Log24

Friday, September 30, 2022

Classics Illustrated: The Bitmap File  by Harlan Kane

Filed under: General — m759 @ 10:21 am

Related Log24 posts

See Vox Lux and Mathieu Omega.

Related book cover

Thursday, September 29, 2022

The 4×6 Problem*

Filed under: General — Tags: , — m759 @ 4:03 pm

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?

Wednesday, September 28, 2022

Bitspace Note

Filed under: General — Tags: , — m759 @ 5:28 pm

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.

The Madness of Art

Filed under: General — m759 @ 7:09 am

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.

*
 

Tuesday, September 27, 2022

The Rockmore Files

Filed under: General — m759 @ 6:53 am

For connoisseurs of bullshit, from The New Yorker  yesterday —

Annals of Inquiry

“A Trip to Infinity” and the Delicate Art
of the Math Documentary

One of the most captivating concepts in mathematics
is now on Netflix.

Monday, September 26, 2022

And …

Filed under: General — Tags: , , , , — m759 @ 10:00 pm

"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. 

A Chevron for Pynchon: The Maltese V

Filed under: General — Tags: , — m759 @ 12:31 pm

Wordwork

Filed under: General — Tags: — m759 @ 4:39 am

A title for Eliot

A  Balera  for Heisenberg.

Sunday, September 25, 2022

Woodwork

Filed under: General — Tags: — m759 @ 11:21 pm

"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 —

"There and back again."

Marvelette Comics

Filed under: General — m759 @ 10:29 pm

From a search in this journal for Postman . . .

Saturday, September 24, 2022

Blue Note for Doctor Sax

Filed under: General — m759 @ 1:08 pm

From posts now tagged Blue Note

Nine and Sixteen: In Search of Common Ground

Filed under: General — Tags: — m759 @ 6:01 am

Friday, September 23, 2022

Annals of Historical Fiction

Filed under: General — Tags: — m759 @ 12:16 pm

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.

Raiders of the Lost Archive … The Jung Genizah

Filed under: General — Tags: — m759 @ 3:41 am

Jung’s four-diamond figure from
Aion — a symbol of the self –

Jung's four-diamond figure showing transformations of the self as Imago Dei

     For those who prefer the Ed Wood approach —

Thursday, September 22, 2022

Affine Dürer

Filed under: General — Tags: — m759 @ 6:21 pm

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


De Colores

Filed under: General — Tags: — m759 @ 8:47 am

See as well . . .

Three-color patterns from 1964,
  rendered as shades of grey —

A rather different approach —

The Tag in the Bag

Filed under: General — Tags: — m759 @ 3:43 am

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:

Wednesday, September 21, 2022

Modal Obit

Filed under: General — Tags: , — m759 @ 7:14 pm


Related meditation . . .
 

Modal Logic.

Outside the White Cube

Filed under: General — Tags: , , — m759 @ 12:01 pm

      

"Remember, remember the fifth of November"

  — Hugo Weaving in 2005

"If it's Tuesday . . ."

Meanwhile, in the World of Meta . . .

Filed under: General — Tags: — m759 @ 11:13 am

The previous post's  Data Meets Meta  tale continues —

Always Going Home

Filed under: General — Tags: — m759 @ 9:09 am

There's a world where I can go
Tell my secrets to
In my room
In my room (in my room)… 

— Beach Boys, 1963

Data, not Meta.

Heist Flick

Filed under: General — m759 @ 2:04 am

"A good public narrative can, at the best of times,
transform an art theft into a lucky break for the gallery."

The Walrus , Sept. 1, 2022 

From a search in this  journal for Goya —

Verse without Words (Title via Kandinsky)

Filed under: General — m759 @ 12:59 am
 

F8 D8

See as well some related posts.

Tuesday, September 20, 2022

Raiders of the Lost Space… Continues.

Filed under: General — Tags: — m759 @ 7:22 pm

From "Raiders of the Lost Space," Sept. 11, 2022 —

'Codes from Symmetry Groups,' Cheng and Sloane, 1989

A related technique appears in a 1989 paper by Cheng and Sloane
that I saw for the first time today:

'Codes from Symmetry Groups,' Cheng and Sloane, 1989

Motif-Space Updates

Filed under: General — Tags: — m759 @ 3:55 am

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

arXiv:cs/0607074 (cs)

[Submitted on 14 Jul 2006]

On Construction of the (24,12,8) Golay Codes

Xiao-Hong PengPaddy Farrell

Download PDF

Two product array codes are used to construct the (24, 12, 8) binary Golay code through the direct sum operation. This construction provides a systematic way to find proper (8, 4, 4) linear block component codes for generating the Golay code, and it generates and extends previously existing methods that use a similar construction framework. The code constructed is simple to decode.

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 —

Monday, September 19, 2022

Anniversary at Tiffany’s

Filed under: General — Tags: , , — m759 @ 9:02 pm

From a Literature Search for Binary [24, 8, 8] Codes

Filed under: General — Tags: , — m759 @ 7:34 pm

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:

The Hymn

Filed under: General — Tags: — m759 @ 10:31 am

"Like fairytales come true . . ." — LaLa Deaton 

"It can happen to you . . ." — Frank Sinatra

Through a Grid, Darkly

Filed under: General — Tags: , — m759 @ 2:41 am

Ob Iter

Filed under: General — Tags: — m759 @ 1:49 am

Mosaic Kaleidoscope

Filed under: General — Tags: — m759 @ 12:04 am

"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.

Sunday, September 18, 2022

Requiem for a Tin Man

Filed under: General — m759 @ 11:49 am

— "Heisenberg group modulo 2" from Wikipedia.   Click to enlarge.

For a related tune, click the Heisenberg link.

Culture Notes from All Over

Filed under: General — m759 @ 10:56 am

Sunday Morning Lockscreen

Filed under: General — m759 @ 9:42 am

Chamonix. Photo credit: Luca Gino, Sime.

"Dimensión de Arco"

Friday, September 16, 2022

Symmetric Generation

Filed under: General — Tags: , — m759 @ 2:20 pm

Symmetric Generation of a Linear Code

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.

Thursday, September 15, 2022

Requiem for a Sleuth

Filed under: General — Tags: , — m759 @ 10:22 pm

A Grid for Agent Smith*

Filed under: General — Tags: — m759 @ 3:23 pm

* See Hugo Weaving in "The Matrix" and "V for Vendetta."

“R We D8ing?”

Filed under: General — Tags: , — m759 @ 1:43 pm

See also "R We D8ing?" and related posts.

Krysten Ritter narrates a podcast that asks 'R We D8ting?'

Literary Symbolism: Math for Roundheads

Filed under: General — Tags: , , — m759 @ 5:47 am

"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/

Wednesday, September 14, 2022

Not Safe for Work?

Filed under: General — Tags: — m759 @ 11:51 pm

      

A Line for Woody

Filed under: General — Tags: , — m759 @ 8:04 pm

 

"Here’s Looking at You, Grid"

Counting symmetries with the orbit-stabilizer theorem

Starr 80: A Barbie for Ken

Filed under: General — Tags: , , — m759 @ 7:27 pm

Related comedy lines:

A Late Quartet

01:13:08.25,01:13:12.35
(STRING QUARTET PLAYING
SLOW, LUSH MELODY)

01:13:22.59,01:13:26.23
"They’re fucking sixteenths,
Steve, stop milking them."

01:13:26.36,01:13:29.78
"Folks, disagree,
but do it nicely, and please…

01:13:30.47,01:13:33.38
…try not to get caught up in mistakes."

A Linear Code with 4×6 Symmetry

Filed under: General — Tags: — m759 @ 12:03 pm

The exercise of 9/11 continues . . .

From 'A Linear Code with 4x6 Symmetry,' a weblog post on 14 Sept. 2022.

As noted in an update at the end of the 9/11 post,
these 24 motifs, along with 3 bricks and 4 half-arrays,
generate a linear code of 12 dimensions. I have not
yet checked the code's minimum weight. 

For Odd Jean-Luc: Alpha Alpha Double Feature

Filed under: General — Tags: — m759 @ 7:16 am

. . . as well as starring in Alpha Dog and in . . .

Tuesday, September 13, 2022

A Helpful Survey of the Literature

Filed under: General — Tags: — m759 @ 9:39 pm

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."

              — Optimus Prime in 2007

      

"Remember, remember the fifth of November"

  — Hugo Weaving in 2005

Cinema News

Filed under: General — Tags: , — m759 @ 6:18 am

From a search in this  journal for Godard —

"I perceived . . . cinema is that which is between things,
not things [themselves] but between one and another."

— Jean-Luc Godard, "Introduction à une véritable histoire
du cinéma
," Albatros , Paris, 1980, p. 145

“We Got This Covered”

Filed under: General — Tags: — m759 @ 3:45 am

The previous post's quotation of the word "leitmotif" suggests a review:

      

See as well Sunday's post "Raiders of the Lost Space."

The Return of Krankheit and Dubious

Filed under: General — m759 @ 2:39 am

In memory of Ramsey Lewis, famed for his recording
of "The In Crowd" —

An old vaudeville routine, slightly adapted :

— Are you a doctor?
— I'm a doctor.
— I'm dubious.
— I'm glad to know you, Miss Dubious.

"The In Crowd" was a leitmotif in the 2015 film "Irrational Man."

Joaquin Phoenix as Dr. Krankheit,
Emma Stone as Miss Dubious —

Monday, September 12, 2022

“Hard Boiled” (Action Movie Title, Hong Kong, 1992)

Filed under: General — Tags: — m759 @ 4:55 pm

The "all-time great actioner" of the above news story is "Hard Boiled,"
a 1992 Hong Kong action film by John Woo. Related art —

Revised New Yorker cover from 5/21/07
Revised version of the
New Yorker  cover of 5/21/07

Sunday, September 11, 2022

Raiders of the Lost Space

Filed under: General — Tags: — m759 @ 2:29 pm

From 1981 —

From today —

Update —

A Magma check of the motif-generated space shows that
its dimension is only 8, not 12 as with the MOG space.
Four more basis vectors can be added to the 24 motifs to
bring the generated space up to 12 dimensions: the left
brick, the middle brick, the top half (2×6), the left half (4×3).
I have not yet checked the minimum weight in the resulting
12-dimensional 4×6 bit-space.

— SHC 4 PM ET, Sept. 12, 2022.

Saturday, September 10, 2022

Solomon’s Mental Health Month

Filed under: General — Tags: , , — m759 @ 12:21 pm

May 2003 was "Solomon's Mental Health Month" in this journal.

An essay linked to on the 9th of May in that month —

"Taking the Veil," by Jessica Kardon

https://web.archive.org/web/20021102182519/
http://www.thespleen.com/otherorgans/otherorgans/
index.php?artID=724

James Hillman, writing in The Soul's Code, argues for his "acorn theory" of human individual identity, and suggests that "each person bears a uniqueness that asks to be lived and that is already present before it can be lived." He insists we are born with a given character, a daimon, the carrier of destiny. This theory is closely linked to the beautiful myth described by Plato in his Republic, when the soul stands before Lachesis and receives his specific soul guardian. Hillman maintains that the daimon will always emerge somehow, even if thwarted or unrecognized.

I never had ambitions that reached fruition in the adult world. I have had only two career interests in my life – both formed precognitively. I wanted to be a mermaid or a nun. By the time I learned – shockingly late – that I could not be a mermaid, I had realized I would not be a nun. I concur with Hillman's emphasis on the persistence of early disposition, and I like to imagine that my dreamy, watery, Victorian and self-righteous psyche has held aspects of both of these early interests, throughout my life.

I was adopted one month after my birth. I was tended by nuns during the first four weeks of my life. Thereafter, I spent my whole educational life in convent schools. It was the sisters of Saint Vincent de Paul that gave me my favorite musical and my early distortions about romantic love and the gender plans of Our Lord. My misconceptions about love and marriage were culled from the Lerner Loewe musical Gigi, a wonderful film based loosely on a Colette novel. I was summoned along with my whole class to the gymnasium to view the movie under the edgy eye of Sister Bernadette.

Sister Bernadette was a large, mesomorphic nun famed for the beatings she gave to boys and girls alike, and feared for the mean zest with which she bestowed her favors upon many of us. I was not beaten – but once, believing I was wearing lipstick, she held my head in a sink and scrubbed my lips until they bled, then slapped me. I recall this with a mild, rueful whimsy. We were all manhandled. In memory, Bernadette seems more like an angry and troubled older sibling than a true figure of authority.

Anyway, I loved Gigi. It fed directly into my Francophilia. I was convinced that at some future date, I, like Gigi, would be trained as a courtesan. I, too, would cause some hard case, experienced roué to abandon his chill and irony. I saw myself strolling down the Champs Elysee with Louis Jordan in rapt attendance, pushing a baby carriage, wearing a hat the size of a manhole cover, hoisting a parasol above that to assure the longevity of my adorable pallor.

The gender plans of Our Lord had recently been revealed to me too. Sister B. had drawn a ladder on the blackboard, a ladder with three rungs. At the top, she explained, were the priests, the nuns, and the monks. These souls had surrendered their lives to God. All would be taken directly to heaven upon their passing from this vale of tears, as we all referred to the world in those lean emotional times. On the middle rung stood the married. If you married and kept the law – which meant leaving every act of marital congress open to the reception of a child, you would be eligible for heaven. If you were foul in marriage, seeking your pleasure, you were going to be damned. On the bottom rung were those selfish souls who had remained single and had imagined their lives their own. This group had never given themselves to Our Lord. They were headed to hell in a sort of preternatural laundry chute.

So we little ladies had two viable options: marry and breed without ceasing – or take the veil.

Despite my hat and perambulator fantasies, once given the sorry news of the ladder, the veil became the clear romantic favorite. Therefore I began my research. I obtained a catalogue of nunnery. It offered photographs of each order, describing the duties of the specific order, and displaying the garb of that order. I was looking for two things – a great looking veil and gown, and a contemplative order. I had no desire to sully my glorious vision of myself with a life in the outer world. It was apparent to me that the teaching of children was going to involve a whole range of miseries – making them cry, telling them the bad news about the ladder, and so forth. This was not for me. I saw myself kneeling on the floor of my pristine little cell, serene and untouched by human hands. Teaching would be certain to interfere with the proper lighting. Yoked to a bunch of messy children, I could not possibly have the opalescent illumination of heaven falling reliably on my upturned visage.

What divided me from my dream of rebirth as a mermaid was the force of what was real: I could not morph. What divided me from my dream of life as a nun was the force of the erotic: I would not abstain.

Now, long years later, I am still underwater, and I am still bending the knee. I live in the blue shadows of hidden grottoes, and I am swimming, too, in the gold of my drifting prayers.

September 7th, this dream. I am standing in a dimly lit room, gazing at a group of heavy, antique silk burqas that look weirdly like Fortuny gowns. A holy woman approaches me, and tells me that my soul will leave my body, and enter these garments. She turns and points at a young girl standing nearby, a child with close-cropped hair and a solemn look. My heart knows her, but my eyes don't.

For a moment I am thinking, exactly as I did in the seventies when holding a joint: "This isn't working." Suddenly, these things: I feel the shape of flame, then I am the shape. I am released into the air, and as pure essence I enter other forms, dissolving in them, gathering my energy back into myself, and flying out again. This was a sensation so exquisite that my dreaming brain woke up and announced to me: "This is a dream about death."

I saw that child again as I flew. This time my eyes knew her. I flew to her, but the flame of my soul would not cohere with hers, this child who was, of course, my own self.

In the shadows alone, I heard myself whisper: "I'm in the wind. I'm in the water."

This lovely dream, which gave me the sublime gift of a little visceral preview of the soul in the death process, also showed me my guardian spirit; divided, but viable.

I pass through my life swimming in one self, kneeling in the other. I thought of Rilke's 29th Sonnet to Orpheus and realized this was what I had been dreaming about all my life, moving between them.

Silent friend of many distances, feel
how your breath enlarges all of space.
Let your presence ring out like a bell
into the night. What feeds upon your face

grows mighty from the nourishment thus offered.
Move through transformation, out and in.
What is the deepest loss that you have suffered?
If drinking is bitter, change yourself to wine.

In this immeasurable darkness, be the power
that rounds your senses in their magic ring,
the sense of their mysterious encounter.

And if the earthly no longer knows your name,
whisper to the silent earth: I'm flowing.
To the flashing water say: I am.

– Stephen Mitchell, translating Rainer Marie Rilke.

by jessica kardon
iowa city, iowa
2002-09-23

See as well yesterday's post "At a Still Point."

Orthogonal Latin Triangles

Filed under: General — Tags: , — m759 @ 1:38 am

From a 1964 recreational-mathematics essay —

Note that the first two triangle-dissections above are analogous to
mutually orthogonal Latin squares . This implies a connection to
affine transformations within Galois geometry. See triangle graphics
in this  journal.

Affine transformation of 'magic' squares and triangles: the triangle Lo Shu 

Update of 4:40 AM ET —

Other mystical figures —

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

"Before time began, there was the Cube."

— Optimus Prime in "Transformers" (Paramount, 2007)

Friday, September 9, 2022

Pillars of Wisdom . . . Count ’Em!

Filed under: General — m759 @ 11:19 pm

Related reading — Program or Be Programmed — 

At a Still Point

Filed under: General — m759 @ 4:43 pm

"The music was as formal as
Job's argument with God.
Her dance was God's reply."

— "A Rose for Ecclesiastes"

Relentless Exploitation Flick

Filed under: General — Tags: — m759 @ 12:19 pm

A New York Times  obituary today reports a death
from the Feast of St. Louis, 2022 —

"Dr. Gottfried said at the time that the world was
undergoing a transformative revolution driven by
'the relentless exploitation of scientific knowledge.'”

Also on that date . . .

The Station

Filed under: General — Tags: — m759 @ 12:52 am

On the Way to Burning Man 2022 —

Chevrons serve as a contrast to the more highly symmetric figures
at left in yesterday morning's Analogy in Mathematics illustration —

Poetry enthusiasts might view the brick at left as
symbolizing the scepter'd isle  off the west coast
of Europe, and the gap between as the English 
Channel. Mind the gap.

Thursday, September 8, 2022

Analogy in Mathematics: Chevron Variations

André Weil in 1940 on analogy in mathematics —

. "Once it is possible to translate any particular proof from one theory to another, then the analogy has ceased to be productive for this purpose; it would cease to be at all productive if at one point we had a meaningful and natural way of deriving both theories from a single one. In this sense, around 1820, mathematicians (Gauss, Abel, Galois, Jacobi) permitted themselves, with anguish and delight, to be guided by the analogy between the division of the circle (Gauss’s problem) and the division of elliptic functions. Today, we can easily show that both problems have a place in the theory of abelian equations; we have the theory (I am speaking of a purely algebraic theory, so it is not a matter of number theory in this case) of abelian extensions. Gone is the analogy: gone are the two theories, their conflicts and their delicious reciprocal reflections, their furtive caresses, their inexplicable quarrels; alas, all is just one theory, whose majestic beauty can no longer excite us. Nothing is more fecund than these slightly adulterous relationships; nothing gives greater pleasure to the connoisseur, whether he participates in it, or even if he is an historian contemplating it retrospectively, accompanied, nevertheless, by a touch of melancholy. The pleasure comes from the illusion and the far from clear meaning; once the illusion is dissipated, and knowledge obtained, one becomes indifferent at the same time; at least in the Gitâ there is a slew of prayers (slokas) on the subject, each one more final than the previous ones."

"The pleasure comes from the illusion" . . .

Exercise:

Compare and contrast the following structure with the three
"bricks" of the R. T. Curtis Miracle Octad Generator (MOG).

http://www.log24.com/log/pix11B/110805-The24.jpg

Note that the 4-row-2-column "brick" at left is quite 
different from the other two bricks, which together
show chevron variations within a Galois tesseract —

Tuesday, September 6, 2022

Literary Master

Filed under: General — Tags: — m759 @ 4:56 pm

Update at 11:19 PM ET —

"We all float down here." — Pennywise the Clown

A comparison of Peter Straub's novel Floating Dragon  (1982)
with Stephen King's novel It  (1986)

"Many people have cited some distinct similarities between Stephen King’s It  and Floating Dragon .  An ancient evil that awakes every thirty years, several main male characters and a single female character who come together to confront that evil, a number of asides around the small town as bystanders are picked off, even a number of scenes and themes in common."

— https://www.fantasybookreview.co.uk/
Peter-Straub/Floating-Dragon.html

From the same webpage —

"As the book rockets towards its ending, Straub really does pull out all the stops. A late chapter is entitled 'through the looking glass' and that really is how the book begins to feel, more like a surreal and disturbing fantasy world than a book set in late twentieth century America. Usually in horror novels the point when reality seriously starts to crumble, whether its visions of grandmothers turning into fish or angel shaped biscuits turning evil, there is always the sense that this must be just a dream and the main characters will wake up. Well not here, the weirder things seem, the deadlier they are, indeed one comment late on in the book by Graham that just because something isn’t real doesn’t mean it can’t kill you seemed almost like Straub’s mission statement."

Tata Note

Filed under: General — m759 @ 3:00 pm

"This volume is the first of three in a series surveying
the theory of theta functions. Based on lectures given by
the author at the Tata Institute of Fundamental Research
in Bombay, these volumes constitute a systematic exposition
of theta functions, beginning with their historical roots as
analytic functions in one variable (Volume I), touching on
some of the beautiful ways they can be used to describe
moduli spaces (Volume II), and culminating in a methodical
comparison of theta functions in analysis, algebraic geometry,
and representation theory (Volume III)."

Digits of August

Filed under: General — Tags: , — m759 @ 1:14 pm

See as well Kipnis on the separatrix, and a notation
that represents a date in September, not August:
 

9/6.


Too clever by half ?

Gell-Mann Meets Bosch* at Hiroshima

Filed under: General — Tags: — m759 @ 3:18 am

Gell-Mann Meets Bosch . . .

At Hiroshima . . .

Iain Aitchison's 'dice-labelled' cuboctahedron at Hiroshima, March 2018

* The Bosch  cuboctahedron is from an exhibition at Napoli in 2021.

See also, from that exhibition's starting date,
the Log24 post Desperately Seeking Symmetry.

Monday, September 5, 2022

Annals of Science: Cognitive Testing

Filed under: General — m759 @ 6:03 pm

See also http://m759.net/wordpress/?s="Block+Design"

2001: A Time Odyssey

Filed under: General — m759 @ 4:15 pm

See as well a search for intelligent life at Santa Cruz —

Related art —

“Come into my parlor . . .”

Filed under: General — Tags: — m759 @ 4:07 am

See as well this  journal on December 12, 2010 — Sunday Painting —

and an Instagram story this morning by Marcela Nowak:


 

Sunday, September 4, 2022

Dice and the Eightfold Cube

Filed under: General — Tags: , , — m759 @ 4:47 pm

At Hiroshima on March 9, 2018, Aitchison discussed another 
"hexagonal array" with two added points… not at the center, but
rather at the ends  of a cube's diagonal axis of symmetry.

See some related illustrations below. 

Fans of the fictional "Transfiguration College" in the play
"Heroes of the Fourth Turning" may recall that August 6,
another Hiroshima date, was the Feast of the Transfiguration.

Iain Aitchison's 'dice-labelled' cuboctahedron at Hiroshima, March 2018

The exceptional role of  0 and  in Aitchison's diagram is echoed
by the occurence of these symbols in the "knight" labeling of a 
Miracle Octad Generator octad —

Transposition of  0 and  in the knight coordinatization 
induces the symplectic polarity of PG(3,2) discussed by 
(for instance) Anne Duncan in 1968.

Saturday, September 3, 2022

1984 Revisited

Filed under: General — m759 @ 2:46 pm

Cube Bricks 1984 —

An Approach to Symmetric Generation of the Simple Group of Order 168

Related material

Note the three quadruplets of parallel edges  in the 1984 figure above.

Further Reading

The above Gates article appeared earlier, in the June 2010 issue of
Physics World , with bigger illustrations. For instance —

Exercise: Describe, without seeing the rest of the article,
the rule used for connecting the balls above.

Wikipedia offers a much clearer picture of a (non-adinkra) tesseract —

      And then, more simply, there is the Galois tesseract

For parts of my own  world in June 2010, see this journal for that month.

The above Galois tesseract appears there as follows:

Image-- The Dream of the Expanded Field

See also the Klein correspondence in a paper from 1968
in yesterday's 2:54 PM ET post

Friday, September 2, 2022

Kyoto Prize

Filed under: General — Tags: — m759 @ 9:43 pm

Related material —

Wittgenstein and Fly from Fly-Bottle

Fly from Fly Bottle

History of Mathematics

Filed under: General — m759 @ 2:54 pm

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 remarksSteinberg Deathdate.

Independence

Filed under: General — m759 @ 11:22 am

On the wife of the fictional billionaire Byron Gogol

Continuing the theme of independence, a less fictional Byron . . .

Thursday, September 1, 2022

Plan 9: A Recurring Theme

Filed under: General — m759 @ 7:23 pm

September Morn Concludes

Filed under: General — Tags: — m759 @ 11:56 am

"This is the worst trip I've ever been on"

Sloop John B lyrics.  

That song was played at the end of the TV series
"The Resort," which concluded today.

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