Sunday, March 31, 2019

Self and Illusion

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

For Women's History Month


Self —


Illusion —

For some related remarks, see Aion in this  journal.

Saturday, March 30, 2019

Overlay Art

Filed under: General — Tags: — m759 @ 2:14 AM

"SH lays an array of selves, fictive and autobiographical,
over each other like transparencies, to reveal deeper patterns."

Benjamin Evans in The Guardian , Sunday, March 10, 2019,
in a review of the new Siri Hustvedt novel Memories of the Future.

See also Self-Blazon and . . .

Friday, March 29, 2019

The Blazon World*

Filed under: General — m759 @ 4:59 PM

“At that instant he saw, in one blaze of light,
an image of unutterable conviction,
the reason why the artist works and lives
and has his being — the reward he seeks —
the only reward he really cares about,
without which there is nothing. It is to snare
the spirits of mankind in nets of magic,
to make his life prevail through his creation,
to wreak the vision of his life, the rude and painful
substance of his own experience, into the congruence
of blazing and enchanted images that are themselves
the core of life, the essential pattern whence
all other things proceed, the kernel of eternity.”

— Thomas Wolfe, Of Time and the River

* Title suggested by that of a Siri Hustvedt novel.
   See also Blazon in this journal.

Front-Row Seed

Filed under: General — Tags: — m759 @ 4:17 PM

"This outer automorphism can be regarded as
the seed from which grow about half of the
sporadic simple groups…." — Noam Elkies

Closely related material —

The Kummer 16_6 Configuration and the Nordstrom-Robinson Code

The top two cells of the Curtis "heavy brick" are also
the key to the diamond-theorem correlation.

Thursday, March 28, 2019


Filed under: General,Geometry — Tags: , — m759 @ 9:35 PM

The previous post, "Dream of Plenitude," suggests . . .

The Kummer 16_6 Configuration and the Nordstrom-Robinson Code

"So here's to you, Nordstrom-Robinson . . . ."

Dream of Plenitude

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

"This time-defying preservation of selves,
this dream of plenitude without loss, is like
a snow globe from heaven, a vision of Eden
before the expulsion."

Judith Shulevitz on Siri Hustvedt in
The New York Times  online, March 26.

See also, in this  journal, the dream of Edenic plenitude 
in the March 20 post "Secret Characters."

Eight and Seven

Filed under: General — Tags: — m759 @ 8:56 AM

'Knight' octad labeling by the 8 points of the projective line over GF(7)    

Wednesday, March 27, 2019


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

"Don't want to end up a cartoon
In a cartoon graveyard" 
— Paul Simon

The Level of the Line

Filed under: General — m759 @ 12:18 PM

"And the songs were most perfect at the level of the line,
embodying the terse and clever brilliance that exists
in the best country music."

The New Yorker , Culture Desk
Postscript: Guy Clark, 1941-2016
By Ian Crouch, May 17, 2016

"To find me a bubble for the spirit level"

Seamus Heaney, 13 April 1939 – 30 August 2013

Tuesday, March 26, 2019


Filed under: General — m759 @ 5:25 PM

In lieu of an eternal blazon . . .

Posts now tagged Guy Clark Day.

(Clark reportedly died on Tuesday, May 17, 2016.)

"Them good old boys were drinking whiskey and rye…."
— Don McLean

Preparatory Cartoons

Filed under: General — m759 @ 1:03 PM

The online New York Times  this afternoon has an article on "the
preparatory cartoon for Raphael’s fresco 'The School of Athens.'" 

Other preparatory cartoons:

The first New Yorker  cover above is from a search for Hustvedt
in this  journal. See the 2003 post "Art at the Vanishing Point."

Monday, March 25, 2019

Clark’s Wake

Filed under: General — m759 @ 11:32 PM

In the online April 1, 2019,  New Yorker


Burying the Lede


"You lose some, you winsome."


(Continued from the previous post.)

In-Between "Spacing" and the "Chôra "
in Derrida: A Pre-Originary Medium?

By Louise Burchill

(Ch. 2 in Henk Oosterling & Ewa Plonowska Ziarek (Eds.),  Intermedialities: Philosophy, Arts, Politics , Lexington Books, October 14, 2010)

"The term 'spacing' ('espacement ') is absolutely central to Derrida's entire corpus, where it is indissociable from those of différance  (characterized, in the text from 1968 bearing this name, as '[at once] spacing [and] temporizing' 1), writing  (of which 'spacing' is said to be 'the fundamental property' 2) and deconstruction (with one of Derrida's last major texts, Le Toucher: Jean-Luc Nancy , specifying 'spacing ' to be 'the first word of any deconstruction' 3)."

1  Jacques Derrida, “La Différance,” in Marges – de la philosophie  (Paris: Minuit, 1972), p. 14. Henceforth cited as  D  .

2  Jacques Derrida, “Freud and the Scene of Writing,” trans. A. Bass, in Writing and  Difference  (Chicago: University of Chicago Press, 1978), p. 217. Henceforth cited as FSW .

3  Jacques Derrida, Le Toucher, Jean-Luc Nancy  (Paris: Galilée, 2000), p. 207.

. . . .

"… a particularly interesting point is made in this respect by the French philosopher, Michel Haar. After remarking that the force Derrida attributes to différance  consists simply of the series of its effects, and is, for this reason, 'an indefinite process of substitutions or permutations,' Haar specifies that, for this process to be something other than a simple 'actualisation' lacking any real power of effectivity, it would need “a soubassement porteur ' – let’s say a 'conducting underlay' or 'conducting medium' which would not, however, be an absolute base, nor an 'origin' or 'cause.' If then, as Haar concludes, différance  and spacing show themselves to belong to 'a pure Apollonism' 'haunted by the groundless ground,' which they lack and deprive themselves of,16 we can better understand both the threat posed by the 'figures' of space and the mother in the Timaeus  and, as a result, Derrida’s insistent attempts to disqualify them. So great, it would seem, is the menace to différance  that Derrida must, in a 'properly' apotropaic  gesture, ward off these 'figures' of an archaic, chthonic, spatial matrix in any and all ways possible…."

16  Michel Haar, “Le jeu de Nietzsche dans Derrida,” Revue philosophique de la France et de l’Etranger  2 (1990): 207-227.

. . . .

… "The conclusion to be drawn from Democritus' conception of rhuthmos , as well as from Plato's conception of the chôra , is not, therefore, as Derrida would have it, that a differential field understood as an originary site of inscription would 'produce' the spatiality of space but, on the contrary, that 'differentiation in general' depends upon a certain 'spatial milieu' – what Haar would name a 'groundless ground' – revealed as such to be an 'in-between' more 'originary' than the play of differences it in-forms. As such, this conclusion obviously extends beyond Derrida's conception of 'spacing,' encompassing contemporary philosophy's continual privileging of temporization in its elaboration of a pre-ontological 'opening' – or, shall we say, 'in-between.'

For permutations and a possible "groundless ground," see
the eightfold cube and group actions both on a set of eight
building blocks arranged in a cube (a "conducting base") and
on the set of seven natural interstices (espacements )  between
the blocks. Such group actions provide an elementary picture of
the isomorphism between the groups PSL(2,7) (acting on the
eight blocks) and GL(3,2) (acting on the seven interstices).


For the Church of Synchronology

See also, from the reported publication date of the above book
Intermedialities , the Log24 post Synchronicity.

Sunday, March 24, 2019

Espacement: Geometry of the Interstice in Literary Theory

Filed under: General — Tags: , , , , — m759 @ 3:28 AM

"You said something about the significance of spaces between
elements being repeated. Not only the element itself being repeated,
but the space between. I'm very interested in the space between.
That is where we come together." — Peter Eisenman, 1982


Parrhesia  No. 3 • 2007 • 22–32

(Up) Against the (In) Between: Interstitial Spatiality
in Genet and Derrida

by Clare Blackburne

Blackburne — www.parrhesiajournal.org 24 —

"The excessive notion of espacement  as the resurgent spatiality of that which is supposedly ‘without space’ (most notably, writing), alerts us to the highly dynamic nature of the interstice – a movement whose discontinuous and ‘aberrant’ nature requires further analysis."

Blackburne — www.parrhesiajournal.org 25 —

"Espacement  also evokes the ambiguous figure of the interstice, and is related to the equally complex derridean notions of chora , différance , the trace and the supplement. Derrida’s reading of the Platonic chora  in Chora L Works  (a series of discussions with the architect Peter Eisenman) as something which defies the logics of non-contradiction and binarity, implies the internal heterogeneity and instability of all structures, neither ‘sensible’ nor ‘intelligible’ but a third genus which escapes conceptual capture.25 Crucially, chora , spacing, dissemination and différance  are highly dynamic concepts, involving hybridity, an ongoing ‘corruption’ of categories, and a ‘bastard reasoning.’26 Derrida identification of différance  in Margins of  Philosophy , as an ‘unappropriable excess’ that operates through spacing as ‘the becoming-space of time or the becoming-time of space,’27 chimes with his description of chora  as an ‘unidentifiable excess’ that is ‘the spacing which is the condition for everything to take place,’ opening up the interval as the plurivocity of writing in defiance of ‘origin’ and ‘essence.’28  In this unfolding of différance , spacing  ‘insinuates  into  presence an  interval,’29 again alerting us to the crucial role of the interstice in deconstruction, and, as Derrida observes  in Positions ,  its  impact  as  ‘a movement,  a  displacement  that  indicates  an  irreducible alterity’: ‘Spacing is the impossibility for an identity to be closed on itself, on the inside of its proper interiority, or on its coincidence with itself. The irreducibility of spacing is the irreducibility of the other.’30"

25. Quoted in Jeffrey Kipnis and Thomas Leeser, eds., 
Chora L Works. Jacques Derrida and Peter Eisenman  
(New York: The Monacelli Press, 1997), 15.

26. Ibid, 25.

27. Derrida, Margins of Philosophy.
(Brighton: The Harvester Press, 1982), 6 and 13.

28. Derrida, Chora L Works , 19 and 10.

29. Ibid, 203.

30. Derrida, Positions , 94.

Saturday, March 23, 2019

Plan 9 Manifesto

Filed under: General — Tags: — m759 @ 7:11 PM

"Arnheim was a particularly important source
for Norway's principal architectural theorist,
Christian Norberg-Schulz."

— Andrew Peter Steen, University of Queensland
doctoral thesis, 2015


"Nine is a very powerful Nordic number."

— Katherine Neville, The Magic Circle

Another Typology

Filed under: General — Tags: , , — m759 @ 11:04 AM

"You said something about the significance of spaces between
elements being repeated. Not only the element itself being repeated,
but the space between. I'm very interested in the space between.
That is where we come together." — Peter Eisenman, 1982

Friday, March 22, 2019

Page Number

Filed under: General — m759 @ 11:10 PM

"A version of this article appears in print on ,
on Page 132 of T Magazine with the headline: Bodies in Motion."

See as well page 132 of the Queensland thesis pictured here yesterday
in light of the 2017 Page film "Flatliners." 

Architectural Theory

Filed under: General — Tags: — m759 @ 10:20 PM

For the late Robert Venturi, who reportedly died on Tuesday, Sept. 18, 2018.

See also The Venturi Manifesto (Log24, Sept. 22, 2018).

Charles Jencks’s Grand Unified Theory

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

"The stars and galaxies seem static, eternal, or moving slowly
in deterministic patterns, becoming the background stage
on which we move. But if we could speed up the sequence,
we would see how dramatic and unpredictable this background
really is — an actor, director, script and stage all at once.
Moreover, it is a unified universe, a single unfolding event
of which we are an embedded part, a narrative of highly
dangerous and fine-tuned events, something more like
a detective thriller with many crimes and last-minute escapes
than the impersonal account of astronomy textbooks.
We are only just beginning to decipher the plot and figure out
the Cosmic Code, as Heinz Pagels puts it."

— Charles Jencks, The Architecture of the Jumping Universe :
A Polemic
  (How Complexity Science is Changing Architecture
and Culture), Academy Editions, 1995, rev. ed. 1997

"A Grand Unified Theory (GUT) is a model in particle physics…."

"Under the GUT symmetry operation these field components
transform into one another. The reason quantum particles 
appear to have different properties in nature is that the unifying
symmetry is broken. The various gluons, quarks and leptons
are analogous to the facets of a cut diamond, which appear
differently according to the way the diamond is held but in
fact are all manifestations of the same underlying object."

— Heinz Pagels, Perfect Symmetry , Bantam paperback, 1986, p. 284

See also the recent post Multifaceted Narrative.

Thursday, March 21, 2019

Geometry of Interstices

Filed under: General — Tags: , , , — m759 @ 10:18 PM

Finite Galois geometry with the underlying field the simplest one possible —
namely, the two-element field GF(2) — is a geometry of  interstices :

For some less precise remarks, see the tags Interstice and Interality.

The rationalist motto "sincerity, order, logic and clarity" was quoted
by Charles Jencks in the previous post.

This  post was suggested by some remarks from Queensland that
seem to exemplify these qualities —


Filed under: General — Tags: , — m759 @ 2:46 PM

See also Eupalinos  in this journal.

Wednesday, March 20, 2019

Secret Characters

Filed under: General — Tags: , , , , — m759 @ 2:23 PM

"Cell 461" quote from Curzio Malaparte superimposed on a scene from
the 1963 Godard film "Le Mépris " ("Contempt") —

"The architecture… beomes closely linked to the script…."

Malaparte's cell number , 461, is somewhat less closely  linked
to the phrase "eternal blazon" —

Irving was quoted here on Dec. 22, 2008

The Tale of
the Eternal Blazon

by Washington Irving

Blazon  meant originally a shield , and then
the heraldic bearings on a shield .
Later it was applied to the art of describing
or depicting heraldic bearings in the proper
manner; and finally the term came to signify 
ostentatious display  and also description or
record by words or other means 
. In Hamlet ,
Act I Sc. 5, the Ghost, while talking with
Prince Hamlet, says:

‘But this eternal blazon must not be
To ears of flesh and blood.’

Eternal blazon  signifies revelation or description
of things pertaining to eternity 

— Irving’s Sketch Book , p. 461

Update of 6:25 PM ET —

"Self-Blazon of Edenic Plenitude"

(The Issuu text is taken from Speaking about Godard , by Kaja Silverman
and Harun Farocki, New York University Press, 1998, page 34.)

Tuesday, March 19, 2019

Architectural Note

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

Casa Malaparte, also known as Villa Malaparte —

Related film image with architectural quotation superimposed —

'Sincerity, order, logic and clarity above all' — Italian rationalist architecture philosophy.

Related art prose —

Composed in Light

Filed under: General — m759 @ 2:13 PM

"Composed in light of both Hiroshima and
Einstein’s general theory of relativity,
Dali’s crucifixion . . . ."

— "The Crucified God: A Death in Pictures,"
by Ed Simon, April 11, 2017, 

See as well Log24,  The Relativity Problem at Hiroshima  (Dec. 3, 2018).

Related material —

Monday, March 18, 2019

“Iacta Est” Continues.

Filed under: General — Tags: — m759 @ 11:16 AM

Update of 4:36 PM ET from The Wall Street Journal


"You, Misirlou, are a dream of delight in the night.

To an oasis, sprinkled by stars above,
Heaven will guide us, Allah will bless our love."

Pulp Fictions

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

The rest of the post "Sermon" referred to in yesterday's
St. Patrick's Day post "Just Another Block in the Wall" —

Sunday, March 17, 2019

Another Lying Rhyme…

Filed under: General — Tags: — m759 @ 11:29 PM

For Tom Stoppard, author of "Jumpers"

"Seven is Heaven" 

          From a webpage of Bill Cherowitzo

" … the Fano plane ,
a set of seven points
grouped into seven lines
that has been called
'the combinatorialist’s coat of arms.' "

— Blake Stacey in a March 14 post 


Filed under: General — m759 @ 4:02 PM

"Watch the trailer." — This journal on Eliza Doolittle Day, 2012.

Carol and Thor... 'easily the best part' in 'Avengers: Endgame' trailer

Midrash — March 14 remarks on geometry from Christchurch, New Zealand

Just Another Block in the Wall

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

Yesterday's post Grundlagen  —

Midrash on yesterday's Grundlagen

A poem linked to here on the above "building blocks" date, in the
Log24 post Sermon of  11 AM ET Sunday, 15 September 2013 —

Saturday, March 16, 2019

Multifaceted Narrative

Filed under: General — Tags: , — m759 @ 2:40 PM

"Here, modernism is defined as an autonomous body
of ideas, having little or no outward reference, placing
considerable emphasis on formal aspects of the work
and maintaining a complicated—indeed, anxious—
rather than a naïve relationship with the day-to-day
world, which is the de facto view of a coherent group
of people, such as a professional or discipline-based
group that has a high sense of the seriousness and
value of what it is trying to achieve. This brisk definition…."

— Jeremy Gray, Plato's Ghost: The Modernist
Transformation of Mathematics
 , Princeton, 2008 

"Even as the dominant modernist narrative was being written,
there were art historians who recognized that it was inaccurate.
The narrative was too focused on France . . . . Nor was it
correct to build the narrative so exclusively around formalism;
modernism was far messier, far more multifaceted than that."

— Jane Kallir, https://www.tabletmag.com/

quoted here on the above date — Sept. 11, 2018.

From some related Log24 posts


Filed under: General — Tags: , , , — m759 @ 12:25 PM

See also eightfold cube.

Friday, March 15, 2019

Nailing Down the Words †

Filed under: General — Tags: — m759 @ 10:40 PM

From a belated New York Times  obituary this evening —

"Ms. Iglauer died on Feb. 13 at a hospital
in Sechelt, British Columbia. She was 101."
[Link added.]

See also the previous two posts.


Filed under: General — Tags: — m759 @ 9:57 PM

out of the horn of dreams of my own life
I wake again into the laughing child

W. S. Merwin


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

The poet W. S. Merwin reportedly died  today.

“Punctuation basically has to do with prose
and the printed word,” he said in the Paris Review
interview. “I came to feel that punctuation was like
nailing the words onto the page. Since I wanted
instead the movement and lightness of the spoken
word, one step toward that was to do away with

— Margalit Fox in The New York Times

See as well Snakes (on a plane) in this  journal.

'Snakes on a Plane' cartoon

Trinity vs. Illuminati

Filed under: General — m759 @ 2:08 PM

Trinity Song —

"For ten years we've been on our own . . . ."

See as well a post of ten years ago:  Angels, Demons, "Symbology"

Illuminati Song —

"Far from the shallow now."


Filed under: General — Tags: , — m759 @ 1:30 PM

See also this  journal on the "Illuminati Tinder" date, June 27, 2018.

Related material — Posts tagged QDOS.

The Breach Report

Filed under: General — m759 @ 12:20 PM

See also two notes of my own, from Nov. 5 and Dec. 24, 1981.

Thursday, March 14, 2019


Filed under: General — Tags: , , , — m759 @ 9:32 PM

Jude Law and a image from a 2013 film
by Lars von Trier starring Stacy Martin:

'You know my methods' image

Habeas Obelisk †

Filed under: General — Tags: — m759 @ 10:04 AM

Axioms vs. constructions in finite geometry

† From a search for obelisk  in this journal.

Wednesday, March 13, 2019

The Origin of Change . . .

Filed under: General — m759 @ 10:00 PM

According to Wallace Stevens:

From Savage Logic

Sunday, March 15, 2009  5:24 PM

The Origin of Change

A note on the figure
from this morning's sermon:

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

"Two things of opposite natures seem to depend
On one another, as a man depends 
On a woman, day on night, the imagined 
On the real. This is the origin of change. 
Winter and spring, cold copulars, embrace 
And forth the particulars of rapture come."

— Wallace Stevens,   
"Notes Toward a Supreme Fiction,"
Canto IV of "It Must Change"

This  post was suggested by the following passage —

" the Fano plane ,
a set of seven points
grouped into seven lines
that has been called
'the combinatorialist’s coat of arms.' "

— Blake Stacey in a post with tomorrow's date:

and by Stacey at another weblog, in a post dated Jan. 29, 2019, 

"(Yes, Bohr was the kind of guy who would choose
the yin-yang symbol as his coat of arms.)"

Yes, Stacey is the kind of guy who would casually dismiss
Bohr's coat of arms. 

Related material — 

(See also Faust in Copenhagen in this  journal)—

» more

Never Say Neverland

Filed under: General — m759 @ 2:02 PM

For Melbourne's Cardinal Pell —

Tuesday, March 12, 2019

In Memoriam

Filed under: General — m759 @ 3:44 PM

The author of the article below reportedly died today.

Back to the Annus Mirabilis, 1905

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

Monday, March 11, 2019


Filed under: General — m759 @ 10:42 PM

An earlier post discussed other meanings for the commercial brand names
underlined above, but the brand name "Attribution" was omitted from that
earlier discussion.

Hence . . .

Attribution by Foursquare — 'Quantify the impact media has....'

Related material — The unattributed phrase "Concepts of Space"
in the previous post

Attribution — The phrase was from the title of a book by Max Jammer.

A search in this journal for Jammer yields posts now tagged . . .

Page Space

(See an example.)


Ant-Man Meets Doctor Strange

Filed under: General — m759 @ 1:22 PM

IMAGE- Concepts of Space

The 4×4 square may also be called the Galois Tesseract .
By analogy, the 4x4x4 cube may be called the Galois Hexeract .

"Think outside the tesseract.

Overarching Metanarratives

Filed under: General — m759 @ 4:15 AM

See also "Overarching + Tesseract" in this  journal. From the results
of that search, some context for the "inscape" of the previous post —

Anticommuting Dirac matrices as spreads of projective lines

Ron Shaw on the 15 lines of the classical generalized quadrangle W(2), a general linear complex in PG(3,2)

Sunday, March 10, 2019

Vocabulary for SXSW:

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

Foursquare, Inscape, Subway 

Foursquare —

Inscape —

Subway —

Art installation, "Crystal Cult" by Josefine Lyche, at an Oslo subway station —

See also today's previous post.


Filed under: General — Tags: — m759 @ 12:08 PM

Related material —

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

Nietzsche on Heraclitus— 'play in necessity' and 'law in becoming'— illustrated.

Saturday, March 9, 2019

Weapons of Mass Distraction

Filed under: General — Tags: — m759 @ 12:46 PM

"Back to the Future" and . . .

I prefer another presentation from the above 
Universal Pictures date — June 28, 2018 —


Space Man from Plato


The Hiroshima Model

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

Commemorating a talk given by Iain Aitchison
at Hiroshima a year ago today.

Friday, March 8, 2019


Filed under: General — m759 @ 1:04 PM

Photo Opportunity

Filed under: General — Tags: — m759 @ 12:30 PM

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

A Logo for Sheinberg

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

Thursday, March 7, 2019

In Reality

Filed under: General — m759 @ 11:45 AM

The previous post, quoting a characterization of the R. T. Curtis
Miracle Octad Generator , describes it as a "hand calculator ."

Other views 

A "natural diagram " —


A geometric object

Counting symmetries with the orbit-stabilizer theorem.

Wednesday, March 6, 2019

A Hand Calculator

Filed under: General — m759 @ 10:28 PM

More Things Considered

Filed under: General — m759 @ 2:56 PM

"And in this he showed me something small,
no bigger than a hazelnut,
lying in the palm of my hand,
and I perceived that it was round as any ball.
I looked at it and thought:  What can this be?
And I was given this general answer:
It is everything which is made. I was amazed
that it could last, for I thought that it was so little
that it could suddenly fall into nothing."

Julian of Norwich

The Relativity Problem and Burkard Polster

Filed under: General,Geometry — Tags: — m759 @ 11:28 AM

From some 1949 remarks of Weyl—

"The relativity problem is one of central significance throughout geometry and algebra and has been recognized as such by the mathematicians at an early time."

— Hermann Weyl, "Relativity Theory as a Stimulus in Mathematical Research," Proceedings of the American Philosophical Society , Vol. 93, No. 7, Theory of Relativity in Contemporary Science: Papers Read at the Celebration of the Seventieth Birthday of Professor Albert Einstein in Princeton, March 19, 1949  (Dec. 30, 1949), pp. 535-541

Weyl in 1946—:

"This is the relativity problem: to fix objectively a class of equivalent coordinatizations and to ascertain the group of transformations S mediating between them."

— Hermann Weyl, The Classical Groups , Princeton University Press, 1946, p. 16

For some context, see Relativity Problem  in this journal.

In the case of PG(3,2), there is a choice of geometric models 
to be coordinatized: two such models are the traditional
tetrahedral model long promoted by Burkard Polster, and
the square model of Steven H. Cullinane.

The above Wikipedia section tacitly (and unfairly) assumes that
the model being coordinatized is the tetrahedral model. For
coordinatization of the square model, see (for instance) the webpage
Finite Relativity.

For comparison of the two models, see a figure posted here on
May 21, 2014 —

Labeling the Tetrahedral Model  (Click to enlarge) —

"Citation needed" —

The anonymous characters who often update the PG(3,2) Wikipedia article
probably would not consider my post of 2014, titled "The Tetrahedral
Model of PG(3,2)
," a "reliable source."

Tuesday, March 5, 2019

The Eightfold Cube and PSL(2,7)

Filed under: General,Geometry — Tags: , , — m759 @ 10:45 PM

For PSL(2,7), this is ((49-1)(49-7))/((7-1)(2))=168.

The group GL(3,2), also of order 168, acts naturally
on the set of seven cube-slicings below —

Another way to picture the seven natural slicings —

Application of the above images to picturing the
isomorphism of PSL(2,7) with GL(3,2) —

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

For a more detailed proof, see . . .

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

Monday, March 4, 2019

Variations on a Theme

Filed under: General — m759 @ 11:11 PM

Found on the Web today —

In a Google search:

At Instagram:

Davos Logos

Filed under: General — Tags: — m759 @ 9:57 PM

A less sophisticated approach to logos —

See also Logos in this  journal.

For those who prefer Latin, there is Verbum.

Sunday, March 3, 2019

In Memoriam

Filed under: General — m759 @ 2:10 PM

"…the legitimate role of religion…."

And of architecture —


Filed under: General — m759 @ 1:00 PM

See as well this  journal on the above date — May 1, 2013 —
within a search for Law+Day+Harvard+Oprah+Uma.

I, like Freeman Dyson, prefer the fiction of Octavia Butler.

Screen Icons:

Filed under: General — m759 @ 10:55 AM

Images That Work  —

Update of 11:29 AM:  See also Icon Parking.

Requiem for an Architect

Filed under: General — m759 @ 1:21 AM

A story from the NY Times  Sunday morning print edition —

"A version of this article appears in print on ,
on Page A1 of the New York edition with the headline: 

Kevin Roche, 96, Is Dead; Famed Modernist Architect."

" When Mr. Roche received the Pritzker in 1982, he delivered
an acceptance speech that displayed both his capacity for
self-deprecating humor and his belief that architecture was
a noble pursuit. He quoted from a letter he had received
complaining that his work was 'moribund' and that the Pritzker
jury 'must be out of their minds' to have given him the prize.

He could only respond, he said, by asking: 'Is not the act of building
an act of faith in the future, and of hope? Hope that the testimony of
our civilization will be passed on to others, hope that what we are doing
is not only sane and useful and beautiful, but a clear and true reflection
of our own aspirations. And hope that it is an art, which will communicate
with the future and touch those generations as we ourselves have been
touched and moved by the past.' "

— Paul Goldberger

Goldberger on Roche's earlier career —

". . . He continued to finish projects Saarinen had started, including
the IBM Pavilion at the 1964 New York World’s Fair, designed
in collaboration with Charles Eames . . . ."

Illustration —

The IBM Pavilion at the 1964 World's Fair

See also the film "Tomorrowland."

"Bad news on the doorstep…." — American Pie

Saturday, March 2, 2019

Angels in Acapulco

Filed under: General — m759 @ 11:32 PM


Fashion Story

Filed under: General — m759 @ 10:47 PM

A death last Sunday —

Meanwhile . . .

Amy Adams attends the 2019 Vanity Fair Oscar Party 
at Wallis Annenberg Center for the Performing Arts on
Sunday, February 24, 2019, in Beverly Hills, California.

"Here was finality indeed, and cleavage!

             — Under the Volcano

Romancing the Heterojunction

Filed under: General — m759 @ 1:20 PM

(The date "September 25, 2002" in the opening of the Alferov video above
may or may not be correct. It will suffice for the Church of Synchronology.)

Schoolgirls for Galois

Filed under: General — m759 @ 12:09 PM

"My God, it's
full of numbers!"

Wikipedia Scholarship (Continued):

Filed under: General — Tags: , — m759 @ 11:21 AM

Ignotum per Ignotius

A Log24 post from yesterday afternoon has the following —

Commentary —

Friday, March 1, 2019

Wikipedia Scholarship (Continued)

Filed under: General — Tags: , , — m759 @ 12:45 PM

This post continues a post from yesterday on the square model of
PG(3,2) that apparently first appeared (presented as such*) in . . .

Cullinane, "Symmetry invariance in a diamond ring,"
Notices of the AMS , pp. A193-194, Feb. 1979.

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

Yesterday's Wikipedia presentation of the square model was today
revised by yet another anonymous author —

Revision history accounting for the above change from yesterday —

The jargon "rm OR" means "remove original research."

The added verbiage about block designs is a smokescreen having
nothing to do with the subject, which is square  representation
of the 35 points and lines.

* The 35 squares, each consisting of four 4-element subsets, appeared earlier
   in the Miracle Octad Generator (MOG) of R. T. Curtis (published in 1976).
  They were not at that time  presented as constituting a finite geometry, 
  either affine (AG(4,2)) or projective (PG(3,2)).

Solomon and the Image

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

"Maybe an image is too strong
Or maybe is not strong enough."

— "Solomon and the Witch,"
      by William Butler Yeats

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