"He played with history and narrative techniques." — Obituary headline
* See his New York Times obituary, online today —
"He played with history and narrative techniques." — Obituary headline
* See his New York Times obituary, online today —
"… the focus of interest for most of the American military attachés
in Europe became tanks and antitank/antiaircraft weapons."
— https://www.benning.army.mil/armor/earmor/
content/issues/2020/Fall/4Candill20.pdf
See also "A Meadow for Trevanian" (Sept. 27, 2021).
A check of the phrase "memory-alpha" in the above URL
reveals that it comes from a 1969 Star Trek episode
written by Shari Lewis and her husband Jeremy Tarcher.
Tarcher reportedly died on Sunday, Sept. 20, 2015.
From this journal on that date —
On the editor of the anthology Space, Space, Space :
"Sloane’s writing is drum-tight, but his approach
is looser; he pulls the reader in and then begins
turning up the heat. He understood that before
a pot can boil, it must simmer." — Stephen King
Of related literary interest to fans of the late Russell Banks,
whose novel title Cloudsplitter refers to Mt. Marcy, the
highest mountain in New York State —
Marcy was a New York State politician who is said to have
coined the above phrase
"to the victor go the spoils."
"Her attention to the nuances of language
is both intuitive and painstaking."
— Testimonials page at
https://www.lesliekendalldye.net/testimonials.html
The birth name of Leslie Kendall Dye was Leslie Engelberg.
Related remarks —
Tom Wolfe in The Painted Word (1975):
“It is important to repeat that Greenberg and Rosenberg
did not create their theories in a vacuum or simply turn up
with them one day like tablets brought down from atop
Green Mountain or Red Mountain (as B. H. Friedman once
called the two men). As tout le monde understood, they
were not only theories but … hot news,
straight from the studios, from the scene.”
Report from Angel Mountain —
"Turn to page three hundred and ninety-four."
The Engelberg Variations —
"… the arrangement of one's books …."
. . . or of one's house committees . . . .
A remark by Esther Dyson on Jan. 19:
See as well the above group-theory author here on Jan. 19.
Related material: "Same Staircase, DIfferent Day."
Sometimes the word "preform" is not a misspelling.
"… there are present in every psyche forms which are unconscious
but nonetheless active — living dispositions, ideas in the Platonic sense,
that preform and continually influence our thoughts and feelings and actions."
The Source: Jung on a facultas praeformandi . . .
Illustration —
"A primordial image . . . .
the axial system of a crystal"
For those who prefer a Jewish approach to these matters —
(Post last updated at about 2:10 PM ET on Jan. 23, 2023.)
Number | Space |
Arithmetic | Geometry |
Discrete | Continuous |
Related literature —
From a "Finite Fields in 1956" post —
The Nutshell:
Related Narrative:
"Death is the mother of beauty." — Wallace Stevens
From the 2020 Feast of St. Wallace Stevens,
who reportedly died in 1955 on August 2 —
Related material —
Exercise: Can each order-4 magic square be obtained by some
transformation like the one above (i.e., preserving affine hyperplanes)?
If not, why not?
Update of 31 Jan. 2023 — Spoiler: Remarks by Tilman Piesk.
From a search in this journal for Hancock —
The late David Crosby on Heaven, Wednesday, January 18 —
"I heard the place is overrated . . . cloudy."
In 2007, April 30 — Walpurgisnacht — was the
release date of the "Back to Black" single . . .
A related music venue —
A related map —
This post was suggested by . . .
Last revised: January 20, 2023 @ 11:39:05
The First Approach — Via Substructure Isomorphisms —
From "Symmetry in Mathematics and Mathematics of Symmetry"
by Peter J. Cameron, a Jan. 16, 2007, talk at the International
Symmetry Conference, Edinburgh, Jan. 14-17, 2007 —
Local or global? "Among other (mostly more vague) definitions of symmetry, the dictionary will typically list two, something like this:
• exact correspondence of parts; Mathematicians typically consider the second, global, notion, but what about the first, local, notion, and what is the relationship between them? A structure M is homogeneous * if every isomorphism between finite substructures of M can be extended to an automorphism of M ; in other words, 'any local symmetry is global.' " |
A related discussion of the same approach —
"The aim of this thesis is to classify certain structures
— Alice Devillers, |
The Wikipedia article Homogeneous graph discusses the local-global approach
used by Cameron and by Devillers.
For some historical background on this approach
via substructure isomorphisms, see a former student of Cameron:
Dugald Macpherson, "A survey of homogeneous structures,"
Discrete Mathematics , Volume 311, Issue 15, 2011,
Pages 1599-1634.
Related material:
Cherlin, G. (2000). "Sporadic Homogeneous Structures."
In: Gelfand, I.M., Retakh, V.S. (eds)
The Gelfand Mathematical Seminars, 1996–1999.
Gelfand Mathematical Seminars. Birkhäuser, Boston, MA.
https://doi.org/10.1007/978-1-4612-1340-6_2
and, more recently,
Gill et al., "Cherlin's conjecture on finite primitive binary
permutation groups," https://arxiv.org/abs/2106.05154v2
(Submitted on 9 Jun 2021, last revised 9 Jul 2021)
This approach seems to be a rather deep rabbit hole.
The Second Approach — Via Induced Group Actions —
My own interest in local-global symmetry is of a quite different sort.
See properties of the two patterns illustrated in a note of 24 December 1981 —
Pattern A above actually has as few symmetries as possible
(under the actions described in the diamond theorem ), but it
does enjoy, as does patttern B, the local-global property that
a group acting in the same way locally on each part induces
a global group action on the whole .
* For some historical background on the term "homogeneous,"
see the Wikipedia article Homogeneous space.
The title describes one approach to longevity
from an obituary for a woman who reportedly
died yesterday at the age of 118.
These dietary supplements are related, if only
metaphorically, to posts now tagged Juneteenth 2007.
In 2007, April 30 — Walpurgisnacht — was also the
release date of the "Back to Black" single . . .
A related music venue —
"Remember your epiphanies on green oval leaves,
deeply deep, copies to be sent if you died to all
the great libraries of the world, including Alexandria?"
"Think of it as a cybernetic version of prayer…."
— Dennis Overbye in today's online New York Times ,
https://www.nytimes.com/2023/01/17/science/
cosmology-universe-programming.html .
Related remarks: The Log24 tag Geheimnis der Einheit, and . . .
Related art — "The Difference," a Log24 post of Epiphany 2010.
See earlier instances of "working backwards" in this journal.
Alan Rickman as Metatron in "Dogma" —
Alan Rickman as Severus Snape at Hogwarts —
Page three hundred and ninety-four —
See also today's previous post.
From my RSS feeds last night —
This journal on Wednesday, December 28, 2022 —
For those who prefer a "liturgical, ecstatic style" —
Organic Symmetry
"Benzene is a natural constituent of petroleum
and is one of the elementary petrochemicals.
Due to the cyclic continuous pi bonds between
the carbon atoms, benzene is classed as an
aromatic hydrocarbon. Benzene is a colorless
and highly flammable liquid with a sweet smell,
and is partially responsible for the aroma of gasoline."
Anti-Organic Symmetry —
Some background . . .
A letter in The Mathematical Intelligencer, January 1988
http://www.log24.com/noindex-pdf/
Cullinane-letter-Artes_Liberales-Intelligencer.pdf —
The three nested icosahedra on the cover of
a recent vulgarized-mathematics book suggest . . .
This is, of course, a highly special case of the much more
general, and much more difficult, n-body problem .
From Gilles Châtelet, Introduction to Figuring Space Metaphysics does have a catalytic effect, which has been described in a very beautiful text by the mathematician André Weil: Nothing is more fertile, all mathematicians know, than these obscure analogies, these murky reflections of one theory in another, these furtive caresses, these inexplicable tiffs; also nothing gives as much pleasure to the researcher. A day comes when the illusion vanishes: presentiment turns into certainty … Luckily for researchers, as the fogs clear at one point, they form again at another.4 André Weil cuts to the quick here: he conjures these 'murky reflections', these 'furtive caresses', the 'theory of Galois that Lagrange touches … with his finger through a screen that he does not manage to pierce.' He is a connoisseur of these metaphysical 'fogs' whose dissipation at one point heralds their reforming at another. It would be better to talk here of a horizon that tilts thereby revealing a new space of gestures which has not as yet been elucidated and cut out as structure. 4 A. Weil, 'De la métaphysique aux mathématiques', (Oeuvres, vol. II, p. 408.) |
For gestures as fogs, see the oeuvre of Guerino Mazzola.
For some clearer remarks, see . . .
Illustrations of object and gestures
from finitegeometry.org/sc/ —
Object
Gestures
An earlier presentation
of the above seven partitions
of the eightfold cube:
|
Related material: Galois.space .
See also earlier references to Mazzola in this journal.
A sequel to the previous post, "How the Darkness Gets In" —
THE PHILOSOPHY OF RUDOLF CARNAP
EDITED BY PAUL ARTHUR SCHILPP
. . . . |
See also . . .
The extraordinary consequences of Einstein’s universe:
Relativity shatters our experience of time
9th January 2023
By Michael David Silberstein
"Professor of Philosophy at Elizabethtown College
and co-athor [sic] of Emergence in Context:
A treatise of twentry [sic] first-century natural philosophy
(Oxford University Press, 2022)."
"… the experience that there is something special about
the character of the present moment. This is what presumably
lead [sic] Einstein to say that
'there is something essential about the Now
which is just outside the realm of science.' "
Silberstein does not give any source for his quotation.
But see the passage from Carnap above.
I do not recommend taking Carnap's — or Silberstein's —
word for anything.
The source of Silberstein's remarks is a publication of an
organization called "Institute of Art and Ideas," or IAI.
Wikipedia on that organization:
"The IAI is responsible for organising the bi-annual festival
HowTheLightGetsIn, the biggest philosophy and music
festival in the world* aimed at 'tackling the dearth of philosophy
in daily life,' in addition to monthly IAI Live events."
* Maya Oppenheim (7 September 2021):
"HowTheLightGetsIn: The world's largest philosophy
and music festival to ask life's big questions."
The Independent.
Other social notes from that May weekend —
Some related reading for Cormac McCarthy —
The title refers to a post discussing a date,
that of last year's Feast of St. Thomas Becket.
Related material —
https://www.nytimes.com/2023/01/09/movies/ruggero-deodato-dead.html .
The tortoise of the previous post suggests . . .
"Is it the good turtle soup
or merely the mock?"
Related material from the above
Toronto premiere date —
From a link target in this journal on April 4, 2004 —
"Puzzle begun I write in the day's space . . . ."
Today's link targets —
Valéry and Rilke, Stevens and Borges . . . and Zeno.
From AP News in The Derrick , Oil City, PA, today —
"Banks lived part of the year in Florida, and for a time
had a home in Jamaica, but he was essentially a man
of the North, with an old Puritan’s sense of consequences.
Snow fell often in his fiction . . . ." — Hillel Italie
Update of 3:33 PM ET —
From a link target in this journal on April 4, 2004 —
"Puzzle begun I write in the day's space . . . ."
Thandiwe Newton in "Reminiscence" (2021) —
The above film is from August 20, 2021.
From that same date —
"… just one aspect of a historical process
that we can legitimately call 'progress' –
not a romantic or utopian or naive ideal,
but an empirical fact that we can see
in graphs and numbers."
… and sometimes elsewhere . . .
"Might be a nice 20 page essay, but a bomb of a book"
— Herbert Gintis on Taleb's Black Swan , review dated April 10, 2012.
This remark might also be applied to Crumey's Mobius Dick :
Related material for Jungians who enjoy synchronicity —
The Log24 posts from the date of the Gintis review — April 10, 2012.
Tuesday, November 8, 2016, was also the publication date
at Princeton University Press for a book by one Herbert Gintis:
Gintis reportedly died yesterday, Jan. 5, 2023.
"He graduated from the University of Pennsylvania
and then attended Harvard University for post-graduate
work in mathematics. After receiving his master's degree,
he grew disillusioned with the field, and while at Harvard,
became a sandal maker with a shop in Harvard Square."
In later years, Gintis was associated with the Santa Fe Institute.
Pullman links in this journal —
http://m759.net/wordpress/?s=wsu.edu .
Specifically . . .
<a href="http://www.wsu.edu:8080/%7Edee/GLOSSARY/SHUCHUNG.HTM"
target="_new" rel="noopener noreferrer">
<strong><em>Shu</em>: Reciprocity</strong></a>
and
<a href="http://www.wsu.edu/%7Edee/GREECE/HERAC.HTM"
target="_new"><font size="6"><b>Logos</b></font></a>
Those links no longer work. See instead . . .
https://web.archive.org/web/20011224032243/
http://www.wsu.edu:8080/~dee/GLOSSARY/SHUCHUNG.HTM
and
https://web.archive.org/web/20011129072406/
http://www.wsu.edu/~dee/GREECE/HERAC.HTM .
Logo from these links:
Wallace Stevens —
"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
Of dense investiture, with luminous vassals."
— “An Ordinary Evening in New Haven” VI
This post was suggested by a "matrix rotator" photo dated 1953-03-02.
Some context — Kracauer's notion of "mass ornament."
Detail of the above screen (click to enlarge) —
See also this journal on the above date — June 10, 2021.
From this journal on May 6, 2009 —
A related picture of images that "reappear metamorphosed
in the coordinate system of the high region" —
(For the backstory, see Geometry of the I Ching
and the history of Chinese philosophy.)
The title is from . . .
https://booksonthewall.com/blog/samuel-beckett-quote-fail-better/ .
This post was suggested by yesterday's Feast of St. Thomas Becket —
A Beckett-related flashback linked to here yesterday —
"To get inside the systems of this work,
whether LeWitt's or Judd's or Morris's,
is precisely to enter
a world without a center,
a world of substitutions and transpositions
nowhere legitimated by the revelations
of a transcendental subject. This is the strength
of this work, its seriousness, and its claim to modernity."
"How a close group of brilliant friends,
in a tiny German university town, laid
the foundations of modern consciousness"
— Headline for the article whose URL is . . .
https://aeon.co/essays/
english-romanticism-was-born-from-a-serious-germanomania
The article was published by Aeon on December 20, 2022,
and is featured in today's Arts & Letters Daily . On the author:
"Andrea Wulf is a historian and the award-winning author
of several books, including the bestselling
The Invention of Nature (2015) and, most recently,
Magnificent Rebels: The First Romantics and
the Invention of the Self (2022). She is a Miller Scholar
and a Fellow of the Royal Society of Literature."
Related material — "The Eight" According to Coleridge.
"The novelist Cormac McCarthy has been a fixture around
the Santa Fe Institute since its embryonic stages in the
early 1980s. Cormac received a MacArthur Award in 1981
and met one of the members of the board of the MacArthur
Foundation, Murray Gell-Mann, who had won the Nobel Prize
in physics in 1969. Cormac and Murray discovered that they
shared a keen interest in just about everything under the sun
and became fast friends. When Murray helped to found the
Santa Fe Institute in 1984, he brought Cormac along, knowing
that everyone would benefit from this cross-disciplinary
collaboration." — https://www.santafe.edu/news-center/news/
cormac-and-sfi-abiding-friendship
Joy Williams, review of two recent Cormac McCarthy novels —
"McCarthy has pocketed his own liturgical, ecstatic style
as one would a coin, a ring, a key, in the service of a more
demanding and heartless inquiry through mathematics and
physics into the immateriality, the indeterminacy, of reality."
A Demanding and Heartless Coin, Ring, and Key:
COIN
RING
"We can define sums and products so that the G-images of D generate
an ideal (1024 patterns characterized by all horizontal or vertical "cuts"
being uninterrupted) of a ring of 4096 symmetric patterns. There is an
infinite family of such 'diamond' rings, isomorphic to rings of matrices
over GF(4)."
KEY
"It must be remarked that these 8 heptads are the key to an elegant proof…."
— Philippe Cara, "RWPRI Geometries for the Alternating Group A8," in
Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference
(July 16-21, 2000), Kluwer Academic Publishers, 2001, ed. Aart Blokhuis,
James W. P. Hirschfeld, Dieter Jungnickel, and Joseph A. Thas, pp. 61-97.
For those who prefer a "liturgical, ecstatic style" —
"If the window is this matrix of ambi- or multivalence,
and the bars of the windows-the grid-are what help us
to see, to focus on, this matrix, they are themselves
the symbol of the symbolist work of art. They function as
the multilevel representation through which the work of art
can allude, and even reconstitute, the forms of Being."
— Page 59, Rosalind Krauss, "Grids," MIT Press,
October , Vol. 9 (Summer, 1979), pp. 50-64
Related material —
Click the above image for a related Log24 post of 15 years ago today.
A related literary remark —
"Imagine Raiders of the Lost Ark set in 20th-century London, and then
imagine it written by a man steeped not in Hollywood movies but in Dante
and the things of the spirit, and you might begin to get a picture…."
— Doug Thorpe in an Amazon.com book review, not of Dark Materials.
Published on Sept. 15, 2022. See as well this journal on that date.
Grids
Author: Rosalind Krauss
Source: October , Vol. 9 (Summer, 1979), pp. 50-64
Published by: The MIT Press
Stable URL: http://www.jstor.org/stable/778321
From page 59:
"Flowing and freezing; glace in French means glass, mirror, and ice;
transparency, opacity, and water. In the associative system
of symbolist thought this liquidity points in two directions.
First, towards the flow of birth-the amniotic fluid, the 'source'-
but then, towards the freezing into stasis or death-
the unfecund immobility of the mirror. For Mallarmé, particularly,
the window functioned as this complex, polysemic sign by which
he could also project the 'crystallization of reality into art.' 5
Mallarmé's Les Fenêtres dates from 1863;
Redon's most evocative window, Le Jour , appeared in 1891
in the volume Songes . If the window is this matrix of
ambi- or multivalence, and the bars of the windows-the grid-
are what help us to see, to focus on, this matrix, they are
themselves the symbol of the symbolist work of art.
They function as the multilevel representation through which
the work of art can allude, and even reconstitute, the forms of Being."
5 Robert G. Cohn, "Mallarmé's Windows," Yale French Studies ,
no. 54 (1977), 23-31.
Another evocative example — See Galois Window in this journal.
"The book I came back to
George Eliot’s Middlemarch. I couldn’t cope with it
as a student; it wasn’t until I was grown up, and married,
and a parent, and trying to teach it myself, that I realised
its majestic scope and depth." — Philip Pullman in
The Guardian, Fri 23 Dec 2022 05.00 EST
Another instance of scope and depth —
"The Amber Spyglass" Log24 post of Wednesday.
See also other references here to Middlemarch.
"Was ist Raum, wie können wir ihn
erfassen und gestalten?"
The Theory and
Organization of the
Bauhaus (1923)
A relevant illustration:
At math.stackexchange.com on March 1-12, 2013:
“Is there a geometric realization of the Quaternion group?” —
The above illustration, though neatly drawn, appeared under the
cloak of anonymity. No source was given for the illustrated group actions.
Possibly they stem from my Log24 posts or notes such as the Jan. 4, 2012,
note on quaternion actions at finitegeometry.org/sc (hence ultimately
from my note “GL(2,3) actions on a cube” of April 5, 1985).
These references will not appeal to those who enjoy modernism as a religion.
(For such a view, see Rosalind Krauss on grids and another writer's remarks
on the religion's 100th anniversary this year.)
Some related nihilist philosophy from Cormac McCarthy —
"Forms turning in a nameless void."
The 'harvard gsd' in the link button below is the Graduate School of Design.
Related material — "News of the World" in this journal.
"Most important for Canetti are certain events
that he calls 'illuminations,' such as his witnessing
of striking workers being mowed down by Viennese
police on July 15, 1927, which was the germ of both
Auto-da-Fé and Crowds and Power. For Canetti,
these epiphanies are moments of metamorphosis,
which he prizes above all in art as well as in life.
Canetti aspired to be a 20th-century Ovid, but
precisely because he was modern, this ambition
landed him, again and again, in paradox, such as
the one expressed in the aphorism that gives this
compilation its title, or in this characteristic maxim:
'It all depends on this: with whom we confuse ourselves .'"
— Hal Foster in The Chronicle of Higher Education ,
"The Best Scholarly Books of 2022," Dec. 21, 2022.
See also this journal on Nov, 25, 2022 —
Last year on this date:
A Riddler Wannabe —
Related material — The Krauss passage quoted as above
by Shechtman in The New Yorker in December 2021 appears
also in a Log24 post of October 18, 2017: "Three Small Grids."
Today's previous post "The Urn" suggests a look at . . .
How to Solve The New York Times Crossword
By Deb Amlen. Illustrations by Elena Xausa.
Animations by Lorenzo Fonda.
That web page is undated, but its HTML source contains
43 instances of the date 2017-10-18.
See as well "Three Small Grids," a post from this journal on 2017-10-18.
Related material — Today's 3:05 PM ET New York Times obituary
for the above crossword guide illustrator, Elena Xausa —
https://www.newyorker.com/magazine/2022/12/26/the-cover-crossword
"The two cover characters, who I’ve been thinking of as ○ and □ . . ."
— Chris Ware on his New Yorker cover for the issue dated Dec. 26, 2022.
(See earlier posts referring to that theory.)
Catching up to Pullman's Oct. 3 remark . . .
See Log24 posts now tagged October 1-2-3.
Midrash from Philip Pullman . . .
"The 1929 Einstein-Carmichael Expedition"
I prefer the 1929 Emch-Carmichael expedition —
This is from . . .
“By far the most important structure in design theory
is the Steiner system S(5, 8, 24).”
— “Block Designs,” by Andries E. Brouwer
(Ch. 14 (pp. 693-746) of Handbook of Combinatorics,
Vol. I, MIT Press, 1995, edited by Ronald L. Graham,
Martin Grötschel, and László Lovász, Section 16 (p. 716))
Circle and Square at the Court of King Minos —
Harmonic analysis based on the circle involves the
circular functions. Dyadic harmonic analysis involves …
For some related history, see (for instance) . . .
When?
Going to dark bed there was a square round Where?
— Ulysses , conclusion of Chapter 17. |
For seekers of a "crazy Christmas knot" —
The commercial logo below may be viewed as
three in-folded Y-shaped orange forked tongues.
See also a Log24 post from Dec. 5, the lawyer's dies natalis.
The above title phrase is from the Windows lockscreen
I encountered at 7:59 AM ET today:
Some related mathematical windmills —
For the eight-limbed star at the top of the quaternion array She drew from her handbag a pale grey gleaming implement that looked by quick turns to me like a knife, a gun, a slim sceptre, and a delicate branding iron—especially when its tip sprouted an eight-limbed star of silver wire. “The test?” I faltered, staring at the thing. “Yes, to determine whether you can live in the fourth dimension or only die in it.” — Fritz Leiber, short story, 1959 |
See as well . . .
From Peter Woit's weblog today —
The New Yorker and the Publicity Stunt
Posted on December 12, 2022 by woit
The wormhole publicity stunt story just keeps going.
Today an article about the Google Santa Barbara lab
and quantum computer used in the publicity stunt
appeared in the New Yorker.
From The New Yorker itself —
See also a very different take from another New Yorker author —
(Cf. Log24, Plan 9 at Yale, Nov. 13, 2017).
The "Cottage Industry" of the title is the "Modernism" racket
of today's 1 AM post — a subsidiary of Academia that
uses some of the same marketing techniques as Hollywood . . .
See also "Plato's Ghost" in this journal.
The above tag "Academy Century" is a nod to an earlier tag,
"Academy Year," that refers to Dec. 7, 2021-Dec. 7, 2022 . . .
the dates of a Deerfield Academy publication and of a Log24 post.
Some remarks from a more advanced academy —
"This year marks the centenary of modernism's annus mirabilis ."
— Johanna Winant in Boston Review, December 7th, 2022.
Some will prefer a different annus mirabilis .
A music producer pawns his current drum device
and acquires a demonic 1970s machine.
Related material —
This post was suggested by a remark made during the filming
of "Edge of Tomorrow," by a Log24 post on the new Nolan film
about Oppenheimer, and by the work of a different Edge:
"… a reality that only my notes can provide."
— Kinbote in Nabokov's novel Pale Fire
* The word "artification" is from yesterday's Letter of the Law.
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