Log24

Friday, November 30, 2018

Latin-Square Structure

Filed under: G-Notes,General,Geometry — m759 @ 2:56 AM

Continued from March 13, 2011

"…as we saw, there are two different Latin squares of order 4…."
— Peter J. Cameron, "The Shrikhande Graph," August 26, 2010

Cameron counts Latin squares as the same if they are isotopic .
Some further context for Cameron's remark—

A new website illustrates a different approach to Latin squares of order 4 —

https://shc7596.wixsite.com/website .

Thursday, November 29, 2018

Icons . . .

Filed under: General — m759 @ 12:05 PM

For the People's Temple of Doom —

Suggested by the oeuvre  of Steven Spielberg —

The Fortune Cookie

Filed under: General — m759 @ 10:54 AM

The mathematician Chuanming Zong in the previous post
has also written about  Aristotle's pyramid scheme

The White Cube

Filed under: G-Notes,General,Geometry — m759 @ 9:57 AM

Clicking on Zong in the above post leads to a 2005 article
in the Bulletin of the American Mathematical Society .

See also the eightfold  cube and interality .

Wednesday, November 28, 2018

Geometry and Experience

Filed under: G-Notes,General,Geometry — m759 @ 9:18 AM

Einstein, "Geometry and Experience," lecture before the
Prussian Academy of Sciences, January 27, 1921–

This view of axioms, advocated by modern axiomatics, purges mathematics of all extraneous elements, and thus dispels the mystic obscurity, which formerly surrounded the basis of mathematics. But such an expurgated exposition of mathematics makes it also evident that mathematics as such cannot predicate anything about objects of our intuition or real objects. In axiomatic geometry the words "point," "straight line," etc., stand only for empty conceptual schemata. That which gives them content is not relevant to mathematics.

Yet on the other hand it is certain that mathematics generally, and particularly geometry, owes its existence to the need which was felt of learning something about the behavior of real objects. The very word geometry, which, of course, means earth-measuring, proves this. For earth-measuring has to do with the possibilities of the disposition of certain natural objects with respect to one another, namely, with parts of the earth, measuring-lines, measuring-wands, etc. It is clear that the system of concepts of axiomatic geometry alone cannot make any assertions as to the behavior of real objects of this kind, which we will call practically-rigid bodies. To be able to make such assertions, geometry must be stripped of its merely logical-formal character by the coordination of real objects of experience with the empty conceptual schemata of axiomatic geometry. To accomplish this, we need only add the proposition: solid bodies are related, with respect to their possible dispositions, as are bodies in Euclidean geometry of three dimensions. Then the propositions of Euclid contain affirmations as to the behavior of practically-rigid bodies.

Geometry thus completed is evidently a natural science; we may in fact regard it as the most ancient branch of physics. Its affirmations rest essentially on induction from experience, but not on logical inferences only. We will call this completed geometry "practical geometry," and shall distinguish it in what follows from "purely axiomatic geometry." The question whether the practical geometry of the universe is Euclidean or not has a clear meaning, and its answer can only be furnished by experience.  ….

Later in the same lecture, Einstein discusses "the theory of a finite
universe." Of course he is not using "finite" in the sense of the field
of mathematics known as "finite geometry " — geometry with only finitely
many points.

Nevertheless, his remarks seem relevant to the Fano plane , an
axiomatically defined entity from finite geometry, and the eightfold cube ,
a physical object embodying the properties of the Fano plane.

 I want to show that without any extraordinary difficulty we can illustrate the theory of a finite universe by means of a mental picture to which, with some practice, we shall soon grow accustomed.

First of all, an observation of epistemological nature. A geometrical-physical theory as such is incapable of being directly pictured, being merely a system of concepts. But these concepts serve the purpose of bringing a multiplicity of real or imaginary sensory experiences into connection in the mind. To "visualize" a theory therefore means to bring to mind that abundance of sensible experiences for which the theory supplies the schematic arrangement. In the present case we have to ask ourselves how we can represent that behavior of solid bodies with respect to their mutual disposition (contact) that corresponds to the theory of a finite universe. 

Tuesday, November 27, 2018

The Saints — Claus, Fe; Fe, Claus.

Filed under: General — m759 @ 1:59 PM

See The Saints in this journal, as well as Claus and Fe.

Organizing the Mine Workers

Filed under: General — m759 @ 11:17 AM

(Continued from August 8th, 2011) —

See also Sunday evening's post At Eternity's Gate.

Fe

Filed under: General — m759 @ 10:38 AM

http://www.log24.com/log/pix18/180808-Cosima_drank_the_purple_kool-aid-500w.jpg

Sunday, November 25, 2018

At Eternity’s Gate

Filed under: General — m759 @ 10:42 PM

A New York Times  theater review from 2002
is now accompanied by an ad for a current film,
"At Eternity's Gate." (Click to enlarge.)

"At Eternity's Gate" opened November 16th, 2018.

From this  journal on that date —

"Right through hell there is a path." — Malcolm  Lowry

Artifacts

Filed under: General — m759 @ 2:00 PM

The word "artifacts" in the above obituary summary
suggests three Log24 posts now tagged with that word.

See as well . . .

"Bad news on the doorstep…." — American Pie

Ricky Jay

Filed under: General — m759 @ 2:05 AM

See also Ricky Jay in this  journal.

Saturday, November 24, 2018

Portfolio

Filed under: G-Notes,General,Geometry — m759 @ 6:29 PM

A new portfolio site:

Portfolio on art and geometry of Steven H. Cullinane

Friday, November 23, 2018

Artfield Studio

Filed under: General,Geometry — m759 @ 12:10 PM

The title is that of an new Internet domain, artfield.studio,
that is used only to store branded links  such as . . .

artfield.studio/trinity-dice

artfield.studio/dirac-and-geometry

artfield.studio/eddington

artfield.studio/kummerhenge

artfield.studio/pinterest .

Some context —

artfield.studio/patrick-blackburn.

Thursday, November 22, 2018

Rosenhain and Göpel Meet Kummer in Projective 3-Space

Filed under: General,Geometry — Tags: — m759 @ 2:07 PM

For further details, see finitegeometry.org/sc/35/hudson.html.

Geometric Incarnation

Filed under: General,Geometry — Tags: — m759 @ 6:00 AM

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

— T. S. Eliot in Four Quartets

Note also the four 4×4 arrays surrounding the central diamond
in the chi  of the chi-rho  page of the Book of Kells

From a Log24 post
of March 17, 2012

"Interlocking, interlacing, interweaving"

— Condensed version of page 141 in Eddington's
1939 Philosophy of Physical Science

Wednesday, November 21, 2018

Opening Credits

Filed under: General,Geometry — Tags: — m759 @ 7:47 PM

From Log24 on Friday, Nov. 16

This evening's New York Times  on an opening-credits designer, 
Pablo Ferro, who reportedly died at 83 on Friday, Nov. 16 —

An example of Ferro's later work in film —

Musical accompaniment from Sunday morning —

'The Eddington Song'

Tuesday, November 20, 2018

Logos

Filed under: General,Geometry — Tags: — m759 @ 12:21 PM

(Continued)

Musical accompaniment from Sunday morning

'The Eddington Song'

Update of Nov. 21 —

The reader may contrast the above Squarespace.com logo
(a rather serpentine version of the acronym SS) with a simpler logo
for a square space (the Galois window ):

Claremont Noir

Filed under: General — m759 @ 11:00 AM

From the Claremont Review of Books

From elsewhere —

See as well posts from Log24 related to
the McClay date above — June 8, 2007.

Lincoln’s Commedia

Filed under: General — m759 @ 2:29 AM

A November 19th story by one Ross A. Lincoln

See as well Commedia  in this  journal.

Monday, November 19, 2018

Pleasure Paradise

Filed under: General — m759 @ 9:34 AM

The title refers to an image reproduced here in
a post of August 1st, 2017. That post also included
the following quotation —

"Remembering speechlessly we seek
the great forgotten language,
the lost lane-end into heaven,
a stone, a leaf, an unfound door.
Where? When?" — Thomas Wolfe 

— From "All the stuff we'd like to buy at
the Back To The Future prop auction
,"
by Meredith Woerner, 11/04/10, 9:30 am

Sunday, November 18, 2018

Space Music

Filed under: General,Geometry — Tags: , , — m759 @ 9:27 AM

'The Eddington Song,' based on 'The Philosophy of Physical Science,' p. 141 (1939)

Update of Nov. 19 —

"Design is how it works." — Steve Jobs

See also www.cullinane.design.

Diamond Theorem Symmetry

Filed under: General,Geometry — m759 @ 1:00 AM

The title is a useful search phrase:

Saturday, November 17, 2018

Representation

Filed under: General,Geometry — Tags: — m759 @ 7:00 AM

See as well . . .

. . . and posts tagged Alperin.

On its current homepage, the American Mathematical Society  
links to a Nov. 15 blog post illustrating the Stan Lee approach
to mathematics:

Stories: "Math needs more stories. All kinds of stories…" 

See too Mathematics and Narrative in this  journal.

Friday, November 16, 2018

The Transposed Squares

Filed under: G-Notes,General,Geometry — m759 @ 9:12 PM
 
 

I.e. (click to enlarge) —

 

Parable of India

Filed under: General — m759 @ 12:42 PM

See too  "When thou seekest me, seek towards India."

William Goldman

Filed under: General — Tags: — m759 @ 10:30 AM

From the above source —

See as well the author Les Daniels in this  journal.

On All Souls’ Day 2018

Filed under: General — m759 @ 2:40 AM

See as well Under the Volcano  and All Souls in this  journal.

Related material —

Thursday, November 15, 2018

Mathematics and Narrative

Filed under: General,Geometry — m759 @ 9:08 PM

Mathematics —

See (for instance) a research group at Ghent University.

For those who prefer narrative . . .

See also . . .

Nocciolo

Filed under: General — m759 @ 8:15 AM

"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

From the previous post

From a cartoon graveyard —

See also, in this  journal, Smallest Perfect and Nocciolo .

Wednesday, November 14, 2018

Phase Space

Filed under: General,Geometry — m759 @ 3:33 AM

"Open the pod bay doors, Bernard."

Tuesday, November 13, 2018

Blackboard Jungle Continues.

Filed under: G-Notes,General,Geometry — m759 @ 6:19 PM

From the 1955 film "Blackboard Jungle" —

From a trailer for the recent film version of A Wrinkle in Time

Detail of the phrase "quantum tesseract theorem":

From the 1962 book —

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

Related mathematics from Koen Thas that some might call a
"quantum tesseract theorem" —

Some background —

Koen Thas, 'Unextendible Mututally Unbiased Bases' (2016)

See also posts tagged Dirac and Geometry. For more
background on finite  geometry, see a web page
at Thas's institution, Ghent University.

Monday, November 12, 2018

Half Crazy

Filed under: General — m759 @ 10:42 PM

Douglas Rain, the voice of HAL in Kubrick's 2001 , reportedly
died at 90 on Sunday, Nov. 11, 2018. A piece from the Sunday,
April 1, 2018, print  edition of The New York Times  recalls that . . .

When HAL says, “I know I’ve made some very poor decisions recently, but I can give you my complete assurance that my work will be back to normal,” Mr. Rain somehow manages to sound both sincere and not reassuring. And his delivery of the line “I think you know what the problem is just as well as I do” has the sarcastic drip of a drawing-room melodrama and also carries the disinterested vibe of a polite sociopath.

Kubrick had Mr. Rain sing the 1892 love song “Daisy Bell” (“I’m half crazy, all for the love of you”) almost 50 times, in uneven tempos, in monotone, at different pitches and even just by humming it. In the end, he used the very first take. Sung as HAL’s brain is being disconnected, it’s from his early programming days, his computer childhood. It brings to an end the most affecting scene in the entire film.

— Gerry Flahive in the online New York Times 
 

"A version of this article appears in print on , on Page AR13 of the New York edition with the headline: HAL 9000 Wasn’t Always So Eerily Calm."

This  journal on the above online date, March 30, 2018 —

"Program or be programmed."
— A saying by Douglas Rushkoff

See as well the following link from this journal
on Armistice Day, the reported date of Mr. Rain's death —

"Halmos + Tombstone."

Raum und Zwischenraum*

Filed under: General — m759 @ 8:42 AM

An Internet search for "Raum und Zwischenraum " this morning
led to a Munich artist who reportedly died on Nov. 11, 2012.

Related material —

Desert Cross, in Log24 on that date, and . . .

* See Zwischenraum  in this journal.

Sunday, November 11, 2018

Zwischenraum

Filed under: General — m759 @ 11:00 PM

Warburg at Cornell U. Press

See also Warburg + Cornell in this journal.

"Yet if this Denkraum ,  this 'twilight region,'  is where the artist and
emblem-maker invent, then, as Gombrich well knew, Warburg also
constantly regrets the 'loss' of this 'thought-space,' which he also
dubs the Zwischenraum  and Wunschraum ."

Memory, Metaphor, and Aby Warburg's Atlas of Images ,
     Christopher D. Johnson, Cornell University Press, 2012, p. 56

Tombstone

Filed under: General — m759 @ 3:33 AM

Search for 'Catch-22' + 'Also sprach'

See also this journal on the above Catch-22 date — July 16, 2014 —
and a search in this journal for "Halmos + Tombstone."

Thursday, November 8, 2018

Reality vs. Axiomatic Thinking

Filed under: G-Notes,General,Geometry — m759 @ 11:16 PM

From https://blogs.scientificamerican.com/…

A  Few  of  My  Favorite  Spaces:
The Fano Plane

The intuition-challenging Fano plane may be
the smallest interesting configuration
of points and lines.

By Evelyn Lamb on October 24, 2015

"…finite projective planes seem like
a triumph of purely axiomatic thinking
over any hint of reality. . . ."

For Fano's axiomatic  approach, see the Nov. 3 Log24 post
"Foundations of Geometry."

For the Fano plane's basis in reality , see the eightfold cube
at finitegeometry.org/sc/ and in this journal.

See as well "Two Views of Finite Space" (in this journal on the date 
of Lamb's remarks — Oct. 24, 2015).

Some context:  Gödel's Platonic realism vs. Hilbert's axiomatics
in remarks by Manuel Alfonseca on June 7, 2018. (See too remarks
in this journal on that date, in posts tagged "Road to Hell.")

Geometry Lesson

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 12:00 AM

From "The Trials of Device" (April 24, 2017) —

Wittgenstein's pentagram and 4x4 'counting-pattern'

Pentagon with pentagram    

See also Wittgenstein in a search for "Ein Kampf " in this journal.

Wednesday, November 7, 2018

The Fact-Checker

Filed under: General — m759 @ 9:43 PM

http://www.log24.com/log/pix18/180831-NYer-back-cover-ad-Lifespan_of_a_Fact.jpg

In memory of Christopher Lehmann-Haupt, who reportedly died
today (Wed., Nov. 7, 2018) at 84 —

See Lehmann-Haupt in this journal on May 23, 2012:

On author Paul Fussell, who died today —

"Vincent B. Sherry, writing in The Cambridge Companion to the Literature of the First World War , called Mr. Fussell’s book 'the fork in the road for Great War criticism.'"  — Christopher Lehmann-Haupt in The New York Times

Actually, the writing was by James Campbell. Sherry was the book's editor. See Campbell's "Interpreting the War," pp. 261-279 of the 2005 (first) printing. The fork is on page 267.

Update of 9:26 PM— In the latest  version of Lehmann-Haupt's article, the fork has disappeared. But Campbell's writing is still misidentified as Sherry's.

Defense Against the Dark Arts

Filed under: General — m759 @ 6:19 AM

"What is the Necropastoral?" was published on April 29th, 2014.
Also on April 29th, 2014 —

See as well Christianity and Culture  by T. S. Eliot.

Tuesday, November 6, 2018

Four Quartets Prize

Filed under: General — m759 @ 9:00 PM

On a poem sequence that won this year's Four Quartets Prize —

"Decomposing and reconstituting bodies and landforms
feed the evolution of Smith’s afrofuturist necropastoral."

Bait and Tackle

Filed under: General — Tags: — m759 @ 1:13 PM

The Bait —

For the tackle, see a 1988 album from The Residents.

Settings and Tools

Filed under: General — m759 @ 11:02 AM

Desert Notes*

Filed under: General — Tags: — m759 @ 3:13 AM

A November 1 LA Times  article about a book to be published today —

Why did Jonathan Lethem
turn toward the desert
in 'The Feral Detective'?

See also searches in this  journal for Desert and, more particularly,
Point Omega and Mojave.

* The title of a book by Barry Holstun Lopez.

On Mathematical Beauty

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 2:18 AM

A phrase from the previous post —
"a size-eight dame in a size-six dress" —
suggests a review . . .

See as well the diamond-theorem correlation and . . .

Why PSL(2,7) is isomorphic to GL(3.2)

Monday, November 5, 2018

Eyes on the Prize

Filed under: General — Tags: , — m759 @ 7:04 PM

High Life at Sils Maria

Filed under: General — Tags: — m759 @ 9:00 AM

Related art —

Sunday, November 4, 2018

Kristen vs. the Space Witch*

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

* We know the former. There is no shortage of candidates for the latter.

“Look Up” — The Breakthrough Prize* Theme This Evening

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

Looking up images for "The Space Theory of Truth" this evening —

Detail  (from the post "Logos" of Oct. 14)

http://www.spaceref.com/news/viewpr.html?pid=53323

Dead Poet

Filed under: General — Tags: — m759 @ 2:01 PM

The New York Times  today on a poet, Judith Kazantzis,
"who died on Sept. 18 at 78" —

"Judith’s oldest sister is Antonia Fraser, the biographer
and novelist and widow of the playwright Harold Pinter."

"Her [Judith’s] death was confirmed by Andy Croft, who runs
Smokestack Books, the publisher of 'Sister Intervention' [sic* ]
(2014), Ms. Kazantzis’ last collection of poetry. He did not
specify the cause or where she died."

Notable lines from that book's poem "In the Garden" —

Two trees of life, not in the woods,
but in the garden.

See also the post "Death Day" in this  journal on Sept. 18.

* The title is actually "Sister Invention ."

Saturday, November 3, 2018

For St. Anselm

Filed under: General — Tags: , , — m759 @ 11:00 PM

"… at his home in San Anselmo . . . ."

See also Anselm in this journal, as well as the Devil's Night post Ojos.

The Space Theory of Truth

Filed under: General — Tags: — m759 @ 10:00 PM

Earlier posts have discussed the "story theory of truth"
versus the "diamond theory of truth," as defined by 
Richard Trudeau in his 1987 book The Non-Euclidean Revolution.

In a New York Times  opinion piece for tomorrow's print edition,*
novelist Dara Horn touched on what might be called 
"the space theory of truth."

When they return to synagogue, mourners will be greeted
with more ancient words: “May God comfort you
among the mourners of Zion and Jerusalem.”
In that verse, the word used for God is hamakom 
literally, “the place.” May the place comfort you.

[Link added.]

The Source —

See Dara Horn in this  journal, as well as Makom.

* "A version of this article appears in print on ,
on Page A23 of the New York edition with the headline: 
American Jews Know This Story."

Foundations of Geometry

Filed under: G-Notes,General,Geometry — m759 @ 1:40 PM

"costruire (o, dirò meglio immaginare) un ente" — Fano, 1892

"o, dirò meglio, costruire" — Cullinane, 2018

Friday, November 2, 2018

Day of the Dead

Filed under: General — m759 @ 9:00 AM

From Wikipedia

Day of the Dead
Observed by Mexico, and regions with large Hispanic populations
Type Cultural 
Syncretic Christian
Significance Prayer and remembrance of friends and family members who have died
Celebrations Creation of altars to remember the dead, traditional dishes for the Day of the Dead
Begins October 31
Ends November 2
Date October 31
Next time 31 October 2019
Frequency Annual
Related to All Saints' Day

"The Day of the Dead (Spanish: Día de Muertos ) is
a Mexican holiday celebrated throughout Mexico,
in particular the Central and South regions,
and by people of Mexican heritage elsewhere.
The multi-day holiday focuses on gatherings
of family and friends to pray for and remember
friends and family members who have died, and
help support their spiritual journey. . . .

The holiday is sometimes called Día de los Muertos 
in Anglophone countries, a back-translation of its
original name, Día de Muertos .

Gradually, it was associated with October 31,
November 1, and November 2 to coincide with the
Western Christianity triduum of Allhallowtide: 
All Saints' EveAll Saints' Day, and All Souls' Day."

—————————————————————————-

The previous post concerned a poet who reportedly
died on October 23, 2018.  This journal on that date —

Elevation of the Hostess

Filed under: General — m759 @ 1:27 AM

Or:  Netflix and Chill on All Souls' Day

Midrash from Huffington Post  (click to enlarge) —

Thursday, November 1, 2018

Formation, Transformation . . . . Solution, Dissolution

Filed under: General,Geometry — m759 @ 8:40 PM

Literary Doodles

Filed under: General — m759 @ 11:59 AM

The Great Doodle of Northrop Frye —

Shown below is a "Story Circle" based on the work of Joseph Campbell.
The author of this particular version is unknown.  

Note that there are 12 steps in the above Story Circle. This suggests
some dialogue from a recent film . . .

Donnie —"We can't ask for help if we don't think there's anyone out there to give it. You have to grasp this concept. And that doesn't have to be fucking Jesus Christ or Buddha or Vanna White."
John — "So, can I choose the genitalia of Raquel Welch?"
Donnie — "I would advise against that, Callahan."
John — "Why?"
Donnie — "'Cause it's not a fucking joke. If you can't look outside yourself and you can't find a higher power, you're fucked."

Read more: https://www.springfieldspringfield.co.uk/movie_script.php?movie=dont-worry-he-wont-get-far-on-foot

The Albee Box

Filed under: General — m759 @ 3:00 AM

See also Albee + Box in this  journal.

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