Eightfold Cube « Search Results

Wednesday, July 11, 2018

Clarity and Precision

Filed under: General,Geometry — m759 @ 9:13 am

"The whole meaning of the word is
looking into something with clarity and precision,
seeing each component as distinct,
and piercing all the way through
so as to perceive the most fundamental reality
of that thing."

For the word itself, try a Web search on
noteworthy phrases above.

“. . . the utterly real thing in writing is
the only thing that counts . . . ."

— Maxwell Perkins to Ernest Hemingway, Aug. 30, 1935

"168"

— Page number in a 2016 Scribner edition
of Stephen King's IT

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Thursday, June 7, 2018

For Dan Brown

Filed under: General,Geometry — Tags: Cullinane Cube, Geometric Theology, Road to Hell, Solomon's Cube — m759 @ 1:09 pm

See also Eightfold Trinity in this journal.

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Wednesday, June 7, 2017

Three Things at Once

Filed under: General,Geometry — Tags: Cube School, Eightfold Metaphysics — m759 @ 1:28 pm

Rosalind Krauss in 1979 —

Nanavira Thera in 1959 —

Cambridge University Press in 1999 —

Saturday, March 4, 2017

At 74

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

New York Times headline about a death
on Friday, March 3, 2017 —

René Préval, President of Haiti
in 2010 Quake, Dies at 74

Tuesday, December 27, 2016

Bright Star

Filed under: General,Geometry — m759 @ 8:15 am

See instances of the title in this journal.

Material related to yesterday evening's post
"Bright and Dark at Christmas" —

The Buddha of Rochester:

See also the Gelman (i.e., Gell-Mann) Prize
in the film "Dark Matter" and the word "Eightfold"
in this journal.

" A fanciful mark is a mark which is invented
for the sole purpose of functioning as a trademark,
e.g., 'Kodak.' "

"… don't take my Kodachrome away." — Paul Simon

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Saturday, September 24, 2016

The Seven Seals

Filed under: General,Geometry — Tags: Myspace China, Seal 7, Seven Seals — m759 @ 7:23 am

From Hermann Weyl's 1952 classic Symmetry —

"Galois' ideas, which for several decades remained
a book with seven seals but later exerted a more
and more profound influence upon the whole
development of mathematics, are contained in
a farewell letter written to a friend on the eve of
his death, which he met in a silly duel at the age of
twenty-one. This letter, if judged by the novelty and
profundity of ideas it contains, is perhaps the most
substantial piece of writing in the whole literature
of mankind."

Some Galois geometry —

See the previous post for more narrative.

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Friday, January 16, 2015

A versus PA

Filed under: General,Geometry — Tags: Defining Form — m759 @ 8:48 pm

"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 series of posts tagged "Defining Form" —

The 4-point affine plane A and
the 7-point projective plane PA —

IMAGE- Triangular models of the 4-point affine plane A and 7-point projective plane PA

The circle-in-triangle of Yale's Figure 30b (PA ) may,
if one likes, be seen as having an occult meaning.

For the mathematical meaning of the circle in PA
see a search for "line at infinity."

A different, cubic, model of PA is perhaps more perspicuous.

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Saturday, November 30, 2013

For Sean Connery

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

On St. Andrew's Day.

A Connery adventure in Kuala Lumpur—

For another Kuala Lumpur adventure, see today's update
to "In Defense of Plato's Realism"—

The July 5, 2007, post linked to
"Plato, Pegasus, and the Evening Star."
For related drama from Kuala Lumpur, see
"Occam's Razor, Plato's Beard."

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Thursday, June 13, 2013

Gate

Filed under: General,Geometry — Tags: Cube School, Field Dream, Field Theology, Vanishing Point — m759 @ 2:13 pm

"Eight is a Gate." — Mnemonic rhyme

Today's previous post, Window, showed a version
of the Chinese character for "field"—

This suggests a related image—

The related image in turn suggests…

Unlike linear perspective, axonometry has no vanishing point,
and hence it does not assume a fixed position by the viewer.
This makes axonometry 'scrollable'. Art historians often speak of
the 'moving' or 'shifting' perspective in Chinese paintings.

Axonometry was introduced to Europe in the 17th century by
Jesuits returning from China.

— Jan Krikke

As was the I Ching. A related structure:

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Wednesday, March 3, 2010

Plato’s Ghost

Filed under: General,Geometry — Tags: Modernism, Narrative Labyrinth — m759 @ 11:07 am

Jeremy Gray, Plato's Ghost: The Modernist Transformation of Mathematics, Princeton, 2008–

"Here, modernism is defined as an autonomous body of ideas, having little or no outward reference, placing considerable emphasis on formal aspects of the work and maintaining a complicated— indeed, anxious— rather than a naïve relationship with the day-to-day world, which is the de facto view of a coherent group of people, such as a professional or discipline-based group that has a high sense of the seriousness and value of what it is trying to achieve. This brisk definition…."

Brisk? Consider Caesar's "The die is cast," Gray in "Solomon's Cube," and yesterday's post—

Group of 8 cube-face permutations generated by reflections in midplanes parallel to faces

This is the group of "8 rigid motions
generated by reflections in midplanes"
of Solomon's Cube.

Related material:

"… the action of G₁₆₈ in its alternative guise as SL(3; Z/2Z) is also now apparent. This version of G₁₆₈ was presented by Weber in [1896, p. 539],* where he attributed it to Kronecker."

— Jeremy Gray, "From the History of a Simple Group," in The Eightfold Way, MSRI Publications, 1998

Here MSRI, an acronym for Mathematical Sciences Research Institute, is pronounced "Misery." See Stephen King, K.C. Cole, and Heinrich Weber.

*H. Weber, Lehrbuch der Algebra, Vieweg, Braunschweig, 1896. Reprinted by Chelsea, New York, 1961.

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Sunday, January 24, 2010

Today’s Sermon

Filed under: General,Geometry — Tags: Octad, Venn Lotus — m759 @ 11:00 am

More Than Matter

Wheel in Webster’s Revised Unabridged Dictionary, 1913

(f) Poetry

The burden or refrain of a song.

⇒ “This meaning has a low degree of authority, but is supposed from the context in the few cases where the word is found.” Nares.

You must sing a-down a-down, An you call him a-down-a. O, how the wheel becomes it! Shak.

“In one or other of G. F. H. Shadbold’s two published notebooks, Beyond Narcissus and Reticences of Thersites, a short entry appears as to the likelihood of Ophelia’s enigmatic cry: ‘Oh, how the wheel becomes it!’ referring to the chorus or burden ‘a-down, a-down’ in the ballad quoted by her a moment before, the aptness she sees in the refrain.”

— First words of Anthony Powell’s novel “O, How the Wheel Becomes It!” (See Library Thing.)

Anthony Powell's 'O, How the Wheel Becomes It!' along with Laertes' comment 'This nothing's more than matter.'

Related material:

Photo uploaded on January 14, 2009
with caption “This nothing’s more than matter”

and the following nothings from this journal
on the same date– Jan. 14, 2009—

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Saturday, February 7, 2009

Saturday February 7, 2009

Filed under: General,Geometry — m759 @ 2:02 pm

Childish Things

(continued from Thursday's
"Through the Looking Glass")

DENNIS OVERBYE

in The New York Times of May 16, 2008
(quoted here on that date):

"From the grave, Albert Einstein poured gasoline on the culture wars between science and religion this week.

A letter the physicist wrote in 1954 to the philosopher Eric Gutkind, in which he described the Bible as 'pretty childish' and scoffed at the notion that the Jews could be a 'chosen people,' sold for $404,000 at an auction in London. That was 25 times the presale estimate."

Einstein did not, at least in the place alleged, call the Bible "childish." Proof:

(Click for larger version.)

Proof that Einstein did not call the Bible 'childish'

The image of the letter is
from the Sept./Oct. 2008
Search Magazine.

By the way, today is
the birthday of G. H. Hardy.

Here is an excerpt from his
thoughts on childish things:

"What 'purely aesthetic' qualities can we distinguish in such theorems as Euclid's or Pythagoras's?…. In both theorems (and in the theorems, of course, I include the proofs) there is a very high degree of unexpectedness, combined with inevitability and economy. The arguments take so odd and surprising a form; the weapons used seem so childishly simple when compared with the far-reaching results; but there is no escape from the conclusions."

Eightfold (2x2x2) cube

"Space: what you
damn well have to see."

— James Joyce, Ulysses

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Wednesday, January 14, 2009

Wednesday January 14, 2009

Filed under: General,Geometry — Tags: Octad, Venn Lotus — m759 @ 2:45 am

Eight is a Gate

From the most highly
rated negative review:

“I never did figure out
what ‘The Eight’ was.”

Various approaches
to this concept
(click images for details):

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Monday, April 28, 2008

Monday April 28, 2008

Filed under: General,Geometry — Tags: 2x4, Brick Space, four-set — m759 @ 7:00 am

Religious Art

The black monolith of
Kubrick's 2001 is, in
its way, an example
of religious art.

Black monolith, proportions 4x9

One artistic shortcoming
(or strength– it is, after
all, monolithic) of
that artifact is its
resistance to being
analyzed as a whole
consisting of parts, as
in a Joycean epiphany.

The following
figure does
allow such
an epiphany.

A 2x4 array of squares

One approach to
the epiphany:

"Transformations play
a major role in
modern mathematics."
– A biography of
Felix Christian Klein

The above 2×4 array
(2 columns, 4 rows)
furnishes an example of
a transformation acting
on the parts of
an organized whole:

The 35 partitions of an 8-set into two 4-sets

For other transformations
acting on the eight parts,
hence on the 35 partitions, see
"Geometry of the 4×4 Square,"
as well as Peter J. Cameron's
"The Klein Quadric
and Triality" (pdf),
and (for added context)
"The Klein Correspondence,
Penrose Space-Time, and
a Finite Model."

For a related structure–
not rectangle but cube–
see Epiphany 2008.

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Tuesday, February 6, 2007

Tuesday February 6, 2007

Filed under: General,Geometry — Tags: Brick Space, Stevens Rock — m759 @ 8:00 am

The Poetics of Space

The title is from Bachelard.
I prefer Stevens:

The rock is the habitation of the whole,
Its strength and measure, that which is near, point A
In a perspective that begins again

At B:  the origin of the mango's rind.
It is the rock where tranquil must adduce
Its tranquil self, the main of things, the mind,

The starting point of the human and the end,
That in which space itself is contained, the gate
To the enclosure, day, the things illumined

By day, night and that which night illumines,
Night and its midnight-minting fragrances,
Night's hymn of the rock, as in a vivid sleep.

— Wallace Stevens,
"The Rock," 1954

Joan Ockman in Harvard Design Magazine (Fall 1998):

"'We are far removed from any reference to simple geometrical forms,' Bachelard wrote…."

No, we are not. See Log24, Christmas 2005:

Compare and contrast:

(Click on pictures for details.)

More on Bachelard from Harvard Design Magazine:

"The project of discerning a loi des quatre éléments would preoccupy him until his death…."

For such a loi, see Theme and Variations and…

The image “http://www.log24.com/log/pix07/070206-Elements.gif” cannot be displayed, because it contains errors.

(Click on design for details.)

Thought for Today:
"If you can talk brilliantly
about a problem, it can create
the consoling illusion that
it has been mastered."
— Stanley Kubrick, American
movie director (1928-1999).

(AP, "Today in History,"
February 6, 2007)

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Sunday, March 26, 2006

Sunday March 26, 2006

Filed under: General,Geometry — Tags: March 26-29 2006 — m759 @ 12:00 am

Midnight in the Garden
continued

Questions posed by
Roberta Smith in the
New York Times
of Jan. 13, 2006:

“‘What is art?’ may be the
art world’s most relentlessly asked
question. But a more pertinent one
right now is, ‘What is an art gallery?'”

— from “Who Needs a
White Cube These Days?“

The image “http://www.log24.com/log/pix06/060320-Masks.jpg” cannot be displayed, because it contains errors.

An example that may help:
London’s White Cube gallery
and its current Liza Lou exhibit,
which is said to convey
“a palpable sense of use,
damage, lost time, lost lives.”

See the previous entry for details.

On the brighter side, we have

Clint Eastwood on the
“Midnight in the Garden
of Good and Evil”
soundtrack CD—

“Accentuate the positive”–

and an entry from last Christmas:

Compare and contrast:

(Click on pictures
for details.)

“Recollect what I have said to you,
that this world is a comedy
to those who think,
a tragedy to those who feel.
This is the quint-essence of all
I have learnt in fifty years!”

— Horace Walpole,
letter to Horace Mann,
5 March, 1772

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