The title is a phrase by Robert Hughes from the previous post.
Monday, August 17, 2020
Saturday, August 10, 2019
Tuesday, April 2, 2019
The Core Experience
"It never occurred to me that someone could so explicitly reject
the core experience of something like Chartres."
— Christopher Alexander to Peter Eisenman, 1982
For a less dramatic core experience , see Hitchcock.
Thursday, September 28, 2017
Core
From the New York Times Wire last night —
"Mr. Hefner … styled himself as an emblem
of the sexual revolution."
From a Log24 post on September 23 —
A different emblem related to other remarks in the above Sept. 23 post —
(On the wall — a Galois-geometry inscape .)
Saturday, July 8, 2017
Monday, April 3, 2017
Tuesday, December 13, 2016
Saturday, September 24, 2016
Core Structure
For the director of "Interstellar" and "Inception" —
At the core of the 4x4x4 cube is …
Cover modified.
Wednesday, August 24, 2016
Core Statements
"That in which space itself is contained" — Wallace Stevens
An image by Steven H. Cullinane from April 1, 2013:
The large Desargues configuration of Euclidean 3-space can be
mapped canonically to the 4×4 square of Galois geometry —
On an Auckland University of Technology thesis by Kate Cullinane —
The thesis reportedly won an Art Directors Club award on April 5, 2013.
Friday, July 1, 2016
Transparent Core
"At the point of convergence the play of similarities and differences
cancels itself out in order that identity alone may shine forth.
The illusion of motionlessness, the play of mirrors of the one:
identity is completely empty; it is a crystallization and
in its transparent core the movement of analogy begins all over
once again." — The Monkey Grammarian by Octavio Paz,
translated by Helen Lane
A more specific "transparent core" —
See all references to this figure
in this journal.
For a more specific "monkey grammarian,"
see W. Tecumseh Fitch in this journal.
Sunday, June 26, 2016
Common Core versus Central Structure
Rubik's Cube Core Assembly — Swarthmore Cube Project, 2008 —
"Children of the Common Core" —
There is also a central structure within Solomon's Cube —
For a more elaborate entertainment along these lines, see the recent film
"Midnight Special" —
Friday, June 12, 2015
Thursday, April 9, 2015
Core Values
"Yankee Doodle went to London" — Song lyric
“Geometry was very important to us in this movie.”
— The Missing ART (Log24, November 7th, 2014)
ART —
"Faculty Approve Theater Concentration, Affirmation
of Integrity" — Recent Harvard Crimson headline
Thursday, February 5, 2015
Core Problem
(As opposed to "The Hard Problem")
Sharon Gaudin at computerworld.com
on artificial intelligence (AI) today—
"Google's [Geoffrey] Hinton said he's most excited
about gains in neural networks that would enable
computers to understand the content of sentences
and documents.
'That is close to the core of Google because
it involves understanding sentences, and if you can
understand what a document is saying, you can do
a much better search,' Hinton said. 'That's a core
AI problem. Can you read a document and know
what it's saying?'"
Sometimes. How about you?
Tuesday, December 30, 2014
Core
JOSEFINE LYCHE
ABSOLUTE ALT. VOL. 2
17. april – 23. mai [2015] —
"I kjernen av mitt arbeid er en pågående
utforskning av esoteriske konsepter…."
"At the core of my work is an ongoing
exploration of esoteric concepts…."
See also
http://issuu.com/tmrk/docs/spritenkunsthall_2015_cut .
Related material: Hard Core.
Sunday, September 21, 2014
Uncommon Noncore
This post was suggested by Greg Gutfeld’s Sept. 4 remarks on Common Core math.
Problem: What is 9 + 6 ?
Here are two approaches suggested by illustrations of Desargues’s theorem.
Solution 1:
9 + 6 = 10 + 5,
as in Common Core (or, more simply, as in common sense), and
10 + 5 = 5 + 10 = 15 as in Veblen and Young:
Solution 2:
In the figure below,
9 + 6 = no. of V’s + no. of A’s + no. of C’s =
no. of nonempty squares = 16 – 1 = 15.
(Illustration from Feb. 10, 2014.)
The silly educationists’ “partner, anchor, decompose” jargon
discussed by Gutfeld was their attempt to explain “9 + 6 = 10 + 5.”
As he said of the jargon, “That’s not math, that’s the plot from ‘Silence of the Lambs.'”
Or from Richard, Frank, and Marcus in last night’s “Intruders”
(BBC America, 10 PM).
Saturday, July 5, 2014
Core Curriculum Vocabulary:
Separatrix and Mulligan
An image from this journal on September 16, 2013:
Mulligan:
“A mulligan, in a game, happens when a player gets a second chance
to perform a certain move or action.” — Wikipedia
New York Times obituary for Richard Mellon Scaife:
“He had the caricatured look of a jovial billionaire promoting ‘family values’
in America: a real-life Citizen Kane with red cheeks, white hair, blue eyes and
a wide smile for the cameras. Friends called him intuitive but not intellectual.
He told Vanity Fair his favorite TV show was ‘The Simpsons,’ and his favorite
book was John O’Hara’s Appointment in Samarra , about a rich young
Pennsylvanian bent on self-destruction.” — Robert D. McFadden
Click image below for some nuclear family values in memory of Scaife:
See also the previous post,
Core Curriculum.
Core Curriculum
This post was suggested by reviews of the David Hare play “Skylight” at
The New York Times , at WorldSocialism.org, and at ChicagoCritic.com.
Vide Atoms in the Family , by Laura Fermi, a book I read in high school.
Thursday, July 3, 2014
Core Mathematics: Arrays
Mathematics vulgarizer Keith Devlin on July 1
posted an essay on Common Core math education.
His essay was based on a New York Times story from June 29,
“Math Under Common Core Has Even Parents Stumbling.”
An image from that story:
The Times gave no source, other than the photographer’s name,
for the above image. Devlin said,
“… the image of a Common Core math worksheet
the Times chose to illustrate its story showed
a very sensible, and deep use of dot diagrams,
to understand structure in arithmetic.”
Devlin seems ignorant of the fact that there is
no such thing as a “Common Core math worksheet.”
The Core is a set of standards without worksheets
(one of its failings).
Neither the Times nor whoever filled out the worksheet
nor Devlin seemed to grasp that the image the Times used
shows some multiplication word problems that are more
advanced than the topic that Devlin called the
“deep use of dot diagrams to understand structure in arithmetic.”
This Core topic is as follows:
For some worksheets that are (purportedly) relevant, see,
for instance…
http://search.theeducationcenter.com/search/
_Common_Core_Label-2.OA.C.4–keywords-math_worksheets,
in particular the worksheet
http://www.theeducationcenter.com/editorial_content/multipli-city:
Some other exercises said to be related to standard 2.OA.C.4:
http://www.ixl.com/standards/ common-core/math/grade-2
|
The Common Core of course fails to provide materials for parents
that are easily findable on the Web and that give relevant background
for the above second-grade topic. It leaves this crucial task up to
individual states and school districts, as well as to private enterprise.
This, and not the parents’ ignorance described in Devlin’s snide remarks,
accounts for the frustration that the Times story describes.
Friday, February 28, 2014
Score
"Once a verbal structure is read, and reread
often enough to be possessed, it 'freezes.'
It turns into a unity in which all parts exist at
once, without regard to the specific movement
of the narrative. We may compare it to the study
of a music score, where we can turn to any
part without regard to sequential performance."
— Northrop Frye in The Great Code
Gardner reportedly died at 65 on February 19.
A post linked to here on that date suggests some
musical remarks.
Saturday, May 11, 2013
Invariant Core
The title is from today's noon post, Core.
It also appears, quoted from Popovič, in Susan Bassnett's
Translation Studies (third edition, Routledge, 2002)—
"It is an established fact in Translation Studies that if a dozen
translators tackle the same poem, they will produce a dozen
different versions. And yet somewhere in those dozen versions there
will be what Popovič calls the ‘invariant core’ of the original poem.
This invariant core, he claims, is represented by stable, basic and
constant semantic elements in the text, whose existence can be
proved by experimental semantic condensation. Transformations, or
variants, are those changes which do not modify the core of meaning
but influence the expressive form. In short, the invariant can be
defined as that which exists in common between all existing
translations of a single work. So the invariant is part of a dynamic
relationship and should not be confused with speculative arguments
about the ‘nature’, the ‘spirit’ or ‘soul’ of the text; the ‘indefinable
quality’ that translators are rarely supposed to be able to capture."
"A writer hopes to leave behind a work no one forgets…."
— Song sung on NBC's Smash tonight
Fulsere vere candidi mihi soles….
— André Weil, The Apprenticeship of a Mathematician
nam unguentum dabo, quod meae puellae
donarunt Veneres Cupidinesque….
— Catullus, quoted in Bassnett's Translation Studies
Core
Promotional description of a new book:
“Like Gödel, Escher, Bach before it, Surfaces and Essences will profoundly enrich our understanding of our own minds. By plunging the reader into an extraordinary variety of colorful situations involving language, thought, and memory, by revealing bit by bit the constantly churning cognitive mechanisms normally completely hidden from view, and by discovering in them one central, invariant core— the incessant, unconscious quest for strong analogical links to past experiences— this book puts forth a radical and deeply surprising new vision of the act of thinking.”
“Like Gödel, Escher, Bach before it….”
Or like Metamagical Themas .
Rubik core:
Non- Rubik cores:
Of the odd nxnxn cube: | Of the even nxnxn cube: |
Related material: The Eightfold Cube and…
“A core component in the construction
is a 3-dimensional vector space V over F2 .”
— Page 29 of “A twist in the M24 moonshine story,”
by Anne Taormina and Katrin Wendland.
(Submitted to the arXiv on 13 Mar 2013.)
Wednesday, April 14, 2021
Raiders of the Lost Coordinates . . .
A pyramid scheme† in memory of the late Bernie Madoff —
![]() |
The above passage from Whitehead’s 1906 book suggests
that the tetrahedral model may be older than Polster thinks.*
This is shown by . . .
† See also “Profzi Scheme.”
* For some related work of the above “D. Mesner,” see
Mesner, D. (1967). “Sets of Disjoint Lines in PG(3, q),”
Canadian Journal of Mathematics, 19, 273-280.
Tuesday, March 16, 2021
Monday, March 15, 2021
The Time Signature
Saturday, March 13, 2021
Eternal Spark
According to Lt. Col. Wayne M. McDonnell in June 1983 —
“… it is accurate to observe that when a person experiences
the out-of- body state he is, in fact, projecting that eternal spark
of consciousness and memory which constitutes the ultimate
source of his identity….”
— Section 27, “Consciousness in Perspective,” of
“Analysis and Assessment of Gateway Process.”
A related quotation —
“In truth, the physical AllSpark is but a shell….”
— https://tfwiki.net/wiki/AllSpark
From the post Ghost in the Shell (Feb. 26, 2019) —
See also, from posts tagged Ogdoad Space —
“Like the Valentinian Ogdoad— a self-creating theogonic system
of eight Aeons in four begetting pairs— the projected eightfold work
had an esoteric, gnostic quality; much of Frye’s formal interest lay in
the ‘schematosis’ and fearful symmetries of his own presentations.”
— From p. 61 of James C. Nohrnberg’s “The Master of the Myth
of Literature: An Interpenetrative Ogdoad for Northrop Frye,”
Comparative Literature , Vol. 53 No. 1, pp. 58-82, Duke University
Press (quarterly, January 2001)
— as well as . . .
Related illustration from posts tagged with
the quilt term Yankee Puzzle —
Sunday, March 7, 2021
Tuesday, March 2, 2021
Iconic Reinvention
“But perhaps its most iconic reinvention came with the longstanding
Marlboro Man campaign, which ran from 1963 to 1971. In an article
by Denver Post journalist Jim Carrier, who spent six months traveling
across the American West to meet former Marlboro Men, we’re told
that the campaign began in late 1954, when ad exec Leo Burnett asked
his top creatives, ‘What is the most masculine image in the U.S. today?’
According to Carrier, ‘Philip Morris, the fourth-largest American tobacco
company, wanted to create a filter cigarette to deal with the rising problem
of smoker’s cough and lung disease. But they had to overcome the early
image of filters as being for sissies.'”
Related story from The New York Times on Monday, March 1 —
Related flashback from this journal on Sunday, February 28 —
Monday, December 28, 2020
Theology for the Wiener Kreis
The previous post suggests a look at The New Yorker today —
Another “core claim” —
“Change arises from the structure of the object.“
See also Wiener Kreis and Schlick.
Thursday, December 24, 2020
Change Arises: A Literary Example
The “Change Arises” part of the title refers to the previous post.
The 1905 “geometric object” there, a 4×4 square, appeared earlier,
in 1869, in a paper by Camille Jordan. For that paper, and the
“literary example” of the title, see “Ici vient M. Jordan .”
This post was suggested by the appearance of Jordan in today’s
memorial post for Peter M. Neumann by Peter J. Cameron.
Related remarks on Jordan and “geometrical objects” from 2016 —
These reflections are available from their author as a postprint.
Friday, November 13, 2020
Deep State, Deep Mind, Deep Structure
. . . .
“In Weber’s hands, the professor and the politician
are not figures to be joined. Each remains a lonely hero
of heavy burden, sent to ride against his particular foe:
the overly structured institution of the modern mind,
the overly structured institution of the modern state.”
See also Chomsky in this journal.
Thursday, October 1, 2020
Annals of Academia
New York magazine’s “The Cut” —
BAD SCIENCE
JULY 14, 2016
Why It Took Social Science Years to Correct a Simple Error
About ‘Psychoticism’
By Jesse Singal
“What should we make of all of this? Partly, of course, this is
a story of conflicting personalities, of competitiveness between
researchers, of academics acting — let’s be frank — like dicks.”
Or, worse, like New York Times reporter Benedict Carey —
A Theory About Conspiracy Theories
In a new study, psychologists tried to get a handle on the personality types that might be prone to outlandish beliefs. By Benedict Carey, New York Times science reporter, . . . . The personality features that were solidly linked to conspiracy beliefs included some usual suspects: entitlement, self-centered impulsivity, cold-heartedness (the confident injustice collector), elevated levels of depressive moods and anxiousness (the moody figure, confined by age or circumstance). Another one emerged from the questionnaire that aimed to assess personality disorders — a pattern of thinking called “psychoticism.” Psychoticism is a core feature of so-called schizo-typal personality disorder, characterized in part by “odd beliefs and magical thinking” and “paranoid ideation.” In the language of psychiatry, it is a milder form of full-blown psychosis, the recurrent delusional state that characterizes schizophrenia. It’s a pattern of magical thinking that goes well beyond garden variety superstition and usually comes across socially as disjointed, uncanny or “off.” In time, perhaps some scientist or therapist will try to slap a diagnosis on believers in Big Lie conspiracies that seem wildly out of line with reality. For now, Dr. Pennycook said, it is enough to know that, when distracted, people are far more likely to forward headlines and stories without vetting their sources much, if at all. |
Some elementary fact-checking reveals that historical definitions
of “psychoticism” vary greatly. Carey forwards this bullshit without
vetting his sources much, if at all.
Monday, September 7, 2020
Remedial Reading
Monday, June 8, 2020
Chariot Race
“Mr. Lowery’s view that news organizations’ ‘core value
needs to be the truth, not the perception of objectivity,’
as he told me, has been winning in a series of battles,
many around how to cover race.”
— Ben Smith in the print New York Times this morning
“Christ is truth.” — St. Gerard Manley Hopkins
See also The Diamond Chariot in posts tagged September Samurai.
This post was suggested by a May 28 death —
Friday, May 8, 2020
Moon Song
“Even when some parts of the show don’t feel like they’re working,
the production is always top notch and eye-popping. The score, too,
is top notch here, but it’s the use of Pink Floyd’s ‘The Dark Side of
the Moon’ that resonates most.”
— Kevin Lever on the Westworld May 3 Season 3 finale
Image from Log24 posts tagged Spectral Valhalla —
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
Sunday, April 5, 2020
Wednesday, March 11, 2020
Visualizing Mathieu Group Generators
Update of March 17, 2020 —
The graphic images illustrate nicely Conder's six 4-cycles, but
their relationship, if any, to his eight 2-cycles is a mystery —
The Conder paper is at
https://core.ac.uk/download/pdf/82622574.pdf.
Saturday, February 22, 2020
Remembering Speechlessly
"Remembering speechlessly we seek
the great forgotten language . . . ."
"At the point of convergence by Octavio Paz, translated by Helen Lane
|
See also other posts now tagged Transparent Things.
Saturday, January 25, 2020
Friday, January 24, 2020
Oettinger Quote
Quote Investigator on May 4, 2010* —
"QI has traced the core of the quotation
to the work of an early researcher in
artificial intelligence, Anthony Oettinger,
who was trying to get a computer to
manipulate the English language."
See as well Oettinger in 1963.
"And that was the state of the art."
— Adapted from Stephen Sondheim
* Cf. this journal on that date.
Thursday, January 2, 2020
Nada for Hemingway
See Nada + Hemingway in this journal.
The above upload date suggests a look at
other posts now tagged Red to Green.
Friday, October 11, 2019
The Flynn Legacy
James R. Flynn (born in 1934), "is famous for his discovery of
the Flynn effect, the continued year-after-year increase of IQ
scores in all parts of the world." —Wikipedia
His son Eugene Victor Flynn is a mathematician, co-author
of the following chapter on the Kummer surface—
Sunday, September 22, 2019
Colorful Tale
“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”
— Hermann Weyl, Philosophy of Mathematics and
Natural Science , Princeton, 1949, p. 237
"The bond with reality is cut."
— Hans Freudenthal, 1962
From page 180, Logicomix — It was a dark and stormy night …
Saturday, June 15, 2019
Actionable Daydream
Wednesday, June 5, 2019
Time Cube
The opening lines of Eliot's Four Quartets —
"Time present and time past
Are both perhaps present in time future,
And time future contained in time past."
Perhaps.
Those who prefer geometry to rhetoric may also prefer
to Eliot's lines the immortal opening of the Transformers saga —
"Before time began, there was the Cube."
One version of the Cube —
Tuesday, May 14, 2019
Surrealistic Pillow Talk
"Plan 9 deals with the resurrection of the dead."
"When the men on the chessboard
get up and tell you where to go . . ."
Saturday, May 4, 2019
The Chinese Jars of Shing-Tung Yau
The title refers to Calabi-Yau spaces.
Four Quartets
. . . Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness.
A less "cosmic" but still noteworthy code — The Golay code.
This resides in a 12-dimensional space over GF(2).
Related material from Plato and R. T. Curtis —
A related Calabi-Yau "Chinese jar" first described in detail in 1905 —
A figure that may or may not be related to the 4x4x4 cube that
holds the classical Chinese "cosmic code" — the I Ching —
ftp://ftp.cs.indiana.edu/pub/hanson/forSha/AK3/old/K3-pix.pdf
Friday, March 29, 2019
The Blazon World*
“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
* Title suggested by that of a Siri Hustvedt novel.
See also Blazon in this journal.
Tuesday, March 5, 2019
A Block Design 3-(16,4,1) as a Steiner Quadruple System:
A Midrash for Wikipedia
Midrash —
Related material —
________________________________________________________________________________
Tuesday, February 26, 2019
Wednesday, October 17, 2018
Aesthetics
From "The Phenomenology of Mathematical Beauty," The Lightbulb Mistake . . . . Despite the fact that most proofs are long, and despite our need for extensive background, we think back to instances of appreciating mathematical beauty as if they had been perceived in a moment of bliss, in a sudden flash like a lightbulb suddenly being lit. The effort put into understanding the proof, the background material, the difficulties encountered in unraveling an intricate sequence of inferences fade and magically disappear the moment we become aware of the beauty of a theorem. The painful process of learning fades from memory, and only the flash of insight remains. We would like mathematical beauty to consist of this flash; mathematical beauty should be appreciated with the instantaneousness of a lightbulb being lit. However, it would be an error to pretend that the appreciation of mathematical beauty is what we vaingloriously feel it should be, namely, an instantaneous flash. Yet this very denial of the truth occurs much too frequently. The lightbulb mistake is often taken as a paradigm in teaching mathematics. Forgetful of our learning pains, we demand that our students display a flash of understanding with every argument we present. Worse yet, we mislead our students by trying to convince them that such flashes of understanding are the core of mathematical appreciation. Attempts have been made to string together beautiful mathematical results and to present them in books bearing such attractive titles as The One Hundred Most Beautiful Theorems of Mathematics . Such anthologies are seldom found on a mathematician’s bookshelf. The beauty of a theorem is best observed when the theorem is presented as the crown jewel within the context of a theory. But when mathematical theorems from disparate areas are strung together and presented as “pearls,” they are likely to be appreciated only by those who are already familiar with them. The Concept of Mathematical Beauty The lightbulb mistake is our clue to understanding the hidden sense of mathematical beauty. The stark contrast between the effort required for the appreciation of mathematical beauty and the imaginary view mathematicians cherish of a flashlike perception of beauty is the Leitfaden that leads us to discover what mathematical beauty is. Mathematicians are concerned with the truth. In mathematics, however, there is an ambiguity in the use of the word “truth.” This ambiguity can be observed whenever mathematicians claim that beauty is the raison d’être of mathematics, or that mathematical beauty is what gives mathematics a unique standing among the sciences. These claims are as old as mathematics and lead us to suspect that mathematical truth and mathematical beauty may be related. Mathematical beauty and mathematical truth share one important property. Neither of them admits degrees. Mathematicians are annoyed by the graded truth they observe in other sciences. Mathematicians ask “What is this good for?” when they are puzzled by some mathematical assertion, not because they are unable to follow the proof or the applications. Quite the contrary. Mathematicians have been able to verify its truth in the logical sense of the term, but something is still missing. The mathematician who is baffled and asks “What is this good for?” is missing the sense of the statement that has been verified to be true. Verification alone does not give us a clue as to the role of a statement within the theory; it does not explain the relevance of the statement. In short, the logical truth of a statement does not enlighten us as to the sense of the statement. Enlightenment , not truth, is what the mathematician seeks when asking, “What is this good for?” Enlightenment is a feature of mathematics about which very little has been written. The property of being enlightening is objectively attributed to certain mathematical statements and denied to others. Whether a mathematical statement is enlightening or not may be the subject of discussion among mathematicians. Every teacher of mathematics knows that students will not learn by merely grasping the formal truth of a statement. Students must be given some enlightenment as to the sense of the statement or they will quit. Enlightenment is a quality of mathematical statements that one sometimes gets and sometimes misses, like truth. A mathematical theorem may be enlightening or not, just as it may be true or false. If the statements of mathematics were formally true but in no way enlightening, mathematics would be a curious game played by weird people. Enlightenment is what keeps the mathematical enterprise alive and what gives mathematics a high standing among scientific disciplines. Mathematics seldom explicitly acknowledges the phenomenon of enlightenment for at least two reasons. First, unlike truth, enlightenment is not easily formalized. Second, enlightenment admits degrees: some statements are more enlightening than others. Mathematicians dislike concepts admitting degrees and will go to any length to deny the logical role of any such concept. Mathematical beauty is the expression mathematicians have invented in order to admit obliquely the phenomenon of enlightenment while avoiding acknowledgment of the fuzziness of this phenomenon. They say that a theorem is beautiful when they mean to say that the theorem is enlightening. We acknowledge a theorem’s beauty when we see how the theorem “fits” in its place, how it sheds light around itself, like Lichtung — a clearing in the woods. We say that a proof is beautiful when it gives away the secret of the theorem, when it leads us to perceive the inevitability of the statement being proved. The term “mathematical beauty,” together with the lightbulb mistake, is a trick mathematicians have devised to avoid facing up to the messy phenomenon of enlightenment. The comfortable one-shot idea of mathematical beauty saves us from having to deal with a concept that comes in degrees. Talk of mathematical beauty is a cop-out to avoid confronting enlightenment, a cop-out intended to keep our description of mathematics as close as possible to the description of a mechanism. This cop-out is one step in a cherished activity of mathematicians, that of building a perfect world immune to the messiness of the ordinary world, a world where what we think should be true turns out to be true, a world that is free from the disappointments, ambiguities, and failures of that other world in which we live. |
How many mathematicians does it take to screw in a lightbulb?
Tuesday, July 31, 2018
Sunday, June 24, 2018
For 6/24
A clue to the relationship between the Kummer (16, 6)
configuration and the large Mathieu group M24 —
Related material —
See too the diamond-theorem correlation.
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
|
Wednesday, February 7, 2018
Conceptual Minimalism
"At the point of convergence by Octavio Paz, translated by Helen Lane
|
See also AS IS.
Friday, November 24, 2017
Scholia
From this evening's online New York Times :
"Eric Salzman, a composer and music critic who
championed a new art form, music theater,
that was neither opera nor stage musical, died
on Nov. 12 at his home in Brooklyn. He was 84."
. . . .
"The first American Music Theater Festival
took place in the summer of 1984.
Among that first festival’s featured works was
'Strike Up the Band!,' Mr. Salzman’s 'reconstructed
and adapted' version of a satirical musical
with a score by George and Ira Gershwin
that had not been staged in 50 years. The director
of that production, Frank Corsaro, died
the day before Mr. Salzman did."
Synchronology check :
"The day before" above was November 11, 2017.
Links from this journal on November 11 —
A Log24 search for Michael Sudduth and an
October 28, 2017, Facebook post by Sudduth.
Detail of Sudduth's Nov. 11 Facebook home page —
Click the above for an enlarged view of the Sudduth profile picture.
Related material :
Aooo.
Friday, November 10, 2017
A Mathematician’s Apology
(Click to enlarge.)
For the paper on Steiner systems, see the bibliographic link in
the previous Log24 post.
See as well Cameron's posts before and after his post above:
Annals of Rarefied Scholarship
From Cambridge Core, suggested by a reference to
that website in the previous post and by the following
bibliographic data . . .
https://doi.org/10.1017/fmp.2016.5
Downloaded from https://www.cambridge.org/core
on 10 Nov 2017 at 19:06:19
See Conwell + Princeton in this journal.
Related art —
Thursday, October 26, 2017
A Center
This post was suggested by a New York Times obituary this evening —
"Tom Mathews, Promoter of Liberal Causes and Candidates, Dies at 96."
Mathews reportedly died on October 14, 2017.
"Mr. Mathews and his business partner Roger Craver 'dreamed for years
of finding the perfect citizen-candidate,' the authors wrote, 'a man or
woman of the center-left with a feel for issues, a history of independence,
a winning television manner and, most important of all, a center — a core
of beliefs more important to him or her than getting elected.'
Dream on.
From the date of Mathews's death:
Posts now tagged A Center for Krauss —
Tuesday, October 17, 2017
Status Symbols
"Status: Defunct" …
As is now its owner, who reportedly
died at 80 on Sunday, October 15, 2017.
In memoriam —
Excerpts from Log24 posts on Sunday night
and yesterday evening —
.
" … listen: there's a hell
of a good universe next door; let's go"
— e. e. cummings
Some literary background —
"At the point of convergence by Octavio Paz, translated by Helen Lane
|
Sunday, September 24, 2017
Figures
"On April 23, 2009 ….
'I’m reminded of the character in "The Silence of the Lambs,"
Hannibal Lecter, a very brilliant man,' the prosecutor said,
recognizing 'his ability to intelligently and articulately discuss
things occurring in society.'
'But at his core, as with Mr. Lecter at his core, he is a sociopath,'
the prosecutor said."
— David Stout in an obituary from this evening's online
New York Times
See also this journal on April 23, 2009, and
a figure from this morning's link Cantina —
.
Saturday, September 23, 2017
The Turn of the Frame
"With respect to the story's content, the frame thus acts
both as an inclusion of the exterior and as an exclusion
of the interior: it is a perturbation of the outside at the
very core of the story's inside, and as such, it is a blurring
of the very difference between inside and outside."
— Shoshana Felman on a Henry James story, p. 123 in
"Turning the Screw of Interpretation,"
Yale French Studies No. 55/56 (1977), pp. 94-207.
Published by Yale University Press.
See also the previous post and The Galois Tesseract.
Friday, August 18, 2017
The Savvy Philosophers
Flashback in Genial, a post of March 6, 2017 —
From a New York Times book review today by
James Ryerson, instructor at The School of The New York Times —
"Savvy philosophers distill their core insight into a short phrase."
Thursday, July 27, 2017
Keeping It Simple
Michiko Kakutani in The New York Times —
"The detective story genre concerns the finding of clues
and the search for hidden designs, and its very form
underscores Mr. Pynchon’s obsession with conspiracies
and the existence of systems too complicated to understand."
— Review of Pynchon's Bleeding Edge , Sept. 10, 2013
Background: "Moss on the Wall," this journal on that date.
A less complicated system —
"Plan 9 deals with the resurrection of the dead."
— Bill Murray in "Ed Wood"
(The plan , as well as the elevation ,
of the above structure is a 3×3 grid.)
Monday, July 10, 2017
Under Bleu Cup
Publishers Weekly on a Nov. 1, 2011, book, Under Blue Cup —
"Krauss’s core argument (what she deems a 'crusade')
is that the 'white cube,' which conceptual and installation
artists have deemed obsolete, actually thrives."
For other "core arguments," see Satuday's post "Common Core"
and the Art Space posts "Odd Core" and "Even Core."
Wednesday, June 28, 2017
Maori Farewell
The second editor mentioned below reportedly died
on June 21, 2017. A page in his memory —
See also "Detail for Hopkins" in this journal on June 21.
For a Maori finale, see "De Haut en Bas " (July 11, 2008).
Friday, May 26, 2017
Day at the Museum
From the 1994 film review linked to above —
Reality Bites – Peter Travers in Rolling Stone , Feb. 1994
"Life after college – the time between graduation and
finding a job that pays your rent without making you puke.
Panic time. By spinning something fresh out of something
familiar, Reality Bites scores the first comedy knockout of
the new year. It also brings out the vibrant best in Winona
Ryder and Ethan Hawke as friends who resist being lovers,
makes a star of Janeane Garofalo as their tart-tongued
buddy and puts Ben Stiller on the map as a director."
Thursday, April 27, 2017
Partner, Anchor, Decompose
See also a figure from 2 AM ET April 26 …
" Partner, anchor, decompose. That's not math.
That's the plot to 'Silence of the Lambs.' "
Monday, March 27, 2017
Groundhog Day and After
Monday, February 20, 2017
Mathematics and Narrative
Mathematics —
Hudson's parametrization of the
4×4 square, published in 1905:
A later parametrization, from this date in 1986:
A note from later in 1986 shows the equivalence of these
two parametrizations:
Narrative —
Posts tagged Memory-History-Geometry.
The mathematically challenged may prefer the narrative of the
Creation Matrix from the religion of the Transformers:
"According to religious legend, the core of the Matrix
was created from Solomus, the god of wisdom,
trapped in the form of a crystal by Mortilus, the god
of death. Following the defeat of Mortilus, Solomus
managed to transform his crystal prison into the Matrix—
a conduit for the energies of Primus, who had himself
transformed into the life-giving computer Vector Sigma."
Friday, February 17, 2017
Fake News: The Definition
See also, on Feb. 8 in this journal, Damning.
Sunday, February 12, 2017
Colorful Tales
“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”
— Hermann Weyl, Philosophy of Mathematics and
Natural Science , Princeton, 1949, p. 237
Harvard University Press on the late Angus Fletcher, author of
The Topological Imagination and Colors of the Mind —
From the Harvard webpage for Colors of the Mind —
Angus Fletcher is one of our finest theorists of the arts,
the heir to I. A. Richards, Erich Auerbach, Northrop Frye.
This… book… aims to open another field of study:
how thought— the act, the experience of thinking—
is represented in literature.
. . . .
Fletcher’s resources are large, and his step is sure.
The reader samples his piercing vision of Milton’s
Satan, the original Thinker,
leaving the pain of thinking
as his legacy for mankind.
A 1992 review by Vinay Dharwadker of Colors of the Mind —
See also the above word "dianoia" in The Echo in Plato's Cave.
Some context …
This post was suggested by a memorial piece today in
the Los Angeles Review of Books —
A Florilegium for Angus Fletcher
By Kenneth Gross, Lindsay Waters, V. N. Alexander,
Paul Auster, Harold Bloom, Stanley Fish, K. J. Knoespel,
Mitchell Meltzer, Victoria Nelson, Joan Richardson,
Dorian Sagan, Susan Stewart, Eric Wilson, Michael Wood
Fletcher reportedly died on November 28, 2016.
"I learned from Fletcher how to apprehend
the daemonic element in poetic imagination."
— Harold Bloom in today's Los Angeles florilegium
For more on Bloom and the daemonic, see a Log24 post,
"Interpenetration," from the date of Fletcher's death.
Some backstory: Dharwadker in this journal.
Wednesday, February 8, 2017
Damning
BuzzFeed, Tuesday, January 10, 2017, on "the damning letter"—
From the Jan. 10 BuzzFeed story —
At the time of the hearing, Judiciary Committee Chairman Strom Thurmond never put the letter into the congressional record, and its contents remained largely unknown. In the only line that was made public at the time — published in June 1986 by Knight Ridder reporter Aaron Epstein — King made clear her opposition to Sessions’ nomination. “For a century, the racial practices that characterized our region were established and enforced by men who, like Mr. Sessions, protested that they, too, were not personally hostile to blacks,” King’s letter said, according to Epstein’s dispatch. |
A searchable text of the alleged 1986 letter, along with the
alleged attached statement, is now available at
https://www.aol.com/article/news/2017/02/08/
coretta-scott-kings-letter-opposing-jeff-sessions-1986-full-text/21709762/.
A search of the letter and statement at that webpage yields
no instances of the phrases "racial practices," "established and enforced,"
or "personally hostile."
Hence the word "alleged" above.
Update of 1:44 PM ET on Feb. 9, 2017:
A relevant Wikipedia article —
Questioned document examination.
Tuesday, February 7, 2017
Saturday, January 28, 2017
Cranking It Up
From "Core," a post of St. Lucia's Day, Dec. 13, 2016 —
In related news yesterday —
California yoga mogul’s mysterious death:
Trevor Tice’s drunken last hours detailed
"Police found Tice dead on the floor in his home office,
blood puddled around his head. They also found blood
on walls, furniture, on a sofa and on sheets in a nearby
bedroom, where there was a large bottle of Grey Goose
vodka under several blood-stained pillows on the floor."
See as well an image from "The Stone," a post of March 18, 2016 —
Some backstory —
“Lord Arglay had a suspicion that the Stone would be
purely logical. Yes, he thought, but what, in that sense,
were the rules of its pure logic?”
—Many Dimensions (1931), by Charles Williams
Sunday, January 15, 2017
Sunday, January 8, 2017
A Theory of Everything
The title refers to the Chinese book the I Ching ,
the Classic of Changes .
The 64 hexagrams of the I Ching may be arranged
naturally in a 4x4x4 cube. The natural form of transformations
("changes") of this cube is given by the diamond theorem.
A related post —
Monday, September 5, 2016
Space Case
The New York Times yesterday evening —
Butor reportedly died on August 24.
This journal on that date —
From Butor's obituary —
"He studied philosophy at the Sorbonne
under the phenomenologist
Gaston Bachelard, writing a thesis on
mathematics and the idea of necessity."
"In 2013 the Académie Française awarded
Mr. Butor its Grand Prix for his life’s work.
Explaining his philosophy in an interview
with the critic and television producer
Georges Charbonnier in 1965, Mr. Butor said,
'Every written word is a victory over death.' "
A search for Bachelard in this journal yields remarks
related to Bachelard's Poetics of Space and to the above
phrase by Wallace Stevens.
Thursday, August 25, 2016
Diamond on the Map
A check of Cora Diamond, editor of the 1976 Wittgenstein
book shown in the previous post, yields …
The date of the above talk was April 3, 2015.
For this journal on that date, see a link, "by Steven H. Cullinane,"
in yesterday's post Core Statements.
Monday, August 8, 2016
A Point of Identity
For a Monkey Grammarian (Viennese Version)
"At the point of convergence by Octavio Paz, translated by Helen Lane
|
A logo that may be interpreted as one-eighth of a 2x2x2 array
of cubes —
The figure in white above may be viewed as a subcube representing,
when the eight-cube array is coordinatized, the identity (i.e., (0, 0, 0)).
Shown below are a few variations on the figure by VCQ,
the Vienna Center for Quantum Science and Technology —
(Click image to enlarge.)
Thursday, August 4, 2016
Routine
Peter Gelzinis in the Boston Herald today —
"What has become painfully clear this week
is that there is no Republican campaign for
the presidency. There is only The Donald,
his
reflex tweets, the folded pieces of paper
he pulls out of his coat pocket and a crazy
stand-up routine that is part Lenny Bruce
and part professor Irwin Corey."
Tuesday, July 5, 2016
For the Children in the Apple Tree (continued)
(See previous posts now tagged Apple Tree Children.)
See as well the comic book in "Midnight Special" —
(Image previously posted in "Common Core vs. Central Structure")
Sunday, July 3, 2016
Another 48 Hours
The Onion on Friday, July 1, 2016 —
From Friday afternoon —
Friday, May 27, 2016
Peer Review
A review of the phrase "Innermost Kernel" in this journal
suggests the following meditation …
"Who am I?" — Existential cry
in "Zoolander" and "Zoolander 2."
A similar question occurs in "Peer Gynt" —
Ben Brantley in yesterday morning's print New York Times *
expressed a nihilistic view of Peer as an onion-peeler —
"Toward the end of Ibsen’s 'Peer Gynt,' a saga of self
under siege, the title character is discovered peeling
an onion, finding in the layers of that humble vegetable
a symbol for the chapters of an eventful life . . . .
… [the director’s] approach is the same one that Peer
applies to the onion: Keep stripping until you find the core.
Of course in Peer’s case what is finally found is
plenty of nothing, an apt conclusion for a man
for whom a solid self remains elusive."
I prefer a view from what Fitzgerald called
"the dark fields of the republic" — the Dordt College view —
* The Times — "A version of this review appears in print on May 26, 2016,
on page C3 of the New York edition with the headline:
'A Saga of Self-Identity, Stripped to Its Core, Still Provokes.' "
Wednesday, March 23, 2016
Requiem for an Actress
The New York Times this evening on the late Rita Gam:
"After generally being typecast in supporting roles
in two dozen films for what Life described as
'her sultry face and insinuating voice,' she recalled
in 1992, 'I looked into the black pit at 40 and
wondered, what do I do for an encore?' "
See also Sidney Lumet in this journal as well as
"Some cartoon graveyards are better than others."
Friday, March 4, 2016
Chess by Other Means
On film director Stanley Kubrick:
From "Kubrick," by Michael Herr, Vanity Fair , August 1999— "He disliked the usual references to his having been a 'chess hustler' in his Greenwich Village days, as though this impugned the gravity and beauty of the exercise, the suggestion that his game wasn’t pour le sport or, more correctly, pour l’art . To win the game was important, to win the money was irresistible, but it was nothing compared with his game, with the searching, endless action of working on his game. But of course he was hustling, he was always hustling; as he grew older and moved beyond still photography, chess became movies, and movies became chess by other means. I doubt that he ever thought of chess as just a game, or even as a game at all. I do imagine that a lot of people sitting across the board from him got melted, fried, and fragmented when Stanley let that cool ray come streaming down out of his eyes— talk about penetrating looks and piercing intelligence; here they’d sat down to a nice game of chess, and all of a sudden he was doing the thinking for both of them." |
On physics writer Peter Woit:
From Part II of an interview with Peter Woit by Gerald Alper "For just a moment, he allows himself to become self reflective: 'I was always a smart kid. A very smart kid. I suppose if I ever took a standardized test I would do very well, especially, in the area of abstract reasoning.' Peter Woit says this as matter-of-factly as if he said, 'When I was a kid my father drove a Chevrolet.' He says it as Kareem Abdul-Jabbar, if asked to describe how he became the person he is, might have said 'I was always a tall kid. A very tall kid. In school, short kids bored me.' I felt I had to say, 'but there must be a few million people in the United States who would also score very high in abstract thinking in the standardized tests and none of them have your interests.' 'The people around here all do. And there are thousands of us all around the world.' 'But there are 7 billion people in the world.' Peter Woit had to concede the mathematical point, but I don't think he appreciated the psychological distinction I was alluding to. There is an astonishing divide between the culture of science and the culture of humanities that C.P. Snow famously alluded to. There is even a greater divide between the culture of pure mathematics and the culture of the earthbound evolutionarily programmed biological world into which we are born. There is a celebrated quip by Dick Cavett that encapsulates this. Reflecting on his famous interview of the then reigning world chess champion, Bobby Fischer, he observed: 'Throughout the interview I could feel the force of his IQ.' Paraphrasing this I could say that throughout the interview, which was at times exhilarating, at times daunting, I could feel the force of his two hundred QMIQ (quantum mechanics IQ). Norman Mailer once commented that the immediacy of television— the fact that most influential people in the world can be brought into your living room— creates the illusion that you have thereby been included in their inner power circle, and to that extent vicariously empowered. But you are no closer to the corridors of power then you were before. Analogously, you can sit just a few feet away from a world-class expert, close enough to reach out and touch them, but you are no closer to their accumulated wisdom— unless you are willing to go home and put in ten thousand hours of hard work trying to raise the level of your understanding." |
Illustration from a post of
Schicksalstag 2009
Monday, February 15, 2016
Global and Local
- "Dirty Laundry" (Henley, Danny Kortchmar) – 5:36
- "The Boys of Summer" (Mike Campbell, Henley) – 4:45
- "All She Wants to Do Is Dance" (Kortchmar) – 4:28
- "Not Enough Love in the World" (Henley, Kortchmar, Benmont Tench) – 3:54
- "Sunset Grill" (Henley, Kortchmar, Tench) – 6:22
- "The End of the Innocence" (Henley, Bruce Hornsby) – 5:14
- "The Last Worthless Evening" (John Corey, Henley, Stan Lynch) – 6:05
- "New York Minute" (Henley, Kortchmar, Jai Winding) – 6:34
- "I Will Not Go Quietly" (Henley, Kortchmar) – 5:41
- "The Heart of the Matter" (Campbell, Henley, J.D. Souther) – 5:21
- "The Garden of Allah" (Corey, Paul Gurian, Henley, Lynch) – 7:02
- "You Don't Know Me at All" (Corey, Henley, Lynch) – 5:36
- "Everybody Knows" (Leonard Cohen, Sharon Robinson) – 6:10
Thursday, June 4, 2015
Molly Bloom on Education
Two pieces by NPR education writer Molly Bloom:
See also yesterday's post on another NPR / Princeton education figure,
Keith Devlin:
An illustration (click for larger view with context):
Friday, May 8, 2015
Spielraum
Review:
Illustrating the Spiegel-Spiel des Gevierts
"At the point of convergence
by Octavio Paz, translated by |
Friday December 5, 2008
|
Tuesday, May 5, 2015
Paz
"At the point of convergence
by Octavio Paz, translated by |
Thursday, April 23, 2015
Colorful Tale
(A sequel to yesterday's ART WARS and this
morning's De Colores )
“Perhaps the philosophically most relevant feature
of modern science is the emergence of abstract
symbolic structures as the hard core of objectivity
behind– as Eddington puts it– the colorful tale
of the subjective storyteller mind.” — Hermann Weyl
(Philosophy of Mathematics and Natural Science ,
Princeton, 1949, p. 237)
See also Deathly Hallows.
Thursday, April 9, 2015
Translation
From an informative April 7 essay in The Nation —
In his marvelous book Is That a Fish in Your Ear?: Translation and the Meaning of Everything , David Bellos demonstrates many of the ways that translation is not only possible but ubiquitous, so thoroughly woven into the fabric of our daily lives—from classrooms to international financial markets, from instruction manuals to poems—that if translation were somehow to become impossible, the world would descend into the zombie apocalypse faster than you can say “je ne sais quoi ." — "Forensic Translation," by Benjamin Paloff |
See also searches in this journal for Core and for Kernel.
See as well Fabric Design and Symplectic.
Tuesday, February 24, 2015
Amy’s After-Party
Tuesday, December 2, 2014
Colorful Tale
"Perhaps the philosophically most relevant feature
of modern science is the emergence of abstract
symbolic structures as the hard core of objectivity
behind— as Eddington puts it— the colorful tale
of the subjective storyteller mind."
— Hermann Weyl in Philosophy of Mathematics
and Natural Science , Princeton, 1949, p. 237
Tom Wolfe on art theorists in The Painted Word (1975) :
"It is important to repeat that Greenberg and Rosenberg
did not create their theories in a vacuum or simply turn up
with them one day like tablets brought down from atop
Green Mountain or Red Mountain (as B. H. Friedman once
called the two men). As tout le monde understood, they
were not only theories but … hot news,
straight from the studios, from the scene."
The Weyl quote is a continuing theme in this journal.
The Wolfe quote appeared here on Nov. 18, 2014,
the reported date of death of Yale graduate student
Natasha Chichilnisky-Heal.
Directions to her burial (see yesterday evening) include
a mention of "Paul Robson Street" (actually Paul
Robeson Place) near "the historic Princeton Cemetery."
This, together with the remarks by Tom Wolfe posted
here on the reported day of her death, suggests a search
for "red green black" —
The late Chichilnisky-Heal was a student of political economy.
The search colors may be interpreted, if one likes, as referring
to politics (red), economics (green), and Robeson (black).
See also Robeson in this journal.
Thursday, September 25, 2014
Mystery
"Welcome to America." — Harrison Ford in "The Devil's Own"
On readings at Mass on Sunday, Sept. 21, 2014 —
"Isaiah 55:8-9: 'For my thoughts are not your thoughts,
neither are your ways my ways, says the Lord.
For as the heavens are higher than the earth,
so are my ways higher than your ways
and my thoughts than your thoughts.'
The Gospel reading… was a perfect complement to
the passage from Isaiah…."
The America piece quoting Isaiah was titled "The Mystery of God."
The author "currently works at Xavier College Preparatory
in Palm Desert, CA, where he teaches theology…."
Related material: This journal that Sunday morning:
See also "The Mystery of God, Part II" —
Other secular stand-ins for "the thing one doesn't know"—
The mysteries of the late Joseph D. McNamara.
Sunday, September 21, 2014
Sermon
The previous post discussed the anatomy of the sum 9 + 6.
A different approach: “A” and “The 6 spreads in A” below —
Thursday, September 18, 2014
Them Apples
John Baez at Google+ has an interesting post on crackpots,
dated September 13, 2014.
Related recent material from this journal:
Sense (Sept. 13) and Sensibility (Sept. 14 and later).
See also a New York Times piece from 2009:
Related material:
“You don’t need to eat a whole apple to know it’s rotten.”
— Warren Siegel
Thursday, September 11, 2014
Oh, Moon of Alabama
The mention of Gauss in today's previous post, along with
recent news, suggested this post.
"How do you get young people excited about space?"
— Megan Garber in The Atlantic , Aug. 16, 2012
Further details: Child Buyers (July 16, 2013).
Thursday, September 4, 2014
Halloween Manifestos, 2013:
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
Sunday, July 13, 2014
Friday, July 4, 2014
Knockout
(Continued from yesterday’s noon post, from “Block That Metaphor,”
and from “Mystery Box III: Inside, Outside“)
“In one corner are the advocates of the Common Core,
led by the Bill and Melinda Gates Foundation, which
helped develop the standards and has defended them
against efforts by some states to roll them back. In the
challengers’ corner, a lineup of foundations and
philanthropists…. Other funders in the opponents’ corner
read like a ‘who’s who’ of well-heeled conservative
philanthropists, including Pittsburgh media magnate
Richard Mellon Scaife….”
— “Meet the Funders Fighting the Common Core,”
from Inside Philanthropy , Feb. 10, 2014
Scaife reportedly died this morning.
Thursday, July 3, 2014
Gates and Windows:
“Gates said his foundation is an advocate for the Common Core State Standards
that are part of the national curriculum and focus on mathematics and language
arts. He said learning ‘needs to be on the edge’ where it is challenging but not
too challenging, and that students receive the basics through Common Core.
‘It’s great to teach other things, but you need that foundation,’ he said.”
— T. S. Last in the Albuquerque Journal , 12:05 AM Tuesday, July 1, 2014
See also the previous post (Core Mathematics: Arrays) and, elsewhere
in this journal,
“Eight is a Gate.” — Mnemonic rhyme:
Wednesday, July 2, 2014
An Apple for Devlin
A columnist for the Mathematical Association of America,
Keith Devlin, yesterday posted an essay on Common Core
math education. A response:
Screenshot from a June 14, 2014, New York Times video.
Friday, March 14, 2014
Friday, February 28, 2014
Code
From Northrop Frye's The Great Code: The Bible and Literature , Ch. 3: Metaphor I — "In the preceding chapter we considered words in sequence, where they form narratives and provide the basis for a literary theory of myth. Reading words in sequence, however, is the first of two critical operations. Once a verbal structure is read, and reread often enough to be possessed, it 'freezes.' It turns into a unity in which all parts exist at once, without regard to the specific movement of the narrative. We may compare it to the study of a music score, where we can turn to any part without regard to sequential performance. The term 'structure,' which we have used so often, is a metaphor from architecture, and may be misleading when we are speaking of narrative, which is not a simultaneous structure but a movement in time. The term 'structure' comes into its proper context in the second stage, which is where all discussion of 'spatial form' and kindred critical topics take their origin." |
Related material:
"The Great Code does not end with a triumphant conclusion or the apocalypse that readers may feel is owed them or even with a clear summary of Frye’s position, but instead trails off with a series of verbal winks and nudges. This is not so great a fault as it would be in another book, because long before this it has been obvious that the forward motion of Frye’s exposition was illusory, and that in fact the book was devoted to a constant re-examination of the same basic data from various closely related perspectives: in short, the method of the kaleidoscope. Each shake of the machine produces a new symmetry, each symmetry as beautiful as the last, and none of them in any sense exclusive of the others. And there is always room for one more shake."
— Charles Wheeler, "Professor Frye and the Bible," South Atlantic Quarterly 82 (Spring 1983), pp. 154-164, reprinted in a collection of reviews of the book. |
For code in a different sense, but related to the first passage above,
see Diamond Theory Roullete, a webpage by Radamés Ajna.
For "the method of the kaleidoscope" mentioned in the second
passage above, see both the Ajna page and a webpage of my own,
Kaleidoscope Puzzle.
Thursday, February 6, 2014
The Representation of Minus One
For the late mathematics educator Zoltan Dienes.
“There comes a time when the learner has identified
the abstract content of a number of different games
and is practically crying out for some sort of picture
by means of which to represent that which has been
gleaned as the common core of the various activities.”
— Article by “Melanie” at Zoltan Dienes’s website
Dienes reportedly died at 97 on Jan. 11, 2014.
From this journal on that date —
A star figure and the Galois quaternion.
The square root of the former is the latter.
Update of 5:01 PM ET Feb. 6, 2014 —
An illustration by Dienes related to the diamond theorem —
See also the above 15 images in …
… and versions of the 4×4 coordinatization in The 4×4 Relativity Problem
(Jan. 17, 2014).
Monday, August 19, 2013
Tale
The tale is not Thomas Nagel's remarks on philosophy
summarized above, but rather the late John Hollander's
remarks on Nowhere:
"We all know where it is they've gone, the dead:
Beyond Noplace, far into wide Nowhere."
See also Nagel's book The View from Nowhere .
Sunday, June 30, 2013
Book Award
"What on earth is
— Said to be an annotation |
In the spirit of the late Thomas Guinzburg…
See also "Concrete Universal" in this journal.
Related material— From a Bloomsday reply
to a Diamond Theory reader's comment, an excerpt—
The reader's comment suggests the following passages from
the book by Stirling quoted above—
Here Stirling plays a role analogous to that of Professor Irwin Corey
accepting the National Book Award for Gravity's Rainbow in 1974.
Monday, May 13, 2013
Game Show
For the late Bob Stewart:
"She was a panelist on many game shows, including
'What’s My Line?' and 'The Hollywood Squares.'"
Translation Studies Continued:
See Cameron's Kernel and…
Sunday, April 28, 2013
C’mon Baby…
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Let's do the twist. The image at left See this journal |
A phrase from yesterday's noon post:
Sinking the Magic 8-Ball .
A scene from the above film is related to this phrase.
Another image from the film poster:
A review of the film:
"The final 'twist' seems to negate the entire story,
like a bad shaggy-dog joke."
Such a joke:
“Words and numbers are of equal value,
for, in the cloak of knowledge,
one is warp and the other woof.”
— The princesses Rhyme and Reason
in The Phantom Tollbooth
"A core component in the construction
is a 3-dimensional vector space V over F2 ."
— Page 29 of "A twist in the M24 moonshine story,"
by Anne Taormina and Katrin Wendland.
(Submitted to the arXiv on 13 Mar 2013.)
The number of points in such a space is, of course, 8.
Friday, April 5, 2013
Reflections (continued)
From a search for Mirror-Play in this journal:
That search was suggested by a much lengthier
search, for Core, that itself was suggested
by yesterday's post (on Katherine Neville's birthday)
titled A Philosopher's Stone.
See, too, Tom Hanks (shown above as symbologist
Robert Langdon) in "Lucky Guy" (reviewed by TIME
yesterday), and a related poem:
Yes, you! You’re the Lucky One…
Prospective purchasers of the poet's work
may consult a press release from LSU Press
dated 4/4/2013. The poet died, apparently*
unlamented by his publisher, on 3/30.
* But only apparently.
Thursday, April 4, 2013
A Philosopher’s Stone
"Core" (in the original, Kern ) is perhaps
not the best translation of hypokeimenon :
See also Heidegger's original German:
Related material: In this journal, "underlie" and "underlying."
Friday, March 29, 2013
Where Credit Is Due
Sunday, December 23, 2012
Digital Recreation
Denzel Washington in Deja Vu (2006), directed by Tony Scott—
See also Tony Scott and four and a half days ago* —
Japanese character
for "field"
Related material from five days ago—
"At the point of convergence by Octavio Paz, translated by |
* More precisely, what will be 4.5 days ago at 3:09 AM ET.
Tuesday, December 18, 2012
Monkey Grammar
For a modern Adam and Eve—
W. Tecumseh Fitch and Gesche Westphal Fitch,
editors of a new four-volume collection titled
Language Evolution (Feb. 2, 2012, $1,360)—
Related material—
"At the point of convergence
by Octavio Paz, translated by |
The "play of mirrors" link above is my own.
Click on W. Tecumseh Fitch for links to some
examples of mirror-play in graphic design—
from, say, my own work in a version of 1977, not from
the Fitches' related work published online last June—
See also Log24 posts from the publication date
of the Fitches' Language Evolution—
Happy birthday to the late Alfred Bester.
Sunday, November 18, 2012
Kernel
Rachel Dodes in The Wall Street Journal
on All Souls' Day, 2012—
"In one of the first lines uttered by Daniel Day-Lewis, playing Abraham Lincoln in the new Steven Spielberg film opening Nov. 9, he says, 'I could be bounded in a nutshell, and count myself a king of infinite space— were it not that I have bad dreams.'
The line was ripped straight from 'Hamlet,' by Lincoln's favorite writer, William Shakespeare. Tony Kushner, the Pulitzer Prize-winning playwright ('Angels in America') who wrote the script for the film, says that Shakespeare, much like Lincoln, 'had extraordinary mastery over the darkest parts of the human spirit.'"
The above quotation omits Shakespeare's words prefacing the nutshell part— "O God."
These same words in a different tongue— "Hey Ram"— have often been quoted as the last words of Gandhi. (See yesterday's noon post.)
"… for the Highest Essence (brahman ),
which is the core of the world, is identical
with the Highest Self (ātman ), the kernel
of man's existence."
— Heinrich Zimmer, Myths and Symbols
in Indian Art and Civilization , Pantheon
Books, 1946, page 142
Related material: A post linked to here on Friday night
that itself links to a different Shakespeare speech.