Monday, January 13, 2025
Friday, August 18, 2023
Friday, July 7, 2023
CORE
The "CORE" reference in the previous post yields, via a search . . .
Within this thesis there are 19 references to the name "Cullinane"
and to my own work, cited as . . .
Cullinane, Steven H., ‘The Diamond Theorem’ (1979)
<http://diamondtheorem.com>
[accessed 6 May 2019]
––– ‘Geometry of the I Ching’ (1989)
<http://finitegeometry.org/sc/64/iching.html>
[accessed 6 May 2019].
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Sunday, June 4, 2023
The Galois Core
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Wednesday, November 16, 2022
Friday, August 12, 2022
Mathematical Games: The Common Core
“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 at Zoltan Dienes’s website
This quote is from a Log24 post of Feb. 6, 2014,
The Representation of Minus One.
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Wednesday, May 25, 2022
Corefire Temple
The words in the above title were suggested by
-
the title, Corefires , of a novel by the late
Colin Cantwell (see previous post). -
the place-name Temple, Texas , in the gas station
scene of "No Country for Old Men," -
Log24 posts on the fictional cinematic Fire Temple,
and by … - a folk etymology for the word "pyramid" —
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Monday, August 16, 2021
In a Nutshell: The Core of Everything
“The great Confucius guided China spiritually for over 2,000 years.
The main doctrine is ' 仁 ' pronounced 'ren', meaning two people,
i.e., human relationship. Modern science has been highly competitive.
I think an injection of the human element will make our subject more
healthy and enjoyable."
— Geometer Shiing-Shen Chern in a Wikipedia article
See the "ren" character in Wiktionary. See as well . . .
"The development of ren ( 仁 ) in early Chinese philosophy,"
By Robin Elliott Curtis, U. of B.C. Master's thesis, 2016 —
Thus, we can conclude that several different forms of
the character ren , were in existence during the
Warring States period. This shows that etymological analyses
focusing exclusively on the combination of 人 and 二 are inadequate.
It should also serve as a warning against “character fetishization,”
or giving “exaggerated status to Chinese characters in the interpretation
of Chinese language, thought, and culture.” 46
46 Edward McDonald 2009, p. 1194.
McDonald, Edward. 2009. “Getting over the Walls of
Discourse: 'Character Fetishization' in Chinese Studies.”
The Journal of Asian Studies 68 (4): 1189 – 1213.
Wikipedia article on Ren in Confucianism:
|
人 + 二 = 仁 (Rén) man on left two on right, the relationship between two human beings, means co-humanity. Originally the character was just written as丨二 [citation needed] representing yin yang, the vertical line is yang (bright, traditionally masculine, heaven, odd numbers), the two horizontal lines are yin (dark, traditionally feminine, earth, even numbers), 仁 is the core of everything. |
"The core of everything" . . . Citation needed ?
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Monday, August 17, 2020
The Silence at the Core
The title is a phrase by Robert Hughes from the previous post.
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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.
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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 .)
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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.
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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.
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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.
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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" —
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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
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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?
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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.
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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).
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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.
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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.
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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.
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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.
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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
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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.)
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Thursday, March 27, 2025
Review
A review of posts tagged Design Theory yields . . .
"… at the core of reality lies a deep and eternal demonium."
— Alicia in the Cormac McCarthy novel Stella Maris.
Vide "CORE" as a starting point for mathematics from
Royal Holloway —
Thursday, February 6, 2025
For the Cambridge Philosophical Society:
The Office Supplies Folder
Courtesy of . . .
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The Office Supplies Folder
The Office Supplies Folder
Sunday, February 2, 2025
Eric Temple Bell on Solomon’s Seal
From pp. 322 ff. of The Development of Mathematics, by Eric Temple Bell, Second Edition, McGraw-Hill, 1945, at https://archive.org/stream/in.ernet.dli.2015.133966/2015.133966. The-Development-Of-Mathematics-Second-Edition_djvu.txt — Rising to a considerably higher level of difficulty, we may instance what the physicist Maxwell called “Solomon’s seal in space of three dimensions,” the twenty-seven real or imaginary straight lines which lie wholly on the general cubic surface, and the forty-five triple tangent planes to the surface, all so curiously related to the twenty-eight bitangents of the general plane quartic curve. If ever there was a fascinating snarl of interlaced theories, Solomon’s seal is one. Synthetic and analytic geometry, the Galois theory of equations, the trisection of hyperelliptic functions, the algebra of invariants and covariants, geometric-algebraic algorithms specially devised to render the tangled configurations of Solomon’s seal more intuitive, the theory of finite groups — all were applied during the second half of the nineteenth century by scores of geometers who sought to break the seal. Some of the most ingenious geometers and algebraists in history returned again and again to this highly special topic. The result of their labors is a theory even richer and more elaborately developed than Klein’s (1884) of the icosahedron. Yet it was said by competent geometers in 1945 that a serious student need never have heard of the twenty-seven lines, the forty-five triple tangent planes, and the twenty-eight bitangents in order to be an accomplished and productive geometer; and it was a fact that few in the younger generation of creative CONTRIBUTIONS FROM GEOMETRY 323 geometers had more than a hazy notion that such a thing as tiie Solomon’s seal of the nineteenth century ever existed. Those rvho could recall from personal experience the last glow of living appreciation that lighted this obsolescent master- piece of geometry and others in the same fading tradition looked back with regret on the dying past, and wished that mathe- matical progress were not always so ruthless as it is. They also sympathized with those who still found the modern geometry of the triangle and the circle worth cultivating. For the differ- ence between the geometry of the twenty-seven lines and that of, say, Tucker, Lemoine, and Brocard circles, is one of degree, not of kind. The geometers of the twentieth century long since piously removed all these treasures to the museum of geometry, where the dust of history quickly dimmed their luster. For those who may be interested in the unstable esthetics rather than the vitality of geometry, we cite a concise modern account1 (exclusive of the connection with hyperclliptic func- tions) of Solomon’s seal. The twenty-seven lines were discovered in 1849 by Cayley and G. Salmon2 (1819-1904, Ireland); the application of transcendental methods originated in Jordan’s work (1869-70) on groups and algebraic equations. Finally, in the 1870’s L. Cremona (1830-1903), founder of the Italian school of geometers, observed a simple connection between the twenty-one distinct straight lines which lie on a cubic surface with a node and the ‘cat’s cradle’ configuration of fifteen straight lines obtained by joining six points on a conic in all possible ways. The ‘mystic hexagram’ of Pascal and its dual (1806) in C. J. Brianchon’s (1783-1864, French) theorem were thus related to Solomon’s seal; and the seventeenth century met the nineteenth in the simple, uniform deduc- tion of the geometry of the plane configuration from that of a corresponding configuration in space by the method of projection. The technique here had an element of generality that was to prove extremely powerful in the discovery and proof of cor- related theorems by projection from space of a given number of dimensions onto a space of lower dimensions. Before Cremona applied this technique to the complete Pascal hexagon, his countryman G. Veronese had investigated the Pascal configura- tion at great length by the methods of plane geometry, as had also several others, including Steiner, Cayley, Salmon, and Kirkman. All of these men were geometers of great talent; 324 THE DEVELOPMENT OF MATHEMATICS Cremona’s flash of intuition illuminated the massed details of all his predecessors and disclosed their simple connections. That enthusiasm for this highly polished masterwork of classical geometry is by no means extinct is evident from the appearance as late as 1942 of an exhaustive monograph (xi + 180 pages) by B. Segre (Italian, England) on The nonsingular cubic surface. Solomon’s seal is here displayed in all its “complicated and many-sided symmetry” — in Cayley’s phrase — as never before. The exhaustive enumeration of special configurations provides an unsurpassed training ground or ‘boot camp’ for any who may wish to strengthen their intuition in space of three dimensions. The principle of continuity, ably seconded by the method of degeneration, consistently applied, unifies the multi- tude of details inherent in the twenty-seven lines, giving the luxuriant confusion an elusive coherence which was lacking in earlier attempts to “bind the sweet influences” of the thirty- six possible double sixes (or ‘double sixers,’ as they were once called) into five types of possible real cubic surfaces, containing respectively 27, 15, 7, 3, 3 real lines. A double six is two sextuples of skew lines such that each line of one is skew to precisely one corresponding line of the other. A more modern touch appears in the topology of these five species. Except for one of the three-line surfaces, all are closed, connected manifolds, while the other three-line is two connected pieces, of which only one is ovoid, and the real lines of the surface are on this second piece. The decompositions of the nonovoid piece into generalized polyhedra by the real lines of the surface are painstakingly classified with respect to their number of faces and other char- acteristics suggested by the lines. The nonovoid piece of one three-line surface is homeomorphic to the real projective plane, as also is the other three-line surface. The topological interlude gives way to a more classical theme in space of three dimensions, which analyzes the group in the complex domain of the twenty- seven lines geometrically, either through the intricacies of the thirty-six double sixes, or through the forty triads of com- plementary Steiner sets. A Steiner set of nine lines is three sets of three such that each line of one set is incident with precisely two lines of each other set. The geometrical significance of permutability of operations in the group is rather more com- plicated than its algebraic equivalent. The group is of order 51840. There is an involutorial transformation in the group for each double six; the transformation permutes corresponding CONTRIBUTIONS FROM GEOMETRY 325 lines of the complementary sets of six of the double six, and leaves each of the remaining fifteen lines invariant. If the double sixes corresponding to two such transformations have four common lines, the transformations are permutable. If the transformations are not permutable, the corresponding double sixes have six common lines, and the remaining twelve lines form a third double six. Although the geometry of the situation may be perspicuous to those gifted with visual imagination, others find the underlying algebraic identities, among even so impressive a number of group operations as 51840, somewhat easier to see through. But this difference is merely one of ac- quired taste or natural capacity, and there is no arguing about it. However, it may be remembered that some of this scintillating pure geometry was subsequent, not antecedent, to many a dreary page of laborious algebra. The group of the twenty- seven lines alone has a somewhat forbidding literature in the tradition of the late nineteenth and early twentieth centuries which but few longer read, much less appreciate. So long as geometry — of a rather antiquated kind, it may be — can clothe the outcome of intricate calculations in visualizable form, the Solomon’s seal of the nineteenth century will attract its de- votees, and so with other famous classics of the geometric imagination. But in the meantime, the continually advancing front of creative geometry will have moved on to unexplored territory of fresher and perhaps wider interest. The world some- times has sufficient reason to be weary of the past in mathe- matics as in everything else. |
See as well a figure from yesterday's Matrix Geometry post —
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Sunday, January 26, 2025
The Diamond Theorem and the Miracle Octad Generator —
The DeepSeek Version
See http://log24.com/log25/
DeepSeek-250126-Print-option-version-of-DTandMOG.pdf .
|
Conclusion "The Diamond Theorem and the MOG exemplify how finite geometry bridges abstract algebra and combinatorics. Their relationship underscores the universality of symmetry in mathematics, from graphic designs to sporadic groups and error-correcting codes. By studying one, insights into the other — and into structures like the Leech lattice — naturally emerge." — DeepSeek R1, Jan. 26, 2025. |
That AI research report from today was suggested by
a VentureBeat article from yesterday —
For a Google Gemini Deep Research report on the same topic,
see a Log24 post from Tuesday, Jan. 21.
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The DeepSeek Version
The DeepSeek Version
Thursday, January 16, 2025
Faustus Revisited
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Monday, November 25, 2024
A Swan Boat for Wiig
"Then moved o’er the waters by might of the wind
that bark like a bird with breast of foam,
till in season due, on the second day,
the curved prow such course had run
that sailors now could see the land,
sea-cliffs shining, steep high hills,
headlands broad." — Beowulf
Or its prowess . . .
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Tuesday, October 8, 2024
Hopfield Prize: Doing Dallas
For fans of associative memory …
There is also, for a mojo dojo casa house . . .
TX+
"Kercheval, Kesey . . . . Kesey, Kercheval."
And as the "Doing Dallas" musical score —
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Sunday, October 6, 2024
“Den Kopf Benützen” — A Phrase from Marfa
Related material —
This morning's post on witchcraft and reason, and related images —
Also from December 1982 —
Addendum for Art Gawkers . . . and P. T. Barnum —
The above review by Perl includes remarks on
Tricks of the Light: Essays on Art and Spectacle
Zone, 270 pp., $32.00.
NOT Crary and Perl —
Jonathan and Einstein in "Arsenic and Old Lace."
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Friday, September 13, 2024
For Harlan Kane: The Yeats Sequel
From Yeats's sequel to "Sailing to Byzantium,"
titled simply "Byzantium" —
Astraddle on the dolphin's mire and blood,
Spirit after spirit! The smithies break the flood,
The golden smithies of the Emperor!
Marbles of the dancing floor
Break bitter furies of complexity,
Those images that yet
Fresh images beget,
That dolphin-torn, that gong-tormented sea.
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Thursday, June 20, 2024
Donald Sutherland Has Died.
From T. S. Eliot and the Dynamic Imagination
by Sarah Kennedy,
Cambridge University Press, 2018 —
Chapter 7
His Dark Materials
Would you have me
False to my nature? Rather say, I play
The Man I am.
– Shakespeare, Coriolanus, III.ii. [Link added.]
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Thursday, May 2, 2024
Hitchcock Studios
The New York Times today reports the death at 90 of
Peggy Mellon Hitchcock, who arranged for Timothy Leary's
accomodation at the Hitchcock Estate, on April 9, 2024 . . .
Also on April 9 —
A rather different Hitchcock image —
This is from a Log24 search for Hitchcock Cube.
"Before time began . . ." — Optimus Prime.
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Tuesday, March 19, 2024
Belgian Puzzle Art
From the Belgian artist of the March 25 New Yorker cover —
“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 at Zoltan Dienes’s website
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Saturday, March 9, 2024
Annals of Deceptive Fiction —
Dark Materials: Milton, Eliot, Pullman
For Pullman, see previous instances of "wilde abyss" in this journal.
For a less fictional approach to the abyss, see the following.
|
From T. S. Eliot and the Dynamic Imagination
Chapter 7
Would you have me – Shakespeare, Coriolanus, III.ii. [Link added.] . . . .
Eliot describes the creative germ as the The phrase echoes Milton’s Paradise Lost :
Into this wilde Abyss,
Eliot’s creative logic retains an aspect of the divine |
"The phrase echoes Milton's Paradise Lost" —
In describing his abyss, Milton invokes not "psychic material" but
rather the classical view of Nature as composed of the four elements
Water, Earth, Air and Fire.
Note that one source* of the "psychic material" phrase in Eliot's work
gives a rather different picture . . .
"And now I should like to return for a moment to Gottfried Benn
and his unknown, dark psychic material —
we might say, the octopus or angel with which the poet struggles."
* "The Three Voices of Poetry," by T. S. Eliot, The Atlantic, April 1954.
Related entertainment . . .
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Dark Materials: Milton, Eliot, Pullman
Dark Materials: Milton, Eliot, Pullman
Taylor: “The Politics of Recognition”
I found the above essay via the references cited in . . .
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Wednesday, February 14, 2024
Live Poet Society
RHYMES for Bergen Feb. 13-14, 2024
one fun
two crew
three see
four core
five live
six tricks
seven heaven
eight gate
nine line
core line crew
see live heaven
gate fun tricks
This post was suggested by the
"Night of Lunacy" post of May 5, 2013.
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Friday, December 22, 2023
Wiki’d
Lewis Carroll's chess Red Queen, from Through the Looking Glass,
is "often confused with" the playing cards Queen of Hearts,
from Alice in Wonderland —
" The King turned pale, and shut his notebook hastily.
'Consider your verdict,' he said to the jury in a low, trembling voice….
. . . . 'No, no!' said the Queen. 'Sentence first—verdict afterward.' "
— Lewis Carroll, Alice in Wonderland
|
The figure at right in the video of today's previous post,
"In Alice in Wonderland , the Red Queen
— College of Natural Resources commencement address,
Berck's address was titled "The Red Queen." |
Berck's dies natalis — "birth into heaven," in Catholic parlance —
was reportedly August 10, 2018. A Log24 synchronology check
yields a different chess-related figure … Actor/director John Huston:
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Thursday, October 12, 2023
Hot Snakes
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Saturday, August 26, 2023
For the Church of Synchronology
Art Blocks in the previous post —
"… making accessibility and IRL viewership a core component" . . .
From this journal on the above art date — April 6, 2021 —
Tuesday, April 6, 2021
|
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Monday, August 14, 2023
Wednesday, August 9, 2023
Waiting for the Low-Hanging Fruit
How many miles to Babylon?*
Three score miles and ten.
Can I get there by candle-light?**
Yes, and back again.
Mary Gaitskill's latest substack meditation —
"I am thinking of Susan Sontag, writer, philosopher,
political activist and some-time pain in the ass;
she went to Sarajevo during the siege in order to
put on a theatrical production of Waiting for Godot.
She didn’t get paid and none of the actors did either.
They rehearsed in the dark and performed by sparse
candlelight . . . ."
"How many bananas ?"
"Drei . . . or else Vier ."
See also the comedy writers of Elsevier —
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Saturday, July 8, 2023
Blacklist Quote from S10 E20, “Arthur Hudson”
"I am what I am. You made a devil's bargain.
Did you really expect me to stop being the devil?"
Read more at: https://tvshowtranscripts.ourboard.org/
viewtopic.php?f=194&t=64076
See as well yesterday's post CORE and Faustus in this journal.
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Friday, June 23, 2023
A Little Drama
The broken pencil in a Dial illustration of June 20 —
"I could a tale unfold . . ." — Hamlet's father's ghost
"Thus the entire little drama, from crystallized carbon
and felled pine to this humble implement, to this
transparent thing, unfolds in a twinkle."
— Vladimir Nabokov, Transparent Things
"… a cardboard tube, more or less the same length as
the inner core of a toilet roll, but thicker. He frowned,
took the roll out, laid it on the desk and poked up it
with the butt end of a pencil. Something slid out.
It looked like a rolled-up black plastic dustbin liner;
but when he unfolded it, he recognised it as the funny
sheet thing he’d found in the strongroom and briefly
described as an Acme Portable Door, before losing
his nerve and changing it to something less facetious."
— Holt, Tom. The Portable Door . Orbit. Kindle Edition.
According to goodreads.com, the Holt book was
"first published March 6, 2003."
See also this journal on March 6, 2003, in a search for
Michelangelo Geometry.
Punchline of the above little drama —
"Try the other end of the pencil, Liz."
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Thursday, June 22, 2023
Unfolded Drama
"I could a tale unfold . . ." — Hamlet's father's ghost
"Thus the entire little drama, from crystallized carbon
and felled pine to this humble implement, to this
transparent thing, unfolds in a twinkle."
— Vladimir Nabokov, Transparent Things
"… a cardboard tube, more or less the same length as
the inner core of a toilet roll, but thicker. He frowned,
took the roll out, laid it on the desk and poked up it
with the butt end of a pencil. Something slid out.
It looked like a rolled-up black plastic dustbin liner;
but when he unfolded it, he recognised it as the funny
sheet thing he’d found in the strongroom and briefly
described as an Acme Portable Door, before losing
his nerve and changing it to something less facetious."
— Holt, Tom. The Portable Door . Orbit. Kindle Edition.
According to goodreads.com, the Holt book was
"first published March 6, 2003."
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Monday, June 19, 2023
The Original Portable Door
"… a cardboard tube, more or less the same length as
the inner core of a toilet roll, but thicker. He frowned,
took the roll out, laid it on the desk and poked up it
with the butt end of a pencil. Something slid out.
It looked like a rolled-up black plastic dustbin liner;
but when he unfolded it, he recognised it as the funny
sheet thing he’d found in the strongroom and briefly
described as an Acme Portable Door, before losing
his nerve and changing it to something less facetious."
— Holt, Tom. The Portable Door . Orbit. Kindle Edition.
According to goodreads.com, the Holt book was
"first published March 6, 2003."
Compare and contrast the "portable door" as a literary device
with the "tesseract" in A Wrinkle in Time (1962).
See also this journal on March 6, 2003.
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Saturday, June 10, 2023
Green, Orange, Black
The colors surrounding Watson's body in the above
"bandeau" photo suggest a review. A search in this journal
for Green+Orange+Black yields . . .
In the above image, the "hard core of objectivity" is represented
by the green-and-white eightfold cube. The orange and black are,
of course, the Princeton colors.
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Sunday, June 4, 2023
“Design is how it works.” — Steve Jobs
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Sunday, May 28, 2023
Annals of Philosophy: Shadow Hacking
In memory of philosopher Ian Hacking, who
reportedly died on May 10, some Log24 posts
are now tagged "Shadow Hacking."
Related material — Plato's Ghost in this journal, and . . .
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Monday, March 20, 2023
Location, Location, Location: 0047
"The distinct emphasis on
the politics of space
constitutes 0047’s core and identity."
— http://0047.org/home/about-2/
(link on "politics of space" added)
Related note for film fans —
I prefer the less stressful TV series “GLOW,” starring Alison Brie —
“In the bluish light emanating from the TV,
EE looked at him, her eyes veiled.”
— Being There , by Jerzy Kosinski
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Thursday, March 2, 2023
Friday, November 18, 2022
The Crimson Riddle
Wednesday's original New York Times headline reporting a Harvard death —
"Henry Rosovsky, Who Redefined
Harvard to Its Core, Dies at 95"
Yesterday that headline was rewritten —
That revision suggests another . . .
An Old Riddle Made New:
"What's black and white and crimson all over?"
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Tuesday, September 13, 2022
A Helpful Survey of the Literature
Some background for the exercise of 9/11 —
Vera Pless, "More on the uniqueness of the Golay codes,"
Discrete Mathematics 106/107 (1992) 391-398 —
"Several people [1-2,6] have shown that
any set of 212 binary vectors of length 24,
distance ≥ 8, containing 0, must be the
unique (up to equivalence) [24,12,8] Golay code."
[1] P. Delsarte and J.M. Goethals, "Unrestricted codes
with the Golay parameters are unique,"
Discrete Math. 12 (1975) 211-224.
[2] A. Neumeier, private communication, 1990.
[6] S.L. Snover, "The uniqueness of the
Nordstrom-Robinson and the Golay binary codes,"
Ph.D. Thesis, Dept. of Mathematics,
Michigan State Univ., 1973.
Related images —
"Before time began, there was the Cube."
"Remember, remember the fifth of November"
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Friday, September 2, 2022
History of Mathematics
Anne Duncan in 1968 on a 1960 paper by Robert Steinberg —
_______________________________________________________________________________
Related remarks in this journal — Steinberg + Chevalley.
Related illustrations in this journal — 4×4.
Related biographical remarks — Steinberg Deathdate.
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Monday, August 22, 2022
Separatrix/Unitrix
Separatrix:
From "Core Curriculum Vocabulary," Log24, July 5, 2014 . . .
Stephen King, Archimedes, and Daisy Buchanan —
Unitrix:
From the 2022 sequel to "365 Days" and "365 Days: This Day" —
Related literary symbolism —
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Tuesday, June 21, 2022
For the Church of Synchronology*
See also this journal on the above Cambridge U. Press date.
"There are many places one can read about twistors
and the mathematics that underlies them. One that
I can especially recommend is the book Twistor Geometry
and Field Theory, by Ward and Wells."
— Peter Woit, "Not Even Wrong" weblog post, March 6, 2020.
* A fictional entity. See Synchronology in this journal.
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Sunday, June 12, 2022
Piercing the Twelve*
From "When Novelists Become Cubists," by Andre Furlani—
"The architectonics of a narrative," Davenport says,
"are emphasized and given a role to play in dramatic effect
when novelists become Cubists; that is, when they see
the possibilities of making a hieroglyph, a coherent symbol,
an ideogram of the total work. A symbol comes into being
when an artist sees that it is the only way to get all the meaning in."
* See "Starlight Like Intuition" by Delmore Schwartz.
The "Twelve" of the title may be regarded as cube edges.
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Wednesday, May 25, 2022
Cargo Cult
From the Amazon.com description of Colin Cantwell's space novel Corefires —
"Of the cargo, the data Crystals are the most important.
Necessary to life in space, they have to be protected at all costs."
Related merchandise — Disney Holocrons:
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Monday, May 23, 2022
Sunday, May 1, 2022
The Coming
"Edward Bulwer-Lytton (infamous author of the opening line,
'It was a dark and stormy night') was a Victorian-era writer.
In 1870, he published a science fiction novel, The Power of
the Coming Race, which describes an underground race of
superhuman angel-like creatures and their mysterious energy
force, Vril, an 'all-permeating fluid' of limitless power."
— From a source linked-to in the post Vril Chick.
"Credit where credit is due" . . .
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Tuesday, February 8, 2022
Directions Out
On reading about DNA:
"Suddenly it was clear to me
that all the beautiful complexity of life
had simplicity at its core," he says.
"This is the kind of thing mathematicians love."
— Eric Lander in "The 2004 TIME 100 — Our list
of the most influential people in the world today"
The date on the above TIME piece is Monday,
Apr. 26, 2004. Remarks in this journal on that date
are now tagged Directions Out.
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Monday, January 24, 2022
Aesthetics Lesson
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Sunday, January 23, 2022
Apperception for Newton
"So we beat on, boats against the current…"
— The Great Gatsby
Thandie Newton in "Reminiscence" (2021) —
The above Screen Rant article is from August 20, 2021.
From that same date —
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Friday, December 31, 2021
Aesthetics in Academia
Related art — The non-Rubik 3x3x3 cube —
The above structure illustrates the affine space of three dimensions
over the three-element finite (i.e., Galois) field, GF(3). Enthusiasts
of Judith Brown's nihilistic philosophy may note the "radiance" of the
13 axes of symmetry within the "central, structuring" subcube.
I prefer the radiance (in the sense of Aquinas) of the central, structuring
eightfold cube at the center of the affine space of six dimensions over
the two-element field GF(2).
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Thursday, September 23, 2021
The Narrow Window
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Sunday, September 5, 2021
Linguistics
A Letterman introduction for Plato's Academy Awards:
"Cunning, Anna. Anna, Cunning." (Rimshot.)
But seriously . . .
"This work [of Wierzbicka and colleagues] has led to
a set of highly concrete proposals about a hypothesized
irreducible core of all human languages. This universal core
is believed to have a fully ‘language-like’ character in the sense
that it consists of a lexicon of semantic primitives together with
a syntax governing how the primitives can be combined
(Goddard, 1998)." — Wikipedia, Semantic Primes
Goddard C. (1998) — Bad arguments against semantic primitives.
Theoretical Linguistics 24:129-156.
Related fiction . . . Lexicon , by Max Barry (2013). See Barry in this journal.
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Tuesday, August 31, 2021
Summer Knowledge
The title is that of a book of poems by Delmore Schwartz.
|
From "Searching for God in the Next Apartment," Throughout Schwartz's poetry a question of belief is central. He thought we could not live without an interpretation of the whole of life, and that modern social orders were inevitably deficient in satisfying this need. He wrote studies and poetry explicitly concerned with the decline of Christian belief and the impossibility of any belief whatsoever. He read Rimbaud's ''Season in Hell,'' Valery's ''Cimetiere Marin,'' Arnold's ''Dover Beach,'' Hardy's ''Oxen,'' Stevens' ''Sunday Morning'' as poems forged in just such a dilemma. His own preferred poem, ''Starlight Like Intuition Pierced the Twelve,'' continued this argument. |
See also Log24 posts tagged Central Myth, and the following image:
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Thursday, August 19, 2021
A Scalpel for Einstein
(A sequel to this morning's post A Subtle Knife for Sean.)
Exhibit A —
Einstein in The Saturday Review, 1949 —
"In any case it was quite sufficient for me
if I could peg proofs upon propositions
the validity of which did not seem to me to be dubious.
For example, I remember that an uncle told me
the Pythagorean theorem before the holy geometry booklet
had come into my hands. After much effort I succeeded
in 'proving' this theorem on the basis of the similarity
of triangles; in doing so it seemed to me 'evident' that
the relations of the sides of the right-angled triangles
would have to be completely determined by one of the
acute angles. Only something which did not in similar fashion
seem to be 'evident' appeared to me to be in need of any proof
at all. Also, the objects with which geometry deals seemed to
be of no different type than the objects of sensory perception,
'which can be seen and touched.' This primitive idea, which
probably also lies at the bottom of the well-known Kantian
problematic concerning the possibility of 'synthetic judgments
a priori' rests obviously upon the fact that the relation of
geometrical concepts to objects of direct experience
(rigid rod, finite interval, etc.) was unconsciously present."
Exhibit B —
Strogatz in The New Yorker, 2015 —
"Einstein, unfortunately, left no … record of his childhood proof.
In his Saturday Review essay, he described it in general terms,
mentioning only that it relied on 'the similarity of triangles.'
The consensus among Einstein’s biographers is that he probably
discovered, on his own, a standard textbook proof in which similar
triangles (meaning triangles that are like photographic reductions
or enlargements of one another) do indeed play a starring role.
Walter Isaacson, Jeremy Bernstein, and Banesh Hoffman all come
to this deflating conclusion, and each of them describes the steps
that Einstein would have followed as he unwittingly reinvented
a well-known proof."
Exhibit C —
Schroeder presents an elegant and memorable proof. He attributes
the proof to Einstein, citing purely hearsay evidence in a footnote.
The only other evidence for Einstein's connection with the proof
is his 1949 Saturday Review remarks. If Einstein did come up with
the proof at age 11 and discuss it with others later, as Schroeder
claims, it seems he might have felt a certain pride and been more
specific in 1949, instead of merely mentioning the theorem in passing
before he discussed Kantian philosophy relating concepts to objects.
Strogatz says that . . .
"What we’re seeing here is a quintessential use of
a symmetry argument… scaling….
Throughout his career, Einstein would continue to
deploy symmetry arguments like a scalpel, getting to
the hidden heart of things."
Connoisseurs of bullshit may prefer a faux-Chinese approach to
"the hidden heart of things." See Log24 on August 16, 2021 —
http://m759.net/wordpress/?p=96023 —
In a Nutshell: The Core of Everything .
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Tuesday, July 20, 2021
Zen in Cuernavaca
|
https://terebess.hu/zen/mesterek/dtsuzuki.html —
From Larry A. Fader, “D. T. Suzuki's Contribution to the West,” In contrast to Jung's approach is the humanistic psychology of Erich Fromm. Fromm was also influenced by Suzuki, but in different ways. Whereas Jung dealt with Zen Buddhism as an aspect of his psychological thought, Suzuki's influence touches closer to the core of Fromm's thought. Fromm organized an influential workshop on Zen Buddhism and psychoanalysis in Cuernavaca, Mexico, and incorporated many concepts which resemble Suzuki's interpretation of Zen into his psychoanalytic writings. The Cuernavaca workshop of 1957, held at Fromm's Mexico home, brought together eminent psychologists expressly for the purpose of exploring Zen Buddhism and psychoanalysis. As such, it marks an important point of contact between thinkers in the field of psychology and D. T. Suzuki's interpretation of Zen. Suzuki addressed the gathering, and his speeches were later published as “Lectures in Zen Buddhism” together with Fromm's address entitled “Psychoanalysis and Zen Buddhism” and that of Richard DeMartino entitled “The Human Situation and Zen Buddhism,” in a volume which Fromm edited and called Zen Buddhism and Psychoanalysis. Fromm organized the Mexico meeting and issued the invitations to its participants as a result of his feeling that psychotherapists—and in particular, psychoanalysts—were at that time “not just interested, but deeply concerned” with Zen. This “concern,” Fromm believed, was a new and potentially important development in the attitude of psychologists. His own address to the workshop, reformulated, as he says, because of “the stimulation of the conference,” includes language and ideas that may be traced to Dr. Suzuki's Cuernavaca lectures. |
See as well Fromm and Frère Jacques, Cuernavaca in this journal.
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Saturday, April 24, 2021
23:13
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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.
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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 —
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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 —
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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.
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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.
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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.
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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.
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Monday, September 7, 2020
Remedial Reading
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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 —
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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 —
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Monday, April 27, 2020
The Cracked Nut
“At that instant he saw, in one blaze of light, an image of unutterable
conviction, the reason why the artist works and lives and has his being –
the reward he seeks –the only reward he really cares about, without which
there is nothing. It is to snare the spirits of mankind in nets of magic,
to make his life prevail through his creation, to wreak the vision of his life,
the rude and painful substance of his own experience, into the congruence
of blazing and enchanted images that are themselves the core of life, the
essential pattern whence all other things proceed, the kernel of eternity.”
— Thomas Wolfe, Of Time and the River
“… the stabiliser of an octad preserves the affine space structure on its
complement, and (from the construction) induces AGL(4,2) on it.
(It induces A8 on the octad, the kernel of this action being the translation
group of the affine space.)”
— Peter J. Cameron,
The Geometry of the Mathieu Groups (pdf)
“The yarns of seamen have a direct simplicity, the whole meaning
of which lies within the shell of a cracked nut. But Marlow was not
typical (if his propensity to spin yarns be excepted), and to him the
meaning of an episode was not inside like a kernel but outside…."
— Joseph Conrad in Heart of Darkness
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Sunday, April 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.
[addtoany]
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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.
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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.
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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.
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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—
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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 …
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Saturday, June 15, 2019
Actionable Daydream
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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 —
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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 . . ."
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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
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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.
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Tuesday, March 5, 2019
A Block Design 3-(16,4,1) as a Steiner Quadruple System:
A Midrash for Wikipedia
Midrash —
Related material —
________________________________________________________________________________
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Tuesday, February 26, 2019
Wednesday, October 17, 2018
Aesthetics
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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?
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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.
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Thursday, March 1, 2018
The Movement of Analogy: Hume vs. Paz
Hume, from posts tagged "four-set" in this journal —
"The mind is a kind of theatre, where several perceptions
successively make their appearance; pass, repass, glide away,
and mingle in an infinite variety of postures and situations.
There is properly no simplicity in it at one time, nor identity
in different, whatever natural propension we may have
to imagine that simplicity and identity."
Paz, from a search for Paz + Identity in this journal —
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"At the point of convergence by Octavio Paz, translated by Helen Lane
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Wednesday, February 7, 2018
Conceptual Minimalism
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"At the point of convergence by Octavio Paz, translated by Helen Lane
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See also AS IS.
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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.
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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:
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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 —
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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 —
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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 —
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" … listen: there's a hell
of a good universe next door; let's go"
— e. e. cummings
Some literary background —
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"At the point of convergence by Octavio Paz, translated by Helen Lane
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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 —
.
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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.
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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."
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