Click image for a larger, clearer version.
Friday, August 1, 2014
Thursday, July 31, 2014
The title phrase means, according to the Encyclopedia of Mathematics,
a null system , and
“A null system is also called null polarity,
a symplectic polarity or a symplectic correlation….
it is a polarity such that every point lies in its own
See Reinhold Baer, “Null Systems in Projective Space,”
Bulletin of the American Mathematical Society, Vol. 51
(1945), pp. 903-906.
An example in PG(3,2), the projective 3-space over the
two-element Galois field GF(2):
See also the 10 AM ET post of Sunday, June 8, 2014, on this topic.
Wednesday, July 30, 2014
Tuesday, July 29, 2014
See “Charles Williams” + Witchcraft in this journal.
Williams was one of the Inklings, a group of Christian
writers that included C. S. Lewis and J. R. R. Tolkien.
In memoriam :
“Margot Adler, an iconic NPR correspondent and Wiccan priestess,
died on Monday July 28 from endometrial cancer at the age of 68.”
See also Log24 posts tagged NPR Magic.
Two items from this morning’s news:
“Sasaki Roshi trained for years in a distinctively strict style of Zen
that he transplanted to the U.S. His students rose at 3 a.m.
for chanting, exhausting hours of meditation and one-on-one
meetings with their teacher, who would pose impenetrable
koans, riddles like: ‘When you see the flower, where is God?’”
For a mathematician’s example of an alleged Zen ideal, see the feast day
this year of St. Gerard Manley Hopkins.
Monday, July 28, 2014
Reductionism is a philosophical position
which holds that a complex system is nothing but
the sum of its parts, and that an account of it can be
reduced to accounts of individual constituents.
1. See e.g. Reductionism in the Interdisciplinary
Encyclopedia of Religion and Science.
”The Website of the Interdisciplinary Encyclopedia on
Religion and Science is edited by the Advanced School
for Interdisciplinary Research (ADSIR), operating at the
Pontifical University of the Holy Cross, Rome….”
For a reductionist Holy Cross, see yesterday’s noon post.
Sunday, July 27, 2014
George Johnson, a science writer, in The New York Times
on July 21, 2014:
“New particles may yet be discovered, and even new laws.
But it is almost taken for granted that everything
from physics to biology, including the mind,
ultimately comes down to four fundamental concepts:
matter and energy interacting in an arena of space and time.”
Ite, missa est.
Saturday, July 26, 2014
Or: Two Rivets Short of a Paradigm
Detail from an author photo:
The philosopher Graham Harman is invested in re-thinking the autonomy of objects and is part of a movement called Object-Oriented-Philosophy (OOP). Harman wants to question the authority of the human being at the center of philosophy to allow the insertion of the inanimate into the equation. With the aim of proposing a philosophy of objects themselves, Harman puts the philosophies of Bruno Latour and Martin Heidegger in dialogue. Along these lines, Harman proposes an unconventional reading of the tool-being analysis made by Heidegger. For Harman, the term tool does not refer only to human-invented tools such as hammers or screwdrivers, but to any kind of being or thing such as a stone, dog or even a human. Further, he uses the terms objects, beings, tools and things, interchangeably, placing all on the same ontological footing. In short, there is no “outside world.”
Harman distinguishes two characteristics of the tool-being: invisibility and totality. Invisibility means that an object is not simply used but is: “[an object] form(s) a cosmic infrastructure of artificial and natural and perhaps supernatural forces, power by which our last action is besieged.” For instance, nails, wooden boards and plumbing tubes do their work to keep a house “running” silently (invisibly) without being viewed or noticed. Totality means that objects do not operate alone but always in relation to other objects–the smallest nail can, for example, not be disconnected from wooden boards, the plumbing tubes or from the cement. Depending on the point of view of each entity (nail, tube, etc.) a different reality will emerge within the house. For Harman, “to refer to an object as a tool-being is not to say that it is brutally exploited as a means to an end, but only that it is torn apart by the universal duel between the silent execution of an object’s reality and the glistening aura of its tangible surface.”
— From “The Action of Things,” an M.A. thesis at the Center for Curatorial Studies, Bard College, by Manuela Moscoso, May 2011, edited by Sarah Demeuse
From Wikipedia, a programming paradigm:
Friday, July 25, 2014
In honor of Ace Greenberg, a major Wall Street player
who reportedly died today at 86:
See also this journal on the date of the above review,
March 9, 2009: First and Last Things.
This post was suggested by…
“Oh, the humanity!” — Reporter’s comment
“It’s going to be accomplished in steps,
this establishment of the Talented
in the scheme of things.”
— Anne McCaffrey, Radcliffe ’47, To Ride Pegasus
From a review of the new film “Magic in the Moonlight”—
“Sophie seems to have some actual talent….
When Sophie meets Aunt Vanessa, she uncovers the spinster’s
long-ago love affair with a member of parliament. It’s eerie.”
Material that is related, if only in story space:
“Just a lying rhyme for seven!” — Playwright Tom Stoppard on Heaven
“The yarns of seamen have a direct simplicity, the whole meaning
of which lies within the shell of a cracked nut. But Marlow was not
typical (if his propensity to spin yarns be excepted), and to him the
meaning of an episode was not inside like a kernel but outside,
enveloping the tale which brought it out only as a glow brings out a
haze, in the likeness of one of these misty halos that sometimes
are made visible by the spectral illumination of moonshine.”
— Joseph Conrad in Heart of Darkness
“By groping toward the light we are made to realize
how deep the darkness is around us.”
— Arthur Koestler, The Call Girls: A Tragi-Comedy,
Random House, 1973, page 118
“Spectral evidence is a form of evidence
based upon dreams and visions.” —Wikipedia
Thursday, July 24, 2014
Wednesday, July 23, 2014
“Lord knows when the cold wind blows
it’ll turn your head around.”
— James Taylor, “Fire and Rain”
“It was the middle of summer, but
the cold wind blew in full force.”
— David Kushner, Jonny Magic and the Card Shark Kids
(Quoted here in House of Cards, June 11, 2014,
a post on magic, cards, and Multnomah County.)
This is a post in memory of artist Otto Piene, who reportedly died
at 86 on Thursday, July 17, 2014, in Berlin.
Tuesday, July 22, 2014
Monday, July 21, 2014
Sunday, July 20, 2014
Paradigms of Geometry:
Continuous and Discrete
The discovery of the incommensurability of a square’s
side with its diagonal contrasted a well-known discrete
length (the side) with a new continuous length (the diagonal).
The figures below illustrate a shift in the other direction.
The essential structure of the continuous configuration at
left is embodied in the discrete unit cells of the square at right.
See Desargues via Galois (August 6, 2013).
Saturday, July 19, 2014
From the date of Piene’s death —
See also Zero Theorem in this journal.
“The title ZERO was the result of months of search
and was finally found more or less by chance.
From the beginning we looked upon the term
not as an expression of nihilism – or a dada-like gag,
but as a word indicating a zone of silence and of
pure possibilities for a new beginning as at the
count-down when rockets take off- zero is the
incommensurable zone in which the old state turns
into the new.”
(Where Entertainment Is God , continued)
Today is the opening of the exhibition ZERO — Zwischen Himmel und Erde
in Friedrichshafen. The Zeppelin Museum is showing wonderful artworks
all related to heaven and earth by various ZERO artists
such as Piene, Mack, Uecker, Klein, Luther, and Manzoni.
ZERO – Zwischen Himmel und Erde
Zeppelin Museum Friedrichshafen
15.05. – 20.07.2014
“Oh, show me the way to the next whiskey bar”
— Song lyric from previous post
“In a technologically advanced 1939, the zeppelin Hindenburg III
arrives in New York City, mooring atop the Empire State Building.”
— Wikipedia on the first scene of the 2004 film
“Sky Captain and the World of Tomorrow“
Friday, July 18, 2014
From The Thin White Duke:
“When I was living in my apartment in Berlin,
I would sing this at breakfast every morning.”
Oh, show me the way to the next whiskey bar
Oh, don’t ask why, no, don’t ask why
For we must find the next whiskey bar
Or if we don’t find the next whiskey bar
I tell you we must die, I tell you we must die
I tell you, I tell you, I tell you we must die
“Wir trauern um Otto Piene, der unerwartet am 17.7 in Berlin gestorben ist.”
The Los Angeles Times on entertainer Elaine Stritch,
who died yesterday (Thursday, July 17, 2014):
“She made few apologies in her career, describing herself as
a ‘Catholic, diabetic, alcoholic, pain in the ass.’” — David Ng
“Band of angels, lead me home.” — Song lyric
Scene from 3:10 to Yuma (1957)
Thursday, July 17, 2014
Continuous Euclidean space to discrete Galois space*
Counting symmetries in Euclidean space:
The reason for these graphic symmetries in affine Galois space —
symmetries of the underlying projective Galois space:
* For related remarks, see posts of May 26-28, 2012.
Wednesday, July 16, 2014
Tuesday, July 15, 2014
|“The theory of poetry, that is to say, the total of the theories of poetry, often seems to become in time a mystical theology or, more simply, a mystique. The reason for this must by now be clear. The reason is the same reason why the pictures in a museum of modern art often seem to become in time a mystical aesthetic, a prodigious search of appearance, as if to find a way of saying and of establishing that all things, whether below or above appearance, are one and that it is only through reality, in which they are reflected or, it may be, joined together, that we can reach them. Under such stress, reality changes from substance to subtlety, a subtlety in which it was natural for Cézanne to say: ‘I see planes bestriding each other and sometimes straight lines seem to me to fall’ or ‘Planes in color…. The colored area where shimmer the souls of the planes, in the blaze of the kindled prism, the meeting of planes in the sunlight.’ The conversion of our Lumpenwelt went far beyond this. It was from the point of view of another subtlety that Klee could write: ‘But he is one chosen that today comes near to the secret places where original law fosters all evolution. And what artist would not establish himself there where the organic center of all movement in time and space– which he calls the mind or heart of creation– determines every function.’ Conceding that this sounds a bit like sacerdotal jargon, that is not too much to allow to those that have helped to create a new reality, a modern reality, since what has been created is nothing less.
— Wallace Stevens, Harvard College Class of 1901, “The Relations between Poetry and Painting” in The Necessary Angel (Knopf, 1951)
For background on the planes illustrated above,
see Diamond theory in 1937.
Monday, July 14, 2014
Maazel reportedly died on Sunday, July 13, 2014.
From a search in this journal for Iconic Notation,
a related image from August 14, 2010—
Continued from August 20, 2013
In honor of Sam Peckinpah, the closing shot of his last film:
“Am I still on?” — Ending line of The Osterman Weekend (1983)
Sunday, July 13, 2014
- An Apple for Devlin (July 2)
- Thanks for having me on (July 11)
- Useful Idiot (Wikipedia article)
- Useful Fictions (a Princeton mathematics
department Spring 2014 course)
“Numbers themselves are fictions, abstractions humans invented
to gain more control over the world.” — Keith Devlin
From today’s New York Times Sunday Review ,
The World According to Maxwell Smart, Part 1
Madonna, “Get Stupid,” a political video from 2008
Saturday, July 12, 2014
“For me it is a sign that we have fundamentally different
conceptions of the work of the intelligence services.”
— Germany’s Chancellor Angela Merkel in
theguardian.com, Saturday, 12 July 2014, 14.32 EDT
Another sort of service, thanks to Dan Brown and Tom Hanks:
Friday, July 11, 2014
A darker requiem, for another musical figure
who also died yesterday:
A sequel to the 1974 film
Thunderbolt and Lightfoot :
Contingent and Fluky
Some variations on a thunderbolt theme:
These variations also exemplify the larger
“Dr. Lightfoot writes mainly on syntactic theory,
language acquisition and historical change, which
he views as intimately related. He argues that
internal language change is contingent and fluky,
takes place in a sequence of bursts, and is best
viewed as the cumulative effect of changes in
individual grammars, where a grammar is a
‘language organ’ represented in a person’s
mind/brain and embodying his/her language
Some syntactic work by another contingent and fluky author
is related to the visual patterns illustrated above.
See Tecumseh Fitch in this journal.
For other material related to the large Verbum cube,
see posts for the 18th birthday of Harry Potter.
That birthday was also the upload date for the following:
See esp. the comments section.
Friday, July 11, 2014
Nick Fury takes the Tesseract…
… which travels back to 1955
(see The Call Girls, Nov. 3, 2013)…
Above: A 1955 cover design by Robert Flynn.
Images from December 1955…
… and a fictional image imagined in an earlier year:
Thursday, July 10, 2014
“Paradigm Talent Agency are supporting with casting.
Emperor is described as a look at a debauched world
of wealth, sex, manipulation and treason.”
Related material from Santa Cruz, California:
Related material from this journal:
“Fiction,” a post of St. Cecilia’s Day, 11/22/2013.
The Decline and Fall of Augustus Gibbons?
Wednesday, July 9, 2014
From this morning’s post:
“Beyond Noplace, far into wide Nowhere” — John Hollander
Vide Le Guin Geometry.
From Monday in this journal —
Related news this morning —
Anne Hollander, Scholar of Style, Dies at 83
By William Yardley in The New York Times ,
10:26 PM ET July 8, 2014
Anne Hollander, a historian who helped elevate
the study of art and dress by revealing the often striking
relationships between the two, died on Sunday at her home
in Manhattan. She was 83.
The cause was cancer, said her husband, the philosopher
. . . .
She received a degree in art history from Barnard College
in 1952. The next year she married the poet John Hollander.
Their marriage ended in divorce.
Related material from this journal last year —
“Be serious, because
The stone may have contempt
For too-familiar hands”
Tuesday, July 8, 2014
“When does a life bend toward freedom?
grasp its direction?”
— Adrienne Rich on page 275 of
Later Poems Selected and New: 1971-2012
The book’s author, Adrienne Rich, died at 82 on
March 27, 2012. See that date in this journal.
See also the following:
|The Diamond Cutters
by Adrienne Rich (1955)
Now, you intelligence
Be serious, because
Be hard of heart, because
Be proud, when you have set
Monday, July 7, 2014
Roger Cooke in The History of Mathematics: A Brief Course
(2nd ed., Wiley-Interscience, 2005)—
“Like all numbers, the number four is bound to occur
in many contexts.”
— Ch. 1: “The Origin and Prehistory of Mathematics,”
Part 3, “Symbols,” footnote 1, page 11.
As is the number 382:
Click the above image for some related material.
“Once the students are taken in by the story, it will be
the instructor’s job to elaborate on the historical
calculations and proofs.”
— Gary S. Stoudt, Professor of Mathematics,
Indiana U. of Pennsylvania, review of Cooke’s book
at the Mathematical Association of America
Roger Cooke in the Notices of the American
Mathematical Society , April 2010 —
“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.
Sunday, July 6, 2014
An essay linked to here on the date of Kuhn’s
death discussed the film “Good Will Hunting”:
“You can be sure that when an experienced movie director
like Gus Van Sant selects an establishing shot for the lead
character, he does so with considerable care, on the advice
of an expert.”
Establishing shots —
1. From a post of January 29, 2014:
2. From a post of April 12, 2011:
Parting shot —
From another post of January 29, 2014:
Note Watson‘s title advice.
Zen ideal —
The title is from this morning’s previous post.
From a theater review in that post—
… “all flying edges and angles, a perpetually moving and hungry soul”
… “a formidably centered presence, the still counterpoint”
A more abstract perspective:
See also Desargues via Galois (August 6, 2013).
And now for the musical!
From Ben Brantley’s July Fourth review of a British play —
“These two redefine the laws not just of chemistry but also of physics, with each coming across as both immovable object and irresistible force…. I was always aware of how ineffably, achingly attracted each was to the other, and of the diametrically opposed ways in which that attraction became flesh….
… His Tom is all flying edges and angles, a perpetually moving and hungry soul who never pauses in the pursuit of his appetites….
… this Kyra is a formidably centered presence, the still counterpoint to Tom’s charming, full-court-press animation….
… The friction and the possibilities of fusion between Kyra and Tom— who must be together and cannot be together— make ‘Skylight’ one of the most intelligently sentimental love stories of our time.”
“The friction and the possibilities of fusion” —
“Rubbin’ sticks and stones together
makes the sparks ignite…
Skyrockets in flight!”
Saturday, July 5, 2014
Separatrix and Mulligan
An image from this journal on September 16, 2013:
“A mulligan, in a game, happens when a player gets a second chance
to perform a certain move or action.” — Wikipedia
New York Times obituary for Richard Mellon Scaife:
“He had the caricatured look of a jovial billionaire promoting ‘family values’
in America: a real-life Citizen Kane with red cheeks, white hair, blue eyes and
a wide smile for the cameras. Friends called him intuitive but not intellectual.
He told Vanity Fair his favorite TV show was ‘The Simpsons,’ and his favorite
book was John O’Hara’s Appointment in Samarra , about a rich young
Pennsylvanian bent on self-destruction.” — Robert D. McFadden
Click image below for some nuclear family values in memory of Scaife:
See also the previous post,