Log24

Monday, February 28, 2022

Church Song

Filed under: General — Tags: — m759 @ 10:24 pm

"February made me shiver . . . ."

Sunday, February 27, 2022

Pyramid vs. Cube … Continued

Filed under: General — m759 @ 9:11 pm

See  Sith Pyramid  and  Jedi Cube .

Related reading . . .

Pyramid:

https://www.theguardian.com/commentisfree/
2022/feb/27/vladimir-putin-russia-ukraine-power

Cube:

"To enter into the world of Putin’s favorite philosophers
is to enter a world full of melodrama, mysticism and
grandiose eschatological visions."

— David Brooks in the online New York Times  on March 3, 2014

Scholium:

This  journal  on the above NY Times  date

Bokeh in Berlin

Filed under: General — m759 @ 12:44 pm

Impenetrability Revisited

Filed under: General — m759 @ 12:11 pm

From a New York Times  obituary  online today —

“He was an absolutely brilliant reader
at taking what seemed to be the knots,
or the impenetrability, or the downright
insanity of a piece of writing, and just
saying, ‘Hey, guys, that’s the point.’”

Jacqueline Rose

See as well Humpty Dumpty and unit e .

Saturday, February 26, 2022

Annals of Architecture:  Brutal Minimalism

Filed under: General — Tags: — m759 @ 11:29 pm

Annals of Meta-Reality . . . Welcome to Hell.

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

See Nolanism and the Kiev Opera.

Beyond Rubik: The Mathieu Cube

Filed under: General — Tags: , — m759 @ 1:18 pm

Click to enlarge.

Thursday, February 24, 2022

Geometric Theology

Filed under: General — Tags: — m759 @ 9:23 pm

Expanding on T. S. Eliot's remark that

"The hint half guessed,
the gift half understood,
is Incarnation"

more posts are now tagged "Geometric Theology."

Wednesday, February 23, 2022

The Punchline

Filed under: General — Tags: — m759 @ 11:59 pm

Maybe Nicolas Cage knows the punchline.

The Unity of Mathematics

Filed under: General — Tags: , — m759 @ 11:30 pm

https://en.wikisource.org/wiki/
A_History_of_Mathematics/
Recent_Times/Theory_of_Functions

See also Gopel in this  journal.

Fandango Tale

Filed under: General — Tags: — m759 @ 11:33 am

In memory of a Procol Harum singer who reportedly died on Feb. 19  —

From a post of Dec. 1, 2011

And so it was that later
as the miller told his tale
that her face, at first just ghostly,
turned a whiter shade of pale

— Procol Harum song at beginning and end
of “The Net” (1995)

“Lord Arglay had a suspicion that the Stone
would be purely logical.  Yes, he thought, but
what, in that sense, were the rules of its pure logic?”

Many Dimensions  (1931), by Charles Williams,
quoted here on Kristallnacht 2011

Leaving the Farm

Filed under: General — Tags: , — m759 @ 1:02 am

From the current online New Yorker , a barnyard elegy:

From the top  of the New Yorker  homepage tonight:

Locking the barn door after the chandelier is gone —

(Click to enlarge.)

Tuesday, February 22, 2022

Borracho

Filed under: General — m759 @ 6:48 pm

The Feuerstein Gambit

Filed under: General — m759 @ 4:06 pm

Feuerstein reportedly died at 86 on Candlemas 2022.

2×8

Filed under: General — m759 @ 2:22 pm

2:22 PM ET on 2/22/22.

Monday, February 21, 2022

“Rebel Regions” … Not Unlike Texas

Filed under: General — m759 @ 2:41 pm

Her Story

Filed under: General — m759 @ 2:12 pm

 The above White Goddess  new-edition publication date:  Oct. 8, 2013.

This  journal on that date

"Please wait as your operating system is initiated."

Stimulus

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

IMAGE- Weyl in 1949 on the relativity problem

"The class is objectively characterized, but not
the individual coordinate assignment."

Tell it to Watchduck, Hermann.

See a related remark by Quack5quack in Raiders of the Lost Coordinates.

Variation on an Old Joke

Filed under: General — Tags: — m759 @ 11:02 am

An image linked to* in Mapping Problem Continued (Log24, 16 July 2012) —

* The link is on the phrase "may be deduced."

Sunday, February 20, 2022

Ceremonial Space

Filed under: General — Tags: — m759 @ 1:23 pm

From posts now tagged iching.space (also a URL) —

IMAGE- Concepts of Space

 

4×4 Nomenclature

Filed under: General — Tags: — m759 @ 2:35 am

The geometry of the 4×4 square may be associated with the name
Galois, as in "the Galois tesseract," or similarly with the name Kummer. 
Here is a Google image search using the latter name —

(Click to enlarge.)

 

Saturday, February 19, 2022

Geek Chic

Filed under: General — Tags: — m759 @ 1:04 pm

"The nightingale tells his fairy tale" — Song lyric

Friday, February 18, 2022

Fairytale Kindergarten

Filed under: General — Tags: , , — m759 @ 1:20 pm

Thursday, February 17, 2022

Parallax Viewpoints

Filed under: General — m759 @ 11:32 pm

In memory of a veteran intelligence officer who
reportedly died on Feb. 13 —

Parallax illustrated, from Wikipedia-- A star on two background colors, blue and red

Related literature —

 

Space Memorial

Filed under: General — m759 @ 1:27 pm

"FILE – Retired Sandinista Gen. Hugo Torres poses for portrait
at his home, in Managua, Nicaragua, May 2, 2018."

— Photo caption from a Feb. 12 Washington Post  obituary 

Also on May 2, 2018 —

Related theology —

Tuesday, February 23, 2016

Revolutionary

Filed under: General — m759 @ 7:14 PM 

From New York Times  obituary today —

"The Rev. Fernando Cardenal, a son of privilege
who embraced Latin America’s poor as a revolutionary
priest and brazenly defied Pope John Paul II’s order to
quit Nicaragua’s leftist cabinet in the 1980s, died on
Saturday in Managua. He was 82."

Photo caption from the same obituary —

"Fernando Cardenal in 1990. As education minister of
Nicaragua under the Sandinistas in the 1980s, he
oversaw a sweeping campaign credited with reducing
illiteracy to 13 percent from 51 percent."

This alleged literacy improvement makes him sound like
Protestant  revolutionary.

For a Catholic  view of literacy, see The Gutenberg Galaxy .

See also the post Being Interpreted (Aug. 14, 2015) — 

Four Dots, Six Lines

Filed under: General — Tags: — m759 @ 1:46 am

"There is  such a thing  as  a tesseract." 

— Mrs. Whatsit in  A Wrinkle in Time  (1962)

"Simplify, simplify." — Henry David Thoreau in Walden  (1854)

Von Franz representation of the I Ching's Hexagram 2, The Receptive
 

A Jungian on this six-line figure:

“They are the same six lines that exist in the I Ching…. Now observe the square more closely: four of the lines are of equal length, the other two are longer…. For this reason symmetry cannot be statically produced and a dance results.”
 
— Marie-Louise von Franz,
   Number and Time  (1970)

Wednesday, February 16, 2022

Meta Mates

Filed under: General — Tags: — m759 @ 11:40 am

Tuesday, February 15, 2022

“… Then We Take Berlin” — Leonard Cohen

Filed under: General — Tags: , — m759 @ 1:01 pm

"Stories are the only way people can absorb information
in any depth" — Stephen Lussier, retired De Beers executive

Related story — De Beer's Consolidated Mine
 

“Nothing Lasts Forever” will screen at Berlinale 
on February 12th at 9 pm at Cubix 7, February 17th
at 9 pm at Cubix 5 and 6, and February 18th at 6 pm
at Cubix 5 and 6. 
— https://moveablefest.com

See as well "Story Theory of Truth" in this  journal.

Shubert Alley as Nightmare Alley

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

Max Bialystock discovers a new playwright

See as well this journal on
the above "Diamond Theory" date:

Monday, February 14, 2022

Cable Girl

Filed under: General — Tags: — m759 @ 3:27 pm

"The Cable Guy isn't necessarily the first one you would expect
to make a comeback, but that's exactly what he has done
this Sunday during the big game."

Read More:
https://www.slashfilm.com/766503/the-trouble-with-super-bowl-ads-is-
theres-no-danger-music-but-there-is-jim-carrey-as-the-cable-guy/

Related material — Cable Girl

Sugar Cube

Filed under: General — Tags: — m759 @ 2:23 pm

Click image for the source

糖果  咖啡 Candy Coffee  (Google translation)

Related cinematic image

Image-- Sugar cube in coffee, from 'Bleu'

Artbusters: Cubism

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

" Welcher Art ist die ursprüngliche Einheit,
daß sie sich in diese Scheidung auseinanderwirft,
und in welchem Sinn sind die Geschiedenen
hier als Wesung der Ab-gründigkeit gerade einig?
Hier kann es sich nicht um irgend eine »Dialektik«
handeln, sondern nur um die Wesung des Grundes
(der Wahrheit also) selbst."

— Heidegger 

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

Sunday, February 13, 2022

Kabbalah for the Metaverse

Filed under: General — Tags: — m759 @ 7:46 pm

From The Atlantic  on February 10, 2022 —

"Facebook Has a Superuser-Supremacy Problem" —

What else is new?
 

From this  journal on June 5, 2019

Also  on June 5, 2019 —

For a Time

Filed under: General — m759 @ 3:44 am

This  journal on the above date —

The New York Times  yesterday reported that the above dancer,
no longer very young, died on February 3, 2022.

Some Log24 flashback images reposted on that  date

See as well two Dec. 22, 2002, posts
now tagged Trifecta —

Saturday, February 12, 2022

Das Geheimnis der Einheit

Filed under: General — Tags: , , — m759 @ 11:13 pm

Thomas Mann on "the mystery of the unity"

Mann on Schopenhauer: Psychoanalysis and 'The Will'

"Denn um zu wiederholen, was ich anfangs sagte:
in dem Geheimnis der Einheit von Ich und Welt,
Sein und Geschehen, in der Durchschauung des
scheinbar Objectiven und Akzidentellen als
Veranstaltung der Seele glaube ich den innersten Kern
der analytischen Lehre zu erkennen." (GW IX 488)

An Einheit-Geheimnis  that is perhaps* more closely related
to pure mathematics** —

"What is the nature of the original unity
that throws itself apart in this separation,
and in what sense are the separated ones
here as the essence of the abyss? 

Here it cannot be a question of any kind of 'dialectic,' 
but only of the essence of the ground
(that is, of truth) itself." [Tr. by Google]

" Welcher Art ist die ursprüngliche Einheit,
daß sie sich in diese Scheidung auseinanderwirft,
und in welchem Sinn sind die Geschiedenen
hier als Wesung der Ab-gründigkeit gerade einig?
Hier kann es sich nicht um irgend eine »Dialektik«
handeln, sondern nur um die Wesung des Grundes
(der Wahrheit also) selbst."

Heidegger 

* Or perhaps not .

** For a relevant Scheidung , see Eightfold Cube.

Food for Thought

Filed under: General — m759 @ 3:54 pm

See also Hamburger Menu.

“What’s up, DOC?”

Filed under: General — m759 @ 2:33 pm

The previous post suggests a review . . .

Friday, February 11, 2022

Space, Piled High and Deep

Filed under: General — Tags: , — m759 @ 11:59 pm

"… out of all things there comes a unity,
and out of a unity all things . . . . "

— Heraclitus, according to de Beer quoting McKirahan

An image we may regard as illustrating 
the group-identity symbol "e" for "Einheit " —

Simplex Sigillum Veri.

For Space Groupies

Filed under: General — Tags: , — m759 @ 5:31 pm

A followup to Wednesday's post Deep Space

Related material from this journal on July 9, 2019

Cube Bricks 1984 —

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

From "Tomorrowland" (2015) —

From other posts tagged 1984 Cubes

De Beer’s Consolidated Mine

http://www.log24.com/log/pix10B/101202-DreidelAndStone.jpg

The misleading image at right above is from the cover of
an edition of Charles Williams's classic 1931 novel 
Many Dimensions  published in 1993 by Wm. B. Eerdmans.

But seriously . . .

Thursday, February 10, 2022

“Kimi, Siri. Siri, Kimi.”

Filed under: General — Tags: — m759 @ 11:35 pm

From "Siri + Wechsler" in this journal —

For Little Man Tate —

IMAGE- Wechsler block-design cubes and related WAIS-R manual

Related material — Wechsler in this journal and
an earlier Siri Hustvedt art novel, from 2003 —

Mark and Lucille, Bill and Violet, Al and Regina,
etc., etc., etc. —

IMAGE- Siri Hustvedt on the name 'Wechsler' in 'What I Loved'

Related material —

Tech News

Filed under: General — m759 @ 3:38 pm

Some personal memories triggered by the above —

The novel The Lathe of Heaven , the film "Paper Towns," and
the images in Instance of a Fingerpost (Log24, July 24, 2015).

Science News:  Bon Voyage!

Filed under: General — m759 @ 1:41 pm

See as well a remark on DNA  here  on Tuesday.

Block Design Subtest: 
Psycoloquy Meets Psycho Loki

Filed under: General — Tags: , — m759 @ 12:07 pm

Related illustration from a search in this  journal for Wechsler

Above: Dr. Harrison Pope, Harvard professor of psychiatry,
demonstrates the use of the Wechsler Adult Intelligence Scale (WAIS)
“block design” subtest.

 — From a Log24 search for “Harrison Pope.”

Wednesday, February 9, 2022

Deep Space

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

For your consideration:

See as well this  journal on "Hardy + Depth."

8!

Filed under: General — Tags: , , , — m759 @ 12:03 am

Conwell, 1910 — 

(In modern notation, Conwell is showing that the complete
projective group of collineations and dualities of the finite
3-space PG (3,2) is of order 8 factorial, i.e. "8!"
In other words, that any  permutation of eight things may be
regarded as a geometric transformation of PG (3,2).)

Later discussion of this same "Klein correspondence"
between Conwell's 3-space and 5-space . . .

A somewhat simpler toy model —

Page from 'The Paradise of Childhood,' 1906 edition

Related fiction —  "The Bulk Beings" of the film "Interstellar."

Tuesday, February 8, 2022

In Search Of . . .

Filed under: General — m759 @ 9:19 pm

Beauty Bare!

Related: https://www.tiktok.com/@stevenhcullinane/
video/7066662037895777582

In memory of Nick Tosches

Filed under: General — Tags: , — m759 @ 1:49 pm

For your consideration:  "Nightmare Alley" Oscar nominations

Costume design, production design, cinematography, Best Picture.

See as well the introduction by Nick Tosches to the novel .

A touch I personally like:  Over the end credits, Hoagy Carmichael's
"Stardust" plays. From related remarks (here abridged) by poet
David Lehman on November 22, 2015 (the feast of St. Cecilia) —

"Every year on this day I think unfailingly of three things:

— that today is Hoagy Carnichael's birthday ….

— that if time were elastic I would write a series of
   popular history novels ….

— that paranoid conspiracy theories are based on
   our fundamental inability to understand events.

From this  journal on November 22, 2015 —

http://www.log24.com/log/pix11C/111127-Ong-PresenceOfTheWord.jpg

Directions Out

Filed under: General — Tags: — m759 @ 12:46 am

On reading about DNA:

"Suddenly it was clear to me 
that all the beautiful complexity of life
had simplicity at its core," he says.
"This is the kind of thing mathematicians love." 

Eric Lander in "The 2004 TIME 100 — Our list
of the most influential people in the world today"

The date on the above TIME piece is Monday,
Apr. 26, 2004. Remarks in this  journal on that date
are now tagged Directions Out.

Monday, February 7, 2022

Science News

Filed under: General — Tags: , , — m759 @ 3:06 pm

See the above science adviser in this  journal —

"Non-Chaos Non-Magic," Feb. 26, 2021.

Morphart Meets Morph Art

Filed under: General — Tags: , — m759 @ 1:51 pm

Warren (PA) Public Library's Instagram
on January 21, 2022 —

Morphart

Morph Art — from Raiders of the Lost Coordinates

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

The IDE of March

Filed under: General — Tags: — m759 @ 12:29 pm

Sunday, February 6, 2022

Ringing the Changes

Filed under: General — Tags: , — m759 @ 11:23 pm

In memory of Hale Trotter, a mathematician who reportedly
died at Princeton, N.J., on Jan. 17, 2022.

Other perspectives —

“The carnival is an incredibly close-knit, hermetic society.” 

— Guillermo del Toro, director and co-writer of
the new remake of "Nightmare Alley"

Dialogue from that remake  —

STAN — How do you ever get a guy to geek?
CLEM — Oh- I ain’t going to crap you up. It ain’t easy.

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

Jumpers for Lehman

Filed under: General — Tags: — m759 @ 5:11 pm

"Leave a space." — Tom Stoppard, "Jumpers"

Animating the Savoir

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

                                             ". . . It is as if
We had come to an end of the imagination,
Inanimate in an inert savoir.

— Wallace Stevens, “The Plain Sense of Things

"In my end . . . ." — T. S. Eliot

Thursday, March 22, 2018

The Diamond Cube

Tags:  — m759 @ 11:32 AM 

. . . .

Here is an animated GIF that shows the basic unit
for the "design cube" pages at finitegeometry.org.

See a note from Sept. 15, 1984
 (perhaps the last day of life for Richard Brautigan).

Saturday, February 5, 2022

Hexagram 61 Revisited

Filed under: General — m759 @ 4:10 pm

The online New York Times  today  reporting a  Jan. 29 death:

"Mr. Dylan asked Mr. Lay to back him on the title track
of his album “Highway 61 Revisited.” In addition to
playing drums, Mr. Lay played a toy whistle on the song’s
memorable opening."
— Richard Sandomir, Feb. 5, 2022, 2:06 p.m. ET

The above link yields a March 11, 2019, YouTube upload:

Some may prefer the theology of Hexagram  61.

“‘Oracle, why did you write
The Grasshopper Lies Heavy?
What are we supposed to learn?'”

— Philip K. Dick

“She began throwing the coins.“

I Ching Hexagram 61: Inner Truth

Other remarks from the above
YouTube upload date — March 11, 2019 —

Mathieu Cube Labeling

Filed under: General — Tags: , , , , — m759 @ 2:08 pm

Shown below is an illustration from "The Puzzle Layout Problem" —

Exercise:  Using the above numerals 1 through 24
(with 23 as 0 and 24 as ∞) to represent the points 
, 0, 1, 2, 3 … 22  of the projective line over GF(23),
reposition the labels 1 through 24 in the above illustration
so that they appropriately* illustrate the cube-parts discussed
by Iain Aitchison in his March 2018 Hiroshima slides on 
cube-part permutations by the Mathieu group M24

A note for Northrop Frye —

Interpenetration in the eightfold cube — the three midplanes —

IMAGE- The Trinity Cube (three interpenetrating planes that split the eightfold cube into its eight subcubes)

A deeper example of interpenetration:

Aitchison has shown that the Mathieu group M24 has a natural
action on the 24 center points of the subsquares on the eightfold
cube's six faces (four such points on each of the six faces). Thus
the 759 octads of the Steiner system S(5, 8, 24) interpenetrate
on the surface of the cube.

* "Appropriately" — I.e. , so that the Aitchison cube octads correspond
exactly, via the projective-point labels, to the Curtis MOG octads.

Classics Illustrated

Filed under: General — m759 @ 12:00 am

From Log24 posts tagged Mind Spider :

http://www.log24.com/log/pix11/110116-ManhattanStarWarsSm.jpg

Friday, February 4, 2022

Down and Up, Up and Down

Filed under: General — m759 @ 11:16 pm

From The Dumbing-Down

The above image appeared here on August 5, 2021.

From an instagram post on that same date
that might be titled "The Wising-Up" —

Movement and Words

Filed under: General — m759 @ 4:12 pm

New York Times  eulogy today for "a wizard of movement and words"—

See as well the previous post and Ballet Blanc .

Couples Therapy . . . Continues.

Filed under: General — Tags: , — m759 @ 3:06 pm

Engineering image uploaded on Sept. 4, 2015 —

Art image from this  journal on that date

Alternate title: 'Lefty Lucy,' by Vermeer.

See as well "Novel Engineering."

The Guralnik Cube

Filed under: General — Tags: — m759 @ 2:04 pm

New York Review of Books , Dec. 16, 2021 issue —
Lorrie Moore on the documentary series "Couples Therapy" —

"Few of the people sitting on the couch avoid the cliché of
one person (a man) playing fruitlessly with a plastic puzzle
while the other speaks tearfully and avails herself of a
Kleenex box. In season 1, there is literally a Rubik’s cube,
and no one ever solves it, an unfortunate but apt metaphor.
During one session, when the cube has been placed out of reach,
one of the husbands gets up to look for it, finding it on a shelf." 

See also . . .

"The bond with reality is cut." — Hans Freudenthal 

A Monolith for Epstein

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

Thursday, February 3, 2022

Through the Asian Looking Glass

Filed under: General — Tags: , , , — m759 @ 10:59 pm

The Miracle Octad Generator (MOG) —
The Conway-Sloane version of 1988:

Embedding Change, Illustrated

See also the 1976 R. T. Curtis version, of which the Conway-Sloane version
is a mirror reflection —

“There is a correspondence between the two systems
of 35 groups, which is illustrated in Fig. 4 (the MOG or
Miracle Octad Generator).”
—R.T. Curtis, “A New Combinatorial Approach to M24,” 
Mathematical Proceedings of the Cambridge Philosophical
Society
 (1976), 79: 25-42

http://www.log24.com/log/pix10A/100514-Curtis1976MOG.jpg

Curtis’s 1976 Fig. 4. (The MOG.)

The Guy Embedding (named for M.J.T., not Richard K., Guy) states that
the MOG is naturally embedded in the codewords of the extended binary
Golay code, if those codewords are generated in lexicographic order.

MOG in LOG embedding

The above reading order for the MOG 4×6 array —
down the columns, from left to right — yields the Conway-Sloane MOG.

Since that is a mirror image of the original Curtis MOG, the reading order
yielding that  MOG is down the columns, from right to left.

"Traditionally, ChineseJapaneseVietnamese and Korean are written vertically
in columns going from top to bottom and ordered from right to left, with each
new column starting to the left of the preceding one." — Wikipedia

The Asian reading order has certain artistic advantages:

Four-Color Structures (Review)

Filed under: General — Tags: , , , — m759 @ 1:30 pm

Four-color decomposition applied to the 8-point binary affine space

Miracle Octad Generator — Analysis of Structure

For those who prefer art that is less abstract — Heartland Sutra.

Wednesday, February 2, 2022

Groundhog Day Metamorphosis

Filed under: General — m759 @ 1:11 pm

" Whether correspondences were achieved by means of
wordplay, atavistic formal resemblances, or serendipitous
coincidences, the attendant metamorphosis of literary
material into Frye's own scripture could become tiresome:
'just another shake of the kaleidoscope.' " [Link added.]

— From p. 61 of "The Master of the Myth of Literature:
An Interpenetrative Ogdoad for Northrop Frye,"
by Nohrnberg, James C., Comparative Literature
Vol. 53 (1), pp. 58-82, Duke University Press, 
January 1, 2001.

Conway’s Game vs. Pure Geometry

Filed under: General — m759 @ 12:00 am

A  question attributed to John Horton Conway
about configurations in his Game of Life

"Indeed, is there a Godlike still-life,
one that can only have existed
for all time . . . . ?"

A simple answer … but not  from Conway's Game —

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

Related remarks:  Ogdoad.

Tuesday, February 1, 2022

Bit Space

Filed under: General — Tags: , — m759 @ 10:54 am

Twelve significant bit-sequences —

Twelve basis vectors, in lexicographic order, for the binary Golay-code space

http://www.log24.com/log/pix11/110412-IconicArt.jpg

Lurching Into the Lexicon

Filed under: General — Tags: — m759 @ 1:25 am

See as well a 2019 Neal Stephenson novel —

FALL; OR, DODGE IN HELL .

From a New York Times  review of that novel:  

"Early choices, or sometimes relatively arbitrary initial conditions,
end up shaping future events and technologies. In this case,
the cosmology, topography and even the theology of an entire
universe — Bitworld — affect Meatspace, and the two realms
are linked in a feedback loop of cause and effect, resources and
outcomes (dollars, computing power)." 

— Charles Yu, June 14, 2019

Powered by WordPress