Log24

Friday, June 14, 2024

For Chris Pine… Amazon Influencer
in “Wonder Woman 1984”

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

Wonder Woman delivers a diamond

Another cultural inflection point:

Harrison Ford and Shia LaBeouf as Father and Son

Susan Sontag,
Notes on “Camp”

This post was suggested by an Instagram ad this evening —

Thursday, March 14, 2024

TIME Date: 1984/09/16

Filed under: General — m759 @ 8:28 am

SPACE Date: 1984/09/15.

Thursday, October 5, 2023

“Are you shining with a real Barbie?” (1984 version)

Filed under: General — Tags: , — m759 @ 1:37 am

The Source: https://txxx.com/videos/446436/corinne-wahl-bobbi-burns-missy-o-shea-unknown-cynthia-s-lee-in-new-york-nights-1984/?kt_lang=en

Saturday, September 3, 2022

1984 Revisited

Filed under: General — m759 @ 2:46 pm

Cube Bricks 1984 —

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

Related material

Note the three quadruplets of parallel edges  in the 1984 figure above.

Further Reading

The above Gates article appeared earlier, in the June 2010 issue of
Physics World , with bigger illustrations. For instance —

Exercise: Describe, without seeing the rest of the article,
the rule used for connecting the balls above.

Wikipedia offers a much clearer picture of a (non-adinkra) tesseract —

      And then, more simply, there is the Galois tesseract

For parts of my own  world in June 2010, see this journal for that month.

The above Galois tesseract appears there as follows:

Image-- The Dream of the Expanded Field

See also the Klein correspondence in a paper from 1968
in yesterday's 2:54 PM ET post

Friday, June 12, 2020

Prelude to Westworld (1984)

Filed under: General — m759 @ 12:45 pm

See also An Epic for Kristen .

Tuesday, October 8, 2019

Also* in 1984

Filed under: General — Tags: — m759 @ 11:32 am
 

American Mathematical Monthly , June-July 1984 

MISCELLANEA, 129

Triangles are square

"Every triangle consists of  n congruent copies of itself"
is true if and only if  n is a square. (The proof is trivial.)
— Steven H. Cullinane

* See Cube Bricks 1984  in previous post.

Tuesday, July 9, 2019

Schoolgirl Space: 1984 Revisited

Cube Bricks 1984 —

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

From "Tomorrowland" (2015) —

From John Baez (2018) —

See also this morning's post Perception of Space 
and yesterday's Exploring Schoolgirl Space.

Sunday, July 29, 2018

1984 Continues.

Filed under: General — m759 @ 2:15 pm

"We want every student to have a fulfilling experience
of higher education that enriches their lives and careers."

Sure you do.

Wednesday, September 13, 2017

Summer of 1984

The previous two posts dealt, rather indirectly, with
the notion of "cube bricks" (Cullinane, 1984) —

Group actions on partitions —

Cube Bricks 1984 —

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

Another mathematical remark from 1984 —

For further details, see Triangles Are Square.

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."

Thursday, March 30, 2017

2010 in 1984

Filed under: General — m759 @ 9:29 pm

Click for a more realistic view of these years.

Saturday, January 14, 2017

1984: A Space Odyssey

Filed under: General,Geometry — m759 @ 2:40 pm

See Eightfold 1984 in this journal.

Related material —

"… the object sets up a kind of
 frame or space or field
 within which there can be epiphany."

"… Instead of an epiphany of being,
we have something like
an epiphany of interspaces."

— Charles Taylor, "Epiphanies of Modernism,"
Chapter 24 of Sources of the Self ,
Cambridge University Press, 1989

"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 University Press, Ithaca, NY, 1962

Epiphany 2017 —

Click to enlarge:

Sunday, May 1, 2016

Sunday Appetizer from 1984

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

Judith Shulevitz in The New York Times
on Sunday, July 18, 2010
(quoted here Aug. 15, 2010) —

“What would an organic Christian Sabbath look like today?”

The 2015 German edition of Beautiful Mathematics ,
a 2011 Mathematical Association of America (MAA) book,
was retitled Mathematische Appetithäppchen —
Mathematical Appetizers . The German edition mentions
the author's source, omitted in the original American edition,
for his section 5.17, "A Group of Operations" (in German,
5.17, "Eine Gruppe von Operationen") —  

Mathematische Appetithäppchen:
Faszinierende Bilder. Packende Formeln. Reizvolle Sätze

Autor: Erickson, Martin —

"Weitere Informationen zu diesem Themenkreis finden sich
unter http://​www.​encyclopediaofma​th.​org/​index.​php/​
Cullinane_​diamond_​theorem
und http://​finitegeometry.​org/​sc/​gen/​coord.​html ."

That source was a document that has been on the Web
since 2002. The document was submitted to the MAA
in 1984 but was rejected. The German edition omits the
document's title, and describes it as merely a source for
"further information on this subject area."

The title of the document, "Binary Coordinate Systems,"
is highly relevant to figure 11.16c on page 312 of a book
published four years after the document was written: the 
1988 first edition of Sphere Packings, Lattices and Groups
by J. H. Conway and N. J. A. Sloane —

A passage from the 1984 document —

Thursday, March 24, 2016

Truth in 1984

Filed under: General,Geometry — Tags: — m759 @ 2:36 pm

"The theory of elliptic curves and modular forms is
one subject where the most diverse branches
of mathematics come together: complex analysis,
algebraic geometry, representation theory, number theory."

— Neal Koblitz, first sentence of 
Introduction to Elliptic Curves and Modular Forms,
First Edition, Springer-Verlag, 1984

Related material —

A quote co-authored by Koblitz appears in today's
earlier post The Wolf Gang.

See also The Proof and the Lie.

Maryna Viazovska's course on elliptic curves and modular forms used the Koblitz text.

Friday, March 4, 2016

Cube Bricks 1984

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

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

Related aesthetics —

"Poincaré said that science is no more a collection of facts
than a house is a collection of bricks. The facts have to be
ordered or structured, they have to fit a theory, a construct
(often mathematical) in the human mind. . . . 

Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to
explain how art fits into our subject and what we mean by beauty.

In attempting to bridge this divide I have always found that
architecture is the best of the arts to compare with mathematics.
The analogy between the two subjects is not hard to describe
and enables abstract ideas to be exemplified by bricks and mortar,
in the spirit of the Poincaré quotation I used earlier."

— Sir Michael Atiyah, "The Art of Mathematics"
     in the AMS Notices , January 2010

Tuesday, August 14, 2012

Hacking 1984

Filed under: General,Geometry — Tags: — m759 @ 10:00 pm

Ian Hacking in 1984

"… theories about mathematics have had a big place in Western philosophy. All kinds of outlandish doctrines have tried to explain the nature of mathematical knowledge. Socrates set the ball rolling by using a proof in geometry to argue for the transmigration of souls. As reported by Plato in Meno , the boy who invents a proof of a theorem did not experiment on the physical world, but used only his mind in response to Socratic questions. Hence he must have had inborn knowledge of the proof and he must have got this knowledge in a previous incarnation.

Mathematics has never since been a subject for such philosophical levity."

See also this afternoon's post.

Tuesday, June 22, 2010

1984 Story (continued)

Filed under: General — m759 @ 8:00 pm

http://www.log24.com/log/pix10A/100622-PeterFinch-Network.jpg

"There are many accounts of
moral and political anger in
the philosophical literature."

— J. M. Bernstein in today's NY Times

J.M. Bernstein is University Distinguished Professor
of Philosophy at the New School for Social Research.

He is the author of a work
that Google Books files under
"Communism and Literature"—

The Philosophy of the Novel:
Lukács, Marxism, and the Dialectics of Form

(University of Minnesota Press, 1984)

Monday, June 21, 2010

1984 Story (continued)

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

This journal’s 11 AM Sunday post was “Lovasz Wins Kyoto Prize.” This is now the top item on the American Mathematical Society online home page—

http://www.log24.com/log/pix10A/100621-LovaszAMS-sm.jpg

Click to enlarge.

For more background on Lovasz, see today’s
previous Log24 post, Cube Spaces, and also
Cube Space, 1984-2003.

“If the Party could thrust its hand into the past and
say of this or that event, it never happened….”

— George Orwell, 1984

Wednesday, November 13, 2024

Group Theory: The Romance of Alias and Alibi*

Filed under: General — Tags: — m759 @ 5:29 am

Alias:

Victor at 194 Tower Avenue  in "The Penguin"

Alibi:

Marcela_234  at Likewise.com

Romance in Numberland:

* Technical terms from pure mathematics —

For scholia on "the cube is being moved around," vide . . .

http://m759.net/wordpress/?s="Stack+Exchange" .

IMAGE- Current math.stackexchange.com logo and a 1984 figure from 'Notes on Groups and Geometry, 1978-1986'

Saturday, September 28, 2024

Architectural Singularity

Filed under: General — Tags: , — m759 @ 5:08 am

Embedded in the Sept. 26  New Yorker  review of Coppola's
Megalopolis is a ghostly transparent pyramidal figure . . .

The pyramidal figure is not unrelated to Scandia.tech

 

American Mathematical Monthly, Vol. 92, No. 6
(June-July 1985), p. 443

 

LETTERS TO THE EDITOR

Material  for this department should be prepared exactly the same way as submitted manuscripts (see the inside front cover) and sent to Professor P. R. Halmos, Department of Mathematics, University of Santa Clara, Santa Clara, CA 95053

Editor:

    Miscellaneum 129 ("Triangles are square," June-July 1984 Monthly ) may have misled many readers. Here is some background on the item.

    That n2 points fall naturally into a triangular array is a not-quite-obvious fact which may have applications (e.g., to symmetries of Latin-square "k-nets") and seems worth stating more formally. To this end, call a convex polytope P  an n-replica  if  P  consists of n mutually congruent polytopes similar to P  packed together. Thus, for n ∈ ℕ,

    (A) An equilateral triangle is an n-replica if and only if n is a square.

    Does this generalize to tetrahedra, or to other triangles? A regular tetrahedron is not a (23)-replica, but a tetrahedron ABCD  with edges AB, BC, and CD  equal and mutually orthogonal is an n-replica if and only if n is a cube. Every triangle satisfies the "if" in (A), so, letting T  be the set of triangles, one might surmise that

    (B) tT (t is an n-replica if and only if n is a square).

     This, however, is false. A. J. Schwenk has pointed out that for any m ∈ ℕ, the 30°-60°-90° triangle is a (3m2)-replica, and that a right triangle with legs of integer lengths a and b is an ((a+ b2)m2)-replica. As Schwenk notes, it does not seem obvious which other values of n can occur in counterexamples to (B). Shifting parentheses to fix (B), we get a "square-triangle" lemma:

    (C) ( tT, t  is an n-replica) if and only if n is a square.
   
    Miscellaneum 129 was a less formal statement of (C), with quotation marks instead of parentheses; this may have led many readers to think (B) was intended. To these readers, my apology.
 

Steven H. Cullinane      
501 Follett Run Road     
Warren, PA 16365         

Tuesday, August 20, 2024

Academic Tribes

Filed under: General — m759 @ 10:21 pm
 

Peter Woit today

(https://www.math.columbia.edu/~woit/wordpress/?p=14092):

From the beginning in 1984 I was dubious about string theory unification, and by the late 1990s could not understand why this was dominating physics departments and popular science outlets, with no acknowledgement of the serious problems and failures of the theory. From talking privately to physicists, it became clear that the field of particle theory had for quite a while become disturbingly tribal. There was a string theory tribe, seeing itself as embattled and fighting less intelligent other tribes for scarce resources. Those within the tribe wouldn’t say anything publicly critical of the theory, since that would not only hurt their own interests, but possibly get them kicked out of the tribe. Those outside the tribe also were very leery of saying anything, partly because they felt they lacked the expertise to do so, partly because they feared retribution from powerful figures in the string theory tribe.

See also http://m759.net/wordpress/?tag=tri-be.

Wednesday, July 31, 2024

My Links — Steven H. Cullinane

Filed under: — m759 @ 4:14 pm

Main webpage of record . . .

Encyclopedia of Mathematics  https://encyclopediaofmath.org/wiki/Cullinane_diamond_theorem

Supplementary PDF from Jan. 6, 2006  https://encyclopediaofmath.org/images/3/37/Dtheorem.pdf

Originally published in paper version . . .

Computer Graphics and Art, 1978  http://finitegeometry.org/sc/gen/Diamond_Theory_Article.pdf
AMS abstract, 1979: "Symmetry Invariance in a Diamond Ring"  https://www.cullinane.design/
American Mathematical Monthly, 1984 and 1985: "Triangles Are Square"  http://finitegeometry.org/sc/16/trisquare.html

Personal sites . . .

Primary —

Personal journal   http://m759.net/wordpress/
Mathematics website  http://finitegeometry.org/sc/
Mathematics Images Gallery  http://m759.net/piwigo/index.php?/category/2

Secondary —

Portfoliobox   https://cullinane.pb.design/
Substack   https://stevenhcullinane.substack.com/  
Symmetry Summary   https://shc759.wordpress.com
Diamond Theory Cover Structure  https://shc7596.wixsite.com/website

SOCIAL:

Pinterest   https://www.pinterest.com/stevenhcullinane/ (many mathematics notes)
Flickr  https://www.flickr.com/photos/m759/ (backup account for images of mathematics notes)
Instagram   https://www.instagram.com/stevencullinane
TikTok   https://www.tiktok.com/@stevenhcullinane
X.com   https://x.com/shc759

OTHER:

Replit viewer/download  https://replit.com/@m759/View-4x4x4?v=1
SourceForge download  https://sourceforge.net/projects/finitegeometry/
Academia.edu   https://stevenhcullinane.academia.edu/ GitHub    https://github.com/m759 (finite geometry site download)
Internet Archive: Notes on Groups and Geometry   https://archive.org/details/NotesOnGroupsAndGeometry1978-1986/mode/2up         

Cited at  . . .

The Diamond Theorem and Truchet Tiles   http://www.log24.com/log22/220429-Basque-DT-1.pdf 
April 2024 UNION article in Spanish featuring the diamond theorem  https://union.fespm.es/index.php/UNION/article/view/1608/1214
April 2024 UNION article in English  http://log24.com/notes/240923-Ibanez-Torres-on-diamond-theorem-Union-April-2024-in-English.pdf
Cullinane in a 2020 Royal Holloway Ph.D. thesis   https://pure.royalholloway.ac.uk/ws/portalfiles/portal/40176912/2020thomsonkphd.pdf         
Squares, Chevrons, Pinwheels, and Bach   https://www.yumpu.com/en/document/read/36444818/fugue-no-21-elements-of-finite-geometry      
Observables  programmed presentation of diamond theorem  https://observablehq.com/@radames/diamond-theory-symmetry-in-binary-spaces
Josefine Lyche — Plato's Diamond  https://web.archive.org/web/20240222064628/http://www.josefinelyche.com/index.php?/selected-exhibitions/platos-diamond/
Josefine Lyche — Diamond Theorem  https://web.archive.org/web/20230921122049/http://josefinelyche.com/index.php?/selected-exhibitions/uten-ramme-nye-rom/

Professional sites . . .

Association for Computing Machinery   https://member.acm.org/~scullinane
bio.site/cullinane … maintenance at https://biosites.com
ORCID bio page   https://orcid.org/0000-0003-1135-419X
Google Scholar   https://scholar.google.com/citations?view_op=list_works&hl=en&hl=en&user=NcjmFwQAAAAJ&sortby=pubdate

Academic repositories:

Harvard Dataverse   https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/KHMMVH
Harvard DASH article on PG(3,2)   https://dash.harvard.edu/handle/1/37373777 

Zenodo website download  https://zenodo.org/records/1038121
Zenodo research notes  https://zenodo.org/search?q=metadata.creators.person_or_org.name%3A%22Cullinane%2C%20Steven%20H.%22&l=list&p=1&s=10&sort=bestmatch

Figurate Geometry at Open Science Framework (OSF)   https://osf.io/47fkd/

arXiv: "The Diamond Theorem"  https://arxiv.org/abs/1308.1075

Friday, May 31, 2024

The Geometry of Hexads and Duads

Filed under: General — Tags: — m759 @ 4:38 am

Not unrelated:  Six-set Geometry.

For some historical background for the first (1984)
result above,
see the second (2013) result.

Friday, November 10, 2023

The Writer as Trickster:  A Date for Loki

Filed under: General — Tags: , , — m759 @ 10:37 am
 

9/15/1984.


More "spots of time": "0915."

Tuesday, November 7, 2023

Dreamcatchers

Filed under: General — m759 @ 1:28 pm

The sort of Adult Services I prefer —

Stephen King's Dreamcatcher  (2001) and Brian De Palma's "Body Double" (1984).

Monday, September 4, 2023

Back-Lot Hollywood

Filed under: General — Tags: , — m759 @ 8:44 am

Thursday, August 17, 2023

Language Game for a Baker’s Wife (Pace Sondheim)

Filed under: General — Tags: — m759 @ 2:24 pm

From a 1984 film,  "2010: The Year We Make Contact" —

Russian — "Piece of pie."
American — "Cake. Piece of cake."

This brief dialogue was suggested by the phrase
"Pineapple Upside-Down Cake," which in turn was
suggested by an image and a dance from the Instagram
page of the talented Jena Malone:

Wednesday, March 8, 2023

Releasing the Crimson Kraken

Filed under: General — m759 @ 10:37 am

From Chomsky's remarks in The New York Times  today

"It is at once comic and tragic, as Borges might have noted,
that so much money and attention should be concentrated
on so little a thing — something so trivial when contrasted
with the human mind, which by dint of language, in the
words of Wilhelm von Humboldt, can make 'infinite use of
finite means,' creating ideas and theories with universal reach."

A search in this  journal for Humboldt University  yields . . .

"Cum grano salis" — Boris Karloff in "The Black Cat."

Sunday, February 26, 2023

TOE

Filed under: General — Tags: — m759 @ 2:24 am


 

Related images from The Crimson Abyss —

1984 —

IMAGE- 'Affine Groups on Small Binary Spaces,' illustration

2010 —

Logo design for Stack Exchange Math by Jin Yang

Friday, January 13, 2023

The “Diamond Space” of Mazzola

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

The Source —

Some similar notions from my own work . . .

The "Digraph" of Mazzola might correspond to a directed graph
indicating the structure of a permutation, as at right below —

Mazzola's "Formula" might correpond to a matrix and translation that
transform the above "Space" of eight coordinates, and his "Gesture"
to a different way of generating affine transformations of that space . . . 
as in my webpage "Cube Space, 1984-2003."

Thursday, January 5, 2023

Logic and Geometry at Harvard

Filed under: General — Tags: — m759 @ 7:56 pm

'If Triangles Are Square' book


See also "Triangles Are Square" in 1984 —

Harvard  Square:

Harvard Square, 1964

Tuesday, January 3, 2023

The Deal

Filed under: General — m759 @ 1:22 pm

The Source: https://txxx.com/videos/446436/corinne-wahl-bobbi-burns-missy-o-shea-unknown-cynthia-s-lee-in-new-york-nights-1984/?kt_lang=en

Wednesday, December 28, 2022

The Santa Fe Institute as Magisterium Wannabe

Filed under: General — Tags: — m759 @ 11:23 am

"The novelist Cormac McCarthy has been a fixture around
the Santa Fe Institute since its embryonic stages in the
early 1980s. Cormac received a MacArthur Award in 1981
and met one of the members of the board of the MacArthur
Foundation, Murray Gell-Mann, who had won the Nobel Prize
in physics in 1969. Cormac and Murray discovered that they
shared a keen interest in just about everything under the sun
and became fast friends. When Murray helped to found the
Santa Fe Institute in 1984, he brought Cormac along, knowing
that everyone would benefit from this cross-disciplinary
collaboration." — https://www.santafe.edu/news-center/news/
cormac-and-sfi-abiding-friendship

Joy Williams, review of two recent Cormac McCarthy novels —

"McCarthy has pocketed his own liturgical, ecstatic style
as one would a coin, a ring, a key, in the service of a more
demanding and heartless inquiry through mathematics and
physics into the immateriality, the indeterminacy, of reality."

A Demanding and Heartless Coin, Ring, and Key:
 

COIN
 

https://www.armstrong.edu/history-journal/history-journal-myth-ritual-and-the-labyrinth-of-king-minos
 

RING


"We can define sums and products so that the G-images of D generate
an ideal (1024 patterns characterized by all horizontal or vertical "cuts"
being uninterrupted) of a ring of 4096 symmetric patterns. There is an 
infinite family of such 'diamond' rings, isomorphic to rings of matrices
over GF(4)."
 

KEY


"It must be remarked that these 8 heptads are the key to an elegant proof…."

— Philippe Cara, "RWPRI Geometries for the Alternating Group A8," in 
Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference 
(July 16-21, 2000), Kluwer Academic Publishers, 2001, ed. Aart Blokhuis,
James W. P. Hirschfeld, Dieter Jungnickel, and Joseph A. Thas, pp. 61-97.
 

For those who prefer a "liturgical, ecstatic style" —

Wednesday, November 30, 2022

Three Representations

Filed under: General — Tags: , , — m759 @ 12:05 pm

'Cube Bricks, 1984,' by Steven H. Cullinane

Cube Bricks, 1984

See also Impenetrability .

Thursday, August 18, 2022

The Razr’s Edge

Filed under: General — Tags: , — m759 @ 2:42 pm

A view from Hollywood

A view from Silicon Valley

A view from the Holiday Hotel

'The Resort' S1E1 - The 2007 Razr

Sunday, June 26, 2022

Mockery Day

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

For Monty Python —

"Glastonbury has been described as having a New Age community[6] 
and possibly being where New Age beliefs originated at the turn of
the twentieth century.[7] It is notable for myths and legends often
related to Glastonbury Tor, concerning Joseph of Arimathea, the 
Holy Grail and King Arthur." — Wikipedia
 

For American Democracy —

Related mockery from 2012

'If Triangles Are Square' book


See also "Triangles Are Square" in 1984

Friday, February 11, 2022

For Space Groupies

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

A followup to Wednesday's post Deep Space

Related material from this journal on July 9, 2019

Cube Bricks 1984 —

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

From "Tomorrowland" (2015) —

From other posts tagged 1984 Cubes

Sunday, February 6, 2022

Animating the Savoir

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

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

— Wallace Stevens, “The Plain Sense of Things

"In my end . . . ." — T. S. Eliot

Thursday, March 22, 2018

The Diamond Cube

Tags:  — m759 @ 11:32 AM 

. . . .

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

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

Monday, September 13, 2021

Cube Space Revisited

Filed under: General — Tags: , , , , — m759 @ 3:02 pm

The above Quanta  article mentions

"Maryna Viazovska’s 2016 discovery of the most efficient
ways of packing spheres in dimensions eight and 24."

From a course to be taught by Viazovska next spring:

The Lovasz reference suggests a review of my own webpage
Cube Space, 1984-2003.

See as well a review of Log24 posts on Packing.

Friday, June 18, 2021

Memorial

Filed under: General — m759 @ 11:59 am

From the previous post:

"Words are events, happenings, not things,
as letters make them appear to be."
— Walter J. Ong, S.J., page 2 in 
"Writing and the Evolution of Consciousness,"

". . . originally delivered by Walter J. Ong
as the 7th Annual 'Sidney Warhaft Memorial Lecture',
January 26, 1984, University of Manitoba, Winnipeg."

A different Sidney Warhaft memorial —

Photographs are also events.

See this journal on the above photo date — Sept. 17, 2014.

“Words Are Events” — Ong, S. J.

Filed under: General — m759 @ 10:59 am

Lest the title of the TV series in the previous post, "The Chi,"
be mistaken for a reference to the Greek letter  chi

"Words are events, happenings, not things,
as letters make them appear to be."
— Walter J. Ong, S.J., page 2 in 
"Writing and the Evolution of Consciousness,"
in Mosaic: An Interdisciplinary Critical Journal ,
Vol. 18, No. 1 (Winter 1985), pp. 1-10 (11 pages,
counting the prefatory page with a photo of Ong).

Published by: University of Manitoba.
https://www.jstor.org/stable/24777620

". . . originally delivered by Walter J. Ong
as the 7th Annual 'Sidney Warhaft Memorial Lecture',
January 26, 1984, University of Manitoba, Winnipeg."

See as well . . .

Saturday, June 5, 2021

Times Square Logic

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

Dialogue from Season 1, Episode 8 of "His Dark Materials" —

Asriel:  And the serpent said, "You shall not surely die, for the Authority doth know that on that day that ye eat thereof, your eyes shall be opened, your daemons shall assume their true form and ye shall be as…"

Both:  "… gods, knowing good and…"

Lyra:  "… evil."

Asriel:  "… Dust ." You see? They have been trying to convince us for centuries that we are born guilty. And that we have to spend a lifetime atoning for the crime of eating an apple. Is there any proof for this heinous stain, this shame, this guilt? No, not at all. We are to take it on faith, and on the word of the Authority.

But Dust… Dust is an elementary particle that we can record, measure, study.

Read more at:
https://tvshowtranscripts.ourboard.org/
viewtopic.php?f=270&t=37981

Related material: Times Square Logic Log24 posts now tagged
"Times Square Logic" include two from April 7, 2015, the date of
Geoffrey Lewis's death.

Lewis played, notably, "Hard Case Williams" in Lust in the Dust  (1984).

Monday, April 5, 2021

Watch Party

Filed under: General — Tags: — m759 @ 6:37 pm

A TV episode  from 2016 —

The above “Lucy” actress in 2014 —

Compare and contrast with the homecoming
bedroom scene in De Palma’s  “Body Double” (1984).

“Like a rose under the April snow . . . .” — Streisand

Saturday, February 6, 2021

WW Review

Filed under: General — m759 @ 12:38 pm

This suggests a review of Wonder Woman and the Dreamstone

Saturday, January 23, 2021

Lockscreen Artspeak Continues.

Filed under: General — Tags: — m759 @ 2:18 pm

The same texts appeared in another Windows lockscreen today —

I prefer the beach huts inspiration in "Body Double" (1984)

Midrash for Hollywood —

Saturday, December 26, 2020

Futon Dream

Filed under: General — m759 @ 12:00 pm

” There’s a line from the movie ‘The Paper Chase’, in which
the fearsome Professor Kingsfield tells a room of first-year
law-school students ‘You come in here with a skull full of mush …
and you leave thinking like a lawyer.’ “

— James Propp on December 14, 2020, in . . .

Children of the Labyrinth.

Related material — Japanese Bed.

Thursday, August 20, 2020

Milking the Sixteenths

Filed under: General — Tags: — m759 @ 8:13 pm

“In the main belly cabin he discovered the reason
for the tropical heat; a naked woman was sweating
and swearing over the maintenance gear surrounding
a transparent incubator. She was tinkering and crawling
over and under the complications like an octopus.
It was his assistant, Dr. Cluny Decco, and Krupp had
never seen her nude before, but his controlled voice
did not betray his delighted amazement.”

— Alfred Bester, The Deceivers . Kindle Edition.

From a post, Dharma Fabric , of January 7, 2020 —

Also* from the Early 80’s

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

See Corinne Wahl in an adaptation of Schnitzler’s  La  Ronde.

Compare and contrast the 4×4 square of the Wahl presentation
with that of the July 26 post  Dirty Dancing Disco.

* A reference to the previous post.

Friday, August 14, 2020

Exercise

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

I prefer the boom box above to the one in Old Wives’ Tale (Aug. 10).

Thursday, July 2, 2020

The Maxwell* Enticement

Filed under: General — Tags: , , , , — m759 @ 5:20 pm

[Update of Sunday morning, July 12, 2020 —

This July 2 post was suggested in part by the July 1 post Magic Child
and in part by the Sept. 15, 1984, date in the image below. For more
details about that date, possibly the death date of author Richard
Brautigan, see "The Life and Death of Richard Brautigan," by
Lawrence Wright, in Rolling Stone  on April 11, 1985.

From that article:

Marcia called him the next night [Sept. 15, 1984]
in Bolinas. He asked if she liked his mind. "I said,
‘Yes, Richard, I like your mind. You have the ability
to jump in and out of spaces. It’s not linear thinking;
it’s exciting, catalytic, random thinking.’ "

Such thinking, though interesting, is not recommended for the
general public.  Sept. 15, 1984, was perhaps Brautigan's last day alive.]

* See Maxwell in posts tagged Gods and Giants.

Wednesday, July 1, 2020

Actress Descending a Staircase

Filed under: General — Tags: , , — m759 @ 3:25 am

The above title was suggested by a scene in Body Double  (1984) . . .

Variations, starring Theresa Russell, on related themes —

The De Palma Balcony in Body Double , and "ready for my closeup" —

"Bing bang, I heard the whole gang!"

Summary — 

Saturday, May 23, 2020

Structure for Linguists

Filed under: General — Tags: , — m759 @ 11:34 am

"MIT professor of linguistics Wayne O’Neil died on March 22
at his home in Somerville, Massachusetts."

MIT Linguistics, May 1, 2020

The "deep  structure" above is the plane cutting the cube in a hexagon
(as in my note Diamonds and Whirls of September 1984).

See also . . .

IMAGE- Redefining the cube's symmetry planes: 13 planes, not 9.

Sunday, March 1, 2020

Notes towards the Ministry of Culture

Filed under: General — Tags: — m759 @ 8:22 pm

Friday, February 21, 2020

To and Fro, Back and …

Filed under: General — Tags: , , , — m759 @ 11:44 pm

Also on January 27, 2017 . . .

For other appearances of John Hurt here,
see 1984 Cubes.

Update of 12:45 AM Feb. 22 —

A check of later obituaries reveals that Hurt may well
have died on January 25, 2017, not January 27 as above.

Thus the following remarks may be more appropriate:

Not to mention what, why, who, and how.

Sunday, February 16, 2020

Zen and the Art

Filed under: General — m759 @ 5:18 pm

(Continued)

Sunday, February 9, 2020

Hors d’Oeuvre

Filed under: General — Tags: , , , , , — m759 @ 1:29 pm

From the May Day 2016 link above, in "Sunday Appetizer from 1984"

The 2015 German edition of Beautiful Mathematics , a 2011 Mathematical Association of America (MAA) book, was retitled Mathematische Appetithäppchen — Mathematical Appetizers . The German edition mentions the author's source, omitted in the original American edition, for his section 5.17, "A Group of Operations" (in German, 5.17, "Eine Gruppe von Operationen")—

Mathematische Appetithäppchen:
Faszinierende Bilder.
Packende Formeln.
Reizvolle Sätze.

Autor: Erickson, Martin —

"Weitere Informationen zu diesem Themenkreis finden sich unter

http://​www.​encyclopediaofma​th.​org/
​index.​php/​Cullinane_​diamond_​theorem

und

http://​finitegeometry.​org/​sc/​gen/​coord.​html ."

That source was a document that has been on the Web since 2002. The document was submitted to the MAA in 1984 but was rejected. The German edition omits the document's title, and describes it as merely a source for "further information on this subject area."

From the Gap Dance link above, in "Reading for Devil's Night" —

Das Nichts nichtet.” — Martin Heidegger.

And "Appropriation Appropriates."

Friday, January 10, 2020

Jan. 9 Review

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

“Work as if you were in the
early days of a better nation.”

— God, according to the author of
    1982 Janine

From Carole A. Holdsworth,
"Dulcinea and Pynchon’s V":

Tanner may have stated it best:

“V. is whatever lights you to
 the end of the street:
 she is also the dark annihilation
 waiting at  the end of the street.”

(Tony Tanner, page 36,
 “V. and V-2,” in
 Pynchon: A Collection
 of Critical Essays.

 Ed. Edward Mendelson.
 Englewood Cliffs, N. J.:
 Prentice-Hall, 1978. 16-55).

She’s a mystery
She’s everything
   a woman should be
Woman in black
   got a hold on me

— Foreigner 4

Tuesday, November 12, 2019

Social Logic

Filed under: General — m759 @ 9:16 am
 

Friday, March 10, 2017

The Transformers

Filed under: General — m759 @ 10:00 PM 

"The transformed urban interior is the spatial organisation of an  achiever, one who has crossed the class divide and who uses space to express his membership of, not aspirations towards, an ascendant class in our society: the class of those people who earn their living by transformation — as opposed to the mere reproduction — of symbols, such as writers, designers, and academics."

— The Social Logic of Space ,
     by Bill Hillier and Julienne Hanson,
     Cambridge University Press, 1984

For another perspective on the achievers, see The Deceivers .

Monday, October 7, 2019

Berlekamp Garden vs. Kinder Garten

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

Stevens's Omega and Alpha (see previous post) suggest a review.

Omega — The Berlekamp Garden.  See Misère Play (April 8, 2019).
Alpha  —  The Kinder Garten.  See Eighfold Cube.

Illustrations —

The sculpture above illustrates Klein's order-168 simple group.
So does the sculpture below.

Froebel's Third Gift: A cube made up of eight subcubes  

Cube Bricks 1984 —

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

Monday, August 19, 2019

A Couple of Tots

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

The title is from the post "Child's Play" of May 21, 2012 . . .

"It seems that only one course is open to the philosopher
who values knowledge and truth above all else. He must
refuse to accept from the champions of the forms the
doctrine that all reality is changeless [and exclusively
immaterial], and he must turn a deaf ear to the other party
who represent reality as everywhere changing [and as only
material]. Like a child begging for 'both', he must declare
that reality or the sum of things is both at once  [το όν τε και
το παν συναμφότερα] (Sophist  246a-249d)."

Related material —

"Schoolgirl Space: 1984 Revisited" (July 9, 2019) and
posts tagged Tetrahedron vs. Square.

Tuesday, August 13, 2019

Putting the Structure  in Structuralism

Filed under: General — Tags: , , , — m759 @ 8:34 pm

The Matrix of Lévi-Strauss —

(From his “Structure and Form: Reflections on a Work by Vladimir Propp.”
Translated from a 1960 work in French. It appeared in English as
Chapter VIII of Structural Anthropology, Volume 2  (U. of Chicago Press, 1976).
Chapter VIII was originally published in Cahiers de l’Institut de Science
Économique Appliquée 
, No. 9 (Series M, No. 7) (Paris: ISEA, March 1960).)

The structure  of the matrix of Lévi-Strauss —

Illustration from Diamond Theory , by Steven H. Cullinane (1976).

The relevant field of mathematics is not Boolean algebra, but rather
Galois geometry.

Saturday, July 6, 2019

Mythos and Logos

Filed under: General — Tags: — m759 @ 8:56 am

Mythos


Logos

The six square patterns which, applied as above to the faces of a cube,
form "diamond" and "whirl" patterns, appear also in the logo of a coal-
mining company —

 .

Related material —

Tuesday, June 25, 2019

Analogy

Filed under: General — Tags: — m759 @ 6:36 am

Tuesday, June 18, 2019

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.

Sunday, June 2, 2019

The Art of Lying

Filed under: General — m759 @ 2:13 pm

(Continued … See “Is Fiction the Art of Lying?” by Mario Vargas Llosa, 
New York Times  essay of October 7, 1984.)

"A non-fiction writer must have the freedom
to imagine the facts they [sic ] use."

Sure they must.

Saturday, December 1, 2018

In Memoriam

Filed under: General — m759 @ 10:06 am

From today's print New York Times  obituary for a screenwriter
who reportedly died last Sunday —

“Indiana Jones and the Temple of Doom,”
a 1984 follow-up to “Raiders of the Lost Ark”
made an estimated $333 million worldwide.

Friday, November 16, 2018

Parable of India

Filed under: General — m759 @ 12:42 pm

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

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.

Saturday, August 25, 2018

“Waugh, Orwell. Orwell, Waugh.”

Filed under: General,Geometry — Tags: , , , — m759 @ 4:00 pm

Suggested by a review of Curl on Modernism —

http://www.log24.com/log/pix18/180825-Ballard-on-Modernism.gif

Related material —

Waugh + Orwell in this journal and

Cube Bricks 1984

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

Monday, June 4, 2018

The Trinity Stone Defined

“Unsheathe your dagger definitions.” — James Joyce, Ulysses

The “triple cross” link in the previous post referenced the eightfold cube
as a structure that might be called the trinity stone .

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

Some small Galois spaces (the Cullinane models)

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 

Tuesday, April 17, 2018

A Necessary Possibility*

Filed under: General,Geometry — Tags: , — m759 @ 10:00 am

"Without the possibility that an origin can be lost, forgotten, or
alienated into what springs forth from it, an origin could not be
an origin. The possibility of inscription is thus a necessary possibility,
one that must always be possible."

— Rodolphe Gasché, The Tain of the Mirror ,
     Harvard University Press, 1986

IMAGE- Harvard University Press, 1986 - A page on Derrida's 'inscription'

An inscription from 2010 —

An inscription from 1984 —

American Mathematical Monthly, June-July 1984, p. 382

MISCELLANEA, 129

Triangles are square

"Every triangle consists of  n congruent copies of itself"
is true if and only if  n is a square. (The proof is trivial.) 
— Steven H. Cullinane

* See also other Log24 posts mentioning this phrase.

Friday, March 23, 2018

From the Personal to the Platonic

Filed under: General,Geometry — Tags: , , — m759 @ 11:01 am

On the Oslo artist Josefine Lyche —

"Josefine has taken me through beautiful stories,
ranging from the personal to the platonic
explaining the extensive use of geometry in her art.
I now know that she bursts into laughter when reading
Dostoyevsky, and that she has a weird connection
with a retired mathematician."

Ann Cathrin Andersen
    http://bryggmagasin.no/2017/behind-the-glitter/

Personal —

The Rushkoff Logo

— From a 2016 graphic novel by Douglas Rushkoff.

See also Rushkoff and Talisman in this journal.

Platonic —

The Diamond Cube.

Compare and contrast the shifting hexagon logo in the Rushkoff novel above 
with the hexagon-inside-a-cube in my "Diamonds and Whirls" note (1984).

Monday, February 12, 2018

The Void

Filed under: General — Tags: — m759 @ 11:46 am

In memory of Professor Donald Lynden-Bell,
Emeritus Professor of Astrophysics at the University of Cambridge

Lynden-Bell with colleagues at Meteor Crater, Arizona, reportedly in 1960 —

Lynden-Bell was one of the subjects of the 2015 film "Star Men."

Related material —

"After peering into the void from a perch 
outside the visitor center, young Henry, 9, 
said he liked the rugged landscape. 
'It’s a good place to film a space movie,' he said.

Funny he should mention that — 
the crater was the setting for the climactic scenes 
of the 1984 sci-fi film 'Starman,' with Jeff Bridges 
and Karen Allen arriving for a rendezvous with 
an alien mother ship."

— Henry Fountain in The New York Times , Jan. 22, 2009

Lynden-Bell reportedly died at 82 on Feb. 5, 2018 (British time).

See as well this  journal on that date.

Friday, November 24, 2017

Scholia

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

From this evening's online New York Times : 

"Eric Salzman, a composer and music critic who
championed a new art form, music theater,
that was neither opera nor stage musical, died
on Nov. 12 at his home in Brooklyn. He was 84."

. . . .

"The first American Music Theater Festival 
took place in the summer of 1984.

Among that first festival’s featured works was 
'Strike Up the Band!,' Mr. Salzman’s 'reconstructed
and adapted' version of a satirical musical
with a score by George and Ira Gershwin
that had not been staged in 50 years. The director
of that production, Frank Corsaro, died 
the day before Mr. Salzman did."

Synchronology check :

"The day before" above was November 11, 2017.

Links from this  journal  on November 11

A Log24 search for Michael Sudduth and an 
October 28, 2017, Facebook post by Sudduth.

Detail of Sudduth's Nov. 11 Facebook home page

Click the above for an enlarged view of the Sudduth profile picture.

Related material :

Harold Schonberg, 1977 review of Corsaro production of Busoni's 'Dr. Faust'

Aooo.

Thursday, November 23, 2017

Lévi-Strauss vs. Propp

Filed under: General,Geometry — Tags: , , , — m759 @ 12:25 pm
​Claude Lévi-Strauss

From his Structure and Form:
Reflections on a Work by Vladimir Propp
” *

To maintain. as I have done. that the permutability of contents is not arbitrary amounts to saying that, if the analysis is carried to a sufficiently deep level, behind diversity we will discover constancy. And, of course. the avowed constancy of form must not hide from us that functions are also permutable.

The structure of the folktale as it is illustrated by Propp presents a chronological succession of qualitatively distinct functions. each constituting an independent genre. One can wonder whether—as with dramatis personae and their attributes— Propp does not stop too soon, seeking the form too close to the level of empirical observation. Among the thirty-one functions that he distinguishes, several are reducible to the same  function reappearing at different  moments of the narrative but after undergoing one or a number of transformations . I have already suggested that this could be true of the false hero (a transformation of the villain), of assigning a difficult task (a transformation of the test), etc. (see p. 181 above), and that in this case the two parties  constituting the fundamental tale would themselves be transformations of each other.

Nothing prevents pushing this reduction even further and analyzing each separate partie  into a small number of recurrent functions, so that several of Propp’s functions would constitute groups of transformations of one and the same function. We could treat the “violation” as the reverse of the “prohibition” and the latter as a negative transformation of the “injunction.” The “departure” of the hero and his “return” would appear as the negative and positive expressions of the same disjunctive function. The “quest” of the hero (hero pursues someone or something) would become the opposite of “pursuit” (hero is pursued by something or someone), etc.

In Vol. I of Structural Anthropology , p. 209, I have shown that this analysis alone can account for the double aspect of time representation in all mythical systems: the narrative is both “in time” (it consists of a succession of events) and “beyond” (its value is permanent). With regard to Propp’s theories my analysis offers another advantage: I can reconcile much better than Propp himself  his principle of a permanent order of wondertale elements with the fact that certain functions or groups of functions are shifted from one tale to the next (pp. 97-98. p. 108) If my view is accepted, the chronological succession will come to be absorbed into an atemporal matrix structure whose form is indeed constant. The shifting of functions is then no more than a mode of permutation (by vertical columns or fractions of columns).

These critical remarks are certainly valid for the method used by Propp and for his conclusions. However. it cannot be stressed enough that Propp envisioned them and in several places formulated with perfect clarity the solutions I have just suggested. Let us take up again from this viewpoint the two essential themes of our discussion: constancy of the content (in spite of its permutability) and permutability of functions (in spite of their constancy).

* Translated from a 1960 work in French.  It appeared in English as Chapter VIII
of Structural Anthropology, Volume 2  (U. of Chicago Press, 1976).  Chapter VIII
was originally published in Cahiers de l’Institut de Science 
Économique Appliquée , 
No. 9 (Series M, No. 7) (Paris: ISEA, March 1960).

See also “Lévi-Strauss” + Formula  in this journal.

Some background related to the previous post

Saturday, November 18, 2017

Cube Space Continued

Filed under: General,Geometry — Tags: , — m759 @ 4:44 am

James Propp in the current Math Horizons  on the eightfold cube

James Propp on the eightfold cube

For another puerile approach to the eightfold cube,
see Cube Space, 1984-2003 (Oct. 24, 2008).

Tuesday, October 31, 2017

One Fell Shmoop

Filed under: General — m759 @ 12:48 pm

https://www.shmoop.com/no-country-for-old-men/coin-symbol.html —

"You know the date on this coin?"

Related material —

This journal on March 7, 2014

From Klein’s 1893  Lectures on Mathematics —

The varieties introduced by Wirtinger may be called 
  Kummer varieties….” — E. Spanier, 1956

From the "varieties introduced by Wirtinger" link above —

 .

Tuesday, September 12, 2017

Think Different

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

The New York Times  online this evening

"Mr. Jobs, who died in 2011, loomed over Tuesday’s
nostalgic presentation. The Apple C.E.O., Tim Cook,
paid tribute, his voice cracking with emotion, Mr. Jobs’s
steeple-fingered image looming as big onstage as
Big Brother’s face in the classic Macintosh '1984' commercial."

James Poniewozik 

Review —

Thursday, September 1, 2011

How It Works

Filed under: Uncategorized — Tags:  — m759 @ 11:00 AM 

"Design is how it works." — Steven Jobs (See Symmetry and Design.)

"By far the most important structure in design theory is the Steiner system S(5, 8, 24)."
 — "Block Designs," by Andries E. Brouwer

. . . .

See also 1984 Bricks in this journal.

Sunday, July 23, 2017

Reality Butts

Filed under: General — m759 @ 3:00 pm

Continuing the 1984  theme

More about 1984 from the above May 1, 2016, post

 

Tuesday, June 20, 2017

Epic

Continuing the previous post's theme  

Group actions on partitions

Cube Bricks 1984 —

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

Related material — Posts now tagged Device Narratives.

Tuesday, May 16, 2017

For Westworld’s Man in Black

Filed under: General — m759 @ 12:00 pm

From University of Chicago Press in 1984:

'Erring,' by Mark C. Taylor, U. of Chicago Press, 1984

"Drawing on Hegel, Nietzsche, Derrida,
and others, Mark Taylor extends—and
goes well beyond—pioneering efforts. . . . "
—G. Douglas Atkins, 
Philosophy and Literature

Update at noon on May 16 —

"Follow the Blood Arroyo to the place
where the snake lays its eggs."

— Westworld, Season 1, Episode 2,
air date October 9, 2016

This suggests a review of Derrida + Serpent 
in this journal.

Tuesday, April 4, 2017

Test

Filed under: General — m759 @ 1:01 pm

See also, in this  journal, St. Cyprian's Day last year.

Wednesday, March 29, 2017

The Crimson Abyss

"And as the characters in the meme twitch into the abyss
that is the sky, this meme will disappear into whatever
internet abyss swallowed MySpace."

—Staff writer Kamila Czachorowski, Harvard Crimson , March 29

1984

IMAGE- 'Affine Groups on Small Binary Spaces,' illustration

2010

Logo design for Stack Exchange Math by Jin Yang
 

Recent posts now tagged Crimson Abyss suggest
the above logo be viewed in light of a certain page 29

"… as if into a crimson abyss …." —

Update of 9 PM ET March 29, 2017:

Prospero's Children  was first published by HarperCollins,
London, in 1999. A statement by the publisher provides
an instance of the famous "much-needed gap." —

"This is English fantasy at its finest. Prospero’s Children 
steps into the gap that exists between The Lion, the Witch
and the Wardrobe
  and Clive Barker’s Weaveworld , and
is destined to become a modern classic."

Related imagery —

See also "Hexagram 64 in Context" (Log24, March 16, 2017).

Art Space Illustrated

Another view of the previous post's art space  —

IMAGE by Cullinane- 'Solomon's Cube' with 64 identical, but variously oriented, subcubes, and six partitions of these 64 subcubes

More generally, see Solomon's Cube in Log24.

See also a remark from Stack Exchange in yesterday's post Backstory,
and the Stack Exchange math logo below, which recalls the above 
cube arrangement from "Affine groups on small binary spaces" (1984).

IMAGE- Current math.stackexchange.com logo and a 1984 figure from 'Notes on Groups and Geometry, 1978-1986'

Tuesday, March 28, 2017

Bit by Bit

Filed under: General,Geometry — Tags: , , , — m759 @ 11:45 am

From Log24, "Cube Bricks 1984" —

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

Also on March 9, 2017 —

For those who prefer graphic  art —

Broken Symmetries  in  Diamond Space  

Friday, March 10, 2017

The Transformers

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

"The transformed urban interior is the spatial organisation of
an achiever, one who has crossed the class divide and who uses
space to express his membership of, not aspirations towards, 
an ascendant class in our society: the class of those people who 
earn their living by transformation— as opposed to the mere
reproduction— of symbols, such as writers, designers, and
academics"

The Social Logic of Space ,
     by Bill Hillier and Julienne Hanson,
     Cambridge University Press, 1984

For another perspective on the achievers, see The Deceivers .

Related material —

Exhibit A:

Exhibit B:

Edwin Schlossberg, 'Still Changes Through Structure' text piece

Exhibit C:

Highbeam Woman

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

See as well the previous post.

Sunday, February 5, 2017

Against Bewitchment

Filed under: General — m759 @ 7:55 pm

A footnote in memory of a preservationist

Title page of a thesis on language by Miles Spencer Kimball from 1984

The previous post's quotation from the Kimball thesis contains
a reference (numbered 23) to the source of Wittgenstein's 
"savages" remarkPhilosophical Investigations , § 194.

Kimball's  remarks quoted in the previous post are from
page 121 of his thesis, under the heading "Wittgenstein's
Battle Against Bewitchment by Language."

From a cinematic example of such bewitchment —

Ein Kampf

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

This is from a master's thesis of 1984.

For the source, see "Ein Kampf" in this journal.

An image from the Saturday Night Live  version —

Sunday, December 25, 2016

Last Christmas*

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

From "Bright Symbol," a post of 12 AM
on December 25, 2015 —

From "Dark Symbol," a post of 12 PM
on December 25, 2015 —

* Title suggested by a song released by Epic Records in 1984.

Thursday, November 3, 2016

Triple Cross

(Continued See the title in this journal, as well as Cube Bricks.)

Cube Bricks 1984 —

An Approach to Symmetric Generation of the Simple Group of Order 168
Related material —

Dirac and Geometry in this journal,
Kummer's Quartic Surface in this journal,
Nanavira Thera in this journal, and
The Razor's Edge  and Nanavira Thera.

See as well Bill Murray's 1984 film "The Razor's Edge"

Movie poster from 1984 —

"A thin line separates
love from hate,
success from failure,
life from death."

Three other dualities, from Nanavira Thera in 1959 —

"I find that there are, in every situation,
three independent dualities…."

(Click to enlarge.)

Friday, September 9, 2016

Ein Kampf

Filed under: General — m759 @ 1:00 pm

(Continued )

A 1984 master's thesis (PDF, 8+ MB) —

"Language, Linguistics, and Philosophy:
A Comparison of the Work of Roman Jakobson
and the Later Wittgenstein, with Some Attention
to the Philosophy of Charles Saunders Peirce,"
by Miles Spencer Kimball.

Two pages from that thesis —

Saturday, August 6, 2016

Mystic Correspondence:

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

The Cube and the Hexagram

The above illustration, by the late Harvey D. Heinz,
shows a magic cube* and a corresponding magic 
hexagram, or Star of David, with the six cube faces 
mapped to the six hexagram lines and the twelve  
cube edges mapped to the twelve hexagram points.
The eight cube vertices correspond to eight triangles
in the hexagram (six small and two large). 

Exercise:  Is this noteworthy mapping** of faces to lines, 
edges to points, and vertices to triangles an isolated 
phenomenon, or can it be viewed in a larger context?

* See the discussion at magic-squares.net of
   "perimeter-magic cubes"

** Apparently derived from the Cube + Hexagon figure
    discussed here in various earlier posts. See also
    "Diamonds and Whirls," a note from 1984.

Thursday, July 14, 2016

Meditation from an April 1

Filed under: General,Geometry — Tags: — m759 @ 9:38 am

Related material from the same day —

See also

Cube Bricks 1984 —

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

The above bricks appeared in some earlier Log24 posts.

Tuesday, July 12, 2016

Hymn

Filed under: General — m759 @ 11:29 am

Yesterday was reportedly the dies natalis  (in the Catholic sense)
of a former president of New York University.

From the conclusion of The Chronicles of Narnia

"The term is over:  the holidays have begun. 
The dream is ended:  this is the morning."

Linda Hamilton's related hymn in the 1984 film "Children of the Corn" —

https://www.youtube.com/watch?v=rpHeTcisyRo .

Wednesday, April 27, 2016

Kubrick’s Rube

Filed under: General — m759 @ 9:23 pm

In memory of a culture jammer *—

* "Mr. Lyons … made a living partly by buying,
reconditioning and selling used cars." —
— Ben Ratliff in The New York Times  this evening.

See also the previous post and, from Feb. 14 in
this  journal, the phrase "more global than local."

Friday, April 8, 2016

Space Cross

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

For George Orwell

Illustration from a book on mathematics —

This illustrates the Galois space  AG(4,2).

For some related spaces, see a note from 1984.

"There is  such a thing as a space cross."
— Saying adapted from a young-adult novel

Monday, April 4, 2016

Cube for Berlin

Foreword by Sir Michael Atiyah —

"Poincaré said that science is no more a collection of facts
than a house is a collection of bricks. The facts have to be
ordered or structured, they have to fit a theory, a construct
(often mathematical) in the human mind. . . . 

 Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to
explain how art fits into our subject and what we mean by beauty.

In attempting to bridge this divide I have always found that
architecture is the best of the arts to compare with mathematics.
The analogy between the two subjects is not hard to describe
and enables abstract ideas to be exemplified by bricks and mortar,
in the spirit of the Poincaré quotation I used earlier."

— Sir Michael Atiyah, "The Art of Mathematics"
in the AMS Notices , January 2010

Judy Bass, Los Angeles Times , March 12, 1989 —

"Like Rubik's Cube, The Eight  demands to be pondered."

As does a figure from 1984, Cullinane's Cube —

The Eightfold Cube

For natural group actions on the Cullinane cube,
see "The Eightfold Cube" and
"A Simple Reflection Group of Order 168."

See also the recent post Cube Bricks 1984

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

Related remark from the literature —

http://www.log24.com/log/pix11B/110918-Felsner.jpg

Note that only the static structure is described by Felsner, not the
168 group actions discussed by Cullinane. For remarks on such
group actions in the literature, see "Cube Space, 1984-2003."

(From Anatomy of a Cube, Sept. 18, 2011.)

Monday, March 21, 2016

Trophy

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

From the 1984 New Orleans film Tightrope

http://www.log24.com/log/pix11A/110615-EastwoodFootball400w.jpg

This post was suggested by the late Yale literary critic
Geoffrey Hartman, who reportedly died on March 14.

" 'Interpretation is like a football game,' Professor Hartman
wrote in 'The Voice of the Shuttle,' a 1969 essay." 

A 2016 obituary by Margalit Fox

Saturday, March 12, 2016

Masonic Melody

Filed under: General — Tags: , , , — m759 @ 1:31 am

"Button your lip baby
Button your coat
Let's go out dancing
Go for the throat"

Read more: Rolling Stones – Mixed Emotions Lyrics | MetroLyrics 

This melody was suggested by a post of February 25, 2016,
by tonight's previous post "Brick-Perfect," and by
the post "Cube Bricks 1984" of March 4, 2016.

"Only connect." — E. M. Forster.

Thursday, March 10, 2016

The Ghost Machine*

Filed under: General — m759 @ 10:12 am

"I had joined the White House early in 1984, after three years
writing Dan Rather's radio commentaries."

— Peggy Noonan, "Confessions of a White House Speechwriter,"
a 1989 New York Times  excerpt from her book What I Saw
at the Revolution

* See also What IS the frequency, Kenneth?

Thursday, November 12, 2015

The Unbaked, the Baked, and the Half-Baked

Filed under: General — Tags: , , — m759 @ 5:07 pm

Consider the trichotomy of the title as applied to the paragraph
by Adam Gopnik in the previous post (The Raw, the Cooked,
and the Spoiled
).

The following quotation seems to place Gopnik's words
among the half -baked.

"L'axe qui relie le cru et le cuit est caractéristique du passage
à la culture; celui qui relie le cru et le pourri, du retour à la nature,
puisque la cuisson accomplit la transformation culturelle du cru
comme la putréfaction en achève la transformation naturelle."

— Claude Lévi-Strauss, Paroles données, p.54, Plon, 1984,
     as quoted in a weblog

See also Lévi-Strauss's bizarre triangle culinaire  (French Wikipedia) —

The source of this structuralist nonsense —
Lévi-Strauss, Claude. 1969. “Le triangle culinaire.”
L’Arc  no. 26: 19-29.

Friday, October 23, 2015

Retro or Not?

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

Happy birthday to the late Michael Crichton (Harvard ’64).

See also Diamond Theory Roulette —

Part of the ReCode Project (http://recodeproject.com).
Based on "Diamond Theory" by Steven H. Cullinane,
originally published in "Computer Graphics and Art" 
Vol. 2 No. 1, February 1977.
Copyright (c) 2013 Radames Ajna 
— OSI/MIT license (http://recodeproject/license).

Related remarks on Plato for Harvard’s
Graduate School of Design

See also posts from the above publication date, March 31,
2006, among posts now tagged “The Church in Philadelphia.”

Saturday, May 23, 2015

Art

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

"Is Fiction the Art of Lying?" by Mario Vargas Llosa

The above link is to a Google Books Search for references
to a 1984 piece in The New York Times .

To find the Times 's  own version, change "Lying" to "Living."

"We tell ourselves stories in order to live." — Joan Didion

Wednesday, February 11, 2015

Dead Reckoning

Filed under: General — Tags: , — m759 @ 5:28 pm

Continued from yesterday evening

IMAGE- Bogart in 'Casablanca' with chessboard

Today's mathematical birthday — 

Claude Chevalley, 11 Feb. 1909 – 28 June 1984.

From MacTutor —

Chevalley's daughter, Catherine Chevalley, wrote about
her father in "Claude Chevalley described by his daughter"
(1988):—

For him it was important to see questions as a whole, to see the necessity of a proof, its global implications. As to rigour, all the members of Bourbaki cared about it: the Bourbaki movement was started essentially because rigour was lacking among French mathematicians, by comparison with the Germans, that is the Hilbertians. Rigour consisted in getting rid of an accretion of superfluous details. Conversely, lack of rigour gave my father an impression of a proof where one was walking in mud, where one had to pick up some sort of filth in order to get ahead. Once that filth was taken away, one could get at the mathematical object, a sort of crystallized body whose essence is its structure. When that structure had been constructed, he would say it was an object which interested him, something to look at, to admire, perhaps to turn around, but certainly not to transform. For him, rigour in mathematics consisted in making a new object which could thereafter remain unchanged.

The way my father worked, it seems that this was what counted most, this production of an object which then became inert— dead, really. It was no longer to be altered or transformed. Not that there was any negative connotation to this. But I must add that my father was probably the only member of Bourbaki who thought of mathematics as a way to put objects to death for aesthetic reasons.

Recent scholarly news suggests a search for Chapel Hill
in this journal. That search leads to Transformative Hermeneutics.
Those who, like Professor Eucalyptus of Wallace Stevens's
New Haven, seek God "in the object itself" may contemplate
yesterday's afternoon post on Eightfold Design in light of the
Transformative post and of yesterday's New Haven remarks and
Chapel Hill events.

Wednesday, November 26, 2014

Class Act

Filed under: General,Geometry — Tags: , — m759 @ 7:18 am

Update of Nov. 30, 2014 —

For further information on the geometry in
the remarks by Eberhart below, see
pp. 16-17 of A Geometrical Picture Book ,
by Burkard Polster (Springer, 1998). Polster
cites a different article by Lemay.

A search for background to the exercise in the previous post
yields a passage from the late Stephen Eberhart:

The first three primes p = 2, 3, and 5 therefore yield finite projective planes with 7, 13, and 31 points and lines, respectively. But these are just the numbers of symmetry axes of the five regular solids, as described in Plato's Timaeus : The tetrahedron has 4 pairs of face planes and corner points + 3 pairs of opposite edges, totalling 7 axes; the cube has 3 pairs of faces + 6 pairs of edges + 4 pairs of corners, totalling 13 axes (the octahedron simply interchanges the roles of faces and corners); and the pentagon dodecahedron has 6 pairs of faces + 15 pairs of edges + 10 pairs of corners, totalling 31 axes (the icosahedron again interchanging roles of faces and corners). This is such a suggestive result, one would expect to find it dealt with in most texts on related subjects; instead, while "well known to those who well know such things" (as Richard Guy likes to quip), it is scarcely to be found in the formal literature [9]. The reason for the common numbers, it turns out, is that the groups of symmetry motions of the regular solids are subgroups of the groups of collineations of the respective finite planes, a face axis being different from an edge axis of a regular solid but all points of a projective plane being alike, so the latter has more symmetries than the former.

[9] I am aware only of a series of in-house publications by Fernand Lemay of the Laboratoire de Didactique, Faculté des Sciences de I 'Éducation, Univ. Laval, Québec, in particular those collectively titled Genèse de la géométrie  I-X.

— Stephen Eberhart, Dept. of Mathematics,
California State University, Northridge, 
"Pythagorean and Platonic Bridges between
Geometry and Algebra," in BRIDGES: Mathematical
Connections in Art, Music, and Science 
, 1998,
archive.bridgesmathart.org/1998/bridges1998-121.pdf

Eberhart died of bone cancer in 2003. A memorial by his
high school class includes an Aug. 7, 2003, transcribed
letter from Eberhart to a classmate that ends…


… I earned MA’s in math (UW, Seattle) and history (UM, Missoula) where a math/history PhD program had been announced but canceled.  So 1984 to 2002 I taught math (esp. non-Euclidean geometry) at C.S.U. Northridge.  It’s been a rich life.  I’m grateful. 
 
Steve
 

See also another informative BRIDGES paper by Eberhart
on mathematics and the seven traditional liberal arts.

Saturday, September 27, 2014

Plan B: Books

Filed under: General — m759 @ 9:48 am
http://www.log24.com/log/pix10B/101008-StartingOut.jpg

Above: Frank Langella in
Starting Out in the Evening

Right: Johnny Depp in
The Ninth Gate

http://www.log24.com/log/pix10B/101008-NinthGate.jpg

“One must proceed cautiously, for this road— of truth and falsehood
in the realm of fiction— is riddled with traps and any enticing oasis
is usually a mirage.”

– “Is Fiction the Art of Lying?” by Mario Vargas Llosa,
New York Times  essay of October 7, 1984

For the title plan, see Sisteen in this journal.

Friday, September 19, 2014

Metaphysics for Gilliam

Filed under: General — m759 @ 9:29 pm

See also…

Related remarks: Diederik Aerts at arXiv.org.

See also Aerts (as above) on the metaphysics of entities  (1984):

Thursday, August 28, 2014

Source of the Finite

Filed under: General,Geometry — Tags: , , — m759 @ 10:20 am

"Die Unendlichkeit  ist die uranfängliche Tatsache: es wäre nur
zu erklären, woher das Endliche  stamme…."

— Friedrich Nietzsche, Das Philosophenbuch/Le livre du philosophe
(Paris: Aubier-Flammarion, 1969), fragment 120, p. 118

Cited as above, and translated as "Infinity is the original fact;
what has to be explained is the source of the finite…." in
The Production of Space , by Henri Lefebvre. (Oxford: Blackwell,
1991 (1974)), p.  181.

This quotation was suggested by the Bauhaus-related phrase
"the laws of cubical space" (see yesterday's Schau der Gestalt )
and by the laws of cubical space discussed in the webpage
Cube Space, 1984-2003.

For a less rigorous approach to space at the Harvard Graduate
School of Design, see earlier references to Lefebvre in this journal.

Monday, July 7, 2014

Tricky Task

Filed under: General,Geometry — Tags: , , — m759 @ 12:25 pm

Roger Cooke in the Notices of the American
Mathematical Society 
, April 2010 —

"Life on the Mathematical Frontier:
Legendary Figures and Their Adventures"

"In most cases involving the modern era, there
are enough documents to produce a clear picture
of mathematical developments, and conjectures
for which there is no eyewitness or documentary
evidence are not needed. Even so, legends do
arise. (Who has not heard the 'explanation' of
the absence of a Nobel Prize in mathematics?)
The situation is different regarding ancient math-
ematics, however, especially in the period before
Plato’s students began to study geometry. Much
of the prehistory involves allegations about the
mysterious Pythagoreans, and sorting out what is
reliable from what is not is a tricky task.

In this article, I will begin with some modern
anecdotes that have become either legend or
folklore, then work backward in time to take a
more detailed look at Greek mathematics, especially
the Pythagoreans, Plato, and Euclid. I hope at the
very least that the reader finds my examples
amusing, that being one of my goals. If readers
also take away some new insight or mathematical
aphorisms, expressing a sense of the worthiness of
our calling, that would be even better."

Aphorism:  "Triangles are square." 

(American Mathematical Monthly , June-July 1984)

Insight:  The Square-Triangle Theorem.

Friday, March 7, 2014

Kummer Varieties

Filed under: General,Geometry — Tags: , , — m759 @ 11:20 am

The Dream of the Expanded Field continues

Image-- The Dream of the Expanded Field

From Klein's 1893 Lectures on Mathematics —

"The varieties introduced by Wirtinger may be called Kummer varieties…."
E. Spanier, 1956

From this journal on March 10, 2013 —

From a recent paper on Kummer varieties,
arXiv:1208.1229v3 [math.AG] 12 Jun 2013,
"The Universal Kummer Threefold," by
Qingchun Ren, Steven V Sam, Gus Schrader, and Bernd Sturmfels —

IMAGE- 'Consider the 6-dimensional vector space over the 2-element field,' from 'The Universal Kummer Threefold'

Two such considerations —

IMAGE- 'American Hustle' and Art Cube

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman 

Update of 10 PM ET March 7, 2014 —

The following slides by one of the "Kummer Threefold" authors give
some background related to the above 64-point vector space and
to the Weyl group of type E7(E7):

The Cayley reference is to "Algorithm for the characteristics of the
triple ϑ-functions," Journal für die Reine und Angewandte
Mathematik  87 (1879): 165-169. <http://eudml.org/doc/148412>.
To read this in the context of Cayley's other work, see pp. 441-445
of Volume 10 of his Collected Mathematical Papers .

Tuesday, February 25, 2014

Singing Contest

Filed under: General — m759 @ 12:00 am

"What a lovely singing voice you must have."
— Bill Murray in Ghostbusters  (1984)

Contestant One Ruth Margraff

Contestant Two Sandra Sangiao 

Thursday, January 23, 2014

For the Snow Queen —

Filed under: General — m759 @ 8:11 am

Dark Epiphanies

Part I: 

Part II:

"A Little Boy and a Little Girl," by Hans Christian Andersen
(second story of the seven that make up The Snow Queen )

Part III:

A former Snow White —

Saturday, January 18, 2014

The Triangle Relativity Problem

Filed under: General,Geometry — Tags: , , , — m759 @ 5:01 pm

A sequel to last night's post The 4×4 Relativity Problem —

IMAGE- Triangle Coordinatization

In other words, how should the triangle corresponding to
the above square be coordinatized ?

See also a post of July 8, 2012 — "Not Quite Obvious."

Context — "Triangles Are Square," a webpage stemming
from an American Mathematical Monthly  item published
in 1984.

Wednesday, January 8, 2014

Not Subversive, Not Fantasy

Filed under: General,Geometry — Tags: , — m759 @ 2:01 pm

The title refers to that of today's previous post, which linked to
a song from the June 1, 1983, album Synchronicity .
(Cf.  that term in this journal.)

For some work of my own from the following year, 1984, see

IMAGE- Internet Archive, 'Notes on Groups and Geometry, 1978-1986'

as well as the Orwellian dictum Triangles Are Square.

(The cubical figure at left above is from the same month,
if not the same day, as Synchronicity —  June 21, 1983.)

Sunday, January 5, 2014

For Amy…

Filed under: General — m759 @ 5:01 pm

And for Scarlett — A Venus Flytrap

From last evening's  John Fogerty 1984 video —

From this morning's paper —

Click the soup for some backstory.

"Assume a can opener."

Sunday, November 24, 2013

Logic for Jews*

The search for 1984 at the end of last evening’s post
suggests the following Sunday meditation.

My own contribution to this genre—

A triangle-decomposition result from 1984:

American Mathematical Monthly ,  June-July 1984, p. 382

MISCELLANEA, 129

Triangles are square

“Every triangle consists of n  congruent copies of itself”
is true if and only if  is a square. (The proof is trivial.)
— Steven H. Cullinane

The Orwell slogans are false. My own is not.

* The “for Jews” of the title applies to some readers of Edward Frenkel.

Saturday, November 23, 2013

Light Years Apart?

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

From a recent attempt to vulgarize the Langlands program:

“Galois’ work is a great example of the power of a mathematical insight….

And then, 150 years later, Langlands took these ideas much farther. In 1967, he came up with revolutionary insights tying together the theory of Galois groups and another area of mathematics called harmonic analysis. These two areas, which seem light years apart, turned out to be closely related.

— Frenkel, Edward (2013-10-01).
Love and Math: The Heart of Hidden Reality
(p. 78, Basic Books, Kindle Edition)

(Links to related Wikipedia articles have been added.)

Wikipedia on the Langlands program

The starting point of the program may be seen as Emil Artin’s reciprocity law [1924-1930], which generalizes quadratic reciprocity. The Artin reciprocity law applies to a Galois extension of algebraic number fields whose Galois group is abelian, assigns L-functions to the one-dimensional representations of this Galois group; and states that these L-functions are identical to certain Dirichlet L-series or more general series (that is, certain analogues of the Riemann zeta function) constructed from Hecke characters. The precise correspondence between these different kinds of L-functions constitutes Artin’s reciprocity law.

For non-abelian Galois groups and higher-dimensional representations of them, one can still define L-functions in a natural way: Artin L-functions.

The insight of Langlands was to find the proper generalization of Dirichlet L-functions, which would allow the formulation of Artin’s statement in this more general setting.

From “An Elementary Introduction to the Langlands Program,” by Stephen Gelbart (Bulletin of the American Mathematical Society, New Series , Vol. 10, No. 2, April 1984, pp. 177-219)

On page 194:

“The use of group representations in systematizing and resolving diverse mathematical problems is certainly not new, and the subject has been ably surveyed in several recent articles, notably [ Gross and Mackey ]. The reader is strongly urged to consult these articles, especially for their reformulation of harmonic analysis as a chapter in the theory of group representations.

In harmonic analysis, as well as in the theory of automorphic forms, the fundamental example of a (unitary) representation is the so-called ‘right regular’ representation of G….

Our interest here is in the role representation theory has played in the theory of automorphic forms.* We focus on two separate developments, both of which are eventually synthesized in the Langlands program, and both of which derive from the original contributions of Hecke already described.”

Gross ]  K. I. Gross, On the evolution of non-commutative harmonic analysis . Amer. Math. Monthly 85 (1978), 525-548.

Mackey ]  G. Mackey, Harmonic analysis as the exploitation of symmetry—a historical survey . Bull. Amer. Math. Soc. (N.S.) 3 (1980), 543-698.

* A link to a related Math Overflow article has been added.

In 2011, Frenkel published a commentary in the A.M.S. Bulletin  
on Gelbart’s Langlands article. The commentary, written for
a mathematically sophisticated audience, lacks the bold
(and misleading) “light years apart” rhetoric from his new book
quoted above.

In the year the Gelbart article was published, Frenkel was
a senior in high school. The year was 1984.

For some remarks of my own that mention
that year, see a search for 1984 in this journal.

Friday, June 21, 2013

Lexicon

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

From the final pages of the new novel
Lexicon , by Max Barry:

"… a fundamental language
of the human mind—
the tongue in which the human animal
speaks to itself at the basest level.
The machine language, in essence…."

"… the questions raised by
this underlying lexicon.
What are its words?
How many are there? ….
Can we learn to speak them?
What does it sound like
when who we are is expressed
in its most fundamental form?
Something to think about."

       R. Lowell

Related material:

IMAGE- Hypokeimenon in Liddell and Scott's Greek-English Lexicon

"… the clocks were striking thirteen." — 1984

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