Entertaining Mr. Slade —
Last night’s post for Oct. 30 (Devil’s Night) displayed a dark side
of actress Kate Beckinsale.
On the brighter side: a date which will live in infamy —
December 7 —
A brighter side of Kate, as a nurse on Pearl Harbor Day —
" The subject is justified by its usefulness
rather than as a 'rite of passage.' ”.
— The late Martin Muldoon reviewing a book,
From Vector Spaces to Function Spaces:
Introduction to Functional Analysis with Applications ,
by Yutaka Yamamoto (SIAM, 2012)
Such an introduction is properly a rite of pure mathematics —
the passage in the title from vector spaces to function spaces.
That passage is one of mathematical beauty.
Usefulness is Hiroshima.
Muldoon reportedly died on August 1, 2019.
This journal on that date had a post titled
Different Meanings: For Whom the Bell .
The "Bell" in that post was the author of a New York Times book review.
I prefer a Stephen King bell —
The post "Triangles, Spreads, Mathieu" of October 29 has been
updated with an illustration from the Curtis Miracle Octad Generator.
Related material — A search in this journal for "56 Triangles."
Fans of non-Christian religions ( like Robert Thurman
in Too Cool for School? ) may enjoy the vampire
oeuvre of Kate Beckinsale —
The above is an image from a Log24
search for Square Inch Space.
See also Harvard ex-president Faust on Hogwarts
and (like the above photo, also on Aug. 13) …
* See previous instances of the title in this journal.
An article in Men's Journal on August 1, 2013 —
For the Church of Synchronology — This journal on August 1, 2013.
The New York Times reports this evening the
death of a Conceptual artist on October 19 —
There are many approaches to constructing the Mathieu
group M24. The exercise below sketches an approach that
may or may not be new.
Exercise:
It is well-known that …
There are 56 triangles in an 8-set.
There are 56 spreads in PG(3,2).
The alternating group An is generated by 3-cycles.
The alternating group A8 is isomorphic to GL(4,2).
Use the above facts, along with the correspondence
described below, to construct M24.
Some background —
A Log24 post of May 19, 2013, cites …
Peter J. Cameron in a 1976 Cambridge U. Press
book — Parallelisms of Complete Designs .
See the proof of Theorem 3A.13 on pp. 59 and 60.
See also a Google search for "56 triangles" "56 spreads" Mathieu.
Update of October 31, 2019 — A related illustration —
Update of November 2, 2019 —
See also p. 284 of Geometry and Combinatorics:
Selected Works of J. J. Seidel (Academic Press, 1991).
That page is from a paper published in 1970.
Update of December 20, 2019 —
The Stuff of Legend —
Stronger Stuff —
For a third stuff — that which dreams are made of — see Mantilla.
“There has never since been any serious question
that the event from which to date the founding of
Harvard College is this vote on October 28, 1636.”
— Samuel Eliot Morison, The Founding of Harvard College
See also D8ing the Joystick (4/04 2018).
From an article on cybersecurity in today's new New Yorker —
Boback and Hopkins formed a corporation.
Hopkins came up with its name, Tiversa ,
a portmanteau of “time” and “universe.”
It was also an anagram of veritas : Latin for
“truth,” but scrambled.
Then there is …
vastier veritas —
"The postwar self became a cipher to be decoded."
— Nathaniel Comfort in Nature , PDF dated 10 October 2019
From a Log24 search for Temple of Doom —
Entertainment from NBC on Friday night —
The above question, and Saturday morning's post on a film director
from Melbourne, suggest an image from December's Melbourne Noir —
(March 8, 2018, was the date of death for Melbourne author Peter Temple.)
* For the title, see Saturday morning's post
"Popular Mechanics: Midnight Upgrade."
The title was suggested by the previous post and by
the title illustration in the weblog of the director,
Leigh Whannell, of the 2018 film “Upgrade.”
Related visual details —
For the Church of Synchronology —
Related remarks: “The Thing and I.”
On the word Gestaltung —
(Here “eidolon” should instead be “eidos .”)
A search for a translation of the book "Facettenreiche Mathematik " —
A paper found in the above search —
A related translation —
See also octad.design.
See as well this journal on the above FlixLatino date: Dec. 3, 2015.
From the end credits for a 2016 TV mini-series
based on the Stephen King novel 11/22/63 —
This post was suggested by the Oct. 22 post
Logos, by the Oct. 11 post Dick Date, and by
the Oct. 11 death of an MIT robotics professor.
Related tasteless humor —
A headline from the print version of the recent
technology issue of The New Yorker :
"Leonardo was something like what we now call a Conceptual artist,
maybe the original one. Ideas — experiments, theories — were
creative ends in themselves."
— Holland Cotter in the online New York TImes this evening
From other Log24 posts tagged Tetrahedron vs. Square —
* Phrase from the previous post, "Overarching Narrative."
In memory of a retired co-director of Galerie St. Etienne
who reportedly died on October 17 . . .
"It is… difficult to mount encyclopedic exhibitions
without an overarching art-historical narrative…."
— Jane Kallir, director of Galerie St. Etienne, in
https://www.tabletmag.com/jewish-arts-and-culture/
visual-art-and-design/269564/the-end-of-middle-class-art
An overarching narrative from the above death date —
See as well the previous post
and "Dancing at Lughnasa."
(With apologies to Susanne K. Langer, née Susanne Katherina Knauth)
See too the buzzard-related Catch-22 song —
The production-company logos for Carpenter B and Bad Robot
in end credits for a 2016 TV mini-series based on the Stephen King
novel 11/22/63 suggest a look at . . .
For the Church of Synchronology —
This weblog on Aug. 11, 2017:
Related entertainment —
Detail:
George Steiner —
"Perhaps an insane conceit."
Perhaps.
See Quantum Tesseract Theorem .
Perhaps Not.
See Dirac and Geometry .
See also a poem by Nick Tosches from the preceding day —
August 11, 2010 — "He Who Is of Name," in which Tosches
addresses actor James Franco (Esquire magazine).
See as well, from this journal recently . . .
Down the Rabbit Hole with James Franco —
… on some unspecified date,* according to
the University of Texas at Austin yesterday.
See also Tate in a Blackboard Jungle post
from December 5, 2013.
* On October 16, 2019 (AMS Day), according to
the Harvard University department of mathematics.
Continued from September 24 —
From today's news . . .
" 'If the nesting doll fits … '
'This is not some outlandish claim. This is reality.' "
Related images from 4 AM ET today —
See as well today's previous post, "Vibe for Ray Bradbury."
Bradbury was the author of the 1955 classic The October Country .
On writer Kate Braverman, who reportedly died on Sunday, October 13:
" She wears floor-length black skirts, swirling black coats,
and black stiletto boots; the San Francisco Chronicle once
described her vibe as 'Morticia Addams gone gypsy.' "
— Katy Waldman in The New Yorker , Feb. 22, 2018
"I need a photo opportunity
I want a shot at redemption
Don't want to end up a cartoon
In a cartoon graveyard"
— Paul Simon, song lyric
For a Braverman photo opportunity, see the dark corner
at lower right in the previous post.
"And the new dumbed-down gallery headings and word salads
of the main wall texts definitely need work."
— Roberta Smith yesterday in The New York Times
on the reopening Museum of Modern Art.
Sample gallery heading and word salad from this journal —
Heading:
Salad:
From a 1962 young-adult novel —
"There's something phoney in the whole setup, Meg thought.
There is definitely something rotten in the state of Camazotz."
Song adapted from a 1960 musical —
"In short, there's simply not
A more congenial spot
For happy-ever-aftering
Than here in Camazotz!"
The previous post, Tetrahedron Dance, suggests a review of . . .
A figure from St. Patrick's Day 2004 that might
represent a domed roof …
Inscribed Carpenter's Square:
In Latin, NORMA
… and a cinematic "Fire Temple" from 2019 —
In related news . . .
Related background: "e. e. cummings" in this journal.
English subtitles: The Tomorrow Man – transcript
The interested reader may consult Google
for the source of the above passage.
The American Mathematical Society has declared that
today is AMS Day.
A different sort of code than in the previous post —
"OCT 14, 2019 • 8:00 PM"
"Culturally, code exists in a nether zone.
We can feel its gnostic effects [link added]
on our everyday reality, but we rarely see it,
and it’s quite inscrutable to non-initiates.
(The folks in Silicon Valley like it that way;
it helps them self-mythologize as wizards.)
We construct top-10 lists for movies, games, TV—
pieces of work that shape our souls.
But we don’t sit around compiling lists of the world’s
most consequential bits of code, even though they
arguably inform the zeitgeist just as much."
— https://slate.com/technology/2019/10/
consequential-computer-code-software-history.html
(The title refers to Log24 posts now tagged Fire Temple.)
In memory of a New Yorker cartoonist who
reportedly died at 97 on October 3, 2019 …
"Read something that means something."
— New Yorker advertising slogan
From posts tagged Tetrahedron vs. Square —
This journal on October 3 —
"There is such a thing as a 4-set."
— Saying adapted from a 1962 young-adult novel.
Illustration (central detail a from the above tetrahedral figure) —
"Visual forms— lines, colors, proportions, etc.—
are just as capable of articulation ,
i.e. of complex combination, as words.
But the laws that govern this sort of articulation
are altogether different from the laws of syntax
that govern language. The most radical difference
is that visual forms are not discursive .
They do not present their constituents successively,
but simultaneously, so the relations determining
a visual structure are grasped in one act of vision."
— Susanne K. Langer, Philosophy in a New Key
Movie poster designer Philip Gips reportedly died on
Thursday, October 3, 2019. This journal on that date:
James R. Flynn (born in 1934), "is famous for his discovery of
the Flynn effect, the continued year-after-year increase of IQ
scores in all parts of the world." —Wikipedia
His son Eugene Victor Flynn is a mathematician, co-author
of the following chapter on the Kummer surface—
John Horgan in Scientific American magazine on October 8, 2019 —
"In the early 1990s, I came to suspect that the quest
for a unified theory is religious rather than scientific.
Physicists want to show that all things came from
one thing: a force, or essence, or membrane
wriggling in eleven dimensions, or something that
manifests perfect mathematical symmetry. In their
search for this primordial symmetry, however,
physicists have gone off the deep end . . . ."
Other approaches —
See "Story Theory of Truth" in this journal and, from the November 2019
Notices of the American Mathematical Society . . .
More fundamental than the label of mathematician is that of human. And as humans, we’re hardwired to use stories to make sense of our world (story-receivers) and to share that understanding with others (storytellers) [2]. Thus, the framing of any communication answers the key question, what is the story we wish to share? Mathematics papers are not just collections of truths but narratives woven together, each participating in and adding to the great story of mathematics itself. The first endeavor for constructing a good talk is recognizing and choosing just one storyline, tailoring it to the audience at hand. Should the focus be on a result about the underlying structures of group actions? . . . .
[2] Gottschall, J. , The Storytelling Animal , — "Giving Good Talks," by Satyan L. Devadoss |
"Before time began, there was the Cube." — Optimus Prime
Note that in the pictures below of the 15 two-subsets of a six-set,
the symbols 1 through 6 in Hudson's square array of 1905 occupy the
same positions as the anticommuting Dirac matrices in Arfken's 1985
square array. Similarly occupying these positions are the skew lines
within a generalized quadrangle (a line complex) inside PG(3,2).
Related narrative — The "Quantum Tesseract Theorem."
The interested reader may consult Google for the source of
the above. For the "Numberland" of the title, see this journal.
From 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
From The Point magazine yesterday, October 8, 2019 —
Parricide: On Irad Kimhi's Thinking and Being .
Book review by Steven Methven.
The conclusion:
"Parricide is nothing that the philosopher need fear . . . .
What sustains can be no threat. Perhaps what the
unique genesis of this extraordinary work suggests is that
the true threat to philosophy is infanticide."
This remark suggests revisiting a post from Monday —
Monday, October 7, 2019
Berlekamp Garden vs. Kinder Garten
|
This journal on the date of Coe's death —
Related material: Today's noon post and a post from August 7, 2006.
The Hudson array mentioned above is as follows —
See also Whitehead and the
Relativity Problem (Sept. 22).
For coordinatization of a 4×4
array, see a note from 1986
in the Feb. 26 post Citation.
American Mathematical Monthly , June-July 1984 — MISCELLANEA, 129 Triangles are square
"Every triangle consists of n congruent copies of itself" |
* See Cube Bricks 1984 in previous post.
Stevens's Omega and Alpha (see previous post) suggest a review.
Omega — The Berlekamp Garden. See Misère Play (April 8, 2019).
Alpha — The Kinder Garten. See Eighfold Cube.
Illustrations —
The sculpture above illustrates Klein's order-168 simple group.
So does the sculpture below.
Cube Bricks 1984 —
Or: Je repars .
From 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
Mathematician Hanfried Lenz reportedly died in Berlin on June 1, 2013.
This journal that weekend —
(A sequel to Simplex Sigillum Veri and
Rabbit Hole Meets Memory Hole)
” Wittgenstein does not, however, relegate all that is not inside the bounds
of sense to oblivion. He makes a distinction between saying and showing
which is made to do additional crucial work. ‘What can be shown cannot
be said,’ that is, what cannot be formulated in sayable (sensical)
propositions can only be shown. This applies, for example, to the logical
form of the world, the pictorial form, etc., which show themselves in the
form of (contingent) propositions, in the symbolism, and in logical
propositions. Even the unsayable (metaphysical, ethical, aesthetic)
propositions of philosophy belong in this group — which Wittgenstein
finally describes as ‘things that cannot be put into words. They make
themselves manifest. They are what is mystical’ ” (Tractatus 6.522).
— Stanford Encyclopedia of Philosophy , “Ludwig Wittgenstein”
From Tractatus Logico-Philosophicus by Ludwig Wittgenstein.
(First published in Annalen der Naturphilosophie ,1921. 5.4541 The solutions of the problems of logic must be simple, since they set the standard of simplicity. Men have always had a presentiment that there must be a realm in which the answers to questions are symmetrically combined — a priori — to form a self-contained system. A realm subject to the law: Simplex sigillum veri. |
Somehow, the old Harvard seal, with its motto “Christo et Ecclesiae ,”
was deleted from a bookplate in an archived Harvard copy of Whitehead’s
The Axioms of Projective Geometry (Cambridge U. Press, 1906).
In accordance with Wittgenstein’s remarks above, here is a new
bookplate seal for Whitehead, based on a simplex —
Kiley in Blackboard Jungle , 1955 —
From the previous post —
"Prenons arbitrairement dans le tableau ci-dessus…."
Related material — "Ici vient M. Jordan."
(Continued.)
The previous post suggests a review of
the following mathematical landmark —
The cited article by Kummer is at . . .
https://archive.org/details/monatsberichtede1864kn/page/246 .
For a first look at octad.space, see that domain.
For a second look, see octad.design.
For some other versions, see Aitchison in this journal.
(For Harlan Kane)
"Once Mr. Overbye identifies a story, he said, the work is
in putting it in terms people can understand. 'Metaphors
are very important to the way I write,' he said. The results
are vivid descriptions that surpass mere translation."
— Raillan Brooks in The New York Times on a Times
science writer, October 17, 2017. Also on that date —
"There is such a thing as a 4-set."
— Saying adapted from a 1962 young-adult novel.
See as well The Black List (Log24, September 27).
"… I was struck by the fusion of drama and music.”
— Autobiographical recollection by a music critic who
reportedly died on Sunday at 83.
Related material — The previous post and …
"When the queen came, they said she was wanton.
Or a witch, or a saint."
— Ursula Whitcher, "Alphabet of Signs"
Related images —
"There's a long literary tradition associating
certain kinds of geometry with horror."
— American Mathematical Society yesterday:
See also yesterday's Log24 post "Transylvania Revisited."
A related post —
Poet Wallace Stevens was born 140 years ago today.
For another 140, see Diamond Theory in 1937.
For some notes related to a Stevens poem from 1937,
see "arrowy, still strings" in this journal.
The previous post suggests . . .
Jim Holt reviewing Edward Rothstein's Emblems of Mind: The Inner Life of Music and Mathematics in The New Yorker of June 5, 1995: "The fugues of Bach, the symphonies of Haydn, the sonatas of Mozart: these were explorations of ideal form, unprofaned by extramusical associations. Such 'absolute music,' as it came to be called, had sloughed off its motley cultural trappings. It had got in touch with its essence. Which is why, as Walter Pater famously put it, 'all art constantly aspires towards the condition of music.' The only art that can rival music for sheer etheriality is mathematics. A century or so after the advent of absolute music, mathematics also succeeded in detaching itself from the world. The decisive event was the invention of strange, non-Euclidean geometries, which put paid to the notion that the mathematician was exclusively, or even primarily, concerned with the scientific universe. 'Pure' mathematics came to be seen by those who practiced it as a free invention of the imagination, gloriously indifferent to practical affairs– a quest for beauty as well as truth." [Links added.] |
A line for James McAvoy —
"Pardon me boy, is this the Transylvania Station?"
See as well Worlds Out of Nothing , by Jeremy Gray.
Cover illustration— Arithmetic and Music,
Borgia Apartments, the Vatican.
See also Rothstein in this journal.
Related posts: The Eightfold Hijacking.
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