"Alpert, an editor for Scientific American , laces his high-IQ
doomsday thriller with clearly explicated and hauntingly beautiful
scientific theories…."
Booklist on The Omega Theory :
"Alpert’s follow-up to his acclaimed first novel, Final Theory (2008),
continues the adventures of science historian David Swift."
See as well this journal on June 1, 2008.
. . . Pace Wallace Stevens.
"The history of the universe can thus be seen as
an endless chain of changes, but Aquinas argued
that there must be some transcendent entity that
initiated the chain, something that is itself
unchanging and that already possesses all of the
properties that worldly objects can come to possess.
He also claimed that this entity must be eternal;
because it is the root of all causes, nothing else
could’ve caused it. And unlike all worldly objects,
the transcendent entity is necessary—it must exist."
— Mark Alpert in Scientific American, 12/23/2019
Hat tip to University Diaries for today's link to…
O Lost (Thomas Wolfe in The Paris Review , Winter 1999).
See as well —
Later in the film… "He's not Einstein… You're Einstein."
Related material at the University of Iowa —
See as well this journal on the above Daily Iowan date.
… Continued from August 26 —
Heidegger, "Hölderlin and the Essence of Poetry,"
translated by Douglas Scott, in Existence and Being ,
Regnery, 1949, pp. 291-316—
See as well Readings for St. Patrick's Day, March 17, 2005.
"December 22, the birth anniversary of India’s famed mathematician
Srinivasa Ramanujan, is celebrated as National Mathematics Day."
— Indian Express yesterday
"Orbits and stabilizers are closely related." — Wikipedia
Symmetries by Plato and R. T. Curtis —
In the above, 322,560 is the order
of the octad stabilizer group .
Exercise: Use the Guitart 7-cycles below to relate the 56 triples
in an 8-set (such as the eightfold cube) to the 56 triangles in
a well-known Klein-quartic hyperbolic-plane tiling. Then use
the correspondence of the triples with the 56 spreads of PG(3,2)
to construct M24.
Click image below to download a Guitart PowerPoint presentation.
See as well earlier posts also tagged Triangles, Spreads, Mathieu.
From some autobiographical remarks by Simon During,
who was featured in the previous post —
For more on the phrase “god professor,” see
“The Ownership of Knowledge in Higher Education
in Australia 1939-1996,” Hannah Forsyth, Ph.D. thesis,
University of Sydney, 2012
Simon During at Utrecht earlier this year —
For the Church of Synchronology, other April 11, 2019, remarks —
See in particular the phrase “Eritis sicut dei ” in the Log24 remarks.
The previous post's link to posts tagged March 8, 2018,
suggests a look at recent thoughts by a Melbourne academic:
Manifesto in Green and Red
The van Dam cited by Polster should not be confused
with the fictional Vandamm of "North by Northwest."
See Pursued by a Biplane (Log24, May 23, 2017).
* For the title, see posts tagged March 8, 2018.
Click to enlarge.
New Yorker art critic Peter Schjeldahl
as quoted today by Margaret Soltan —
Unlike computers. See ReactiveX and Observable.
|
Frindle, Helen. The Sentient Shield . “But why, I am not aware or can’t remember anything; previous lives, contracts, whatever.” “Perhaps not, but the block has been removed. As I understand blocks are placed because the person would not be able to cope with the information of their past life, or lives, or experiences that may have been so terrible. It seems however that what is happening is that you are now needed to wake up and remember and that is why the block has been removed.” “Wake up. I don’t understand. I am sorry, I keep repeating myself but I don’t understand!” Maddy shook her herself and went quiet, she thought perhaps she needed to listen to Pam. “At this present time no, but it has been removed and you will begin to become, let’s say, more aware and remember.” “Remember what, here I go again, it seems like a riddle to me and I am beginning to feel very odd, in fact even a little frightened. It seems as if we are venturing into things that are rather supernatural.” |
Amen. See also The Crosswicks Curse.
From The New York Times on Dec. 11 —
See also some other posts in this journal now tagged "Design Notes Dec. 11."
"Thus the nature of reality comes into question…."
— Frindle, Helen. The Sentient Shield , author's preface.
Austin Macauley Publishers Ltd. Kindle edition.
Published on December 11, 2018:
————————————————————————————————————–
This journal on December 11, 2018 —
* See as well other references to Harlan Kane in this journal.
The above image is from
"A Four-Color Theorem:
Function Decomposition Over a Finite Field,"
http://finitegeometry.org/sc/gen/mapsys.html.
These partitions of an 8-set into four 2-sets
occur also in Wednesday night's post
Miracle Octad Generator Structure.
This post was suggested by a Daily News
story from August 8, 2011, and by a Log24
post from that same date, "Organizing the
Mine Workers" —
(Adapted from Encyclopaedia Britannica,
Eleventh Edition (1911), Crystallography .)
(Adapted from Eightfold Geometry, a note of April 28, 2010.
See also the recent post Geometry of 6 and 8.)
The architecture of the recent post
Geometry of 6 and 8 is in part
a reference to the Klein quadric.
For the above title, see posts tagged Eternal Color.
From this evening's online New York Times —
Related imaterial —
A scene from the film of the above book —
|
https://www.laphamsquarterly.org/memory/all
timestamp=1574874536
"In This Is All:
By Jim Holt |
Related material: This journal on the above date — 11/27/2019.
A search for "deep space" in this journal yields
the following meditation:
|
Alfred Bester, Tiger! Tiger!:
|
In Memoriam:
See also, from posts now tagged Abyssus, a quote from Simone Weil —
"Adam and Eve sought for divinity in vital energy —
in a tree, a fruit. But it is prepared for us on some
dead wood, geometrically squared, upon which
hangs a corpse."
Just as
the finite space PG(3,2) is
the geometry of the 6-set, so is
the finite space PG(5,2)
the geometry of the 8-set.*
Selah.
* Consider, for the 6-set, the 32
(16, modulo complementation)
0-, 2-, 4-, and 6-subsets,
and, for the 8-set, the 128
(64, modulo complementation)
0-, 2-, 4-, 6-, and 8-subsets.
Update of 11:02 AM ET the same day:
See also Eightfold Geometry, a note from 2010.
* “Canonicity” is a reference to the previous post.
See as well Tetrahedron vs. Square and Algebra for Schoolgirls.
Review:
Note the "Milestones" date of receipt — 25 January 2012.
This journal on the eve of the above "Milestones" date —
See as well some notes from the date of the above death:
Related material: Endgame (November 7, 1986).
David Corfield on "Aesthetic Theory and Artistic Practice" —
"… British naturalism of the nineteenth century is seen to be
based on a theory of art whose origin lies in eighteenth century
philosophy. Collingwood believes this to be a false theory,
as first made clear artistically by Cezanne. Note also that
Collingwood should feel the need to depart from abstract
argument to include the case study.
Exercise: with minimal changes make the above true for
the philosophy of mathematics. Once done, we see how
we should expect to find a philosophy of mathematics
in each mathematician, even if it only functions implicitly.
See Philosophy as Normative or Descriptive.
Last revised on July 12, 2010 at 11:02:44."
See as well some philosophical remarks by the late
William J. Richardson, S.J., quoted here on July 12, 2010.
In memory of William J. Richardson, S.J., who reportedly
died at 97 on 10 December 2016…
This journal on that date —
"What the piece of art is about is the gray space in the middle."
— David Bowie, as quoted in the above Crimson piece.
Bowie's "gray space" is the space between the art and the beholder.
I prefer the gray space in the following figure —
Context: The Trinity Stone (Log24, June 4, 2018).
See as well a search for Gray Space in this journal.
Related material: The Schwartz Omega .
“Looking carefully at Golay’s code
is like staring into the sun.”
The previous post quoted some dialogue from Victor Hugo's
novel about the French Revolution, Ninety-Three.
This suggests a look at the following non-fiction book:
Compare and contrast with the novel The Eight , by Katherine Neville,
about chess and the French Revolution.
Neville's birthday, April 4, plays a major role in her novel. The dies natalis
(in the Roman Catholic sense) of the above Birth of the Chess Queen
author, on the other hand, was reportedly November 20, 2019.
Following a link in this journal from November 20 leads to remarks
that might interest the subjects of an upcoming film, "The Two Popes."
From this journal on the above date — April 13, 2014 (Gray Space) —
Review of Seeing Gray , a book by pastor Adam Hamilton
of the United Methodist Church of the Resurrection
in Leawood, Kansas, a suburb of Kansas City—
“Adam Hamilton invites us to soulful gray space
between polarities, glorious gray space that is holy,
mysterious, complex, and true. Let us find within
our spirits the courage and humility to live and learn
in this faithful space, to see gray, to discern a more
excellent way.”
—Review by United Methodist Bishop Hope Morgan Ward
The above flashback was suggested by CBS Sunday Morning today —
See also Romanesque in this journal.
Adam Gopnik in The New Yorker today, quoting
the late Clive James's description of …
" … an adaptation of 'War and Peace': 'Dead ground is
the territory you can’t judge the extent of until you approach it:
seen from a distance, it is unseen. Almost uniquely amongst
imagined countries, Tolstoy’s psychological landscape is
without dead ground— the entire vista of human experience is
lit up with an equal, shadowless intensity, so that separateness
and clarity continue even to the horizon.' "
A search result gives what is apparently the original date for
a story that Ars Technica republished yesterday for Black Friday
(see previous post) —
Another story, also from November 25, 2013 —
* See Stephanies in this journal.
See also Best Picture and, more generally, The Accountant.
Shown below are Aitchison's March 2018 M24 permutations
and their relabeling, with digits only, for MAGMA checking.
In the versions below, r g b stand for red, green, blue.
Infinity has been replaced by 7 (because a digit was needed,
and the position of the infinity symbol in the Aitchison cube
was suited to the digit 7).
(r7,r1)(b2,g4)(r3,r5)(r6,g0)
mu0= (g7,g2)(r4,b1)(g6,g3)(g5,b0)
(b7,b4)(g1,r2)(b5,b6)(b3,r0)
mu1 = (r7,r2,)(b3,g5)(r4,r6)(r0,g1)
(g7,g3)(r5,b2)(g0,g4)(g6,b1)
(b7,b5)(g2,r3)(b6,b0)(b4,r1)
mu2 = (r7,r3)(b4,g6)(r5,r0)(r1,g2)
(g7,g4)(r6,b3)(g1,g5)(g0,b2)
(b7,b6)(g3,r4)(b0,b1)(b5,r2)
mu3 = (r7,r4)(b5,g0)(r6,r1)(r2,g3)
(g7,g5)(r0,b4)(g2,g6)(g1,b3)
(b7,b0)(g4,r5)(b1,b2)(b6,r3)
mu4 = (r7,r5)(b6,g1)(r0,r2)(r3,g4)
(g7,g6)(r1,b5)(g3,g0)(g2,b4)
(b7,b1)(g5,r6)(b2,b3)(b0,r4)
mu5 = (r7,r6)(b0,g2)(r1,r3)(r4,g5)
(g7,g0)(r2,b6)(g4,g1)(g3,b5)
(b7,b2)(g6,r0)(b3,b4)(b1,r5)
mu6 = (r7,r0)(b1,g3)(r2,r4)(r5,g6)
(g7,g1)(r3,b0)(g5,g2)(g4,b6)
(b7,b3)(g0,r1)(b4,b5)(b2,r6)
Table 1 —
0 1 2 3 4 5 6 7
r 1 2 3 4 5 6 7 8
g 9 10 11 12 13 14 15 16
b 17 18 19 20 21 22 23 24
The wReplace program was used with Table 1 above
to rewrite mu0-mu6 for MAGMA.
The resulting code for MAGMA —
|
G := sub< Sym(24) |
(8,3)(20,14)(5,7)(1,10)
(8,4)(21,15)(6,1)(2,11)
(8,5)(22,9)(7,2)(3,12)
(8,6)(23,10)(1,3)(4,13)
(8,7)(17,11)(2,4)(5,14)
(8,1)(18,12)(3,5)(6,15)
G; |
The Aitchison generators passed the MAGMA test.
(A title for Harlan Kane.)
Cartoon caption from The New Yorker issue dated Dec. 2, 2019 —
“Someday I’ll buy a little place in the country
and take my finger off the Zeitgeist.”
This (along with the previous post) suggests a Log24 search for Zeitgeist.
That search concludes, appropriately for today, with a meditation
on giving thanks.
For the circular rectangle, see today's earlier post "Enter Jonathan Miller…."
A recent view of the above address —
The late Jonathan Miller on the existence of the soul:
"The idea of a disembodied person makes no sense
at all, any more than the idea of a circular rectangle
makes sense."
Yesterday's post on a recent sci-fi film suggests a look at LA news . . .
|
From the LA Times Monday morning — “He was working at the Children’s Television Workshop, as the treasurer or something, and I felt that wasn’t an important enough job for him,” Fuchs said. “At that time, we were doing a lot of acquisitions so he was buying music and concerts from around the world. I once asked him how he liked it, and Frank said: ‘I don’t know. There are no answers in this business.’” Biondi is credited with helping establish the successful model of a premium subscription channel…. |
As opposed to an unsuccessful model —
See also "High Life" (from a post of April 1 this year) —
Earlier posts now tagged Coup de Dés suggest a current film review:
Saturday evening's post Diamond Globe suggests a review of …
Iain Aitchison on symmetric generation of M24 —
* A Greek version for the late John SImon:
«Ἀνερρίφθω κύβος».
Critic John Simon reportedly died at 94 on Sunday in Valhalla, N.Y. —
A search for Simon in this journal yields …
|
Wednesday March 10, 2004 — m759 @ 4:07 AM “Language was no more than a collection of meaningless conventional signs, and life could absurdly end at any moment. He [Mallarmé] became aware, in Millan’s* words, ‘of the extremely fine line
separating absence and presence, being and nothingness, life and death, which later … he could place at the very centre of his work and make the cornerstone of his personal philosophy and his mature poetics.’ “ — John Simon, "Squaring the Circle" * A Throw of the Dice: The Life of Stéphane Mallarmé , by Gordon Millan |
See also Cornerstone.
Peter Parker : How could you do all of this?
Quentin Beck : You'll see, Peter. People… need to believe.
From Sunday morning, a "green vault" hyperbolic paraboloid —
"A characteristic property of hyperbolic geometry
is that the angles of a triangle add to less
than a straight angle (half circle)." — Wikipedia
A related image —
From "Back to the Saddle," a post of Nov. 23, 2010 —
"A characteristic property of hyperbolic geometry
is that the angles of a triangle add to less
than a straight angle (half circle)." — Wikipedia
See as well . . .
An image from All Souls' Day 2010 —
This is from earlier posts tagged Permutahedron.
See also
Wallace Stevens:
A World of Transforming Shapes.
From that book (click to enlarge) —
"Before time began, there was the Cube."
— Optimus Prime.
Also from earlier posts tagged Permutahedron —
For Harlan Kane —
“… We found,
If we found the central evil, the central good….
… we and the diamond globe at last were one.”
— "Asides on the Oboe," by Wallace Stevens
This post was suggested by a death on the night of
Friday, November 22 — St. Cecilia's Day.
For the oboe connection, see an obituary.
In memory of Gahan Wilson, "too cool for school" —
Porsche.com on Ferdinand Alexander Porsche, who reportedly
died at 76 in Salzburg on 5 April 2012 —
"The credo of his design work was:
'Design must be functional and functionality has to
be translated visually into aesthetics, without gags
that have to be explained first.'
F.A. Porsche:
'A coherently designed product requires no adornment;
it should be enhanced by its form alone.'
The design’s appearance should be readily comprehensible
and not detract from the product and its function.
His conviction was: 'Good design should be honest.' "
See also last night's 11:32 PM post, and posts tagged Structural Logic.
This flashback was suggested by today's essay
"The Lamentation of Doctor Faustus," by Andrew Marzoni.
Representing Schoolgirl Space
From a book reviewed in the April 1923
Bulletin of the American Mathematical Society —
From a later book —
"Her wall is filled with pictures" — Chuck Berry
For the late Walter J. Minton, publisher at G. P. Putnam's Sons …
"Walter graduated from the Lawrenceville School in New Jersey…."
— New York Times obituary, Wednesday, Nov. 20, 2019
See that school in the post Bloomsday Trinity of June 22, 2016.
RED
_____________________________________________________________________________
GRAY
______________________
Arya on Rothko
Another game featured in the above film —
“In Wolfenstein 3D , the player assumes the role of an American
soldier of Polish descent… attempting to escape from the Nazi
stronghold of Castle Wolfenstein.” — Wikipedia
… See also this journal’s Wolfenstein.
From Harvest Moon Day, 2019 —
From yesterday —
From St. Bridget's Day, 2012 —
See also Hermann Weyl and T. S. Eliot on time.
(As opposed to the new Ford Mustang Mach-E)
Not to be confused with …
Impenetrability vs. Interpenetration
The previous post discussed impenetrability .
To give the opposing concept of interpenetration
a fair hearing, see . . .
More generally, see a search for interpenetration in this journal.
(And for Mustang Sally)
|
'When I use a word,' Humpty Dumpty said, in rather a scornful tone, 'it means just what I choose it to mean — neither more nor less.' 'The question is,' said Alice, 'whether you can make words mean so many different things.' 'The question is,' said Humpty Dumpty, 'which is to be master — that's all.' Alice was too much puzzled to say anything; so after a minute Humpty Dumpty began again. 'They've a temper, some of them — particularly verbs: they're the proudest — adjectives you can do anything with, but not verbs — however, I can manage the whole lot of them! Impenetrability! That's what I say!' 'Would you tell me please,' said Alice, 'what that means?' 'Now you talk like a reasonable child,' said Humpty Dumpty, looking very much pleased. 'I meant by "impenetrability" that we've had enough of that subject, and it would be just as well if you'd mention what you mean to do next, as I suppose you don't mean to stop here all the rest of your life.' 'That's a great deal to make one word mean,' Alice said in a thoughtful tone. 'When I make a word do a lot of work like that,' said Humpty Dumpty, 'I always pay it extra.' |
From a Log24 search for Deep Beauty —
From a related search —
For the Church of Synchronology —
An image from this journal on the above Dick date, Feb. 9, 2011 —
The German mathematician Wolf Barth in the above post is not the
same person as the Swiss artist Wolf Barth in today's previous post.
An untitled, undated, picture by the latter —
Compare and contrast with an "elements" picture of my own —
— and with . . .
“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
"A great many other properties of E-operators
have been found, which I have not space
to examine in detail."
— Sir Arthur Eddington, New Pathways in Science ,
Cambridge University Press, 1935, page 271.
The following 4×4 space, from a post of Aug. 30, 2015,
may help:
The next time she visits an observatory, Emma Stone
may like to do a little dance to …
Oh, the red leaf looks to the hard gray stone
To each other, they know what they mean
— Suzanne Vega, “Songs in Red and Gray“
Easy E
Not So Easy: E-Operators
"A great many other properties of E-operators
have been found, which I have not space
to examine in detail."
— Sir Arthur Eddington, New Pathways in Science ,
Cambridge University Press, 1935, page 271.
(This book also presents Eddington's unfortunate
speculations on the fine-structure constant.)
A sequel to yesterday morning's Lit for Brats —
From a search in this journal for Salinger —
“… the wind was noisy the way it is in spooky movies
on the night the old slob with the will gets murdered.”
— From the opening sentence of the first Holden Caulfield
story, published in the Collier’s of December 22, 1945
See as well the previous post.
Rules for a game codesigned by Ellie Black, the cartoonist
of yesterday's post Cutting-Edge Prize —
… Continued from other posts so tagged.
"Was ist Raum, wie können wir ihn
erfassen und gestalten?"
Another approach to changing the game —
See also a search here for a phrase related to
last night's Country Music Association awards
speech by Reba McEntire — "Rule the World."
From November 13, 2005 —
Detail from a Log24 post of September 23, 2019 —
Cartoon by Ellie Black in The New Yorker , uploaded there on the above date.
See the title phrase, by Delmore Schwartz, in this journal.
See also . . .
|
From Daniel Rockmore's CV — BOOKS, FILMS, EXHIBITS . . . . Concinnitas , a fine art print project with Parasol Press, Yale Art Gallery, and Bernard Jacobson Galleries. Openings at AnneMarie Verna Gallery (Zurich, SZ, Dec. 2014), Elizabeth Leach Gallery (Portland, OR, Jan. 2015), Greg Kucera Gallery (Seattle, WA, Jan. 2015), Yale Art Gallery (New Haven, CT, Jan. 2015). . . . . |
. . . and Concinnitas in this journal … as well as — related to a formula
from the Concinnitas project — "Thirteen??" by David Mumford.
|
Friday, March 10, 2017
The Transformers
|
The misleading image at right above is from the cover of
an edition of Charles Williams's classic 1931 novel
Many Dimensions published in 1993 by Wm. B. Eerdmans.
Compare and constrast —
Cover of a book by Douglas Hofstadter
The trailer pictured above is from the 2016 film Blood Father .
See as well the blood father of Wonderland's Alice:
A Lexicon for Housman — See the posts of June 21, 2013.
From A.E. Housman's 1892 lecture in the previous post —
"In the day when the strong men shall bow themselves,
and desire shall fail…."
Today's readers may be less familiar than was Housman's 1892
audience with the source of those phrases —
|
"Nor again will I pretend that, as Bacon asserts, `the pleasure and delight of knowledge and learning far surpasseth all other in nature'. This is too much the language of a salesman crying his own wares. The pleasures of the intellect are notoriously less vivid than either the pleasures of sense or the pleasures of the affections; and therefore, especially in the season of youth, the pursuit of knowledge is likely enough to be neglected and lightly esteemed in comparison with other pursuits offering much stronger immediate attractions. But the pleasure of learning and knowing, though not the keenest, is yet the least perishable of pleasures; the least subject to external things, and the play of chance, and the wear of time. And as a prudent man puts money by to serve as a provision for the material wants of his old age, so too he needs to lay up against the end of his days provision for the intellect. As the years go by, comparative values are found to alter: Time, says Sophocles, takes many things which once were pleasures and brings them nearer to pain. In the day when the strong men shall bow themselves, and desire shall fail, it will be a matter of yet more concern than now, whether one can say `my mind to me a kingdom is'; and whether the windows of the soul look out upon a broad and delightful landscape, or face nothing but a brick wall."
– A.E. Housman, Inaugural Lecture as Professor of Latin,
http://spenceralley.blogspot.com/2016/01/ |
A geometric diagram by the late Andrew Jobbings (1951-2019) —
From a book review quoted here on the date of Jobbings's death —
"Dodge is eventually brought back to life, or a kind of virtual afterlife,
in the 'Bitworld' where he exists as ones and zeros. Initially inchoate,
Dodge’s mind evolves, along with the digital environment he creates
around him, a kind of information-age Genesis story that Stephenson
describes evocatively."
This journal on the last full day of Matthiessen's life —
The terms glitch and cross-carrier in the previous post
suggest a review —
|
|
For some backstory, see Glitch, Gerard Manley Hopkins, Inscape —
particularly the post A Balliol Star.
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