1979 —
2022 —
Wednesday, November 2, 2022
Tuesday, November 1, 2022
Grimes Rhymes
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Disney Overtones
From other Log24 posts tagged "The Phantom Date" —
“… her mouth is red and large, with Disney overtones. But it is her eyes,
a pale green of surprising intensity, that hold me.”
— Violet Henderson in Vogue , 30 August 2017
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From “Goethe on All Souls’ Day”
The above title is that of a Log24 post on St. Cecilia's Day in 2017
that quoted some earlier All Souls' Day remarks from Berlin.
From that post —
Exercise: Explain why the lead article in the November issue of
Notices of the American Mathematical Society misquotes Weyl
and gives the misleading impression that the example above,
the eightfold cube , might be part of the mathematical pursuit
known as geometric group theory .
Background: Earlier instances here of the phrase "geometric group theory."
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Monday, October 31, 2022
Folklore vs. Mathematics
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Sunday, October 30, 2022
Rethinking October 18th
The New York Times today reported a death on October 18th,
the Feast of St. Luke.
See also Luke in this journal. Some will prefer Cool Hand Luke to
the alleged gospel author.
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Saturday, October 29, 2022
Quarterly
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Boolean Halloween
From Log24 posts tagged Boole vs. Galois —
Kauffman‘s fixation on the work of Spencer-Brown is perhaps in part
due to Kauffman’s familiarity with Boolean algebra and his ignorance of
Galois geometry. See other posts now tagged Boole vs. Galois.
See also “A Four-Color Epic” (April 16, 2020).
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Friday, October 28, 2022
“If there’s a rock ’n’ roll heaven…”
See also "hell of a band" in this journal.
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The Lexeme “Deploy”
From an Oct. 26 elegy in the form of a book review …
From a search in this journal for "deploy" —
Related art —
As for "Miracles and Visionaries," I prefer the literature associated
with the 1974 Miracle Octad Generator of R. T. Curtis.
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Thursday, October 27, 2022
The Zombie Doctrine
A reference to neoliberalism in today's news suggests a look at
a British journalist's remarks from April 2016 . . .
"Like communism, neoliberalism is
the God that failed. But the zombie doctrine
staggers on . . . ."
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Wednesday, October 26, 2022
The Big Rock
Big Rock
"I'm going to hit this problem
with a big rock."
– Mathematical saying, quoted here
on St. Peter's Day 2008
"I see a red door and I want it painted black" — The Rolling Stones
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The Hunt for Galois October
"… Évariste was born on October 25, 1811."
— Eric Temple Bell, Men of Mathematics
Related material —
But seriously . . .
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Tuesday, October 25, 2022
Monday, October 24, 2022
Turning Eight: Double Twist
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Sunday, October 23, 2022
Mathematical Intelligencer News
For Pekonen in this journal, see
From the Finland Station (25 April 2022).
See as well an obituary from Finland.
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Saddle Design: The Little Big Horn
Related material —
CLIPPED FROM The Californian , Salinas, California,
28 July 2001, Saturday • Page 25 —
The above 2001 article on Cruz Saddlery in Salinas is about the family
of "Sacheen Littlefeather," whose real name was reportedly Maria Louise Cruz.
For more about Maria/Sacheen, see yesterday's San Francisco Chronicle :
"Sacheen Littlefeather was a Native American icon.
Her sisters say she was an ethnic fraud."
From that article —
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Saturday, October 22, 2022
The Concrete of Destiny
Also on October 3rd . . . The Concrete of Destiny .
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An Artist’s Phrase: “Form from Morf” — Josefine Lyche
See also . . .
Illustration . . .
Metadata —
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Friday, October 21, 2022
Dimensional Positioning*
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The Fort/Da Game
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Design Award
Continuing the "Design Awards" series of posts . . .
See as well, from a search in this journal for Caprica . . .
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Thursday, October 20, 2022
Déjà Vu All Over Again
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Wednesday, October 19, 2022
Key Seeks Keyhole
Meanwhile, in this journal on the above date of death —
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Tuesday, October 18, 2022
Arco
The above image of an 18 Sept. post commemorates a Sept. 18 death.
Related material: Kiss of the Spider Woman and Dramarama.
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Square Ice
See as well remarks here from 23 Dec. 2014
on the Greek word "stoicheia."
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“I’m In with the In Crowd” …
… "and moss grows fat on a rolling stone."
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Monday, October 17, 2022
A Sinuous Scholium
The previous post suggests A Scholium for St. Bridget . . .
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Sunday, October 16, 2022
Models for Accelerated Learning
The author of the above Math Academy story is one Jay Mathews:
As a model for accelerated learning, I prefer Kate Demianova.
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The Demianova Epiphany
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Images for Siri
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For Broomsday: Turning Eight
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Saturday, October 15, 2022
Concept Art
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A Box of Nothing . . .
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Friday, October 14, 2022
Recreational Crystallography
"Boron atoms and metal atoms can form a configuration . . . ."
See as well other posts now tagged Death Valley Days.
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The Harlan Kane Story
See as well "Sunset Boulevard" in this journal.
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The Old Hollywood Runaround
Fake News headline from the previous post —
"Treasure Seeker Trapped in Burial Vault"
Illustration —
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Thursday, October 13, 2022
Triangle Entertainment
A link in memory of a Princeton-educated mathematics professor who
reportedly died on June 22, 2022 . . . Some non-Princeton triangles.
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The Watson Instagram
A routine check for the accuracy of Watson's quotation yields the source
of Didion's remarks — a 1975 UC Riverside commencement address.
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Prickly Paradigm Press
A search for background on the previous post's Eliot Weinberger yields,
from Berlin . . .
"In 2000 he was the first US writer to be honoured with
the Order of the Aztec Eagle from the Mexican government."
— "2000 zeichnete ihn die mexikanische Regierung als ersten
US-amerikanischen Autor mit dem Order of the Aztec Eagle aus."
The Aztec Eagle with a serpent in its beak, landing on a prickly pear,
is pictured on the flag of Mexico.
See also Weinberger's work at Prickly Paradigm Press.
Related material: Other Log24 posts tagged Prickly.
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Wednesday, October 12, 2022
Kaleidoscopic Structuralism…
"Think about anything often enough, from enough angles,
and it’s bound to splinter and refract. Our minds are like
kaleidoscopes, packed with mirrors we twist to see the
world anew. Sometimes we’re twisting consciously,
sometimes unconsciously. But no matter what, we end up
seeing patterns that are more a product of the tool in hand
than of the world on its other end."
— Henry M. Cowles in The Los Angeles Review of Books ,
October 11, 2022
Cowles on the book under review —
"… Patrick House’s Nineteen Ways of Looking at Consciousness ,
a new book on neuroscience and its limits. Lest readers jump to
the wrong conclusion: The referent in House’s title, though also
poetic, is not Stevens but rather Nineteen Ways of Looking at
Wang Wei , an anthology of attempts to translate a four-line poem
from the Tang Dynasty."
"The referent" anthology is, according to Google Books,
"a close reading of different translations of a single poem."
The close reader is Eliot Weinberger, who appeared here in 2011 …
The "my own" link above is to "Pilate Goes to Kindergarten."
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Monday, October 10, 2022
The 10/10 Business
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Seeking the Path
See also a Log24 search for "The Path."
Related material from a similar search
for "Nanavira Thera" —
"I am glad you have discovered that the situation is comical:
ever since studying Kummer I have been, with some difficulty,
refraining from making that remark."
— Nanavira Thera, Seeking the Path [Early Letters, 17 July 1958].
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Hidden Structure
The following note from Oct. 10, 1985, was not included
in my finitegeometry.org/sc pages.
See some related group actions on the cuboctahedron at right above.
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Sunday, October 9, 2022
Cutting Edge
"For Marker, memory isn’t passive; it’s an act of resistance—
the edge that cuts a path into the future—and the effective work
of memory is the very definition of art."
— July 30, 2012 in The New Yorker… Richard Brody on the late
film editor Chris Marker.
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Sunday Sermon
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Saturday, October 8, 2022
For Fans of Religious Lunacy … The Firebird Date
("Raiders of the Lost Spell" continues.)
The above flashback to a 2002 post was suggested by a search in
this journal for "Firebird" that yielded, as the only result . . .
http://www.amazon.com/
Witch-Seldom-Firebird-Nancy-Springer/dp/0142302201/.
That URL connects to The Hex Witch of Seldom at Amazon.com.
That book was reportedly published by Firebird on September 16, 2002,
the date of the above Log24 post.
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Chandler Davis, 1926-2022
Log24 art (colored Unicode symbols) from the above date of death:
"Click the red symbol, and …"
— Adapted from "The Matrix."
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Cultural Correlation
The phrase "cultural correlations" from the previous post suggests . . .
From this journal on Bloomsday 2008 —
The holy image
denoting belief and revelation
may be interpreted as
a black hole or as a
symbol by James Joyce :
|
When? Going to dark bed there was a square round Sinbad the Sailor roc’s auk’s egg in the night of the bed of all the auks of the rocs of Darkinbad the Brightdayler. Where?
— Ulysses , conclusion of Chapter 17. |
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Friday, October 7, 2022
From Mysticism to Mathematics… And Back Again
See the previous post as well as posts now tagged Soul and Spirit.
|
Soul
|
Spirit
|
The mirror has two faces (at least).
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Thursday, October 6, 2022
From Mysticism to Mathematics
[Klein, 1983] S. Klein.
"Analogy and Mysticism and the Structure of Culture
(and Comments & Reply)"
Current Anthropology , 24 (2):151–180, 1983.
The citation above is from a 2017 paper —
"Analogy-preserving Functions:
A Way to Extend Boolean Samples,"
by M. Couceiro, N. Hug, H. Prade, G, Richard.
26th International Joint Conference on Artificial Intelligence
(IJCAI 2017), Aug. 2017, Melbourne, Australia. pp.1-7, ff.
That 2017 paper discusses Boolean functions .
Some more-recent remarks on these functions
as pure mathematics —
"On the Number of Affine Equivalence Classes
of Boolean Functions," by Xiang-dong Hou,
arXiv:2007.12308v2 [math.CO]. Rev. Aug. 18, 2021.
See also other posts now tagged Analogy and Mysticism.
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Wednesday, October 5, 2022
Physicality
"Battles argues that 'the experience of the physicality
of the book is strongest in large libraries,' and stand
among the glass cube at the center of the British Library,
the stacks upon stacks in Harvard’s Widener Library, or
the domed portico of the Library of Congress and tell me
any differently."
— Ed Simon, Binding the Ghost: Theology, Mystery, and
the Transcendence of Literature. Hardcover – April 19, 2022.
… And back to cube:
Related meditation: Beer Summit.
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Tuesday, October 4, 2022
Images from April 1, 2004
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Monday, October 3, 2022
Old Code
In memory of a mathematics professor who
reportedly died on May 21, 2022 —
"… mouses over to a file …." Or a folder.
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The Abstract and the Concrete
The above art by Steven H. Cullinane is not unrelated to
art by Josefine Lyche. Her work includes sculpted replicas
of the above abstract Platonic solids, as well as replicas of
my own work related to properties of the 4×6 rectangle above.
Symmetries of both the solids and the rectangle may be
viewed as permutations of parts — In the Platonic solids,
the parts are permuted by continuous rotations of space itself.
In the rectangle, the parts are permuted by non-continuous
transformations, as in the I Ching . . . i.e., by concrete illustrations
of change.
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Sunday, October 2, 2022
Saturday, October 1, 2022
Mexican Beach Bum Glam
Also on the above Berlin date —
Wednesday, November 6, 2013
|
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Imagine.
"… a hyper-intellectual fable that riddles you into a house
of mirrors from which you wonder if you’ll ever emerge.
(Imagine packaging the universe’s most existential questions
as Abbott and Costello’s 'Who’s on First?' routine.)"
— Book review by Michael Callahan in The New York Times
on September 19, 2022.
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Friday, September 30, 2022
Classics Illustrated: The Bitmap File by Harlan Kane
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Thursday, September 29, 2022
The 4×6 Problem*
The exercise posted here on Sept. 11, 2022, suggests a
more precisely stated problem . . .
The 24 coordinate-positions of the 4096 length-24 words of the
extended binary Golay code G24 can be arranged in a 4×6 array
in, of course, 24! ways.
Some of these ways are more geometrically natural than others.
See, for instance, the Miracle Octad Generator of R. T. Curtis.
What is the size of the largest subcode C of G24 that can be
arranged in a 4×6 array in such a way that the set of words of C
is invariant under the symmetry group of the rectangle itself, i.e. the
four-group of the identity along with horizontal and vertical reflections
and 180-degree rotation.
Recent Log24 posts tagged Bitspace describe the structure of
an 8-dimensional (256-word) code in a 4×6 array that has such
symmetry, but it is not yet clear whether that "cube-motif" code
is a Golay subcode. (Its octads are Golay, but possibly not all its
dodecads; the octads do not quite generate the entire code.)
Magma may have an answer, but I have had little experience in
its use.
* Footnote of 30 September 2022. The 4×6 problem is a
special case of a more general symmetric embedding problem.
Given a linear code C and a mapping of C to parts of a geometric
object A with symmetry group G, what is the largest subcode of C
invariant under G? What is the largest such subcode under all
such mappings from C to A?
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Wednesday, September 28, 2022
Bitspace Note
Update of 5:20 AM ET on Sept. 29. 2022 —
The octads of the [24, 8, 8] cube-motif code
can be transformed by the permutation below
into octads recognizable, thanks to the Miracle
Octad Generator (MOG) of R. T. Curtis, as
belonging to the Golay code.
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The Madness of Art
The title is by Henry James.*
For examples, see the Sept. 19 webpage below . . .
… and, in this journal, posts from that same date now tagged Cube Codes.
*
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Tuesday, September 27, 2022
The Rockmore Files
For connoisseurs of bullshit, from The New Yorker yesterday —
“A Trip to Infinity” and the Delicate Art
|
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Monday, September 26, 2022
And …
"Remember, remember
the eighth of September."
Update of 6 AM Sept. 27:
A search for related material
on The Eighth of September
yields a Pablo Neruda poem
and a Barbara Stevens Sullivan
novel, both with that title.
Also by Sullivan . . .
See as well a Log24 post from 2016, "The Mystery of O,"
on June 29, the Feast of Saints Peter and Paul.
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Sunday, September 25, 2022
Woodwork
"The actor Nick Offerman, himself an accomplished woodworker
and a member of Ms. Hiller’s legion of admirers, called her an
'Obi-Wan Kenobi level master.'"
— The New York Times this evening, obituary by Clay Risen
for Nancy Hiller.
Related woodwork note —
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Saturday, September 24, 2022
Nine and Sixteen: In Search of Common Ground
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Friday, September 23, 2022
Data + Meta = WTF
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Data versus Meta … Continues.
Click the above to search this journal for "Dead End."
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Annals of Historical Fiction
In memory of historical novelist Hilary Mantel, who reportedly
died yesterday, two images dealing with this year's Sept. 11 —
The image from Rome was suggested by yesterday's Dürer post and
by the year 1514 in the life of Thomas Cromwell, Mantel's main topic.
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Raiders of the Lost Archive … The Jung Genizah
Jung’s four-diamond figure from
Aion — a symbol of the self –
For those who prefer the Ed Wood approach —
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Thursday, September 22, 2022
Affine Dürer
The previous post's image illustrating the
ancient Lo Shu square as an affine transformation
suggests a similar view of Dürer's square.
That view illustrates the structural principle
underlying the diamond theorem —
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De Colores
See as well . . .
Three-color patterns from 1964,
rendered as shades of grey —
A rather different approach —
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The Tag in the Bag
The above image is from a tweet dated Jan. 11, 2018.
Related material from this journal — That date, in posts
now tagged In the Bag. Those posts are followups to
a remark by Nabokov:
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Wednesday, September 21, 2022
Outside the White Cube
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Meanwhile, in the World of Meta . . .
The previous post's Data Meets Meta tale continues —
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Always Going Home
There's a world where I can go
Tell my secrets to
In my room
In my room (in my room)…
— Beach Boys, 1963
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Heist Flick
"A good public narrative can, at the best of times,
transform an art theft into a lucky break for the gallery."
From a search in this journal for Goya —
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Verse without Words (Title via Kandinsky)
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Tuesday, September 20, 2022
Raiders of the Lost Space… Continues.
From "Raiders of the Lost Space," Sept. 11, 2022 —
A related technique appears in a 1989 paper by Cheng and Sloane
that I saw for the first time today:
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Motif-Space Updates
A linear code of length 24, dimension 8, and minimum weight 8
(a "[24, 8, 8] code") that was discussed in recent posts tagged
Bitspace might, viewed as a vector space, be called "motif space."
Yesterday evening's post "From a Literature Search for Binary [24, 8, 8] Codes"
has been updated. A reference from that update —
Computer Science > Information Theory
|
| Comments: | To appear in IEEE Trans. on Information Theory Vol. 24 No. 8 |
| Subjects: | Information Theory (cs.IT) |
| Cite as: | arXiv:cs/0607074 [cs.IT] |
From Peng and Farrell, 2006 —
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Monday, September 19, 2022
From a Literature Search for Binary [24, 8, 8] Codes
For one example of a binary [24, 8, 8] code, see other bitspace posts.
It is not clear whether that example is a subcode of the Golay code.
See also
http://www.codetables.de/BKLC/
Tables.php?q=2&n0=1&n1=256&k0=1&k1=256
and
http://www.codetables.de/BKLC/BKLC.php?q=2&n=12&k=8 .
Update of 3:22 AM ET on 20 September 2022 —
Update of 3:44 AM ET 20 September 2022 —
Another relevant document:
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The Hymn
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Mosaic Kaleidoscope
"The kaleidoscope of peoples, parties and religions…."
— Description of Vienna in the early 20th century from
"Black Gold and Yellow Star" by Jerome Segal (PDF, 16 pp.)
See as well Mosaic and Kaleidoscope in this journal.
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Sunday, September 18, 2022
Requiem for a Tin Man
— "Heisenberg group modulo 2" from Wikipedia. Click to enlarge.
For a related tune, click the Heisenberg link.
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Friday, September 16, 2022
Symmetric Generation
The above is about a subspace of the
24-dimensional vector space over GF(2)
. . . "An entire world of just 24 squares,"
to adapt a phrase from other Log24
posts tagged "Promises."
Update of 1:45 AM ET Sept. 18, 2022 —
It seems* from a Magma calculation that
the resemblance of the above extended
cube-motif code to the Golay code is only
superficial.
Without the highly symmetric generating codewords that were added
to extend its dimension from 8 to 12, the cube-motifs code apparently
does , like the Golay code, have nonzero weights of only 8, 12, 16, and 24 —
Perhaps someone can prove there is no way that adding more generating
codewords can turn the cube-motif code into the Golay code.
* The "seems" is because I have not yet encountered any of these
relatively rare (42 out of 4096) purported weight-4 codewords. Their
apparent existence may be due to an error in my typing of 0's and 1's.
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Thursday, September 15, 2022
A Grid for Agent Smith*
* See Hugo Weaving in "The Matrix" and "V for Vendetta."
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Literary Symbolism: Math for Roundheads
"The Virginia Cavalier is a concept that attaches the qualities
of chivalry and honor to the aristocratic class in Virginia history
and literature. Its origin lies in the seventeenth century, when
leading Virginians began to associate themselves with the
Royalists, or Cavaliers, who fought for and remained loyal to
King Charles I during the English Civil Wars (1642–1648)."
— https://encyclopediavirginia.org/entries/virginia-cavalier-the/
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