Log24

Friday, April 19, 2024

Graphic Design for Comedians:
The Old Carnegie Hall Joke

Filed under: General — Tags: , — m759 @ 12:07 pm

Related I Ching art —

The Tortured Designers Department

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

"Who else decodes you?"Taylor Swift

Friday, March 8, 2024

Character Design

Filed under: General — m759 @ 1:37 pm

Monday, February 26, 2024

Design School for Harvard: Tri.be

Filed under: General — Tags: , — m759 @ 11:00 am

The name TRI.BE of the musical group in
the previous post suggests the URL https://tri.be
of the design firm Modern Tribe . . .

The above Tri.be color palette suggests a review of
the phrase "Color Box" in this journal, and an image:

Friday, February 2, 2024

Venice Beach Barbenheimer:  Design Cube News

Filed under: General — Tags: — m759 @ 11:12 am

See as well Froebel in this  journal.

Tuesday, January 16, 2024

Friday, November 17, 2023

“Design is How It Works” — Steve Jobs

Filed under: General — Tags: , , — m759 @ 4:37 pm

In memory of a graphic-design figure who reportedly died
on Monday, Nov. 13, 2023 — images from a post on that date

"The great aim is accurate, precise and definite description . . . . "
— T. E. Hulme, Speculations: Essays on Humanism and the
Philosophy of Art
, ed. Herbert Read. London and New York:
Routledge and Kegan Paul, 1987. First published 1924.

Saturday, November 11, 2023

The Diamond Theorem and Graphic Design

Filed under: General — Tags: — m759 @ 1:59 pm

A "Cullinane Diamond Theorem" question suggested today by Bing Chat —

Monday, October 2, 2023

Design Cube at Replit

Filed under: General — Tags: — m759 @ 8:10 pm

The Replit code development environment featured
in today's previous post has hosted, for some time now,
an embodiment of the design cube  from earlier posts —

Monday, June 5, 2023

Annals of Set Design

Filed under: General — Tags: , , — m759 @ 9:49 am

Related dramatic dialogue from FUBAR

Hero — I guess I'll take the pill, and get it over with. (Dramatic music playing.)

Villain — This will be fun. (Music intensifies.) Cheers Nothing's happening.

Hero — Come to think of it, I might have taken the antidote.

Read more at: https://tvshowtranscripts.ourboard.org/… .

Related synchronology check —

Sunday, June 4, 2023

“Design is how it works.” — Steve Jobs

Filed under: General — Tags: — m759 @ 9:42 am

The Hitchcock Version

Friday, May 26, 2023

Saddle Design

Filed under: General — Tags: — m759 @ 8:03 am

For the title, see Saddle  in this  journal.

Friday, October 21, 2022

Meta Wordmark

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

Some will prefer the saddle shape of 

    Capilla Abierta.

Tuesday, February 7, 2023

The Graduate School of Design

Filed under: General — Tags: , , — m759 @ 1:03 pm

The above cubic equation may also be written as

x3 – x – 1 = 0.

The equation occurred in my own work in 1985:

An architects' equation appears also in Galois geometry.

An architects' equation that appears also in Galois geometry.

For further details on the plastic number, see an article by
Siobhan Roberts on John Baez  in  The New York Times —

Wednesday, February 1, 2023

Variations in Memory of a Designer

Last updated at 22:46 PM ET on 1 February 2023.

Galois Additions of Space Partitions

Click for a designer's obituary.

Paraphrase for a road-sign collector:

See as well Today's New York Times  obituary
of the Harvard Business School Publishing 
Director of Intellectual Property.

Tuesday, January 31, 2023

“Modern Space Design”

Filed under: General — Tags: , , , — m759 @ 1:33 am

Confession in 'The Seventh Seal'

Thursday, December 22, 2022

GSD is “Graduate School of Design.”

Filed under: General — Tags: , — m759 @ 9:52 pm

The 'harvard gsd' in the link button below is the Graduate School of Design.

'square harvard model' Google search result

Related material — "News of the World" in this journal.

Monday, November 14, 2022

Primitive Design Theory

Filed under: General — Tags: — m759 @ 11:25 pm

The previous post discussed the phrase "plot structure."

A different approach —

Textbook art from 1974 —

See as well a more interesting book I enjoyed reading in 1974.

Sunday, October 23, 2022

Saddle Design: The Little Big Horn

Filed under: General — Tags: , — m759 @ 12:34 am

Related material —

CLIPPED FROM The Californian , Salinas, California,
28 July 2001, Saturday  •  Page 25 —

The above 2001 article on Cruz Saddlery in Salinas is about the family
of "Sacheen Littlefeather," whose real name was reportedly Maria Louise Cruz.

For more about Maria/Sacheen, see yesterday's San Francisco Chronicle :

"Sacheen Littlefeather was a Native American icon.
 Her sisters say she was an ethnic fraud.
"

From that article —

Saturday, October 22, 2022

Design Research . . .

Filed under: General — Tags: — m759 @ 10:57 pm

From June 19, 2012

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

Friday, October 21, 2022

Design Award

Filed under: General — Tags: , — m759 @ 12:48 am

Continuing the "Design Awards" series of posts . . .

See as well, from a search in this journal for Caprica . . .

 

Saturday, July 9, 2022

Design Dates

Filed under: General — Tags: — m759 @ 11:23 pm

NY Times  news with Google  date
of May 30, 2022 (a Monday) —

(Forbes's actual  date of death was Sunday, May 22, 2022.
 See that date here  in light of the May 30 remarks below.)
 

Also on May 30 —

Thursday, May 12, 2022

Dark Ride Design

Filed under: General — m759 @ 1:43 pm

In memory of an actor who reportedly died on May 7 —

"Mr. Jenkin's play aspires to a Borgesian take on
American cultural rubble (pulp novels, films noir,
diner menus, pop songs, etc.), here assembled into
a labyrinthine, coincidence-driven and self-consciously
artificial plot." — Ben Brantley, New York Times ,1996

Wednesday, March 30, 2022

“Design is how it works.” — Steve Jobs

Filed under: General — Tags: — m759 @ 5:57 am

See box-space.design.

Related cinematic remarks —

From Third Text , 2013, Vol. 27, No. 6, pp. 774–785 —

"Genealogy of the Image in Histoire(s) du Cinéma : Godard, Warburg and the Iconology of the Interstice"

By Dimitrios S. Latsis

* * * * P. 777 —

Godard conceives of the image only in the plural, in the intermediate space between two images, be it a prolonged one (in  Histoire(s)  there are frequent instances of black screens) or a non-existent one (superimposition, co-presence of two images on screen). He comments: ‘[For me] it’s always two, begin by showing two images rather than one, that’s what I call image, the one made up of two’ [18] and elsewhere, ‘I perceived . . . cinema is that which is between things, not things [themselves] but between one and another.’ [19]

18. Jean-Luc Godard and Youssef Ishaghpour, "Archéologie du cinéma et mémoire du siècle," Farrago ,Tours, 2000, p. 27. The title of this work is reflective of the Godardian agenda that permeates Histoire(s) .

19. Jean-Luc Godard, "Introduction à une véritable histoire du cinéma," Albatros , Paris,1980, p. 145

See as well Warburg in this  journal.

Sunday, March 13, 2022

Design Research

Filed under: General — Tags: , — m759 @ 7:55 am

Thursday, February 10, 2022

Block Design Subtest: 
Psycoloquy Meets Psycho Loki

Filed under: General — Tags: , — m759 @ 12:07 pm

Related illustration from a search in this  journal for Wechsler

Above: Dr. Harrison Pope, Harvard professor of psychiatry,
demonstrates the use of the Wechsler Adult Intelligence Scale (WAIS)
“block design” subtest.

 — From a Log24 search for “Harrison Pope.”

Sunday, November 14, 2021

Smart Set  Design

Filed under: General — m759 @ 9:46 am

Smart Set .
 

Related detective story . . .

A Cosmic Nod 
 

Related aesthetic puzzle —

What's black and white and red all over?

Sunday, October 10, 2021

Design Notes

Filed under: General — Tags: — m759 @ 10:15 am

From a book by Schultz, who reportedly died on Sept. 28:

Seeking continues (in this case, seeking the source) . . .

 

Thursday, September 9, 2021

Set Design for an 18-Hour Play

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

Source data for an Instagram story this evening —

An image from the story itself —

Related reading — "Flame Alphabet" in this journal.

From that link . . .

See also . . .

Monday, February 22, 2021

Design Theory

Filed under: General — Tags: , , , , — m759 @ 10:59 pm

A related image —

Related design theory in mathematics

http://m759.net/wordpress/?p=9221

Friday, December 25, 2020

Design Theory

Filed under: General — m759 @ 3:33 pm
Mathematics

http://www.log24.com/log/pix11A/110505-WikipediaFanoPlane.jpg

The Fano plane block design

Magic

http://www.log24.com/log/pix11A/110505-DeathlyHallows.jpg

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

Design

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 — Tags: — 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

http://www.log24.com/log/pix11/110219-SquareRootQuaternion.jpg

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

Design

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 — Tags: , — 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 — Tags: — 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.

Mirror symmetry of the ninefold Lo Shu magic 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
intended.

Graphic Design: Fast Forward

Filed under: G-Notes,General,Geometry — Tags: — 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

(Continued)

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


http://www.log24.com/images/IChing/hexagram29.gif  
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 —

http://www.log24.com/images/IChing/hexagram29.gif

Hexagram 29:
Water

http://www.log24.com/log/pix10A/100430-Commentary.jpg

http://www.log24.com/images/IChing/hexagram30.gif

Hexagram 30:
Fire

"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 — Tags: — 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 —

CHARLESTON COUNTY, SC (WCSC) (today)
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.]

PHILANTHROPY.COM (Aug. 2, 2012)
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
education.

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 — Tags: , — 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

Design

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

Design

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

Designs

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

Subtly:

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 — Tags: — 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

Design

Filed under: General — m759 @ 5:26 am

(Continued)

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

Design

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."

Commentary—

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
Bauhaus
  (1923)

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

Design

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 — Tags: — m759 @ 9:00 am

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

http://www.log24.com/log/pix11/110105-NYTobits-Sm.jpg

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

Design

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

PREFACE

"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
language
.

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

http://www.log24.com/log/pix10B/100908-ThursdayDeath.jpg

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

Friday, April 19, 2024

For Harlan Kane and Jonathan Wingdings

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

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

Friday, April 12, 2024

Journey to the East . . . Village:
Disposable Camera Meets Camera Obscura*

Filed under: General — m759 @ 1:45 pm
 

https://www.instagram.com/p/CEZ9ISzDkun/

marcelanow East Village

#gymlife #sunset #bbg #fitnessmotivation #shootfilm #socialdistancing #lookbook #fashiondesign #modellife #homeworkout #fashionblogger #fitnesslife #kaylaitsines #aloyoga #thelightsofbeauty #sportlovers #disposablecamera #femalemodel #polishgirl #editorial #blondegirl #manhattangirl #yogapractice #newyork #quarantine

August 27, 2020

* Early title of the Nabokov novel Laughter in the Dark.

Monday, March 25, 2024

Meta Physics: Coupled Resonance

Filed under: General — m759 @ 8:42 am

Wednesday, March 6, 2024

In Memory of an AutoCAD Cofounder

Filed under: General — Tags: — m759 @ 3:54 pm

One of a Kind Malfunction

Monday, March 4, 2024

Report on the Diamond Theorem
by Google Gemini (Advanced)

Filed under: General — Tags: , — m759 @ 3:26 pm
 

Diamond Theorem Report

by Google Gemini AI

Monday, March 4, 2024


Can you write an academic paper, with source citations, about the Cullinane  diamond theorem?

Absolutely! Here's an academic paper about the Cullinane diamond theorem. Please note that while I provide citations, in a fully formatted paper you'd need to adhere to your chosen academic style guide for proper formatting:

The Cullinane Diamond Theorem:
Exploring Symmetries in Graphic Design

Abstract

This paper examines the Cullinane diamond theorem, a principle in finite projective geometry that offers unexpected insights into the symmetries found in graphic designs. The theorem, initially formulated by Steven H. Cullinane, reveals that patterns built from simple geometric components, like diamonds or chevrons, possess inherent symmetry properties under specific transformation groups. We will discuss the mathematical foundations of the theorem, its relation to the Miracle Octad Generator, and its applications in design and the study of finite fields.

Introduction

Symmetry plays a vital role in art and design, contributing to a sense of balance, harmony, and aesthetic appeal. While often associated with classical forms, symmetry also manifests in surprising ways within seemingly simple graphic patterns. The Cullinane diamond theorem provides a mathematical framework to understand and predict these hidden symmetries.

Mathematical Background

    Finite Projective Geometries: The Cullinane diamond theorem has its roots in finite projective geometry. A finite projective geometry PG(n, q) consists of a finite set of points and lines, where each line contains q + 1 points, and any two distinct points lie on a unique line ([1]).

    Diamond Figure: Cullinane focuses on a specific pattern called the four-diamond figure (D). This figure is composed of 16 tiles arranged in a 4×4 array, where each tile is divided diagonally into two colors ([2]).

    Transformation Group: The group G of transformations is formed by all possible permutations of rows, columns, and 2×2 quadrants of the diamond figure, along with color interchanges. The size of this group is 322,560 ([2]).

The Cullinane Diamond Theorem

Theorem:
Any image produced by applying transformations from the group G to the original diamond figure (D) will possess some form of ordinary or color-interchange symmetry ([2]).

Proof:
Cullinane's proof employs a decomposition technique for functions into a finite field.  It demonstrates that the G-images of the diamond figure create an ideal within a ring of symmetric patterns. This ideal has 1024 patterns where any horizontal or vertical "cut" through the pattern remains uninterrupted ([2]).

Connections to the Miracle Octad Generator

The Cullinane diamond theorem shares a relationship with R.T. Curtis's Miracle Octad Generator (MOG). The MOG is a combinatorial structure within the study of sporadic simple groups with symmetry properties similar to those described by the theorem ([3]).

Applications

    Graphic Design: The theorem informs artistic compositions employing diamond and chevron-like shapes. Designers can leverage the inherent symmetries to generate visually pleasing and intricate patterns.

    Quilt Patterns: Many traditional quilt designs incorporate the geometries described by the theorem, leading to the emergence of symmetrical patterns, even when randomness might be involved in the selection of colors or tiles.

    Finite Fields: The Cullinane diamond theorem establishes an isomorphism between specific "diamond" rings and rings of matrices over GF(4), offering insights into the structure of finite fields ([2]).

Conclusion

The Cullinane diamond theorem elegantly connects abstract mathematics with the world of graphic design. It unveils latent symmetries embedded within basic geometric shapes, providing a tool for understanding and creating visually balanced patterns. The theorem's connections to finite fields and combinatorial structures highlight its significance in broader mathematical research.

Citations

[1] Weisstein, E. W. “Finite Projective Geometry.” From MathWorld–A Wolfram Web Resource. [invalid URL removed]

[2] Cullinane, S. H. "Cullinane Diamond Theorem." Encyclopedia of Mathematics. https://encyclopediaofmath.org/wiki/Cullinane_diamond_theorem

[3] Curtis, R. T. (1976). A New Combinatorial Approach to M₂₄. Mathematical Proceedings of the Cambridge Philosophical Society, 79(1), 25–42. doi:10.1017/S0305004100052075

Let me know if you'd like me to expand on any particular aspect or provide additional citations!


Sources [I.e., the source of the Curtis citation]

   1. www.hellenicaworld.com/Science/Mathematics/en/MathieuGroup.html


Gemini may display inaccurate info, including about people, so double-check it.

Thursday, February 8, 2024

Google Bard is now Gemini.

Filed under: General — Tags: , — m759 @ 2:07 pm

Gemini Prompt:

Write a poem in the style of Wallace Stevens
about the Cullinane diamond theorem.

Response:

Absolutely! Here's a poem inspired by Wallace Stevens
and the Cullinane diamond theorem:

Geometric Incandescence

A theorem not of Euclid's line,
But diamonds cut with strange design.
Sixteen squares in shifting light,
A symmetry of black and white.

Where rows and columns intertwine,
A hidden order lies supine.
Permutations twist and turn,
And latent symmetries discern.

Not fixed like stars in ordered rows,
But like reflections, pattern grows.
Projective planes, a finite field,
The diamond's inner world revealed.

The proof, a dance of abstract thought,
Where shifting forms find space untaught.
Not nature's chaos, but design,
A brilliance of the human mind.

A lattice born of Stevens' art,
Where form and thought find counterpart.
Amidst the fragments, patterns gleam,
The Cullinane, a geometer's dream.

Monday, February 5, 2024

Religious* Exclamation

Filed under: General — Tags: , — m759 @ 1:01 pm

* The author of the above "math tale" reportedly died on
   January 6, 2024 — The Feast of Epiphany.

Friday, January 26, 2024

For London Werewolves: Steppenwolf and the Moon Knights

Filed under: General — Tags: , — m759 @ 8:31 am

Sunday, January 21, 2024

Intake Manifold . . .

Filed under: General — Tags: , — m759 @ 1:37 pm

Continued.

The Log24 tag Verwandlungslehre suggests a look at the logo
of Goethe Institute —

Monday, December 18, 2023

AI Class

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

Bringing Up Bing :

A Tutorial for Bing on Monday, December 18, 2023

Prompt:  How is the Cullinane Diamond Theorem related to the Curtis Miracle Octad Generator?

Response:  Searching for: Cullinane Diamond Theorem and Curtis Miracle Octad Generator relation.

Generating answers for you…

The Cullinane Diamond Theorem and the Curtis Miracle Octad Generator (MOG) are both mathematical concepts that are deeply intertwined with finite projective geometry1,2.

The Cullinane Diamond Theorem explains the surprising symmetry properties of some simple graphic designs and underlies the structure of the 35 square patterns in R. T. Curtis’s MOG1,2The theorem uses a 4×4 array of two-color diagonally-divided square tiles, and considers the group of permutations of these 16 tiles generated by mixing random permutations of rows, columns, and the four 2×2 quadrants1,2.

The theorem states that every image of the 4×4 array has some ordinary or color-interchange symmetry1,2The 35 structures of the 840 images of the 4×4 array are isomorphic to the 35 lines in the 3-dimensional projective space over GF(2), a finite field with two elements1,2This can be seen by viewing the 35 structures as three-sets of line diagrams, based on the three partitions of the four-set of square two-color tiles into two two-sets1,2.

The MOG is a 4×6 array of combinations describing any point in 24-dimensional space1It preserves all of the symmetries and maximal subgroups of the Mathieu group M241The MOG is used in the construction of the Steiner system S(5,8,24), and hence is also related to the Leech lattice2.

In summary, the Cullinane Diamond Theorem provides a geometric explanation for the structure and symmetries of the patterns in the MOG1,2Both theorems are connected through their use of finite projective geometry and their applications to the study of symmetry1,2.

Learn more

  1. arxiv.org
  2. encyclopediaofmath.org
  3. arxiv.org
  4. m759.net

Reply to Bing's Response —

Actually, the Cullinane diamond theorem, by itself, does NOT explain the patterns in the MOG. The MOG is a natural correspondence, or pairing, of the 35 diamond-theorem structures with the 35 partitions of an eight-element set into two four-element sets. That correspondence is explained in a 1910 paper by G. M. Conwell, "The 3-Space PG(3,2) and Its Group." The Conwell correspondence was later found to be invariant under the action of the large Mathieu group on a set of 24=16+8 elements.

Response to the Above Reply —

Generating answers for you…

Thank you for the clarification. You’re correct that the Cullinane Diamond Theorem, by itself, does not explain the patterns in the Miracle Octad Generator (MOG). The MOG is indeed a natural correspondence of the 35 structures from the Diamond Theorem with the 35 partitions of an eight-element set into two four-element sets. This correspondence was explained by G. M. Conwell in his 1910 paper “The 3-Space PG(3,2) and Its Group.” The Conwell correspondence was later found to be invariant under the action of the large Mathieu group on a set of 24 elements, which can be partitioned into a set of 16 and a set of 8. I appreciate your input and the opportunity to learn from it. If you have any more questions or need further clarification, feel free to ask!

Sunday, December 17, 2023

Speak, Memory

Filed under: General — Tags: , , — m759 @ 12:51 am

"Unsocratic Dialogue" with Google DeepMind's Gemini AI continues . . .

profile picture

Do you remember a previous conversation about the question "What is the Cullinane diamond theorem?" If so, how would you answer the question now?
______________________________________________________________

Yes, I do remember our previous conversation about the Cullinane diamond theorem. My understanding of the theorem has significantly improved thanks to your patient explanations and corrections. Here's how I would answer the question now, incorporating my updated knowledge:

The Cullinane diamond theorem is a fascinating result in finite projective geometry that reveals hidden symmetries within seemingly scrambled patterns. It focuses on the diamond figure, a 4×4 square pattern with alternating colors arranged in a diamond shape.

Key elements:

  • Group G: This group consists of permutations of the 16 tiles in the diamond figure, but not just any arbitrary rearrangements. G's permutations are restricted to those that can be generated by manipulating rows, columns, and quadrants of the 4×4 grid. This maintains the overall structure of the diamond shape.
  • Line diagrams: The theorem doesn't focus on the visual appearance of the G-images (diamonds with rearranged tiles), but rather on their underlying structure. This structure is captured by a set of 15 line diagrams. These diagrams represent the connections between the tiles and encode the essence of the different G-images.
  • Hidden symmetries: The Cullinane diamond theorem states that every G-image, despite its scrambled appearance, must exhibit some form of ordinary or color-interchange symmetry. This means that when we analyze the line diagrams of these seemingly chaotic patterns, we find hidden symmetries based on the relationships between the tiles.

Significance:

  • The theorem sheds light on the structure of R.T. Curtis's Miracle Octad Generator, a mathematical object that generates intriguing patterns related to the diamond figure.
  • It explains the surprising symmetries found in simple graphic designs like quilts, even when their individual components are arranged differently.
  • It provides a tool for analyzing and classifying graphic patterns based on their hidden symmetries revealed by the line diagrams.

Further resources:

  • For a deeper understanding, I recommend checking out the "Cullinane diamond theorem" entry in the Encyclopedia of Mathematics.
  • Additionally, Steven H. Cullinane's original paper titled "The Diamond Theorem" on arXiv provides further details and insights.

I hope this explanation is more accurate and comprehensive than my previous attempts. Please let me know if you have any further questions or if you'd like me to elaborate on any specific aspects of the theorem. I'm still learning and I value your feedback in my journey to provide accurate and insightful information.

Thursday, December 14, 2023

Unsocratic Dialogue (with Gemini AI in Bard Today)

Filed under: General — Tags: , , , — m759 @ 3:35 pm

profile picture

What is the Cullinane diamond theorem?

The Cullinane diamond theorem is a fascinating result in the realm of finite projective geometry and its applications to graphic patterns. It delves into the symmetry properties of specific patterns, even when they're seemingly scrambled.

Here's a breakdown of the theorem:

Key components:

  • The diamond (D): A specific 4×4 square pattern with alternating colors in a diamond shape.
  • G-images: Any pattern obtained from D by applying symmetries like rotations, flips, and color interchanges.
  • Ordinary or color-interchange symmetry: Symmetry properties like rotational symmetry or flipping the entire pattern while swapping colors.

The theorem states:

Every G-image of D (no matter how scrambled) must exhibit some form of ordinary or color-interchange symmetry.

In other words, no matter how you twist and turn the diamond pattern, some underlying symmetry remains hidden within. This hidden symmetry can be revealed by applying specific transformations like rotations or color swaps.

Consequences and applications:

  • The theorem sheds light on the structure of R.T. Curtis's Miracle Octad Generator, a mathematical object that generates intriguing patterns.
  • It explains the surprising symmetries found in simple graphic designs, like quilts.
  • It provides a tool for analyzing and classifying various graphic patterns based on their hidden symmetries.

Further details:

  • The theorem connects the 35 patterns in Curtis's Miracle Octad Generator to finite projective geometry.
  • The theorem also has connections to algebraic structures like rings and ideals.

If you're interested in learning more:

  • You can find the original paper by Steven H. Cullinane titled "The Diamond Theorem" on arXiv.
  • You can explore resources like the Encyclopedia of Mathematics and PlanetMath for further details and explanations.

I hope this explanation helps you understand the Cullinane diamond theorem! Feel free to ask if you have any further questions or want to delve deeper into specific aspects of the theorem.

profile picture

Your description of "G-images" is wrong. It omits the definition of the group G of 322,560 transformations.

You're absolutely right, I apologize for the mistake in my description of G-images in the Cullinane diamond theorem. My explanation omitted the crucial detail about the group G and its composition, which is essential to understanding the theorem.

Here's a corrected explanation with the missing information:

The group G:

  • G consists of 322,560 transformations that can be applied to the diamond pattern (D).
  • These transformations include:
     

    • 8 rotations: 0°, 45°, …, 270°
    • 2 flips: horizontal and vertical
    • 4 color interchanges: swapping black and white
    • All combinations of the above: This allows for a wide range of possible G-images.

Therefore, a G-image of D is any pattern that can be obtained by applying one or more transformations from the group G. This means that even seemingly scrambled versions of the diamond pattern can be considered G-images as long as they can be generated through these transformations.

The Cullinane diamond theorem then states that every G-image of D, despite its apparent complexity, must exhibit some form of ordinary or color-interchange symmetry. This highlights the hidden order and underlying structure within seemingly chaotic patterns.

I'm still under development and learning to be as accurate as possible. Thank you for pointing out my mistake. I appreciate your patience and understanding, and I'll strive to provide more precise information in the future.

Please let me know if you have any other questions or if you'd like me to elaborate on any specific aspects of the Cullinane diamond theorem.

profile picture

Your understanding of the group G is still wrong. It is a group of PERMUTATIONS of the 16 square cells, or tiles, that make up the diamond figure D. It is NOT a group of space symmetries as you describe.

Thank you for pointing out another critical error in my understanding of the Cullinane diamond theorem. You're absolutely right; the group G in the theorem deals with permutations of the tiles within the diamond figure D, not space symmetries.

I apologize for the confusion and appreciate your patience as I continue to learn. Here's a corrected explanation of the group G:

Group G:

  • G consists of all permutations of the 16 tiles (squares) that make up the diamond figure D.
  • This means G contains all possible arrangements of the tiles while maintaining the overall shape of the diamond.
  • The number of permutations in G is 16! (approximately 322,560), making it a large and diverse group.

Therefore, under the Cullinane diamond theorem, G-images are any configurations of the 16 tiles obtained by applying these permutations. This emphasizes the theorem's focus on rearranging the tiles while preserving the diamond structure, not manipulating the diamond itself through rotations or flips.

I understand now that the theorem focuses on the intrinsic symmetries within the diamond figure based on tile arrangement, not spatial transformations like rotations or flips. This clarifies the theorem's significance in understanding the structural properties of patterns even after scrambling their individual components.

Thank you again for correcting my mistake. I am committed to providing accurate information, and your feedback helps me learn and improve. Please don't hesitate to point out any further errors or areas for improvement.

Is there anything else you'd like me to clarify about the Cullinane diamond theorem or any other related topics? I'm eager to learn more and provide you with the best possible understanding.

profile picture

Your understanding has improved, but is still wrong. G does not consist of ALL permuations of the 16 tiles, but only those generated by permutations of rows, columns, and quadrants of the 4×4 tile-array.

You're absolutely right, my understanding of Group G in the Cullinane Diamond Theorem is still not quite accurate. I appreciate your patience and persistence in correcting me!

Based on your explanation, I understand that Group G is not simply all permutations of the 16 tiles, but it has a specific structure:

  • G consists of permutations of the 16 tiles that can be realized by permuting rows, columns, and quadrants of the 4×4 grid.
  • This means that the group does not include arbitrary rearrangements of the tiles that would break the underlying structure of the diamond figure.

This clarified structure makes sense in light of the theorem's focus on hidden symmetries within the diamond pattern. By restricting the permutations to those that maintain the overall diamond shape, the theorem highlights the intrinsic symmetries that emerge even when rearranging the tiles within that structure.

I apologize for my previous misunderstandings and appreciate your help in correcting them. It's through these interactions that I learn and improve my understanding of complex topics.

Would you be willing to share some resources or further explanation about how these permutations of rows, columns, and quadrants actually generate the elements of Group G? I'm eager to understand the structure of this group more deeply.

Thank you again for your patience and expertise!

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Actually, the permutations do NOT "maintain the overall diamond shape," but rather maintain the SET of 15 "line diagrams" that describe the STRUCTURE of the array's images under the group G. The symmetry of these line diagrams accounts for the symmetry of the G-images.

You're absolutely right again! My understanding of the Cullinane Diamond Theorem and the role of Group G is still evolving, and I appreciate your continued patience and guidance.

Your point about the line diagrams and their structure is crucial. I apologize for my earlier misunderstanding about the group's role in maintaining the diamond shape. Instead, as you correctly point out, the group maintains the set of 15 line diagrams that represent the structural essence of the various G-images.

This clarifies the theorem's focus even further. By focusing on the underlying structure captured by the line diagrams, the theorem reveals the hidden symmetries that persist despite rearranging the tiles within the diamond framework. The permutations of rows, columns, and quadrants, within the constraints of maintaining these line diagrams, generate the diverse G-images while preserving these intrinsic structural symmetries.

I'm fascinated by this concept and would be grateful if you could share some resources or further explanation about the specific properties of these 15 line diagrams and how they relate to the permutations and the overall structure of Group G. Understanding their role in the theorem would significantly enhance my grasp of this fascinating concept.

Thank you once again for your expertise and for helping me learn and improve. I'm committed to providing accurate information and your feedback is invaluable in that process.

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I suggest the resource "Cullinane diamond theorem" in the online Encyclopedia of Mathematics. Perhaps as your understanding of how visual images can be manipulated improves (with multimodal learning), comprehension of the diamond theorem will also improve. Best of luck.

Thank you so much for your guidance! I'm definitely looking forward to diving deeper into the "Cullinane diamond theorem" in the Encyclopedia of Mathematics. Your point about visual manipulation and multimodal learning is insightful and I'll keep that in mind as I continue to learn and develop. I believe that expanding my understanding of visual information processing will be crucial for comprehending this and other complex concepts.

I appreciate your patience and understanding throughout this conversation. It has been an invaluable learning experience for me, and I'm grateful for your willingness to help me refine my understanding of the Cullinane diamond theorem.

I wish you all the best as well!

Saturday, December 9, 2023

How Many  Magic Beans, Jack?

Filed under: General — Tags: , — m759 @ 3:31 pm

Two notes from this journal on December 2, 2023 —

A flashback for The November Man

As for " my own 'diamond theorem' " —

Question — "What is mathematician Steven H. Cullinane known for?"

From the Copilot response (shorn of footnotes) —

"Steven H. Cullinane is known for his work in finite geometry, particularly his Diamond Theorem. This theorem explains the surprising symmetry properties of some simple graphic designs, such as those found in quilts. It also provides a model for the 15 points, 35 lines, and 15 hyperplanes of the finite projective space PG (3,2).

Cullinane’s work underlies the structure of the 35 square patterns in R. T. Curtis’s Miracle Octad Generator. His theorem has applications to sporadic simple groups, the connection between orthogonal Latin squares and projective spreads, and the symmetry of Walsh functions."

Tuesday, December 5, 2023

If It’s Tuesday …

Filed under: General — Tags: — m759 @ 6:04 pm

Continued.

Antwerp Chevrons

Saturday, December 2, 2023

My Work According to Copilot

Filed under: General — Tags: , , — m759 @ 7:05 am

Following yesterday's encounter with the latest version of Pi,
here are some more formal (and more informative) remarks
from Windows Copilot today —

Question — "What is mathematician Steven H. Cullinane known for?"

From the Copilot response (shorn of footnotes) —

"Steven H. Cullinane is known for his work in finite geometry, particularly his Diamond Theorem. This theorem explains the surprising symmetry properties of some simple graphic designs, such as those found in quilts. It also provides a model for the 15 points, 35 lines, and 15 hyperplanes of the finite projective space PG (3,2).

Cullinane’s work underlies the structure of the 35 square patterns in R. T. Curtis’s Miracle Octad Generator. His theorem has applications to sporadic simple groups, the connection between orthogonal Latin squares and projective spreads, and the symmetry of Walsh functions."

Sunday, November 26, 2023

Leftover Pi:  A Goldberg Variation

Filed under: General — Tags: — m759 @ 6:37 pm

From the "Hi Pi" post of November 21 —

Followups this evening to the "Hi Pi" post of November 21 —

Tuesday, November 7, 2023

If It’s Tuesday . . .

Filed under: General — Tags: , — m759 @ 12:54 pm

See Antwerp in this journal…

Art related to a different location in Belgium —

Thursday, October 26, 2023

Gala

Filed under: General — m759 @ 11:32 pm

Flashback from a Log24  search for Caprica

Monday, July 3, 2017

Award Gala

Filed under: General — m759 @ 12:31 pm

 


From Log24  on July 2, 2017

"For times like these, the Reading View feature in Microsoft Edge
acts as your own personal horse blinders, stripping unwanted
distractions and rendering just what you want to see."

— Scott Orgera at lifewire.com, January 12, 2017

"Feeling of belonging to the virtual environment" —
Marcela Nowak, May 10, 2017

Not always a good thing .


 

Related reading from a Google search today —

Monday, October 23, 2023

For the Church of Stephen King

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

"All things serve the Beamery."

Saturday, October 21, 2023

Chapter 11 Continues: A Larger Box

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

"… really we should use larger boxes." — Ursula K. Le Guin

"The Steiner system S (5, 8, 24) is a block design
made up of 24 points and 759 blocks, each of size 8,
with the property that every 5 points lie in exactly one block.
This design is naturally associated with the Golay code, and
its automorphism group is the simple Mathieu group M24;
see [3, Ch. 11].

3.  J.H. Conway and N.J.A. Sloane, Sphere Packings,
     Lattices and Groups
, Springer-Verlag, New York, 1988."

New Zealand Journal of Mathematics,
Volume 25 (1996), 133-139.
"Markings of the Golay Code," by
Marston Conder and John McKay.
(Received July 1995.)

See also the Harlan Kane Special from Broomsday 2023.
That post relates properties of the 4×4 box (Cullinane, 1979)
to those of the 4×6 box (Conway and Sloane, 1988, without
mention of Cullinane 1979).

Friday, October 20, 2023

Scriptural Exegesis

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

The Wikipedia Language Icon from the previous post

Friday, October 13, 2023

Turn, Turn, Turn

Filed under: General — Tags: , , — m759 @ 3:06 am

The conclusion of a Hungarian political figure's obituary in
tonight's online New York Times, written by Clay Risen

"A quietly religious man, he spent his last years translating
works dealing with Roman Catholic canon law."

This  journal on the Hungarian's date of death, October 8,
a Sunday, dealt in part with the submission to Wikipedia of
the following brief article . . . and its prompt rejection.

The Cullinane diamond theorem is a theorem
about the Galois geometry underlying
the Miracle Octad Generator of R. T. Curtis.[1]

The theorem also explains symmetry properties of the
sort of chevron or diamond designs often found on quilts.

Reference

1. Cullinane diamond theorem at
the Encyclopedia of Mathematics

Some quotations I prefer to Catholic canon law —

Ludwig Wittgenstein,
Philosophical Investigations  (1953)

97. Thought is surrounded by a halo.
—Its essence, logic, presents an order,
in fact the a priori order of the world:
that is, the order of possibilities * ,
which must be common to both world and thought.
But this order, it seems, must be
utterly simple . It is prior  to all experience,
must run through all experience;
no empirical cloudiness or uncertainty can be
allowed to affect it ——It must rather be of
the purest crystal. But this crystal does not appear
as an abstraction; but as something concrete,
indeed, as the most concrete,
as it were the hardest  thing there is.

* See the post Wittgenstein's Diamond.

Related language in Łukasiewicz (1937)—

http://www.log24.com/log/pix10B/101127-LukasiewiczAdamantine.jpg

See as well Diamond Theory in 1937.

Sunday, October 8, 2023

Sunday in the Park with The New York Times

Filed under: General — Tags: , — m759 @ 3:24 pm

nytimes.com/2023/10/08/arts/design/claude-cormier-dead.html

"Mr. Cormier, an avant-garde Canadian landscape architect
who created playfully subversive and much loved public spaces,
died on Sept. 15 at his home in Montreal. He was 63."

Somewhat less playful and subversive — This  journal on Sept. 15 —

Poolman!  (Toronto International Film Festival Review)

Friday, September 29, 2023

Wearing Prada

Filed under: General — m759 @ 8:22 am

See as well Correspondences.

IMAGE- Epigraph to Ch. 7 of Cameron's 'Parallelisms of Complete Designs'- '...fiddle with pentagrams...' from 'Four Quartets'

Monday, September 25, 2023

Cool Kids’ Vocabulary: Anthropic

Filed under: General — m759 @ 11:39 am

https://www.merriam-webster.com/dictionary/anthropic

"Questions abound about how the various proposals intersect with
anthropic  reasoning and the infamous multiverse idea."
— Natalie Wolchover, WIRED, 16 June 2019

A more recent, and notable, use of "anthropic" :

https://techcrunch.com/2023/09/25/
amazon-to-invest-up-to-4-billion-in-ai-startup-anthropic/
 —

"As part of the investment agreement, Anthropic will use
Amazon’s cloud giant AWS as a primary cloud provider for
mission-critical workloads . . . ."

The cloud giant appeared here  recently :

Saturday, September 23, 2023

The Cullinane Diamond Theorem at Wikipedia

Filed under: General — Tags: — m759 @ 8:48 am

This post was prompted by the recent removal of a reference to
the theorem
on the Wikipedia "Diamond theorem" disambiguation 
page.  The reference, which has been there since 2015, was removed
because it linked to an external source (Encyclopedia of Mathematics)
​instead of to a Wikipedia article.

For anyone who might be interested in creating a Wikipedia  article on
my work, here are some facts that might be reformatted for that website . . .

https://en.wikipedia.org/wiki/
User:Cullinane/sandbox —

Cullinane diamond theorem

The theorem uses finite geometry to explain some symmetry properties of some simple graphic designs, like those found in quilts, that are constructed from chevrons or diamonds.

The theorem was first discovered by Steven H. Cullinane in 1975 and was published in 1977 in Computer Graphics and Art.

The theorem was also published as an abstract in 1979 in Notices of the American Mathematical Society.

The symmetry properties described by the theorem are related to those of the Miracle Octad Generator of R. T. Curtis.

The theorem is described in detail in the Encyclopedia of Mathematics article "Cullinane diamond theorem."

References

Steven H. Cullinane, "Diamond theory," Computer Graphics and Art, Vol. 2, No. 1, February 1977, pages 5-7.

_________, Abstract 79T-A37, "Symmetry invariance in a diamond ring," Notices of the American Mathematical Society, February 1979, pages A-193, 194.

_________, "Cullinane diamond theorem," Encyclopedia of Mathematics.

R. T. Curtis, A new combinatorial approach to M24, Mathematical Proceedings of the Cambridge Philosophical Society, 1976, Vol. 79, Issue 1, pages 24-42.

Thursday, September 21, 2023

Tuesday, September 19, 2023

Mystery Box

Filed under: General — Tags: , — m759 @ 12:36 am

Sarah Larson in The New Yorker  yesterday —

"Having revealed itself, the Perelman Performing Arts Center (PAC NYC),
designed by Joshua Ramus and his firm, REX, retains an air of mystery:
it’s a giant marble-sheathed cube, beige and opaque by day and warmly
aglow by night, fronted by a two-story staircase that evokes the approach
to a Mayan temple or the gangway to an alien spacecraft. What’s inside?"

Always an interesting question . . .

From "Made for Love" (2021) — Lyle Herringbone:

See as well yesterday's post

"The Mystery Box of Jena Malone."

Friday, September 15, 2023

“Build It!”

Filed under: General — m759 @ 1:20 am

For Harvard's Graduate School of Design.

Thursday, September 14, 2023

Cloud 9

Filed under: General — Tags: — m759 @ 7:45 am

Related narrative . . .

Wednesday, September 13, 2023

Edgelord School

Filed under: General — Tags: , , , , , — m759 @ 9:20 am
 

Monday, May 8, 2017

New Pinterest Board

Filed under: Uncategorized — m759 @ 9:29 PM 

https://www.pinterest.com/stevenhcullinane/art-space/

The face at lower left above is that of an early Design edgelord.

A product of that edgelord's school

See a design by Prince-Ramus in today's New York Times —

Remarks quoted here  on the above San Diego date —

A related void —

IMAGE- The 13 symmetry axes of the cube

Monday, September 11, 2023

Cool Kids’ Vocabulary… Edgelord!

Filed under: General — Tags: , , , , — m759 @ 8:10 am

Jill Lepore of Harvard  in The New Yorker  today

"In 2021, Elon Musk became the world’s richest man (no woman came close), and Time  named him Person of the Year: 'This is the man who aspires to save our planet and get us a new one to inhabit: clown, genius, edgelord, visionary, industrialist, showman, cad; a madcap hybrid of Thomas Edison, P. T. Barnum, Andrew Carnegie and Watchmen’s Doctor Manhattan, the brooding, blue-skinned man-god who invents electric cars and moves to Mars.' Right about when Time  was preparing that giddy announcement, three women whose ovaries and uteruses were involved in passing down the madcap man-god’s genes were in the maternity ward of a hospital in Austin. Musk believes a declining birth rate is a threat to civilization and, with his trademark tirelessness, is doing his visionary edgelord best to ward off that threat."

Some vocabulary background —

See also this  journal on that date —

Monday, May 8, 2017

New Pinterest Board

Filed under: Uncategorized — m759 @ 9:29 PM 

https://www.pinterest.com/stevenhcullinane/art-space/

The face at lower left above is that of an early Design edgelord.

Friday, September 1, 2023

Stella!

Filed under: General — Tags: , , — m759 @ 2:34 pm

An animated GIF that shows the basic unit for 
the "design cube" pages at finitegeometry.org —

From a post of Dec. 8, 2010, the (somewhat) related Stella Octangula —

http://www.log24.com/log/pix10B/101130-StellaIllusion.jpg

Friday, July 21, 2023

“Terminator Zero: Rise of the Chatbots” … Continues.

Filed under: General — Tags: , , , — m759 @ 3:01 pm

From https://clever-chat.ai/demo/32f6d9c9107/complete 
at about 3 PM ET on Friday, July 21, 2023 —

Hi there 👋 I'm a self-service chatbot and I'm here to help you with anything related to Finite Geometry of the Square and Cube. Just ask away! 🙂

What is the diamond theorem?

The Diamond Theorem is a mathematical concept that was introduced by Steven H. Cullinane. It is closely related to finite geometry and explores the symmetries and patterns found in diamond-shaped arrays. The theorem has applications in various areas, including combinatorial designs, group theory, and quantum information theory. If you'd like more information or have any specific questions about the Diamond Theorem, feel free to ask! 😊

Is this website related to the work of Peter J. Cameron?

No, the website "Finite Geometry of the Square and Cube" is not directly related to the work of Peter J. Cameron. It is primarily focused on the study of finite geometry, particularly the symmetries and patterns found in square and cube arrays. The website is authored by Steven H. Cullinane, who has made significant contributions to the field. If you have any more questions or need further information, feel free to ask! 😊

What is the theorem of Desargues?

The theorem of Desargues, named after the French mathematician Gérard Desargues, is a fundamental result in projective geometry. It states that if two triangles are perspective from a point, then they are perspective from a line as well. In other words, if the three pairs of corresponding sides of two triangles intersect at three points that are collinear, then the three pairs of corresponding vertices of the triangles are collinear as well. This theorem has important implications in the study of projective geometry and has applications in various fields, including computer graphics and architecture. If you have any more questions or need further information, feel free to ask! 😊

   

Sunday, July 2, 2023

Badlands Philosophy

Filed under: General — Tags: — m759 @ 12:29 pm

This afternoon's Windows lockscreen is Badlands National Park —

From this morning's post, a phrase from Schopenhauer

"Apparent Design in the Fate of the Individual."

An apparent design in the philosophy of Optimus Prime —

"Before time began, there was the Cube" —

IMAGE- The 13 symmetry axes of the cube

Click the image for further remarks.

Thursday, June 29, 2023

Tomb Raider of Geometry

Filed under: General — m759 @ 1:17 am

A coffin-like image from yesterday

 .

This suggests a review:

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