"Some philosophical pieces are like symphonies,
others like quartets."
— Gustav Bergmann, "Frege's Hidden Nominalism,"
The Philosophical Review ,
Vol. 67, No. 4 (Oct., 1958), pp. 437-459
See also Annals of Religion.
Wednesday, February 29, 2012
Universals Revisited
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Metamorphoses of an Author
"… I'm never sure why I like Auster books.
They have that appealing shiny-ness,
that makes me go 'oooh'
then put my hands out to touch it
even though I know I shouldn't,
much like someone giving you
a plate of mercury to play with. "
— Review at goodreads.com
See also Auster as a T-1000 Terminator
in yesterday's post Page.
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Tuesday, February 28, 2012
Page
A followup to this morning's post Stolen Glory—
Columbia's Butler Library "plays a role in
Paul Auster's 2009 novel Invisible ,
where the novel's main protagonist, Adam Walker,
takes a job as a 'page' in the library's stacks." —Wikipedia
Part I (from Feb. 24)—
Part II— (Click to enlarge)
For the page's source, see Butler Library.
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Stolen Glory
From University Diaries yesterday—
"A writer for The Atlantic applauds Santorum's attack on universities
as secular, amoral indoctrination machines.
What can UD say to this?…."
Below is a screenshot of the new home page for
Columbia University Department of Mathematics.
The impressive building in the photo is not the math department.
The building is actually Columbia's Butler Library.
"Along the front and sides of the library are inscribed the names of
Homer, Herodotus, Sophocles, Plato, Aristotle, Desmosthenes,
Cicero, Virgil, Horace, Tacitus, Saint Augustine, Aquinas, Dante,
Cervantes, Shakespeare, Milton, Voltaire, and Goethe." —Wikipedia
The inscribed names outline a defense of liberal education
perhaps more robust than the Feb. 26 effort of Andrew Delbanco,
which University Diaries calls "tepid." (See the previous Log24 post.)
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Monday, February 27, 2012
Reflection
"But even if the religious note is dissonant to some of us,
it seems hard to come up with a better formulation
of what a college should strive to be: an aid to reflection…."
— Andrew Delbanco, Chronicle of Higher Education , Feb. 26, 2012
Another aid to reflection—
The logo of an institution that advertised today in the Chronicle
next to Delbanco's article—
Click logo for context. The institution's original name
was Hesperian College.
For some background, see Evening Star in this journal.
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Annals of Religion
"Allegorical pictures of contemporary events
have a way of weaving in and out
between the symbolic and the semi-psychotic."
— Adam Gopnik in The New Yorker , issue dated March 5, 2012
See also Venue and Weaveworld .
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Sunday, February 26, 2012
Margaret’s Haiku
Margaret Soltan this morning posted a haiku about a fox in her garden.
Related material— The Ninth Gate* versus The Ninth Configuration.
* For some backstory, see pop physics.
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Sermon for Nabokov
"In linear algebra, the basis of a vector space
is an alphabet in which all vectors
can be expressed uniquely. The thing to remember
is that there are many such alphabets."
— "A Vector Alphabet of Interstellar Travel,"
by Yoon Ha Lee
See also Starflight in this journal.
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Garden of Good and Evil
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Saturday, February 25, 2012
The Rock
(Continued. See previous post and Red and Gray in this journal.)
“Give faith a fighting chance.” —Country song
From a post of June 3, 2007—
Related illustration relevant to theology—
For some background, see Cube Trinity in this journal.
For greater depth, see Levering’s Scripture and Metaphysics:
Aquinas and the Renewal of Trinitarian Theology ,
Blackwell, 2004, page 150.
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Cuber (continued)
Click images for further details.
See also Crimson Tide, Rubik, and Cuber.
For another monochromatic enigma without
guaranteed equality of results, see
Finite Geometry of the Square and Cube.
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Friday, February 24, 2012
Thursday, February 23, 2012
Minimalist Whirl
See St. Bridget's Cross
on the Web and in this journal.
Related material—
(Click images to enlarge.)
From Tablet magazine on St. Bridget's Day, 2012—
From Tablet magazine today—
Of greater secular interest—
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Wednesday, February 22, 2012
For Ash Wednesday
"And the light shone in darkness and
Against the Word the unstilled world still whirled
About the centre of the silent Word."
— T. S. Eliot, "Ash Wednesday"
This suggested a search for commentary on
Conrad Aiken's phrase "where whirled and well."
Of the nine (Google) search results, one is not from
my own journal entries—
[PDF] TIME! TIME! TIME!
https://circle.ubc.ca/bitstream/id/131009/UBC_1968_A8%20C33.pdf
File Format: PDF/Adobe Acrobat
by G Cameron – 1968 – Related articles
well where whirled and well where whirled and well—
-3. The stress on words such as "wing" is expanded for use
in Aiken's musical paragraph as follows: …
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Tuesday, February 21, 2012
Cuckoos’ Nest
See …
- St. Dunstan in this journal,
- Location for a film based on The Midwich Cuckoos ,
- Andrew Amesbury's weblog today, and
- St. Dunstan's Garden
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For Mardi Gras
See Dennis Overbye in today's New York Times
and Imago Creationis in this journal.
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Photo Opportunity
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Monday, February 20, 2012
Coxeter and the Relativity Problem
In the Beginning…
"As is well known, the Aleph is the first letter of the Hebrew alphabet."
– Borges, "The Aleph" (1945)
From some 1949 remarks of Weyl—
"The relativity problem is one of central significance throughout geometry and algebra and has been recognized as such by the mathematicians at an early time."
— Hermann Weyl, "Relativity Theory as a Stimulus in Mathematical Research," Proceedings of the American Philosophical Society , Vol. 93, No. 7, Theory of Relativity in Contemporary Science: Papers Read at the Celebration of the Seventieth Birthday of Professor Albert Einstein in Princeton, March 19, 1949 (Dec. 30, 1949), pp. 535-541
Weyl in 1946—:
"This is the relativity problem: to fix objectively a class of equivalent coordinatizations and to ascertain the group of transformations S mediating between them."
— Hermann Weyl, The Classical Groups , Princeton University Press, 1946, p. 16
Coxeter in 1950 described the elements of the Galois field GF(9) as powers of a primitive root and as ordered pairs of the field of residue-classes modulo 3—
"… the successive powers of the primitive root λ or 10 are
λ = 10, λ2 = 21, λ3 = 22, λ4 = 02,
λ5 = 20, λ6 = 12, λ7 = 11, λ8 = 01.
These are the proper coordinate symbols….
(See Fig. 10, where the points are represented in the Euclidean plane as if the coordinate residue 2 were the ordinary number -1. This representation naturally obscures the collinearity of such points as λ4, λ5, λ7.)"
Coxeter's Figure 10 yields...
The Aleph
The details:
Coxeter's phrase "in the Euclidean plane" obscures the noncontinuous nature of the transformations that are automorphisms of the above linear 2-space over GF(3).
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Saturday, February 18, 2012
Symmetry
From the current Wikipedia article "Symmetry (physics)"—
"In physics, symmetry includes all features of a physical system that exhibit the property of symmetry—that is, under certain transformations, aspects of these systems are 'unchanged', according to a particular observation. A symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is 'preserved' under some change.
A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries. Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups (see Symmetry group)."….
"A discrete symmetry is a symmetry that describes non-continuous changes in a system. For example, a square possesses discrete rotational symmetry, as only rotations by multiples of right angles will preserve the square's original appearance."
Note the confusion here between continuous (or discontinuous) transformations and "continuous" (or "discontinuous," i.e. "discrete") groups .
This confusion may impede efforts to think clearly about some pure mathematics related to current physics— in particular, about the geometry of spaces made up of individual units ("points") that are not joined together in a continuous manifold.
For an attempt to forestall such confusion, see Noncontinuous Groups.
For related material, see Erlanger and Galois as well as the opening paragraphs of Diamond Theory—
Symmetry is often described as invariance under a group of transformations. An unspoken assumption about symmetry in Euclidean 3-space is that the transformations involved are continuous.
Diamond theory rejects this assumption, and in so doing reveals that Euclidean symmetry may itself be invariant under rather interesting groups of non-continuous (and a-symmetric) transformations. (These might be called noncontinuous groups, as opposed to so-called discontinuous (or discrete ) symmetry groups. See Weyl's Symmetry .)
For example, the affine group A on the 4-space over the 2-element field has a natural noncontinuous and asymmetric but symmetry-preserving action on the elements of a 4×4 array. (Details)
(Version first archived on March 27, 2002)
Update of Sunday, February 19, 2012—
The abuse of language by the anonymous authors
of the above Wikipedia article occurs also in more
reputable sources. For instance—
Some transformations referred to by Brading and Castellani
and their editees as "discrete symmetries" are, in fact, as
linear transformations of continuous spaces, themselves
continuous transformations.
This unfortunate abuse of language is at least made explicit
in a 2003 text, Mathematical Perspectives on Theoretical
Physics (Nirmala Prakash, Imperial College Press)—
"… associated[*] with any given symmetry there always exists
a continuous or a discrete group of transformations….
A symmetry whose associated group is continuous (discrete)
is called a continuous (discrete ) symmetry ." — Pp. 235, 236
[* Associated how?]
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Logo
Pentagram design agency on the new Windows 8 logo—
"… the logo re-imagines the familiar four-color symbol
as a modern geometric shape"—
Sam Moreau, Principal Director of User Experience for Windows,
yesterday—
On Redesigning the Windows Logo—
"To see what is in front of one's nose
needs a constant struggle." —George Orwell
That is the feeling we had when Paula Scher
(from the renowned Pentagram design agency)
showed us her sketches for the new Windows logo.
Related material:
- A Four-Color Theorem,
- The Galois Window, and
-
An illustration from
Finite Geometry of the Square and Cube—
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Friday, February 17, 2012
Pregeometry and Finite Geometry
Today's previous post, on the Feb. 2012 Scientific American
article "Is Space Digital?", suggested a review of a notion
that the theoretical physicist John Archibald Wheeler called
pregeometry .
From a paper on that topic—
"… the idea that geometry should constitute
'the magic building material of the universe'
had to collapse on behalf of what Wheeler
has called pregeometry (see Misner et al. 1973,
pp. 1203-1212; Wheeler 1980), a somewhat
indefinite term which expresses “a combination
of hope and need, of philosophy and physics
and mathematics and logic” (Misner et al. 1973,
p. 1203)."
— Jacques Demaret, Michael Heller, and
Dominique Lambert, "Local and Global Properties
of the World," preprint of paper published in
Foundations of Science 2 (1): 137-176
Misner, C. W., Thorne, K. S. and Wheeler, J. A.
1973, Gravitation , W.H. Freeman and Company:
San Francisco.
Wheeler, J.A. 1980, "Pregeometry: Motivations
and Prospects," in: Quantum Theory and Gravitation ,
ed. A.R. Marlow, Academic Press: New York, pp. 1-11.
Some related material from pure mathematics—
Click image for further details.
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Physics vs. Geometry
Physics
The February 2012 issue of Scientific American
has a cover article titled "Is Space Digital?".
The article discusses whether physical space
"is made of chunks. Blocks. Bits."
Maybe it is, maybe it isn't.
Geometry
The word "space" in pure mathematics
(as opposed to physics) applies to
a great variety of structures.
Some are continuous, some are not.
For some purely mathematical structures
that are not continuous, (i.e., are made of
"chunks, blocks, bits") see finitegeometry.org/sc —
in particular, the pages on Finite Geometry and Physical Space
and on Noncontinuous Groups.
The geometry of these structures may or may not eventually
be relevant to the "21st-century physics" discussed
in the February Scientific American.
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Thursday, February 16, 2012
Truth and Fiction
Readings—
- Facts Are Stupid (Dan Kois at Slate.com yesterday)
- Tim O'Brien Quotes (cached from Goodreads.com)
- The Story Theory of Truth
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Midnight in the Garden
(Continued from February 10.)
A passage suggested by the T.S. Eliot epigraphs in
Parallelisms of Compete Designs , by a weblog post
of Peter J. Cameron yesterday, and by this journal's
"Within You Without You" posts—
— Joseph Campbell, The Inner Reaches of Outer Space:
Metaphor as Myth and as Religion , New World Library,
Second Edition, St. Bridget's Day 2002, page 106
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Wednesday, February 15, 2012
A Job for St. Valentine
Maureen Dowd's NY Times column today is on exorcism.
Related material— This morning's update at the end of
yesterday morning's Valentine's Day post Notable Transitions.
See also another post for St. Valentine — The Ninth Configuration.
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Tuesday, February 14, 2012
The Ninth Configuration
The showmanship of Nicki Minaj at Sunday's
Grammy Awards suggested the above title,
that of a novel by the author of The Exorcist .
The Ninth Configuration —
The ninth* in a list of configurations—
"There is a (2d-1)d configuration
known as the Cox configuration."
— MathWorld article on "Configuration"
For further details on the Cox 326 configuration's Levi graph,
a model of the 64 vertices of the six-dimensional hypercube γ6 ,
see Coxeter, "Self-Dual Configurations and Regular Graphs,"
Bull. Amer. Math. Soc. Vol. 56, pages 413-455, 1950.
This contains a discussion of Kummer's 166 as it
relates to γ6 , another form of the 4×4×4 Galois cube.
See also Solomon's Cube.
* Or tenth, if the fleeting reference to 113 configurations is counted as the seventh—
and then the ninth would be a 153 and some related material would be Inscapes.
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Notable Transitions
This morning's New York Times gives a folklorist's
view of The Great Gatsby—
"Daisy Buchanan, he argued in a 1960 article,
is a Jazz Age incarnation of the beautiful,
seductive Fairy Queen of Celtic lore."
— Margalit Fox, obituary of Tristram P. Coffin,
who died at 89 on January 31st, 2012
See also…
Two screenshots in memory of fashion and fine-art photographer
Lillian Bassman, who died yesterday at 94—
Update of 10:10 AM EST Wed., Feb. 15, 2012…
In memory of Dory Previn, a song for "Hanna" and "Lord of the Rings" star Cate Blanchett.
Previn died yesterday, on Valentine's Day. Perhaps an inspiration for a lyric by Leonard Cohen?
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Monday, February 13, 2012
Why Now?
From the 2011 film "Hanna"—
Marissa: Why now, Erik?
Erik: Kids grow up.
From the 50th Anniversary Edition
(January 31, 2012) of A Wrinkle in Time—
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Ms. Lincoln
Suggested by a USA Today story on last night's Grammy ratings,
by the showmanship of Nicki Minaj, and by…
"Lincoln was one of many singers influenced by Billie Holiday." —Wikipedia
Related material—
- St. Bridget's Day, 2012 (a Roman Catholic holiday)
- Egress (in memory of Etta James)
- Feast of the Assumption, 2010 (another Roman Catholic holiday)
"Apart from that, Ms. Lincoln…"
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Sunday, February 12, 2012
Rhetorical Answer
NOW ENJOY BRILLIANT COLLEGE COURSES
IN YOUR HOME OR CAR!
The sun was burning down….
There was a trembling in the air as the unnamed colors
and landforms took on definition, a clarity of outline and extent….
This is where we sat through his hushed hour, a torchlit sky,
the closeness of hills barely visible at high white noon.
— DeLillo, Don, Point Omega
Midi là-haut, Midi sans mouvement
En soi se pense et convient à soi-même…
Tête complète et parfait diadème,
Je suis en toi le secret changement.
— Valéry, Paul, "Le Cimetière Marin"
… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.
— Darío, Rubén, "Los Tres Reyes Magos"
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Saturday, February 11, 2012
Sports
"News and Traffic. Sports and Weather. These were his acid terms
for the life he’d left behind, more than two years of living with
the tight minds that made the war. It was all background noise,
he said, waving a hand. He liked to wave a hand in dismissal."
— DeLillo, Don (2010-02-02), Point Omega
Send in the Clowns. (Click to enlarge.)
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Grids
See Notes for a Haiku.
Related material—
A novel published on Groundhog Day, 2010—
— as well as Conceptual Art, Josefine Lyche's
"Grids, You Say?" and The Speed of Thought.
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Friday, February 10, 2012
24 Hour Psycho
From "Kill Bill: Vol. 1"—
The Bride: [Japanese] I need Japanese steel.
Related material —
Yodogawa, 1982 (see yesterday evening's Psycho) and…
See also this afternoon's 5:01 post.
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Pensée
Wednesday, February 1, 2012
Politics
|
Related material—
See also At the Still Point (a post in memory of film editor Sally Menke).
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Garden of Good and Evil
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Thursday, February 9, 2012
ART WARS continued
On the Complexity of Combat—
The above article (see original pdf), clearly of more
theoretical than practical interest, uses the concept
of "symmetropy" developed by some Japanese
researchers.
For some background from finite geometry, see
Symmetry of Walsh Functions. For related posts
in this journal, see Smallest Perfect Universe.
Update of 7:00 PM EST Feb. 9, 2012—
Background on Walsh-function symmetry in 1982—
(Click image to enlarge. See also original pdf.)
Note the somewhat confusing resemblance to
a four-color decomposition theorem
used in the proof of the diamond theorem.
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Wednesday, February 8, 2012
Beach Boy
(Continued from March 28, 2006, and February 6, 2012)
Paris—
Sylvia Beach and James Joyce at Shakespeare and Company
See also Walking into Eternity.
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Old Sport
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Lichtung!
(Continued from Dec. 5, 2002)
From Bad…
|
Braucht´s noch Text? |
To Verse—
|
manche meinen |
|
by Ernst Jandl |
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Tuesday, February 7, 2012
Zip Enter Get a Quote
![IMAGE- Top of NY Times obits page, morning of Feb. 7th, 2012, with ad saying ZIP [ENTER] GET A QUOTE](http://www.log24.com/log/pix12/120207-DarknessSearch.jpg)
Okay… http://m759.net/wordpress/?p=16365.
See also last night's 11:48 post and Erin Burnett in "Glad Rags."
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Random Walk
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Barcelona
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Monday, February 6, 2012
Straight Talk
Tonight's TV, in brief—
AUDITION:
At 10, Smash. At 11, Erin Burnett OutFront (repeat).
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Beach Boy
| Cached from artnet.com |
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|
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In memory of a dealer in artists' ephemera,
Steven Leiber, who died on January 28, 2012—
a link to a post from the date of Leiber's death—
See also Me and My Shadow, a post from
the date the above photo was offered for sale.
Related ephemeral art— a post titled, with irony,
Introduction to Harmonic Analysis.
Related non -ephemeral art—
Mathematical Imagery.
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Savage Logic
|
Saturday, October 16, 2010 m759 @ 12:00 PM Brightness at Noon continued – Sir William Rowan Hamilton, See also this journal on 1/09, 2010. |
This post was suggested by the date
of a user comment in Wikipedia.
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Sunday, February 5, 2012
Sermon Highlight
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Sunday Morning
CBS Sunday Morning 's piece on
the number pi today suggested…
Hexagram 20, Contemplation/View,
from the website Rightreading.com
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Saturday, February 4, 2012
Ein Satz
|
4 × 5 = ̲2̲0̲ . Related material— The link "Ten is a Hen" "She's told a detective story without violence, Judy Davis, shown above in |
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Cock Tale (continued)
The late Ben Gazzara as Jackie Treehorn
in "The Big Lebowski"—
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Office Visit
From the screenplay of "The Number 23"—
INT. NATHANIEL'S INSTITUTE, STAIRWELL – NIGHT
Agatha climbs a dark staircase. Layers of dust
testify to years of neglect.
INT. 3RD FLOOR CORRIDOR – CONTINUOUS
Agatha finds ROOM 318. A rusting door plaque reads,
"DR. SIRIUS LEARY, M.D. PSYCHIATRY."
For related material, see "Leary + Cuernavaca" and "Prime Cut."
Happy belated 2/3 birthday to Walter Sparrow.
Related material— Two other occurrences of "318" in this journal—
in another horror story, "The Sweet Smell of Avon,"
and in a quote from the Feast of St. Nicholas, 2010—
"When Novelists Become Cubists," by Andre Furlani—
"A symbol comes into being when an artist sees that
it is the only way to get all the meaning in.
Genius always proceeds by faith" (312).
The unparaphrasable architectonic text
"differs from other narrative in that the meaning
shapes into a web, or globe, rather than along a line" (318).
[The references are to page numbers in
Guy Davenport's The Geography of the Imagination .]
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Friday, February 3, 2012
Souvenir
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Unusual Suspects
"… 'Mes chers frères, n'oubliez jamais,
quand vous entendrez vanter le progrès des lumières,
que la plus belle des ruses du diable
est de vous persuader qu'il n'existe pas!'
Le souvenir de ce célèbre orateur
nous conduisit naturellement vers le sujet des académies,
et mon étrange convive m'affirma qu'il ne dédaignait pas,
en beaucoup de cas, d'inspirer la plume, la parole et la conscience
des pédagogues, et qu'il assistait presque toujours en personne,
quoique invisible, à toutes les séances académiques."
— Baudelaire, "Le Joueur Généreux"
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Thursday, February 2, 2012
Rien de Rien*
In memory of the longtime co-editor of Series A of the
Journal of Combinatorial Theory , who died on January 12th,
2012, here is a link to a Log24 post of that date.
* For the title, see January 19th.
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Die Nichtung
"It seems that Hilbert had no taste for philosophers….
Hans Rademacher told this reviewer that, after Heidegger
once lectured in Göttingen, Hilbert gleefully repeated
to everyone the phrase "Das Nichts nichtet die Nichtung ."
— Gian-Carlo Rota, Discrete Thoughts , 2nd ed., p. 233
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Die Lichtung
See January 4th, 2012.
(This link resulted from an application of Heidegger's
philosophy of "the opening" and "the shining" (Die Lichtung ).)
See also The Shining of May 29.
Update of 12:19 AM Feb. 3, 2012—
The undated (but cached by Google on January 4th, 2012)
unsigned post from a deleted weblog linked to above as
"an application" is also available in a version that is signed
(but still undated).
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The Opening
From ShiftLock in this journal—
"Philosophy knows nothing of the opening."
— Heidegger
See also a post of September 25, 2009,
and a film whose opening was on that date.
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Wednesday, February 1, 2012
Politics
"Should we arbitrate life and death
at a round table or a square one?"
See also the two previous posts,
Disturbing Archimedes and Tesseract.
Update—
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Disturbing Archimedes
Princeton University Press on a book it will publish in March—
Circles Disturbed: The Interplay of
Mathematics and Narrative
"… brings together important thinkers in mathematics,
history, and philosophy to explore the relationship
between mathematics and narrative.
The book's title recalls the last words of the great
Greek mathematician Archimedes before he was
slain by a Roman soldier— 'Don't disturb my circles' …."
Related material—
Archimedes's Vicious Circle
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