Sunday, September 30, 2018


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

Click the above for an example.

Iconology of the Eightfold Cube

Filed under: General,Geometry — Tags: , — m759 @ 11:13 AM

Found today in an Internet image search, from the website of
an anonymous amateur mathematics enthusiast

Forming Gray codes in the eightfold cube with the eight
I Ching  trigrams (bagua ) —

Forming Gray codes in the eightfold cube with the eight I Ching trigrams (bagua)

This  journal on Nov. 7, 2016

A different sort of cube, from the makers of the recent
Netflix miniseries "Maniac" —

See also Rubik in this  journal.

Saturday, September 29, 2018

“Ikonologie des Zwischenraums”

Filed under: G-Notes,General,Geometry — Tags: , , — m759 @ 9:29 AM

The title is from Warburg. The Zwischenraum  lines and shaded "cuts"
below are to be added together in characteristic two, i.e., via the
set-theoretic symmetric difference  operator.

Some small Galois spaces (the Cullinane models)

Friday, September 28, 2018


Filed under: General — m759 @ 4:48 PM

ART WARS Midrash

Filed under: General — m759 @ 9:00 AM

"When times are mysterious
Serious numbers
Will always be heard."
— Paul Simon,
"When Numbers Get Serious"

"There is a pleasantly discursive treatment of
Pontius Pilate's unanswered question 'What is truth?'"

— H. S. M. Coxeter, introduction to Richard J. Trudeau's remarks
on the "story theory" of truth as opposed to the "diamond theory"
of truth in The Non-Euclidean Revolution  (1987)

The deaths of Roth and Grünbaum on September 14th,
The Feast of the Holy Cross, along with Douthat's column
today titled "Only the Truth Can Save Us Now," suggest a
review of

Elements of Number Theory, by Vinogradov .

Thursday, September 27, 2018

Branko Grünbaum, 1929-2018

Filed under: General — m759 @ 7:59 PM

See an American Mathematical Society obituary
and a Seattle Times  obituary.

Cube Meditation

Filed under: General — Tags: — m759 @ 1:12 PM

See also "Eternal Recreation" (Christmas Eve, 2012).

Wednesday, September 26, 2018

Analogies Between Analogies

Filed under: General — m759 @ 8:05 PM

On the new Netflix series "Maniac" —

(Spoiler alert)

"The treatment Owen and Annie sign up for promises to fix
its subjects’ brains with just three little pills—A, B, and C—
administered one after another over the span of three days.
The first forces you to relive your trauma;
the second exposes your blind spots; and
the third pill forces a confrontation."

— Kara Weisenstein at vice.com, Sept. 26, 2018, 12:19 PM

See also, from Log24 earlier 

A.  Monday — Mathematics as Art
B.  Tuesday — Trinity and Denkraum  Revisited
C.  Wednesday — Trinity Tale

'Out of nothing' opening of 'Maniac' at Netflix

Trinity Tale

Filed under: General — m759 @ 11:34 AM

For Flowers and  Brown —

See also, in this  journal, A Fellow of Trinity . 

Tuesday, September 25, 2018

Denkraum Revisited

Filed under: General — m759 @ 6:00 PM

See also this  journal on Sept. 14
and related posts tagged Interstice.


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

See some posts related to three names
associated with Trinity College, Cambridge —

Atiyah + Shaw + Eddington .

Monday, September 24, 2018

Mathematics as Art

Filed under: General — m759 @ 8:45 AM

[Revised throughout the day on Sept. 24, 2018.]

"Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to explain
how art fits into our subject and what we mean by beauty."

— Sir Michael Atiyah, quoted here on April 4, 2016

Atiyah's remarks today on the Riemann hypothesis, based on his earlier
remarks on "arithmetic physics" and α, the fine-structure constant,
seem to exemplify the "magic and mystery" approach.

From some previous Log24 posts

AMS on 'mathematics, magic, and mystery,' April 2014

MAA on 'mathematics, magic, and mystery,' April 2014

Update of 6:06 PM ET the same day —


For related magic and mystery, see Log24 posts tagged on090405.

Sunday, September 23, 2018

Three Times Eight

Filed under: General,Geometry — Tags: — m759 @ 9:21 AM

The New York Times 's Sunday School today —

I prefer the three bricks of the Miracle Octad Generator —

Image result for mog miracle octad bricks

Saturday, September 22, 2018

Minimalist Configuration

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 11:03 PM

From the previous post

From Wikipedia

From Log24

The Venturi Manifesto

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 1:00 PM

Venturi reportedly died on Tuesday, September 18.*

See also this journal on that date.

* Fact check:

Symmetric Generation, by Curtis

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 10:15 AM

Norwegian artist Josefine Lyche —

Lyche's shirt honors the late Kurt Cobain.

"Here we are now, entertain us."

Symmetric Generation, by Netflix

Filed under: General — Tags: , — m759 @ 5:05 AM

Suggested by the previous post . . .

'Out of nothing' opening of 'Maniac' at Netflix

"The pattern is the pattern."

Friday, September 21, 2018

Symmetric Generation, by Nao

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

"The creation of a new world
        starts now.
Once again I am tied
        to the logic of this

Bill Murray and Scarlett Johansson in 'Lost in Translation'


Filed under: G-Notes,General,Geometry — Tags: — m759 @ 4:36 AM

Thursday, September 20, 2018

Clash of the Titans

Filed under: General — Tags: , — m759 @ 6:18 PM

1971 Mystery Box

Filed under: General — m759 @ 8:15 AM

Vincent Canby in The New York Times 
January 28, 1971, reviews the film "The Statue" —

There is not much point in going into the dialogue,
but you'll get the idea from the line spoken by
a little girl who is shown gazing in wonderment
at the copy of Michelangelo's work in the
Piazza della Signoria in Florence.
"Golly," she says, "if that's David, I'd like to see Goliath!"
"The Statue" may have the distinction of being the first
adolescent comedy about penis envy. 

In keeping with filmmaker J.J. Abrams's philosophy of the "mystery box"

Canby's phrase "you'll get the idea" suggests a Log24 review . . .


Wednesday, September 19, 2018

Speaking of Strange Tales …

Filed under: General — Tags: — m759 @ 9:33 AM


In Memoriam:

Filed under: General — Tags: — m759 @ 8:49 AM

Denis Mostyn Norden, writer, broadcaster and television presenter,
born 6 February 1922; died 19 September 2018.



For Abraham Warburg —


"Que cantaba el Rey David."


Filed under: General — Tags: — m759 @ 6:45 AM


See also Watchmen in this journal.

Tuesday, September 18, 2018

Death Day

Filed under: General — Tags: , — m759 @ 11:20 PM

"Birthday, death-day — what day is not both?" — Updike




Monday, September 17, 2018

For Wakanda

Filed under: General — m759 @ 9:00 PM


The 123 Configurations

Filed under: General,Geometry — m759 @ 8:35 AM



Lying at the Axis

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

Or:  Zero Dark Zero

" Lying at the axis of everything, zero is both real and imaginary. Lovelace was fascinated by zero; as was Gottfried Leibniz, for whom, like mathematics itself, it had a spiritual dimension. It was this that let him to imagine the binary numbers that now lie at the heart of computers: 'the creation of all things out of nothing through God's omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing.' He also wrote, 'The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and nonbeing.' "

— A footnote from page 229 of Sydney Padua's
    April 21, 2015, book on Lovelace and Babbage

Sunday, September 16, 2018


Filed under: General — m759 @ 11:05 PM
<h1 id="top">
Bacow Heads to Home State of Michigan 
In Quest to Fix Harvard’s Image Problem

<div class="article-byline" style="display: none;">
By <a href='/writer/1213317/Kristine_E._Guillaume/'>
Kristine E. Guillaume</a> 
and <a href='/writer/1213264/Jamie_D._Halper/'>
Jamie D. Halper</a>, 
Crimson Staff Writers

<time class="article-date"
   title="Updated September 16, 2018 at 11:04p.m.">
   September 16, 2018

Husserl for Beginners

Filed under: General — m759 @ 10:31 PM


See also Trivial + Affine and Eidetic Reduction.

Frames Per Second

Filed under: General — m759 @ 12:00 AM

See the previous post and "Frames Per Second."

Saturday, September 15, 2018

Sick Framing

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


Satire on Saturday Night

Filed under: General — Tags: — m759 @ 10:00 PM


See as well some other  remarks from March 28, 2014.

Ig Nobel “One Plus One”

Filed under: General — Tags: — m759 @ 1:42 PM


Jean-Luc Godard in this journal on Thursday

"I perceived . . . cinema is that which is between things,
not things [themselves] but between one and another."

Also on Thursday —

"Scientific luminaries gathered at Harvard University’s
historic Sanders Theatre  on Thursday to honor
notable achievements this year…. It was the
28th First Annual Ig Nobel Prize Ceremony …."



Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 9:50 AM

Tieszen— 'Kurt Godel and Phenomenology' — 1992

Update of 10:18 AM the same day —

See also Logicomix  in this  journal and, at Harvard,


  • September 6, 2018:  Eric Maskin, Amartya Sen and I
    are giving a course this semester: 'Axiomatic Reasoning'
    (PHIL 273B). Introduction to Axiomatic Reasoning gives a
    general sense of what we intend to cover.

Update of 10:48 AM the same day —


See Log24 on the date of Tieszen's death.

Eidetic Reduction in Geometry

Filed under: G-Notes,General,Geometry — Tags: , , , — m759 @ 1:23 AM

"Husserl is not the greatest philosopher of all times.
He is the greatest philosopher since Leibniz."

Kurt Gödel as quoted by Gian-Carlo Rota

Some results from a Google search —

Eidetic reduction | philosophy | Britannica.com

Eidetic reduction, in phenomenology, a method by which the philosopher moves from the consciousness of individual and concrete objects to the transempirical realm of pure essences and thus achieves an intuition of the eidos (Greek: “shape”) of a thing—i.e., of what it is in its invariable and essential structure, apart …

Phenomenology Online » Eidetic Reduction

The eidetic reduction: eidos. Method: Bracket all incidental meaning and ask: what are some of the possible invariate aspects of this experience? The research …

Eidetic reduction – New World Encyclopedia

Sep 19, 2017 – Eidetic reduction is a technique in Husserlian phenomenology, used to identify the essential components of the given phenomenon or experience.

Terminology: Eidos

For example —

The reduction of two-colorings and four-colorings of a square or cubic
array of subsquares or subcubes to lines, sets of lines, cuts, or sets of
cuts between the subsquares or subcubes.

See the diamond theorem and the eightfold cube.

* Cf. posts tagged Interality and Interstice.

Friday, September 14, 2018

Warburg at Cornell, Continued

Filed under: General — Tags: — m759 @ 9:29 AM

Warburg at Cornell U. Press

See also Epiphany 2017 —


Filed under: G-Notes,General,Geometry — Tags: — m759 @ 1:00 AM


I Ching Geometry search result

Underlying the I Ching  structure  is the finite affine space
of six dimensions over the Galois field with two elements.

In this field,  "1 + 1 = 0,"  as noted here Wednesday.

See also other posts now tagged  Interstice.


Thursday, September 13, 2018

Iconology of the Interstice

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 6:25 AM

The title is from the 2013 paper by Latsis in the previous post.


The symmetries of the interstices at right underlie
the symmetries of the images at left.

Godard and Interality

Filed under: General,Geometry — Tags: , — m759 @ 12:14 AM

The previous post, "One Plus One," suggests some further
art-historical remarks on interality

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. 775

My discussion will focus on the significance of the concept of the ‘space in-between,’ its importance for Godard’s work and its role in a relational historiography of images more broadly. I hope to corroborate how Godard functions as a twenty-first century archaeologist of the moving image, constructing a meta-cinematic collage that, while consisting of an indexing of (almost exclusively) pre-existing filmic samples, ends up becoming a hybrid work of art in its own right. Godard, in the final analysis, expands the Warburgian programme of iconology into that of a cinematographic iconology of the interstice.

* * * * 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

* * * * P. 783 —

If it is in ‘the in-between’ that thought is born, then for Godard cinematography as ‘a form that thinks  . . . was born with the advent of modern painting.’ [62]

62. Godard and Ishaghpour, op. cit., pp 45–46.

* * * * P. 785

Warburg commented on the signification of the black spaces that he placed between images in his analysis of the network of intervals in  Mnemosyne , by quoting Johann Wolfgang Goethe’s dictum ‘the truth inhabits the middle space.’ [68] This citation induces a feeling of déjà-vu for the viewer of Histoire(s). The link was not missed by Warburg himself, as one of his diary entries testifies: ‘We can compare this phenomenon [the iconology of the interval] to that of the cinematic montage, the domain of the interpretation is an intervallic one.’  [69]

68. Warburg,  Mnemosyne , pp 135–146.

69. Warburg is quoted in Didi-Huberman, L’image survivante, p. 503. (Georges Didi-Huberman, L’image survivante. Histoire de l’art et temps des fantômes selon Aby Warburg , Minuit, Paris, 2002)

Wednesday, September 12, 2018

One Plus One

Filed under: General — Tags: — m759 @ 11:10 AM




Tuesday, September 11, 2018

Art-Historical Narrative

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

Art history from Galerie St. Etienne

Summer Solstice Notes

By Fritz Leiber

Filed under: General — m759 @ 6:00 AM

Spider and Snake on cover of Fritz Leiber's novel Big Time

Anthony Hopkins at Dolly's Little Diner in Slipstream

Sir Anthony Hopkins in "Slipstream." See "Home from Home."

Monday, September 10, 2018

Big Time

Filed under: General — m759 @ 11:48 PM



Your OS

Filed under: General — m759 @ 3:33 AM


"Alan Watts wrote of The Making of a Counter Culture  in the San Francisco Chronicle  in 1969, 'If you want to know what is happening among your intelligent and mysteriously rebellious children, this is the book. The generation gap, the student uproar, the New Left, the beats and hippies, the psychedelic movement, rock music, the revival of occultism and mysticism, the protest against our involvement in Vietnam, and the seemingly odd reluctance of the young to buy the affluent technological society—all these matters are here discussed, with sympathy and constructive criticism, by a most articulate, wise, and humane historian.' "

The University of California Press

"Please wait as your operating system is initiated."


Sunday, September 9, 2018

Plan 9 Continues.

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 9:00 AM

"The role of Desargues's theorem was not understood until
the Desargues configuration was discovered. For example,
the fundamental role of Desargues's theorem in the coordinatization
of synthetic projective geometry can only be understood in the light
of the Desargues configuration.

Thus, even as simple a formal statement as Desargues's theorem
is not quite what it purports to be. The statement of Desargues's theorem
pretends to be definitive, but in reality it is only the tip of an iceberg
of connections with other facts of mathematics."

— From p. 192 of "The Phenomenology of Mathematical Proof,"
by Gian-Carlo Rota, in Synthese , Vol. 111, No. 2, Proof and Progress
in Mathematics
(May, 1997), pp. 183-196. Published by: Springer.

Stable URL: https://www.jstor.org/stable/20117627.

Related figures —

Note the 3×3 subsquare containing the triangles ABC, etc.

"That in which space itself is contained" — Wallace Stevens

Saturday, September 8, 2018


Filed under: General,Geometry — Tags: — m759 @ 9:26 PM

'Space' in Chinese

For example —

'Projective space' in Chinese

See also Interality in this journal.


Filed under: General,Geometry — m759 @ 2:00 AM

Affine groups on small binary spaces

Friday, September 7, 2018

The Enormous Snowflake

Filed under: General — m759 @ 2:01 PM

A literary reference suggested by the previous post and by
today's 2 AM post "Show" —


See also Snowflake in this  journal.

Carnival and Mystery

Filed under: General — m759 @ 1:15 PM

From a search in this journal for "Public Square" —

See also Gresham in this journal.

A Square for Sims

Filed under: General — m759 @ 3:00 AM

The American Mathematical Society on Wednesday, September 5,
reported a death from October 23 last year

AMS obituary for mathematician Charles C. Sims

See also Higman-Sims and 5×5 in this  journal.


Filed under: General — m759 @ 2:00 AM

In memory of a showman who reportedly died on August 31


See also this journal on August 31.

Thursday, September 6, 2018

Identity Crisis

Filed under: General — m759 @ 6:29 PM

(Continued from 12 AM Sept. 4)

New York Times
Editors’ Choice
11 New Books We Recommend This Week

Sept. 6, 2018

Identity — whatever that even means — has been having a moment, lately. The political climate forces us all to decide grimly what bunker will welcome us, and the new culture wars spur people to define themselves before somebody else does it for them to possibly violent effect. Identity may be abstract and elusive, but that doesn’t mean it doesn’t have real-world consequences. So our recommended titles this week turn a spotlight on the subject, from Francis Fukuyama’s “Identity” to Kwame Anthony Appiah’s “The Lies That Bind” to two books about identity politics on college campuses: “The Splintering of the American Mind,” by William Egginton, and “The Coddling of the American Mind,” by Greg Lukianoff and Jonathan Haidt. (Those similar titles are no coincidence: Both books hark back to Allan Bloom’s classic “The Closing of the American Mind.”) We also have a book about the Spanish man who for decades falsely claimed to be a Holocaust survivor, and a joint biography of the mother and daughter who gave their names to the Myers-Briggs personality test. In other realms, there’s a biography of the tennis legend Arthur Ashe; new fiction from Gary Shteyngart, Ben Marcus and Tsitsi Dangarembga; and an essay collection about the role of the “dead girl” in popular culture, which posits that — in that case, anyway — the absence of identity is the whole point.

Gregory Cowles
Senior Editor, Books

See also  Identity + Paz  in this  journal.


Filed under: General — m759 @ 5:00 PM


Wednesday, September 5, 2018

Multifaceted Narrative

Filed under: General,Geometry — Tags: — m759 @ 8:19 PM



See also, in this  journal, 23-cycle.

Update of Sept. 6, 2018, 9:05 AM ET:  "The Cubist Method"

Multifaceted narrative by James Joyce —


Multifaceted structures in pure mathematics, from Plato and R. T. Curtis  —

Counting symmetries with the orbit-stabilizer theorem

Midnight Art

Filed under: General — Tags: — m759 @ 3:03 AM


See also 12 AM Sept. 4 in this  journal, "Identity Crisis."

Related material — "Overarching" in this journal.

Update of 4:12 AM ET —

The name of the New Yorker  artist in the Identity Crisis post,
Tamara Shopsin, has now been added to the illustrated excerpt.

See as well . . .



Tuesday, September 4, 2018

MBTI at the Church of St. Frank*

Filed under: General — m759 @ 10:45 AM

(Suggested by the previous post)


* For the church, see Kermode + Garber.

Identity Crisis

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



See also 5×5  in this  journal.

Monday, September 3, 2018


Filed under: General — m759 @ 3:40 AM

For the title, see Paranoia Strikes Deep (Dec. 1, 2011).

Related reading —


Sunday, September 2, 2018

Picture Yourself …

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



Saturday, September 1, 2018

Another 48 Hours

Filed under: General — Tags: — m759 @ 9:29 PM


Backstory:  See The Plaid Overnight Case in this journal.

Investigators: First 48 Hours Most Critical
In Locating Missing Children Who Entered
Portal To Fantastical World

See as well a post from 10:16 PM ET Thursday, August 30, 2018.

Nicht Spielerei

Filed under: General — m759 @ 2:56 PM


"The absence of adults forces children to practice their social skills."

This is from . . .


See also . . .

The Enlivened Obituary

Filed under: General — m759 @ 1:45 PM

" Martin Shubik, an economist whose prescient visions
of a computerized world and pioneering applications
of game theory to everyday life enlivened what has been
described as the dismal science, died on Aug. 22 at his
home in Branford, Conn. He was 92."

Sam Roberts in The New York Times  yesterday

From Sylvia Nasar's A Beautiful Mind


Ron Shaw — D. 21 June 2016

The date of Ron Shaw's 2016 death appears to be June 21:


All other Internet sources I have seen omit the June 21 date.

This  journal on that date —


Powered by WordPress