A version more explicitly connected to finite geometry —
For the six synthematic totals , see The Joy of Six.
Thursday, April 30, 2020
Wednesday, April 29, 2020
Curtis at Pilsen, Thursday, July 5, 2018
For an account by R. T. Curtis of how he discovered the Miracle Octad Generator,
see slides by Curtis, “Graphs and Groups,” from his talk on July 5, 2018, at the
Pilsen conference on algebraic graph theory, “Symmetry vs. Regularity: The first
50 years since Weisfeiler-Leman stabilization” (WL2018).
See also “Notes to Robert Curtis’s presentation at WL2018,” by R. T. Curtis.
Meanwhile, here on July 5, 2018 —
| Simultaneous perspective does not look upon language as a path because it is not the search for meaning that orients it. Poetry does not attempt to discover what there is at the end of the road; it conceives of the text as a series of transparent strata within which the various parts—the different verbal and semantic currents—produce momentary configurations as they intertwine or break apart, as they reflect each other or efface each other. Poetry contemplates itself, fuses with itself, and obliterates itself in the crystallizations of language. Apparitions, metamorphoses, volatilizations, precipitations of presences. These configurations are crystallized time: although they are perpetually in motion, they always point to the same hour—the hour of change. Each one of them contains all the others, each one is inside the others: change is only the oft-repeated and ever-different metaphor of identity.
— Paz, Octavio. The Monkey Grammarian |
The 2018 Log24 post containing the above Paz quote goes on to quote
remarks by Lévi-Strauss. Paz’s phrase “series of transparent strata”
suggests a review of other remarks by Lévi-Strauss in the 2016 post
“Key to All Mythologies.“
Comments Off on Curtis at Pilsen, Thursday, July 5, 2018
Tuesday, April 28, 2020
The Art Issue
“A sort of pointillist mosaic”
— Author David Mitchell on the film adaptation of
his novel Cloud Atlas .
See also the previous post, Cloud Atlas of Unknowing.
“Art isn’t easy.” — Sondheim.
Comments Off on The Art Issue
Monday, April 27, 2020
The Cracked Nut
“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
“… the stabiliser of an octad preserves the affine space structure on its
complement, and (from the construction) induces AGL(4,2) on it.
(It induces A8 on the octad, the kernel of this action being the translation
group of the affine space.)”
— Peter J. Cameron,
The Geometry of the Mathieu Groups (pdf)
“The yarns of seamen have a direct simplicity, the whole meaning
of which lies within the shell of a cracked nut. But Marlow was not
typical (if his propensity to spin yarns be excepted), and to him the
meaning of an episode was not inside like a kernel but outside…."
— Joseph Conrad in Heart of Darkness
Comments Off on The Cracked Nut
Sunday, April 26, 2020
Crux
This post was suggested by a David Justice weblog post yesterday,
Coincidence and Cosmos. Some related remarks —
“The yarns of seamen have a direct simplicity, the whole meaning
of which lies within the shell of a cracked nut. But Marlow was not
typical (if his propensity to spin yarns be excepted), and to him the
meaning of an episode was not inside like a kernel but outside,
enveloping the tale which brought it out only as a glow brings out a
haze, in the likeness of one of these misty halos that sometimes
are made visible by the spectral illumination of moonshine.”
— Joseph Conrad in Heart of Darkness
“By groping toward the light we are made to realize
how deep the darkness is around us.”
— Arthur Koestler, The Call Girls: A Tragi-Comedy,
Random House, 1973, page 118
See as well posts now tagged Crux.
Comments Off on Crux
The Triangle of Art
This post was suggested by yesterday morning's link to The Fano Hallows.
"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
A symbol related to The Fano Hallows —
Comments Off on The Triangle of Art
Saturday, April 25, 2020
The Grandfather Clock
“Well, I’ve helped to wind up the clock —
I might as well hear it strike!”
— Said to be a quotation from the grandfather
of a “pirate radio” founder who reportedly died
at 79 on April 20.
See as well this journal on the night of April 20 —
Wheel Turnin’ ’Round and ’Round —
and a search for “Wheel of Time.”
Comments Off on The Grandfather Clock
Form and Order
“Brahms maintained a classical sense of
form and order in his works….” — Wikipedia
For example —
The above Cologne sextet upload date suggests a review.
See posts now tagged The Fano Hallows.
Comments Off on Form and Order
Friday, April 24, 2020
Art at Cologne
This post was suggested by a New York Review of Books article
on Cologne artist Gerhard Richter in the May 14, 2020, issue —
“The Master of Unknowing,” by Susan Tallman.
Some less random art —
Comments Off on Art at Cologne
Thursday, April 23, 2020
Octads and Geometry
See the web pages octad.group and octad.us.
Related geometry (not the 759 octads, but closely related to them) —
#/media/File:150614-PG-3-2-schoolgirls-arrangement.png)
The 4×6 rectangle of R. T. Curtis
illustrates the geometry of octads —
Curtis splits the 4×6 rectangle into three 4×2 "bricks" —
.
"In fact the construction enables us to describe the octads
in a very revealing manner. It shows that each octad,
other than Λ1, Λ2, Λ3, intersects at least one of these ' bricks' —
the 'heavy brick' – in just four points." . . . .
— R. T. Curtis (1976). "A new combinatorial approach to M24,"
Mathematical Proceedings of the Cambridge Philosophical Society ,
79, pp 25-42.
Comments Off on Octads and Geometry
Dead Poet Joke
From the subtitles of the recent Kristen Stewart film “Underwater” —
427
00:30:26,144 –> 00:30:27,476
He’d always say
he had a new joke,
428
00:30:27,478 –> 00:30:29,445
and then he’d tell
the same stupid joke.
429
00:30:29,447 –> 00:30:32,785
I was… laughing at that joke.
430
00:30:34,053 –> 00:30:35,685
Yeah, what was it?
431
00:30:35,687 –> 00:30:38,654
What did the fish say when
it bumped into the brick wall?
April 11 was the dies natalis , in the Catholic sense, of John Horton Conway.
Related material: Other posts containing the phrase “brick wall.”
Comments Off on Dead Poet Joke
Wednesday, April 22, 2020
One with Everything
The title is of course from an old joke about mystic philosophies.
Related remarks by John Archibald Wheeler —
“Remarkable issues connected with the puzzle of existence
confront us today in Hermann Weyl’s domain of thought.
Four among them I bring before you here as especially interesting:
(1) What is the machinery of existence?
(2) What is deeper foundation of the quantum principle?
(3) What is the proper position to take about the existence of
the “continuum” of the natural numbers? And
(4) What can we do to understand time as an entity, not precise and
supplied free of charge from outside physics, but approximate and
yet to be derived from within a new and deeper time-free physics?
In brief, how come time?
What about the continuum?
How come the quantum?
What is existence?”
— John A. Wheeler, “Hermann Weyl and the Unity of Knowledge,”
American Scientist 74, no. 4 (1986): 366–75. Reprinted in
John A. Wheeler, At Home in the Universe
(American Institute of Physics, December 1, 1995).
The above bibliographic data is from . . .
Schrank, Jeffrey. Inventing Reality: Stories We Create To Explain Everything .
Gatekeeper Press. Kindle Edition, March 14, 2020.
For further scholarly details, see a version at JSTOR:
“…the article is adapted from the concluding address given at
the Hermann Weyl Centenary Congress, University of Kiel, 3 July 1985.”
— https://www.jstor.org/stable/27854250.
I prefer Charles Williams on “the Unity of Knowledge.”
See the 15 instances of the phrase “the Unity” in his 1931 novel Many Dimensions .
Comments Off on One with Everything
Puzzle Pictures
|
A doodle from 2012’s Feast of the Epiphany—
A doodle based on a post for Twelfth Night, 2003—
|
Comments Off on Puzzle Pictures
Arts at Cambridge
Click here to enlarge. See also Hexagram 59, Feng Shui.
Comments Off on Arts at Cambridge
Deep Horizon
For some mathematical background, see Deep + Hardy.
Related entertainment —
Related non-entertainment —
Comments Off on Deep Horizon
Tuesday, April 21, 2020
Living Water
The Tesseract Timeline:
Where The Cube Has Been In The …
www.cinemablend.com › news › the-tesseract-timeline-…
Mar 13, 2019 – With HYDRA. In 1942, Johann Schmidt, a.k.a.
the Red Skull, arrived in Tønsberg to procure the Tesseract
from an ancient church. While he …
Related material from posts tagged Aqua
(suggested by a name in the previous post) —
Comments Off on Living Water
Cold Comfort Continues
Comments Off on Cold Comfort Continues
Monday, April 20, 2020
The Date
Comments Off on The Date
Geometry for Poets
From Atomicity and Quanta by James Jeans,
Cambridge University Press, 1926, pp. 55-56 —
| “So far as we can at present conjecture, the investigation of the structure which produces this atomicity appears to be the big problem in the path of the quantum-theory. To conform to the principle of relativity, the new atomicity must admit of expression in terms of the space-time continuum, although we have seen that it cannot be an atomicity of the continuum itself. It may conceivably be an atomicity of its metric properties, such as determine its curvatures. We may perhaps form a very rude picture of it by imagining the curvature of the continuum in the neighbourhood of an atom not to be of the continuous nature imagined by Weyl, but to occur in finite chunks—a straight piece, then a sudden bend, then another straight bit, and so on. A small bit of the continuum viewed through a five-dimensional microscope might look rather like a cubist picture; and, conversely, perhaps a cubist picture looks rather more like a little fragment of the continuum than like anything else.” |
This is, of course, not the “atomicity” of the previous post.
For examples of that atomicity, a concept of pure geometry
rather than of physics, see …
Faure, C. A., and Frölicher, A., “Fundamental Notions of
Lattice Theory,” in Modern Projective Geometry (2000).
(Mathematics and Its Applications, vol 521. Springer, Dordrecht.)
Related art (a “cubist picture”) —
Juan Gris, Fruit Dish and Carafe , 1914
Comments Off on Geometry for Poets
Sunday, April 19, 2020
Easter Egg for Wittgenstein
Comments Off on Easter Egg for Wittgenstein
Saturday, April 18, 2020
Dark Passage
Comments Off on Dark Passage
Cold Comfort
“Where there is meat, there are flies.”
— John Archibald Wheeler
|
“ Simon’s head was tilted slightly up. ‘What are you doing out here all alone? Simon shook. ‘There isn’t anyone to help you. — William Golding |
Comments Off on Cold Comfort
Friday, April 17, 2020
Academic Games and the Plague
See also the previous post.
The above date “4 avril 2016”
suggests a review of that date
in this journal: “Cube for Berlin.”
Comments Off on Academic Games and the Plague
Expanding (and Mixing) Metaphors
“But while Camus was writing for the moment,
he was also writing for the future. He was making art
out of what happens between antibodies and germs,
expanding metaphors from the molecular level.”
— Laura Marris on translating The Plague
Another remark on dramatic irony —
See as well “two-way mirror” in this journal.
Comments Off on Expanding (and Mixing) Metaphors
A Mechanism of Fission
The above title was suggested by the previous post, Explosive Remarks.
Comments Off on A Mechanism of Fission
Explosive Remarks
“Here is the background to Wheeler’s explosive remarks.
John Archibald Wheeler, director of the Center
for Theoretical Physics at the University of Texas,
is one of the world’s top theoretical physicists.
In 1939 he and Niels Bohr published a paper on
‘The Mechanism of Nuclear Fission”
that laid the groundwork for atomic and hydrogen bombs.
Wheeler later played major roles in their development.”
For a rather different explosion of Wheeler’s views, see the previous post.
Comments Off on Explosive Remarks
Introduction to Quantum Woo
“In his big book, Gravity [sic ], Wheeler puts our space
into what he calls superspace, and speculates on the
most basic physical laws which operate on superspace.
He comes to the (to me) surprising conclusion that the
rock-bottom laws are the laws of the propositional calculus!”
— Martin Gardner, letter to Donald E. Knuth, 8 January 1976,
on cover of Notices of the American Mathematical Society ,
March 2011 issue.
Fact check —
Related reading —
Comments Off on Introduction to Quantum Woo
Thursday, April 16, 2020
A Four-Color Epic
“A love story of epic, epic, epic proportion” — Kristen Stewart
See also the following letter to Knuth on four-color enthusiast
Spencer-Brown, as well as Tim Robinson on the same subject
in his book My Time in Space .
Comments Off on A Four-Color Epic
Wednesday, April 15, 2020
Death Warmed Over
In memory of the author of My Time in Space * —
Tim Robinson, who reportedly died on April 3 —
See also an image from a Log24 post, Gray Space —
Related material from Robinson’s reported date of death —
* First edition, hardcover, Lilliput Press, Ireland, April 1, 2001.
Comments Off on Death Warmed Over
Refutation
A post by David Justice today suggests a review —
A more literary approach to refutation —
|
“He is real,” said the boy, passionately. “He’s not a fool. He’s real.” “Listen,” said his father. “When you go down the garden there’s nobody there. Is there?” “No,” said the boy. “Then you think of him, inside your head, and he comes.” “No,” said Small Simon. “I have to make marks. On the ground. With my stick.” “That doesn’t matter.” “Yes, it does.” — John Collier, “Thus I Refute Beelzy.” |
Comments Off on Refutation
Oslo Prophet (after Varignon)
Comments Off on Oslo Prophet (after Varignon)
“Causal Invariance” According to Wolfram
Stephen Wolfram yesterday —
“Causal invariance may at first seem like a rather obscure property.
But in the context of our models, we will see in what follows that
it may in fact be the key to a remarkable range of fundamental features
of physics, including relativistic invariance, general covariance, and
local gauge invariance, as well as the possibility of objective reality in
quantum mechanics.”
From . . .
Comments Off on “Causal Invariance” According to Wolfram
Tuesday, April 14, 2020
Confluence, or:
Church Diamond Continued
The above article leads to remarks by Stephen Wolfram published today :
See also “Invariance” as the title of the previous post here.
Comments Off on Confluence, or:
Invariance
Note the resemblance to Plato’s Diamond.
Click the Pritchard passage above for an interactive version.
Comments Off on Invariance
Monday, April 13, 2020
Tribute
The May 2020 Notices of the American Mathematical Society has a
memorial tribute article on Goro Shimura, who died on May 3, 2019.
See also this journal on May 3, 2019 in posts now tagged Wondertale.
Related ethnic remark: “As a Chinese jar…” — T. S. Eliot
“Things can get muddled further….”
— Webpage on the Japanese word
Indeed they can :
Comments Off on Tribute
Cubes and Axes
See also this journal on November 29, 2011 —The Flight from Ennui.
Related illustration from earlier in 2011 —
See also this journal on 20 Sept. 2011 — Relativity Problem Revisited —
as well as Congregated Light.
Comments Off on Cubes and Axes
Sunday, April 12, 2020
Blackboard Jungle Continues.
From a post this morning by Peter J. Cameron
in memory of John Horton Conway —
| ” This happened at a conference somewhere in North America. I was chairing the session at which he was to speak. When I got up to introduce him, his title had not yet been announced, and the stage had a blackboard on an easel. I said something like ‘The next speaker is John Conway, and no doubt he is going to tell us what he will talk about.’ John came onto the stage, went over to the easel, picked up the blackboard, and turned it over. On the other side were revealed five titles of talks. He said, ‘I am going to give one of these talks. I will count down to zero; you are to shout as loudly as you can the number of the talk you want to hear, and the chairman will judge which number is most popular.’ “ |
From Log24 on August 21, 2014 —
Thursday, August 21, 2014
NoxFiled under: Uncategorized — m759 @ 1:00 AM ( A sequel to Lux ) “By groping toward the light we are made to realize — Arthur Koestler, The Call Girls: A Tragi-Comedy ,
Robin Williams and the Stages of Math i) shock & denial A related description of the process — “You know how sometimes someone tells you a theorem, — Tom Leinster yesterday at The n-Category Café |
Comments Off on Blackboard Jungle Continues.
Saturday, April 11, 2020
Process
“… the Jesuit religious order, whose intensive, extensive ordination process
typically takes about 10 years”
— The above link in The New York Times today leads to . . .
For the Church of Synchronology —
A post in this journal on the above Jesuit date — Aug. 11, 2013 —
leads to a John Hurley at Wolfram Demonstrations . . .
This may or may not be the John Hurley described in the
LinkedIn page below (click for further details):
Comments Off on Process
Dream
“All the schools of philosophy, from ancient Greece to the Enlightenment
encyclopedists, have dreamt of one day arriving at total and definitive
knowledge, a knowledge that encompasses the world. Indeed, the dream
lives on in the minds of some scientists today.”
— “Does Basic Research Have Meaning?” by Laurent Lafforgue —
“La recherche fondamentale a-t-elle un sens?
Quelques remarques d’un mathématicien catholique,”
Conférence donnée à l’Université de Notre-Dame,
aux États-Unis, le 20 mai 2011. Voici la version anglaise
de cette conférence (traduite par Hélène Wilkinson)
Et voici Larkin in Devs —
See too “musical brocade” in this journal.
Comments Off on Dream
Friday, April 10, 2020
The Extremadura Passion
“At the spiritual level, the biggest oeuvre (in my eyes)
accomplished by a man, was the Passion
of the Christ and his death on the cross…”
— Quotation said to be by Grothendieck, replying to
a 1987 letter from Juan Antonio Navarro González .
The quotation is from . . .
Comments Off on The Extremadura Passion
For Pleasantly Discursive Day
See “Pleasantly Discursive” in this journal.
Comments Off on For Pleasantly Discursive Day
Thursday, April 9, 2020
A Mad Night’s Work, or: Passover for Figaro
Comments Off on A Mad Night’s Work, or: Passover for Figaro
Symmetry: Toro, Torino
For the Toro , see Pierre Cartier in 2001 on the barber of Seville and
“The evolution of concepts of space and symmetry.”
For the Torino , see . . .
“… the ultimate goal of the present essay
which is to illustrate the historic
evolution of the concepts of Space and Symmetry “
— Pp. 157-158 of the above book.
See also Fré et al. , “The role of PSL(2,7) in M-theory”
(2018-2019) at http://arxiv.org/abs/1812.11049v2 ,
esp. Section 4, “Theory of the simple group PSL(2,7)”
on pages 11-27, and remarks on PSL(2,7) in this journal.
Related material —
Comments Off on Symmetry: Toro, Torino
Wednesday, April 8, 2020
For LA Boulevardiers
Comments Off on For LA Boulevardiers
Follow the Ring
Click the ring for Pierre Cartier on the barber of Seville
and “The evolution of concepts of space and symmetry.”
Comments Off on Follow the Ring
Ironweed Meditation
Andrew Cusack’s post today on architecture in Albany
suggests a review of the 1988 film Ironweed.
The dies natalis (in the Catholic sense) of that film’s
director was reportedly July 13, 2016.
Comments Off on Ironweed Meditation
A Midrash for Steiner
(The late Mark Steiner, not the late George Steiner.)
See Katherine Neville’s novel The Eight ,
Log24 posts tagged Crucible Raiders, and
St. Isidore, whose feast day is April 4 —
Mark Steiner’s book The Applicability of Mathematics
as a Philosophical Problem (Harvard University Press, 2002,
$36.50) is available for free at a website named for St. Isidore.)
Comments Off on A Midrash for Steiner
Tuesday, April 7, 2020
Eichler’s Amazing Bridge
The following historical remarks are quoted here because
of the above Quanta Magazine article from yesterday.
From Richard Taylor, “Modular arithmetic: driven by
inherent beauty and human curiosity,” The Letter of the
Institute for Advanced Study [IAS], Summer 2012,
pp. 6– 8 (link added) :
“Stunningly, in 1954, Martin Eichler (former IAS Member)
found a totally new reciprocity law . . . .” See as well —
Comments Off on Eichler’s Amazing Bridge
Monday, April 6, 2020
Sunday, April 5, 2020
“She do the Dickens in different voices”
From this journal on August 9, 2019 —
Perhaps not.
From an Instagram account, also on August 9, 2019 — (click to enlarge) —
Comments Off on “She do the Dickens in different voices”
Plan 9 from The New York Times
Click the image above for a tweet on the advertised IQ test.
Click the image below for the tweet’s details of the IQ test’s billing plan.
Comments Off on Plan 9 from The New York Times
Saturday, April 4, 2020
A Schicksalstag for the Author of The Eight
Comments Off on A Schicksalstag for the Author of The Eight
Devising Entities…
The previous post displayed a photo from November 2014.
Remarks quoted here in November 2014 —
“Before time began, there was the Cube.”
— Optimus Prime
Comments Off on Devising Entities…
Friday, April 3, 2020
Versions
A headline today —
Amazon’s ‘Tales From The Loop’ is
A Kinder, Gentler Version Of ‘Black Mirror’ —
From a search in this journal for “Loop” —
See also yesterday’s post “Mirror, Mirror.”
Comments Off on Versions
Thursday, April 2, 2020
Clarity and Precision
Continued from August 2, 2019
( a date suggested by the following search ) —
An image from “The 7/11 Meditation” ( Log24 on August 2, 2019 ) —
The search suggested above on 7/11, 2018, yields . . .
Comments Off on Clarity and Precision
Wednesday, April 1, 2020
Meditation for the Cruelest Month
From a post of September 30, 2003 —
Comments Off on Meditation for the Cruelest Month
Post for the SF*
See as well Log24 on the above arXiv date — “Compare and Contrast.”
The same date two years earlier was Easter Sunday.
* An abbreviation by Paul Erdős.
Comments Off on Post for the SF*
The Ghost
Related material —
Sunday’s Plan 9 from Yale as well as
http://www.arcadiainstitution.org/?page_id=16 and
https://www.flickr.com/photos/lselibrary/4114751310/in/photolist-7gBbd7.
Comments Off on The Ghost
Books at Perlego
" How small is the evil that may be safely ignored…? "
— "QBass" at Wikipedia, April 1, 2020
Good question.
Comments Off on Books at Perlego