Log24

Thursday, April 4, 2019

Expanding the Spielraum . . .

Filed under: General — Tags: — m759 @ 9:27 PM

Continues . . .

. . . with Stephen King.

Saturday, June 3, 2017

Expanding the Spielraum (Continued*)

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

Or:  The Square

"What we do may be small, but it has
 a certain character of permanence."
— G. H. Hardy

* See Expanding the Spielraum in this journal.

Wednesday, April 12, 2017

Expanding the Spielraum

Filed under: General,Geometry — Tags: , — m759 @ 9:48 AM

Cézanne's Greetings.

"Cézanne ignores the laws of classical perspective . . . ."

— Voorhies, James. “Paul Cézanne (1839–1906).”
In Heilbrunn Timeline of Art History .  New York:
The Metropolitan Museum of Art, 2000–. (October 2004)

Some others do not.

This is what I called "the large Desargues configuration
in posts of April 2013 and later.

Sunday, December 11, 2016

Expanding the Spielraum

Filed under: General — m759 @ 11:00 AM

(Continued)

Tony Stark's "little gray area" remark to Peter Parker 
in the previous post suggests an elementary calculation:

Compare to a remark from Wikipedia:

"This is the total area of
the 88 modern constellations 
in the sky."

— Wikipedia, Square degree

Wednesday, June 15, 2016

Expanding the Spielraum

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

Continues

Rubik cube in the heading of the homepage of the Notices of the American Mathematical Society

"My AMS invited address at the SIAM Annual Meeting July 11–15
in Boston discusses the extension of eigenvectors and singular
vectors from matrices to higher order tensors."

Bernd Sturmfels in the June-July 2016 AMS Notices

See also Sturmfels in this  journal — for instance, in
"Expanding the Spielraum," a post of Feb. 3, 2015 —

Thursday, May 26, 2016

Expanding the Spielraum

Filed under: General — m759 @ 1:45 AM

(Continued)

The physicist Hendrik van Dam was mentioned in recent posts.

He reportedly died at 78 on February 11, 2013.

A post from that date, and a followup —

Monday, October 26, 2015

Expanding the Spielraum

Filed under: General — m759 @ 4:00 PM

(Continued)

Halloween meditation  on  the Tummelplatz  at Innsbruck

"Die Ritter und Knappen des nahegelegenen Ambras
pflegten hier ihre Rosse zu tummeln, woher sich auch
der Name Tummelplatz  schreibt."

"The knights and squires of nearby Ambras used to let their
steeds romp here, whence came the name Tummelplatz ." 

— Quelle: Ludwig von Hörmann, "Der Tummelplatz  bei Amras,"
in: Der Alpenfreund , 1. Band, Gera 1870, S. 72 – 73.

See as well Sigmund Freud, Erinnern, Wiederholen und Durcharbeiten
(1914) —

"Wir eröffnen ihm die Übertragung als den Tummel­platz ,
auf dem ihm gestattet wird, sich in fast völliger Freiheit
zu entfalten, und auferlegt ist, uns alles vorzuführen,
was sich an pathogenen Trieben im Seelenleben des
Analysierten verborgen hat."

"We admit it into the transference as a playground
in which it is allowed to expand in almost complete freedom
and in which it is expected to display to us everything in the
way of pathogenic instincts that is hidden in the patient's mind."

This passage has been discussed by later psychotherapists,
notably Russell Meares.  Dr. Meares, working from a translation
that has "playground" for Freud's Tummelplatz , uses Spielraum  
in place of Freud's own word.

For related material in this  journal, see Expanding the Spielraum.
An illustration from that search —

IMAGE- Concepts of Space

Thursday, June 18, 2015

Expanding the Spielraum

Filed under: General — Tags: — m759 @ 2:25 PM

(Continued from Feb. 3, 2015)

IMAGE- Spielfeld (1982-83), by Wolf Barth

The above artist  Wolf Barth is not the same person
as the mathematician  Wolf Barth quoted in the 
previous post.  For further background on the artist, see
an article in Neue Zürcher Zeitung  from Nov. 15, 2013.

Saturday, April 18, 2015

Expanding the Spielraum

Filed under: General — Tags: — m759 @ 1:30 PM

Continues.

See also today's previous post and the new film "Beyond the Reach,"
filmed in northwest New Mexico —

IMAGE- Map of northwest New Mexico

Tuesday, February 3, 2015

Expanding the Spielraum

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

A short poem by several authors:

"The role of
the 16 singular points
on the Kummer surface
is now played by
the 64 singular points
on the Kummer threefold."

— From Remark 2.4 on page 9 of
"The Universal Kummer Threefold,"
by Qingchun Ren, Steven V Sam,
Gus Schrader, and Bernd Sturmfels,
http://arxiv.org/abs/1208.1229v3,
August 6, 2012 — June 12, 2013.

See also "Expanded Field" in this journal.

IMAGE- Concepts of Space

Illustration from "Sunday School," July 20, 2014.

Other Log24 background:  Kummer, Spielraum, Art Space.

Monday, October 26, 2015

Expanding the Seagram Spielraum

Filed under: General — m759 @ 11:20 PM

From the previous post, Expanding the Spielraum

"The knights and squires of nearby Ambras used to let their
steeds romp here, whence came the name Tummelplatz ." 

— Quelle: Ludwig von Hörmann, "Der Tummelplatz  bei Amras,"
in: Der Alpenfreund , 1. Band, Gera 1870, S. 72 – 73.

"Integrity, Craftsmanship, Tradition"

Thursday, July 2, 2015

Hausdorff’s Spielraum

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

Continued from January 31, 2015 .

Deepening the Spielraum

Filed under: General,Geometry — Tags: — m759 @ 2:00 AM

(A sequel to Expanding the Spielraum (Feb. 3, 2015))

"Knowledge, wisdom even, lies in depth, not extension."

Tim Parks in The New York Review of Books ,
     5 PM ET on June 26, 2015

See also Log24 posts on the following figure —

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

Friday, February 6, 2015

The Annotated Spielraum

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

Comments on two sub-images from yesterday's
The Big Spielraum  (image, 1 MB) that may or
may not interest Emma Watson —

The Potter Sub-Image

This is from a link in a July 8, 2011, post:

The above "Childhood's End" link leads to
a midrash on the Harry Potter series:

"After pg. 759 in Harry Potter and the 
Deathly Hallows 
, my childhood ended."

The Carmichael Sub-Image

The number of the last page in the last Harry Potter
book is 759.  This number may, for those with
cabalistic tendencies, be interpreted as the
number 3*23*11 from a 1931 mathematics paper:

Thursday, February 5, 2015

The Big Spielraum

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

From the Office for the Arts at Harvard:

Harvard Thinks Big VI

College Events Board

Location: Sanders Theatre, Memorial Hall,
45 Quincy Street, Cambridge
Parking: none

On Sale Date: 1/29/2015
How to get tickets: The Harvard Box Office
617-496-2222

Thursday 2/5 08:00 PM

Ticket Prices: Free. Harvard ID only.
2 tickets per person per ID.
Tickets valid until 7:45PM. 

Ticket Availability: Good 

The Harvard College Events Board presents Harvard Thinks Big VI, a night of big ideas and thinking beyond traditional boundaries. On Thursday February 5th at 8 pm in Sanders Theatre, 7 Harvard professors and lecturers will speak for ten minutes each to discuss a topic that intrigues and excites them. This annual event was first started in order to introduce the Harvard community to the fascinating research and developments from some of the greatest minds on campus. 

See as well The Big Spielraum  (1 MB).

Monday, February 2, 2015

Spielraum as Ω

Filed under: General,Geometry — Tags: , — m759 @ 6:29 PM
 

From "Origins of the Logical Theory of Probability: von Kries, Wittgenstein, Waismann," by Michael Heidelberger —

"Von Kries calls a range of objective possibilities of a hypothesis or event (under given laws) its Spielraum   (literally: play space), which can mean ‘room to move’, ‘leeway’, ‘latitude of choice’, ‘degree of freedom’ or ‘free play’ and ‘clearance’ – or even ‘scope’. John Maynard Keynes translated it as ‘field’, but the term ‘range’ has generally been adopted in English. Von Kries now holds that if numerical probability were to make any sense at all it must be through this concept of the Spielraum  . Von Kries’s theory is therefore called a ‘Spielraum  theory’ or ‘range theory of probability’."

— International Studies in the Philosophy of Science , Volume 15, Issue 2, 2001, pp. 177-188

See also the tag Points Omega
(Scroll down to January 11-12, 2015.)

Related material:

"Now, for example, in how far are
the six sides of a symmetric die
'equally possible' upon throwing?"

— From "The Natural-Range Conception
     of Probability," by Dr. Jacob Rosenthal,
     page 73 in Time, Chance, and
     Reduction: Philosophical Aspects of
     Statistical 
Mechanics , ed. by 
     Gerhard Ernst and Andreas Hüttemann, 
     Cambridge U. Press, 2010, pp. 71-90

Sunday, February 1, 2015

Spielraum III

Filed under: General — Tags: — m759 @ 11:30 PM

From today's Super Bowl Halftime:

Click for image in context.

See also Spielraum  in this journal.

Saturday, January 31, 2015

Spielraum II

Filed under: General — Tags: — m759 @ 8:45 PM

For those who prefer Heidegger to Hausdorff:

Spielraum

Filed under: General — Tags: — m759 @ 1:27 PM

From the concluding paragraph of a new book by
mathematician Michael Harris:

"A team of eminent scholars is completing a definitive
edition of Hausdorff’s collected works—'unique
in the annals of mathematical publishing'— with the
care befitting the literary figure he undoubtedly was….
he is honored as, perhaps, the first modern
mathematician to give a name to what we have been
calling the 'relaxed field'— he called it the
'Spielraum  of thought'— and as a mathematician
who never lost his sensitivity to his chosen field’s
problematic attractions while remaining fully aware that
every veil lifted only reveals another veil."

— Harris, Michael, Mathematics without Apologies:
Portrait of a Problematic Vocation  
(2015-01-18) 
(pp. 324-325). Princeton U. Press. Kindle Edition. 

Related material:  Spiel ist nicht Spielerei .

Friday, April 5, 2019

A Definite Field

Filed under: General — m759 @ 10:45 AM

"We render the compulsion harmless, and indeed useful,
by giving it the right to assert itself in a definite field.
We admit it into the transference as a playground…."

— Sigmund Freud, 1914, "Remembering, Repeating,
and Working-Through" (See "Expanding the Spielraum,"
Oct. 26, 2015, in this  journal.)

An indefinite field —


A definite field —

A circular I Ching

Monday, October 22, 2018

Story Space

Filed under: General — Tags: — m759 @ 4:48 PM

A better term than "phase space" might be "story space."

See as well Expanding the Spielraum.

Sunday, June 4, 2017

Sequel to “The Square”* —

Filed under: General — m759 @ 3:03 PM

The Cube

CodePen logo, pictured here on May 28, 2017

From YouTube, "The Cube," published on April 6, 2016

Meanwhile, also on April 6, 2016, at 2:01 AM ET 

* See The Pinterest Directive and Expanding the Spielraum.

Thursday, April 20, 2017

Point 8777*

Filed under: General — m759 @ 2:42 PM

Or:  Expanding the Spielraum, continued

Wikipedia on author Michael Connelly

Connelly had planned on following his father’s early choice of
career in building construction and started out at the 
University of Florida in Gainesville as a building construction major.
After earning grades that were lower than expected, Connelly went
to see Robert Altman’s film The Long Goodbye (1973) and was
enchanted by what he saw. The film, based on Raymond Chandler’s 
1953 novel of the same name, inspired Connelly to want to become
a mystery writer. Connelly went home and read all of Chandler's
works featuring Philip Marlowe, a detective in Los Angeles during
the 1940s and ‘50s, and decided to switch majors to journalism with
a minor in creative writing.[4] He was a student of Harry Crews.

[See also

https://blogs.wsj.com/speakeasy/2012/11/24/
the-teacher-michael-connelly-never-forgot/
.]

A 2002 novel by Connelly — City of Bones .

Two scenes from a 2014 TV pilot based on the 2002 novel —

The "Bosch" pilot does not state the address, but its location in the
Hollywood Hills suggests a review of Heinlein Lottery in this journal. 

"Bonedigger Bonedigger
 Dogs in the moonlight"
 — Paul Simon

* Title suggested by that of the previous post, "Point Zero."

Friday, June 3, 2016

Bruins and van Dam

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

A review of some recent posts on Dirac and geometry,
each of which mentions the late physicist Hendrik van Dam:

The first of these posts mentions the work of E. M. Bruins.
Some earlier posts that cite Bruins:

Thursday, April 30, 2015

Meditation on an Icon

Filed under: General — m759 @ 2:01 AM

IMAGE- Brian Bard on 'Heidegger's Reading of Heraclitus'

See also Legespiel  in this journal.

Saturday, February 28, 2015

Elegy with Stars

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

This evening's New York Times —

"William Thomas McKinley, a prolific American composer
whose music was infused with the jazz he had performed
since childhood, died on Feb. 3 at his home in Reading,
Mass. He was 76.

He died in his sleep, his son Elliott said."

"William Thomas McKinley: Elegy for Strings (2006)

[Elliott McKinley]  

137 views as of 9:45 PM ET Feb. 28, 2015

Published on Feb 11, 2015

Composed as an elegy and tribute for friends and family
that have passed, spurred by the passing of McKinley's
long time friend, drummer Roger Ryan. The performance
heard here is by the Seattle Symphony under the direction
of Gerard Schwarz. 

Photos by Elliott McKinley (Rho Ophiuchi nebula complex…
and the Pleiades…) shot at Cherry Springs State Park."

Related material from the date of McKinley's death —
Expanding the Spielraum.

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 .

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."

Friday, September 27, 2019

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"

Tuesday, September 24, 2019

American Mathematical Society News

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

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

Friday, August 30, 2019

The Coxeter Aleph

Filed under: General — Tags: — m759 @ 4:21 AM

(Continued)

The previous post displayed part of a page from
a newspaper published the day Olivia Newton-John
turned 21 — Friday, September 26, 1969.

A meditation, with apologies to Coleridge:

In Xanadu did Newton-John
A stately pleasure-square decree
Where Aleph the sacred symbol ran
Through subsquares measureless to man.

A related video —

Beware, beware, her flashing eyes, her floating hair:

Set design —

As opposed to block design

Tuesday, August 27, 2019

Tiger Leaps

Filed under: General — Tags: , — m759 @ 10:33 AM

Walter Benjamin on 'a tiger's leap into the past'

See also Tiger in this journal, esp.

The image “http://www.log24.com/log/pix05/050123-Tiger.JPG” cannot be displayed, because it contains errors.   and . . .

other "Death and the Spirit" posts.

Friday, August 16, 2019

Nocciolo

Filed under: General — Tags: , , — m759 @ 10:45 AM

(Continued)

IMAGE- 'Nocciolo': A 'kernel' for Pascal's Hexagrammum Mysticum: The 15 2-subsets of a 6-set as points in a Galois geometry.

A revision of the above diagram showing
the Galois-addition-table structure —

Related tables from August 10

See "Schoolgirl Space Revisited."

Saturday, August 10, 2019

Schoolgirl Space* Revisited:

Filed under: General — Tags: , — m759 @ 10:51 PM

The Square "Inscape" Model of
the Generalized Quadrangle W(2)

Click image to enlarge.

* The title refers to the role of PG (3,2) in Kirkman's schoolgirl problem.
For some backstory, see my post Anticommuting Dirac Matrices as Skew Lines
and, more generally, posts tagged Dirac and Geometry.

Frases de Cómic

Filed under: General — Tags: — m759 @ 4:03 PM

Thursday, August 8, 2019

Release Date

Filed under: General — Tags: — m759 @ 4:17 AM

From this  journal on that date

Piano roll for "I am sixteen going on seventeen" —

Saturday, July 27, 2019

Make America Strange Again

Filed under: General — Tags: — m759 @ 10:59 PM

Suggested by the previous post, "The Swarm" —

“‘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

The Swarm

Filed under: General — Tags: — m759 @ 10:31 PM

“Design Is How It Works.” — Steve Jobs

Filed under: General — Tags: — m759 @ 9:59 PM

The Stephen King Intelligence Test

Filed under: General — Tags: , — m759 @ 4:41 PM


Related images —

See also other posts tagged Arti Facts.

This  post was suggested by those posts and by the following
attempt at humor —

Tonality

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

https://languagelog.ldc.upenn.edu/nll/?p=22045

. . . the ancient Chinese made music the pinnacle of wisdom.

There was a Classic of Music (Yuè jīng 樂經), but it was lost already by the Han Dynasty (206 BC-220 AD).  Yet we know the esteem in which music was held by the ancient Chinese from passages in the classics like the following:

The Master heard the Shao in Qi and for three months did not notice the taste of the meat he ate. He said, 'I never dreamt the joys of music could reach such heights.'(D.C. Lau)

Analects  7.14

Shao is the music of the mythical emperor, Shun 舜.

Qi one of the Warring States.

Extensive commentary here.

Another instance of the sublimity of music in ancient China is the description of the performance of the Yellow Emperor's "The Pond of Totality" in chapter 14 of the Zhuang Zi  (see Victor H. Mair, tr., Wandering on the Way  [Bantam, 1994; University of Hawaii Press, 1998], pp. 132-136, available here).

Conversely, language studies in traditional China were referred to as "minor learning" (xiǎoxué 小學).

November 5, 2015 @ 4:05 pm · Filed by Victor Mair under Language and musicLanguage and philosophy

See also Ervin Wilson in Wikipedia, and a Log24 post from
the date of his death — December 8, 2016.

Monday, July 22, 2019

The Four Diamonds Meet the Five Red Herrings

Filed under: General — Tags: — m759 @ 11:34 AM

Lord Peter Wimsey (Balliol 1912) on the Balliol-Trinity rivalry at Oxford:

See also Balliol College in the post subtitled Spidey Goes to Church.

Signed, Sealed, Delivered

Filed under: General — Tags: — m759 @ 5:58 AM

Visual Languages

Filed under: General — Tags: — m759 @ 4:48 AM

Good question. See also this  journal on the above date —

September 15, 2018.

Space, Time, Form

Filed under: General — Tags: — m759 @ 3:33 AM

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

Click the image for some remarks on a related novel.

Saturday, July 20, 2019

Humor for Professor X

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

Thursday, July 18, 2019

Split

Filed under: General — Tags: — m759 @ 6:55 PM

"My words say split, but my words they lie" — Bruce Springsteen

See a search for "Split" in this journal.

Tuesday, July 16, 2019

Schoolgirl Space for Quantum Mystics

Filed under: General — Tags: , — m759 @ 2:16 PM

From a post on St. Andrew's Day, 2017

See also "E-Numbers" and "E-Girls."

Sunday, July 14, 2019

Old Pathways in Science:

Filed under: General — Tags: , — m759 @ 12:37 PM

The Quantum Tesseract Theorem Revisited

From page 274 — 

"The secret  is that the super-mathematician expresses by the anticommutation
of  his operators the property which the geometer conceives as  perpendicularity
of displacements.  That is why on p. 269 we singled out a pentad of anticommuting
operators, foreseeing that they would have an immediate application in describing
the property of perpendicular directions without using the traditional picture of space.
They express the property of perpendicularity without the picture of perpendicularity.

Thus far we have touched only the fringe of the structure of our set of sixteen E-operators.
Only by entering deeply into the theory of electrons could I show the whole structure
coming into evidence."

A related illustration, from posts tagged Dirac and Geometry —

Anticommuting Dirac matrices as spreads of projective lines

Compare and contrast Eddington's use of the word "perpendicular"
with a later use of the word by Saniga and Planat.

Saturday, July 13, 2019

Which Roof?

Filed under: General — Tags: , , — m759 @ 10:15 AM

Related material — Tetrahedron vs. Square and Cézanne's Greetings

Compare and contrast:

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

Friday, July 12, 2019

“Hello, old friend.” — Anthony Hopkins, Westworld S2 E6

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

See as well the previous post.

Ex Fano* Continues.

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

Professor Corbató reportedly died today.

* See Ex Fano  in this journal.

Instrumental

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

The title is from a New York Times  correction in the previous post.

Introduction

'The Eddington Song'

Main Body

Piano roll for "I am sixteen going on seventeen" —

Medal of 9/15/06

Backstory:  Posts tagged Root Circle.

Thursday, July 11, 2019

Small World Continues.

Filed under: General — Tags: — m759 @ 11:08 PM

The book Ex-Prodigy  quoted above is by Norbert Wiener.

The Fano Correction

Friday, July 5, 2019

The Motive for Metaphor

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

"János Bolyai was a nineteenth-century mathematician who
set the stage for the field  of non-Euclidean geometry."

Transylvania Now , October 26, 2018

 

From  Coxeter and the Relativity Problem

http://www.log24.com/log/pix11/110107-Aleph-Sm.jpg

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"

Wednesday, June 19, 2019

Diagram

Filed under: General — Tags: — m759 @ 11:36 AM

This post was suggested by the July 2006 posts now tagged Crazy Diamond.

Tuesday, June 18, 2019

The 7/11 Manifesto

Filed under: General — Tags: — m759 @ 10:07 PM

See 7/11, 2006.

Related material — Dabblers in the Collective Unconscious.

The Crooning

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

For fans of the story theory of truth  

 A "tale as old as time . . ."
 — Song lyric,  Beauty and the Beast

Nicholas Hoult as X-Men "Beast" Hank McCoy

See also the previous post, "Equals Tolkien?"

Related material The real  McCoy

Equals Tolkien?

Filed under: General — Tags: — m759 @ 12:34 PM

Paris Review

Filed under: General — Tags: — m759 @ 3:33 AM

"The loveliness of Paris seems somehow sadly gay." — Song lyric

Stewart also starred in "Equals" (2016). From a synopsis —

"Stewart plays Nia, a writer who works at a company that extols
the virtues of space exploration in a post-apocalyptic society.
She falls in love with the film's main character, Silas (Nicholas Hoult),
an illustrator . . . ."

Space art in The Paris Review

For a different sort of space exploration, see Eightfold 1984.

June Moon Croon

Filed under: General — Tags: — m759 @ 12:02 AM

Monday, June 17, 2019

The Callahan Turtle

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

By Stephen King

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

Salvation by Grace

Filed under: General — Tags: , — m759 @ 3:18 PM

High Society

Filed under: General — Tags: , — m759 @ 1:16 PM

From the date in the above Google search result —

 See as well Jeremy Gray in this  journal.

Thursday, June 13, 2019

The Reality Blocks

Filed under: General — Tags: — m759 @ 9:24 PM

The new Log24 tag "Eightfold Metaphysics" used in the previous post
suggests a review of posts that were tagged "The Reality Blocks" on May 24.

Then there is, of course, the May 24 death of Murray Gell-Mann, who
hijacked from Buddhism the phrase "eightfold way."

See Gell-Mann in this journal and May 24, 2003.

Tuesday, June 11, 2019

Relish

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

"Center loosens, forms again elsewhere." — Roger Zelazny

See also an image in memory of the Coppertone artist
from a post of May 18, 2006

The image “http://www.log24.com/log/pix06A/060517-StarAndDiamond.bmp” cannot be displayed, because it contains errors.

“My God, it’s
full of stars!”

Monday, June 10, 2019

Revelations of a Transcendental Subject

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

(Namely, Plato's ghost)

Background: "Transcendental subject" is Kant's term for, more or less, the self.

Rosalind Krauss in 1978 —

"To get inside the systems of this work,
whether LeWitt's or Judd's or Morris's,
is precisely to enter
a world without a center,
a world of substitutions and transpositions 
nowhere legitimated by the revelations
of a transcendental subject. This is the strength
of this work, its seriousness, and its claim to modernity." 

More from Krauss —

A book by an author with somewhat wider "cultural experience" —

See also "Plato's Diamond" in this journal.

Saturday, June 8, 2019

Nowhere Legitimated

Filed under: General — Tags: — m759 @ 10:28 PM

Art Object, continued and continued

Filed under: General — Tags: , — m759 @ 1:21 PM

Notes on a remark by Chuanming Zong

See as well posts mentioning "An Object of Beauty."

Update of 12 AM June 11 — A screenshot of this post 
is now available at  http://dx.doi.org/10.17613/hqk7-nx97 .

Tuesday, May 28, 2019

Hogwash for Brattlefilm

Filed under: General — Tags: — m759 @ 10:54 PM

Related material — Khurana in this journal and
in The Harvard Crimson .

“Simplification in Its Purest Form”

Filed under: General — Tags: — m759 @ 10:08 PM

For students of the Hogwash School of Witchcraft and Wizardry —

"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." 

— Sean Carroll in The New York Times  today 
in an opinion piece titled "The Physicist Who
Made Sense of the Universe"

Related remarks:  See a Log24 search for "Simpli".

The Khurana Embarrassment

Filed under: General — Tags: — m759 @ 12:36 PM

(A title for Harlan Kane)

Friday, May 24, 2019

Stevens and the Hoary Sages

Filed under: General — Tags: — m759 @ 11:05 AM

See also other posts now tagged The Reality Blocks.

Tuesday, May 21, 2019

Inside the White Cube

Filed under: General — Tags: , , — m759 @ 11:01 AM

(Continued)

Monday, May 20, 2019

The Bond with Reality

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


"The bond with reality is cut."

— Hans Freudenthal, 1962

Indeed it is.

Sunday, May 19, 2019

The Building Blocks of Geometry

Filed under: General — Tags: , — m759 @ 10:21 PM

From "On the life and scientific work of Gino Fano
by Alberto Collino, Alberto Conte, and Alessandro Verra,
ICCM Notices , July 2014, Vol. 2 No. 1, pp. 43-57 —

" Indeed, about the Italian debate on foundations of Geometry, it is not rare to read comments in the same spirit of the following one, due to Jeremy Gray13. He is essentially reporting Hans Freudenthal’s point of view:

' When the distinguished mathematician and historian of mathematics Hans Freudenthal analysed Hilbert’s  Grundlagen he argued that the link between reality and geometry appears to be severed for the first time in Hilbert’s work. However, he discovered that Hilbert had been preceded by the Italian mathematician Gino Fano in 1892. . . .' "

13 J. Gray, "The Foundations of Projective Geometry in Italy," Chapter 24 (pp. 269–279) in his book Worlds Out of Nothing , Springer (2010).


Restoring the severed link —

Structure of the eightfold cube

See also Espacement  and The Thing and I.
 

Related material —

 
 

Friday, May 10, 2019

I Ching g6

Filed under: General — Tags: , , — m759 @ 12:25 PM

For fans of Resonance Science

"When the men on the chessboard
get up and tell you where to go …."

Thursday, May 9, 2019

Defense Against the Dark Arts

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

F. Lanier Graham chess set (king-queen arrangement by the Wachowskis)

Monday, May 6, 2019

Possibilities

Filed under: General — Tags: — m759 @ 12:25 PM

Related materialThe last three posts —

The Crimson Abyss,
Transgressive Politics at Harvard, and
"Thousand" Rhetoric

— as well as Saturday's The Chinese Jars of Shing-Tung Yau.

Sunday, May 5, 2019

“Thousand” Rhetoric

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

Compare and contrast —

"A Thousand Possibilities"
— Title of a Harvard Crimson  May 3 column

See also The Thousand  in this  journal.

Transgressive Politics at Harvard

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

Related material —

See also the previous post.

The Crimson Abyss

Filed under: General — Tags: — m759 @ 12:20 PM

Continues.

The following conference has just ended.

Yau's actual 70th birthday was April 4.

Saturday, May 4, 2019

The Long Strange Trip of Abstract Art

Filed under: General — Tags: , — m759 @ 9:23 PM

In memory of an art collector's April 24 death —

See also Log24 on April 24

Inside the White Cube

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

Structure of the eightfold cube

See also Espacement  and The Thing and I.

The Chinese Jars of Shing-Tung Yau

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

The title refers to Calabi-Yau spaces.

T. S. Eliot —

Four Quartets

. . . Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness.

A less "cosmic" but still noteworthy code — The Golay code.

This resides in a 12-dimensional space over GF(2).

Related material from Plato and R. T. Curtis

Counting symmetries with the orbit-stabilizer theorem

A related Calabi-Yau "Chinese jar" first described in detail in 1905

Illustration of K3 surface related to Mathieu moonshine

A figure that may or may not be related to the 4x4x4 cube that
holds the classical  Chinese "cosmic code" — the I Ching

ftp://ftp.cs.indiana.edu/pub/hanson/forSha/AK3/old/K3-pix.pdf

Wednesday, May 1, 2019

The Medium and the Message

Filed under: General — Tags: — m759 @ 6:45 PM

In memory of Quentin Fiore — from a Log24 search for McLuhan,
an item related to today's previous post . . .

Related material from Log24 on the above-reported date of death —

See also, from a search for Analogy in this journal . . .

 .

Wednesday, April 3, 2019

The Malkovich Pictures

Filed under: General — Tags: — m759 @ 10:27 PM

". . . humanity battling an unseen force . . . ." —

Quantum Space Elements?

Nocturnal Object of Beauty

Filed under: General — Tags: — m759 @ 2:41 AM

http://www.log24.com/log/pix11B/110712-ObjectOfBeauty.jpg
 

 

What is going on in this picture?
 

Monday, February 25, 2019

The Deep Six

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

". . . this notion of ‘depth’ is an elusive one
even for a mathematician who can recognize it. . . ."

— G. H. Hardy, A Mathematician's Apology

See Six-Set in this journal.

“Far from the shallow now”

Filed under: General,Geometry — Tags: , , , — m759 @ 12:06 AM

See posts tagged depth.

See as well Eddington Song and the previous post.

Sunday, February 24, 2019

Exceeding His Grasp

Filed under: General,Geometry — Tags: , , , — m759 @ 4:09 PM

See also Hudson Hawk in this  journal.

Saturday, February 23, 2019

Code Rain

Filed under: General — Tags: — m759 @ 11:30 PM

See 031105-code in this journal, the Wachowskis
at Wikipedia, and The Omega Matrix in this journal.

Austrian Wins Kyoto Prize (Revisited)

Filed under: General — Tags: — m759 @ 3:29 PM

For the title, see Schwarzenegger and "Clockwork Orange"
in the June 2005 post "All in the Timing."

Related music — Taps for Donen

Donen reportedly died on Thursday.
See this journal on that day for a related
New York Times  meditation.

Thursday, February 21, 2019

Frenkel on “the Rashomon Effect”

Filed under: General — Tags: , — m759 @ 1:44 PM

Earlier in Frenkel's above opinion piece —

"What this research implies is that we are not just hearing
different 'stories' about the electron, one of which may be
true. Rather, there is one true story, but it has many facets,
seemingly in contradiction, just like in 'Rashomon.' 
There is really no escape from the mysterious — some
might say, mystical — nature of the quantum world."

See also a recent New Yorker  version of the fashionable cocktail-party
phrase "the Rashomon effect."

For a different approach to the dictum "there is one true story, but
it has many facets," see . . .

"Read something that means something."
New Yorker  motto

Monday, February 18, 2019

The Joy of Six

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


__________________________________________________________________________

See also the previous post.

I prefer the work of Josefine Lyche on the smallest perfect number/universe.

Context —

Lyche's Lynx760 installations and Vigeland's nearby Norwegian  clusterfuck.

Quantum Choreography

Filed under: General — Tags: — m759 @ 1:06 PM

In the beginning of the 1954 film "Seven Brides for Seven Brothers,"
Adam, oldest of the brothers, is paired with Milly. The problem then is
to find brides for Adam's six brothers.

Above is a video illustration, published on Aug. 12, 2016, of the six couples. 
Matching them involves some choreography.

See also this  journal on Aug. 12, 2016 — "Dustbucket Physics" —

" through the proposition machine of quantum mechanics
comes pregeometry; pregeometry makes geometry;
geometry gives rise to matter and the physical laws
and constants of the universe." 

— Harvard professor Peter Galison, 
     defender of the faith of Scientism

For a different sort of quantum "proposition machine," see posts tagged
Dirac and Geometry.

Thursday, February 7, 2019

Geometry of the 4×4 Square: The Kummer Configuration

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

From the series of posts tagged Kummerhenge

A Wikipedia article relating the above 4×4 square to the work of Kummer —

A somewhat more interesting aspect of the geometry of the 4×4 square
is its relationship to the 4×6 grid underlying the Miracle Octad Generator
(MOG) of R. T. Curtis.  Hudson's 1905 classic Kummer's Quartic Surface
deals with the Kummer properties above and also foreshadows, without
explicitly describing, the finite-geometry properties of the 4×4 square as
a finite affine 4-space — properties that are of use in studying the Mathieu
group M24  with the aid of the MOG.

Sunday, January 13, 2019

The Clifford Narrative

Filed under: General — Tags: — m759 @ 3:17 AM

See also Clifford in this  journal, in particular 
The Matrix for Quantum Mystics 
(Log24, St. Andrew's Day, 2017).

Saturday, December 22, 2018

The Hat Tip

Filed under: General — Tags: , — m759 @ 9:59 PM

"Form the turtle!"
— Rex Harrison, quoted here
on March 12, 2005.

Cremona-Richmond

Filed under: General,Geometry — Tags: , — m759 @ 12:34 PM

The following are some notes on the history of Clifford algebras
and finite geometry suggested by the "Clifford Modules" link in a
Log24 post of March 12, 2005

A more recent appearance of the configuration —

Thursday, December 20, 2018

Slow

Filed under: General — Tags: , — m759 @ 8:12 PM

Some images suggested by the previous post and by the date
of the documentary below — March 12, 2005 —

See also Slow Art.

Wednesday, December 12, 2018

An Inscape for Douthat

Some images, and a definition, suggested by my remarks here last night
on Apollo and Ross Douthat's remarks today on "The Return of Paganism" —

Detail of Feb. 20, 1986, note by Steven H. Cullinane on Weyl's 'relativity problem'

Kibler's 2008 'Variations on a theme' illustrated.

In finite geometry and combinatorics,
an inscape  is a 4×4 array of square figures,
each figure picturing a subset of the overall 4×4 array:


 

Related material — the phrase
"Quantum Tesseract Theorem" and  

A.  An image from the recent
      film "A Wrinkle in Time" — 

B.  A quote from the 1962 book —

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

Friday, December 7, 2018

The Angel Particle

Filed under: G-Notes,General,Geometry — Tags: , , — m759 @ 7:15 PM

(Continued from this morning)

Majorana spinors and fermions at ncatlab

The Gibbons paper on the geometry of Majorana spinors and the Kummer configuration

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

— T. S. Eliot in Four Quartets

Geometric incarnation and the Kummer configuration

See also other Log24 posts tagged Kummerhenge.

Tuesday, November 13, 2018

Blackboard Jungle Continues.

Filed under: G-Notes,General,Geometry — Tags: — 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.

Wednesday, October 24, 2018

Shadowlands

Filed under: General — Tags: , — m759 @ 4:38 AM

The previous post suggests a review.

Following the above reference to March 30, 2016 —

Following the above reference to Lovasz —

The Path of Logic

Filed under: General — Tags: , — m759 @ 3:05 AM

Thursday, September 20, 2018

Clash of the Titans

Filed under: General — Tags: , — m759 @ 6:18 PM

Saturday, September 1, 2018

Another 48 Hours

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

http://www.log24.com/log/pix18/180901-Elliott-Gould-in-Oceans-8.jpg

Backstory:  See The Plaid Overnight Case in this journal.

Investigators: First 48 Hours Most Critical
In Locating Missing Children Who Entered
Portal To Fantastical World

See as well a post from 10:16 PM ET Thursday, August 30, 2018.

Friday, August 31, 2018

Perception of Number

Filed under: General,Geometry — Tags: — m759 @ 8:31 PM

Review of yesterday's post Perception of Space

From Harry Potter and the Philosopher's Stone  (1997),
republished as "… and the Sorcerer's Stone ," Kindle edition:

http://www.log24.com/log/pix18/180830-Harry_Potter_Phil_Stone-wand-movements-quote.jpg

In a print edition from Bloomsbury (2004), and perhaps in the
earliest editions, the above word "movements" is the first word
on page 168:

http://www.log24.com/log/pix18/180830-Harry_Potter-Phil_Stone-Bloomsbury-2004-p168.jpg

Click the above ellipse for some Log24 posts on the eightfold cube,
the source of the 168 automorphisms ("movements") of the Fano plane.

"Refined interpretation requires that you know that
someone once said the offspring of reality and illusion
is only a staggering confusion."

— Poem, "The Game of Roles," by Mary Jo Bang

Related material on reality and illusion
an ad on the back cover of the current New Yorker

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

"Hey, the stars might lie, but the numbers never do." — Song lyric

Thursday, August 30, 2018

Twenty Years

Filed under: General — Tags: — m759 @ 10:16 PM

This post was suggested by the final inside page, 23,
of next Sunday's New York Times Book Review ,
"Memorabilia/ Happy 20th Anniversary, Harry Potter."

http://www.log24.com/log/pix18/180830-Harry_Potter-20th-NYT-500w.jpg

From VOA Learning English, June 26, 2017

J.K. Rowling's Harry Potter Books
Turn 20 Years Old

. . . .

" J.K. Rowling’s first book about Harry and his friends at Hogwarts School of Witchcraft and Wizardry was released on June 26, 1997.

The publisher, Bloomsbury, only released 500 copies to stores in Britain and sent 500 to British libraries.

Now, thanks to 450 million more copies of the first book and six others, Harry Potter and his friends are known around the world.

Adults and children loved the books. But 12 publishers rejected the first one, known in many countries as 'Harry Potter and the Philosopher’s Stone.' "

. . . .

See as well this  journal on June 26, 2017 in
posts now tagged Ron Shaw In Memoriam.

Monday, August 6, 2018

Summer in Philadelphia

Filed under: General — Tags: — m759 @ 2:59 PM

http://www.log24.com/log/pix18/180806-Old_City_Hall-Philadelphia.jpg

See also this  journal on June 21st, 2013.

Thursday, July 12, 2018

The Bell

Filed under: General — Tags: , — m759 @ 6:11 PM

Three hidden keys open three secret gates
Wherein the errant will be tested for worthy traits
And those with the skill to survive these straits
Will reach The End where the prize awaits

— Ready Player One , by Ernest Cline

"Look, my favorite expression is,
'When you go up to the bell, ring it,
or don’t go up to the bell.'
We’ve gone too far. We have to ring the bell."

Mel Brooks on "The Producers"
     in The New York Times  today.

A 2016 Scribner edition of Stephen King's IT —

Related material —

Mystery box  merchandise from the 2011  J. J. Abrams film  Super 8 

Kummerhenge Illustrated

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

      

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

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

"Omega is as real  as we need it to be."

— Burt Lancaster in "The Osterman Weekend"

Wednesday, July 11, 2018

Titans

Filed under: General — Tags: — m759 @ 5:01 PM

"By The Boston Globe

July 10, 2018

The private jets have begun clogging the jetways
in Sun Valley, Idaho, which can only mean one thing:
'Billionaire summer camp’' has begun.

The annual Allen & Company conference, the investment
firm’s invite-only gathering of some of the world’s most
powerful corporate titans, officially begins on Wednesday."

In other news —

"NASHVILLE, Tenn. 

Get ready to see the Titans in training camp."

See also another  post now tagged "Clash of the Titans."

Thursday, June 21, 2018

Dirac and Geometry (continued)

"Just fancy a scale model of Being 
made out of string and cardboard."

Nanavira Thera, 1 October 1957,
on a model of Kummer's Quartic Surface
mentioned by Eddington

"… a treatise on Kummer's quartic surface."

The "super-mathematician" Eddington did not see fit to mention
the title or the author of the treatise he discussed.

See Hudson + Kummer in this  journal.

See also posts tagged Dirac and Geometry.

Saturday, June 9, 2018

SASTRA paper

Filed under: General,Geometry — Tags: — m759 @ 11:14 PM

Now out from behind a paywall . . .

The diamond theorem at SASTRA —

Tuesday, May 22, 2018

Doppelgänger

Filed under: General — Tags: — m759 @ 3:06 AM

The previous post suggests a media review.

Doppelgangers from the wonderful world of entertainment —

   

"We have a clip." — Kalle  (Kristen Wiig on SNL)

Sunday, May 20, 2018

Some Style

Filed under: General,Geometry — Tags: — m759 @ 1:03 AM

Dialogue from the 1984 fourth draft of the script, as found on the Web,
for "Back to the Future" (1985) (apparently some changes were made
in the filming) —

A sort of "flux capacitor" (see previous post) —

The Rolls-Royce Cullinan

 plus "e" for Einstein 

Saturday, May 19, 2018

Flux Capacitor

Filed under: General,Geometry — Tags: , — m759 @ 4:13 PM

For Tom Hanks and Dan Brown —

Symbologist Robert Langdon views a corner of Solomon's Cube

From "Raiders of the Lost Images" —

"The cube shape of the lost Mother Box,
also known as the Change Engine,
is shared by the Stone in a novel by
Charles Williams, Many Dimensions .
See the Solomon's Cube webpage."

See as well a Google search for flux philosophy
https://www.google.com/search?q=flux+philosophy.

Wednesday, May 16, 2018

Church and Temple

Filed under: General — Tags: , , , — m759 @ 10:48 AM

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