Log24

Saturday, September 21, 2019

Six Dots

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

See other posts now tagged Six Dots.

Related narrative:  Raiders of the Lost Ring .

Thursday, June 6, 2019

Strange Dots

Filed under: General — Tags: , — m759 @ 3:43 PM

(Continued)

Sunday, May 26, 2019

Sunday Shul: Connecting the Dots

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

"It's very easy to say, 'Well, Jeff couldn't quite connect these dots,'"
director Jeff Nichols told BuzzFeed News. "Well, I wasn't actually
looking at the dots you were looking at."

— Posted on March 21, 2016, at 1:11 p.m,
Adam B. Vary, BuzzFeed News Reporter

"Magical arrays of numbers have been the talismans of mathematicians and mystics since the time of Pythagoras in the sixth century B.C. And in the 16th century, Rabbi Isaac ben Solomon Luria devised a cosmological world view that seems to have prefigured superstring theory, at least superficially. Rabbi Luria was a sage of the Jewish cabalist movement — a school of mystics that drew inspiration from the arcane oral tradition of the Torah.

According to Rabbi Luria's cosmology, the soul and inner life of the hidden God were expressed by 10 primordial numbers [sic ], known as the sefirot. [Link added.]"

— "Things Are Stranger Than We Can Imagine,"
by Malcolm W. BrowneNew York Times Book Review ,
Sunday, March 20, 1994

Friday, June 30, 2017

Connecting Dots

Filed under: General — Tags: — m759 @ 8:23 PM

From a post of Sunday, Dec. 19, 2004 —

Sunday Sermon
on Saturday’s Numbers

The image “http://www.log24.com/log/pix04B/041219-Line.jpg” cannot be displayed, because it contains errors.

The "dots" of this  post's title were subscribers to
a literary journal co-edited by poet Adrienne Rich.

Tuesday, June 27, 2017

Connecting the Dots

Filed under: General — Tags: — m759 @ 6:00 PM

See also The Mystic Hexastigm.

Monday, June 26, 2017

Four Dots

Analogies — “A : B  ::  C : D”  may be read  “A is to B  as  C is to D.”

Gian-Carlo Rota on Heidegger…

“… The universal as  is given various names in Heidegger’s writings….

The discovery of the universal as  is Heidegger’s contribution to philosophy….

The universal ‘as‘ is the surgence of sense in Man, the shepherd of Being.

The disclosure of the primordial as  is the end of a search that began with Plato….
This search comes to its conclusion with Heidegger.”

— “Three Senses of ‘A is B’ in Heideggger,” Ch. 17 in Indiscrete Thoughts
See also Four Dots in this journal.

Some context:  McLuhan + Analogy.

Tuesday, August 17, 2021

Mythical Figure

Filed under: General — Tags: — m759 @ 12:55 PM

A phrase from the previous post : "modern society's mythical figures."

A mythical figure from Claude Lévi-Strauss

The above image is from a study of Lévi-Strauss's "Canonical Formula" …

Saturday, August 3, 2019

As:  A Four-Set

Filed under: General — Tags: , — m759 @ 11:04 AM

For further details, click on the image below.

Wednesday, June 5, 2019

The Tigerman Kaballah

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

See also Life of Pi   in this  journal.

Monday, May 27, 2019

But Seriously . . .

Filed under: General — Tags: , — m759 @ 9:32 PM

McLuhan on Analogy.

I prefer the simple "four dots" figure
of the double colon:

For those who prefer stranger analogies . . .

Actors from "The Eiger Sanction" —

Doctor Strange on Mount Everest —

Dr. Strange at beyondtheopposites.com on 2016/12/02

See as well this  journal on the above Strange date, 2016/12/02,
in posts tagged Lumber Room.

Sunday, May 26, 2019

Burning Bright

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

Gell-Mann's 'eightfold way' as 'a mosaic of simple triangular building blocks' — George Johnson, 1999

Compare and contrast with . . .

The Brightburn Logo:

Related material from the May 12 post

"The Collective Unconscious
in a Cartoon Graveyard
" —

"When they all finally reach their destination —
a deserted field in the Florida Panhandle…." 

" When asked about the film's similarities to the 2015 Disney movie Tomorrowland , which also posits a futuristic world that exists in an alternative dimension, Nichols sighed. 'I was a little bummed, I guess,' he said of when he first learned about the project. . . . 'Our die was cast. Sometimes this kind of collective unconscious that we're all dabbling in, sometimes you're not the first one out of the gate.' "

Saturday, May 25, 2019

Brand On Breyer

Filed under: General — Tags: — m759 @ 1:37 PM

Or:  One Quark for Muster Mark​

"In this way the eight trigrams came into being." — Richard Wilhelm

Detail:

Midrash:

Friday, May 24, 2019

Hidden Eightfold Patterns

Filed under: General — Tags: — m759 @ 5:23 PM

Sunday, January 20, 2019

Scope Resolution

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

Wikipedia on a programming term

The scope resolution operator helps to identify
and specify the context to which an identifier refers,
particularly by specifying a namespace. The specific
uses vary across different programming languages
with the notions of scoping.  In many languages
the scope resolution operator is written

 "::".

In a completely different context, these four dots might represent
a geometric object  — the four-point plane .

Tuesday, October 17, 2017

The Movement of Analogy

Filed under: General,Geometry — Tags: , — m759 @ 4:20 PM

The title is a phrase by Octavio Paz from today's post
"Status Symbols."

Other phrases from a link target in Sunday's post 
The Strength at the Centre

                                a single world
In which he is and as and is are one.

See also Four Dots in this journal.

Tuesday, October 10, 2017

Dueling Formulas

Filed under: G-Notes,General,Geometry — Tags: , , — m759 @ 12:35 PM

Continued from the previous post and from posts
now tagged Dueling Formulas

The four-diamond formula of Jung and
the four-dot "as" of Claude Lévi-Strauss:

Simplified versions of the diamonds and the dots
 

The Ring of the Diamond Theorem          ::

I prefer Jung. For those who prefer Lévi-Strauss —

     First edition, Cornell University Press, 1970.

A related tale — "A Meaning, Like."

Saturday, August 12, 2017

Images from 1984

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

For the author of a Harvard Crimson  opinion piece yesterday on 1984 ,
two images adapted from a 1984 film —

Mola Ram from 'Temple of Doom'

See also, in this  journal, Hume's phrase "perfect nonentity."

Tuesday, July 11, 2017

A Date at the Death Cafe

Filed under: General,Geometry — Tags: , — m759 @ 8:48 PM

The New York TImes  reports this evening that
"Jon Underwood, Founder of Death Cafe Movement,"
died suddenly at 44 on June 27. 

This  journal on that date linked to a post titled "The Mystic Hexastigm."

A related remark on the complete 6-point   from Sunday, April 28, 2013

(See, in Veblen and Young's 1910 Vol. I, exercise 11,
page 53: "A plane section of a 6-point in space can  
be considered as 3 triangles perspective in pairs
from 3 collinear points with corresponding sides
meeting in 3 collinear points." This is the large  
Desargues configuration. See Classical Geometry
in Light of Galois Geometry
.)

This  post was suggested, in part, by the philosophical ruminations
of Rosalind Krauss in her 2011 book Under Blue Cup . See 
Sunday's post  Perspective and Its Transections . (Any resemblance
to Freud's title Civilization and Its Discontents  is purely coincidental.)

Friday, June 30, 2017

Hurriedly Put Together

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

The previous post quoted one theologian on a book
by another theologian, saying its tone "is patronizing
and its arguments are hurriedly put together."

For a more leisurely sort of argument, see a 1995* remark 
by a mathematician, Ronald Shaw, quoted here on the morning
of Tuesday, June 27, in an update at the end of the previous day's
post "Upgrading to Six" —

". . . recall the notions of Eddington (1936) . . . ."

* In "Finite Geometry, Dirac Groups and the
Table of Real Clifford Algebras
," pages 59-99 of
R. Ablamowicz and P. Lounesto (eds.),
Clifford Algebras and Spinor Structures ,
Kluwer Academic Publishers, 1995.

Thursday, June 29, 2017

Rumors

Filed under: General — Tags: — m759 @ 9:29 PM

Berger reportedly died on Tuesday, June 27. See the patronizing title
"Connecting the Dots" of a Log24 post on that date.

Wednesday, June 28, 2017

In Memory of Steve Jobs …

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

And his June 12, 2005, "Connecting the Dots" address at Stanford —

Monday, June 26, 2017

Upgrading to Six

This post was suggested by the previous post — Four Dots —
and by the phrase "smallest perfect" in this journal.

Related material (click to enlarge) —

Detail —

From the work of Eddington cited in 1974 by von Franz —

See also Dirac and Geometry and Kummer in this journal.

Updates from the morning of June 27 —

Ron Shaw on Eddington's triads "associated in conjugate pairs" —

For more about hyperbolic  and isotropic  lines in PG(3,2),
see posts tagged Diamond Theorem Correlation.

For Shaw, in memoriam — See Contrapuntal Interweaving and The Fugue.

Saturday, April 8, 2017

A Perfect Nonentity

Filed under: General,Geometry — Tags: , — m759 @ 8:25 AM

The title is from Hume:

 "And were all my perceptions removed by death,
and could I neither think, nor feel, nor see, nor love,
nor hate, after the dissolution of my body, I should
be entirely annihilated, nor do I conceive what is
further requisite to make me a perfect nonentity."

— Book I, Part IV, Section vi  of  
    A Treatise of Human Nature

"What is further requisite" — Perhaps  

This four-dot notation ("as") is from a search for Lévi-Strauss in this journal.

See also "That I Am."

Friday, April 7, 2017

Personal Identity

Filed under: General,Geometry — Tags: , — m759 @ 2:40 PM

From "The Most Notorious Section Phrases," by Sophie G. Garrett
in The Harvard Crimson  on April 5, 2017 —

This passage reminds me of (insert impressive philosophy
that was not in the reading).

This student is just being a show off. We get that they are smart
and well read. Congrats, but please don’t make the rest of the us
look bad in comparison. It should be enough to do the assigned
reading without making connections to Hume’s theory of the self.

Hume on personal identity (the "self")

For my part, when I enter most intimately into what I call myself, I always stumble on some particular perception or other, of heat or cold, light or shade, love or hatred, pain or pleasure. I never can catch myself at any time without a perception, and never can observe any thing but the perception. When my perceptions are removed for any time, as by sound sleep, so long am I insensible of myself, and may truly be said not to exist. And were all my perceptions removed by death, and could I neither think, nor feel, nor see, nor love, nor hate, after the dissolution of my body, I should be entirely annihilated, nor do I conceive what is further requisite to make me a perfect nonentity.
. . . .

I may venture to affirm of the rest of mankind, that they are nothing but a bundle or collection of different perceptions, which succeed each other with an inconceivable rapidity, and are in a perpetual flux and movement. Our eyes cannot turn in their sockets without varying our perceptions. Our thought is still more variable than our sight; and all our other senses and faculties contribute to this change: nor is there any single power of the soul, which remains unalterably the same, perhaps for one moment. The mind is a kind of theatre, where several perceptions successively make their appearance; pass, repass, glide away, and mingle in an infinite variety of postures and situations. There is properly no simplicity in it at one time, nor identity in different, whatever natural propension we may have to imagine that simplicity and identity. The comparison of the theatre must not mislead us. They are the successive perceptions only, that constitute the mind; nor have we the most distant notion of the place where these scenes are represented, or of the materials of which it is composed.

Related material —
Imago Dei  in this journal.

The Ring of the Diamond Theorem

Backstory —
The previous post
and The Crimson Abyss.

Saturday, February 11, 2017

The God Identity

Filed under: General — Tags: , — m759 @ 1:00 PM

The previous post suggests a related concept, in which
"I Am that I Am" is replaced by "I am as  I am." —

Sunday, November 6, 2016

Fourplay

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

On a renovation of Manhattan's Irish Repertory Theatre:

"Performances in the new space began on May 17, 2016."

This journal on May 17, 2016

Click the image below for a related story. 

See also Cartesian Theatre, a post of April 19, 2004.

Saturday, August 27, 2016

Folk Notation

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

See the Chautauqua Season post of June 25
and a search for Notation  in this journal.

See as well the previous post and Bullshit Studies .

Saturday, June 25, 2016

Season

Filed under: General — Tags: — m759 @ 3:00 PM

Detail —

 

See also a search in this journal for Notation .

Saturday, May 28, 2016

Plan 4

Filed under: General — Tags: , — m759 @ 2:45 AM

See a search in this journal for "As Is."

Tuesday, May 17, 2016

Bullshit Studies

Filed under: General,Geometry — Tags: , , , — m759 @ 1:06 AM

The originator of the phrase 'Fab Four' reportedly
died at 80 on Saturday, May 14, 2016.

This suggests a review of another noted four-set.

The above image is from a study of Lévi-Strauss's "Canonical Formula"

Midrash —

Log24 post titled 'As Is'

[Above photo of Lévi-Strauss and formula added June 6, 2016.]

Saturday, November 21, 2015

Brightness at Noon*

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM

A recent not-too-bright book from Princeton —

Some older, brighter books from Tony Zee

Fearful Symmetry  (1986) and
Quantum Field Theory in a Nutshell  (2003).

* Continued.

Wednesday, August 5, 2015

Inking

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

From Doctorow's 'Jolene: A Life'

See also Go Set a Structure and Tombstone.

Tuesday, October 7, 2014

As Is

Filed under: General — Tags: , — m759 @ 10:05 PM

"That simple operator, 'as,' turns out to carry within its philosophical grammar
a remarkable complex field* of operations…."

Charles Altieri,  Painterly Abstraction in Modernist American Poetry,
Cambridge University Press, 1989, page 343

See also Rota on Heidegger (What "As" Is, July 6, 2010), and Lead Belly
on the Rock Island Line — "You got to ride it like you find it."

* Update of Oct. 10, 2014: See also "Complex + Grid" in this journal.

Monday, November 11, 2013

The Mystic Hexastigm…

Filed under: General,Geometry — Tags: , , — m759 @ 11:00 AM

Or: The Nutshell

What about Pascal?

For some background on Pascal's mathematics,
not his wager, see

Richmond, H. W., 
"On the Figure of Six Points in Space of Four Dimensions," 
Quarterly Journal of Pure and Applied Mathematics , 
Volume 31 (1900), pp. 125-160,
dated by Richmond March 30,1899

Richmond, H. W.,
"The Figure Formed from Six Points in Space of Four Dimensions,"
Mathematische Annalen , 
Volume 53 (1900), Issue 1-2, pp 161-176,
dated by Richmond February 1, 1899

See also Nocciolo  in this journal.

Recall as well that six points in space may,
if constrained to lie on a circle, be given
a religious interpretation.  Richmond's
six points are secular and more general.

Monday, October 7, 2013

Post-Production (continued)

Filed under: General,Geometry — Tags: , — m759 @ 1:00 PM

This journal on Oct. 2, the date of death for
the developer of mathematical Braille —

Clicking on the image of St. Peter's Square in that post led to

Braille, as noted in last midnight's post, is based
on a six-dot cell. For some pure mathematics of
the six-dot cell, see 

Modeling the 21-point plane
with outer automorphisms of S6

Two quotations that seem relevant —

"When Death tells a story, you really have to listen"
Cover of The Book Thief

"This is not theology, this is mathematics."
Steven H. Cullinane, Sept. 22, 2013

The Book of Abraham

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

On Abraham Nemeth, the developer of Braille
for blind students of mathematics —

"… he began tinkering with the six-dot cell
that is the foundation of Braille."

For a different six-dot cell, see Nocciolo .

"Throughout his life, he dedicated much of his
spare time to creating Braille versions of Jewish
texts, including helping to proofread a Braille
Hebrew Bible in the 1950s." — Nemeth's obituary

Those who prefer entertainment may consult  The Book of Eli.

Sunday, April 28, 2013

The Octad Generator

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

… And the history of geometry  
Desargues, Pascal, Brianchon and Galois
in the light of complete n-points in space.

(Rewritten for clarity at about 10 AM ET April 29, with quote from Dowling added.
Updated with a reference to a Veblen and Young exercise (on p. 53) on April 30.)

Veblen and Young, Projective Geometry, Vol. I ,
Ginn and Company, 1910, page 39:

"The Desargues configuration. A very important configuration
is obtained by taking the plane section of a complete space five-point."

Each of figures 14 and 15 above has 15 points and 20 lines.
The Desargues configuration within each figure is denoted by
10 white points and 10 solid lines, with 3 points on each line and
3 lines on each point. Black  points and dashed  lines indicate the
complete space five-point and lines connecting it to the plane section
containing the Desargues configuration.

In a 1915 University of Chicago doctoral thesis, Archibald Henderson
used a complete space six -point to construct a configuration of
15 points and 20 lines in the context not of Desargues '  theorem, but
rather of Brianchon 's theorem and of the Pascal  hexagram.
Henderson's 1915 configuration is, it turns out, isomorphic to that of
the 15 points and 20 lines in the configuration constructed via a
complete space five -point five years earlier by Veblen and Young.
(See, in Veblen and Young's 1910 Vol. I, exercise 11, page 53:
"A plane section of a 6-point in space can  be considered as
3 triangles perspective in pairs from 3 collinear points with
corresponding sides meeting in 3 collinear points." This is the
large  Desargues configuration. See Classical Geometry in Light of 
Galois Geometry
.)

For this large  Desargues configuration see April 19.
For Henderson's complete six –point, see The Six-Set (April 23).
That post ends with figures relating the large  Desargues configuration
to the Galois  geometry PG(3,2) that underlies the Curtis
Miracle Octad Generator  and the large Mathieu group M24 —

IMAGE- Geometry of the Six-Set, Steven H. Cullinane, April 23, 2013

See also Note on the MOG Correspondence from April 25, 2013.

That correspondence was also discussed in a note 28 years ago, on this date in 1985.

Tuesday, July 6, 2010

What “As” Is

Filed under: General,Geometry — Tags: , , , , — m759 @ 8:00 PM

or:  Combinatorics (Rota) as Philosophy (Heidegger) as Geometry (Me)

“Dasein’s full existential structure is constituted by
the ‘as-structure’ or ‘well-joined structure’ of the rift-design*…”

— Gary Williams, post of January 22, 2010

Background—

Gian-Carlo Rota on Heidegger…

“… The universal as  is given various names in Heidegger’s writings….

The discovery of the universal as  is Heidegger’s contribution to philosophy….

The universal ‘as‘ is the surgence of sense in Man, the shepherd of Being.

The disclosure of the primordial as  is the end of a search that began with Plato….
This search comes to its conclusion with Heidegger.”

— “Three Senses of ‘A is B’ in Heideggger,” Ch. 17 in Indiscrete Thoughts

… and projective points as separating rifts

Image-- The Three-Point Line: A Finite Projective Space

    Click image for details.

* rift-design— Definition by Deborah Levitt

Rift.  The stroke or rending by which a world worlds, opening both the ‘old’ world and the self-concealing earth to the possibility of a new world. As well as being this stroke, the rift is the site— the furrow or crack— created by the stroke. As the ‘rift design‘ it is the particular characteristics or traits of this furrow.”

— “Heidegger and the Theater of Truth,” in Tympanum: A Journal of Comparative Literary Studies, Vol. 1, 1998

Saturday, May 22, 2004

Saturday May 22, 2004

Filed under: General — Tags: — m759 @ 3:00 PM

A Form

John Leonard in the June 10, 2004, New York Review of Books, on E. L. Doctorow:

"… he's got urgent things to say and seeks some form to say them in, or a form that will tease and torture secret meanings out of what he thinks he already knows, or a form, like a wishing well, down which to dream, scream, or drown."

48. The Well

The Judgment

The Well. The town may be changed,
But the well cannot be changed.
It neither decreases nor increases.
They come and go and draw from the well.
If one gets down almost to the water
And the rope does not go all the way,
Or the jug breaks, it brings misfortune.

From the Book of Ecclesiastes 12:6

or ever the silver cord be loosed, or the golden bowl be broken, or the pitcher be broken at the fountain, or the wheel broken at the cistern

From Chuck Polisher's I Ching Lexicon:

See also the following form, discussed in

Balanchine's Birthday
(1/9/03) and in

Art Theory
for Yom Kippur

(10/5/03)

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