An illustration from posts tagged Holy Field GF(3) —
See also a Log24 search for "Four Gods."
Monday, April 18, 2022
Sunday, April 17, 2022
Annals of Iconic Simplicity
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 —
From Google Books:
Bibliographic data —
Another architectural memorial, from the reported date of Lippert's death —
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Wednesday, January 29, 2020
The 2013 Simplicity Conference…
… is reviewed by the American Mathematical Society (AMS) in
the February 2020 issue (online Jan. 27) of the AMS Notices :
See as well Simplicity Conference in this journal.
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Tuesday, October 23, 2018
Simplicity Versus Complexity
Simplicity (Click for some complexity.)
Complexity (Click for some simplicity.)
A passage from the 2011 book Idea Man that was suggested by
a recent New Yorker article on the book's author, the late Paul Allen —
Left-click image to enlarge.
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Sunday, October 21, 2018
Monday, August 27, 2018
Geometry and Simplicity
From …
Thinking in Four Dimensions
By Dusa McDuff
"I’ve got the rather foolhardy idea of trying to explain
to you the kind of mathematics I do, and the kind of
ideas that seem simple to me. For me, the search
for simplicity is almost synonymous with the search
for structure.
I’m a geometer and topologist, which means that
I study the structure of space …
. . . .
In each dimension there is a simplest space
called Euclidean space … "
— In Roman Kossak, ed.,
Simplicity: Ideals of Practice in Mathematics and the Arts
(Kindle Locations 705-710, 735). Kindle Edition.
For some much simpler spaces of various
dimensions, see Galois Space in this journal.
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Sunday, December 11, 2016
Complexity to Simplicity via Hudson and Rosenhain*
*The Hudson of the title is the author of Kummer's Quartic Surface (1905).
The Rosenhain of the title is the author for whom Hudson's 4×4 diagrams
of "Rosenhain tetrads" are named. For the "complexity to simplicity" of
the title, see Roger Fry in the previous post.
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Complexity to Simplicity
Cézanne "showed how it was possible to pass
from the complexity of the appearance of things
to the geometrical simplicity which design demands."
— Roger Fry in the catalogue for the 1910 London
exhibition "Manet and the Post-Impressionists,"
according to …
See also A Roger Fry Reader
(edited by Christopher Reed,
University of Chicago Press, 1996).
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Saturday, July 27, 2013
Simplicity
(Continued from July 16)
From the schedule of an April 2013 philosophical conference:
Why should anyone care what Zwicky thinks?
1. Her writings. In particular, Plato as Artist .
2. Her husband. See Robert Bringhurst in this journal.
3. A reading by Zwicky and Bringhurst on March 20, 2013.
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Sunday, August 18, 2024
“Like a Kernel”
|
“The yarns of seamen have a direct simplicity, — Joseph Conrad in Heart of Darkness
“By groping toward the light we are made to realize
— Arthur Koestler, The Call Girls: A Tragi-Comedy, |
From an obituary of Alain Delon, who reportedly died today . . .
|
"He starred in the 1976 French best picture winner, 'Mr. Klein,' as a wartime German art dealer threatened by being mistaken for a Jewish man with the same name." |
See as well Felix Christian Klein in this journal.
And then there is being mistaken for a fictional archaeologist
with the same name.
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Saturday, June 15, 2024
Screwing Up a Space
Flashback to April 12, 2011 —
|
In the landscape of minimalism, John McCracken cuts a unique figure. He is often grouped with the “light and space” artists who formed the West Coast branch of the movement. Indeed, he shares interests in vivid color, new materials, and polished surfaces with fellow Californians enamored of the Kustom Kar culture. On the other hand, his signature works, the “planks” that he invented in 1966 and still makes today, have the tough simplicity and aggressive presence of New York minimalism…. “They kind of screw up a space because they lean,” McCracken has said of the planks. Their tilting, reflective surfaces activate the room, leaving the viewer uncertain of traditional boundaries. He notes that the planks bridge sculpture (identified with the floor) and painting (identified with the wall)…. His ultimate goal, as with all mystics, is unity— not just of painting and sculpture, but of substance and illusion, of matter and spirit, of art and life. Such ideas recall the utopian aspirations of early modernists like Piet Mondrian and Wassily Kandinsky. Related Art —
Unity
—Roman numeral I For a related figure, see a film review by A. O. Scott at The New York Times (September 21, 2010)— “You Will Meet a Tall Dark Stranger” begins with an unseen narrator— , sounding a lot like — paraphrasing . You may remember the quotation from high school English, about how life is a tale told by an idiot, full of sound and fury, signifying nothing. The observation is attributed to the playwright himself (“Shakespeare once said”), rather than to Macbeth, whose grim experience led him to such nihilism, but never mind. In context, it amounts to a perfectly superfluous statement of the obvious. If life signifies nothing, perhaps the tall dark figure above signifies something . Discuss. |
Related (if only phonetically) drama . . . Detective Cruz at Planck's Café.
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Thursday, February 29, 2024
Masonic Mojo Dojo Casa House
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Tuesday, December 12, 2023
If It’s Tuesday…
|
“The yarns of seamen have a direct simplicity, — Joseph Conrad in Heart of Darkness
“By groping toward the light we are made to realize
— Arthur Koestler, The Call Girls: A Tragi-Comedy, |
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Monday, November 27, 2023
Problems with the Process
Condensed from Peter J. Cameron's weblog today —
|
“Words that tear and strange rhymes” "In his youth, Paul Simon thought of himself as a poet . . . . And surprisingly often he describes problems with the process:
For me, things were somewhat similar. Like many people, I wrote poetry in my youth. Julian Jaynes says something like 'Poems are rafts grasped at by men drowning in inadequate minds', but I think I knew from early on that one of the main reasons was to practise my writing, so that when I had something to say I could say it clearly. When Bob Dylan renounced the over-elaborate imagery of Blonde on Blonde for the clean simplicity of John Wesley Harding, I took that as a role model. Could Simon’s experience happen in mathematics? It is possible to imagine that an important mathematical truth is expressed in 'words that tear and strange rhymes'. More worryingly, an argument written in the most elegant style could be wrong, and we may be less likely to see the mistake because the writing is so good." |
The problem with the process in this case is Cameron's misheard lyrics.
From https://www.paulsimon.com/track/kathys-song-2/ —
And a song I was writing is left undone
I don’t know why I spend my time
Writing songs I can’t believe
With words that tear and strain to rhyme
A rather different artist titled a more recent song
"Strange Rhymes Can Change Minds."
See also . . .
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Thursday, November 23, 2023
Speak, Memory: 12 Panes or 16?
"Blackboard Jungle," 1955 —
"Through the unknown, remembered gate . . . ."
A differently remembered gate —
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Wednesday, August 17, 2022
Cold Comfort Dam
"And, as with all retold tales that are in people's hearts,
there are only good and bad things and black and white
things and good and evil things and no in-between anywhere."
— John Steinbeck, author's epigraph to The Pearl
From the Season 4 finale of Westworld :
uploading Dolores's pearl at Hoover Dam —
For those who prefer greater theological simplicity . . .
Optimus Prime on a different Hoover Dam figure, that of
the AllSpark: "Before time began, there was the Cube."
Simplifying even more . . .
“A set having three members is a single thing
wholly constituted by its members but distinct from them.
After this, the theological doctrine of the Trinity as
‘three in one’ should be child’s play.”
– Max Black, Caveats and Critiques: Philosophical Essays
in Language, Logic, and Art , Cornell U. Press, 1975
As above, Black's theology forms a cube.
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Monday, April 18, 2022
A Space Between
From yesterday's post "Annals of Iconic Simplicity" —
On the founding of Princeton Architectural Press:
"'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.'"
Some context —
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Tuesday, February 8, 2022
Directions Out
On reading about DNA:
"Suddenly it was clear to me
that all the beautiful complexity of life
had simplicity at its core," he says.
"This is the kind of thing mathematicians love."
— Eric Lander in "The 2004 TIME 100 — Our list
of the most influential people in the world today"
The date on the above TIME piece is Monday,
Apr. 26, 2004. Remarks in this journal on that date
are now tagged Directions Out.
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Sunday, January 2, 2022
Annals of Modernism: UR–Grid
The above New Yorker art illustrates the 2×4 structure of
an octad in the Miracle Octad Generator of R. T. Curtis.
Enthusiasts of simplicity may note how properties of this eight-cell
2×4 grid are related to those of the smaller six-cell 3×2 grid:
See Nocciolo in this journal and . . .
Further reading on the six-set – eight-set relationship:
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Wednesday, September 15, 2021
The Razor and the Touchstone
It is often good to remember that writers of headlines (and subheadlines)
are usually not the same people as the authors of the following texts.
In particular, in the above example, neither the word "touchstone" nor
the use of "enquires" to mean "enquiries" appears in the text proper.
Still, the mixed metaphor of "razor" as "touchstone" is not without interest.
See The Eightfold Cube and Modernist Cuts.
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Wednesday, September 2, 2020
Little Metal Letters
From a report of another August 14 death —
“… on Dec. 7, 1941, ‘it seemed as though everyone at Harvard
came to the Crimson building that night, and anxiously
hung over the ticker tape [i.e., teletype ] machine to watch the
little metal letters hammer out the words that told the story.'”
— Dan Huntington Fenn Jr., quoted in his Boston Globe obituary.
“Simplicity, clarity, showing the text” — The late Howell Binkley.
“To expand the words and music and dance” . . .
See Coconut Dance.
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Thursday, May 14, 2020
Art Issue*
"… the beautiful object
that stood in
for something else.”
— Holland Cotter quoting an art historian
in The New York Times on May 13
From a post of April 27, 2020 —
“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
The beautiful object —
Something else —
* The title is a reference to other posts now also tagged Art Issue.
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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
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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.
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Monday, October 7, 2019
Oblivion
(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 —
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Sunday, August 4, 2019
Bright Club
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Monday, January 7, 2019
Resonant Clarity
|
Abstract for a talk at the City University of New York:
The Experience of Meaning Once the question of truth is settled, and often prior to it, what we value in a mathematical proof or conjecture is what we value in a work of lyric art: potency of meaning. An absence of clutter is a feature of such artifacts: they possess a resonant clarity that allows their meaning to break on our inner eye like light. But this absence of clutter is not tantamount to 'being simple': consider Eliot's Four Quartets or Mozart's late symphonies. Some truths are complex, and they are simplified at the cost of distortion, at the cost of ceasing to be truths. Nonetheless, it's often possible to express a complex truth in a way that precipitates a powerful experience of meaning. It is that experience we seek — not simplicity per se , but the flash of insight, the sense we've seen into the heart of things. I'll first try to say something about what is involved in such recognitions; and then something about why an absence of clutter matters to them. |
For some context, see posts tagged Artifacts.
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Friday, August 17, 2018
Hogwarts Peak
Or: Misery, Jessica … Jessica, Misery .
Related material from The Harvard Crimson —
"The beach and the castle on the hill and the waves
would always be here, always moving, always changing,
but always constant."
— Robert Miranda, "The Simplicity of Waves," August 8, 2018
Related material on waves (i.e. , "Fourier's laboratory") —
See also this journal on August 8.
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Monday, July 16, 2018
Greatly Exaggerated Report
"The novel has a parallel narrative that eventually
converges with the main story."
— Wikipedia on a book by Foer's novelist brother
Public Squares
An image from the online New York Times
on the date, July 6,
of the above Atlantic article —
An image from "Blackboard Jungle," 1955 —
"Through the unknown, remembered gate . . . ."
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Friday, July 6, 2018
Blackboard Jungle — The Prequel
An image from the online New York Times today —
Blackboard Jungle , 1955 —
"Through the unknown, remembered gate . . . ."
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Monday, July 2, 2018
Another Letterman Intro
Recognitions, Corrections; Corrections, Recognitions.
"It is the dawning of the second gestalt
in relation to the first
that is the experience of meaning."
— Jan Zwicky in "The Experience of Meaning"
(at 27:36 of 44:36 in the video of her talk)
Related remarks by the author of The Corrections —
" Even friends of The Recognitions have found it a daunting
text. Jonathan Franzen, the best known of the book's current
day champions, has offered both praise and words of warning
to potential readers. 'I loved it,' he proclaimed in the pages
of The New Yorker back in 2002, where he held up Gaddis's
novel as the preeminent example of what Franzen calls 'the
Status model' of literature. Authors who subscribe to the
'Status model' embrace fiction as the springboard for
'a discourse of genius and art-historical importance' freed
from the demands of the marketplace or the requirements of
mass consumption. Yet even Franzen acknowledges the toll
exacted by this particular masterpiece. He declares that The
Recognitions is 'the most difficult book I ever voluntarily read
in its entirety,' adding that he completed the task 'as a kind
of penance.' "
Now try Euclid.
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Sunday, July 1, 2018
Deutsche Ordnung
The title is from a phrase spoken, notably, by Yul Brynner
to Christopher Plummer in the 1966 film “Triple Cross.”
Related structures —
Greg Egan’s animated image of the Klein quartic —
For a smaller tetrahedral arrangement, within the Steiner quadruple
system of order 8 modeled by the eightfold cube, see a book chapter
by Michael Huber of Tübingen —
For further details, see the June 29 post Triangles in the Eightfold Cube.
See also, from an April 2013 philosophical conference:
| Abstract for a talk at the City University of New York:
The Experience of Meaning Once the question of truth is settled, and often prior to it, what we value in a mathematical proof or conjecture is what we value in a work of lyric art: potency of meaning. An absence of clutter is a feature of such artifacts: they possess a resonant clarity that allows their meaning to break on our inner eye like light. But this absence of clutter is not tantamount to ‘being simple’: consider Eliot’s Four Quartets or Mozart’s late symphonies. Some truths are complex, and they are simplified at the cost of distortion, at the cost of ceasing to be truths. Nonetheless, it’s often possible to express a complex truth in a way that precipitates a powerful experience of meaning. It is that experience we seek — not simplicity per se , but the flash of insight, the sense we’ve seen into the heart of things. I’ll first try to say something about what is involved in such recognitions; and then something about why an absence of clutter matters to them. |
For the talk itself, see a YouTube video.
The conference talks also appear in a book.
The book begins with an epigraph by Hilbert —
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Thursday, March 1, 2018
The Movement of Analogy: Hume vs. Paz
Hume, from posts tagged "four-set" in this journal —
"The mind is a kind of theatre, where several perceptions
successively make their appearance; pass, repass, glide away,
and mingle in an infinite variety of postures and situations.
There is properly no simplicity in it at one time, nor identity
in different, whatever natural propension we may have
to imagine that simplicity and identity."
Paz, from a search for Paz + Identity in this journal —
|
"At the point of convergence by Octavio Paz, translated by Helen Lane
|
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Monday, November 27, 2017
The Golay Code via Witt’s Construction
Hansen, Robert Peter, "Construction and Simplicity of
the Large Mathieu Groups" (2011). Master's Theses. 4053.
http://scholarworks.sjsu.edu/etd_theses/4053.
See also The Matrix Meets the Grid (Log24, Nov. 24).
More generally, see SPLAG in this journal.
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Thursday, May 18, 2017
Bit Plot
From a May 15 review of a new book by Douglas Coupland, author of
the 1991 book Generation X: Tales for an Accelerated Culture .
"Minimalists are actually extreme hoarders:
they hoard space." — Douglas Coupland
The title of Coupland's new book suggests a review of Schmeikal
in this journal …
Coupland's above remark on hoarders suggests a look at
a wealthy California collector whom, were he not wealthy,
some might call a hoarder.
“I buy things because they strike an emotional bell,
they appeal to my curiosity, to the thrill of discovery
of the extraordinary in the ordinary,” Mr. Cotsen told
The Denver Post in 1998. “They appeal to my sense
of humor, and to my search for the beauty in simplicity.”
He added, “I decided I had a collection when there was
no more space to put anything.”
By the time he died at 88 on May 8 in Beverly Hills, Calif.,
Mr. Cotsen (pronounced COAT-zen) had donated about
half of the material in his collections to institutions like the
Asian Art Museum in San Francisco, Princeton University
and the Museum of International Folk Art in Santa Fe, N.M.
— Richard Sandomir in the online New York Times , May 17
Cotsen reportedly died at 88 on May 8.
See also this journal on that date —
|
Monday, May 8, 2017
New Pinterest Board
|
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Friday, April 7, 2017
Personal Identity
From "The Most Notorious Section Phrases," by Sophie G. Garrett
in The Harvard Crimson on April 5, 2017 —
This passage reminds me of (insert impressive philosophy
that was not in the reading).
This student is just being a show off. We get that they are smart
and well read. Congrats, but please don’t make the rest of the us
look bad in comparison. It should be enough to do the assigned
reading without making connections to Hume’s theory of the self.
Hume on personal identity (the "self") —
|
For my part, when I enter most intimately into what I call myself, I always stumble on some particular perception or other, of heat or cold, light or shade, love or hatred, pain or pleasure. I never can catch myself at any time without a perception, and never can observe any thing but the perception. When my perceptions are removed for any time, as by sound sleep, so long am I insensible of myself, and may truly be said not to exist. And were all my perceptions removed by death, and could I neither think, nor feel, nor see, nor love, nor hate, after the dissolution of my body, I should be entirely annihilated, nor do I conceive what is further requisite to make me a perfect nonentity. I may venture to affirm of the rest of mankind, that they are nothing but a bundle or collection of different perceptions, which succeed each other with an inconceivable rapidity, and are in a perpetual flux and movement. Our eyes cannot turn in their sockets without varying our perceptions. Our thought is still more variable than our sight; and all our other senses and faculties contribute to this change: nor is there any single power of the soul, which remains unalterably the same, perhaps for one moment. The mind is a kind of theatre, where several perceptions successively make their appearance; pass, repass, glide away, and mingle in an infinite variety of postures and situations. There is properly no simplicity in it at one time, nor identity in different, whatever natural propension we may have to imagine that simplicity and identity. The comparison of the theatre must not mislead us. They are the successive perceptions only, that constitute the mind; nor have we the most distant notion of the place where these scenes are represented, or of the materials of which it is composed. |
Related material —
Imago Dei in this journal.
Backstory —
The previous post
and The Crimson Abyss.
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Monday, April 11, 2016
Princeton Style
The previous post contained a remark from Princeton
on the January 1, 2016, death of a mathematician.
"There's a certain Princeton style that focuses on
precision, centrality and simplicity."
See also …
For a different sort of style, see Death on New Year's Day.
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Gospel of the Nobodies
"Principles before personalities" — AA saying
Principles
From an April 8 Princeton obituary of a mathematician —
" Moore embodied a 'Princeton style' that made him
a challenging and influential presence in the careers
of his students, said Joseph Neisendorfer, a professor
of mathematics at the University of Rochester who
received his Ph.D. in mathematics from Princeton in
1972. Because of Moore's style, his students would
write theses that 'almost without exception' were
significant advances in mathematics, Neisendorfer said.
'There's a certain Princeton style that focuses on
precision, centrality and simplicity. He was a superb
mathematician and he exercised a lot of influence
by imparting his style to his students,' Neisendorfer said.
'He epitomized the Princeton style.' "
Personalities
Gospel of the Nobodies
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Tuesday, May 12, 2015
Zinsser Obituary
"William Zinsser, a writer, editor and teacher
whose book ‘On Writing Well’ sold more than
1.5 million copies by employing his own literary
craftsmanship to urge clarity, simplicity, brevity
and humanity, died on Tuesday [May 12, 2015]
at his home in Manhattan. He was 92."
— Douglas Martin in the online New York Times
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Saturday, March 14, 2015
Unicode Diamonds
The following figure, intended to display as
a black diamond, was produced with
HTML and Unicode characters. Depending
on the technology used to view it, the figure
may contain gaps or overlaps.
◢◣
◥◤
Some variations:
◤◥
◣◢
◤◥
◢◣
◤◣
◢◥
◤◣
◥◢
Such combined Unicode characters —
◢ black lower right triangle,
◣ black lower left triangle,
᭘ black upper left triangle,
᭙ black upper right triangle
— might be used for a text-only version of the Diamond 16 Puzzle
that is more easily programmed than the current version.
The tricky part would be coding the letter-spacing and
line-height to avoid gaps or overlaps within the figures in
a variety of browsers. The w3.org visual formatting model
may or may not be helpful here.
Update of 11:20 PM ET March 15, 2015 —
Seekers of simplicity should note that there is
a simple program in the Processing.js language, not using
such Unicode characters, that shows many random affine
permutations of a 4×4 diamond-theorem array when the
display window is clicked.
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Sunday, September 14, 2014
Sermon
Epigraphs from Parallelisms of Complete Designs
by Peter J. Cameron (Cambridge University Press, 1976)
Introduction
Through the unknown, remembered gate
When the last of earth left to discover
Is that which was the beginning
(T. S. Eliot: Little Gidding)
I The existence theorem
Here the impossible union
Of spheres of existence is actual
(T. S. Eliot: The Dry Salvages)
II The parallelogram property
A condition of complete simplicity
(Costing not less than everything)
(T. S. Eliot: Little Gidding)
III Steiner points and Veblen points
You say I am repeating
Something I have said before. I shall say it again.
Shall I say it again?
(T. S. Eliot: East Coker)
IV Edge-colourings of complete graphs
And hollyhocks that aim too high
Red into grey and tumble down
(T. S. Eliot: East Coker)
V Biplanes and metric regularity
Two and two, necessarye conjunction,
Holding eche other by the hand or the arm
Whiche betokeneth concorde.
(T. S. Eliot: East Coker)
VI Automorphism groups
At the still point of the turning world. Neither flesh nor fleshless;
Neither from nor towards; at the still point, there the dance is,
But neither arrest nor movement.
(T. S. Eliot: Burnt Norton)
VII Resolutions and partition systems
… fiddle with pentagrams
Or barbituric acids, or dissect
The recurrent image into pre-conscious terrors .. .
(T. S. Eliot: The Dry Salvages)
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Friday, July 25, 2014
Magic in the Moonshine
“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
“Spectral evidence is a form of evidence
based upon dreams and visions.” —Wikipedia
See also Moonshine (May 15, 2014) and, from the date of the above
New York Times item, two posts tagged Wunderkammer .
Related material: From the Spectrum program of the Mathematical
Association of America, some non-spectral evidence.
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Thursday, May 15, 2014
Moonshine
“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
Photo of full moon over Oslo last night by Josefine Lyche:
A scene from my film viewing last night:
Some background (click to enlarge):
Note:
The “I, Frankenstein” scene above should not be interpreted as
a carrying of Martin Gardner through a lyche gate. Gardner
is, rather, symbolized by the asterisk in the first image from
the above Google search.
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Friday, March 14, 2014
Wednesday, November 13, 2013
Rated X
New York Times theater critic Ben Brantley
last night at 10 PM ET on the opening of a
play by Samuel Beckett —
"The cause of this incontinent mirth?
The dirtiest joke of all time. I mean life itself.
No playwright of the 20th century, and quite
possibly ever, has told this joke with the
clarity, simplicity and richness of Beckett."
Related material — This journal yesterday.
See also Lead Balloon.
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Thursday, September 5, 2013
Kernel and Glow
"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
Kernel — See Nocciolo.
Glow — See Moonshine and Moonshine II.
See also Cold Open (Jan. 29, 2011) and
Where Entertainment is God (Aug. 25, 2013).
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Sunday, July 28, 2013
Sermon
(Simplicity continued)
"Understanding a metaphor is like understanding a geometrical
truth. Features of various geometrical figures or of various contexts
are pulled into revealing alignment with one another by the
demonstration or the metaphor.
What is 'revealed' is not that the alignment is possible; rather,
that the alignment is possible reveals the presence of already-
existing shapes or correspondences that lay unnoticed. To 'see' a
proof or 'get' a metaphor is to experience the significance of the
correspondence for what the thing, concept, or figure is ."
— Jan Zwicky, Wisdom & Metaphor , page 36 (left)
Zwicky illustrates this with Plato's diamond figure
from the Meno on the facing page— her page 36 (right).
A more sophisticated geometrical figure—
Galois-geometry key to
Desargues' theorem:
| D | E | F | |
| S' | P | Q | R |
| S | P' | Q' | R' |
| O | P1 | Q1 | R1 |
For an explanation, see
Classical Geometry in Light of Galois Geometry.
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Tuesday, July 16, 2013
Child Buyers
The title refers to a classic 1960 novel by John Hersey.
“How do you get young people excited about space?”
— Megan Garber in The Atlantic , Aug. 16, 2012
(Italics added.) (See previous four posts.)
Allyn Jackson on “Simplicity, in Mathematics and in Art,”
in the new August 2013 issue of Notices of the American
Mathematical Society—
“As conventions evolve, so do notions of simplicity.
Franks mentioned Gauss’s 1831 paper that
established the respectability of complex numbers.”
This suggests a related image by Gauss, with a
remark on simplicity—
Here Gauss’s diagram is not, as may appear at first glance,
a 3×3 array of squares, but is rather a 4×4 array of discrete
points (part of an infinite plane array).
Related material that does feature the somewhat simpler 3×3 array
of squares, not seen as part of an infinite array—
Marketing the Holy Field
Click image for the original post.
For a purely mathematical view of the holy field, see Visualizing GL(2,p).
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Wednesday, February 13, 2013
Form:
Story, Structure, and the Galois Tesseract
Recent Log24 posts have referred to the
"Penrose diamond" and Minkowski space.
The Penrose diamond has nothing whatever
to do with my 1976 monograph "Diamond Theory,"
except for the diamond shape and the connection
of the Penrose diamond to the Klein quadric—
The Klein quadric occurs in the five-dimensional projective space
over a field. If the field is the two-element Galois field GF(2), the
quadric helps explain certain remarkable symmetry properties
of the R. T. Curtis Miracle Octad Generator (MOG), hence of
the large Mathieu group M24. These properties are also
relevant to the 1976 "Diamond Theory" monograph.
For some background on the quadric, see (for instance)…
See also The Klein Correspondence,
Penrose Space-Time, and a Finite Model.
Related material:
|
"… one might crudely distinguish between philosophical – J. M. E. Hyland. "Proof Theory in the Abstract." (pdf) |
Those who prefer story to structure may consult
- today's previous post on the Penrose diamond
- the remarks of Scott Aaronson on August 17, 2012
- the remarks in this journal on that same date
- the geometry of the 4×4 array in the context of M24.
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Wednesday, October 24, 2012
In a Nutshell
"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
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Thursday, May 5, 2011
On Art and Magic
Two Blocks Short of a Design:
A sequel to this morning’s post on Douglas Hofstadter
Photo of Hofstadter by Mike McGrath taken May 13, 2006 |
Related material — See Lyche’s “Theme and Variations” in this journal
and Hofstadter’s “Variations on a Theme as the Essence of Imagination”
— Scientific American October 1982
A quotation from a 1985 book by Hofstadter—
“… we need to entice people with the beauties of clarity, simplicity, precision,
elegance, balance, symmetry, and so on.
Those artistic qualities… are the things that I have tried to explore and even
to celebrate in Metamagical Themas . (It is not for nothing that the word
‘magic’ appears inside the title!)”
The artistic qualities Hofstadter lists are best sought in mathematics, not in magic.
An example from Wikipedia —
|
Mathematics
The Fano plane block design |
Magic
The Deathly Hallows symbol— |
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Tuesday, April 12, 2011
Unique Figure
In the landscape of minimalism, John McCracken cuts a unique figure. He is often grouped with the “light and space” artists who formed the West Coast branch of the movement. Indeed, he shares interests in vivid color, new materials, and polished surfaces with fellow Californians enamored of the Kustom Kar culture. On the other hand, his signature works, the “planks” that he invented in 1966 and still makes today, have the tough simplicity and aggressive presence of New York minimalism….
“They kind of screw up a space because they lean,” McCracken has said of the planks. Their tilting, reflective surfaces activate the room, leaving the viewer uncertain of traditional boundaries. He notes that the planks bridge sculpture (identified with the floor) and painting (identified with the wall)….
His ultimate goal, as with all mystics, is unity— not just of painting and sculpture, but of substance and illusion, of matter and spirit, of art and life. Such ideas recall the utopian aspirations of early modernists like Piet Mondrian and Wassily Kandinsky.
Related Art —
Unity
—Roman numeral I
as well as capital I
For a related figure, see a film review by A. O. Scott at The New York Times (September 21, 2010)—
“You Will Meet a Tall Dark Stranger” begins with an unseen narrator— , sounding a lot like — paraphrasing . You may remember the quotation from high school English, about how life is a tale told by an idiot, full of sound and fury, signifying nothing. The observation is attributed to the playwright himself (“Shakespeare once said”), rather than to Macbeth, whose grim experience led him to such nihilism, but never mind. In context, it amounts to a perfectly superfluous statement of the obvious.
If life signifies nothing, perhaps the tall dark figure above signifies something . Discuss.
Related Art Criticism —
For more on light and space, see this journal on the date of McCracken’s death—
Note planks.
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Sunday, April 3, 2011
On to Chicago!
Commentary on last night—
Tonight: The After-Party.
In related news…
"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 , quoted here in
Cold Open (Saturday night, January 29, 2011)
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Saturday, January 29, 2011
Cold Open
"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
Some background—
An image from yesterday's search
God, TIme, Hopkins
"We got tom-toms over here bigger than a monster
Bla Bla Bla Bla Bla Bla Bla Bla"
— "Massive Attack"
"I'm just checking your math on that. Yes, I got the same thing."
"Live… Uh, check that… From New York, it's Saturday Night! "
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Thursday, December 2, 2010
Caesarian
The Dreidel Is Cast
The Nietzschean phrase "ruling and Caesarian spirits" occurred in yesterday morning's post "Novel Ending."
That post was followed yesterday morning by a post marking, instead, a beginning— that of Hanukkah 2010. That Jewish holiday, whose name means "dedication," commemorates the (re)dedication of the Temple in Jerusalem in 165 BC.
The holiday is celebrated with, among other things, the Jewish version of a die— the dreidel . Note the similarity of the dreidel to an illustration of The Stone* on the cover of the 2001 Eerdmans edition of Charles Williams's 1931 novel Many Dimensions—
For mathematics related to the dreidel , see Ivars Peterson's column on this date fourteen years ago.
For mathematics related (if only poetically) to The Stone , see "Solomon's Cube" in this journal.
Here is the opening of Many Dimensions—
For a fanciful linkage of the dreidel 's concept of chance to The Stone 's concept of invariant law, note that the New York Lottery yesterday evening (the beginning of Hanukkah) was 840. See also the number 840 in the final post (July 20, 2002) of the "Solomon's Cube" search.
Some further holiday meditations on a beginning—
Today, on the first full day of Hanukkah, we may or may not choose to mark another beginning— that of George Frederick James Temple, who was born in London on this date in 1901. Temple, a mathematician, was President of the London Mathematical Society in 1951-1953. From his MacTutor biography—
"In 1981 (at the age of 80) he published a book on the history of mathematics. This book 100 years of mathematics (1981) took him ten years to write and deals with, in his own words:-
those branches of mathematics in which I had been personally involved.
He declared that it was his last mathematics book, and entered the Benedictine Order as a monk. He was ordained in 1983 and entered Quarr Abbey on the Isle of Wight. However he could not stop doing mathematics and when he died he left a manuscript on the foundations of mathematics. He claims:-
The purpose of this investigation is to carry out the primary part of Hilbert's programme, i.e. to establish the consistency of set theory, abstract arithmetic and propositional logic and the method used is to construct a new and fundamental theory from which these theories can be deduced."
For a brief review of Temple's last work, see the note by Martin Hyland in "Fundamental Mathematical Theories," by George Temple, Philosophical Transactions of the Royal Society, A, Vol. 354, No. 1714 (Aug. 15, 1996), pp. 1941-1967.
The following remarks by Hyland are of more general interest—
"… one might crudely distinguish between philosophical and mathematical motivation. In the first case one tries to convince with a telling conceptual story; in the second one relies more on the elegance of some emergent mathematical structure. If there is a tradition in logic it favours the former, but I have a sneaking affection for the latter. Of course the distinction is not so clear cut. Elegant mathematics will of itself tell a tale, and one with the merit of simplicity. This may carry philosophical weight. But that cannot be guaranteed: in the end one cannot escape the need to form a judgement of significance."
— J. M. E. Hyland. "Proof Theory in the Abstract." (pdf)
Annals of Pure and Applied Logic 114, 2002, 43-78.
Here Hyland appears to be discussing semantic ("philosophical," or conceptual) and syntactic ("mathematical," or structural) approaches to proof theory. Some other remarks along these lines, from the late Gian-Carlo Rota—
See also "Galois Connections" at alpheccar.org and "The Galois Connection Between Syntax and Semantics" at logicmatters.net.
* Williams's novel says the letters of The Stone are those of the Tetragrammaton— i.e., Yod, He, Vau, He (cf. p. 26 of the 2001 Eerdmans edition). But the letters on the 2001 edition's cover Stone include the three-pronged letter Shin , also found on the dreidel . What esoteric religious meaning is implied by this, I do not know.
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Tuesday, July 6, 2010
Thoreau on Group Theory
"Instead of a million count half a dozen." —Walden
"Of all the symmetric groups, S6 is perhaps the most remarkable."
— Notes 2 (Autumn 2008), apparently by Robert A. Wilson,
for Group Theory, MTH714U
For a connection of MTH714U with Walden, see "Window, continued."
For a connection of "Window" with the remarkable S6, see Inscapes.
For some deeper background, see Wilson's "Exceptional Simplicity."
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Window, continued
| “Simplicity, simplicity, simplicity! I say, let your affairs be as two or three, and not a hundred or a thousand; instead of a million count half a dozen, and keep your accounts on your thumb-nail.” — Henry David Thoreau, Walden This quotation is the epigraph to |
From Peter J. Cameron’s review notes for
his new course in group theory—
From Log24 on June 24—
Geometry Simplified
(an affine space with subsquares as points
and sets of subsquares as hyperplanes)
(a projective space with, as points, sets
of line segments that separate subsquares)
Exercise—
Show that the above geometry is a model
for the algebra discussed by Cameron.
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Monday, April 26, 2010
Types of Ambiguity
From Ursula K. Le Guin’s novel
The Dispossessed: An Ambiguous Utopia (1974)—
Chapter One
“There was a wall. It did not look important. It was built of uncut rocks roughly mortared. An adult could look right over it, and even a child could climb it. Where it crossed the roadway, instead of having a gate it degenerated into mere geometry, a line, an idea of boundary. But the idea was real. It was important. For seven generations there had been nothing in the world more important than that wall.
Like all walls it was ambiguous, two-faced. What was inside it and what was outside it depended upon which side of it you were on.”
Note—
“We note that the phrase ‘instead of having a gate it degenerated into mere geometry’ is mere fatuousness. If there is an idea here, degenerate, mere, and geometry in concert do not fix it. They bat at it like a kitten at a piece of loose thread.”
— Samuel R. Delany, The Jewel-Hinged Jaw: Notes on the Language of Science Fiction (Dragon Press, 1977), page 110 of revised edition, Wesleyan University Press, 2009
(For the phrase mere geometry elsewhere, see a note of April 22. The apparently flat figures in that note’s illustration “Galois Affine Geometry” may be regarded as degenerate views of cubes.)
Later in the Le Guin novel—
“… The Terrans had been intellectual imperialists, jealous wall builders. Even Ainsetain, the originator of the theory, had felt compelled to give warning that his physics embraced no mode but the physical and should not be taken as implying the metaphysical, the philosophical, or the ethical. Which, of course, was superficially true; and yet he had used number, the bridge between the rational and the perceived, between psyche and matter, ‘Number the Indisputable,’ as the ancient founders of the Noble Science had called it. To employ mathematics in this sense was to employ the mode that preceded and led to all other modes. Ainsetain had known that; with endearing caution he had admitted that he believed his physics did, indeed, describe reality.
Strangeness and familiarity: in every movement of the Terran’s thought Shevek caught this combination, was constantly intrigued. And sympathetic: for Ainsetain, too, had been after a unifying field theory. Having explained the force of gravity as a function of the geometry of spacetime, he had sought to extend the synthesis to include electromagnetic forces. He had not succeeded. Even during his lifetime, and for many decades after his death, the physicists of his own world had turned away from his effort and its failure, pursuing the magnificent incoherences of quantum theory with its high technological yields, at last concentrating on the technological mode so exclusively as to arrive at a dead end, a catastrophic failure of imagination. Yet their original intuition had been sound: at the point where they had been, progress had lain in the indeterminacy which old Ainsetain had refused to accept. And his refusal had been equally correct– in the long run. Only he had lacked the tools to prove it– the Saeba variables and the theories of infinite velocity and complex cause. His unified field existed, in Cetian physics, but it existed on terms which he might not have been willing to accept; for the velocity of light as a limiting factor had been essential to his great theories. Both his Theories of Relativity were as beautiful, as valid, and as useful as ever after these centuries, and yet both depended upon a hypothesis that could not be proved true and that could be and had been proved, in certain circumstances, false.
But was not a theory of which all the elements were provably true a simple tautology? In the region of the unprovable, or even the disprovable, lay the only chance for breaking out of the circle and going ahead.
In which case, did the unprovability of the hypothesis of real coexistence– the problem which Shevek had been pounding his head against desperately for these last three days. and indeed these last ten years– really matter?
He had been groping and grabbing after certainty, as if it were something he could possess. He had been demanding a security, a guarantee, which is not granted, and which, if granted, would become a prison. By simply assuming the validity of real coexistence he was left free to use the lovely geometries of relativity; and then it would be possible to go ahead. The next step was perfectly clear. The coexistence of succession could be handled by a Saeban transformation series; thus approached, successivity and presence offered no antithesis at all. The fundamental unity of the Sequency and Simultaneity points of view became plain; the concept of interval served to connect the static and the dynamic aspect of the universe. How could he have stared at reality for ten years and not seen it? There would be no trouble at all in going on. Indeed he had already gone on. He was there. He saw all that was to come in this first, seemingly casual glimpse of the method, given him by his understanding of a failure in the distant past. The wall was down. The vision was both clear and whole. What he saw was simple, simpler than anything else. It was simplicity: and contained in it all complexity, all promise. It was revelation. It was the way clear, the way home, the light.”
Related material—
Time Fold, Halloween 2005, and May and Zan.
See also The Devil and Wallace Stevens—
“In a letter to Harriet Monroe, written December 23, 1926, Stevens refers to the Sapphic fragment that invokes the genius of evening: ‘Evening star that bringest back all that lightsome Dawn hath scattered afar, thou bringest the sheep, thou bringest the goat, thou bringest the child home to the mother.’ Christmas, writes Stevens, ‘is like Sappho’s evening: it brings us all home to the fold’ (Letters of Wallace Stevens, 248).”
— “The Archangel of Evening,” Chapter 5 of Wallace Stevens: The Intensest Rendezvous, by Barbara M. Fisher, The University Press of Virginia, 1990
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Sunday, February 14, 2010
Example
From Alexandre Borovik's new book
Mathematics Under the Microscope
(American Mathematical Society, 2010)–
Related material:
Finite Geometry and Physical Space
(Good Friday, 2009)
This kindergarten-level discussion of
the simple group of order 168
also illustrates Thoreau's advice:
"Simplicity, simplicity, simplicity!"
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Tuesday, January 13, 2009
Tuesday January 13, 2009
Something Traditional —
“German Chancellor Dr. Angela Merkel is the Charlemagne Prize laureate of 2008…. The prize will be awarded on 1 May, Ascension Day.”
Something Modern —
Previously undescribed in this journal:
| A NOTE BY THE DESIGNER
“The traditional chess set, with its naturalistic images of medieval armies, suggests a game between combatants who enjoy the winning of battles. This chess set, with its articulated images of abstract force, suggests a game between contestants who enjoy the process of thinking.
The primary principle of this design… is that the operating reality or function of each piece– both its value and how it moves– is embodied in a simple self-expressive form….  Design Copyright F. Lanier Graham 1967
— F. Lanier Graham, 1967 |
For those whose tastes in recreation are less rational, there is also the legendary chess set of Charlemagne described in novels by Katherine Neville. (See ART WARS.)
Related material: this journal on the First of May, 2008, the date of last year’s Charlemagne award.
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Friday, December 19, 2008
Friday December 19, 2008
Inside the
White Cube
White Cube
Part I: The White Cube
Part II: Inside
Part III: Outside
For remarks on religion
related to the above, see
Log24 on the Garden of Eden
and also Mark C. Taylor,
"What Derrida Really Meant"
(New York Times, Oct. 14, 2004).
For some background on Taylor,
see Wikipedia. Taylor, Chairman
of the Department of Religion at
Columbia University, has a
1973 doctorate in religion from
Harvard University. His opinion
of Derrida indicates that his
sympathies lie more with
the serpent than with the angel
in the Tansey picture above.
For some remarks by Taylor on
the art of Tansey relevant to the
structure of the white cube
(Part I above), see Taylor's
The Picture in Question:
Mark Tansey and the
Ends of Representation
(U. of Chicago Press, 1999):
|
From Chapter 3,
"Sutures* of Structures," p. 58: "What, then, is a frame, and what is frame work? This question is deceptive in its simplicity. A frame is, of course, 'a basic skeletal structure designed to give shape or support' (American Heritage Dictionary)…. when the frame is in question, it is difficult to determine what is inside and what is outside. Rather than being on one side or the other, the frame is neither inside nor outside. Where, then, Derrida queries, 'does the frame take place….'" * P. 61:
|
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Wednesday, September 10, 2008
Wednesday September 10, 2008
Hitler on
Democracy
Democracy
The Fuehrer's wisdom seems especially appropriate today, in light of John McCain's recent "sex education for kindergarteners" and "lipstick" ads:
"… thus in the primitive simplicity of their minds they more readily fall victims to the big lie than the small lie, since they themselves often tell small lies in little matters but would be ashamed to resort to large-scale falsehoods. It would never come into their heads to fabricate colossal untruths, and they would not believe that others could have the impudence to distort the truth so infamously…. The grossly impudent lie always leaves traces behind it, even after it has been nailed down."
"I'm Joseph Goebbels, and
I approve this message."
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Saturday, December 16, 2006
Saturday December 16, 2006
Cubism1 as Multispeech2
— From Pedagogy, Praxis, Ulysses
A quotation omitted from the above excerpt:
In Ulysses, there is "… the same quality of simultaneity as in cubist collage. Thus, for example, Bloom surveys the tombstones at Paddy Dignam's funeral and, in the midst of platitudinous and humorous thoughts, remembers Molly 'wanting to do it at the window'…."
Related material from quotations at the poetry journal eratio:
"The guiding law of the great variations in painting is one of disturbing simplicity. First things are painted; then, sensations; finally, ideas. This means that in the beginning the artist's attention was fixed on external reality; then, on the subjective; finally, on the intrasubjective. These three stages are three points on a straight line."
— Jose Ortega y Gasset ("On Point of View in the Arts," an essay on the development of cubism)
Related material on
tombstones and windows:
Geometry's Tombstones,
Galois's Window, and
Architecture of Eternity.
See also the following part
of the eratio quotations:
Quotations arranged by
Gregory Vincent St. Thomasino
Wednesday, February 1, 2006
Wednesday February 1, 2006
“Good Night and Good Luck”
— Morgan Freeman, closing remarks
at the Screen Actors Guild Awards
on January 29, 2006
 A History of Death |
 |
Review by Stephen Hunter
of “Good Night and Good Luck”–
“The film, therefore, is like
a child’s view of these events,
untroubled by complexity,
hungry for myth and simplicity.”
“A larger poem for a larger audience….
A mythological form, a festival sphere,
A great bosom, beard and being,
alive with age.”
— Wallace Stevens, quoted in
Log24, January 29, 2006
Stephen Hunter on Senator McCarthy:
He “forever tarnished
by association the reputations
of the security services
charged with keeping us safe
from the actual–
yes, Virginia, there was
such a thing– Red menace.”
Comments Off on Wednesday February 1, 2006
Tuesday, November 1, 2005
Tuesday November 1, 2005
The above seal is from an ad (pdf) for an Oct. 21 lecture, "The Nature of Space," by Sir Michael Atiyah, sponsored by the American Mathematical Society.
The picture in the seal is of Plato's Academy.
"The great philosopher Plato excluded from his Academy anyone who had not studied geometry. He would have been delighted to admit Sir Michael Atiyah, who was for a time Savilian Professor of Geometry at Oxford…"
Would he?
Sir Michael Atiyah's
Anti-Platonism
"Mathematics is an evolution from the human brain, which is responding to outside influences, creating the machinery with which it then attacks the outside world. It is our way of trying to reduce complexity into simplicity, beauty and elegance….
I tend to think that science and mathematics are ways the human mind looks and experiences– you cannot divorce the human mind from it. Mathematics is part of the human mind. The question whether there is a reality independent of the human mind, has no meaning– at least, we cannot answer it."
— Sir Michael Atiyah, interview in Oslo, May 2004
"For Plato, the Forms represent truth, or reality…. these Forms are independent of the mind: they are eternal, unchanging and perfect."
— Roy Jackson (pdf)
Atiyah's denial of a reality independent of the human mind may have something to do with religion:
"Socrates and Plato were considered 'Christians before Christ'; they paved the way for the coming of Christianity by providing it with philosophical and theoretical foundations that would be acceptable to the western mind.
In the analogy of the cave, the sun represents the Form of the Good. In the same way that the sun is the source of all things and gives light to them, the Form of the Good is over and above the other Forms, giving them light and allowing us to perceive them. Therefore, when you have awareness of the Form of the Good you have achieved true enlightenment. In Christianity, the Form of the Good becomes God: the source of all things."
— Roy Jackson, The God of Philosophy (pdf)
See also the previous entry.
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Tuesday, June 21, 2005
Tuesday June 21, 2005
Art History
“I studied with Reinhardt and I found that a fantastic course. I think he was really very stimulating….
Art history was very personal through the eyes of Ad Reinhardt.”
— Robert Morris,
Smithsonian Archives of American Art
Related material:
“The Road to Simplicity Followed by Merton’s Friends: Ad Reinhardt and Robert Lax” in The Merton Annual 13 (2000) 245-256, by Paul J. Spaeth, library director at St. Bonaventure University
The Merton here is Trappist monk Thomas Merton. Here is Merton in a letter to poet Robert Lax on the death of their friend Ad Reinhardt, sometimes called the “black monk” of abstract art:
“Make Mass beautiful silence like big black picture speaking requiem. Tears in the shadows of hermit hatch requiems blue black tone. Sorrows for Ad in the oblation quiet peace request rest. Tomorrow is solemns in the hermit hatch for old lutheran reinhardt commie paintblack… Tomorrow is the eternal solemns and the barefoots and the ashes and the masses, oldstyle liturgy masses without the colonels… Just old black quiet requiems in hermit hatch with decent sorrows good by college chum.”
— from J. S. Porter, “Farewell to a Monk,”
Antigonish Review, Winter 1997
Comments Off on Tuesday June 21, 2005
Friday, September 17, 2004
Friday September 17, 2004
God is in…
The Details
From an entry for Aug. 19, 2003 on
conciseness, simplicity, and objectivity:
Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale "block design" subtest. Another Harvard psychiatrist, Armand Nicholi, is in the news lately with his book The Question of God: C.S. Lewis and Sigmund Freud Debate God, Love, Sex, and the Meaning of Life.
For the meaning of the Old-Testament logos above, see the remarks of Plato on the immortality of the soul at For the meaning of the New-Testament logos above, see the remarks of R. P. Langlands at |
On Harvard and psychiatry: see
The Crimson Passion:
A Drama at Mardi Gras
(February 24, 2004)
This is a reductio ad absurdum of the Harvard philosophy so eloquently described by Alston Chase in his study of Harvard and the making of the Unabomber, Ted Kaczynski. Kaczynski's time at Harvard overlapped slightly with mine, so I may have seen him in Cambridge at some point. Chase writes that at Harvard, the Unabomber "absorbed the message of positivism, which demanded value-neutral reasoning and preached that (as Kaczynski would later express it in his journal) 'there is no logical justification for morality.'" I was less impressed by Harvard positivism, although I did benefit from a course in symbolic logic from Quine. At that time– the early 60's– little remained at Harvard of what Robert Stone has called "our secret culture," that of the founding Puritans– exemplified by Cotton and Increase Mather.
From Robert Stone, A Flag for Sunrise:
"Our secret culture is as frivolous as a willow on a tombstone. It's a wonderful thing– or it was. It was strong and dreadful, it was majestic and ruthless. It was a stranger to pity. And it's not for sale, ladies and gentlemen."
Some traces of that culture:
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A web page
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A contemporary
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A more appealing view of faith was offered by PBS on Wednesday night, the beginning of this year's High Holy Days:
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Armand Nicholi: But how can you believe something that you don't think is true, I mean, certainly, an intelligent person can't embrace something that they don't think is true — that there's something about us that would object to that.
Jeremy Fraiberg: Well, the answer is, they probably do believe it's true. Armand Nicholi: But how do they get there? See, that's why both Freud and Lewis was very interested in that one basic question. Is there an intelligence beyond the universe? And how do we answer that question? And how do we arrive at the answer of that question? Michael Shermer: Well, in a way this is an empirical question, right? Either there is or there isn't. Armand Nicholi: Exactly. Michael Shermer: And either we can figure it out or we can't, and therefore, you just take the leap of faith or you don't. Armand Nicholi: Yeah, now how can we figure it out? Winifred Gallagher: I think something that was perhaps not as common in their day as is common now — this idea that we're acting as if belief and unbelief were two really radically black and white different things, and I think for most people, there's a very — it's a very fuzzy line, so that — Margaret Klenck: It's always a struggle. Winifred Gallagher: Rather than — I think there's some days I believe, and some days I don't believe so much, or maybe some days I don't believe at all. Doug Holladay: Some hours. Winifred Gallagher: It's a, it's a process. And I think for me the big developmental step in my spiritual life was that — in some way that I can't understand or explain that God is right here right now all the time, everywhere. Armand Nicholi: How do you experience that? Winifred Gallagher: I experience it through a glass darkly, I experience it in little bursts. I think my understanding of it is that it's, it's always true, and sometimes I can see it and sometimes I can't. Or sometimes I remember that it's true, and then everything is in Technicolor. And then most of the time it's not, and I have to go on faith until the next time I can perhaps see it again. I think of a divine reality, an ultimate reality, uh, would be my definition of God. |
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Gallagher seemed to be the only participant in the PBS discussion that came close to the Montessori ideals of conciseness, simplicity, and objectivity. Dr. Montessori intended these as ideals for teachers, but they seem also to be excellent religious values. Just as the willow-tombstone seems suited to Geoffrey Hill's style, the Pythagorean sangaku pictured above seems appropriate to the admirable Gallagher.
Tuesday, June 8, 2004
Tuesday June 8, 2004
Anomaly
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Robert Quine, 61, By BEN SISARIO Robert Quine, a noted guitarist of the New York rock scene of the 1970’s and 80’s who played with Richard Hell, Lou Reed and others, died last week in his home in Manhattan. He was 61. He was found dead by the police on Saturday, said James Marshall, a friend. The police found a note and said they believed the death was a suicide but are awaiting a medical examiner’s report. Mr. Marshall said he believed Mr. Quine died on May 31. In the loud world of New York punk, where crude simplicity trumped most conventional notions of musical skill, Mr. Quine stood out as a stylish virtuoso…. “He was an extraordinary mixture of taste, intelligence, and rock ‘n’ roll abilities, coupled with major technique and a scholar’s memory for every decent guitar lick ever played under the musical sun,” Mr. Reed said…. Mr. Quine was an anomaly in the punk scene. Older than most of his fellow musicians, he had a law degree and was nearly bald, and wore button-down shirts and sport coats and described his appearance as that of a “deranged insurance salesman.”…. His uncle, the philosopher W. V. Quine, died in 2000. |
| “Anomalies must be expected along the conceptual frontier between the temporal and the eternal.” — The Death of Adam, by Marilynne Robinson, Houghton Mifflin, 1998, essay on Marguerite de Navarre “D’exterieur en l’interieur entre |
Comments Off on Tuesday June 8, 2004
Monday, September 29, 2003
Monday September 29, 2003
Magic Hawaii
Today, the birthday of singer Jerry Lee Lewis, is also the feast of St. Michael and All Angels.
In honor of Lewis:
Killer Radio, an entry of July 31, 2003, that contains the following…
“When the light came she was sitting on the bed beside an open suitcase, toying with her diamond rings. She saw the light first in the depths of the largest stone.”
— Paul Preuss, Broken Symmetries,
scene at Diamond Head, Oahu,
Hawaii
In honor of the angels:
Mathematics as an Adequate Language,
by Israel Gelfand, Sept. 2, 2003, which contains the following…
“Many people consider mathematics to be a boring and formal science. However, any really good work in mathematics always has in it: beauty, simplicity, exactness, and crazy ideas. This is a strange combination. I understood earlier that this combination is essential on the example of classical music and poetry. But it is also typical in mathematics. It is not by chance that many mathematicians enjoy serious music.
This combination of beauty, simplicity, exactness, and crazy ideas is, I think, common to both mathematics and music.”
These qualities seem also to be sought by practitioners of religion and physics… for example, by the spiritually-minded physicist in Preuss’s Broken Symmetries. Skeptics might prefer, to the word “religion,” the word (pronounced with a sneer) “magic.”
What do we find if, following in the footsteps of Gelfand and Preuss, we do a Google search on the following words…
The search yields two results:
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The Pupil: Poems by W. S. Merwin.
The above link is to a poem, “Prophecy,” that seems suitable for these, the High Holy Days at the end of one year and the beginning of another.
For a follow-up to the poem, see
The Shining of Lucero. - “Striking Through the Mask, or
The Allegorical Meanings
in Moby Dick.”
These two selections, both on the theme of light and darkness, offer a language that is perhaps more adequate than mathematics for dealing with the nature of the High Holy Days. For a more lighthearted approach to these concerns, also with a Hawaiian theme, see
Comments Off on Monday September 29, 2003
Tuesday, August 19, 2003
Tuesday August 19, 2003
Intelligence Test
From my August 31, 2002, entry quoting Dr. Maria Montessori on conciseness, simplicity, and objectivity:
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Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale "block design" subtest.
Another Harvard psychiatrist, Armand Nicholi, is in the news lately with his book The Question of God: C.S. Lewis and Sigmund Freud Debate God, Love, Sex, and the Meaning of Life.
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Pope |
Nicholi |
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Old |
New |
For the meaning of the Old-Testament logos above, see the remarks of Plato on the immortality of the soul at
For the meaning of the New-Testament logos above, see the remarks of R. P. Langlands at
The Institute for Advanced Study.
For the meaning of life, see
The Gospel According to Jill St. John,
whose birthday is today.
Monday, August 18, 2003
Monday August 18, 2003
Entries since Xanga’s
August 10 Failure:
Sunday, August 17, 2003 2:00 PM
A Thorny Crown of…
From the first episode of
the television series
“The West Wing“:
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Original airdate: Sept. 22, 1999 MARY MARSH CALDWELL MARY MARSH JOSH TOBY [A stunned silence. Everyone stares at Toby.] TOBY (CONT.) JOSH |
Going There, Part I
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Crown of Ideas Kirk Varnedoe, 57, art historian and former curator of the Museum of Modern Art, died Thursday, August 14, 2003. From his New York Times obituary: ” ‘He loved life in its most tangible forms, and so for him art was as physical and pleasurable as being knocked down by a wave,’ said Adam Gopnik, the writer and a former student of his who collaborated on Mr. Varnedoe’s first big show at the Modern, ‘High & Low.’ ‘Art was always material first — it was never, ever bound by a thorny crown of ideas.’ ” For a mini-exhibit of ideas in honor of Varnedoe, see Verlyn Klinkenborg on Varnedoe: “I was always struck by the tangibility of the words he used…. It was as if he were laying words down on the table one by one as he used them, like brushes in an artist’s studio. That was why students crowded into his classes and why the National Gallery of Art had overflow audiences for his Mellon Lectures earlier this year. Something synaptic happened when you listened to Kirk Varnedoe, and, remarkably, something synaptic happened when he listened to you. You never knew what you might discover together.” Perhaps even a “thorny crown of ideas“?
“Crown of Thorns” Varnedoe’s death coincided with “To what extent does this idea of a civic life produced by sense of adversity correspond to actual life in Brasília? I wonder if it is something which the city actually cultivates. Consider, for example the cathedral, on the monumental axis, a circular, concrete framed building whose sixteen ribs are both structural and symbolic, making a structure that reads unambiguously as a crown of thorns; other symbolic elements include the subterranean entrance, the visitor passing through a subterranean passage before emerging in the light of the body of the cathedral. And it is light, shockingly so….” — Modernist Civic Space: The Case of Brasilia, by Richard J. Williams, Department of History of Art, University of Edinburgh, Scotland |
Going There, Part II
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Simple, Bold, Clear Art historian Kirk Varnedoe was, of course, not the only one to die on the day of the Great Blackout. Claude Martel, 34, a senior art director of The New York Times Magazine, also died on Thursday, August 14, 2003. Janet Froelich, the magazine’s art director, describes below a sample of work that she and Martel did together: “A new world of ideas”
Froelich notes that “the elements are simple, bold, and clear.” For another example of elements with these qualities, see my journal entry The flag design in that entry
Note that the elements of the flag design have the qualities described so aptly by Froelich– simplicity, boldness, clarity:
They share these qualities with the Elements of Euclid, a treatise on geometrical ideas. For the manner in which such concepts might serve as, in Gopnik’s memorable phrase, a “thorny crown of ideas,” see “Geometry for Jews” in ART WARS: Geometry as Conceptual Art. See also the discussion of ideas in my journal entry on theology and art titled Understanding: On Death and Truth and the discussion of the word “idea” (as well as the word, and the concept, “Aryan”) in the following classic (introduced by poet W. H. Auden):
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Saturday, August 16, 2003 6:00 AM
Varnedoe’s Crown
Kirk Varnedoe, 57, art historian and former curator of the Museum of Modern Art, died Thursday, August 14, 2003.
From his New York Times obituary:
” ‘He loved life in its most tangible forms, and so for him art was as physical and pleasurable as being knocked down by a wave,’ said Adam Gopnik, the writer and a former student of his who collaborated on Mr. Varnedoe’s first big show at the Modern, ‘High & Low.’ ‘Art was always material first — it was never, ever bound by a thorny crown of ideas.’ “
For a mini-exhibit of ideas in honor of Varnedoe, see
Verlyn Klinkenborg on Varnedoe:
“I was always struck by the tangibility of the words he used…. It was as if he were laying words down on the table one by one as he used them, like brushes in an artist’s studio. That was why students crowded into his classes and why the National Gallery of Art had overflow audiences for his Mellon Lectures earlier this year. Something synaptic happened when you listened to Kirk Varnedoe, and, remarkably, something synaptic happened when he listened to you. You never knew what you might discover together.”
Perhaps even a “thorny crown of ideas”?
“Crown of Thorns”
Cathedral, Brasilia
Varnedoe’s death coincided with
the Great Blackout of 2003.
“To what extent does this idea of a civic life produced by sense of adversity correspond to actual life in Brasília? I wonder if it is something which the city actually cultivates. Consider, for example the cathedral, on the monumental axis, a circular, concrete framed building whose sixteen ribs are both structural and symbolic, making a structure that reads unambiguously as a crown of thorns; other symbolic elements include the subterranean entrance, the visitor passing through a subterranean passage before emerging in the light of the body of the cathedral. And it is light, shockingly so….”
— Modernist Civic Space: The Case of Brasilia, by Richard J. Williams, Department of History of Art, University of Edinburgh, Scotland
Friday, August 15, 2003 3:30 PM
ART WARS:
The Boys from Brazil
It turns out that the elementary half-square designs used in Diamond Theory
also appear in the work of artist Nicole Sigaud.
Sigaud’s website The ANACOM Project has a page that leads to the artist Athos Bulcão, famous for his work in Brasilia.
From the document
Conceptual Art in an
Authoritarian Political Context:
Brasilia, Brazil,
by Angélica Madeira:
“Athos created unique visual plans, tiles of high poetic significance, icons inseparable from the city.”
As Sigaud notes, two-color diagonally-divided squares play a large part in the art of Bulcão.
The title of Madeira’s article, and the remarks of Anna Chave on the relationship of conceptual/minimalist art to fascist rhetoric (see my May 9, 2003, entries), suggest possible illustrations for a more politicized version of Diamond Theory:
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Fahne, |
Dr. Mengele, |
Is it safe?
These illustrations were suggested in part by the fact that today is the anniversary of the death of Macbeth, King of Scotland, and in part by the following illustrations from my journal entries of July 13, 2003 comparing a MOMA curator to Lady Macbeth:
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Die Fahne Hoch, |
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Thursday, August 14, 2003 3:45 AM
Famous Last Words
The ending of an Aug. 14 Salon.com article on Mel Gibson’s new film, “The Passion”:
” ‘The Passion’ will most likely offer up the familiar puerile, stereotypical view of the evil Jew calling for Jesus’ blood and the clueless Pilate begging him to reconsider. It is a view guaranteed to stir anew the passions of the rabid Christian, and one that will send the Jews scurrying back to the dark corners of history.”
— Christopher Orlet
“Scurrying”?! The ghost of Joseph Goebbels, who famously portrayed Jews as sewer rats doing just that, must be laughing — perhaps along with the ghost of Lady Diana Mosley (née Mitford), who died Monday.
This goes well with a story that Orlet tells at his website:
“… to me, the most genuine last words are those that arise naturally from the moment, such as
Joseph Goebbels |
Voltaire’s response to a request that he foreswear Satan: ‘This is no time to make new enemies.’ ”
For a view of Satan as an old, familiar, acquaintance, see the link to Prince Ombra in my entry last October 29 for Goebbels’s birthday.
Wednesday, August 13, 2003 3:00 PM
Best Picture
For some reflections inspired in part by
- Today’s anniversary of a
1727 Moravian Pentecost, - An April 7, 2003,
lecture at Moravian College, and - St. Bonaventure’s 1259
remarks on the Trinity,
Tuesday, August 12, 2003 4:44 PM
Atonement:
A sequel to my entry “Catholic Tastes” of July 27, 2003.
Some remarks of Wallace Stevens that seem appropriate on this date:
“It may be that one life is a punishment
For another, as the son’s life for the father’s.”
— Esthétique du Mal, Wallace Stevens
“Unless we believe in the hero, what is there
To believe? ….
Devise, devise, and make him of winter’s
Iciest core, a north star, central
In our oblivion, of summer’s
Imagination, the golden rescue:
The bread and wine of the mind….”
— Examination of the Hero in a Time of War, Wallace Stevens
Etymology of “Atonement”:
“Middle English atonen, to be reconciled, from at one, in agreement“
At One
“… We found,
If we found the central evil, the central good….
… we and the diamond globe at last were one.”
— Asides on the Oboe, Wallace Stevens
Tuesday, August 12, 2003 1:52 PM
Franken & ‘Stein,
Attorneys at Law
“Tue August 12, 2003 04:10 AM ET
NEW YORK (Reuters) – Fox News Network is suing humor writer Al Franken for trademark infringement over the phrase ‘fair and balanced’ on the cover of his upcoming book, saying it has been ‘a signature slogan’ of the network since 1996.”
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Franken: |
‘Stein: |
For answers, click on the pictures
of Franken and ‘Stein.
Comments Off on Monday August 18, 2003
Sunday, April 27, 2003
Sunday April 27, 2003
ART WARS:
Graphical Password
From a summary of “The Design and Analysis of Graphical Passwords“:
“Results from cognitive science show that people can remember pictures much better than words….
The 5×5 grid creates a good balance between security and memorability.”
— Ian Jermyn, New York University; Alain Mayer, Fabian Monrose, Michael K. Reiter, Bell Labs, Lucent Technologies; Aviel Rubin, AT&T Labs — Research
Illustration — Warren Beatty as
a graphical password:
“Town & Country,”
released April 27, 2001
Those who prefer the simplicity of a 3×3 grid are referred to my entry of Jan. 9, 2003, Balanchine’s Birthday. For material related to the “Town & Country” theme and to Balanchine, see Leadbelly Under the Volcano (Jan. 27, 2003). (“Sometimes I live in the country, sometimes I live in town…” – Huddie Ledbetter). Those with more sophisticated tastes may prefer the work of Stephen Ledbetter on Gershwin’s piano preludes or, in view of Warren Beatty’s architectural work in “Town & Country,” the work of Stephen R. Ledbetter on window architecture.
As noted in Balanchine’s Birthday, Apollo (of the Balanchine ballet) has been associated by an architect with the 3×3, or “ninefold” grid. The reader who wishes a deeper meditation on the number nine, related to the “Town & Country” theme and more suited to the fact that April is Poetry Month, is referred to my note of April 27 two years ago, Nine Gates to the Temple of Poetry.
Intermediate between the simplicity of the 3×3 square and the (apparent) complexity of the 5×5 square, the 4×4 square offers an introduction to geometrical concepts that appears deceptively simple, but is in reality fiendishly complex. See Geometry for Jews. The moral of this megilla?
32 + 42 = 52.
Comments Off on Sunday April 27, 2003
Friday, April 25, 2003
Friday April 25, 2003
Mark
Today is the feast of Saint Mark. It seems an appropriate day to thank Dr. Gerald McDaniel for his online cultural calendar, which is invaluable for suggesting blog topics.
Yesterday's entry "Cross-Referenced" referred to a bizarre meditation of mine titled "The Matthias Defense," which combines some thoughts of Nabokov on lunacy with some of my own thoughts on the Judeo-Christian tradition (i.e., also on lunacy). In this connection, the following is of interest:
From a site titled Meaning of the Twentieth Century —
"Freeman Dyson has expressed some thoughts on craziness. In a Scientific American article called 'Innovation in Physics,' he began by quoting Niels Bohr. Bohr had been in attendance at a lecture in which Wolfgang Pauli proposed a new theory of elementary particles. Pauli came under heavy criticism, which Bohr summed up for him: 'We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that is not crazy enough.' To that Freeman added: 'When a great innovation appears, it will almost certainly be in a muddled, incomplete and confusing form. To the discoverer, himself, it will be only half understood; to everyone else, it will be a mystery. For any speculation which does not at first glance look crazy, there is no hope!' "
— Kenneth Brower, The Starship and the Canoe, 1979, pp. 146, 147
It is my hope that the speculation, implied in The Matthias Defense, that the number 162 has astonishing mystical properties (as a page number, article number, etc.) is sufficiently crazy to satisfy Pauli and his friend Jung as well as the more conventional thinkers Bohr and Dyson. It is no less crazy than Christianity, and has a certain mad simplicity that perhaps improves on some of that religion's lunatic doctrines.
Some fruits of the "162 theory" —
Searching on Google for muses 162, we find the following Orphic Hymn to Apollo and a footnote of interest:
27 Tis thine all Nature's music to inspire,
28 With various-sounding, harmonising lyre;
29 Now the last string thou tun'ft to sweet accord,
30 Divinely warbling now the highest chord….
"Page 162 Verse 29…. Now the last string…. Gesner well observes, in his notes to this Hymn, that the comparison and conjunction of the musical and astronomical elements are most ancient; being derived from Orpheus and Pythagoras, to Plato. Now, according to the Orphic and Pythagoric doctrine, the lyre of Apollo is an image of the celestial harmony…."
For the "highest chord" in a metaphorical sense, see selection 162 of the 1919 edition of The Oxford Book of English Verse (whose editor apparently had a strong religious belief in the Muses (led by Apollo)). This selection contains the phrase "an ever-fixèd mark" — appropriately enough for this saint's day. The word "mark," in turn, suggests a Google search for the phrase "runes to grave" Hardy, after a poem quoted in G. H. Hardy's A Mathematician's Apology.
Such a search yields a website that quotes Housman as the source of the "runes" phrase, and a further search yields what is apparently the entire poem:
Smooth Between Sea and Land
by A. E. Housman
Smooth between sea and land
Is laid the yellow sand,
And here through summer days
The seed of Adam plays.Here the child comes to found
His unremaining mound,
And the grown lad to score
Two names upon the shore.Here, on the level sand,
Between the sea and land,
What shall I build or write
Against the fall of night?Tell me of runes to grave
That hold the bursting wave,
Or bastions to design
For longer date than mine.Shall it be Troy or Rome
I fence against the foam
Or my own name, to stay
When I depart for aye?Nothing: too near at hand
Planing the figured sand,
Effacing clean and fast
Cities not built to last
And charms devised in vain,
Pours the confounding main.(Said to be from More Poems (Knopf, 1936), p. 64)
Housman asks the reader to tell him of runes to grave or bastions to design. Here, as examples, are one rune and one bastion.
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Represents |
Dagaz: (Pronounced thaw-gauze, but with the "th" voiced as in "the," not unvoiced as in "thick") (Day or dawn.)
From Rune Meanings:
Dagaz means "breakthrough, awakening, awareness. Daylight clarity as opposed to nighttime uncertainty. A time to plan or embark upon an enterprise. The power of change directed by your own will, transformation. Hope/happiness, the ideal. Security and certainty. Growth and release. Balance point, the place where opposites meet."
Also known as "the rune of transformation."
For the Dagaz rune in another context, see Geometry of the I Ching. The geometry discussed there does, in a sense, "hold the bursting wave," through its connection with Walsh functions, hence with harmonic analysis.
Temple of Athena Nike on the Nike Bastion, the Acropolis, Athens. Here is a relevant passage from Paul Valéry's Eupalinos ou L'Architecte about another temple of four columns:
Et puis… Écoute, Phèdre (me disait-il encore), ce petit temple que j'ai bâti pour Hermès, à quelques pas d'ici, si tu savais ce qu'il est pour moi ! — Où le passant ne voit qu'une élégante chapelle, — c'est peu de chose: quatre colonnes, un style très simple, — j'ai mis le souvenir d'un clair jour de ma vie. Ô douce métamorphose ! Ce temple délicat, nul ne le sait, est l'image mathématique d'une fille de Corinthe que j'ai heureusement aimée. Il en reproduit fidèlement les proportions particulières. Il vit pour moi !
Four columns, in a sense more suited to Hardy's interests, are also a recurrent theme in The Diamond 16 Puzzle and Diamond Theory.
Apart from the word "mark" in The Oxford Book of English Verse, as noted above, neither the rune nor the bastion discussed has any apparent connection with the number 162… but seek and ye shall find.
Comments Off on Friday April 25, 2003
Friday, December 6, 2002
Friday December 6, 2002
Great Simplicity
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is the day that Daisetsu Suzuki attained satori,
according to the Zen Calendar. “Daisetsu” is
said to mean “Great Simplicity.”
For those who prefer Harry Potter and
Diagon Alley, here is another calendar:
To Have and Have Not
Those who prefer traditional Western religions may like a site on the Trinity that contains this:
“Zen metaphysics is perhaps most succinctly set forth in the words ‘not-two.” But even when he uses this expression, Suzuki is quick to assert that it implies no monism. Not-two, it is claimed, is not the same as one.* But when Suzuki discusses the relationship of Zen with Western mysticism, it is more difficult to escape the obvious monistic implications of his thinking. Consider the following:
We are possessed of the habit of looking at Reality by dividing it into two… It is all due to the human habit of splitting one solid Reality into two, and the result is that my ‘have’ is no ‘have’ and my ‘have not’ is no ‘have not.’ While we are actually passing, we insist that the gap is impassable.**”
*See: Daisetz T. Suzuki, ‘Basic Thoughts Underlying Eastern Ethical and Social Practice’ in Philosophy and Culture — East and West: East-West Philosophy in Practical Perspective, ed. Charles A. Moore (Honolulu: University of Hawaii Press, 1968), p. 429
** Daisetsu Teitaro Suzuki, Mysticism Christian and Buddhist (London: George Allen & Unwin, 1957, Unwin paperback, 1979), p. 57.
Personally, I am reminded by Suzuki’s satori on this date that today is the eve of the anniversary of Pearl Harbor. I am also reminded by the rather intolerant tract on the Trinity quoted above that the first atomic bomb was exploded in the New Mexico desert at a test site named Trinity. Of course, sometimes intolerance is justified.
Concluding unscientific postscript:
On the same day in 1896 that D. T. Suzuki attained satori,
lyricist Ira Gershwin was born.
Dies irae, dies illa.
Comments Off on Friday December 6, 2002
Saturday, August 31, 2002
Saturday August 31, 2002
Today’s birthday: Dr. Maria Montessori
THE MONTESSORI METHOD: CHAPTER VI
HOW LESSONS SHOULD BE GIVEN
“Let all thy words be counted.”
Dante, Inf., canto X.
CONCISENESS, SIMPLICITY, OBJECTIVITY.
…Dante gives excellent advice to teachers when he says, “Let thy words be counted.” The more carefully we cut away useless words, the more perfect will become the lesson….
Another characteristic quality of the lesson… is its simplicity. It must be stripped of all that is not absolute truth…. The carefully chosen words must be the most simple it is possible to find, and must refer to the truth.
The third quality of the lesson is its objectivity. The lesson must be presented in such a way that the personality of the teacher shall disappear. There shall remain in evidence only the object to which she wishes to call the attention of the child….
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Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale “block design” subtest.
Mathematicians mean something different by the phrase “block design.”
A University of London site on mathematical design theory includes a link to my diamond theory site, which discusses the mathematics of the sorts of visual designs that Professor Pope is demonstrating. For an introduction to the subject that is, I hope, concise, simple, and objective, see my diamond 16 puzzle.
Comments Off on Saturday August 31, 2002