on the death of the other  City Hall architect.

Friday, January 17, 2020

Design Theory

Filed under: General — Tags: , — m759 @ 12:57 PM

On a recently deceased professor emeritus of architecture
at Princeton —

"… Maxwell  'established the school as a principal
center of design research, history and theory.' ”

"This is not the Maxwell you're looking for."

Monday, December 16, 2019

Design Notes Dec. 11

Filed under: General — Tags: — m759 @ 3:01 AM

From The New York Times on Dec. 11 —

See also some other posts in this  journal now tagged "Design Notes Dec. 11."

Sunday, August 25, 2019

Design Theory

Filed under: General — Tags: , , — m759 @ 7:58 PM

"Mein Führer Steiner"

See Hitler Plans and Quadruple System.

"There is  such a thing as a quadruple system."

— Saying adapted from a 1962 young-adult novel

Friday, August 9, 2019

Design Theory

Filed under: General — Tags: , — m759 @ 6:48 PM

Click to enlarge:

Block Designs?

Saturday, July 27, 2019

Design Is How It Works.” — Steve Jobs

Filed under: General — Tags: — m759 @ 9:59 PM

Tuesday, March 5, 2019

Design Warmed Over

Filed under: General — m759 @ 1:00 PM

Today's announcement of the 2019 Pritzker Architecture Prize
to Arata Isozaki suggests a review.

Isozaki designed the Museum of Contemporary Art building
in Los Angeles in 1986.

A related article from May 19, 2010 —

An excerpt from the Walker article — 

Throwback fun with Chermayeff and Geismar —

Other news published on May 19, 2010 —

See also "Character of Permanence" in this  journal.

A Block Design 3-(16,4,1) as a Steiner Quadruple System:

Filed under: General — Tags: , — m759 @ 11:19 AM

A Midrash for Wikipedia 

Midrash —

Related material —


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

Friday, January 25, 2019

Design Theory

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

Last night's post "Night at the Social Media" suggests . . .

A 404 for Katherine Neville (born on 4/04) —

Monday, July 30, 2018

Design in Academia

Filed under: General — m759 @ 10:45 PM

Related material —

See esp. the No. Land link.

Friday, May 25, 2018

Grid Design

Filed under: General — Tags: — m759 @ 2:00 PM

Click the grid for the tag 5×5 in this journal.

A related book —

See also the previous post, Bucharest Semiotics.

Friday, May 4, 2018

Art & Design

Filed under: General,Geometry — m759 @ 4:00 PM


A star figure and the Galois quaternion.

The square root of the former is the latter.

See also a passage quoted here a year ago today
(May the Fourth, "Star Wars Day") —

Cube symmetry subgroup of order 8 from 'Geometry and Symmetry,' Paul B. Yale, 1968, p.21

Sunday, April 8, 2018


Filed under: General,Geometry — m759 @ 11:00 PM

From a Log24 post of Feb. 5, 2009 —

Design Cube 2x2x2 for demonstrating Galois geometry

An online logo today —

See also Harry Potter and the Lightning Bolt.


Tuesday, January 23, 2018

Graphic Design

Filed under: General — m759 @ 12:00 PM

By Wink-Minneapolis

Wednesday, November 22, 2017

Design is how it works” — Steve Jobs

Filed under: General,Geometry — m759 @ 1:00 PM

News item from this afternoon —

Apple AI research on 'mapping systems'

The above phrase "mapping systems" suggests a review
of my own very different  "map systems." From a search
for that phrase in this journal —

Map Systems (decomposition of functions over a finite field)

See also "A Four-Color Theorem: Function Decomposition
Over a Finite Field.

Thursday, October 19, 2017

Design Grammar***

Filed under: G-Notes,General,Geometry — m759 @ 10:22 PM

The elementary shapes at the top of the figure below mirror
the looking-glass property  of the classical Lo Shu square.

The nine shapes at top left* and their looking-glass reflection
illustrate the looking-glass reflection relating two orthogonal
Latin squares over the three digits of modulo-three arithmetic.

Combining these two orthogonal Latin squares,** we have a
representation in base three of the numbers from 0 to 8.

Adding 1 to each of these numbers yields the Lo Shu square.

* The array at top left is from the cover of
Wonder Years:
Werkplaats Typografie 1998-2008

** A well-known construction.

*** For other instances of what might be
called "design grammar" in combinatorics,
see a slide presentation by Robin Wilson.
No reference to the work of Chomsky is

Graphic Design: Fast Forward

Filed under: G-Notes,General,Geometry — m759 @ 8:18 PM

Typographical: » 

Eightfold Cube:


Friday, June 23, 2017

Annals of Art and Design

Filed under: General — Tags: — m759 @ 10:12 PM

The life of Mr. Breder is not unrelated to that of Carl Andre.

See also, in this  journal, Bulk Apperception.

Wednesday, June 21, 2017

Design Is How It Works: A Bedtime Story

Filed under: General — m759 @ 9:48 PM


Monday, June 19, 2017

Design Is How It Works”*

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

* See the title in this  journal.

Wednesday, March 29, 2017

Design Abyss

Filed under: General — Tags: , , — m759 @ 1:00 PM

Hexagram 29,
The Abyss (Water)

This post was suggested by an August 6, 2010, post by the designer
(in summer or fall, 2010) of the Stack Exchange math logo (see
the previous Log24 post, Art Space Illustrated) —

http://www.8164.org/☵☲/  .

In that post, the designer quotes the Wilhelm/Baynes I Ching  to explain
his choice of Hexagram 63, Water Over Fire, as a personal icon —

"When water in a kettle hangs over fire, the two elements
stand in relation and thus generate energy (cf. the
production of steam). But the resulting tension demands
caution. If the water boils over, the fire is extinguished
and its energy is lost. If the heat is too great, the water
evaporates into the air. These elements here brought in
to relation and thus generating energy are by nature
hostile to each other. Only the most extreme caution
can prevent damage."

See also this  journal on Walpurgisnacht (April 30), 2010 —


Hexagram 29:



Hexagram 30:

"Hates California,
it's cold and it's damp.

Image--'The Fire,' by Katherine Neville

A thought from another German-speaking philosopher

"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."

See also The Crimson 's abyss in today's 4:35 AM post Art Space, Continued.

Friday, December 2, 2016

A Small Witt Design*

Filed under: General — Tags: — m759 @ 2:00 PM

The New York Times 's  online T Magazine  yesterday —

"A version of this article appears in print on December 4, 2016, on page
M263 of T Magazine with the headline: The Year of Magical Thinking."

* Thanks to Emily Witt for inadvertently publicizing the
   Miracle Octad Generator  of R. T. Curtis, which
   summarizes the 759 octads found in the large Witt design.

Monday, October 31, 2016

Best Costume Design

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

"So, how do we sift truth from belief? How do we write
our own histories, personally or culturally, and thereby
define ourselves? How do we penetrate years, centuries,
of historical distortion to find original truth? Tonight, this
will be our quest."

Robert Langdon, symbologist, in "The Da Vinci Code."

"… in Spain. There they are robes worn by priests."

— Langdon, op. cit.

Thursday, June 30, 2016

Design Luminosity

Filed under: General — Tags: — m759 @ 3:13 PM

Peter Woit today

"At CERN the LHC has reached design luminosity,* and is
breaking records with a fast pace of new collisions. This may
have something to do with the report that the LHC is also 
about to tear open a portal to another dimension." 

See also the following figure from the Log24 Bion posts

— and Greg Egan's short story "Luminous":

"The theory was, we’d located part of the boundary
between two incompatible systems of mathematics –
both of which were physically true, in their respective
domains. Any sequence of deductions which stayed
entirely on one side of the defect – whether it was the
'near side', where conventional arithmetic applied, or
the 'far side', where the alternative took over – would
be free from contradictions. But any sequence which
crossed the border would give rise to absurdities –
hence S could lead to not-S."

Greg Egan, Luminous
   (Kindle Locations 1284-1288). 

* See a definition.

Thursday, December 3, 2015

Design Wars

Filed under: General,Geometry — Tags: — m759 @ 4:04 PM

"… if your requirement for success is to be like Steve Jobs,
good luck to you." 

— "Transformation at Yahoo Foiled by Marissa Mayer’s 
Inability to Bet the Farm," New York Times  online yesterday

"Design is how it works." — Steve Jobs

Related material:  Posts tagged Ambassadors.

Sculpture by Josefine Lyche of Cullinane's eightfold cube at Vigeland Museum in Oslo

Friday, October 9, 2015

Cube Design

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

For Aaron Sorkin and Walter Isaacson

Related material — 
Bauhaus CubeDesign Cube, and
Nabokov's Transparent Things .

Thursday, July 23, 2015

Design Cube

Filed under: General — m759 @ 8:24 PM

Broken Symmetries  in  Diamond Space —

Monday, July 13, 2015

Block Designs Illustrated

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

The Fano Plane —

"A balanced incomplete block design , or BIBD
with parameters , , , , and λ  is an arrangement
of b  blocks, taken from a set of v  objects (known
for historical reasons as varieties ), such that every
variety appears in exactly r  blocks, every block
contains exactly k  varieties, and every pair of
varieties appears together in exactly λ  blocks.
Such an arrangement is also called a
(, v , r , k , λ ) design. Thus, (7, 3, 1) [the Fano plane] 
is a (7, 7, 3, 3, 1) design."

— Ezra Brown, "The Many Names of (7, 3, 1),"
     Mathematics Magazine , Vol. 75, No. 2, April 2002

W. Cherowitzo uses the notation (v, b, r, k, λ) instead of
Brown's (b , v , r , k , λ ).  Cherowitzo has described,
without mentioning its close connection with the
Fano-plane design, the following —

"the (8,14,7,4,3)-design on the set
X = {1,2,3,4,5,6,7,8} with blocks:

{1,3,7,8} {1,2,4,8} {2,3,5,8} {3,4,6,8} {4,5,7,8}
{1,5,6,8} {2,6,7,8} {1,2,3,6} {1,2,5,7} {1,3,4,5}
{1,4,6,7} {2,3,4,7} {2,4,5,6} {3,5,6,7}."

We can arrange these 14 blocks in complementary pairs:

{1,2,3,6} {4,5,7,8}
{1,2,4,8} {3,5,6,7}
{1,2,5,7} {3,4,6,8}
{1,3,4,5} {2,6,7,8}
{1,3,7,8} {2,4,5,6}
{1,4,6,7} {2,3,5,8}
{1,5,6,8} {2,3,4,7}.

These pairs correspond to the seven natural slicings
of the following eightfold cube —

Another representation of these seven natural slicings —

The seven natural eightfold-cube slicings, by Steven H. Cullinane

These seven slicings represent the seven
planes through the origin in the vector
3-space over the two-element field GF(2).  
In a standard construction, these seven 
planes  provide one way of defining the
seven projective lines  of the Fano plane.

A more colorful illustration —

Block Design: The Seven Natural Slicings of the Eightfold Cube (by Steven H. Cullinane, July 12, 2015)

Wednesday, July 8, 2015

Design Thinking

Filed under: General — m759 @ 11:14 AM

This post was suggested in part by last night's post
of 11:14 PM ET, Southern Charm, and by a post
of 11/14 last year, Another Opening, Another Show.

See also Design Thinking at Wikipedia and the following
two quotations —

Dr. Gerrita Postlewait's contract for Superintendent
of Charleston County Schools was approved and
signed in a meeting with school board members 
Wednesday morning, a school system official says….
From 2006 to 2013, she was the chief K-12 officer for
the Stupski Foundation, a San Francisco-based
education reform nonprofit. [See related page.]

Chris Tebben, executive director of Grantmakers for
Education, says the [Stupski] foundation was among
the first to consider how the problem-solving approach
known as “design thinking” could play a role in improving

Related cinematic remarks:  Robot Overlords (now on-demand).

Wednesday, March 18, 2015

Logo Design

Filed under: General — m759 @ 9:11 PM

See also today's previous post and Cartoon Graveyard.

Monday, March 2, 2015

Elements of Design

Filed under: General — m759 @ 1:28 AM

From "How the Guggenheim Got Its Visual Identity,"
by Caitlin Dover, November 4, 2013 —

For the square and half-square in the above logo
as independent design elements, see 
the Cullinane diamond theorem.

For the circle and half-circle in the logo,
see Art Wars (July 22, 2012).

For a rectangular space that embodies the name of
the logo's design firm 2×4, see Octad in this journal.

Thursday, December 25, 2014


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

Click image for some related posts.

Friday, June 6, 2014

ART WARS: Fundamentals of Design

Filed under: General — m759 @ 8:15 PM

Thanks to the Museum of Modern Art for pointing out
a new emphasis on design  in U.S. Army Field Manual 5-0.
MoMA supplies a link to an article from May 3, 2010:

Design Thinking Comes to the U.S. Army.

An excerpt from the manual:

An approach to this text by Harvard's legendary "unreliable reader"—

The Unreliable Narrator meets The Unreliable Reader
Aaron Diaz at Dresden Codak

"The risks multiply, especially when a problem involves 26 March 2010…."

Tuesday, May 27, 2014


Filed under: General — Tags: — m759 @ 2:00 PM

In memory of a graphic designer
who reportedly died this morning:

IMAGE- Massimo Vignelli, his wife Lella, and cube

Wednesday, April 9, 2014

Inspired by Design

Filed under: General — m759 @ 10:00 PM

It’s 10 PM.  Do you know where your childen are?

Monday, February 3, 2014


Filed under: General — Tags: , — m759 @ 7:00 AM

This journal a year ago yesterday

“Some designs work subtly.
Others are successful through sheer force.”

Penelope Green


Sheer force:

IMAGE- The Cartier diamond ring from 'Inside Man'

Thursday, September 26, 2013

Design Mastery

Filed under: General — m759 @ 4:48 PM

For T.S. Eliot on his birthday, a film review—

"… the Coens are… elegantly asserting design mastery…."

— Peter Bradshaw, review of "Inside Llewyn Davis" 
    in The Guardian  on May 18, 2013

Related material— Two Log24 posts from that date

Black Hole Revisited and Midnight in Bakhtin.

The former post presents a Jewish approach to
Eliot's concept of time and "the still point."
The latter post presents a more sophisticated approach. 

Perhaps the Coens' design mastery extends to the phrase
"time stops" of Kerouac. See the remarks by Dean Moriarty
in On the Road  quoted here in the previous post (Sept. 24).

The Coens' film contains, Bradshaw says, "a smoulderingly
Kerouac-y poet, played by Garrett Hedlund." Hedlund played
not Kerouac, but Moriarty, in the 2012 film of On the Road .

Monday, November 5, 2012

Design Cubes

Filed under: General,Geometry — m759 @ 9:48 PM

Continued from April 2, 2012.

Some predecessors of the Cullinane design cubes of 1984
that lack the Cullinane cubes' symmetry properties

Kohs cubes (see 1920 article)
Wechsler cubes (see Wechsler in this journal), and
Horowitz  cubes (see links below).

Horowitz Design Cubes Package

Horowitz Design Cubes (1971)

1973 Horowitz Design Cubes Patent

Horowitz Biography

Tuesday, October 30, 2012


Filed under: General — m759 @ 5:26 AM


IMAGE- Harvard Crimson story on the late John M. Johansen, architect, Harvard '39

Attention must be paid.

Monday, October 22, 2012

Design Awards Gala

Filed under: General — m759 @ 1:06 AM

"The Cooper-Hewitt National Design Museum
held its design awards gala at Pier 60
in Manhattan on Wednesday night…."

Click on "gala" above for a New York Times  story.
Click on "Wednesday" above for a Log24 post.

A link from the latter may be viewed,
in retrospect, as honoring the late
Sylvia Kristel of the Netherlands, 
who reportedly died Wednesday.

The link is to an image of a webpage 
at the site Polen voor Nederlanders,
i.e., Poland for Netherlanders.

The Log24 post was titled Café Society.

Image from http://www.polenvoornederlanders.nl/ .

Monday, June 25, 2012

Design (continued)

Filed under: General — m759 @ 1:28 AM

The New York Times  this morning reports the death
last Tuesday (June 19, 2012) in Boston
of Gerhard Kallman, a Brutalist architect
born in Berlin in 1915.

Some Log24 images from the date of his death

IMAGE- Log24 on June 19, 2012-Gropius and the North Face of Harvard Design

The above view shows the south side of Kirkland Street (at Quincy).

IMAGE- Map from http://www.map.harvard.edu/

A more appealing architectural image, from the other side
of Kirkland Street—

IMAGE- Adolphus Busch Hall, 29 Kirkland St., Cambridge, MA

Tuesday, June 19, 2012


Filed under: General — m759 @ 12:00 PM

The New York Times online front page last night

"Microsoft introduced its own tablet computer,
called Surface, illustrating the pressure
Apple's success has put on it to marry
software and hardware more tightly."


IMAGE- The Marriage of Heaven and Hell-- Swedenborg Chapel and the Harvard Graduate School of Design

Google Maps image

Related material

"Was ist Raum, wie können wir ihn
 erfassen und gestalten?"

Walter Gropius,

The Theory and
Organization of the

Update of Feb. 3, 2013:
See also The Perception of Doors in this journal.

Sunday, November 6, 2011

Design Sermon

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

''Most people make the mistake of thinking design is what it looks like,''
says Steve Jobs, Apple's C.E.O. ''People think it's this veneer—
that the designers are handed this box and told, 'Make it look good!'
That's not what we think design is. It's not just what it looks like and feels like.
Design is how it works.''

— "The Guts of a New Machine," by Rob Walker,
New York Times Magazine , Sunday, Nov. 30, 2003

IMAGE- June 29, 2011, review of Zenna Henderson's 'The Anything Box'

See also, from the day of the above Anything Box  review—
St. Peter's Day, 2011— two Log24 posts—
The Shattered Mind and Rome After Dark.

Related boxes… Cosmic Cube and Design Cube.

Thursday, August 25, 2011


Filed under: General,Geometry — Tags: — m759 @ 11:07 PM

"Design is how it works." — Steven Jobs (See yesterday's Symmetry.)

Today's American Mathematical Society home page—

IMAGE- AMS News Aug. 25, 2011- Aschbacher to receive Schock prize

Some related material—

IMAGE- Aschbacher on the 2-local geometry of M24

IMAGE- Paragraph from Peter Rowley on M24 2-local geometry

The above Rowley paragraph in context (click to enlarge)—

IMAGE- Peter Rowley, 2009, 'The Chamber Graph of the M24 Maximal 2-Local Geometry,' pp. 120-121

"We employ Curtis's MOG
 both as our main descriptive device and
 also as an essential tool in our calculations."
— Peter Rowley in the 2009 paper above, p. 122

And the MOG incorporates the
Geometry of the 4×4 Square.

For this geometry's relation to "design"
in the graphic-arts sense, see
Block Designs in Art and Mathematics.

Tuesday, March 29, 2011

Design Theory

Filed under: General,Geometry — m759 @ 2:12 AM

See the new note Configurations and Squares at finitegeometry.org/sc/.

Wednesday, January 5, 2011

Riff Design

Filed under: General — m759 @ 9:00 AM

"Leave a space." — Tom Stoppard, in a play about philosophers


The word "riff" at top in the Times  obits is from an ad for Google's Chrome browser.
The white space is artificial, made by deleting last  year's dead.

Scene from 'A Good Year'

A Good Year

For further details, click on the image below.

'The Power Of The Center: A Study of Composition in the Visual Arts,' by Rudolf Arnheim

Tuesday, November 9, 2010


Filed under: General — m759 @ 5:01 PM

A Theory of Pure Design

by Denman Waldo Ross

Lecturer on the Theory of Design
in Harvard University

Boston and New York
Houghton, Mifflin and Company, 1907


"My purpose in this book is to elucidate, so far as I can, the
principles which underlie the practice of drawing and painting
as a Fine Art.  Art is generally regarded as the expression of
feelings and emotions which have no explanation except per-
haps in such a word as inspiration , which is expletive rather
than explanatory
.  Art is regarded as the one activity of man
which has no scientific basis, and the appreciation of Art is
said to be a matter of taste in which no two persons can be
expected to agree.  It is my purpose in this book to show how,
in the practice of Art, as in all other practices, we use certain
terms and follow certain principles.  Being defined and ex-
plained, these terms and principles may be known and under-
stood by everybody.  They are, so to speak, the form of the

While an understanding of the terms and principles of Art
will not, in itself, enable any one to produce important works,
such works are not produced without it.  It must be understood,
however, that the understanding of terms and principles
is not, necessarily, an understanding in words.  It may lie in
technical processes and in visual images and may never rise,
or shall I say fall, to any formulation in words, either spoken
or written."


One of Ross's protégés, Jack Levine, died yesterday at 95. He
is said to have remarked, "I want to paint with the dead ones."

Related material: This journal on the day of Levine's death
and on the day of Martin Gardner's death.

The latter post has an image illustrating Ross's remarks on
formulations in words—

Image-- The Case of the Lyche Gate Asterisk

For further details, see Finale, Darkness Visible, and Packed.

Wednesday, September 8, 2010

Grand Design

Filed under: General — m759 @ 2:22 AM

From Harvard's 2010 Phi Beta Kappa ceremony

Think of all the history you’ve read. It started somewhere.
It started at absolute zero, is what you thought.
Just because you couldn’t know what came before.
But imagine: something did.

"To help the graduates find rightness, two addresses are at the heart of the exercises ceremony.
 One is by a poet, who reads a work written for the occasion.
 The other is by an 'orator,' a guest invited to offer timely discourse."

From this morning's New York Times


Related material—

Immediately following Inspector Pine in this morning's Times  obituary list
is Virginia B. Smith, a former president of Vassar College. Smith died at 87 on August 27.

From her obituary—

Ms. Smith is survived by her partner of 57 years, Florence Oaks.

Tuesday, August 17, 2010

Riff Design

Filed under: General — Tags: , — m759 @ 5:09 AM

From yesterday

Call and Response

“One would call out, in the standardized abbreviations of their science, motifs or initial bars of classical compositions, whereupon the other had to respond with the continuation of the piece, or better still with a higher or lower voice, a contrasting theme, and so forth. It was an exercise in memory and improvisation….”

The Glass Bead Game

Today’s New York Times  has an obituary for Bernard Knox, classics professor. Knox died on July 22. On that date this journal happened to have a post, “Soul Riff,” featuring a professor— shown below. Click on the professor for a very relevant classical quotation.

The Soul Riff  post also contained the above secondary title—

Call and Response

Doonesbury 2/29/08-- Assignment: Identify Sources

For a response from the next day,
March 1, click on the professor

Saturday, August 7, 2010

Rift Designs

Filed under: General — m759 @ 8:28 PM

From the current index to obituaries at Telegraph.co.uk—

Teufel is also featured in today's New York Times

"Mr. Teufel became a semicelebrity, helped in no small part by his last name, which means 'devil' in German."

From Group Analysis ,  June 1993, vol. 26 no. 2, 203-212—

The Problem of Good and Evil

by Ronald Sandison, Ledbury, Herefordshire HR8 2EY, UK

In my contribution to the Group Analysis Special Section: "Aspects of Religion in Group Analysis" (Sandison, 1993) I hinted that any consideration of a spiritual dimension to the group involves us in a discussion on whether we are dealing with good or evil spirits. But if we say that God is in the group, why is not the Devil there also? Can good and evil coexist in the same group matrix? Is the recognition of evil "nothing but" the ability to distinguish between good and bad? If not, then what is evil? Is it no more than the absence of good?

These and other questions were worked on at a joint Institute of Group Analysis and Group-Analytic Society (London) Workshop entitled "The Problem of Good and Evil." We considered the likelihood that good and evil coexist in all of us, as well as in the whole of the natural world, not only on earth, but in the cosmos and in God himself What we actually do with good and evil is to split them apart, thereby shelving the problem but at the same time creating irreconcilable opposites. This article examines this splitting and how we can work with it psychoanalytically.

This suggests a biblical remark—

"Now there was a day… when the sons of God
came to present themselves before the Lord,
and Satan came also among them."

Job 1:6, quoted by Chesterton in The Man Who Was Thursday

Sandison died on June 18. See the Thursday, August 5, Log24 post "The Matrix."

Teufel died on July 6. See the Log24 posts for that day.

The title of this  post, "rift designs," refers to a recurring theme in the July 6 posts. It is taken from Heidegger.

From a recent New Yorker  review of Absence of Mind  by Marilynne Robinson—

"Robinson is eloquent in her defense of the mind’s prerogatives, but her call for a renewed metaphysics might be better served by rereading Heidegger than by dusting off the Psalms."

Following this advice, we find—

"Propriation gathers the rift-design of the saying and unfolds it  in such a way that it becomes the well-joined structure of a manifold showing."

p. 415 of Heidegger's Basic Writings , edited by David Farrell Krell, HarperCollins paperback, 1993

"Das Ereignis versammelt den Aufriß der Sage und entfaltet ihn zum Gefüge des vielfältigen Zeigens." 

— Heidegger, Weg zur Sprache

Saturday, January 23, 2021

Tiny Dancer

Filed under: General — Tags: — m759 @ 12:45 AM

The above image was suggested by a link in a
Philadelphia Inquirer  obituary from yesterday evening.

Exercise: What is controlled by the middle-finger string?

Sunday, January 17, 2021

“Signs and Symbols”

Filed under: General — Tags: — m759 @ 11:42 PM

The title is from Nabokov.

Related: A sign or symbol known to
techies as “the hamburger.”
See also “White Palace” earlier tonight.

The above image appeared earlier in posts
now tagged “Darkinbad the Brightdayler.”

Wednesday, December 30, 2020

Space Force

Filed under: General — Tags: — m759 @ 10:08 PM

New Yorker  video  today, at 14:00-14:25 —

“What’s good about KenKen, and Sudoku, and crosswords,
all of those puzzles like that, is that they have grids to be filled in,
empty squares. I think there is something about human nature
that we want to fill up spaces. And if you’re a puzzle person,
or almost anybody, and you see an empty grid, you want to
put something in those spaces. It gives a feeling of satisfaction
that you don’t get often in life and that really feels good.”

— Will Shortz, New York Times  puzzle editor

“I can’t get no… satisfaction….” — The Rolling Stones

The New Yorker  recently restarted the Weiner story,
which includes —

“… the fall of 2017, when he began a twenty-one-month
prison sentence for sexting with a minor.”

“You want to put something in those spaces.”

— Will Shortz, New York Times  puzzle editor

Yes, you do.

Weiner is now with a Brooklyn countertops company called IceStone.

Monday, December 21, 2020

Re Volvo

Filed under: General — Tags: — m759 @ 10:49 AM

A passage quoted above

“The crystal was a sort of magnifying glass,
vastly enlarging the things inside the block.
Strange things they were, too.”

Thursday, December 17, 2020

Square Space at Wikipedia

Filed under: General — Tags: — m759 @ 11:45 PM

The State of Square-Space Art at Wikipedia  as of December 16, 2020,
after a revision by an anonymous user on that date:

See also Square Space at Squarespace.

Saturday, December 12, 2020

Globe Services

Filed under: General — Tags: — m759 @ 1:16 PM

“Perhaps only Shakespeare manages to create at the highest level
both images and people; and even Hamlet  looks second-rate
compared with Lear .”

— Iris Murdoch, “Against Dryness,” 1961

Byline from a 2019 post — ‘GLOBE STAFF AND NEW SERVICES’ —


Above: Dr. Harrison PopeHarvard professor of psychiatry,
demonstrates the use of the Wechsler Adult Intelligence Scale
“block design” subtest.

 — From a Log24 search for “Harrison Pope.”

Related drama — Other posts tagged Plastic Elements.

Sunday, December 6, 2020

The Undoing

Filed under: General — m759 @ 10:16 PM

Today’s earlier post “Binary Coordinates” discussed a Dec. 6
revision to the Wikipedia article on PG(3,2), the projective
geometry of 3 dimensions over the 2-element field GF(2).

The revision, which improved the article, was undone later today
by a clueless retired academic, one William “Bill” Cherowitzo,
a professor emeritus of mathematics at U. of Colorado at Denver.
(See his article “Adventures of a Mathematician in Wikipedia-land,”
MAA Focus , December 2014/January 2015.)

See my earlier remarks on this topic . . . specifically, on this passage —

“A 3-(16,4,1) block design has 140 blocks
of size 4 on 16 points, such that each triplet
of points is covered exactly once. Pick any
single point, take only the 35 blocks
containing that point, and delete that point.
The 35 blocks of size 3 that remain comprise
a PG(3,2) on the 15 remaining points.”

As I noted on November 17, this is bullshit. Apparently Cherowitzo
never bothered to find out that an arbitrary  “3-(16,4,1) block design
(an example of a Steiner quadruple system ) does not  yield a PG(3,2).

PG(3,2) is derived from the classical  3-(16,4,1) block design formed by the affine
space of 4 dimensions over GF(2).  That  design has 322,560 automorphisms.
In contrast, see a 3-(16,4,1) block design that is  automorphism-free.

Thursday, November 26, 2020

Art Site

Filed under: General — m759 @ 12:46 PM


Sunday, November 22, 2020

An Orison for Anthony

Filed under: General — m759 @ 11:53 AM

— Cloud Atlas , by David Mitchell (2004).

Monday, November 2, 2020

Q Bits

Filed under: General — Tags: — m759 @ 6:34 PM

The new domain name  q-bits.space  does not refer to
the q in “quantum ,” but rather to the q that symbolizes
the order of a Galois field .

See the Wikipedia article “Finite field.”

The “space” suffix refers to a web page on geometry.

Friday, October 30, 2020

Game for Devil’s Night in an Election Year

Filed under: General — Tags: — m759 @ 10:25 AM

From the designer of Q-bitz

Tuesday, October 27, 2020

“To Illustrate My Last Remark”*

Filed under: General — Tags: — m759 @ 9:32 AM

* Song lyric, soundtrack album of
Midnight in the Garden of Good and Evil

Monday, October 26, 2020

Annals of Artspeak

Filed under: General — Tags: , — m759 @ 9:14 PM

See also LeWitt in this journal.

Saturday, October 24, 2020


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

Wikipedia on what has been called “the doily” —

“The smallest non-trivial generalized quadrangle
is GQ(2,2), whose representation* has been dubbed
‘the doily’ by Stan Payne in 1973.”

A later publication relates the doily to grids.

From Finite Generalized Quadrangles , by Stanley E. Payne
and J. A. Thas, December 1983, at researchgate.net, pp. 81-82—

“Then the lines … define a 3×3 grid G  (i.e. a grid
consisting of 9 points and 6 lines).”
. . . .
“So we have shown that the grid G  can completed [sic ]
in a unique way to a grid with 8 lines and 16 points.”
. . . .
“A 4×4 grid defines a linear subspace
of  the 2−(64,4,1) design, i.e. a 4×4 grid
together with the affine lines on it is AG(2,4).”

A more graphic approach from this journal —

Seven is Heaven...

Click the image for further details.

* This wording implies that GQ(2,2) has a unique
visual representation. It does not. See inscape .

Friday, October 23, 2020

Language Game:  The Doily Curse

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

“Quadrangle” is also a mathematical term.

Example: The Doily.

See also  The Crosswicks Curse .

Thursday, September 17, 2020

Structure and Mutability . . .

Filed under: General — Tags: , , — m759 @ 9:51 PM

Continues in The New York Times :

“One day — ‘I don’t know exactly why,’ he writes — he tried to
put together eight cubes so that they could stick together but
also move around, exchanging places. He made the cubes out
of wood, then drilled a hole in the corners of the cubes to link
them together. The object quickly fell apart.

Many iterations later, Rubik figured out the unique design
that allowed him to build something paradoxical:
a solid, static object that is also fluid….” — Alexandra Alter

Another such object: the eightfold cube .

Thursday, September 10, 2020

Of London Bondage

Filed under: General — Tags: , — m759 @ 12:38 PM

“After years in hiding, latex fashion re-emerged in the late 1950s,
thanks to the British designer John Sutcliffe, who created the world’s
first catsuit – the prototype rubber-fetish garment. …

The 1960s British spy series The Avengers was monumental
in bringing rubberwear to the masses. The show’s feminist heroine,
Emma Peel (played by Diana Rigg), was styled in a latex, Sutcliffe-
inspired catsuit. With Peel as a media archetype, latex’s second-skin
look wasn’t just sexy, it was superhuman.

Sutcliffe capitalised on the obsession with his products, and founded
AtomAge Magazine in 1972. The periodical, filled with artful and erotic
bondage imagery, gained a huge following among fetishists, and made
quite the splash on London’s progressive fashion scene. ”

By Cassidy George, bbc.com, 8th January 2020

See also an image from a Log24 post  commemorating that date —

Wednesday, September 9, 2020

Arrow Theme

Filed under: General — m759 @ 11:20 AM

The abstract arrows below in an image from yesterday’s Design post . . .

. . . are a background feature of the Castello Sforzesco website generally,
and not specifically of Corraini’s 2016 graphic design presentation.

The arrows apparently come from repetitions of this motif —

Similar arrow motifs appear at the castle’s main page

Wednesday, September 2, 2020

Little Metal Letters

Filed under: General — Tags: — m759 @ 2:00 PM

From a report of another August 14 death —

“… on Dec. 7, 1941, ‘it seemed as though everyone at Harvard
came to the Crimson building that night, and anxiously
hung over the ticker tape [i.e., teletype ] machine to watch the
little metal letters hammer out the words that told the story.'”

— Dan Huntington Fenn Jr., quoted in his Boston Globe obituary.

“Simplicity, clarity, showing the text” — The late Howell Binkley.

“To expand the words and music and dance” . . .

See Coconut Dance.

Monday, August 17, 2020

And Thereby Hangs . . . A Black Belt?

Filed under: General — Tags: — m759 @ 1:40 AM

Context —

Accompanying dialogue —

Nina Kate is, among other things, a latex designer:

Latex design suggested by a recent Jaime King meditation
on the AA phrase Hungry, Angry, Lonely, Tired: HALT

Gotta work on that acronym.” — Tony Stark —

Tuesday, August 11, 2020

The Scrolling

Filed under: General — m759 @ 11:35 AM

Heller: I'm a weapons designer. (grabs Shoveler's collar) I've got 
what you need.
Shoveler: A--All right. We'll--we'll come back. We'll visit all of you 
people, later. Thank you, sir.
Heller: No no no no no. I--I don't live here. I'm here for the ladies. 
You know. Here, take my card. 

|Aromatherapy                  Laser Hair Removal|
|               Doctor A. Heller                 |
|               Weapons Designer                 |
|              Innovator, Inventor               |
|                 World Changer                  |
|                                                |
|                 Old Funhouse                   |
|              Heller Fairgrounds                |
|              Test Site Number 7                |
|Carnival Rides                   Chicken Rentals|

My name's Heller. Say it with me.
Heller&Shoveler: Heller.
Shoveler: All right. Thank you. (he absently puts Heller's card in his 

Wednesday, August 5, 2020

Multifaceted Unities

Filed under: General — Tags: , , — m759 @ 10:45 AM

Facettenreiche  Grundlage:

Multifaceted Foundation: Facettenreiche Grundlage

Tuesday, July 28, 2020

Checked Cell*

Filed under: General — m759 @ 10:20 AM

* For the title —

See as well some related philosophy.

Wednesday, July 15, 2020

A Four-Color Diamond

Filed under: General — m759 @ 10:16 PM

Browsing related to the graphic  design theory described in the previous post
yielded a four-color diamond illustrating design at Microsoft —

For some related mathematics  see . . .

The Four-Color Diamond’s 2007 Source —

See also Log24 posts from August 2007 now tagged The Four-Color Ring.

Category Theory

Filed under: General — m759 @ 3:00 AM

A related quotation:

“By far the most important structure in design theory
is the Steiner system S(5, 8, 24).”

— “Block Designs,” by Andries E. Brouwer
(Ch. 14 (pp. 693-746) of Handbook of Combinatorics,
Vol. I, MIT Press, 1995, edited by Ronald L. Graham,
Martin Grötschel, and László Lovász, Section 16 (p. 716))

See also the webpage Block Designs in Art and Mathematics
and Log24 posts tagged Plastic Elements.

Tuesday, June 30, 2020

Classics of Jewish Humor —

Filed under: General — Tags: — m759 @ 7:07 PM

The Polish starlet joke

Related material — Costume design for New Year’s Eve.

“Show me all  the blueprints.” —  attributed to Howard Hughes.

Sunday, June 28, 2020

“Here We Are Now, Entertain Us.” — Nirvana, “Teen Spirit”

Filed under: General — m759 @ 5:00 PM

Or: Kipling and the Temple of Doom

See also Kipling and The Temple.

This post was suggested by a remark of Holland Cotter in The New York Times
on April 19, 2012 —

“An 18th-century Jain diagram of the cosmos turns the universe
into a kind of salvational board game. “

Hence . . .

Saturday, June 27, 2020


Filed under: General — Tags: — m759 @ 1:00 AM

Wednesday, June 24, 2020

Hollywood Nights

Filed under: General — m759 @ 3:01 AM

The conclusion of an obituary for a former resident of Laurel Canyon —

“He would go to all these old junk shops and buy
black-and-white photos of nobody actors,’’
Mr. Klein said. “He didn’t want stills of the stars.
He said, ‘Actors that never made it — that’s
the real Hollywood.’ ’’

— Guy Trebay in The New York Times , June 23

Related music and art — Posts tagged Hollywood Nights.

Thursday, June 18, 2020

Sister Act

Filed under: General — m759 @ 3:53 PM
Maria Shriver, a contributor for NBC’s “TODAY,” remembered her aunt as an “extraordinary woman.”

Smith “had a great career on behalf of this country as ambassador to Ireland promoting peace there and also started very special arts for people with intellectual disabilities,” Shriver said on the 3rd hour of “TODAY.”

“So I take solace in the fact that she is joining every other member of her family up in heaven. So it’s nice for her,” she added.

Smith was born on Feb. 20, 1928, in Boston, Massachusetts to Rose and Joseph Kennedy.

Related graphic design:

Feb. 20 square and June 17 Circle.

Related entertainment: “The Foreigner” (2017 film) and . . .

Monday, June 15, 2020

Blues for Mr. Caplan

Filed under: General — Tags: — m759 @ 2:59 PM

“Mr. Caplan, an essayist, professor, lecturer and consultant on design,
died on June 4 in his apartment on the Upper West Side of Manhattan.
He was 95.” — Penelope Green in The New York Times  today.

This  journal on that date —

Related cultural icons —

” James, Alec.  Alec, James.”

Sunday, June 14, 2020

PC Language Game

Filed under: General — Tags: — m759 @ 3:33 PM

The above Nat Friedman is not to be confused with
the Nat Friedman of “Hyperseeing,” discussed here June 12.

“One game is real and one’s a metaphor.
Untold times this wisdom’s come too late.
Battle of White has raged on endlessly.
Everywhere Black will strive to seal his fate.
Continue a search for thirty-three and three.
Veiled forever is the secret door.”
— Katherine Neville, aka Cat Velis, in The Eight,
Ballantine Books, January 1989, page 140

Related literary remarks —

The Old Man and the Bull

The Old Man and the Topic

Wednesday, May 13, 2020

Adventures in the Book Trade

Filed under: General — m759 @ 1:06 PM

Click the Springer “train of thought” advertisement below to enlarge.


A line for Stephen King:

“She gets the locomotive, I get the caboose.”

. . . . . . .

Cover of 'The Institute,' a novel by Stephen King

Cover Design: Will Staehle / Unusual Co.

Sunday, May 10, 2020


Filed under: General — m759 @ 4:11 PM

In memory of an architect who reportedly died yesterday at 88,
a search in this journal  for capilla  (Spanish for chapel).

Wednesday, April 22, 2020

Puzzle Pictures

Filed under: General — m759 @ 6:27 PM

A doodle from 2012’s  Feast of the Epiphany


A doodle based on a post for Twelfth Night, 2003

IMAGE- Quilt blocks- Devil's Claws and Yankee Puzzle

IMAGE- 'Yankee Doodle went to London' with musical notes

Sunday, April 5, 2020

“She do the Dickens in different voices”

Filed under: General — m759 @ 9:10 PM

From this journal on August 9, 2019

Block Designs?

Perhaps not.

From an Instagram account, also on August 9, 2019 — (click to enlarge) —

Monday, March 30, 2020

More Academic Ugliness

Filed under: General — m759 @ 6:13 PM

The Boston Globe  on the dead architect of the previous post

“Mr. McKinnell, who was a fellow of the American Institute of Architects
and the American Academy of Arts and Sciences, and a member of the
Royal Institute of British Architects, taught for many years at the
Harvard Graduate School of Design and the Massachusetts Institute of
Technology School of Architecture and Planning.”

Some ugly rhetoric to go with the ugly architecture —

Friday, February 28, 2020


Filed under: General — Tags: — m759 @ 4:58 PM

See as well this  journal on that date — Oct. 25, 2013.

Tuesday, February 11, 2020

Steam Heat (Pace Stephen King and Bob Fosse)

Filed under: General — m759 @ 12:23 AM

[Steam calliope plays] As a stationary object,
it always needs to be activated.
— Kara Walker at


Backstory —

See also this  journal on the above "catastrophe" weekend.

Sunday, February 9, 2020

Build It And They Will …

Filed under: General — m759 @ 8:42 PM

See also "Missing Pieces" (October 3, 2009).

Thursday, January 30, 2020

Poster Boy

Filed under: General — Tags: — m759 @ 7:00 PM

Cover of 'The Institute,' a novel by Stephen King
                                                          Cover Design: Will Staehle / Unusual Co.

This post is in memory of "Wes Wilson, Psychedelic Poster Pioneer,"
who died at 82 on January 24, according to the NY Times  today. 
Related material — This  journal on January 24.

Friday, January 17, 2020

September Morn

Filed under: General — Tags: — m759 @ 10:17 PM

Epigraph from Ch. 4 of Design Theory , Vol. I:

"Es is eine alte Geschichte,
 doch bleibt sie immer neu 
 —Heine (Lyrisches Intermezzo  XXXIX)

This epigraph was quoted here earlier on
the morning of September 1, 2011.

Wednesday, January 15, 2020

Paradigm Shift

Filed under: General — Tags: — m759 @ 1:33 PM

Sheehan, 'Making Sense of Heidegger,' p. 39

Illustration, from a search in this journal for “Symplectic” —

IMAGE- A symplectic structure -- i.e. a structure that is symplectic (meaning plaited or woven).

Some background:  Rift-design  in this journal and

Tuesday, January 7, 2020

Evening of the Iguana

Filed under: General — m759 @ 7:42 PM

Art notes —

See also the "Night of the Iguana" logo by Saul Bass,
a student of Gyorgy Kepes.

Postscript for synchronologists — 

See this  journal on that date:  Nov. 6, 2011.

Monday, January 6, 2020

A 2020 Manifesto

Filed under: General — Tags: — m759 @ 1:33 PM

Art as Experience (Minus Baldessari)

Filed under: General — Tags: — m759 @ 12:36 PM

In memory of an artist who reportedly died in Venice, CA, on Jan. 2 —

Two quotes from the website Quotes Sayings

"I always felt like I was right out of Dickens, looking in the window
of the Christmas feast, but not at the feast." — John Baldessari

IS A DEAD EXPERIENCE" — John Baldessari

The "dead experience" quote is actually from Gyorgy Kepes:

Wednesday, January 1, 2020

Exploring Inner Space* at The New York Times

Filed under: General — Tags: — m759 @ 11:35 AM

From Corrections: Jan. 1, 2020

The astronomy article, by Dennis Overbye, is dated Dec. 23* (a Monday).

The above reference to "Tuesday" is explained by the fine print
at the bottom of the Science Times  article — "A version of this article
appears in print on [Tuesday] , Section D, Page 6 of the
New York edition with the headline: In Battle of Giant Telescopes,
Outlook for the U.S. Dims." 

From the article as quoted on Thursday, Dec. 26,  
at https://uclafacultyassociation.blogspot.com

"Now, as the wheels of the academic and government bureaucracy begin to turn, many American astronomers worry that they are following in the footsteps of their physicist colleagues. In 1993, Congress canceled the Superconducting Super Collider, and the United States ceded the exploration of inner space to Europe and CERN, which built the Large Hadron Collider, 27 miles in diameter, where the long-sought Higgs boson was eventually discovered.

The United States no longer builds particle accelerators. There could come a day, soon, when Americans no longer build giant telescopes. That would be a crushing disappointment to a handful of curious humans stuck on Earth, thirsting for cosmic grandeur. In outer space, nobody can hear you cry."

Source: https://www.nytimes.com/2019/12/23/science/telescopes-magellan-hawaii-astronomy.html

Related material from this  journal on April 2, 2019 —

Cover design by Greg Stadnyk, available in an animated gif.

* See also this  journal on Dec. 23.

Tuesday, December 17, 2019

A Singular Eye

Filed under: General — Tags: , , — m759 @ 8:08 PM

Photographer Key Heyman, 89, dies

Cover design by Will Staehle.

Heyman reportedly died on Dec. 10, 2019.
See this  journal  on that date.

Wednesday, December 11, 2019

Miracle Octad Generator Structure

Filed under: General — Tags: , , — m759 @ 11:44 PM

Miracle Octad Generator — Analysis of Structure

(Adapted from Eightfold Geometry, a note of April 28, 2010.
See also the recent post Geometry of 6 and 8.)


Filed under: General — Tags: — m759 @ 11:26 AM

The Seagram Case

Filed under: General — Tags: — m759 @ 10:48 AM

From a search in this journal for Seagram

A Seagram 'colorful tale'

Klein Quadric

Filed under: General — Tags: , — m759 @ 1:06 AM

The architecture of the recent post 
Geometry of 6 and 8 is in part
a reference to the Klein quadric.

Saturday, November 23, 2019

Salzburg Requiem

Filed under: General — m759 @ 9:59 AM

Porsche.com on Ferdinand Alexander Porsche, who reportedly
died at 76 in Salzburg on 5 April 2012 —

"The credo of his design work was:

'Design must be functional and functionality has to 
be translated visually into aesthetics, without gags
that have to be explained first.' 

F.A. Porsche:
'A coherently designed product requires no adornment;
it should be enhanced by its form alone.'

The design’s appearance should be readily comprehensible
and not detract from the product and its function.
His conviction was: 'Good design should be honest.' "

See also last night's 11:32 PM post, and posts tagged Structural Logic.

Thursday, November 14, 2019


Filed under: General — Tags: , — m759 @ 8:18 AM

Rules for a game codesigned by Ellie Black, the cartoonist
of yesterday's post Cutting-Edge Prize

Tuesday, November 12, 2019

Social Logic

Filed under: General — m759 @ 9:16 AM

Friday, March 10, 2017

The Transformers

Filed under: General — m759 @ 10:00 PM 

"The transformed urban interior is the spatial organisation of an  achiever, one who has crossed the class divide and who uses space to express his membership of, not aspirations towards, an ascendant class in our society: the class of those people who earn their living by transformation — as opposed to the mere reproduction — of symbols, such as writers, designers, and academics."

— The Social Logic of Space ,
     by Bill Hillier and Julienne Hanson,
     Cambridge University Press, 1984

For another perspective on the achievers, see The Deceivers .

Tuesday, October 29, 2019

Triangles, Spreads, Mathieu

Filed under: General — Tags: , — m759 @ 8:04 PM

There are many approaches to constructing the Mathieu
group M24. The exercise below sketches an approach that
may or may not be new.


It is well-known that

 There are 56 triangles in an 8-set.
There are 56 spreads in PG(3,2).
The alternating group An is generated by 3-cycles.
The alternating group Ais isomorphic to GL(4,2).

Use the above facts, along with the correspondence
described below, to construct M24.

Some background —

A Log24 post of May 19, 2013, cites

Peter J. Cameron in a 1976 Cambridge U. Press
book — Parallelisms of Complete Designs .
See the proof of Theorem 3A.13 on pp. 59 and 60.

See also a Google search for “56 triangles” “56 spreads” Mathieu.

Update of October 31, 2019 — A related illustration —

Update of November 2, 2019 —

See also p. 284 of Geometry and Combinatorics:
Selected Works of J. J. Seidel
  (Academic Press, 1991).
That page is from a paper published in 1970.

Update of December 20, 2019 —

Friday, October 25, 2019

Facettenreiche Gestaltung

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

On the word Gestaltung

IMAGE- T. Lux Feininger on 'Gestaltung'

(Here “eidolon” should instead be “eidos .”)

A search for a translation of the book "Facettenreiche Mathematik " —

A paper found in the above search —

A related translation —

See also octad.design.

Wednesday, October 23, 2019

Art-Historical Narrative*

Filed under: General — Tags: , — m759 @ 9:25 PM

"Leonardo was something like what we now call a Conceptual artist,
maybe the original one.   Ideas —  experiments, theories —  were
creative ends in themselves."

— Holland Cotter in the online New York TImes  this evening

From other Log24 posts tagged Tetrahedron vs. Square —

* Phrase from the previous post, "Overarching Narrative."

Overarching Narrative

Filed under: General — Tags: , — m759 @ 8:13 PM

In memory of a retired co-director of Galerie St. Etienne
who reportedly died on October 17 . . .

"It is difficult to mount encyclopedic exhibitions
without an overarching art-historical narrative…."

—  Jane Kallir, director of Galerie St. Etienne, in

An overarching narrative from the above death date

See as well the previous post 
and "Dancing at Lughnasa."

Friday, October 18, 2019

Wall Texts

Filed under: General — Tags: — m759 @ 2:46 AM

"And the new dumbed-down gallery headings and word salads
of the main wall texts definitely need work."

— Roberta Smith yesterday in The New York Times
    on the reopening Museum of Modern Art.

Sample gallery heading and word salad from this  journal  


From the Terrace.


Spinning the Wake.

Friday, October 11, 2019

Illustrating Nightmares

Filed under: General — m759 @ 11:30 PM

Movie poster designer Philip Gips reportedly died on
Thursday, October 3, 2019. This journal on that date:

A Sense of the Landmarks.

Thursday, October 3, 2019

Apocalypse* Note

Filed under: General — Tags: — m759 @ 7:00 PM

For a first look at octad.space, see that domain.
For a second look, see octad.design.
For some other versions, see Aitchison in this journal.

* The X-Men character.

Tuesday, September 3, 2019

Annals of Square Space

Filed under: General — Tags: — m759 @ 9:23 AM


Toy Story:

Space Story:

See Square Space (hosted by Squarespace):

Friday, August 30, 2019

The Coxeter Aleph

Filed under: General — Tags: — m759 @ 4:21 AM


The previous post displayed part of a page from
a newspaper published the day Olivia Newton-John
turned 21 — Friday, September 26, 1969.

A meditation, with apologies to Coleridge:

In Xanadu did Newton-John
A stately pleasure-square decree
Where Aleph the sacred symbol ran
Through subsquares measureless to man.

A related video —

Beware, beware, her flashing eyes, her floating hair:

Set design

As opposed to block design

Wednesday, August 28, 2019

Tiger’s Leap  to 1905

Filed under: General — Tags: , — m759 @ 3:03 PM

Walter Benjamin on 'a tiger's leap into the past'

See other posts
now tagged
Crosswicks Curse.


Click to enlarge:

Block Designs?

Older Posts »

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