Log24

Tuesday, October 22, 2019

Elegy

Filed under: General — Tags: — m759 @ 6:05 pm

See as well a search for Nabokov's Carpet.

Logos

Filed under: General — Tags: — m759 @ 5:22 pm

The production-company logos for Carpenter B and Bad Robot
in end credits for a 2016 TV mini-series based on the Stephen King
novel 11/22/63  suggest a look at . . .

For the Church of Synchronology — 
This  weblog on Aug. 11, 2017:

Symmetry's Lifeboat and Archimedes for Jews.

Monday, October 21, 2019

Algebra and Space… Illustrated.

Filed under: General — Tags: , — m759 @ 4:26 pm

Related entertainment —

Detail:

   George Steiner

"Perhaps an insane conceit."

 

Perhaps.

 

See Quantum Tesseract Theorem .

 

Perhaps Not.

 

 See Dirac and Geometry .

New Key

Filed under: General — Tags: — m759 @ 4:22 am

 

Sunday, October 20, 2019

In Memory of Nick Tosches

Filed under: General — Tags: — m759 @ 7:55 pm

See also a poem by Nick Tosches from the preceding day —
August 11, 2010 — "He Who Is of Name,"  in which Tosches
addresses actor James Franco (Esquire  magazine).

See as well, from this  journal recently . . .

Down the Rabbit Hole   with James Franco 

Talented Writer Dies

Filed under: General — m759 @ 12:43 pm

MSRI (Pronounced “Misery”)

Filed under: General — Tags: — m759 @ 10:29 am

Saturday, October 19, 2019

John Tate Died…

Filed under: General — m759 @ 9:20 am

on some unspecified date,* according to
the University of Texas at Austin yesterday.

See also Tate in a Blackboard Jungle post 
from December 5, 2013.

* On October 16, 2019  (AMS Day),  according to 
the Harvard University department of mathematics.

Hexagram 19

Filed under: General — m759 @ 6:55 am

The image “http://www.log24.com/log/pix05B/051202-Hex19.jpg” cannot be displayed, because it contains errors.

Click the above image
for its source.

See also Hexagram 19
in this journal.

Friday, October 18, 2019

Russianization

Filed under: General — Tags: — m759 @ 8:43 pm

Continued from September 24 —

From today's news . . .

" 'If the nesting doll fits '
'This is not some outlandish claim. This is reality.' " 

Related images from 4 AM ET today —

See as well today's previous post, "Vibe for Ray Bradbury."
Bradbury was the author of the 1955 classic The October Country .

Vibe for Ray Bradbury

Filed under: General — Tags: — m759 @ 12:22 pm

On writer Kate Braverman, who reportedly died on Sunday, October 13:

" She wears floor-length black skirts, swirling black coats,
and black stiletto boots;  the San Francisco Chronicle  once
described her vibe as 'Morticia Addams gone gypsy.' " 

Katy Waldman in The New Yorker , Feb. 22, 2018

"I need a photo opportunity
I want a shot at redemption
Don't want to end up a cartoon
In a cartoon graveyard"

— Paul Simon, song lyric

For a Braverman photo opportunity, see the dark corner
at lower right in the previous post.

4 A.M. Reality Checks

Filed under: General — Tags: — m759 @ 4:00 am

Wall Texts

Filed under: General — Tags: — m759 @ 2:46 am

"And the new dumbed-down gallery headings and word salads
of the main wall texts definitely need work."

— Roberta Smith yesterday in The New York Times
    on the reopening Museum of Modern Art.

Sample gallery heading and word salad from this  journal  

Heading:

From the Terrace.

Salad:

Spinning the Wake.

A Song for St. Luke’s Day

Filed under: General — m759 @ 1:19 am

From a 1962 young-adult novel —

"There's something phoney in the whole setup, Meg thought.
There is definitely something rotten in the state of Camazotz."

Song adapted from a 1960 musical —

"In short, there's simply not
A more congenial spot
For happy-ever-aftering
Than here in Camazotz!"

Thursday, October 17, 2019

Annals of Architectural Theory

Filed under: General — Tags: , — m759 @ 6:16 pm

Related material — See Jencks and
some other Log24 posts now tagged

Dancing About Architecture.

Dance of the Fire Temple

Filed under: General — Tags: , , — m759 @ 10:13 am

The previous post, Tetrahedron Dance, suggests a review of . . .

A figure from St. Patrick's Day 2004 that might
represent a domed  roof 

Inscribed Carpenter's Square:

In Latin, NORMA

 and a cinematic "Fire Temple" from 2019 

In related news . . .

Related background "e. e. cummings" in this  journal.

Tetrahedron Dance

Filed under: General — Tags: , , , — m759 @ 9:42 am

John Lithgow in "The Tomorrow Man" (2019)

" connect the dots…."

IMAGE- 'The geometry of the dance' is that of a tetrahedron, according to Peter Pesic

Watch Your Six, John

Filed under: General — m759 @ 12:42 am

English subtitles: The Tomorrow Man – transcript

The interested reader may consult Google 
for the source of the above passage. 

Wednesday, October 16, 2019

For AMS Day

Filed under: General — m759 @ 12:26 pm

The American Mathematical Society has declared that
today is AMS Day.

A different sort of code than in the previous post —

Gnostic Effects

Filed under: General — Tags: — m759 @ 11:41 am

"OCT 14, 2019  •  8:00 PM"

"Culturally, code exists in a nether zone.
We can feel  its gnostic effects  [link added]
on our everyday reality, but we rarely see it,
and it’s quite inscrutable to non-initiates.
(The folks in Silicon Valley like it that way;
it helps them self-mythologize as wizards.)
We construct top-10 lists for movies, games, TV—
pieces of work that shape our souls.
But we don’t sit around compiling lists of the world’s
most consequential bits of code, even though they
arguably inform the zeitgeist just as much."

— https://slate.com/technology/2019/10/
consequential-computer-code-software-history.html

Omens

Filed under: General — Tags: — m759 @ 10:49 am

Not your average Bartleby and Loki.

Tuesday, October 15, 2019

The Cartoonist’s Wife

Filed under: General — Tags: — m759 @ 8:37 pm

On an author mentioned in the previous post's obituary:

The author's book —

Inside the Fire Temple

Filed under: General — Tags: , — m759 @ 8:00 pm

(The title refers to Log24 posts now tagged Fire Temple.)

In memory of a  New Yorker  cartoonist who
reportedly died at 97 on October 3, 2019  …

"Read something that means something." 
New Yorker  advertising slogan

From posts tagged Tetrahedron vs. Square

This  journal on October 3

"There is  such a thing as a 4-set."
— Saying adapted from a 1962 young-adult novel.

Illustration (central detail   from the above tetrahedral figure) —

A White Stone for Bloom

Filed under: General — Tags: , — m759 @ 12:00 am

Excerpt from a long poem by Eliza Griswold 
in a recent New Yorker —

Monday, October 14, 2019

Harold Bloom: July 11, 1930 — October 14, 2019

Filed under: General — Tags: — m759 @ 4:42 pm

Advanced Studies Date

Filed under: General — Tags: — m759 @ 3:49 pm

Related post:  The Joy of Six.

Sunday, October 13, 2019

Langer

Filed under: General — Tags: — m759 @ 11:00 am

"Visual forms— lines, colors, proportions, etc.—
are just as capable of articulation ,
i.e. of complex combination, as words.
But the laws that govern this sort of articulation
are altogether different from the laws of syntax
that govern language. The most radical difference
is that visual forms are not discursive .
They do not present their constituents successively,
but simultaneously, so the relations determining
a visual structure are grasped in one act of vision."

— Susanne K. LangerPhilosophy in a New Key

Saturday, October 12, 2019

SNL Drill

Filed under: General — Tags: — m759 @ 8:21 pm

"Hellboy  was theatrically released on April 12, 2019,
  to negative reviews . . . ." — Wikipedia

 

Glass Beads

Filed under: General — Tags: — m759 @ 7:05 pm

(A sequel to the previous post, Marbles)

'Magister Ludi,' or 'The Glass Bead Game,' by Hermann Hesse

Click the book cover for some related posts.

Marbles

Filed under: General — m759 @ 9:34 am

In memory of some Trinity mathematicians:

 

Night at the Museum

Filed under: General — m759 @ 12:00 am

Being There, by Jerzy Kosinski

Friday, October 11, 2019

Illustrating Nightmares

Filed under: General — m759 @ 11:30 pm

Movie poster designer Philip Gips reportedly died on
Thursday, October 3, 2019. This journal on that date:

A Sense of the Landmarks.

The Flynn Legacy

Filed under: General — Tags: — m759 @ 9:26 pm

TRON Legacy: back door

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— 

Dick Date (YouTube, August 7, 2013)

Filed under: General — Tags: , , — m759 @ 3:47 pm

Down the Rabbit Hole  with Stephen King

Quest

Filed under: General — m759 @ 3:45 am

John Horgan in Scientific American  magazine on October 8, 2019 —

"In the early 1990s, I came to suspect that the quest
for a unified theory is religious rather than scientific.
Physicists want to show that all things came from
one thing a force, or essence, or membrane
wriggling in eleven dimensions, or something that
manifests perfect mathematical symmetry. In their
search for this primordial symmetry, however,
physicists have gone off the deep end . . . ."

Other approaches —

See "Story Theory of Truth" in this  journal and, from the November 2019  
Notices of the American Mathematical Society . . .

Story Driven

More fundamental than the label of mathematician is that of human. And as humans, we’re hardwired to use stories to make sense of our world (story-receivers) and to share that understanding with others (storytellers) [2]. Thus, the framing of any communication answers the key question, what is the story we wish to share? Mathematics papers are not just collections of truths but narratives woven together, each participating in and adding to the great story of mathematics itself.

The first endeavor for constructing a good talk is recognizing and choosing just one storyline, tailoring it to the audience at hand. Should the focus be on a result about the underlying structures of group actions? . . . .

[2] Gottschall, J. , The Storytelling Animal ,
       Houghton Mifflin Harcourt, 2012.

— "Giving Good Talks,"  by Satyan L. Devadoss

"Before time began, there was the Cube." — Optimus Prime

Wednesday, October 9, 2019

The Joy of Six

Note that in the pictures below of the 15 two-subsets of a six-set,
the symbols 1 through 6 in Hudson's square array of 1905 occupy the
same positions as the anticommuting Dirac matrices in Arfken's 1985
square array. Similarly occupying these positions are the skew lines
within a generalized quadrangle (a line complex) inside PG(3,2).

Anticommuting Dirac matrices as spreads of projective lines

Related narrative The "Quantum Tesseract Theorem."

Numberland Continues: “Hence in the 6”

Filed under: General — m759 @ 4:01 pm

The interested reader may consult Google for the source of
the above. For the "Numberland" of the title, see this journal.

Philosophical Infanticide

Filed under: General — Tags: — m759 @ 5:51 am

From Wallace Stevens —

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
Of dense investiture, with luminous vassals."

— “An Ordinary Evening in New Haven” VI

From The Point  magazine yesterday, October 8, 2019
Parricide:  On Irad Kimhi's Thinking and Being .
Book review by Steven Methven.

The conclusion:

"Parricide is nothing that the philosopher need fear . . . .
What sustains can be no threat. Perhaps what the
unique genesis of this extraordinary work suggests is that
the true threat to philosophy is infanticide."

This remark suggests revisiting a post from Monday

Monday, October 7, 2019

Berlekamp Garden vs. Kinder Garten

Filed under: General — m759 @ 11:00 PM

Stevens's Omega and Alpha (see previous post)
suggest a review.

Omega — The Berlekamp Garden. 
                  See Misère Play (April 8, 2019).
Alpha  —  The Kinder Garten. 
                  See Eighfold Cube.

. . . .

Tuesday, October 8, 2019

An Ordinary Day in New Haven

Filed under: General — Tags: , — m759 @ 7:30 pm

This  journal on the date of Coe's death 

Related material:  Today's  noon post and a post from August 7, 2006.

Kummer at Noon

Filed under: General — Tags: — m759 @ 12:00 pm

The Hudson array mentioned above is as follows —

See also Whitehead and the
Relativity Problem
(Sept. 22).

For coordinatization  of a 4×4
array, see a note from 1986
in the Feb. 26 post Citation.

Also* in 1984

Filed under: General — Tags: — m759 @ 11:32 am
 

American Mathematical Monthly , June-July 1984 

MISCELLANEA, 129

Triangles are square

"Every triangle consists of  n congruent copies of itself"
is true if and only if  n is a square. (The proof is trivial.)
— Steven H. Cullinane

* See Cube Bricks 1984  in previous post.

Monday, October 7, 2019

Berlekamp Garden vs. Kinder Garten

Filed under: General — Tags: — m759 @ 11:00 pm

Stevens's Omega and Alpha (see previous post) suggest a review.

Omega — The Berlekamp Garden.  See Misère Play (April 8, 2019).
Alpha  —  The Kinder Garten.  See Eighfold Cube.

Illustrations —

The sculpture above illustrates Klein's order-168 simple group.
So does the sculpture below.

Froebel's Third Gift: A cube made up of eight subcubes  

Cube Bricks 1984 —

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

Lenz

Filed under: General — m759 @ 2:56 pm

Or:  Je repars .

From Wallace Stevens —

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
Of dense investiture, with luminous vassals."

— “An Ordinary Evening in New Haven” VI

Mathematician Hanfried Lenz reportedly died in Berlin on June 1, 2013.

This journal that weekend

Oblivion

Filed under: General — Tags: , , — m759 @ 1:09 pm

(A sequel to Simplex Sigillum Veri and
Rabbit Hole Meets Memory Hole)

” Wittgenstein does not, however, relegate all that is not inside the bounds
of sense to oblivion. He makes a distinction between saying  and showing
which is made to do additional crucial work. ‘What can be shown cannot
be said,’ that is, what cannot be formulated in sayable (sensical)
propositions can only be shown. This applies, for example, to the logical
form of the world, the pictorial form, etc., which show themselves in the
form of (contingent) propositions, in the symbolism, and in logical
propositions. Even the unsayable (metaphysical, ethical, aesthetic)
propositions of philosophy belong in this group — which Wittgenstein
finally describes as ‘things that cannot be put into words. They make
themselves manifest. They are what is mystical’ ” (Tractatus  6.522).

Stanford Encyclopedia of Philosophy , “Ludwig Wittgenstein

From Tractatus Logico-Philosophicus  by Ludwig Wittgenstein.

(First published in Annalen der Naturphilosophie ,1921.
English edition first published 1922 by Kegan Paul, Trench and Trübner. This translation first published 1961 by Routledge & Kegan Paul. Revised edition 1974.)

5.4541

The solutions of the problems of logic must be simple, since they set the standard of simplicity.

Men have always had a presentiment that there must be a realm in which the answers to questions are symmetrically combined — a priori — to form a self-contained system.

A realm subject to the law: Simplex sigillum veri.

Somehow, the old Harvard seal, with its motto “Christo et Ecclesiae ,”
was deleted from a bookplate in an archived Harvard copy of Whitehead’s
The Axioms of Projective Geometry  (Cambridge U. Press, 1906).

In accordance with Wittgenstein’s remarks above, here is a new
bookplate seal for Whitehead, based on a simplex

Saturday, October 5, 2019

Midnight Landmarks

Filed under: General — Tags: , , — m759 @ 12:00 am

Friday, October 4, 2019

Kiley Cornered

Filed under: General — m759 @ 1:31 pm

Kiley in Blackboard Jungle , 1955 —

IMAGE- Richard Kiley in 'Blackboard Jungle,' with grids and broken records

From the previous post

"Prenons arbitrairement dans le tableau ci-dessus…."

Related material — "Ici vient M. Jordan."

Kummerhenge

Filed under: General — Tags: — m759 @ 12:26 pm

(Continued.)

The previous post suggests a review of
the following mathematical  landmark —

The 'Ici vient M. Jordan' paper

The cited article by Kummer is at . . .

https://archive.org/details/monatsberichtede1864kn/page/246 .

Thursday, October 3, 2019

A Sense of the Landmarks

Filed under: General — m759 @ 8:49 pm

Cary Grant in 'North by Northwest'

Or the Oak Bar at the Plaza?

"Paging Mr. Kaplan."

From the reported date of Mr. Conner's death —

Apocalypse* Note

Filed under: General — Tags: , — m759 @ 7:00 pm

For a first look at octad.space, see that domain.
For a second look, see octad.design.
For some other versions, see Aitchison in this journal.

* The X-Men character.

Quarks for Poets

Filed under: General — Tags: , — m759 @ 12:53 pm

The title was suggested by a recent New Yorker  poem.

From NewScientist.com

Related material: The remarks of Mysterio in "Spider-Man: Far From Home."

The Overbye Metaphors

Filed under: General — Tags: — m759 @ 12:00 pm

(For Harlan Kane)

"Once Mr. Overbye identifies a story, he said, the work is
in putting it in terms people can understand. 'Metaphors
are very important to the way I write,' he said. The results
are vivid descriptions that surpass mere translation."

— Raillan Brooks in The New York Times  on a Times
science writer, October 17, 2017.  Also on that date —

"There is  such a thing as a 4-set."
— Saying adapted from a 1962 young-adult novel.

See as well The Black List (Log24, September 27).

Wednesday, October 2, 2019

Struck by the Fusion

Filed under: General — Tags: — m759 @ 2:50 pm

"… I was struck by the fusion of drama and music.”

— Autobiographical recollection by a music critic who
reportedly died on Sunday at 83.

Related material — The previous post and

Social Climbing

Filed under: General — Tags: — m759 @ 2:13 pm

"When the queen came, they said she was wanton.
Or a witch, or a saint."

Ursula Whitcher,  "Alphabet of Signs"

Related images —

Algebra for Jews

Filed under: General — Tags: — m759 @ 1:28 pm

(A sequel to Geometry for Jews.)

The Lévi-Strauss formula —

Related posts: Dueling.

A Long Literary Tradition

Filed under: General — Tags: , — m759 @ 12:38 pm

"There's a long literary tradition associating
certain kinds of geometry with horror."

— American Mathematical Society yesterday:

See also yesterday's Log24 post "Transylvania Revisited."

A related post —

Harvard Showbiz.

Stevens at 140

Filed under: General — m759 @ 12:38 am

Poet Wallace Stevens was born 140 years ago today.

For another 140, see Diamond Theory in 1937.

For some notes related to a Stevens poem from 1937,
see "arrowy, still strings" in this journal.

Tuesday, October 1, 2019

Transylvania Revisited

Filed under: General — Tags: , — m759 @ 2:10 pm

The previous post suggests . . .

Jim Holt reviewing Edward Rothstein's Emblems of Mind: The Inner Life of Music and Mathematics  in The New Yorker  of June 5, 1995:

"The fugues of Bach, the symphonies of Haydn, the sonatas of Mozart: these were explorations of ideal form, unprofaned by extramusical associations. Such 'absolute music,' as it came to be called, had sloughed off its motley cultural trappings. It had got in touch with its essence. Which is why, as Walter Pater famously put it, 'all art constantly aspires towards the condition of music.'

The only art that can rival music for sheer etheriality is mathematics. A century or so after the advent of absolute music, mathematics also succeeded in detaching itself from the world. The decisive event was the invention of strange, non-Euclidean geometries, which put paid to the notion that the mathematician was exclusively, or even primarily, concerned with the scientific universe. 'Pure' mathematics came to be seen by those who practiced it as a free invention of the imagination, gloriously indifferent to practical affairs– a quest for beauty as well as truth." [Links added.]

A line for James McAvoy —

"Pardon me boy, is this the Transylvania Station?"

Bolyai 'worlds out of nothing' quote

See as well Worlds Out of Nothing ,  by Jeremy Gray.

Hijacking the Vatican

Filed under: General — Tags: , — m759 @ 12:42 pm

Rothstein's 'Emblems of Mind,' 1995, cover illustrations by Pinturicchio from Vatican

Cover illustration— Arithmetic and Music,
Borgia Apartments, the Vatican.

See also Rothstein in this journal.

Related posts: The Eightfold Hijacking.

Monday, September 30, 2019

Sacred Woo*

Filed under: General — Tags: — m759 @ 11:26 pm

Victor Zuckerkandl, 'Sound and Symbol,' p. 338

* The title refers to a recent Sunday Doonesbury cartoon.

Defining a Space

Filed under: General — Tags: , — m759 @ 8:57 pm

See also Nada Brahma  in this  journal.

Binarily Augmented Multiplicity

Filed under: General — Tags: — m759 @ 1:21 pm

September Singularity

Filed under: General — Tags: — m759 @ 1:00 pm

(A sequel to the previous post, Multiplicity on Michaelmas.)

"Tony is on the couch . . ."   Cf.  The Analyst , Michaelmas evening.

"Tony Stark: That's how I wished it happened.
Binarily Augmented Retro-Framing, or BARF.
God, I gotta work on that acronym.
An extremely costly method of hijacking the
hippocampus to . . . clear traumatic memories. Huh."

Multiplicity on Michaelmas

Filed under: General — Tags: , , — m759 @ 5:54 am

"We need a multiplicity of viewpoints."

— Philip Pullman in a New Yorker  interview
     published yesterday 

See as well Pullman's "Golden Compass"
in posts tagged

Nothing New.

Sunday, September 29, 2019

The Analyst

Filed under: General — Tags: , — m759 @ 8:00 pm

"The analyst, by freeing himself from the 'enchainment to past and future',
casts off the arbitrary pattern and waits for new aesthetic form to emerge,
which will (it is hoped) transform the content of the analytic encounter."

— From Psychoanalytic Aesthetics: The British School ,
by Nicola GloverChapter 4  

Shana Tova .

Spiritual Kin

Filed under: General — Tags: , , , — m759 @ 12:00 pm

"The 15 Puzzle and the Magic Cube
are spiritual kin …."

"Metamagical Themas"  column,
Douglas R. Hofstadter, Scientific American ,
Vol. 244, No. 3 (March 1981), pp. 20-39

As are the 15 Schoolgirls and the Eightfold Cube.

Stage Direction: “Comments Off.”

Filed under: General — Tags: , , , — m759 @ 11:29 am

The previous post dealt with "magic" cubes, so called because of the
analogous "magic" squares. Douglas Hofstadter has written about a
different, physical , object, promoted as "the  Magic Cube," that Hofstadter
felt embodied "a deep invariant":

Dominus Illuminatio (from the Oxford motto)

Filed under: General — Tags: — m759 @ 10:01 am

Related literary remarks — Raiders of the Lost Birthday.

Saturday, September 28, 2019

Annals of Misleading Titles

Filed under: General — m759 @ 1:06 pm

Google search result: 'The Code,' by O'Mara

For Dan Brown fans — See posts now tagged Masonic Bricks.

Friday, September 27, 2019

Country Matters or: Ventrickolist

Filed under: General — m759 @ 7:27 pm

Richard Sandomir in this evening's online New York Times

On Sept. 24, 1950, Jimmy Nelson, a skinny 21-year-old ventriloquist, was introduced by Ed Sullivan on his Sunday night variety show, “Toast of the Town,” as “the greatest I’ve ever seen in his field.”

Mr. Nelson was clean-cut and genial, with an air of boyish mischief. His dummy was a smart aleck in a suit and bow tie.

“My name is Danny O’Day,” the dummy said to the audience. 

“This schnookle standing next to me is Jimmy Nelson. The kid thinks he’s a ventrickolist.”

“That’s ventriloquist,” Mr. Nelson said, starting a rapid-fire exchange with his dummy.

“Ventrickolist,” Danny said.

“Ventriloquist,” Mr. Nelson said.

It was an auspicious national debut….

Nelson reportedly died at 90 on Tuesday, September 24, 2019.

The remarks on Harvard existential nihilism posted here on that date
suggest a graphic illustration …

Venn trick o'list —

Nothing Galore

See as well a post from the preceding day,
Rabbit Hole Meets Memory Hole.

The Black List

Filed under: General — Tags: , , — m759 @ 11:46 am

"… Max Black, the Cornell philosopher, and others have pointed out
how 'perhaps every science must start with metaphor and end with
algebra, and perhaps without the metaphor there would never have
been any algebra' …."

— Max Black, Models and Metaphors, Cornell U. Press, 1962,
page 242, as quoted in Dramas, Fields, and Metaphors, by 
Victor Witter Turner, Cornell U. Press, paperback, 1975, page 25
 

Metaphor —

Algebra —

The 16 Dirac matrices form six anticommuting sets of five matrices each (Arfken 1985, p. 214):

1. alpha_1alpha_2alpha_3alpha_4alpha_5,

2. y_1y_2y_3y_4y_5,

3. delta_1delta_2delta_3rho_1rho_2,

4. alpha_1y_1delta_1sigma_2sigma_3,

5. alpha_2y_2delta_2sigma_1sigma_3,

6. alpha_3y_3delta_3sigma_1sigma_2.

SEE ALSO:  Pauli Matrices

REFERENCES:

Arfken, G. Mathematical Methods for Physicists, 3rd ed.  Orlando, FL: Academic Press, pp. 211-217, 1985.

Berestetskii, V. B.; Lifshitz, E. M.; and Pitaevskii, L. P. "Algebra of Dirac Matrices." §22 in Quantum Electrodynamics, 2nd ed.  Oxford, England: Pergamon Press, pp. 80-84, 1982.

Bethe, H. A. and Salpeter, E. Quantum Mechanics of One- and Two-Electron Atoms.  New York: Plenum, pp. 47-48, 1977.

Bjorken, J. D. and Drell, S. D. Relativistic Quantum Mechanics.  New York: McGraw-Hill, 1964.

Dirac, P. A. M. Principles of Quantum Mechanics, 4th ed.  Oxford, England: Oxford University Press, 1982.

Goldstein, H. Classical Mechanics, 2nd ed.  Reading, MA: Addison-Wesley, p. 580, 1980.

Good, R. H. Jr. "Properties of Dirac Matrices." Rev. Mod. Phys. 27, 187-211, 1955.

Referenced on Wolfram|Alpha:  Dirac Matrices

CITE THIS AS:

Weisstein, Eric W.  "Dirac Matrices."

From MathWorld— A Wolfram Web Resource. 
http://mathworld.wolfram.com/DiracMatrices.html

Desiring the exhilarations of changes:
The motive for metaphor, shrinking from
The weight of primary noon,
The A B C of being,

The ruddy temper, the hammer
Of red and blue, the hard sound—
Steel against intimation—the sharp flash,
The vital, arrogant, fatal, dominant X.

— Wallace Stevens, "The Motive for Metaphor"

Algebra for Schoolgirls

Filed under: General — Tags: , , — m759 @ 8:37 am

The 15 points of the finite projective 3-space PG(3,2)
arranged in tetrahedral form:

The letter labels, but not the tetrahedral form,
are from The Axioms of Projective Geometry , by
Alfred North Whitehead (Cambridge U. Press, 1906).

The above space PG(3,2), because of its close association with
Kirkman's schoolgirl problem, might be called "schoolgirl space."

Screen Rant  on July 31, 2019:

A Google Search sidebar this morning:

Apocalypse Soon!

Thursday, September 26, 2019

Identity

Filed under: General — Tags: , — m759 @ 8:53 am


Related story:

E is for Einheit

Personalities …

Filed under: General — Tags: , — m759 @ 8:06 am

For Dan Brown 

It’s a combination of elation and fear, a certain kind of terror,”
Dr. Scott-Warren, a lecturer at Cambridge University, said
Thursday [Sept. 19] in an interview, describing his feelings.

“As a scholar, you get a sense of the fixed landmarks,” he said.
“Suddenly to have a new landmark to come right up through
the ground is quite disconcerting; there’s something alarming
about that.”

Wednesday, September 25, 2019

Before Personalities …

Filed under: General — Tags: — m759 @ 6:10 pm

Connecting the Dots

Filed under: General — Tags: , — m759 @ 5:27 pm

"A scholar in England suspected annotations in a First Folio
at the Free Library of Philadelphia were John Milton’s, so he
connected the dots . . . ." — The New York Times  last Thursday

It’s a combination of elation and fear, a certain kind of terror,”
Dr. Scott-Warren, a lecturer at Cambridge University, said
Thursday in an interview, describing his feelings.

“As a scholar, you get a sense of the fixed landmarks,” he said.
“Suddenly to have a new landmark to come right up through
the ground is quite disconcerting; there’s something alarming
about that.”
. . . .

"Dr. Scott-Warren  studies the history of books as material objects …."

Halloween Global Joy

Filed under: General — m759 @ 10:45 am

"The sad truth is that, by and large, mathematics is feared
and perhaps even openly disliked in the popular culture of
the majority of countries across the globe. At the very least,
math is often perceived as 'hard' and 'sterile,' pehaps even
remote, and unforgiving."

James Tanton, Halloween 2018

Related material —

Language Game

Filed under: General — Tags: , — m759 @ 9:28 am

Previous posts now tagged Pyramid Game suggest

A possible New Yorker  caption:   " e . . . (ab) . . . (cd) . "

Caption Origins —

Playing with shapes related to some 1906 work of Whitehead:

Hollywood Headlines

Filed under: General — Tags: — m759 @ 8:25 am

'Assassin's Creed' . . . . Read more "

 

 

Tuesday, September 24, 2019

In Memoriam

Filed under: General — m759 @ 9:46 pm

"Robert Hunter, the man behind the poetic and mystical
words for many of the Grateful Dead’s finest songs, died
Sept. 23 at at his home in San Rafael, Calif. He was 78."

— By John Rogers in The Washington Post ,
​September 24, 2019, at 5:58 p.m. EDT 

In memoriam The Annotated  "Ripple."

Emissary

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

Thursday, September 12, 2019

Tetrahedral Structures

Filed under: General — Tags:  —
m759 @ 8:11 PM 

In memory of a Church emissary  who reportedly died on  September 4 . . . .

Playing with shapes related to some 1906 work of Whitehead:

Russianization

Filed under: General — m759 @ 11:00 am

From a Log24 search for Dolgachev

"The purpose of mathematics cannot be derived from 
an activity inferior to it but from a higher sphere of
human activity, namely, religion."

— Igor Shafarevitch, 1973 remark published in 1982.

"Perhaps."

— Steven H. Cullinane, February 13, 2019 
 

A Hollywood version

American Mathematical Society News

Filed under: General — Tags: — m759 @ 10:15 am

  "Specifically, on May 6 of this year …." …

If I Had a Hammer …

Filed under: General — m759 @ 9:32 am

Fire and Ice: Dom vs. DOM

Filed under: General — m759 @ 8:56 am

The "Dom" of the title is the cathedral of Cologne.
The DOM is the Document Object Model of HTML:

Existential Lust

Filed under: General — m759 @ 8:22 am

For more-recent existential vibrations, see yesterday morning's post
on a Crimson  philosopher's "Finding Purpose Through Nihilism."

Monday, September 23, 2019

First and Last Things

Filed under: General — Tags: — m759 @ 7:55 pm

“We shall now give a brief summary of the beginnings of the Glass Bead Game….

The Game was at first nothing more than a witty method for developing memory and ingenuity among students and musicians. And as we have said, it was played both in England and Germany before it was ‘invented’ here in the Musical Academy of Cologne, and was given the name it bears to this day, after so many generations, although it has long ceased to have anything to do with glass beads."

Reflections in a Cartoon Graveyard

Filed under: General — Tags: , — m759 @ 11:58 am

Images from this  journal related to the above cartoon —

(Click images for related posts.)

Hard Candy on Good Friday 2006

A sketch adapted from Girl Scouts of Palo Alto —

Finding Purpose

Filed under: General — m759 @ 10:47 am

There is also  finding purpose through dating

(from the source code for the above Crimson  article)

Related material — D8ing.

Rabbit Hole Meets Memory Hole:

Filed under: General — Tags: , , — m759 @ 9:11 am

The disappearance of "Christo et Ecclesiae" at Harvard

Rabbit Hole 

Memory Hole

The above Harvard seal in a PDF —

The same page, minus the seal, today at the Internet Archive — 

For a larger image of the seal-less page, click here.

Happy Fall 2019!

Click to enlarge.

Sunday, September 22, 2019

Colorful Tale

Filed under: General — Tags: , , — m759 @ 7:59 pm

“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

Indeed it is.

From page 180, Logicomix — It was a dark and stormy night

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

Whitehead and the Relativity Problem

Filed under: General — Tags: , — m759 @ 2:00 pm

"This is the relativity problem: to fix objectively a class of
equivalent coordinatizations and to ascertain the group of
transformations S mediating between them."
— Hermann Weyl, The Classical Groups,
    Princeton University Press, 1946, p. 16

Simplex Sigillum Veri

Filed under: General — m759 @ 5:21 am

(Continued from November 27, 2010.)

The previous post suggests a review of a Tilman Piesk
illustration, with the general form of a 4-simplex, from
the Wikipedia article titled Simplex .  As the article 
notes, the lines shown connecting points are those of a
tesseract.

Tetrahedral tesseract adapted from Piesk illustration in Wikipedia 'Simplex' article

Saturday, September 21, 2019

Annals of Random Fandom

Filed under: General — Tags: , , , — m759 @ 5:46 pm

For Dan Brown fans …

… and, for fans of The Matrix, another tale
from the above death date: May 16, 2019 —

An illustration from the above
Miracle Octad Generator post:

Related mathematics — Tetrahedron vs. Square.

Explorer or Inventor?

Filed under: General — m759 @ 11:26 am

Detail from an OpenScholar tutorial —

The above phrase from Cicero means, according to 
the usual translation, "explorer of truth."

Some may prefer a different translation of "inventore."

Related material —

 

Extremely  Limited Book Preview

Filed under: General — m759 @ 9:42 am

See also A Counting-Pattern.

Exploring Egypt: The Sequel to Exploring Schoolgirl Space*

Filed under: General — Tags: — m759 @ 9:02 am

     * See Schoolgirl Space in this journal.

Six Dots

Filed under: General — Tags: — m759 @ 8:11 am

See other posts now tagged Six Dots.

Related narrative:  Raiders of the Lost Ring .

Friday, September 20, 2019

The Sun Ra Poet

Filed under: General — Tags: — m759 @ 1:33 pm

"Mr. Dalachinsky was in his element on Sept. 14 at the Islip Art Museum
on Long Island, where he gave a reading after having attended a concert
by the Sun Ra Arkestra earlier that afternoon in Manhattan. Not long after
the reading, his wife said, he had a stroke and a cerebral hemorrhage.
He died the next day at Southside Hospital in Bay Shore. He was 72."

— Neil Genzlinger in The New York Times  today

Also on Sept. 14 —

See as well Curse of the Fire Temple.

Garbage-Pail Kid

Filed under: General — Tags: — m759 @ 10:02 am

In the spirit of the Linz website in the previous post
the title refers to New Yorker  writer Adam Gopnik:

Garbage-Pail Kids: Adam Bomb

Tuesday, November 7, 2017

Polarities and Correlation

Filed under: Uncategorized — Tags:  
— m759 @ 11:00 PM 

Adam Gopnik on Philip Roth

Adam Gopnik on Philip Roth and Mickey Sabbath

See also a search in this  journal for Polarity + Correlation.

Das Humankapital , or:  The Jews and Linz*

Filed under: General — m759 @ 8:42 am

From the above aldaily.com link —

https://www.nybooks.com/articles/2019/10/10/
jia-tolentino-song-my-self-care/

From a review of

Trick Mirror:  Reflections on Self-Delusion 
by Jia Tolentino
Random House, 303 pp., $27.00

… as she grew up in Texas. In a way, she was primed for the illimitable expanse of the Internet by her Christian upbringing, which teaches its followers that everyone on earth is being watched by God. It gave her a flight of optimism, before this same system slowly but surely “metastasize[d] into a wreck”: “this feverish, electric, unlivable hell.” While the Internet was meant to allow you to reach out to any- and everyone without a hint of the cruel discriminations that blight our world, it turned into the opposite, a forum where individuals are less speaking to other people than preening and listening to themselves—turning themselves into desirable objects to be coveted by all. It became, that is, the perfect embodiment of consumer capitalism, where everything can be touted in the marketplace.

How, Tolentino asks, did the idea take hold that “ordinary personhood would seamlessly adjust itself around whatever within it would sell”? How did our basic humanity come to be “reframed as an exploitable viral asset”? 

Related course — "History and Human Capital" at Harvard, a course
taught last spring by professors Claudia Goldin and Lawrence Katz —

Related reading — "Human Capital," by Claudia Goldin:

The above material suggested this post's title, "Das Humankapital ."

The same phrase is also the title of a perceptive website from Linz, Austria.

* For the alternative title, see a Wikipedia article on The Jew of Linz .

Thursday, September 19, 2019

OOP

Filed under: General — Tags: , — m759 @ 12:00 pm

"… objects have a notion of 'this' or 'self.' " — Wikipedia

For related notions, see other posts tagged Quark Rock and

"Before time began, there was the Cube." — Optimus Prime

Marvel Gospel

Filed under: General — Tags: — m759 @ 11:28 am

Sound familiar?

Wednesday, September 18, 2019

The Siegfried Line

Filed under: General — m759 @ 9:01 pm

See also this  journal on the above date (Jan. 27, 2012).

Backstory:  Search this journal for sciencenews.

Powers of X

Filed under: General — Tags: , — m759 @ 11:45 am

Screen Rant  on July 31, 2019 —

The above space PG(3,2), because of its close association with
Kirkman's schoolgirl problem, might be called "schoolgirl space."

See as well a Log24 post from the above Screen Rant  date —

The Epstein Chronicles, or:  Z  is for Zorro .

Toy Problems

Filed under: General — Tags: — m759 @ 10:45 am

The above story's conclusion —

" … the current state of the art in quantum computing is still
not quite ready for solving anything but toy problems and
testing basic algorithms."

From "Annals of Square Space" (Log24, Sept. 3, 2019) —

" 'Before I go somewhere for a story, I have a certain understanding of
what form it will take, and when I get there, it’s always far, far more
complicated,' says the journalist and poet Eliza Griswold, over lunch
in Gramercy Park.  'They begin with a neat little bow' — she pantomimes
tying it, her wide blue eyes growing wider — 'and then:  kaboom.' ”

— VOGUE Lives: Eliza Griswold, August 27, 2010, 9:10 AM,
     by Megan O'Grady

Battle Song

Filed under: General — Tags: — m759 @ 9:53 am

Catch 22 song: 'Straighten Up and Fly Right'

The Perpetual Identity Crisis

Filed under: General — Tags: — m759 @ 8:56 am

"There is  such a thing as a 4-set." — Saying adapted
from a 1962 young-adult novel.

Midrash — An image posted here on August 6

Unity

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

“I” as black monolith:

http://www.log24.com/log/pix11/110412-32x192plusmargin6.bmp

Unity

Roman numeral I
as well as capital I.

Dimensions: 6×1.

Tuesday, September 17, 2019

For Cambridge 38*

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

* A reference to a Harvard Crimson  article from February 28, 1963.

The Quarks and the Rock

Filed under: General — Tags: — m759 @ 7:30 am

Excerpt from a long poem by Eliza Griswold 
in the current New Yorker

Monday, September 16, 2019

Gropius Moritat

Filed under: General — Tags: — m759 @ 11:43 pm

Related material

See as well, from the fiftieth anniversary of Gropius's death,
Log24 posts now tagged Gropius Moritat.

Emergence

Filed under: General — Tags: , , — m759 @ 10:01 am

"Elementary particles are the most fundamental building blocks
of nature, and their study would seem to be an expression of
simplification in its purest form. The essence of complexity
research, by contrast, is the emergence of new kinds of order
that are only manifest when systems are large and messy."

— Sean Carroll in an opinion piece that concludes as follows:

The above plug for Sean Carroll's book
The Big Picture : On the Origins of
Life, Meaning, and the Universe Itself
   
suggests

'Forty-two' in 'The Padre'

Equilibrium

Filed under: General — Tags: — m759 @ 3:50 am

From the previous post

Postscript for Weisheit the Rabbi :  Grammaton.

Sunday, September 15, 2019

Changes Interlock

Filed under: General — m759 @ 12:07 pm

"Changes interlock…." — John Dewey

Indeed they do.

'The Eddington Song'

For Weisheit, the Rabbi

Filed under: General — m759 @ 3:30 am

See also Log24 remarks from the date of Greene's death
in posts now tagged Bregnans

A page related to Eleanor Cook's "wonderful first line"
quoted above from A Reader's Guide to Wallace Stevens :

A Reader's Guide to Eleanor Cook

Saturday, September 14, 2019

Landscape Art

Filed under: General — Tags: , — m759 @ 11:18 am

From "Six Significant Landscapes," by Wallace Stevens (1916) —

VI
 Rationalists, wearing square hats,
 Think, in square rooms,
 Looking at the floor,
 Looking at the ceiling.
 They confine themselves
 To right-angled triangles.
 If they tried rhomboids,
 Cones, waving lines, ellipses —
 As, for example, the ellipse of the half-moon —
 Rationalists would wear sombreros.
 

The mysterious 'ellipse of the half-moon'?

But see "cones, waving lines, ellipses" in Kummer's Quartic Surface 
(by R. W. H. T. Hudson, Cambridge University Press, 1905) and their
intimate connection with the geometry of the 4×4 square.

The Inappropriate Capstone

Filed under: General — Tags: , — m759 @ 4:59 am

The All-Night Record Player

Filed under: General — Tags: , — m759 @ 4:00 am

See "Politics of Experience" and "Blue Guitar."

IMAGE- Scene from 'Oblivion' (2013) 

Friday, September 13, 2019

Follow the Adjective

Filed under: General — Tags: — m759 @ 12:14 pm

 Eddie?

Schoolgirl Space…

Filed under: General — Tags: , — m759 @ 4:56 am

According to Wikipedia

See also Schoolgirl Space in this journal.

« Newer PostsOlder Posts »

Powered by WordPress