The inscription link in the previous post suggests
a review of the rather paradoxical concept of
"necessary possibility."
See a deconstructionist view , a scholarly view,
and a graphic view.
Thursday, January 31, 2013
Necessary Possibility
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Scholarship in 1961…
… Before Derrida's writings on Plato and on inscription
A remark by the late William Harris:
"Scholarship has many dark ages, and they do not all fall
in the safe confines of remote antiquity."
For more about Harris, see the previous post.
Discussing an approach to solving a geometrical problem
from section 86e of the Meno , Harris wrote that
"… this is a very important element of method and purpose,
one which must be taken with great seriousness and respect.
In fact it is as good an example of the master describing for us
his method as Plato ever gives us. Tricked by the appearance
of brevity and unwilling to follow through Plato's thought on
the road to Euclid, we have garbled or passed over a unique
piece of philosophical information."
Harris, though not a geometer, was an admirable man.
His remark on the Meno method is itself worthy of respect.
In memory of Harris, Plato, and pre-Derrida scholarship, here
are some pages from 1961 on the problem Harris discussed.
A pair of figures from the 1961 pages indicates how one view of the
section 86e problem (at right below) resembles the better-known
demonstration earlier in the Meno of how to construct
a square of area 2 —
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Wednesday, January 30, 2013
The Problem Problem
Given these choices for a solution ,
what is a suitable problem ?
The problem sketched on Jan. 22 was a joke.
A more serious triangle-circle-square problem:
Introductory commentary from the same source—
See also a description of this problem by the late William Harris,
Harvard '48, Professsor Emeritus of Classics at Middlebury College,
who died on February 22, 2009*—
"… this is a very important element of method and purpose,
one which must be taken with great seriousness and respect.
In fact it is as good an example of the master describing for us
his method as Plato ever gives us. Tricked by the appearance
of brevity and unwilling to follow through Plato's thought on
the road to Euclid, we have garbled or passed over a unique
piece of philosophical information."
The problem itself, from the Perseus site:
[87a] whether a certain area is capable of being inscribed as a triangular space in a given circle: they reply—“I cannot yet tell whether it has that capability; but I think, if I may put it so, that I have a certain helpful hypothesis for the problem, and it is as follows: If this area is such that when you apply it to the given line of the circle you find it falls short by a space similar to that which you have just applied, then I take it you have one consequence, and if it is impossible for it to fall so, then some other. Accordingly I wish to put a hypothesis, before I state our conclusion as regards inscribing this figure [87b] in the circle by saying whether it is impossible or not.” In the same way with regard to our question about virtue, since we do not know either what it is or what kind of thing it may be, we had best make use of a hypothesis in considering whether it can be taught or not, as thus: what kind of thing must virtue be in the class of mental properties, so as to be teachable or not? In the first place, if it is something dissimilar or similar to knowledge, is it taught or not—or, as we were saying just now, remembered? Let us have no disputing about the choice of a name: [87c] is it taught? Or is not this fact plain to everyone—that the one and only thing taught to men is knowledge?
Meno
I agree to that.
Socrates
Then if virtue is a kind of knowledge, clearly it must be taught?
Meno
Certainly.
Socrates
So you see we have made short work of this question—if virtue belongs to one class of things it is teachable, and if to another, it is not.
Meno
To be sure.
For further details, consult (for instance) a 1955 paper at JSTOR.
* See a post from that date in this journal.
See also a remark by Harris:
"Scholarship has many dark ages, and they do not all fall
in the safe confines of remote antiquity."
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Abstract Possibility
Today's NY Times "Stone Links" to philosophy include
a link to a review of a collection of Hilary Putnam's papers.
Related material, from Putnam's "What is Mathematical
Truth?" (Historia Mathematica 2 (1975): 529-543)—
"In this paper I argue that mathematics should be interpreted realistically – that is, that mathematics makes assertions that are objectively true or false, independently of the human mind, and that something answers to such mathematical notions as ‘set’ and ‘function’. This is not to say that reality is somehow bifurcated – that there is one reality of material things, and then, over and above it, a second reality of ‘mathematical things’. A set of objects, for example, depends for its existence on those objects: if they are destroyed, then there is no longer such a set. (Of course, we may say that the set exists ‘tenselessly’, but we may also say the objects exist ‘tenselessly’: this is just to say that in pure mathematics we can sometimes ignore the important difference between ‘exists now’ and ‘did exist, exists now, or will exist’.) Not only are the ‘objects’ of pure mathematics conditional upon material objects; they are, in a sense, merely abstract possibilities. Studying how mathematical objects behave might better be described as studying what structures are abstractly possible and what structures are not abstractly possible."
See also Wittgenstein's Diamond and Plato's Diamond.
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Tuesday, January 29, 2013
Clash of the Caped Crusaders
The New Yorker , quoted here yesterday, on a meeting in 1638 of Galileo and Milton—
"… it’s like those comic-book specials in which Superman meets Batman…."
Related news yesterday from The Hollywood Reporter—
Phillips's upcoming Superman film stars Amy Adams.
Other entertainment:
Log24 posts from the day of Phillips's death—
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Binder
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Midnight in the Garden
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Monday, January 28, 2013
Serpents’ Eyes Only
"The serpent's eyes shine as he wraps around the vine" — Don Henley
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Encounter
"Sometime in 1638, John Milton visited Galileo Galilei in Florence. The great astronomer was old and blind and under house arrest, confined by order of the Inquisition, which had forced him to recant his belief that the earth revolves around the sun, as formulated in his 'Dialogue Concerning the Two Chief World Systems.' Milton was thirty years old—his own blindness, his own arrest, and his own cosmological epic, 'Paradise Lost,' all lay before him….
Beyond the sheer pleasure of picturing the encounter— it’s like those comic-book specials in which Superman meets Batman— there’s something strange about imagining these two figures inhabiting the same age. Though Milton was the much younger man, in some ways his world system seems curiously older than the astronomer’s empirical universe."
— Jonathan Rosen, The New Yorker , June 2, 2008, "Return to Paradise"
More in the spirit of Superman and Batman:
"Huh. You know what? Galileo didn't even write this."
"What!"
"The poem is signed John Milton."
"John Milton ?" The influential English poet who wrote
Paradise Lost was a contemporary of Galileo's and a
savant who conspiracy buffs put at the top of their list
of Illuminati suspects. Milton's alleged affiliation with
Galileo's Illuminati was one legend Langdon
suspected was true. Not only had Milton made a
well documented 1638 pilgrimage to Rome to
"commune with enlightened men," but he had held
meetings with Galileo during the scientist's house
arrest, meetings portrayed in many Renaissance
paintings….
"Milton knew Galileo, didn't he?" Vittoria said, finally
pushing the folio over to Langdon. "Maybe he wrote
the poem as a favor?"
— Angels & Demons , by Dan Brown
(first published in 2000)
See also this journal on August 16, 2009.
Addendum for Aaron Swartz (see today's previous post)—
"The Vatican, it seemed, took their archives
a bit more seriously than most." — Dan Brown
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PEP Talk
Review: A page linked to here on Jan. 25—
psychoanalyst Heinz Kohut on the "nuclear self"—
The Psychoanalytic Electronic Publishing (PEP) website has a
paper on Kohut's concept— "Nuclear Conflict and the Nuclear Self"—
to which access is restricted:
Perhaps the late Aaron Swartz (below) now has freer access
to this and other restricted reading.
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Sunday, January 27, 2013
Patrick’s Days
Continued from previous post —
For what it's worth…
A birth and a death, each on the Feast of St. Patrick
"Donald Frederick Hornig was born on March 17, 1920, in Milwaukee
and attended Harvard, earning his undergraduate degree there
in 1940 and his Ph.D. in 1943, both in chemistry. His dissertation
was titled 'An Investigation of the Shock Wave Produced by an Explosion'…."
— "Donald Hornig, Last to See First A-Bomb, Dies at 92,"
New York Times print version today (p. A20, New York edition)
A death elsewhere in Wisconsin 92 years later, on March 17, 2012—
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Citation Needed
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Sunday School
"The newspaper Diario de Santa Maria reported
that the fire started at around 2 a.m. at the Kiss club
in the city at the southern tip of Brazil, near the borders
with Argentina and Uruguay." more »
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Ay Que Bonito
Meditations for 2 AM —
- Hylton's Quine in the previous post
- Hopkins on the paperback publication date of Hylton's Quine
- Ay Que Bonito Es Volar
- The Hallowed Crucible
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Shining Forth
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Saturday, January 26, 2013
Nine Years
Excerpt from an essay cached nine years ago:
"The current dominant conceptual framework
which pictures the self as an inner entity
is slowly breaking up. And I am convinced that
some, if not all, of the approaches to the self
sketched here will form the basis for a new
conceptual framework…."
Context for the essay:
A journal issue titled "The Opening of Narrative Space" (pdf, 475 KB)
For one sort of narrative space, see Giordano Bruno in this journal.
See also Nine Years.
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Friday, January 25, 2013
Where Credit Is Due
Harvard's President Faust:
Last evening's post Moondance was suggested by a check
in this journal of the date October 10, 2012. That date was
in turn suggested by the date of the above remarks.
Wer immer strebend sich bemüht,
Den können wir erlösen.
Who always striving efforts makes,
For him there is salvation.
— Faust Part 2, Act V, Scene 7: Mountain Gorges.
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Matchmaker, Matchmaker
A Google search for images matching
Amy Adams's door in the 2005 film
"Standing Still" yields a surprising result.
Related material: Adams in "Doubt" (2008).
See also A Touch of Glass.
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Public/Private
"I decided that there was a public Elise
and a private Elise, and they're not necessarily
the same person." — Amy Adams interview
on the 2005 film "Standing Still"
A division between public and private, from
"Standing Still"—
"This movie reminded me of The Big Chill
(which I also loved)…."
See, too, a different door and a different Elise
in a post from Tuesday, Jan. 22, 2013.
Also from that post—
"By recalling the past and freezing the present
he could open the gates of time…."
— Mark Helprin, In Sunlight and in Shadow
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Thursday, January 24, 2013
Moondance
The title was suggested by an ad for a film that opens
at 10 PM EST today: "Hansel & Gretel: Witch Hunters."
Related material: Grimm Day 2012, as well as
Amy Adams in Raiders of the Lost Tesseract
and in a Film School Rejects page today.
See also some Norwegian art in
Trish Mayo's Photostream today and in
Omega Point (Log24, Oct. 15, 2012)—
Monday, October 15, 2012
|
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Object Lesson
Suggested by yesterday's Garden Path
Commentary by Trish Mayo on a photo at Flickr:
Gazing Globe
These beautiful garden ornaments have a long history, beginning in the 13th century when they were made in Venice, Italy of hand-blown glass. They have been called by many names: Gazing Globe, Garden Globe, Witch Ball, Butler Globe and Globe of Happiness.
Legends formed about the mysterious powers of the globes. They were said to bring happiness, good luck and prosperity to those who owned it, known to ward off evil spirits, misfortune, illness and witches!
Some say the ball should be placed near the entrance to a house so that if a witch came by she would not be able to get past her reflection as she cannot tear herself away from her own image. Other accounts say a witch cannot bear to see her own reflection so she will not come near a "witch’s ball". A witch cannot sneak up on a person gazing into a globe as he can see if a witch approaches from behind. The smaller ball made of colored glass as opposed to the reflective kind was believed to attract and trap evil spirits.
Spiritually speaking, as one peers into the globe he can experience "oneness" with the universe.
The gazing globes practical purposes included being strategically placed on a path near the front entrance so that you could see when someone was coming for a visit. In Victorian times, the "Butler Ball" served as a mirror for servants to see when guests were needing assistance without staring at them throughout the meal. Another practical use was in the foyer of the home. Parents could keep a close eye on their daughter and her date as he bid her goodnight.
Today the globe is used ornamentally, allowing the whole garden, including the sky, to be viewed with one glance.
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Under Covers
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Cube Space
For the late Cardinal Glemp of Poland,
who died yesterday, some links:
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Wednesday, January 23, 2013
DNA and a Galois Field
From Ewan Birney's weblog today:
| WEDNESDAY, 23 JANUARY 2013
Using DNA as a digital archive media Today sees the publication in Nature of “Toward practical high-capacity low-maintenance storage of digital information in synthesised DNA,” a paper spearheaded by my colleague Nick Goldman and in which I played a major part, in particular in the germination of the idea. |
Birney appeared in Log24 on Dec. 30, 2012, quoted as follows:
"It is not often anyone will hear the phrase 'Galois field' and 'DNA' together…."
— Birney's weblog on July 3, 2012, "Galois and Sequencing."
Birney's widespread appearance in news articles today about the above Nature publication suggests a review of the "Galois-field"-"DNA" connection.
See, for instance, the following papers:
- Gail Rosen and Jeff Moore. "Investigation of Coding Structure in DNA," IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Hong Kong, April 2003. [pdf]
- Gail Rosen. "Finding Near-Periodic DNA Regions using a Finite-Field Framework," 2nd IEEE Genomic Signal Processing Workshop (GENSIPS), Baltimore, MD, May 2004. [pdf]
- Gail Rosen. "Examining Coding Structure and Redundancy in DNA," IEEE Engineering in Medicine and Biology Magazine, Volume 25, Issue 1, January/February 2006. [pdf]
A Log24 post of Sept. 17, 2012, also mentions the phrases "Galois field" and "DNA" together.
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Garden Path
(Continued from Epiphany 2012)
Yesterday's link to the post Special Topics suggests
a review of the garden of forking paths.
An example of such paths, given in the Special Topics
post, came from a paper describing the modular group:
Here is another view of the modular group's
forking paths:
"Tree for modular group" from the
Algebra page of the University of Glasgow
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Tuesday, January 22, 2013
Für Elise
Elise in "The Adjustment Bureau" (release date: March 4, 2011)—
A quote for this unlikely pair:
"Harry decides his chief peacetime duty is to use his
gift for gab to further his 'overriding purpose,' namely:
'By recalling the past and freezing the present he could
open the gates of time and through them see all
allegedly sequential things as a single masterwork
with neither boundaries nor divisions.' Once he opens
these gates, Harry will flood his audience with his
redemptive epiphanic impression that 'the world was
saturated with love.' "
— Liesl Schillinger, review of Mark Helprin's novel
In Sunlight and in Shadow in The New York Times ,
Oct. 5, 2012
A more realistic pair: Chuck Schumer and Iris Weinshall.
See also Adjustment Team (Wikipedia) and Gnostic Dick (Log24).
For some more-serious material, see another review by Schillnger
in a Log24 post of August 17, 2006— Special Topics.
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But Seriously…
Introductory Aramaic
See also a theater review in yesterday's print NY Times
and a video in today's online Times:
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The Problem Problem
For connoisseurs of psychological tests,
here is an inverse puzzle:
Given these choices for a solution ,
what is a suitable problem ?
There is, of course, no single right answer.
One path to an answer might involve
a British webpage and the recent film Branded.
Max von Sydow in Branded (2012)
(See, too, related remarks on The Queen's Privy Council.)
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Raven Light
"…a fundamental cognitive ability known as 'fluid' intelligence: the capacity to solve novel problems, to learn, to reason, to see connections and to get to the bottom of
…matrices are considered the gold standard of fluid-intelligence tests. Anyone who has taken an intelligence test has seen matrices like those used in the Raven’s: three rows, with three graphic items in each row, made up of squares, circles, dots or the like. Do the squares get larger as they move from left to right? Do the circles inside the squares fill in, changing from white to gray to black, as they go downward? One of the nine items is missing from the matrix, and the challenge is to find the underlying patterns— up, down and across— from six possible choices. Initially the solutions are readily apparent to most people, but they get progressively harder to discern. By the end of the test, most test takers are baffled."
— Dan Hurley, "Can You Make Yourself Smarter?," NY Times , April 18, 2012
See also "Raven Steals the Light" in this journal.
Related material:
Plan 9 from MIT and, perhaps exemplifying crystallized rather than fluid intelligence, Black Diamond.
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Monday, January 21, 2013
Shining Forth
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Sunday, January 20, 2013
On the Road
(For Your Consideration continued)
Today's New York Times story on Jacobin magazine
suggests the following sequel to a Jan. 10 post on
Spielberg's Lincoln .
The magazine has, the Times says,
"earned [its creator] Mr. Sunkara, now a ripe 23,
extravagant praise from members of a (slightly) older
guard who see his success as heartening sign that
the socialist 'brand'— to use a word he throws around
with un-self-conscious ease— hasn’t been totally
killed off by Tea Party invective." —Jennifer Schuessler
Jacobin magazine, summer 2012 double issue—
A related trinity of the Left:
Playwright Tom Stoppard, his son actor Ed Stoppard
(shown below in the 2012 film Branded ), and the late
activist Aaron Swartz—
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Inaugural Poem
"I, the Rock, I, the River, I, the Tree
I am yours—your passages have been paid."
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In the Details
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Field of Dreams
The Presidential Medal of Freedom, the highest honor
that can be bestowed on a civilian, was presented to
Stan Musial at the White House on Feb 15, 2011.
Meanwhile…
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Saturday, January 19, 2013
Executioner’s Song
See also, from the the above uploading date, Taylor Made,
with its linked-to passage from a book by Charles Taylor.
For some more recent background, see
- "Fallen" in this journal,
- the film by that name,
- Wednesday evening's execution in Virginia, and
- Wednesday afternoon's Treasure Hunt
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Tears in the Rain
Top of the front page, tonight's online New York Times—
Click the above image for the story of a rather different cyclist.
See also some images from Guy Fawkes Day, 2003—
Related material:
Blade Runner in this journal and posts tagged "Fawkes"—
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Friday, January 18, 2013
Solomon’s Rep-tiles
"Rep-tiles Revisited," by Viorel Nitica, in MASS Selecta: Teaching and Learning Advanced Undergraduate Mathematics , American Mathematical Society,
"The goal of this note is to take a new look at some of the most amazing objects discovered in recreational mathematics. These objects, having the curious property of making larger copies of themselves, were introduced in 1962 by Solomon W. Golomb [2], and soon afterwards were popularized by Martin Gardner [3] in Scientific American…."
2. S. W. Golomb: "Replicating Figures in the Plane," Mathematical Gazette 48, 1964, 403-412
3. M. Gardner: "On 'Rep-tiles,' Polygons That Can Make Larger and Smaller Copies of Themselves," Scientific American 208, 1963, 154-157
Two such "amazing objects"—
|
Triangle |
Square |
For a different approach to the replicating properties of these objects, see the square-triangle theorem.
For related earlier material citing Golomb, see Not Quite Obvious (July 8, 2012; scroll down to see the update of July 15.).
Golomb's 1964 Gazette article may now be purchased at JSTOR for $14.
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Thursday, January 17, 2013
Brazil Revisited
Yesterday's post Treasure Hunt, on a Brazilian weblog,
suggests a review of Brazil in this journal. The post
most relevant to yesterday's remarks is from
August 15, 2003, with a link, now broken, to the work
of Brazilian artist Nicole Sigaud* that also uses the
four half-square tiles used in 1704 by Sebastien Truchet
and somewhat later by myself in Diamond Theory
(see a 1977 version).
A more recent link that works:
|
http://vismath9.tripod.com/sigaud/e-index.html ANACOM PROJECT
APPLICATIONS
© 1997 – 2002 Nicole Sigaud |
* Sigaud shares the interests of her fellow Brazilian
whose weblog was the subject of yesterday's
Treasure Hunt.—
"For many years I have dedicated myself to the study
of medieval magic, demonology, Kabbalah, Astrology,
Alchemy, Tarot and divination in general."
— Nicole Sigaud (translated by Google) in a self-profile:
http://www.recantodasletras.com.br/autor.php?id=78359.
I do not share the interest of these authors in such matters,
except as they are reflected in the works of authors like
Charles Williams and Umberto Eco.
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Wednesday, January 16, 2013
Treasure Hunt
The Mathematical Association of America (MAA)
newsmagazine Focus for December 2012/January 2013:
The Babylonian tablet on the cover illustrates the
"Mathematical Treasures" article.
A search for related material yields a Babylonian tablet
reproduced in a Brazilian weblog on July 4, 2012:
In that weblog on the same day, July 4, 2012,
another post quotes at length my Diamond Theory page,
starting with the following image from that page—
That Brazilian post recommends use of geometry together
with Tarot and astrology. I do not concur with this
recommendation, but still appreciate the mention.
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Hamming It Up
Or: Dr. Arroway Flies Again
Today's math news mentioning the Hamming Medal
suggests…
Richard Hamming (d. 1998) as a real-life counterpart to
the techno-wizard S. R. Hadden in the 1997 film Contact .
Hamming devised a famous error-correcting code.
"You gotta be true to your code." —Sinatra
Review of a more recent Jodie Foster film, Flightplan :
"Is she crazy, or is she the victim of a conspiracy
that would have to be fragile, if not tortured, in its logic?"
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Medals
National…
International…
Click medal for some background. The medal may be regarded
as illustrating the 16-point Galois space. (See previous post.)
Related material: Jews in Hyperspace.
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Space Race
Japanese character
for "field"
This morning's leading
New York Times obituaries—
For other remarks on space, see
Galois + Space in this journal.
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Tuesday, January 15, 2013
Speeds
The Speed of Thought
"I love Quicksilver. I've been using it since nearly the beginning,
and I cannot live without it…. I just type, and things happen,
pretty much at the speed of thought."
See also Speed of Thought in this journal and
Madeleine L'Engle on kything .
The Speed of Inference
See this journal on the above date— April 22, 2011:
Romancing the Hyperspace —and, more generally,
all April 2011 references to romancing .
See also a contributor to Edge.org:
"Sciences can move at the speed of inference
when individuals only need to consider logic and evidence.
Yet sciences move glacially (Planck's 'funeral by funeral')
when the typical scientist, dependent for employment
on a dense ingroup network, has to get the majority of her
guild to acknowledge fundamental, embarrassing
disciplinary errors."
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Wrap Party
"The serpent's eyes shine
As he wraps around the vine"
— Don Henley, lyric from
1995 Greatest Hits album
"…the film proceeds with implacable logic…."
— Roger Ebert, 2005 review of the
Jodie Foster film Flightplan
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Monday, January 14, 2013
Quicksilver vs. Bat-Crazed and Moony
The Acceptance Speech Award
"A humble master with a quicksilver imagination"
— Daniel Day-Lewis on Steven Spielberg, acceptance speech
at Sunday night's Golden Globe Awards
"Robert [Downey Jr.], I want to thank you for everything, for your
bat-crazed, rapid-fire brain, the sweet intro."
— Jodie Foster accepting the Cecil B. DeMille award Sunday night
And the acceptance speech award goes to…
Presenter Robert Downey Jr. and Accepter Jodie Foster
Related material—
Also from Jodie Foster's DeMille Award speech:
"I can’t help but get moony, you know. This feels like the end
of one era and the beginning of something else. Scary and
exciting, and now what?"
A tweet from Aaron Swartz on Dec. 9, 2012:
See as well three posts from this journal on that same date.
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Moses Supposes
See also…
Spelling Bee:
Manifesto I vs. Manifesto II—
I The Commonist Manifesto
II The Anti-Commonist Manifesto
Google's Choice:
The People's Choice:
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Sunday, January 13, 2013
Spinning in Infinity
A note for day 13 of 2013
How the cube's 13 symmetry planes*
are related to the finite projective plane
of order 3, with 13 points and 13 lines—
For some background, see Cubist Geometries.
* This is not the standard terminology. Most sources count
only the 9 planes fixed pointwise under reflections as
"symmetry planes." This of course obscures the connection
with finite geometry.
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Puzzles
The late Aaron Swartz on a 1978 psychological study—
"But the puzzles kept coming—
and they kept getting harder. 'This isn’t fun anymore,'
the kids cried. But still, there were more puzzles."
Related material from Log24's Mathcamp —
"…Heaven and Hell relays. your team starts in hell,
when you get one right, one person can go to heaven
and work on heaven questions, but first they have to
pass through purgatory. aka this means entertain
the people running purgatory."
— Imaginary Thoughts and Irrational Ideas weblog
See also Swartz on philosophy:
"I’ve just been finding little bits and pieces
in all sorts of strange places: psychology experiments,
business books, philosophy, self-help, math, and
my friends. But since there’s no community around it,
it’s hard to discuss it with anyone…."
From the date of these weblog posts by Swartz,
a post from this journal—
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Crown Heights Story
See yesterday's post "There Will Be Aaron"
(about a death in Crown Heights, Brooklyn)
and earlier posts now tagged "Sorkin."
Related material— Delphic.
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Saturday, January 12, 2013
There Will Be Aaron
I learned this afternoon of a significant death:
See a NY Times obit and "RIP, Aaron Swartz."
The latter quotes Swartz himself:
"Obviously shades of Sinclair here…"
Related material:
-
Sinclair's shade in a recent Daniel Day-Lewis film—
"Bakersfield’s close-up in 'There Will Be Blood'"— - Friday morning's post Grapevine Hill
- and this morning's post Abstract.
Not so related:
-
This journal on the date— Feb. 23, 2010— of
Shellie Branco's post, linked to above, on Bakersfield,
Upton Sinclair, Taft CA, and "Blood"…A post titled Fish Story
on secular vocabulary and San Diego.
(Content last updated 4:16 EST Jan. 12, 2013.)
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Abstract*
|
Saturday January 12, 2013, MAA Invited Paper Session on Room 2, Upper Level, San Diego 9:30 a.m. Mathematicians develop habits of thought and employ |
Remarks for a dead mathematician—
Click on the above image for the original post.
Then click on the Harmonic Analysis link for
some exposition by Folland.
* As opposed to concrete —
See yesterday morning's Grapevine Hill and…
| SFGate 1/12/13 — Californians bring out gloves, hats for cold spell http://www.sfgate.com/news/us/article/ Zookeepers-growers-prepare-for- California-freeze-4185448.php A 40-mile stretch of a major highway north of The California Highway Patrol shut the Grapevine "There must have been 1,000 Mack trucks lined up," |
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Friday, January 11, 2013
Grapevine Hill
See also the song at the end of yesterday morning's
"For Your Consideration."
The setting for that song, "Hot Rod Lincoln," is—
according to Wikipedia— the road described in Ch. 3
of Eugene Burdick's classic 1956 novel
The Ninth Wave . (See above.)
See also A Dante for Our Times.
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Thursday, January 10, 2013
For Your Consideration
From the World Socialist Web Site:
Note the bend sinister in the address bar:
Related remarks:
Related music: "Pulled out of San Pedro late one night…"
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Wednesday, January 9, 2013
Bad Idea
For the 2013 Joint Mathematics Meetings in San Diego,
which start today, a cartoon by Andrew Spann—
(Click for larger image.)
Related remarks:
This journal on the Feast of Epiphany, 2013—
"The Tesseract is where it belongs: out of our reach."
— The Avengers' Nick Fury, played by Samuel L. Jackson
"You never know what could happen.
If you have Sam, you’re going to be cool."
— The late David R. Ellis, film director
If anyone in San Diego cares about the relationship
of Spann's plane to Fury's Tesseract, he or she may
consult Finite Geometry of the Square and Cube.
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Eve and Cleavage
From a poem by Frances Frost—
"The upper peak, the shattered rock that cleaves the northward sky
remains alone untaken by the darkness"
— "From a Mountain-Top," The North American Review ,
December 1939 (Vol. 248, No. 2, page 301)
For some material related to the Frost poem,
if only by verbal coincidence, see shattered + rock in this journal.
See also rock + cleavage.
For the relationship to Eve, see New Year's Eve, 2012,
and the following image by Karolin Schnoor, who also
illustrated the New York Times op-ed piece "Catholic
Education, in Need of Salvation" published online on
Epiphany 2013 (see last evening's Log24 post)—
For some context, see Establishment of the Talented.
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Django
"Catherine, Duchess of Cambridge, is 31."
— The Associated Press this morning, Jan. 9.
See also, in honor of the date of the Duchess's birth—
1982 Jan. 9— Django in this journal.
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Tuesday, January 8, 2013
Vermont Throws Itself Together
"The way, when we climb a mountain,
Vermont throws itself together"
— Wallace Stevens, "July Mountain"
For another view of reality in New Haven, see the
brief biography of Vermont poet Frances Frost
at the Yale University Library. From that biography:
"She was survived by her son, the poet Paul Blackburn,
and by her daughter, Sister Marguerite of the Order
of St. Joseph."
See also a figure from The New York Times published
online on Epiphany, 2013:
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Star Wars (continued)
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Necessary Angel
Old Stone-Cutter
His gravestones are his everlasting children.
He loves to get his cramped left hand around
the solid faithful feeling of his chisel
and dig the names of those below the ground
or the family names of provident ones above
who cross their fingers and defy the fates
and acknowledge death their enemy and master
by ordering headstones with their birthing dates.
He carves his holy head, a solemn cherub
with granite wings and childish eyes cast down.
Those who prefer a willowed urn, disliking
angels, can go and die in another town.
(From The North American Review , Vol. 248, No. 2,
1939, page 301)
Solemn cherub by Albrecht Dürer in 1514—
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Nine is a Vine (continued)
In honor of a famed architecture critic,
here is a link to Bruno's Atria.
See also Giordano Bruno in this journal.
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Tempular
Temporal note: The time of this post, 8:09 AM ET, may be regarded
as a reference to the date 8/09 in the year of our Lord 2010. See also,
in this journal on that date, "Angels in the Architecture (continued)."
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Monday, January 7, 2013
A Rainbow for Li
"Not only was he world class, highly regarded and effective,
but he also offered a story, a lesson, or a playful insight
that was there if you were paying attention."
— Tribute to the late Tingye Li, past president of the
Optical Society of America, who died on Dec. 27
See also Object Lesson.
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Sunday, January 6, 2013
True Fury
For the Feast of Epiphany:
A trip back to December 1955—
Meditations for Three Kings Day (Feast of Epiphany)—
"Show me all the blueprints." — Leonardo DiCaprio as Howard Hughes
"The Tesseract is where it belongs: out of our reach." — Samuel L. Jackson as Nick Fury
"Here was finality indeed, and cleavage!" — Malcolm Lowry's Under the Volcano (1947)
Click images for some background.
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Saturday, January 5, 2013
Vector Addition in a Finite Field
The finite (i.e., Galois) field GF(16),
according to J. J. Seidel in 1974—
The same field according to Steven H. Cullinane in 1986,
in its guise as the affine 4-space over GF(2)—
The same field, again disguised as an affine 4-space,
according to John H. Conway and N.J.A. Sloane in
Sphere Packings, Lattices, and Groups , first published in 1988—
The above figure by Conway and Sloane summarizes, using
a 4×4 array, the additive vector-space structure of the finite
field GF(16).
This structure embodies what in Euclidean space is called
the parallelogram rule for vector addition—
(Thanks to June Lester for the 3D (uvw) part of the above figure.)
For the transition from this colored Euclidean hypercube
(used above to illustrate the parallelogram rule) to the
4×4 Galois space (illustrated by Cullinane in 1979 and
Conway and Sloane in 1988— or later… I do not have
their book’s first edition), see Diamond Theory in 1937,
Vertex Adjacency in a Tesseract and in a 4×4 Array,
Spaces as Hypercubes, and The Galois Tesseract.
For some related narrative, see tesseract in this journal.
(This post has been added to finitegeometry.org.)
Update of August 9, 2013—
Coordinates for hypercube vertices derived from the
parallelogram rule in four dimensions were better
illustrated by Jürgen Köller in a web page archived in 2002.
Update of August 13, 2013—
The four basis vectors in the 2002 Köller hypercube figure
are also visible at the bottom of the hypercube figure on
page 7 of “Diamond Theory,” excerpts from a 1976 preprint
in Computer Graphics and Art , Vol. 2, No. 1, February 1977.
A predecessor: Coxeter’s 1950 hypercube figure from
“Self-Dual Configurations and Regular Graphs.”
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Friday, January 4, 2013
Basics
"When you study the basics very thoroughly,
you never know where it may end."
— Ulrich Schneider, U. of Munich physicist,
in a science story by Charles Choi today
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Thursday, January 3, 2013
Two Poems and Some Images
From an obituary of singer Patti Page, who died on New Year's Day—
"Clara Ann Fowler was born Nov. 8, 1927, in Claremore, Okla., and grew up in Tulsa. She was one of 11 children and was raised during the Great Depression by a father who worked for the railroad.
She told the Times that her family often did not have enough money to buy shoes. To save on electricity bills, the Fowlers listened to only a few select radio programs. Among them was 'Grand Ole Opry.'"
See also two poems by Wallace Stevens and some images related to yesterday's Log24 post.
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Wednesday, January 2, 2013
PlanetMath link
Update of May 27, 2013:
The post below is now outdated. See
http://planetmath.org/cullinanediamondtheorem .
__________________________________________________________________
The brief note on the diamond theorem at PlanetMath
disappeared some time ago. Here is a link to its
current URL: http://planetmath.org/?op=getobj;from=lec;id=49.
Update of 3 PM ET Jan. 2, 2013—
Another item recovered from Internet storage:
Click on the Monthly page for some background.
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Tuesday, January 1, 2013
The Simplest Situation
Thanks to a Harvard math major for the following V. I. Arnold quote
in a weblog post yesterday titled "Abstraction and Generality"—
"… the author has attempted to adhere to the principle of
minimal generality, according to which every idea should first
be clearly understood in the simplest situation;*
only then can the method developed be extended to
more complicated cases.
— Vladimir I. Arnold, Lectures on Partial Differential Equations
(Russian edition 1997; English translation 2004),
Preface to the second Russian edition
Thanks also to the math major for his closing post today.
* For instance… Natalie Angier's New Year's meditation
on a Buddha Field—
"… the multiverse as envisioned in Tibetan Buddhism,
'a vast system of 1059 [sic ; corrected to 10^59 on Jan. 3]
universes, that together are called a Buddha Field,' said
Jonathan C. Gold, who studies Buddhist philosophy at
Princeton."
— versus a search in this journal for "Japanese character" that yields…
Japanese character
for "field"
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