The date at the end of yesterday’s noon post was May 25, 2010.
This, together with Keith Devlin’s Twitter page today, suggests
a review of that date.
Res ipsa loquitur.
The date at the end of yesterday’s noon post was May 25, 2010.
This, together with Keith Devlin’s Twitter page today, suggests
a review of that date.
Res ipsa loquitur.
Here and at Catholics for Classical Education.
See also Tom Wolfe on manifestos —
— and part of an interesting Sept. 2, 2014, manifesto by
Common Core supporter Keith Devlin:
“Graduate students of mathematics are introduced to further
assumptions (about handling the infinite, and various other issues),
equally reasonable and useful, and in accord both with our everyday
intuitions (insofar as they are relevant) and with the rest of
mainstream mathematics. And on the basis of those assumptions,
you can prove that
1 + 2 + 3 + … = –1/12.
That’s right, the sum of all the natural numbers equals –1/12.
This result is so much in-your-face, that people whose mathematics
education stopped at the undergraduate level (if they got that far)
typically say it is wrong. It’s not. Just as with the 0.999… example,
where we had to construct a proper meaning for an infinite decimal
expansion before we could determine what its value is, so to we
have to define what that infinite sum means. ….”
For a correction to Devlin’s remarks, see a physics professor’s weblog post —
“From a strictly mathematical point of view,
the equation 1+2+3+4+ … = -1/12 is incorrect,
and involves confusing the Dirichlet series with
the zeta function.” — Greg Gbur, May 25, 2010
The title refers to the previous post.
Click image for some context.
For further context, see some
mathematics from Halloween 1978.
See also May 12, 2014.
This morning’s previous post may be regarded as an example of
the Harvard Business School’s “case system.”
A search for this topic yields another example:
Harvard professor Peter Galison discusses the case system’s
origin at Harvard Law School in his book Image and Logic:
A Material Culture of Microphysics —
No Image, No Logic
(Click to enlarge.)
“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
“There is such a thing as a three-set.”
— Saying adapted from a novel by Madeleine L’Engle
“For those who like this sort of thing,
this is the sort of thing they like.”
The Folding
Cynthia Zarin in The New Yorker , issue dated April 12, 2004—
“Time, for L’Engle, is accordion-pleated. She elaborated,
‘When you bring a sheet off the line, you can’t handle it
until it’s folded, and in a sense, I think, the universe can’t
exist until it’s folded — or it’s a story without a book.’”
The geometry of the 4×4 square array is that of the
3-dimensional projective Galois space PG(3,2).
This space occurs, notably, in the Miracle Octad Generator (MOG)
of R. T. Curtis (submitted to Math. Proc. Camb. Phil. Soc. on
15 June 1974). Curtis did not, however, describe its geometric
properties. For these, see the Cullinane diamond theorem.
Some history:
Curtis seems to have obtained the 4×4 space by permuting,
then “folding” 1×8 binary sequences into 4×2 binary arrays.
The original 1×8 sequences came from the method of Turyn
(1967) described by van Lint in his book Coding Theory
(Springer Lecture Notes in Mathematics, No. 201 , first edition
published in 1971). Two 4×2 arrays form each 4×4 square array
within the MOG. This construction did not suggest any discussion
of the geometric properties of the square arrays.
[Rewritten for clarity on Sept. 3, 2014.]
The titles of the previous three posts refer to
Hermann Weyl’s 1918 book Raum, Zeit, Materie
(Space, Time, Matter).
This suggests a look at a poetically parallel 1950 title —
The Lion, the Witch and the Wardrobe —
and at its underlying philosophy:
I am among “those who do not know that this great myth became Fact.”
I do, however, note that some other odd things have become fact.
Those who wish more on this topic may consult:
See also Christmas Eve, 2012.
“It’s going to be accomplished
in steps, this establishment
of the talented….”
— To Ride Pegasus , by
Anne McCaffrey (Radcliffe ’47)
A possible answer to the 1923 question of Walter Gropius, “Was ist Raum?“—
See also yesterday’s Source of the Finite and the image search
on the Gropius question in last night’s post.
Yesterday's 11 AM post was a requiem for a brutalist architect.
Today's LA Times has a related obituary:
"Architectural historian Alan Hess, who has written several books on
Mid-Century Modern design, said Meyer didn't have a signature style,
'which is one reason he is not as well-known as some other architects
of the period. But whatever style he was working in, he brought a real
sense of quality to his buildings.'
A notable example is another bank building, at South Beverly Drive
and Pico Boulevard, with massive concrete columns, a hallmark of
the New Brutalism style. 'This is a really good example of it,' Hess said."
— David Colker, 5:43 PM LA time, Aug. 28, 2014
A related search, suggested by this morning's post Source of the Finite:
(Click to enlarge.)
"Die Unendlichkeit ist die uranfängliche Tatsache: es wäre nur
zu erklären, woher das Endliche stamme…."
— Friedrich Nietzsche, Das Philosophenbuch/Le livre du philosophe
(Paris: Aubier-Flammarion, 1969), fragment 120, p. 118
Cited as above, and translated as "Infinity is the original fact;
what has to be explained is the source of the finite…." in
The Production of Space , by Henri Lefebvre. (Oxford: Blackwell,
1991 (1974)), p. 181.
This quotation was suggested by the Bauhaus-related phrase
"the laws of cubical space" (see yesterday's Schau der Gestalt )
and by the laws of cubical space discussed in the webpage
Cube Space, 1984-2003.
For a less rigorous approach to space at the Harvard Graduate
School of Design, see earlier references to Lefebvre in this journal.
"To every man upon this earth,
Death cometh soon or late.
And how can man die better
Than facing fearful odds,
For the ashes of his fathers,
and the temples of his gods…?"
— Macaulay, quoted in the April 2013 film "Oblivion"
"Leave a space." — Tom Stoppard, "Jumpers"
Related material: The August 16, 2014, sudden death in Scotland
of an architect of the above Cardross seminary, and a Log24 post,
Plato's Logos, from the date of the above photo: June 26, 2010.
See also…
Here “eidolon” should instead be “eidos .”
An example of eidos — Plato's diamond (from the Meno ) —
(Continued from Aug. 19, 2014)
“Christian contemplation is the opposite
of distanced consideration of an image:
as Paul says, it is the metamorphosis of
the beholder into the image he beholds
(2 Cor 3.18), the ‘realisation’ of what the
image expresses (Newman). This is
possible only by giving up one’s own
standards and being assimilated to the
dimensions of the image.”
— Hans Urs von Balthasar,
The Glory of the Lord:
A Theological Aesthetics,
Vol. I: Seeing the Form
[ Schau der Gestalt ],
Ignatius Press, 1982, p. 485
A Bauhaus approach to Schau der Gestalt :
I prefer the I Ching ‘s approach to the laws of cubical space.
“Bryan Cranston won an Emmy for lead actor in a drama series Monday…”
“Tu es le pianiste….” — Log24 post 641
Two images from posts tagged ‘Objects of Beauty‘ —
“And be these juggling fiends no more believed,
That palter with us in a double sense….”
See Shadowlands in this journal.
The film so titled was directed by Richard Attenborough,
President of the Royal Academy of Dramatic Art,
who reportedly died on Sunday, August 24, 2014.
“It’s all in Plato, all in Plato:
bless me, what do they
teach them at these schools!”
— C. S. Lewis
“Richard Samuel Attenborough, Baron Attenborough, CBE
(… 29 August 1923 – 24 August 2014) was an English actor,
film director, producer and entrepreneur. He was the President of
the Royal Academy of Dramatic Art (RADA).” — Wikipedia
In the Miracle Octad Generator (MOG):
The above details from a one-page note of April 26, 1986, refer to the
Miracle Octad Generator of R. T. Curtis, as it was published in 1976:
From R. T. Curtis (1976). A new combinatorial approach to M24,
Mathematical Proceedings of the Cambridge Philosophical Society ,
79, pp 25-42. doi:10.1017/S0305004100052075.
The 1986 note assumed that the reader would be able to supply, from the
MOG itself, the missing top row of each heavy brick.
Note that the interchange of the two squares in the top row of each
heavy brick induces the diamond-theorem correlation.
Note also that the 20 pictured 3-subsets of a 6-set in the 1986 note
occur as paired complements in two pictures, each showing 10 of the
3-subsets.
This pair of pictures corresponds to the 20 Rosenhain tetrads among
the 35 lines of PG(3,2), while the picture showing the 2-subsets
corresponds to the 15 Göpel tetrads among the 35 lines.
See Rosenhain and Göpel tetrads in PG(3,2). Some further background:
(The title is from a post of July 8, 2010.)
“What is important is the ability to tell stories through character.”
— Diana Gabaldon, author of the Outlander series of novels
An image from the bottom line of images in the previous post:
In memory of Scottish folk singer Jean Redpath,
who reportedly died on Thursday, August 21:
See also this journal on August 21.
The bottom three lines of an image search:
For a meditation on the bottom line, see Mary Gaitskill’s story
“The Agonized Face.” See also George C. Scott reciting from
the Scottish play in The Exorcist III.
See Madeleine + Folded.
An illustration (click to enlarge) —
Related material: Posts from the above upload date, 10/1/10.
( A sequel to Lux )
“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
Robin Williams and the Stages of Math
i) shock & denial
ii) anger
iii) bargaining
iv) depression
v) acceptance
A related description of the process —
“You know how sometimes someone tells you a theorem,
and it’s obviously false, and you reach for one of the many
easy counterexamples only to realize that it’s not a
counterexample after all, then you reach for another one
and another one and find that they fail too, and you begin
to concede the possibility that the theorem might not
actually be false after all, and you feel your world start to
shift on its axis, and you think to yourself: ‘Why did no one
tell me this before?’ “
— Tom Leinster yesterday at The n-Category Café
(As opposed to an alleged bearer of lux .)
(Here “eidolon” should instead be “eidos.”)
An example of Gestaltung :
This journal on the day of Feininger’s death, and the day before —
The 256 Code (Thursday, July 7, 2011) and Nordstrom-Robinson Automorphisms.
In memory of one who sent in the clowns:
See also Plan 9 in this journal, as well as Saturday’s posts.
To Feb. 11, 2012:
“News and Traffic. Sports and Weather. These were his acid terms
for the life he’d left behind, more than two years of living with
the tight minds that made the war. It was all background noise,
he said, waving a hand. He liked to wave a hand in dismissal.”
— DeLillo, Don (2010-02-02), Point Omega
Send in the Clowns. (Click to enlarge.)
The above flashback was suggested by Lev Grossman’s verb “trafficked”
in yesterday’s posts, and by the song lyric “show us the way to
the next little girl.”
"Shakespeare, Dante, Milton, Homer: those writers trafficked in
witches and fairies and ghosts and monsters. Why shouldn’t I?"
— Novelist Lev Grossman in The New York Times this afternoon
Grossman's father was the poet Allen Grossman.
See that Grossman in this journal, as well as a search for Holy Water.
For the Thin White Duke —
The Next Whiskey Bar:
Saturday, August 16, 2014, 6:00 pm in UTC+02
at LYNX 760 in Oslo, Norway.
In memory of a Manhattan real-estate developer
who reportedly died on August 9, 2014 —
a post from that date a year earlier.
Click on the Tower for further details.
The webpage Rosenhain and Göpel Tetrads in PG(3,2)
has been updated to include more material on symplectic structure.
“Mr. Ryckmans translated, into English, the ‘Analects,’
the collection of sayings attributed to Confucius.”
— A New York Times obituary this evening
See also this morning’s post on Confucius.
A prequel to today's noon post
Rosalind Krauss in "Grids" —
"The physical qualities of the surface, we could say,
are mapped onto the aesthetic dimensions of
the same surface. And those two planes—
the physical and the aesthetic— are demonstrated
to be the same plane…. the bottom line of the grid is
a naked and determined materialism.”
A writer I prefer:
Barsotti's classic illustrated:
The naked and determined Annette Bening in "The Grifters" —
“. . . the bottom line of the grid is a naked and determined materialism.”
— Rosalind Krauss, quoted by Josefine Lyche
See also http://www.dailymotion.com/video/
x164rmi_britt-ekland-nude-wicker-man-1973_people.
Robin Williams and the Stages of Grief
A weblog post from Jan. 25, 2014 (click image to enlarge)—
Clues for a Mystery (Click links for more details)—
Clue 1: A June 11,* 2014, math death.
Clue 2: The answer is a surname.
Midrash for Will Hunting:
See Nanavira Thera at Wikipedia and space notes from September 2012.
* According to a (perhaps inaccurate) math department.
June 10, according to other sources cited by the department.
“The Pope’s visit to South Korea is the first part of a very intelligent
opening to Asia,” said Lionel Jensen, associate professor of East Asian
Languages and Cultures at the University of Notre Dame.
— Madison Park, CNN this morning
A not-so-intelligent opening —
“Could it be that the familiar and beloved figure of Confucius
was invented by Jesuit priests? In Manufacturing Confucianism,
Lionel M. Jensen reveals this very fact….”
For some background, see an Atlantic Monthly article from 1999,
“Confucius and the Scholars,” by Charlotte Allen.
Some background for the part of the 2002 paper by Dolgachev and Keum
quoted here on January 17, 2014 —
Related material in this journal (click image for posts) —
Illustration from a discussion of a symplectic structure
in a 4×4 array quoted here on January 17, 2014 —
See symplectic structure in this journal.
* The final words of Point Omega , a 2010 novel by Don DeLillo.
See also Omega Matrix in this journal.
Don't forget to send us your strip!
* A reference to mathematician Peter J. Cameron as Lord Summerisle.
(Continued from August 9, 2014.)
Syntactic:
Symplectic:
"Visual forms— lines, colors, proportions, etc.— are just as capable of
articulation , i.e. of complex combination, as words. But the laws that govern
this sort of articulation are altogether different from the laws of syntax that
govern language. The most radical difference is that visual forms are not
discursive . They do not present their constituents successively, but
simultaneously, so the relations determining a visual structure are grasped
in one act of vision."
– Susanne K. Langer, Philosophy in a New Key
For examples, see The Diamond-Theorem Correlation
in Rosenhain and Göpel Tetrads in PG(3,2).
This is a symplectic correlation,* constructed using the following
visual structure:
.
* Defined in (for instance) Paul B. Yale, Geometry and Symmetry ,
Holden-Day, 1968, sections 6.9 and 6.10.
“Something in your eyes I see
Soon begins bewitching me”
Some illustrations:
Chess Knight
(in German, Springer)
See also…
More technically (click image for details):
From The Mathematics of Language:
10th and 11th Biennial Conference….
Berlin, Springer, 2010 —
“Creation Myths of Generative Grammar
and the Mathematics of Syntactic Structures”
by Geoffrey K. Pullum, University of Edinburgh
Abstract
“Syntactic Structures (Chomsky [6]) is widely believed to have laid
the foundations of a cognitive revolution in linguistic science, and
to have presented (i) the first use in linguistics of powerful new ideas
regarding grammars as generative systems, (ii) a proof that English
was not a regular language, (iii) decisive syntactic arguments against
context-free phrase structure grammar description, and (iv) a
demonstration of how transformational rules could provide a formal
solution to those problems. None of these things are true. This paper
offers a retrospective analysis and evaluation.”
Syntactic Structure —
See the Lightfoot of today’s previous post:
Symplectic Structure —
See the plaited, or woven, structure of August 6:
.
See also Deep Structure (Dec. 9, 2012).
“In 1977, Golan directed Operation Thunderbolt….”
* See a search for Lightfoot in this journal.
01:13:08.25,01:13:12.35
(STRING QUARTET PLAYING
SLOW, LUSH MELODY)
01:13:22.59,01:13:26.23
They’re fucking sixteenths,
Steve, stop milking them.
01:13:26.36,01:13:29.78
Folks, disagree,
but do it nicely, and please…
01:13:30.47,01:13:33.38
…try not to get caught up in mistakes.
01:13:35.17,01:13:38.21
When I was your age,
I met the great Pablo Casals.
01:13:38.34,01:13:40.85
I was so intimidated
I could barely speak.
01:13:40.98,01:13:43.19
He must have sensed this, because…
01:13:43.31,01:13:46.99
…instead of a chat,
he asked me to play.
01:13:47.12,01:13:49.93
He requested the prelude
to the Fourth Bach suite.
01:13:51.62,01:13:54.80
I focused, took a deep breath,
began, the notes started to flow,
01:13:54.93,01:13:58.67
the music’s in the air, and it was
the worst music I ever made.
01:13:58.80,01:14:00.28
(STUDENTS CHUCKLE)
01:14:01.13,01:14:05.44
I played so badly,
I got halfway through and had to stop.
01:14:05.57,01:14:07.71
“Bravo,” he said, “Well done.”
01:14:08.94,01:14:13.85
Then, he asked me to play the allemande.
“A second chance,” I think to myself.
01:14:15.48,01:14:17.05
I never played worse.
01:14:18.48,01:14:22.06
“Wonderful. Splendid,” he praised me.
01:14:22.19,01:14:26.73
And when I left that night,
I felt terrible about my performance,
01:14:26.86,01:14:30.50
but what really bothered me
wasn’t my playing, it was Casals.
01:14:30.63,01:14:32.30
The insincerity.
01:14:33.90,01:14:36.50
Years later, I met him in Paris
01:14:36.63,01:14:40.41
and by then I was professional,
we played together.
01:14:40.54,01:14:45.08
We became acquaintances,
and one evening, over a glass of wine…
01:14:46.94,01:14:51.32
…I confessed to him what I thought
of his horseshit all those years ago.
01:14:51.45,01:14:53.22
(LAUGHTER)
01:14:55.12,01:14:59.09
And he got angry. His demeanor changed,
he grabbed his cello,
01:14:59.22,01:15:02.50
“Listen,” he said.
And he played this phrase.
01:15:03.63,01:15:07.58
(PLAYS DYNAMIC, DRAMATIC PHRASE)
01:15:19.08,01:15:22.06
“Didn’t you play that? Fingering.
01:15:22.18,01:15:25.96
You did.
It was novel to me. It was good.
01:15:26.08,01:15:31.09
And here, didn’t you attack
this passage with an up-bow like this?”
01:15:45.14,01:15:49.08
Casals emphasized the good stuff,
the things he enjoyed.
01:15:50.87,01:15:55.65
He encouraged. And for the rest,
leave that to the morons,
01:15:55.78,01:16:00.85
or whatever it is in Spanish,
who judge by counting faults.
01:16:00.98,01:16:03.62
“I can be grateful,
and so must you be,” he said,
01:16:03.75,01:16:09.03
“for even one singular phrase,
one transcendent moment.”
01:16:09.33,01:16:10.33
Hmm?
01:16:11.40,01:16:16.64
– Wow.
– Yeah, wow. Pablo Casals. Champion.
01:16:17.90,01:16:21.82
Once more, with feeling please. Feeling!
01:16:25.21,01:16:29.05
(SLOW, LUSH MELODY RESUMES)
See also a video of this scene and a post from this date ten years ago.
See a post, The Omega Matrix, from the date of her death.
Related material:
"When Death tells a story, you really have to listen."
— Cover of The Book Thief
A scene from the film of the above book —
“Looking carefully at Golay’s code is like staring into the sun.”
Some context — "Mathematics, Magic, and Mystery" —
See posts tagged April Awareness 2014.
From Wikipedia — Abuse of language —
“… in mathematics, a use of terminology in a way that is not formally correct
but that simplifies exposition or suggests the correct intuition.”
The phrase “symplectic structure” in the previous post
was a deliberate abuse of language. The real definition:
From Gotay and Isenberg, "The Symplectization of Science,"
Gazette des Mathématiciens 54, 59-79 (1992):
"… what is the origin of the unusual name 'symplectic'? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure 'line complex group' the 'symplectic group.'
… the adjective 'symplectic' means 'plaited together' or 'woven.'
This is wonderfully apt…."
The above symplectic structure** now appears in the figure
illustrating the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2).
Some related passages from the literature:
* The title is a deliberate abuse of language .
For the real definition of "symplectic structure," see (for instance)
"Symplectic Geometry," by Ana Cannas da Silva (article written for
Handbook of Differential Geometry, vol 2.) To establish that the
above figure is indeed symplectic , see the post Zero System of
July 31, 2014.
** See Steven H. Cullinane, Inscapes III, 1986
"Philosophy is a battle against the bewitchment [Verhexung ]
of our intelligence by means of our language."
— Wittgenstein, Philosophical Investigations , Section 109
"The philosophy of logic speaks of sentences and words
in exactly the sense in which we speak of them in ordinary life
when we say e.g. 'Here is a Chinese sentence,' or 'No, that only
looks like writing; it is actually just an ornament' and so on."
— Wittgenstein, Philosophical Investigations , Section 108
Monday, June 30, 2014
High Concept
|
“… which is our actual experience” — Joan Didion
— Ludwig Wittgenstein, Philosophical Investigations
In memory of radio personality Steve Post,
a link to some remarks on the date of his death.
"We tell ourselves stories in order to live…. We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the 'ideas' with which we have learned to freeze the shifting phantasmagoria which is our actual experience." |
See also a post from May 4, 2011 (the date, according to a Google
search, of untitled notes regarding a matrix called Omega).
“This is a divorce case that was before us on an earlier occasion.”
Wild:
From the director of The Wild Bunch —
Brady:
From The New York Times —
Version from "The Avengers" (2012) —
Version from Josefine Lyche (2009) —
See also this journal on the date that the above Avengers video was uploaded.
"There is such a thing as a tesseract." — Madeleine L'Engle
An approach via the Omega Matrix:
See, too, Rosenhain and Göpel as The Shadow Guests .
Shown below is the matrix Omega from notes of Richard Evan Schwartz.
See also earlier versions (1976-1979) by Steven H. Cullinane.
Backstory: The Schwartz Notes (June 1, 2011), and Schwartz on
the American Mathematical Society's current home page:
Dialogue from “The Osterman Weekend”—
01:57:22 “Why did he make us try to believe Omega existed?”
01:57:25 ….
01:57:26 “The existence of Omega has not been disproved.
01:57:28 Don’t you understand that?
01:57:31 Omega is as real as we need it to be.”
See also Omega elsewhere in this journal.
Update of 9:15 PM ET —
Horwich reportedly died on July 21, 2014.
For a different perspective on smart art, see the Log24 posts of April 2013.
Continued from the Facebook-related post of February 4, 2014:
In related news at the website of the
American Mathematical Society today:
Multimillion-Dollar Minds
“The Multimillion-Dollar Minds of 5 Mathematical Masters,”
by Kenneth Chang, ran in the New York Times on June 23, 2014.
The piece reports the award of $3 million “Breakthrough” prizes….
The prizes are financed by Yuri Milner, “a Russian who dropped out
of graduate studies in physics and became a successful investor in
Internet companies like Facebook,” and Mark Zuckerberg,
the founder of Facebook….
Related material: Requiem for a Cat (March 27, 2012).
“Break on through to the other side” — The Doors
Click image for a larger, clearer version.
The title phrase (not to be confused with the film 'The Zero Theorem')
means, according to the Encyclopedia of Mathematics,
a null system , and
"A null system is also called null polarity,
a symplectic polarity or a symplectic correlation….
it is a polarity such that every point lies in its own
polar hyperplane."
See Reinhold Baer, "Null Systems in Projective Space,"
Bulletin of the American Mathematical Society, Vol. 51
(1945), pp. 903-906.
An example in PG(3,2), the projective 3-space over the
two-element Galois field GF(2):
See also the 10 AM ET post of Sunday, June 8, 2014, on this topic.
See “Charles Williams” + Witchcraft in this journal.
Williams was one of the Inklings, a group of Christian
writers that included C. S. Lewis and J. R. R. Tolkien.
In memoriam :
“Margot Adler, an iconic NPR correspondent and Wiccan priestess,
died on Monday July 28 from endometrial cancer at the age of 68.”
— Huffington Post 07/28/2014 5:39 pm EDT
See also Log24 posts tagged NPR Magic.
Two items from this morning’s news:
“Sasaki Roshi trained for years in a distinctively strict style of Zen
that he transplanted to the U.S. His students rose at 3 a.m.
for chanting, exhausting hours of meditation and one-on-one
meetings with their teacher, who would pose impenetrable
koans, riddles like: ‘When you see the flower, where is God?'”
For a mathematician’s example of an alleged Zen ideal, see the feast day
this year of St. Gerard Manley Hopkins.
Wikipedia article:
Reductionism is a philosophical position
which holds that a complex system is nothing but
the sum of its parts, and that an account of it can be
reduced to accounts of individual constituents.[1]
1. See e.g. Reductionism in the Interdisciplinary
Encyclopedia of Religion and Science.
“The Website of the Interdisciplinary Encyclopedia on
Religion and Science is edited by the Advanced School
for Interdisciplinary Research (ADSIR), operating at the
Pontifical University of the Holy Cross, Rome….”
For a reductionist Holy Cross, see yesterday’s noon post.
George Johnson, a science writer, in The New York Times
on July 21, 2014:
“New particles may yet be discovered, and even new laws.
But it is almost taken for granted that everything
from physics to biology, including the mind,
ultimately comes down to four fundamental concepts:
matter and energy interacting in an arena of space and time.”
Related material:
Ite, missa est.
Or: Two Rivets Short of a Paradigm
Detail from an author photo:
From rivet-rivet.net:
The philosopher Graham Harman is invested in re-thinking the autonomy of objects and is part of a movement called Object-Oriented-Philosophy (OOP). Harman wants to question the authority of the human being at the center of philosophy to allow the insertion of the inanimate into the equation. With the aim of proposing a philosophy of objects themselves, Harman puts the philosophies of Bruno Latour and Martin Heidegger in dialogue. Along these lines, Harman proposes an unconventional reading of the tool-being analysis made by Heidegger. For Harman, the term tool does not refer only to human-invented tools such as hammers or screwdrivers, but to any kind of being or thing such as a stone, dog or even a human. Further, he uses the terms objects, beings, tools and things, interchangeably, placing all on the same ontological footing. In short, there is no “outside world.” Harman distinguishes two characteristics of the tool-being: invisibility and totality. Invisibility means that an object is not simply used but is: “[an object] form(s) a cosmic infrastructure of artificial and natural and perhaps supernatural forces, power by which our last action is besieged.” For instance, nails, wooden boards and plumbing tubes do their work to keep a house “running” silently (invisibly) without being viewed or noticed. Totality means that objects do not operate alone but always in relation to other objects–the smallest nail can, for example, not be disconnected from wooden boards, the plumbing tubes or from the cement. Depending on the point of view of each entity (nail, tube, etc.) a different reality will emerge within the house. For Harman, “to refer to an object as a tool-being is not to say that it is brutally exploited as a means to an end, but only that it is torn apart by the universal duel between the silent execution of an object’s reality and the glistening aura of its tangible surface.” — From "The Action of Things," an M.A. thesis at the Center for Curatorial Studies, Bard College, by Manuela Moscoso, May 2011, edited by Sarah Demeuse |
From Wikipedia, a programming paradigm:
See also posts tagged Turing's Cathedral, and Alley Oop (Feb. 11, 2003).
In honor of Ace Greenberg, a major Wall Street player
who reportedly died today at 86:
See also this journal on the date of the above review,
March 9, 2009: First and Last Things.
This post was suggested by…
“Oh, the humanity!” — Reporter’s comment
“It’s going to be accomplished in steps,
this establishment of the Talented
in the scheme of things.”
— Anne McCaffrey, Radcliffe ’47, To Ride Pegasus
From a review of the new film “Magic in the Moonlight”—
“Sophie seems to have some actual talent….
When Sophie meets Aunt Vanessa, she uncovers the spinster’s
long-ago love affair with a member of parliament. It’s eerie.”
Material that is related, if only in story space:
(Continued from April 8, 2013.)
See Two Blocks Short of a Design (May 5, 2011).
“Just a lying rhyme for seven!” — Playwright Tom Stoppard on Heaven
Related material in this journal: Lying Rhyme and Happy Birthday.
“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.
"Lord knows when the cold wind blows
it'll turn your head around."
— James Taylor, "Fire and Rain"
Ricky Jay's head turns around in "The Amazing Maleeni,"
episode 8 of season 7 of "The X-Files."
"It was the middle of summer, but
the cold wind blew in full force."
— David Kushner, Jonny Magic and the Card Shark Kids
(Quoted here in House of Cards, June 11, 2014,
a post on magic, cards, and Multnomah County.)
Related material:
Recent posts on artist Otto Piene and the Whiskey Bar song,
as well as the following Multnomah County story from yesterday's
online NY Times :
This is a post in memory of artist Otto Piene, who reportedly died
at 86 on Thursday, July 17, 2014, in Berlin.
*For the title, see Alternate Reality, a post of Saturday, July 19, 2014.
See also Piene and paradigms, and Paradigm Shift from the date of death
for Piene and Hartsfield.
Paradigms of Geometry:
Continuous and Discrete
The discovery of the incommensurability of a square’s
side with its diagonal contrasted a well-known discrete
length (the side) with a new continuous length (the diagonal).
The figures below illustrate a shift in the other direction.
The essential structure of the continuous configuration at
left is embodied in the discrete unit cells of the square at right.
See Desargues via Galois (August 6, 2013).
“Zero is a group of artists founded by Heinz Mack and
Otto Piene….” — Wikipedia
“The title ZERO was the result of months of search
and was finally found more or less by chance.
From the beginning we looked upon the term
not as an expression of nihilism – or a dada-like gag,
but as a word indicating a zone of silence and of
pure possibilities for a new beginning as at the
count-down when rockets take off- zero is the
incommensurable zone in which the old state turns
into the new.”
(Where Entertainment Is God , continued)
In memory of artist Otto Piene — a news item from last May
at the ZERO Foundation website on an exhibition that closes tomorrow —
2014-05-15
Today is the opening of the exhibition ZERO — Zwischen Himmel und Erde
in Friedrichshafen. The Zeppelin Museum is showing wonderful artworks
all related to heaven and earth by various ZERO artists
such as Piene, Mack, Uecker, Klein, Luther, and Manzoni.
ZERO – Zwischen Himmel und Erde
Zeppelin Museum Friedrichshafen
15.05. – 20.07.2014
www.zeppelin-museum.de
“Oh, show me the way to the next whiskey bar”
— Song lyric from previous post
“In a technologically advanced 1939, the zeppelin Hindenburg III
arrives in New York City, mooring atop the Empire State Building.”
— Wikipedia on the first scene of the 2004 film
“Sky Captain and the World of Tomorrow“
From The Thin White Duke:
“When I was living in my apartment in Berlin,
I would sing this at breakfast every morning.”
Oh, show me the way to the next whiskey bar
Oh, don’t ask why, no, don’t ask why
For we must find the next whiskey bar
Or if we don’t find the next whiskey bar
I tell you we must die, I tell you we must die
I tell you, I tell you, I tell you we must die
Read more: David Bowie – Alabama Song Lyrics | MetroLyrics
See also…
“Wir trauern um Otto Piene, der unerwartet am 17.7 in Berlin gestorben ist.”
The Los Angeles Times on entertainer Elaine Stritch,
who died yesterday (Thursday, July 17, 2014):
“She made few apologies in her career, describing herself as
a ‘Catholic, diabetic, alcoholic, pain in the ass.'” — David Ng
“Band of angels, lead me home.” — Song lyric
Scene from 3:10 to Yuma (1957)
Related material:
* For related remarks, see posts of May 26-28, 2012.
"I need a photo opportunity, I want a shot at redemption.
Don't want to end up a cartoon in a cartoon graveyard."
– Paul Simon
"The theory of poetry, that is to say, the total of the theories of poetry, often seems to become in time a mystical theology or, more simply, a mystique. The reason for this must by now be clear. The reason is the same reason why the pictures in a museum of modern art often seem to become in time a mystical aesthetic, a prodigious search of appearance, as if to find a way of saying and of establishing that all things, whether below or above appearance, are one and that it is only through reality, in which they are reflected or, it may be, joined together, that we can reach them. Under such stress, reality changes from substance to subtlety, a subtlety in which it was natural for Cézanne to say: 'I see planes bestriding each other and sometimes straight lines seem to me to fall' or 'Planes in color…. The colored area where shimmer the souls of the planes, in the blaze of the kindled prism, the meeting of planes in the sunlight.' The conversion of our Lumpenwelt went far beyond this. It was from the point of view of another subtlety that Klee could write: 'But he is one chosen that today comes near to the secret places where original law fosters all evolution. And what artist would not establish himself there where the organic center of all movement in time and space– which he calls the mind or heart of creation– determines every function.' Conceding that this sounds a bit like sacerdotal jargon, that is not too much to allow to those that have helped to create a new reality, a modern reality, since what has been created is nothing less.
— Wallace Stevens, Harvard College Class of 1901, "The Relations between Poetry and Painting" in The Necessary Angel (Knopf, 1951) |
For background on the planes illustrated above,
see Diamond theory in 1937.
Related material:
Lead obituary in today’s online New York Times and Los Angeles Times —
Maazel reportedly died on Sunday, July 13, 2014.
From a search in this journal for Iconic Notation,
a related image from August 14, 2010—
See also…
Epiphany
Continued from August 20, 2013
In honor of Sam Peckinpah, the closing shot of his last film:
“Am I still on?” — Ending line of The Osterman Weekend (1983)
See…
"Numbers themselves are fictions, abstractions humans invented
to gain more control over the world." — Keith Devlin
Related material:
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