"Galois' ideas, which for several decades remained
a book with seven seals but later exerted a more
and more profound influence upon the whole
development of mathematics, are contained in
a farewell letter written to a friend on the eve of
his death, which he met in a silly duel at the age of
twenty-one. This letter, if judged by the novelty and
profundity of ideas it contains, is perhaps the most
substantial piece of writing in the whole literature
of mankind."
"A good, involving mystery featuring strong characters and
prose as smooth as the brim of a fedora, this novel makes
smart points about writing, publishing and the cult of mysteries."
The universe of texts can be seen as a landscape. In it one can make out mountains and valleys, rivers and lakes, castles, farmyards and inner-city slums. On the horizon of the scene visualized in this way, the Bible and Homer appear as gigantic ice-covered mountains. The vast, tranquil lake of Aristotle’s texts, where fishermen idly throw their nets and philologists row their boats, occupies a part of the valley bottom. There, the tumbling waterfall of Nietzsche is captured by the broad river of modern pragmatism. Towering above everything, the Gothic cathedral of St Thomas Aquinas’s Summae dominates the cathedral square of the city, in which the roofs and gables of Baroque speculations jostle one another. In the suburbs of this city, one catches sight of the Romantic, Realist and Modernist housing-blocks and factories of more recent litera¬ ture; somewhat apart from all these stands a small, apparently insignificant house resembling scaffolding more than a finished building: Wittgenstein’s building.
This little house is called the Tractatus. This name isn’t the product of a one-track mind. For when one enters the house, one notices immediately that this is not a place that has lost track of things. Quite the opposite: It is a place of mirror- images. The house stands on six foundation pillars which support one another by means of cross-beams organized in a hierarchy. In the middle, however, there rises a seventh pillar whose function it is to cut through the building and free it from the ground. So the house with all its corners, angles and joints is protected, armoured and impregnable. And yet, and for that very reason, it is threatened with collapse and disappearance without trace – condemned in advance and from the outset.
The building is set out: It consists of propositions. Every proposition presupposes all the preceding ones and is itself the 76 presupposition of all the following propositions. Proposition by proposition, anyone who enters progresses through the prescribed rooms, and his step is supported by consistencies. Suddenly, with one proposition, one single proposition, the ground gives way beneath his feet. He falls head first into the abyss.
Wittgenstein’s house is situated in a suburb of that city whose cathedral square is dominated by the towers of Thomas Aquinas’s cathedral. The small, modest pillars of Wittgenstein’s house support one another according to the same logico- philosophical method as the pillars of the cathedral support one another. But there appears to be a world of difference between the cathedral and the little house: The cathedral is a ship pointing in the direction of heaven, and the little house is a trap-door pointing in the direction of a bottomless abyss. But be careful: May Thomas Aquinas not have been right in saying after his revelation that everything he had written before was like straw? May not the heaven above the cathedral be the same black hole as the abyss beneath the little house? May not Wittgenstein’s little house be the cathedral of today? And those mirrors whose images simultaneously mirror one another, may they not be our equivalent of stained-glass windows?
The landscape portrayed in this essay, it goes without saying, is a metaphor. Is it possible to identify it as Vienna? And is it possible for anyone entering Wittgenstein’s little house in that unlikely place to make out a hint of the unsayable? What we cannot speak about we must pass over in silence. 77
"In computer science, "IO" or "I/O" is commonly used
as an abbreviation for input/output, which makes the
.io domain desirable for services that want to be
associated with technology. .io domains are often used
for open source projects, application programming
interfaces ("APIs"), startup companies, browser games,
and other online services."
“"I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”
A less poetic meditation on the above 4x4x4 design cube —
"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."
" While quantum theory has proven to be supremely successful
since its development a century ago, physicists have struggled to
unify it with gravity to create one overarching ‘theory of everything.’ "
"Edward Bulwer-Lytton (infamous author of the opening line,
'It was a dark and stormy night') was a Victorian-era writer.
In 1870, he published a science fiction novel, The Power of the Coming Race, which describes an underground race of
superhuman angel-like creatures and their mysterious energy
force, Vril, an 'all-permeating fluid' of limitless power."
"Imagine a powerful man as a ship, like the Titanic. That ship is a huge enterprise. When it strikes an iceberg, there are a lot of people on board desperate to patch up holes — not because they believe in or even care about the ship, but because their own fates depend on the enterprise."
The University of the Basque Country
(Basque: Euskal Herriko Unibertsitatea, EHU ;
Spanish: Universidad del País Vasco, UPV ; UPV/EHU)
is a Spanish public university of the Basque Autonomous Community.
— Wikipedia
Comments Off on The Diamond Theorem in Basque Country
"… What Paris says to me is love story, awash with painters,
shots of the Seine, Champagne. Thank God I have a
can’t-miss notion to sell you. I call it ‘Midnight in Paris.’ ”
“Romantic title,” I had to admit. “Is there a script?”
“Actually, there’s nothing on paper yet, but I can spitball
the main points,” he said, slipping on his tap shoes.
“Maybe some other time,” I said, mindful of Cubbage’s
unbroken string of theatrical Hiroshimas.
— Woody Allen
The above passage is in memory of a French film director
who, like the reporter in yesterday's post Primary Colors,
reportedly died on April 21, 2022.
"In his classic essay of 1955 'The Structural Study of Myth' Levi-Strauss came up with a universal formula of mythopoeic dynamics
[fx(a) : fy(b) :: fx(b) : fa-1(y)]
that he called canonical 'for it can represent any mythic transformation'. This formulation received its consummation in the four massive Mythologiques volumes, the last of which crystallises the fundamental dialectics of mythopoeic thought: that there is 'one myth only' and the primal ground of this 'one' is 'nothing'. The elucidation of the generative matrix of the myth-work is thus completed as is the self-totalisation of both the thinker and his object."
So there.
At least one mathematician has claimed that the Levi-Strauss formula makes sense. (Jack Morava, arXiv pdf, 2003.)
I prefer the earlier (1943) remarks of Hermann Hesse on transformations of myth:
"…in the spirit of the Glass Bead Game, everything actually was all-meaningful, that every symbol and combination of symbols led not hither and yon, not to single examples, experiments, and proofs, but into the center, the mystery and innermost heart of the world, into primal knowledge. Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created."
The previous post suggests two quotes by Elizabeth Janeway
from her review of the second volume of The Human Predicament ,
an unfinished trilogy by Richard Hughes.
"The Human Predicament poses a universal question, and Hughes
is grappling with it really as a structuralist philosopher."
"Hughes's style is kaleidoscopic , the shaking of vivid moments together
until a pattern emerges."
Derrida was the final speaker on the final day. He remained a silent observer for much of the symposium. He looked on as Lacan rose to his feet with obscure questions at the end of each lecture, and as Barthes gently asked for clarification on various moot points. Eventually, however, Derrida, unused to speaking to large audiences, took to the stage, quietly shuffled his notes, and began, ‘Perhaps something has occurred in the history of the concept of structure that could be called an “event”…’ He spoke for less than half an hour. But by the time he was finished the entire structuralist project was in doubt, if not dead. An event had occurred: the birth of deconstruction.
Salmon, Peter. An Event, Perhaps(pp. 2-3).
Verso Books (Oct. 2020). Kindle Edition.
Salmon today at Arts & Letters Daily —
Comments Off on “The History of the Concept of Structure”
The square array above does not contain Arfken's variant
labels for ρ1, ρ2, and ρ3, although those variant labels were
included in Arfken's 1985 square array and in Arfken's 1985 list of six anticommuting sets, copied at MathWorld as above.
The omission of variant labels prevents a revised list of the
six anticommuting sets from containing more distinct symbols
than there are matrices.
Red: If I may offer some counsel –
“Do not go where the path may lead.
Go instead where there is no path
and leave a trail.”
In the spirit of that, I bring an unusual case….
This post is in honor of Thandiwe Newton,
who left a Westworld trail —
"'There was a space between the academic,
theory-heavy M.I.T. Press and the coffeetableism
of Rizzoli,' Mr. Lamster wrote, adding that
Princeton Architectural Press would fill the gap
with 'the voice of the young practitioner.'"
The New York Times today has an obituary for
Kevin Lippert, the founder and publisher of
Princeton Architectural Press, who reportedly
died at 63 on March 29, 2022.
“'There was a space between the academic,
theory-heavy M.I.T. Press and the coffeetableism
of Rizzoli,' Mr. Lamster wrote, adding that
Princeton Architectural Press would fill the gap
with 'the voice of the young practitioner.'
Mr. Lippert championed emerging architects.
He published Steven Holl’s seminal architectural
manifesto, 'Anchoring,' in 1989, and wrote the
introduction to the book of the same name.
Mr. Holl, in a tribute to Mr. Lippert on his website,
called him 'a committed intellectual and impresario
for the culture of architecture.'”
— Katharine Q. Seelye, April 17, 2022, 2:21 p.m. ET
From the cited tribute to Lippert on Holl's website —
"An excerpt from his publisher’s foreword to Anchoring :
In its iconic simplicity, his work seems to be about
the language of architecture, not in the allusive sense
used by postmodernists nor in the paradigmatic sense
used by so-called 'deconstructivists' but at the level of
essences of tropes and morphs… He is the only
American architect of his generation to be directly
influenced by the main lines in modern philosophy and
music, that is to say, by the line leading from Husserl
through to Heidegger and by separate achievements
of Bartok and Schonberg ."
Actually, although the above "iconic simplicity" passage,
up to the ellipsis after "morphs," is from the foreword
by Lippert, the references that follow the ellipsis — to
Husserl, Heidegger, Bartok, and Schonberg — are not
from Lippert's foreword, but from the introduction by
one Kenneth Frampton —
"It’s important, as art historian Reinhard Spieler has noted,
that after a brief, unproductive stay in Paris, circa 1907,
Kandinsky chose to paint in Munich. That’s where he formed
the Expressionist art group Der Blaue Reiter (The Blue Rider) —
and where he avoided having to deal with cubism."
"Reviewing Ms. Allen’s staging of Ibsen’s 'When We Dead Awaken'
at Stage West in 1977, Mr. Barnes wrote that
it had 'speed, conviction and perception.'"
A related post by Terry Tao on September 14, 2007 —
The comments on Tao's post contain a reference to Polya's classic Induction and Analogy in Mathematics . (See pp. 15-17.) Polya notes
on page 15 —
"Generalization, Specialization, and Analogy often concur
in solving mathematical problems. Let us take as an example
the proof of the best known theorem of elementary geometry,
the theorem of Pythagoras. The proof that we shall discuss is
not new; it is due to Euclid himself (Euclid VI, 31)."
Comments Off on Pythagoras via Tao, Polya, and Euclid
On Sept. 12, 2001, The Washington Post published an opinion essay by General Boyd in which he wrote,
“While we may feel at the moment as though we are
in a trance, we are, in fact, awakening.”
Update of 11:30 AM ET April 1, 2022 — A simpler version:
The above picture may be used to to introduce the concept of a "shape constant"
in similar figures — like the shape constant pi in a circle or the square root of 2
in a square. In each of the three similar figures at right above, the ratio of the
triangular area to the area of the attached square is a shape constant …
the same, because of their similarity, for each of the three shapes. Since the
areas of the top two triangles at right sum to that of the enclosed triangle at left,
their attached square areas sum to the area of the bottom square, Q.E.D.
"In The Girl Before, the house is almost a shapeshifter as it fits
the needs of the story. Sometimes it feels like an art gallery,
with its inhabitants on display. It's a smart home (of course it is),
and its automated locks and lights and creepily intuitive A.I.
give it the feel of a high-tech prison. Sometimes it's a mausoleum
for Jane, who's dealing with the recent pain of a miscarriage.
Sometimes it's a fortress for Emma, who's dealing with the recent
trauma of a home invasion." — Joe Reid at Primetimer.com.
Related story elements — Two deaths, from March 17 and 19.
They went to Björk’s house. She cooked salmon.
She had seen “The Witch” and introduced Eggers
to Sjón, who had written a novel about seventeenth-
century witchcraft in Iceland. When he got home,
Eggers read Sjón’s books. “I was, like, this guy’s
a fucking magician,” Eggers said. “He sees all time,
in time, out of time.”
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
"… Wade’s entire life is built around the squid attack. In the episode’s opening, we see that 34 years ago, young Wade was at a carnival in Hoboken, New Jersey, proselytizing as a Jehovah’s Witness when the squid emitted a psychic blast that killed three million people in the New York area. Just before the attack, a girl led him into a house of mirrors, feigning interest in hooking up with him in order to steal his clothes, leaving him naked and humiliated in the fairground attraction. But the cruel prank also saved his life, as mirrors can apparently repel the squid's psychic blast."
Related literary remarks —
"It may have been by chance, and it may have had the side effect of being easy to read, but this way of putting a novel together offered a bridge between the miniaturist in Doerr and the seeker of world-spanning connections. He could focus on the details of every piece in the narrative, but there was pleasure, too, in placing them against each other. Sometimes he would lay out all these micro chapters on the floor so he could see them and discover the resonances between characters across space and time.
'That’s the real joy,' Doerr said, 'the visceral pleasure that comes from taking these stories, these lives, and intersecting them, braiding them.'"
— "A version of this article appears in print on Sept. 20, 2021, Section C, Page 4 of the New York edition with the headline: Bringing His Readers To Higher Ground."
Comments Off on Watchmen Squid Game: Pronoun Trouble
