Log24

Tuesday, April 2, 2013

Rota in a Nutshell

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

"The proof of Desargues' theorem of projective geometry
comes as close as a proof can to the Zen ideal.
It can be summarized in two words: 'I see!' "

— Gian-Carlo Rota in Indiscrete Thoughts (1997)

Also in that book, originally from a review in Advances in Mathematics,
Vol. 84, Number 1, Nov. 1990, p. 136:

IMAGE- Rota's review of 'Sphere Packings, Lattices and Groups'-- in a word, 'best'

Related material:

Pascal and the Galois nocciolo ,
Conway and the Galois tesseract,
Gardner and Galois.

See also Rota and Psychoshop.

Thursday, March 14, 2013

Nutshell continued

Filed under: Uncategorized — Tags: , — m759 @ 8:00 AM

For the new Jesuit pope (see previous post)

Now among Log24 posts tagged "Khora" is one
from July 15, 2010, dealing with a book called
Deconstruction in a Nutshell: A Conversation with
Jacques Derrida 
, edited and with a commentary by
John D. Caputo (Fordham University Press, 1997).

Related material:

"Khora  is the felix culpa  of a passion for the impossible,
the happy fault of a poetics of the possible, the heartless
heart of an ethical and religious eschatology.
Khora  is the devil that justice demands we give his due."

— John D. Caputo, conclusion of "Abyssus Abyssum Invocat :
A Response to Kearney." Caputo's remarks followed
Richard Kearney's "Khora  or God?," pp. 107-122 in
A Passion for the Impossible: John D. Caputo in Focus ,
edited by Mark Dooley, State University of New York Press,
Albany, 2003. See "Abyssus " on pp. 123-127.

See also other uses here of the phrase "In a Nutshell."

Wednesday, October 4, 2017

Text and Context

Filed under: Geometry — m759 @ 11:00 AM

Text —

"A field is perhaps the simplest algebraic structure we can invent."

— Hermann Weyl, 1952

Context —

See also yesterday's Personalized Book Search.

Full text of Symmetry  – Internet Archive —

https://archive.org/details/Symmetry_482

A field is perhaps the simplest algebraic 143 structure
we can invent. Its elements are numbers. Characteristic
for its structure are the operations of addition and 

From a Log24 search for Mathematics+Nutshell —

IMAGE- History of Mathematics in a Nutshell

Monday, October 2, 2017

The Nut Analogy

Filed under: Uncategorized — m759 @ 12:01 PM

For fans of the 'in a nutshell' quote from 'Hamlet'

Published as the final chapter, Chapter 13, in
Episodes in the History of Modern Algebra (1800-1950) ,
edited by Jeremy J. Gray and Karen Hunger Parshall,
American Mathematical Society, July 18, 2007,  pages 301-326.

See also this  journal on the above McLarty date —
May 24, 2003:  Mental Health Month, Day 24.

Monday, June 26, 2017

Four Dots

Filed under: Uncategorized — Tags: , , , — m759 @ 9:57 AM

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

Gian-Carlo Rota on Heidegger…

"… The universal as  is given various names in Heidegger's writings….

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

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

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

— "Three Senses of 'A is B' in Heideggger," Ch. 17 in Indiscrete Thoughts
 

See also Four Dots in this journal. 

Some context:  McLuhan + Analogy.

Sunday, April 16, 2017

Art Space Paradigm Shift

Filed under: Uncategorized — m759 @ 1:00 AM

This post's title is from the tags of the previous post

 

The title's "shift" is in the combined concepts of

Space and Number

From Finite Jest (May 27, 2012):

IMAGE- History of Mathematics in a Nutshell

The books pictured above are From Discrete to Continuous ,
by Katherine Neal, and Geometrical Landscapes , by Amir Alexander.

For some details of the shift, see a Log24 search for Boole vs. Galois.
From a post found in that search —

"Benedict Cumberbatch Says
a Journey From Fact to Faith
Is at the Heart of Doctor Strange
"

io9 , July 29, 2016

" 'This man comes from a binary universe
where it’s all about logic,' the actor told us
at San Diego Comic-Con . . . .

'And there’s a lot of humor in the collision
between Easter [ sic ] mysticism and
Western scientific, sort of logical binary.' "

[Typo now corrected, except in a comment.]

Friday, August 19, 2016

Princeton University Press in 1947

Filed under: Uncategorized — Tags: , — m759 @ 11:17 AM

From a review, in the context of Hollywood, of a Princeton
University Press book on William Blake from 1947 —

Wednesday, August 10, 2016

Analogies Test

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

Obituary for Wilford Stanton Miller, author in 1926
of the Miller Analogies Test  —  
         

Marshall McLuhan writing to Ezra Pound on Dec. 21, 1948—

"The American mind is not even close to being amenable
to the ideogram principle as yet.  The reason is simply this.
America is 100% 18th Century. The 18th century had
chucked out the principle of metaphor and analogy—
the basic fact that as A is to B so is C to D.  AB:CD.   
It can see AB relations.  But relations in four terms are still
verboten.  This amounts to deep occultation of nearly all
human thought for the U.S.A.

I am trying to devise a way of stating this difficulty as it exists.  
Until stated and publicly recognized for what it is, poetry and
the arts can’t exist in America."

A line for W. S. Miller, taken from "Annie Hall" —

"You know nothing of my work."

Thursday, June 2, 2016

Bullshit Studies

Filed under: Uncategorized — Tags: — m759 @ 11:30 AM

(Continued)

"The allusion to 'the most precious square of sense' shows
Shakespeare doing an almost scholastic demonstration of
the need for a ratio and interplay among the senses as
the very constitution of rationality."

— Marshall McLuhan, The Gutenberg Galaxy ,
University of Toronto Press, 1962, page 13

"What Shakespeare refers to in Lear  as the 'precious
square of sense' probably has reference to the traditional
'square of opposition' in logic and to that four-part analogy
of proportionality which is the interplay of sense and reason."     

— McLuhan, ibid. , page 241

This is of course nonsense, and, in view of McLuhan's pose
as a defender of the Catholic faith, damned  nonsense.

Epigraph by McLuhan —

"The Gutenberg Galaxy  develops a mosaic or field
approach to its problems."

I prefer a different "mosaic or field" related to the movable
blocks  of Fröbel, not the movable type  of Gutenberg.

Sunday, May 29, 2016

The Ideogram Principle …

Filed under: Uncategorized — Tags: — m759 @ 4:23 PM

According to McLuhan

Marshall McLuhan writing to Ezra Pound on Dec. 21, 1948—

"The American mind is not even close to being amenable
to the ideogram principle as yet.  The reason is simply this.
America is 100% 18th Century. The 18th century had
chucked out the principle of metaphor and analogy—
the basic fact that as A is to B so is C to D.  AB:CD.   
It can see AB relations.  But relations in four terms are still
verboten.  This amounts to deep occultation of nearly all
human thought for the U.S.A.

I am trying to devise a way of stating this difficulty as it exists.  
Until stated and publicly recognized for what it is, poetry and
the arts can’t exist in America."

For context, see Cameron McEwen,
"Marshall McLuhan, John Pick, and Gerard Manley Hopkins."
(Renascence , Fall 2011, Vol. 64 Issue 1, 55-76)

A relation in four terms

A : B  ::  C : D   as   Model : Crutch  ::  Metaphor : Ornament —

See also Dueling Formulas and Symmetry.

Saturday, November 21, 2015

Brightness at Noon*

Filed under: Uncategorized — m759 @ 12:00 PM

A recent not-too-bright book from Princeton —

Some older, brighter books from Tony Zee

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

* Continued.

Friday, August 14, 2015

Being Interpreted

Filed under: Uncategorized — Tags: — m759 @ 12:31 AM

The ABC of things —

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

The ABC of words —

A nutshell

Book lessons —

IMAGE- History of Mathematics in a Nutshell

Thursday, September 11, 2014

A Class by Itself

Filed under: Uncategorized — Tags: — m759 @ 9:48 AM

The American Mathematical Society yesterday:

Harvey Cohn (1923-2014)
Wednesday September 10th 2014

Cohn, an AMS Fellow and a Putnam Fellow (1942), died May 16 at the age of 90. He served in the Navy in World War II and following the war received his PhD from Harvard University in 1948 under the direction of Lars Ahlfors. He was a member of the faculty at Wayne State University, Stanford University, Washington University in St. Louis, the University of Arizona, and at City College of New York, where he was a distinguished professor. After retiring from teaching, he also worked for the NSA. Cohn was an AMS member since 1942.

Paid death notice from The New York Times , July 27, 2014:

COHN–Harvey. Fellow of the American Mathematical Society and member of the Society since 1942, died on May 16 at the age of 90. He was a brilliant Mathematician, an adoring husband, father and grandfather, and faithful friend and mentor to his colleagues and students. Born in New York City in 1923, Cohn received his B.S. degree (Mathematics and Physics) from CCNY in 1942. He received his M.S. degree from NYU (1943), and his Ph.D. from Harvard (1948) after service in the Navy (Electronic Technicians Mate, 1944-46). He was a member of Phi Beta Kappa (Sigma Chi), won the William Lowell Putnam Prize in 1942, and was awarded the Townsend Harris Medal in 1972. A pioneer in the intensive use of computers in an innovative way in a large number of classical mathematical problems, Harvey Cohn held faculty positions at Wayne State University, Stanford, Washington University Saint Louis (first Director of the Computing Center 1956-58), University of Arizona (Chairman 1958-1967), University of Copenhagen, and CCNY (Distinguished Professor of Mathematics). After his retirement from teaching, he worked in a variety of capacities for the National Security Agency and its research arm, IDA Center for Computing Sciences. He is survived by his wife of 63 years, Bernice, of Laguna Woods, California and Ft. Lauderdale, FL, his son Anthony, daughter Susan Cohn Boros, three grandchildren and one great-granddaughter.

— Published in The New York Times  on July 27, 2014

See also an autobiographical essay found on the web.

None of the above sources mention the following book, which is apparently by this same Harvey Cohn. (It is dedicated to "Tony and Susan.")

From Google Books:

Advanced Number Theory, by Harvey Cohn
Courier Dover Publications, 1980 – 276 pages
(First published by Wiley in 1962 as A Second Course in Number Theory )

Publisher's description:

" 'A very stimulating book … in a class by itself.'— American Mathematical Monthly

Advanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject.

The book is divided into three parts. Part I is concerned with background material — a synopsis of elementary number theory (including quadratic congruences and the Jacobi symbol), characters of residue class groups via the structure theorem for finite abelian groups, first notions of integral domains, modules and lattices, and such basis theorems as Kronecker's Basis Theorem for Abelian Groups.

Part II discusses ideal theory in quadratic fields, with chapters on unique factorization and units, unique factorization into ideals, norms and ideal classes (in particular, Minkowski's theorem), and class structure in quadratic fields. Applications of this material are made in Part III to class number formulas and primes in arithmetic progression, quadratic reciprocity in the rational domain and the relationship between quadratic forms and ideals, including the theory of composition, orders and genera. In a final concluding survey of more recent developments, Dr. Cohn takes up Cyclotomic Fields and Gaussian Sums, Class Fields and Global and Local Viewpoints.

In addition to numerous helpful diagrams and tables throughout the text, appendices, and an annotated bibliography, Advanced Number Theory  also includes over 200 problems specially designed to stimulate the spirit of experimentation which has traditionally ruled number theory."

User Review –

"In a nutshell, the book serves as an introduction to Gauss' theory of quadratic forms and their composition laws (the cornerstone of his Disquisitiones Arithmeticae) from the modern point of view (ideals in quadratic number fields). I strongly recommend it as a gentle introduction to algebraic number theory (with exclusive emphasis on quadratic number fields and binary quadratic forms). As a bonus, the book includes material on Dirichlet L-functions as well as proofs of Dirichlet's class number formula and Dirichlet's theorem in primes in arithmetic progressions (of course this material requires the reader to have the background of a one-semester course in real analysis; on the other hand, this material is largely independent of the subsequent algebraic developments).

Better titles for this book would be 'A Second Course in Number Theory' or 'Introduction to quadratic forms and quadratic fields'. It is not a very advanced book in the sense that required background is only a one-semester course in number theory. It does not assume prior familiarity with abstract algebra. While exercises are included, they are not particularly interesting or challenging (if probably adequate to keep the reader engaged).

While the exposition is *slightly* dated, it feels fresh enough and is particularly suitable for self-study (I'd be less likely to recommend the book as a formal textbook). Students with a background in abstract algebra might find the pace a bit slow, with a bit too much time spent on algebraic preliminaries (the entire Part I—about 90 pages); however, these preliminaries are essential to paving the road towards Parts II (ideal theory in quadratic fields) and III (applications of ideal theory).

It is almost inevitable to compare this book to Borevich-Shafarevich 'Number Theory'. The latter is a fantastic book which covers a large superset of the material in Cohn's book. Borevich-Shafarevich is, however, a much more demanding read and it is out of print. For gentle self-study (and perhaps as a preparation to later read Borevich-Shafarevich), Cohn's book is a fine read."

Thursday, June 26, 2014

The McLuhan Dimension

Filed under: Uncategorized — Tags: , — m759 @ 2:56 AM

"History is a deep and complicated puzzle—
especially when it involves more dimensions than time."

Introduction to a novella in Analog Science Fiction

IMAGE- Marshall McLuhan

IMAGE- Annenberg Hall at Harvard

IMAGE- Search for 'quilt geometry' yields a result from Annenberg Media.

"Annenberg Hall" at Harvard was originally part of a memorial for
Civil War dead. Formerly "Alumni Hall," it was renamed in 1996.

Wednesday, May 21, 2014

Through the Vanishing Point*

Filed under: Uncategorized — Tags: , — m759 @ 9:48 AM

Marshall McLuhan in "Annie Hall" —

"You know nothing of my work."

Related material — 

"I need a photo opportunity
I want a shot at redemption
Don't want to end up a cartoon
In a cartoon graveyard"

— Paul Simon

It was a dark and stormy night…

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

— Page 180, Logicomix

A photo opportunity for Whitehead
(from Romancing the Cube, April 20, 2011)—

IMAGE- Whitehead on Fano's construction of the 15-point projective Galois space over GF(2)

See also Absolute Ambition (Nov. 19, 2010).

* For the title, see Vanishing Point in this journal.

Monday, November 11, 2013

The Mystic Hexastigm…

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

Or: The Nutshell

What about Pascal?

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

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

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

See also Nocciolo  in this journal.

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

Tuesday, May 14, 2013

Raiders of the Lost Aleph

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

See Coxeter + Aleph in this journal.

Epigraph to "The Aleph," a 1945 story by Borges:

"O God! I could be bounded in a nutshell,
and count myself a King of infinite space…"
– Hamlet, II, 2

Tuesday, April 2, 2013

Baker on Configurations

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

The geometry posts of Sunday and Monday have been
placed in finitegeometry.org as

Classical Geometry in Light of Galois Geometry.

Some background:

See Baker, Principles of Geometry , Vol. II, Note I
(pp. 212-218)—

On Certain Elementary Configurations, and
on the Complete Figure for Pappus's Theorem

and Vol. II, Note II (pp. 219-236)—

On the Hexagrammum Mysticum  of Pascal.

Monday's elucidation of Baker's Desargues-theorem figure
treats the figure as a 15420configuration (15 points, 
4 lines on each, and 20 lines, 3 points on each).

Such a treatment is by no means new. See Baker's notes
referred to above, and 

"The Complete Pascal Figure Graphically Presented,"
a webpage by J. Chris Fisher and Norma Fuller.

What is new in the Monday Desargues post is the graphic
presentation of Baker's frontispiece figure using Galois geometry :
specifically, the diamond theorem square model of PG(3,2).

See also Cremona's kernel, or nocciolo :

Baker on Cremona's approach to Pascal—

"forming, in Cremona's phrase, the nocciolo  of the whole."

IMAGE- Definition of 'nocciolo' as 'kernel'

A related nocciolo :

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

Click on the nocciolo  for some
geometric background.

Sunday, May 27, 2012

Finite Jest

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

IMAGE- History of Mathematics in a Nutshell

The books pictured above are From Discrete to Continuous ,
by Katherine Neal, and Geometrical Landscapes , by Amir Alexander.

Commentary—

“Harriot has given no indication of how to resolve
such problems, but he has pasted in in English,
at the bottom of his page, these three enigmatic
lines:

‘Much ado about nothing.
Great warres and no blowes.
Who is the foole now?’

Harriot’s sardonic vein of humour, and the subtlety of
his logical reasoning still have to receive their full due.”

— “Minimum and Maximum, Finite and Infinite:
Bruno and the Northumberland Circle,” by Hilary Gatti,
Journal of the Warburg and Courtauld Institutes ,
Vol. 48 (1985), pp. 144-163

Monday, May 21, 2012

Brightness at Noon

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

Occultation according to McLuhan

Marshall McLuhan writing to Ezra Pound  on Dec. 21, 1948—

"The American mind is not even close to being amenable to the ideogram principle as yet.  The reason is simply this. America is 100% 18th Century. The 18th century had chucked out the principle of metaphor and analogy— the basic fact that as A is to B so is C to D.  AB:CD.   It can see AB relations.  But relations in four terms are still verboten.  This amounts to deep occultation of nearly all human thought for the U.S.A.

I am trying to devise a way of stating this difficulty as it exists.  Until stated and publicly recognized for what it is, poetry and the arts can’t exist in America."

For context, see Cameron McEwen, "Marshall McLuhan, John Pick, and Gerard Manley Hopkins." (Renascence , Fall 2011, Vol. 64 Issue 1, 55-76)

Friday, September 16, 2011

Art, Jung, Toronto

Filed under: Uncategorized — Tags: — m759 @ 9:29 AM

http://www.log24.com/log/pix11B/110916-ArtJungToronto-NYT.jpg

Related art—

Midnight's Icons,

http://www.log24.com/log/pix11B/110915-Jung-FourDiamonds.gif

Faust in Toronto,

http://www.log24.com/log/pix11B/110916-NYT-Faust.jpg

and…

McLuhan 'tetrad' figure with four diamonds surrounding a fifth, the medium

McLuhan and the Four Diamonds

(Wikipedia figure)

"Visually, a tetrad can be depicted as
 four diamonds forming an X…."

" X never, ever, marks the spot."

Sunday, August 14, 2011

Sunday Review

Filed under: Uncategorized — Tags: — m759 @ 3:33 PM

The Sunday New York Times  today—

http://www.log24.com/log/pix11B/110814-GablerNYT500w.jpg

This suggests…

The Elusive Small Idea—

Part I:

McLuhan and the Seven Snow Whites

http://www.log24.com/log/pix11B/110814-GablerNYT500w7white.jpg

Part II (from "Marshall, Meet Bagger," July 29):

"Time for you to see the field."

http://www.log24.com/log/pix11B/110814-TheFieldGF8.jpg

For further details, see the 1985 note
"Generating the Octad Generator."

McLuhan was a Toronto Catholic philosopher.
For related views of a Montreal Catholic philosopher,
see the Saturday evening post.

Friday, July 29, 2011

Marshall, Meet Bagger

Filed under: Uncategorized — Tags: — m759 @ 8:28 AM

Marshall McLuhan writing to Ezra Pound on Dec. 21, 1948—

"The American mind is not even close to being amenable to the ideogram principle as yet.  The reason is simply this.  America is 100% 18th Century.  The 18th century had chucked out the principle of metaphor and analogy— the basic fact that as A is to B so is C to D.  AB:CD.  It can see AB relations.  But relations in four terms are still verboten.  This amounts to deep occultation of nearly all human thought for the U.S.A.

I am trying to devise a way of stating this difficulty as it exists.  Until stated and publicly recognized for what it is, poetry and the arts can’t exist in America."

"Time for you to see the field." —Bagger Vance

The field — See June 2010.

Friday, January 7, 2011

Coxeter and the Aleph

Filed under: Uncategorized — Tags: — m759 @ 10:31 AM

In a nutshell

Epigraph to "The Aleph," a 1945 story by Borges:

O God! I could be bounded in a nutshell,
and count myself a King of infinite space…
— Hamlet, II, 2

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

The story in book form, 1949

A 2006 biography of geometer H.S.M. Coxeter:

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

The Aleph (implicit in a 1950 article by Coxeter):

http://www.log24.com/log/pix11/110107-The1950Aleph-Sm.jpg

The details:

(Click to enlarge)

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

Related material: Group Actions, 1984-2009.

Friday, November 19, 2010

Absolute Ambition

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

"It's my absolute ambition that you are touched to the core of your being with the content…."

— Julie Taymor on Spider-Man: Turn Off the Dark  (Playbill video, undated)

Another ambitious comic-book promotion —

"What Logicomix  does that few works in any medium do is to make intellectual passion palpable. That is its greatest strength. And it’s here that its form becomes its substance."

— Judith Roitman, review (pdf, 3.7 MB) of Logicomix: An Epic Search for Truth , in …

http://www.log24.com/log/pix10B/101119-AMSnoticesSm.jpg

 The December 2010 AMS Notices  cover has excerpts from Logicomix.

Related material:

"In the classical grammarians’ sense of the power of form over 'content' and style over 'substance,' he originated the phrase, 'the medium is the message.'"

— Joseph P. Duggan on Marshall McLuhan at The University Bookman

See also, in this  journal, The Medium is the Message, Wechsler, and Blockheads .

Thursday, July 15, 2010

Brightness at Noon, continued

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

"What exactly was Point Omega?"

This is Robert Wright in Nonzero: The Logic of Human Destiny.

Wright is discussing not the novel Point Omega  by Don DeLillo,
but rather a (related) concept of  the Jesuit philosopher Pierre Teilhard de Chardin.

My own idiosyncratic version of a personal "point omega"—

Image- Josefine Lyche work (with 1986 figures by Cullinane) in a 2009 exhibition in Oslo

Click for further details.

The circular sculpture in the foreground
is called by the artist "The Omega Point."
This has been described as
"a portal that leads in or out of time and space."

For some other sorts of points, see the drawings
on the wall and Geometry Simplified

Image-- The trivial two-point affine space and the trivial one-point projective space, visualized

The two points of the trivial affine space are represented by squares,
and the one point of the trivial projective space is represented by
a line segment separating the affine-space squares.

For related darkness  at noon, see Derrida on différance
as a version of Plato's khôra

(Click to enlarge.)

Image-- Fordham University Press on Derrida, differance, and khora

The above excerpts are from a work on and by Derrida
published in 1997 by Fordham University,
a Jesuit institutionDeconstruction in a Nutshell

Image-- A Catholic view of Derrida

For an alternative to the Villanova view of Derrida,
see Angels in the Architecture.

Saturday, April 24, 2010

Go Ask Alice

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

McLuhan in Space  by Richard Cavell—

As the word "through" in the title of Through the Vanishing Point hints… key reference points for McLuhan and Parker in writing Through the Vanishing Point  were the "Alice" books.

[The footnote symbol here is mine.]

Alice Rae, McLuhan's Unconscious, doctoral dissertation, School of History and Politics, University of Adelaide, May 2008

What McLuhan calls the "unconscious"' is more often named by him as Logos, "acoustic space" or the "media environment," and I trace the debts that these concepts owe not only to Freud and Jung, but to Aristotle, St. Thomas Aquinas, gestalt theory, art theory, Henri Bergson, Pierre Teilhard de Chardin, Wyndham Lewis, Siegfried Giedion, Harold Innis, the French symbolist poets of the late nineteenth century and the British modernists of the early twentieth.

The declaration section of the thesis is dated November 19, 2008.

Related material— Halloween 2005 and The Gospel According to Father Hardon.

A work suggested by Ander Monson's new Vanishing Point . (See April 17 and April 23, together with the April 22 picture of a non-Euclidean  point in the context of "The Seventh Symbol.")

Tuesday, March 16, 2010

Gameplayers of the Academy

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

New Game

In memory of a Jesuit who died on February 22 (see yesterday's "For the Ides of March")–

“The Game in the Ship cannot be approached as a job, a vocation, a career, or a recreation. To the contrary, it is Life and Death itself at work there. In the Inner Game, we call the Game Dhum Welur, the Mind of God."

— M. A. Foster, The Gameplayers of Zan

"… for Othello, no less than his creator Shakespeare, death without speechmaking is almost unthinkable."

"Walter Ong," by Jeet Heer (Book & Culture, July/August 2004)

"This Jack, joke, poor potsherd, patch, matchwood…."

— Jesuit quote at David Lavery's weblog today

See also this journal on February 22, the date of the Jesuit death. A post on that date mentions Ong and his teacher McLuhan, and displays a McLuhan figure related to the "joke" quote above–

McLuhan 'tetrad' figure with four diamonds surrounding a fifth, the medium

Click figure for background.

Ong discussed "agonistic" culture.
See "Sunday's Theater" and a film
based on the novel discussed there–

Menin... First line, in Greek, of the Iliad

Classics 101

IMAGE- Anthony Hopkins in 'The Human Stain'

Prof. Coleman Silk introduces
freshmen to academic values

For academic gameplayers who prefer
less emotionally challenging subjects,
there is Othello Online —

http://www.log24.com/log/pix10/100316-NewGame.jpg

"New Game. You May Pass for White to Start."

Monday, February 22, 2010

Annals of Philosophy

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

The Medium is the Message

http://www.log24.com/log/pix10/100222-McLuhan.jpg
Marshall McLuhan

From the Wikipedia article
on Marshall McLuhan–

McLuhan 'tetrad' figure with four diamonds surrounding a fifth, the medium

From yesterday

(Click images for some background.)

Ian McKellen at 'Neverwas' diamond windows

Related material:

Feast of St. Louis, 2003,

a web page on McLuhan's
student Walter J. Ong, S. J.,

and Jung and the Imago Dei

Sunday, February 21, 2010

Reflections, continued

Filed under: Uncategorized — Tags: — m759 @ 2:02 PM

"The eye you see him with is the same
eye with which he sees you."

– Father Egan on page 333
of Robert Stone's A Flag for Sunrise
(Knopf hardcover, 1981)

Part I– Bounded in a Nutshell

http://www.log24.com/log/pix10/100221-Neverwas2.jpg

Ian McKellen at a mental hospital's diamond-shaped window in "Neverwas"

Part II– The Royal Castle

http://www.log24.com/log/pix10/100221-Newverwas11.jpg

Ian McKellen at his royal castle's diamond-shaped window in "Neverwas"

Part III– King of Infinite Space

http://www.log24.com/log/pix10/100221-KingOfInfiniteSpace.jpg

H.S.M. Coxeter crowns himself "King of Infinite Space"

Related material:

See Coxeter in this journal.

Wednesday, April 8, 2009

Wednesday April 8, 2009

Filed under: Uncategorized — m759 @ 8:00 PM
Where Entertainment
Is God

“For every kind of vampire,
  there is a kind of cross.”
  — Thomas Pynchon in     
    Gravity’s Rainbow   

“Since 1963, when Pynchon’s first novel, V., came out, the writer– widely considered America’s most important novelist since World War II– has become an almost mythical figure, a kind of cross between the Nutty Professor (Jerry Lewis’s) and Caine in Kung Fu.”

Nancy Jo Sales in the November 11, 1996, issue of New York Magazine

A Cross Between

(Click on images for their
  source in past entries.)


In a Nutshell:

Plato’s Ghost evokes Yeats’s lament that any claim to worldly perfection inevitably is proven wrong by the philosopher’s ghost….”

— Princeton University Press on Plato’s Ghost: The Modernist Transformation of Mathematics (by Jeremy Gray, September 2008)

“She’s a brick house…”
 — Plato’s Ghost according to   
Log24, April 2007 

“First of all, I’d like
to thank the Academy.”
Remark attributed to Plato

Jerry Lewis Wins an Oscar at Last-- TIME magazine



David Carradine displays a yellow book-- the Princeton I Ching.

Click on the Yellow Book.”

Wednesday, February 4, 2009

Wednesday February 4, 2009

Filed under: Uncategorized — Tags: — m759 @ 1:23 PM
Overkill
 
In memory of
James Joyce and of
Patrick McGoohan.
who both died on
a January 13th —
Scene from 'The Seventh Seal
Baby Blues cartoon on global positioning systems

 

Related material:

The phrase
"Habitat Global Village"
in the previous entry.

Marshall McLuhan was
apparently the originator
of the phrase
"global village."

The phrase, coined by McLuhan,
 a Catholic, should be associated
more with Rome than
with Americus, Georgia.

"The association is the idea."
— Ian Lee, The Third Word War

Number Six meets Global Village
 

Wednesday, January 28, 2009

Wednesday January 28, 2009

Filed under: Uncategorized — Tags: , — m759 @ 7:59 AM
ACTUAL BEING
continued from
October 25, 2008

John Updike at Boston Public Library, 2006, photo by Robert Spencer for The New York Times
 

"The only wealth he bestowed on his subjects lay in the richness of his descriptive language, the detailed fineness of which won him comparisons with painters like Vermeer and Andrew Wyeth."

Christopher Lehmann-Haupt in today's International Herald Tribune  

 

"These people have discovered how to turn dreams into reality. They know how to enter their dream realities. They can stay there, live there, perhaps forever."

— Alfred Bester on the inmates of Ward T in his 1953 short story, "Disappearing Act"

Related material:
"Is Nothing Sacred?"
 

 

When?

Going to dark bed there was a square round Sinbad the Sailor roc's auk's egg in the night of the bed of all the auks of the rocs of Darkinbad the Brightdayler.

Where?

Black disc from end of Ch. 17 in Ulysses

Ulysses, conclusion of Episode 17

 

Cover of 'Through the Vanishing Point,' by Marshall McLuhan and Harley Parker

Happy Feast of
St. Thomas Aquinas.

Sunday, December 31, 2006

Sunday December 31, 2006

Filed under: Uncategorized — Tags: — m759 @ 8:00 PM
Tools of
Christ Church
(Continued from
St. Thomas Becket’s day)

The author of the thesis
“Conversations with the Dead”

described in this morning’s entry,

Aesthetics of Evil
vs. Christ Church
,

is Darren Joseph Danylyshen.

 
This may be the same
Darren Danylyshen who has
taught at St. Stephen’s SS
(a Catholic secondary school
in Bowmanville, Ontario).
 
Following a link in the
section of that school’s site
beneath the title
“St. Stephen’s Goes Hollywood,”
we find the following:
 
The image “http://www.log24.com/log/pix06B/061231-McLuhan.jpg” cannot be displayed, because it contains errors.
 
This ties in rather neatly with the
“Tools of Christ Church” entry
for last Friday–
St. Thomas Becket’s day–
and with the fact that
today would be the feast day
of Marshall McLuhan,
if McLuhan were a saint.
(McLuhan, a Catholic, died on
Dec. 31, 1980.)
 
Related material:
 
The Communion of Saints as
the Association of Ideas
 

Wednesday, September 6, 2006

Wednesday September 6, 2006

Filed under: Uncategorized — Tags: — m759 @ 5:26 PM
Hamlet's Transformation

"O God, I could be bounded in a nutshell   
and count myself a king of infinite space,
were it not that I have bad dreams."
Hamlet

Background:

  1. Monday's "In a Nutshell,"
  2. Tuesday's "The King of Infinite Space," and
  3. this morning's "Bad Dreams."

Hamlet, 2.2:

"… Something have you heard
Of Hamlet's transformation; so call it,
Sith nor the exterior nor the inward man
Resembles that it was…."

The transformation:

The image “http://www.log24.com/theory/images/DTinscapes4-Trans.gif” cannot be displayed, because it contains errors.

         Click on picture for details.

Related material:

Figures of Speech (June 7, 2006) and
Ursprache Revisited (June 9, 2006).

 

Monday, September 4, 2006

Monday September 4, 2006

Filed under: Uncategorized — Tags: — m759 @ 7:20 PM
In a Nutshell:
 
The Seed

"The symmetric group S6 of permutations of 6 objects is the only symmetric group with an outer automorphism….

This outer automorphism can be regarded as the seed from which grow about half of the sporadic simple groups…."

Noam Elkies, February 2006

This "seed" may be pictured as

The image “http://www.log24.com/log/pix06A/DTinscapes4-2.gif” cannot be displayed, because it contains errors.

group actions on a linear complex

within what Burkard Polster has called "the smallest perfect universe"– PG(3,2), the projective 3-space over the 2-element field.

Related material: yesterday's entry for Sylvester's birthday.

Sunday, September 3, 2006

Sunday September 3, 2006

Filed under: Uncategorized — Tags: , — m759 @ 1:00 PM
Sylvester's Birthday

The following figure from a June 11, 1986, note illustrates Sylvester's "duads" and  "synthemes" using the concept of an "inscape"  (part B of the figure).  As R. T. Curtis and Noam Elkies have explained, the duads and synthemes lead to constructions of many of the sporadic simple groups.

The image “http://www.log24.com/log/pix06A/DTanoutC.jpg” cannot be displayed, because it contains errors.
 

Sunday, January 15, 2006

Sunday January 15, 2006

Filed under: Uncategorized — Tags: , — m759 @ 7:59 AM

Inscape

My entry for New Year's Day links to a paper by Robert T. Curtis*
from The Arabian Journal for Science and Engineering
(King Fahd University, Dhahran, Saudi Arabia),
Volume 27, Number 1A, January 2002.

From that paper:

"Combinatorially, an outer automorphism [of S6] can exist because the number of unordered pairs of 6 letters is equal to the number of ways in which 6 letters can be partitioned into three pairs. Which is to say that the two conjugacy classes of odd permutations of order 2 in S6 contain the same number of elements, namely 15. Sylvester… refers to the unordered pairs as duads and the partitions as synthemes. Certain collections of five synthemes… he refers to as synthematic totals or simply totals; each total is stabilized within S6 by a subgroup acting triply transitively on the 6 letters as PGL2(5) acts on the projective line. If we draw a bipartite graph on (15+15) vertices by joining each syntheme to the three duads it contains, we obtain the famous 8-cage (a graph of valence 3 with minimal cycles of length 8)…."

Here is a way of picturing the 8-cage and a related configuration of points and lines:

The image “http://www.log24.com/theory/images/Cremona-Richmond.gif” cannot be displayed, because it contains errors.

Diamond Theory shows that this structure
can also be modeled by an "inscape"
made up of subsets of a
4×4 square array:

The image “http://www.log24.com/theory/images/Inscape.gif” cannot be displayed, because it contains errors.

The illustration below shows how the
points and lines of the inscape may
be identified with those of the
Cremona-Richmond configuration.

The image “http://www.log24.com/theory/images/Inscape2.gif” cannot be displayed, because it contains errors.

* "A fresh approach to the exceptional automorphism and covers of the symmetric groups"

Friday, September 24, 2004

Friday September 24, 2004

Filed under: Uncategorized — Tags: — m759 @ 6:49 PM

Readings for
Yom Kippur

The film Pi is, in part, about an alleged secret name of God that can be uttered only on Yom Kippur.  This is my personal version of such a name– not an utterance, but instead a picture:

6:49:32 PM
Sept. 24, 2004

Complete graph K6

The Details:

 

Sylvester's Music 

The Unity of Mathematics

720 in the Book

Synthemes and Spreads (pdf)

(Appendix A of
"Classification of
Partial Spreads in PG(4,2)
,"
by Leonard H. Soicher et al.)

Wednesday, September 3, 2003

Wednesday September 3, 2003

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

Reciprocity

From my entry of Sept. 1, 2003:

"…the principle of taking and giving, of learning and teaching, of listening and storytelling, in a word: of reciprocity….

… E. M. Forster famously advised his readers, 'Only connect.' 'Reciprocity' would be Michael Kruger's succinct philosophy, with all that the word implies."

— William Boyd, review of Himmelfarb, New York Times Book Review, October 30, 1994

Last year's entry on this date: 

 

Today's birthday:
James Joseph Sylvester

"Mathematics is the music of reason."
— J. J. Sylvester

Sylvester, a nineteenth-century mathematician, coined the phrase "synthematic totals" to describe some structures based on 6-element sets that R. T. Curtis has called "rather unwieldy objects." See Curtis's abstract, Symmetric Generation of Finite Groups, John Baez's essay, Some Thoughts on the Number 6, and my website, Diamond Theory.

The picture above is of the complete graph K6  Six points with an edge connecting every pair of points… Fifteen edges in all.

Diamond theory describes how the 15 two-element subsets of a six-element set (represented by edges in the picture above) may be arranged as 15 of the 16 parts of a 4×4 array, and how such an array relates to group-theoretic concepts, including Sylvester's synthematic totals as they relate to constructions of the Mathieu group M24.

If diamond theory illustrates any general philosophical principle, it is probably the interplay of opposites….  "Reciprocity" in the sense of Lao Tzu.  See

Reciprocity and Reversal in Lao Tzu.

For a sense of "reciprocity" more closely related to Michael Kruger's alleged philosophy, see the Confucian concept of Shu (Analects 15:23 or 24) described in

Shu: Reciprocity.

Kruger's novel is in part about a Jew: the quintessential Jewish symbol, the star of David, embedded in the K6 graph above, expresses the reciprocity of male and female, as my May 2003 archives illustrate.  The star of David also appears as part of a graphic design for cubes that illustrate the concepts of diamond theory:

Click on the design for details.

Those who prefer a Jewish approach to physics can find the star of David, in the form of K6, applied to the sixteen 4×4 Dirac matrices, in

A Graphical Representation
of the Dirac Algebra
.

The star of David also appears, if only as a heuristic arrangement, in a note that shows generating partitions of the affine group on 64 points arranged in two opposing triplets.

Having thus, as the New York Times advises, paid tribute to a Jewish symbol, we may note, in closing, a much more sophisticated and subtle concept of reciprocity due to Euler, Legendre, and Gauss.  See

The Jewel of Arithmetic and

The Golden Theorem.

Thursday, June 26, 2003

Thursday June 26, 2003

Filed under: Uncategorized — Tags: , — m759 @ 5:00 AM

ART WARS:
Art at the Vanishing Point

From the web page Art Wars:

"For more on the 'vanishing point,'
or 'point at infinity,' see
Midsummer Eve's Dream."

On Midsummer Eve, June 23, 2003, minimalist artist Fred Sandback killed himself.

Sandback is discussed in The Dia Generation, an April 6, 2003, New York Times Magazine article that is itself discussed at the Art Wars page.

Sandback, who majored in philosophy at Yale, once said that

"Fact and illusion are equivalents."

Two other references that may be relevant:

The Medium is
the Rear View Mirror
,

which deals with McLuhan's book Through the Vanishing Point, and a work I cited on Midsummer Eve  …

Chapter 5 of Through the Looking Glass:

" 'What is it you want to buy?' the Sheep said at last, looking up for a moment from her knitting.

'I don't quite know yet,' Alice said very gently.  'I should like to look all round me first, if I might.'

'You may look in front of you, and on both sides, if you like,' said the Sheep; 'but you ca'n't look all round you — unless you've got eyes at the back of your head.'

But these, as it happened, Alice had not got: so she contented herself with turning round, looking at the shelves as she came to them.

The shop seemed to be full of all manner of curious things — but the oddest part of it all was that, whenever she looked hard at any shelf, to make out exactly what it had on it, that particular shelf was always quite, empty, though the others round it were crowded as full as they could hold.

'Things flow about so here!' she said at last in a plaintive tone…."

 "When Alice went
     through the vanishing point
"
 

Tuesday, September 3, 2002

Tuesday September 3, 2002

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

Today's birthday: James Joseph Sylvester

"Mathematics is the music of reason." — J. J. Sylvester

Sylvester, a nineteenth-century mathematician, coined the phrase "synthematic totals" to describe some structures based on 6-element sets that R. T. Curtis has called "rather unwieldy objects." See Curtis's abstract, Symmetric Generation of Finite Groups, John Baez's essay, Some Thoughts on the Number 6, and my website, Diamond Theory. See also the abstract of a December 7, 2000, talk, Mathematics and the Art of M. C. Escher, in which Curtis notes that graphic designs can "often convey a mathematical idea more eloquently than pages of symbolism."

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