“A set having three members is a single thing
wholly constituted by its members but distinct from them.
After this, the theological doctrine of the Trinity as
‘three in one’ should be child’s play.”
– Max Black, Caveats and Critiques: Philosophical Essays
in Language, Logic, and Art , Cornell U. Press, 1975
Related material—
In memory of Sir Andrew Huxley, OM, who died on May 30, 2012
C. P. Snow on G. H. Hardy at Trinity College, Cambridge—
He played his games and indulged his eccentricities.
He was living in some of the best intellectual company
in the world— G. E. Moore, Whitehead, Bertrand Russell,
Trevelyan, the high Trinity society which was shortly to
find its artistic complement in Bloomsbury. (Hardy himself
had links with Bloomsbury, both of personal friendship
and of sympathy.)
See also "Max Black" + Trinity in this journal.
(The sequel to yesterday's Matrix Problem Reloaded)
Wikipedia on the sci-fi weblog io9.com—
Newitz explained the significance of the name "io9":
"Well, io9s are input-output devices that let you see into the future.
They're brain implants that were outlawed because they drove
anyone who used one insane. We totally made that (device) up
to name the blog."
— Jenna Wortham at wired.com, Jan. 2, 2008
From io9.com itself—
"Science fiction writer Ken MacLeod has another term for io9ers.
He calls them rapture fuckers.*"
For the relevance of the term "revolutions" in this post's title, see
Wikipedia on Ken MacLeod.
I prefer to associate the number 9 with The Holy Field.
* MacLeod used this phrase in one of his novels, Newton's Wake.
For Frigg's Day—
"The newest badass fantasy flick to hit theaters is Snow White and the Huntsman , out today, and I believe it proves my theory that Kristen Stewart is the Keanu Reeves of her generation…. With few lines but a lot of convincingly heroic facial expressions, Kristen Stewart does a great job channeling Keanu Reeves in The Matrix (one of the dwarfs even calls her 'the one'!)."
— Annalee Newitz this morning, "The Awesome Terribleness of Snow White and the Huntsman "
See also yesterday's Matrix Problem.
Poster from Walpurgisnacht 2012
Raven’s Progressive Matrices problem:
Click the problem for a related story.
For some related geometry, see Elements Diamond.
See also a post (Dream Time, May 3, 2010)
about geometry and an earlier Walpurgisnacht.
“To say more is to say less.”
― Harlan Ellison, as quoted at goodreads.com
Saying less—
The "New Books" link in today's Arts & Letters Daily leads to a review of Andrew Delbanco's College: What it Was, Is, and Should
Some, like Delbanco, remind us what the word ‘professor’ once meant: ‘A person who professes a faith, as in the Puritan churches, where the profession was made before the congregation as a kind of public initiation.’
I am not now, nor have I ever been, a professor.
I did, however, once profess the following:
This 1988 letter advocated viewing pure mathematics as one of the liberal arts. Twenty-four years later, that position still seems worth defending.
Arithmetic (i.e., number theory) and geometry are, by the way, two of the seven traditional liberal arts.
(Continued from May 29, 2002)
May 29, 1832—
Évariste Galois, Lettre de Galois à M. Auguste Chevalier—
Après cela, il se trouvera, j'espère, des gens qui trouveront leur profit à déchiffrer tout ce gâchis.
(Later there will be, I hope, some people who will find it to their advantage to decipher all this mess.)
Martin Gardner on the above letter—
"Galois had written several articles on group theory, and was merely annotating and correcting those earlier published papers."
– The Last Recreations , by Martin Gardner, published by Springer in 2007, page 156.
Commentary from Dec. 2011 on Gardner's word "published" —
Jamie James in The Music of the Spheres
(Springer paperback, 1995), page 28—
Pythagoras constructed a table of opposites
from which he was able to derive every concept
needed for a philosophy of the phenomenal world.
As reconstructed by Aristotle in his Metaphysics,
the table contains ten dualities….
|
Limited |
Unlimited |
Of these dualities, the first is the most important;
all the others may be seen as different aspects
of this fundamental dichotomy.
For further information, search on peiron + apeiron or
consult, say, Ancient Greek Philosophy , by Vijay Tankha.
The limited-unlimited contrast is not unrelated to the
contrasts between
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
New York Lottery today—
Without imagination, these digits are a meaningless jumble.
With imagination…
608 might refer to June 8, the Saint's Day of Gerard Manley Hopkins.
(See the date July 29, 2002, that appeared in an earlier post today
as the publication date of Geometrical Landscapes . In this
journal, a post on that date, "At Random," referred to Hopkins.)
8516 might refer to 8/5/1916. A check of a hometown newspaper
on that date yields…
"St. Joseph's Garden Party and Bazaar 22, 23, 24.
Pictures. Everybody Welcome. Admission to Garden Ten Cents"
And in the evening…
937 might refer to a post on the nihilistic philosophy of Joan Didion, and
7609 might refer to an occurrence of these digits in a link
to "7/11" in a post from the feast of St. Ignatius of Loyola last year.
For a more cynical view of lottery hermeneutics, see
"High on RAM (overload)," by Jo Lyxe.
Happy birthday to Stevie Nicks.
Hard Science Fiction weekend at Dragon Press Bookstore
Saturday May 26:
11am-noon Playing with the net up:
Hard Science Fiction in the era of
short attention spans, crowd-sourcing,
and rapid obsolescence
( Greg Benford, James Cambias, Kathryn Cramer)
….
3pm-4:30 Technological optimism and pessimism;
utopia and dystopia; happy endings & sad endings:
what do these oppositions have to do with one another?
Are they all the same thing? How are they different
from one another? Group discussion.
My own interests in this area include…
(Click image for some context)
The above was adapted from a 1996 cover—
Vintage Books, July 1996. Cover: Evan Gaffney.
For the significance of the flames,
see PyrE in the book. For the significance
of the cube in the altered cover, see
The 2×2×2 Cube and The Diamond Archetype.
See also Finite Geometry and Physical Space.
Related material from MacTutor—
The paper by J. W. Shirley, Binary numeration before Leibniz, Amer. J. Physics 19 (8) (1951), 452-454, contains an interesting look at some mathematics which appears in the hand written papers of Thomas Harriot [1560-1621]. Using the photographs of the two original Harriot manuscript pages reproduced in Shirley’s paper, we explain how Harriot was doing arithmetic with binary numbers. Leibniz [1646-1716] is credited with the invention [1679-1703] of binary arithmetic, that is arithmetic using base 2. Laplace wrote:-
However, Leibniz was certainly not the first person to think of doing arithmetic using numbers to base 2. Many years earlier Harriot had experimented with the idea of different number bases…. |
For a discussion of Harriot on the discrete-vs.-continuous question,
see Katherine Neal, From Discrete to Continuous: The Broadening
of Number Concepts in Early Modern England (Springer, 2002),
pages 69-71.
Today is commencement day at College of the Desert.
Without Graduation
(from a poem by Jorie Graham)
With Graduation
Click either passage above for some commentary.
For The Hunger Games
Spoiler Alert
For readers unfamilar either with the film "Point of No Return"
or with the "Raven's Progressive Matrices" intelligence test,
here is a spoiler alert. This post links to details of both.
Backstory— The above film and Raven in this journal
Part I: Problem b in this intelligence test
Part II: Take Your Pick in this journal (Dec. 16, 2011)
Part III: Pick
|
From her left arm hung a black handbag that closed with a drawstring and from which protruded the tip of a silvery object about which I found myself apprehensively curious. Her right arm was raised and bent, the elbow touching the door frame, the hand brushing back the very dark bangs from her forehead to show me the sigil, as if that had a bearing on her question. The sigil was an eight-limbed asterisk made of fine dark lines and about as big as a silver dollar. An X superimposed on a plus sign. It looked permanent.
 Except for the bangs she wore her hair pinned up. Her ears were flat, thin-edged, and nicely shaped, with the long lobes that in Chinese art mark the philosopher. Small square silver flats with rounded corners ornamented them. Her face might have been painted by Toulouse-Lautrec or Degas. The skin was webbed with very fine lines; the eyes were darkly shadowed and there was a touch of green on the lids (Egyptian?—I asked myself); her mouth was wide, tolerant, but realistic. Yes, beyond all else, she seemed realistic. |
|
You’re not afraid to show yourself at your lowest ebb. In Lit, you stop breast-feeding because you’ve started drinking again. You describe yourself hiding in a closet with a bottle of whiskey, a bottle of Listerine, and a spit bowl. It’s not a proud moment. The temptation in Lit was to either make myself seedy or show some glamour. But there wasn’t any. It was just dark, dark, dark for days. Ugly. Were you surprised by how deeply people related to this dark stuff? If I’m doing my job then I’m able to make the strange seem familiar. Bad memoirs try to make the strange stranger, to provide something for people to gawk at. I try to create an experience where no matter how bizarre something is, it seems normal. I don’t want readers to balk, I want them to be in the experience. My goal isn’t for people to go, “Oh, poor little Mary Karr,” but rather to have the reader go, “I can be an asshole too,” or just to have enthusiasm for the possibility for change. |
Last October, Harvard celebrated its 375th anniversary
with Pandemonium. For remarks of a different sort,
see Andrew Cusack on Walpurgisnacht.
(Rhetorical question on the NY Times online front page,
10:01 PM May 23, 2012, in teaser for "The Stone" column
about Philip K. Dick, "Sci-Fi Philosopher")
Perhaps The Last Airbender ?
The NY Times philosophy column "The Stone" is currently about gnosticism
and science fiction.
The Last Airbender is about an avatar who is master of the four elements
air, water, earth, and fire. For a more sophisticated approach to gnosticism
and the four elements, see Irenaeus: Against Heresies.
See, too, Elements Diamond in this journal.
On author Paul Fussell, who died today—
"Vincent B. Sherry, writing* in The Cambridge Companion
to the Literature of the First World War , called Mr. Fussell’s
book 'the fork in the road for Great War criticism.'"
— Christopher Lehmann-Haupt in The New York Times
"When you come to a fork in the road…"
* Actually, the writing was by James Campbell. Sherry was the book's editor.
See Campbell's "Interpreting the War," pp. 261-279 of the 2005 (first) printing.
The fork is on page 267.
Update of 9:26 PM— In the latest version of Lehmann-Haupt's article, the fork
has disappeared. But Campbell's writing is still misidentified as Sherry's.
See Bagombo Snuff Box and
"Will this be on the test?"
|
"In logic, the law of excluded middle (or the principle of excluded middle) is the third of the so-called three classic laws of thought. It states that for any proposition, either that proposition is true, or its negation is. The law is also known as the law (or principle) of the excluded third (or of the excluded middle), or, in Latin, principium tertii exclusi. Yet another Latin designation for this law is tertium non datur: 'no third (possibility) is given.'" |
"Clowns to the left of me, jokers to the right"
— Songwriter who died on January 4, 2011.
Online NY Times on the date of the songwriter's death—
"A version of this review appeared in print
on January 4, 2011, on page C6 of the New York edition."
"The philosopher Hubert Dreyfus and his former student
Sean Dorrance Kelly have a story to tell, and it is not
a pretty tale for us moderns. Ours is an age of nihilism,
they say, meaning not so much that we have nothing
in which to believe, but that we don’t know how to choose
among the various things to which we might commit
ourselves. Looking down from their perches at Berkeley
and Harvard, they see the 'human indecision that
plagues us all.'"
For an application of the excluded-middle law, see
Non-Euclidean Blocks and Deep Play.
Violators of the law may have trouble* distinguishing
between "Euclidean" and "non-Euclidean" phenomena
because their definition of the latter is too narrow,
based only on examples that are historically well known.
See the Non-Euclidean Blocks footnote.
* Followers of the excluded-middle law will avoid such
trouble by noting that "non-Euclidean" should mean
simply "not Euclidean in some way "— not necessarily
in a way contradicting Euclid's parallel postulate.
But see Wikipedia's defense of the standard, illogical,
usage of the phrase "non-Euclidean."
Postscript—
Tertium Datur
"Here I am, stuck in the middle with you."
we are just like a couple of tots…
— Sinatra
Born 1973 in Bergen. Lives and works in Oslo.
Education
2000 – 2004 National Academy of Fine Arts, Oslo
1998 – 2000 Strykejernet Art School, Oslo, NO
1995 – 1998 Philosophy, University of Bergen
University of Bergen—
|
It might therefore seem that the idea of digital and analogical systems as rival fundaments to human experience is a new suggestion and, like digital technology, very modern. In fact, however, the idea is as old as philosophy itself (and may be much older). In his Sophist, Plato sets out the following ‘battle’ over the question of ‘true reality’: What we shall see is something like a battle of gods and giants going on between them over their quarrel about reality [γιγαντομαχία περì της ουσίας] ….One party is trying to drag everything down to earth out of heaven and the unseen, literally grasping rocks and trees in their hands, for they lay hold upon every stock and stone and strenuously affirm that real existence belongs only to that which can be handled and offers resistance to the touch. They define reality as the same thing as body, and as soon as one of the opposite party asserts that anything without a body is real, they are utterly contemptuous and will not listen to another word. (…) Their adversaries are very wary in defending their position somewhere in the heights of the unseen, maintaining with all their force that true reality [την αληθινήν ουσίαν] consists in certain intelligible and bodiless forms. In the clash of argument they shatter and pulverize those bodies which their opponents wield, and what those others allege to be true reality they call, not real being, but a sort of moving process of becoming. On this issue an interminable battle is always going on between the two camps [εν μέσω δε περι ταυτα απλετος αμφοτέρων μάχη τις (…) αει συνέστηκεν]. (…) It seems that only one course is open to the philosopher who values knowledge and truth above all else. He must refuse to accept from the champions of the forms the doctrine that all reality is changeless [and exclusively immaterial], and he must turn a deaf ear to the other party who represent reality as everywhere changing [and as only material]. Like a child begging for 'both', he must declare that reality or the sum of things is both at once [το όν τε και το παν συναμφότερα] (Sophist 246a-249d). The gods and the giants in Plato’s battle present two varieties of the analog position. Each believes that ‘true reality’ is singular, that "real existence belongs only to" one side or other of competing possibilities. For them, difference and complexity are secondary and, as secondary, deficient in respect to truth, reality and being (την αληθινήν ουσίαν, το όν τε και το παν). Difference and complexity are therefore matters of "interminable battle" whose intended end for each is, and must be (given their shared analogical logic), only to eradicate the other. The philosophical child, by contrast, holds to ‘both’ and therefore represents the digital position where the differentiated two yet belong originally together. Here difference, complexity and systematicity are primary and exemplary. It is an unfailing mark of the greatest thinkers of the tradition, like Plato, that they recognize the digital possibility and therefore recognize the principal difference of it from analog possibilities.
— Cameron McEwen, "The Digital Wittgenstein," |
* See that phrase in this journal.
A web search for the author Cameron McEwen mentioned
in today's noon post was unsuccessful, but it did yield an
essay, quite possibly by a different Cameron McEwen, on
"The fundamental difference between analog
and digital systems may be understood as
underlying philosophical discourse since the Greeks."
The University of Bergen identifies the Wittgenstein
McEwen as associated with InteLex of Charlottesville.
The title of this post may serve to point out an analogy*
between the InteLex McEwen's analog-digital contrast
and the Euclidean-Galois contrast discussed previously
in this journal.
The latter contrast is exemplified in Pilate Goes to Kindergarten.
* An analogy, as it were, between analogies.
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
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)
"An occultation is an event that occurs
when one object is hidden by another object
that passes between it and the observer.
The word is used in astronomy…"
AP story, 10:26 PM EDT May 20, 2012—
See also Darkness Visible in this journal.
(11 PM EDT, the time of this post, is noon
the next day in Tokyo. The above eclipse was
seen in Japan on May 21, 2012, in the morning.)
Film ad in today's New York Times (see previous post)—
Applying this advice—
* See today's Times Colonist .
Maureen Dowd misquoting Joyce today—
Dowd's confusion seems derived from that of Richard John Neuhaus—
From Sunday Dinner in this journal—
|
Guess Who's Coming to Dinner? Judith Shulevitz at The New York Times "What would an organic Christian Sabbath look like today?" |
Menu: Sardi's, not Sardis.
Here is a link to a copy of the home page of a Turkish
author quoted here on May 4, 2012… in honor of
archaeologist Crawford Greenewalt Jr., who reportedly
died on that date. Greenewalt was an expert on the
ancient city of Sardis, in what is now western Turkey.
The May 4 quote was about
"Heraclitus’s Aion and His Transformations."
(A post suggested by an ad in this evening's online New York Times )
"After being brought to the village's Patriarch… Mick learns
the intent of the colony and how they operate."
— Summary of a story by Orson Scott Card, a Latter-Day Saint.
For some context, see Saints Have Powers in this journal.
Related material —
The Saturday Evening Post and tonight's Saturday Night Live .
"The group of 8" is a phrase from politics, not mathematics.
Of the five groups of order 8 (see today's noon post),
the one pictured* in the center, Z2 × Z2 × Z2 , is of particular
interest. See The Eightfold Cube. For a connection of this
group of 8 to the last of the five pictured at noon, the
quaternion group, see Finite Geometry and Physical Space.
* The picture is of the group's cycle graph.
38, 23, 7B
May 19, 2012 9:06 AM
Expert: Facebook targeting all 7B people on Earth
(CBS News) NEW YORK — After all the hype, Facebook's
stock fell flat on its first day of trading. Shares in the
social networking giant opened at 38 dollars, shot up briefly,
then fell— and finished just 23 cents higher.
Midrash— "Fullness… Multitude"
Continued from Banderas (Aug. 18, 2011)—
Balakrishnan's Banners
See also The Colors of Halloween and Smiling Buddha.
"… this campaign, relatively speaking, will not be
fierce or hotly contested. Instead it'll be disappointing,
embarrassing, and over very quickly, like a hand job
in a Bangkok bathhouse." — Matt Taibbi in Rolling Stone
From a film released Friday, April 13th, 2012—
"Time for you to see the field." — Bagger Vance, as quoted here yesterday.
* Title courtesy of David Foster Wallace.
From "Crude Foyer," a Wallace Stevens poem—
In which we read the critique of paradise
And say it is the work
Of a comedian, this critique….
Related comedy — Finality and Cleavage.
* TV series starring the above actors. See Wikipedia.
(Continued from yesterday evening)
On Max Bialystock's Spider-Man Godspell Seminar—
"… for surrealism to be entertaining
onstage, it must be shaped into
some kind of satisfying form."
— Charles Isherwood
in today's New York Times
(RSS: Wed, 16 May 2012 00:37:17 GMT)
From Fritz Leiber's 1959 story "Damnation Morning" —
She drew from her handbag a pale grey gleaming
implement that looked by quick turns to me
like a knife, a gun, a slim sceptre, and a delicate
branding iron— especially when its tip sprouted
an eight-limbed star of silver wire.
“The test?” I faltered, staring at the thing.
“Yes, to determine whether you can live
in the fourth dimension or only die in it.”
(Continued from Sunday, April 22, 2012)
Xbox Background—
Design Sermon from Sunday, November 6, 2011, and
The X Box from Monday, November 7, 2011.
Six PM EDT is midnight in Paris.
Así Que Pasen Cinco Años
Theater review from The Guardian—
" 'Impossible' was how the Spanish playwright
Lorca described his own 1931 'legend of time
in three acts and five scenes,' which draws
strongly on the surrealist influences and experiments
of his close friends Salvador Dali and Luis Buñuel."
Related material—
This afternoon's previous post Murió Fuentes and,
from this date five years ago…
From the NY Times philosophy column "The Stone"
yesterday at 5 PM—
Timothy Williamson, Wykeham Professor of Logic at Oxford,
claims that all the theorems of mathematics
"… are ultimately derived from a few simple axioms
by chains of logical reasoning, some of them
hundreds of pages long…."
Williamson gives as an example recent (1986-1995)
work on Fermat's conjecture.
He does not, however, cite any axioms or "chains of
logical reasoning" in support of his claim that
a proof of Fermat's conjecture can be so derived.
Here is a chain of reasoning that forms a crucial part
of recent arguments for the truth of Fermat's conjecture—
K. A. Ribet, "On modular representations of Gal(Q̄/Q)
arising from modular forms," Invent. Math. 100 (1990), 431-476.
Whether this chain of reasoning is in fact logical is no easy question.
It is not the sort of argument easily reduced to a series of purely
logical symbol-strings that could be checked by a computer.
Few mathematicians, even now, can follow each step
in the longer chain of reasoning that led to a June 1993 claim
that Fermat's conjecture is true.
Williamson is not a mathematician, and his view of
Fermat's conjecture as a proven fact is clearly based
not on logic, but on faith.
Steve Cropper on the late Donald Dunn—
"He's in the hotel right now."
Click image for a related post.
An earlier verse in 1 John—
1 John 1:5 "This then is the message
which we have heard of him,
and declare unto you, that God is light,
and in him is no darkness at all."
Catechism from a different cult—
"Who are you, anyway?"
— Question at 00:41 of 15:01,
Rainbow Bridge (Part 5 of 9) at YouTube
See also the video accompanying artist Josefine Lyche's version
of the 2×2 case of the diamond theorem.
* Title of a Robert Stone novel
Mormon Mitt Romney at the Baptist school Liberty University today:
"The task set before you four years ago
is now completed in full."
I do not know what that task was. In this journal four years ago,
the task was lottery hermeneutics… a subject I doubt is taught
at Liberty University.
The New York lottery numbers from Sunday, May 11, 2008,
in a May 12 post four years ago could be interpreted as
pointing to the date 3/13—
Say, 3/13, 2006— a date on which this journal quoted some
remarks on the biblical phrase "the fullness of time."
Those remarks were neither Baptist nor
Mormon, but rather Presbyterian.
Today's previous post was "Midnight in Oslo (continued)."
The link "a 4-element set" in "Midnight"
was to a more elaborate structure in a post titled "Tesseract."
In memory of an Oslo "hero of midnight"
(a phrase quoted here last September 1)—
A search for material that is more entertaining—
Odin 's Tesseract.
See also a related Hollywood story in The Washington Post .
Last evening's Geometry of the Dance discussed
a book on the Norwegian mathematician
Niels Henrik Abel. The post dealt with the group
S4 of 24 permutations of a 4-element set.
"In that open field
If you do not come too close, if you do not come too close,
On a summer midnight, you can hear the music…."
— The dance in Four Quartets
For a summer midnight related to the group S4,
see Midnight in Oslo from last August.
"At the still point…." — T. S. Eliot
"…a dance results." — Marie-Louise von Franz
Peter Pesic uses a dance metaphor to explain
finite group theory, with permutations of four elements
represented by symmetries of a tetrahedron—
For a different approach to the dance metaphor, see
the dance in Four Quartets and Poetry's Bones.
In that open field
If you do not come too close, if you do not come too close,
On a summer midnight, you can hear the music
Of the weak pipe and the little drum
And see them dancing around the bonfire
The association of man and woman
In daunsinge, signifying matrimonie—
A dignified and commodiois sacrament.
Two and two, necessarye coniunction….
In memory of author Maurice Sendak,
who has died at 83—
"President Obama and his family read from
Where the Wild Things Are at this year’s
White House Easter Egg Roll." —ABC News
See also Easter Act and Shaggy Dance.
| SPOILER ALERT
This post links to a column that |
The title is from a column by Stanley Fish
on The Hunger Games books in today's
online New York Times . The column
was posted at 9 PM EDT on May 7th, but I
did not see it until this morning.
Fish says—
"In the end… [spoiler details omitted]…
children… 'don’t know they play
on a graveyard'…."
For some literary background, see last night's post
on the May 7th, 2012, NY Times obituaries as well
as the May 7th, 2006, Log24 post featuring 24 squares
arranged in a rectangular frame.
See also Frame Tales and, more generally,
The King and the Corpse.
"Et cetera, et cetera, et cetera." — Yul Brynner
Leading The New York Times obituaries on the evening of
May 7th, 2012, was "Bob Stewart, Inventor of Game Shows"—
From a publication linked to here on May 4th,
the reported date of Stewart's death—
A PASSAGE TO INDIA—
For Eastern illusion involving a (presumably different)
"Bob Stewart," see this journal on May 7th six years ago.
John Baez wrote in 1996 ("Week 91") that
"I've never quite seen anyone come right out
and admit that triality arises from the
permutations of the unit vectors i, j, and k
in 3d Euclidean space."
Baez seems to come close to doing this with a
somewhat different i , j , and k — Hurwitz
quaternions— in his 2005 book review
quoted here yesterday.
See also the Log24 post of Jan. 4 on quaternions,
and the following figures. The actions on cubes
in the lower figure may be viewed as illustrating
(rather indirectly) the relationship of the quaternion
group's 24 automorphisms to the 24 rotational
symmetries of the cube.
This post continues the April 9 post
commemorating Élie Cartan's birthday.
That post mentioned triality .
Here is John Baez reviewing
On Quaternions and Octonions:
Their Geometry, Arithmetic, and Symmetry
by John H. Conway and Derek A. Smith
(A.K. Peters, Ltd., 2003)—
"In this context, triality manifests itself
as the symmetry that cyclically permutes
the Hurwitz integers i , j , and k ."
Related material— Quaternion Acts in this journal
as well as Finite Geometry and Physical Space.
“… Which makes it a gilt-edged priority that one of us
gets into that Krell lab and takes that brain boost.”
— American adaptation of Shakespeare's Tempest , 1956
From "The Onto-theological Origin of Play:
Heraclitus and Plato," by Yücel Dursun, in
Lingua ac Communitas Vol 17 (October 2007)—
"Heraclitus’s Aion and His Transformations
The saying is as follows:
αἰὼν παῖς ἐστι παίζων, πεττεύων·
παιδὸς ἡ βασιληίη
(Aion is a child playing draughts;
the kingship is the child’s)
(Krell 1972: 64).*
* KRELL, David Farrell.
“Towards an Ontology of Play:
Eugen Fink’s Notion of Spiel,”
Research in Phenomemology ,
2, 1972: 63-93.
This is the translation of the fragment in Greek by Krell.
There are many versions of the translation of the fragment….."
See also Child's Play and Froebel's Magic Box.
Update of May 5— For some background
from the date May 4 seven years ago, see
The Fano Plane Revisualized.
For some background on the word "aion,"
see that word in this journal.
"… a long seat, or a seat with a back,
or a throne for the Queen;
or again, a cross, a doorway, etc."
"… etc., etc." — Yul Brynner
“The key is the cocktail that begins the proceedings.”
– Brian Harley, Mate in Two Moves
See also yesterday's Endgame , as well as Play and Interplay
from April 28… and, as a key, the following passage from
an earlier April 28 post—
| Euclidean geometry has long been applied to physics; Galois geometry has not. The cited webpage describes the interplay of both sorts of geometry— Euclidean and Galois, continuous and discrete— within physical space— if not within the space of physics . |
In memory of actress Patricia Medina—
RxQ
Medina, who died at 92 on April 28, starred in the 1954 Alan Ladd film The Black Knight .
April 28 is also the date the above photo appeared in this journal. See Play and Interplay.
"There is a pleasantly discursive treatment of
Pontius Pilate's unanswered question 'What is truth?'"
— H. S. M. Coxeter, 1987
Returning to the Walpurgisnacht posts
Decomposition (continued) and
Decomposition– Part III —
Some further background…
SAT
(Not a Scholastic Aptitude Test)
"In computer science, satisfiability (often written
in all capitals or abbreviated SAT) is the problem
of determining if the variables of a given Boolean
formula can be assigned in such a way as to
make the formula evaluate to TRUE."
— Wikipedia article Boolean satisfiability problem
For the relationship of logic decomposition to SAT,
see (for instance) these topics in the introduction to—
Advanced Techniques in Logic Synthesis,
Optimizations and Applications* —
Click image for a synopsis.
* Edited by Sunil P. Khatri and Kanupriya Gulati
From this journal last Christmas—
Sunday, December 25, 2011Frage"Woher dieser Sprung von Endlichen zum Unendlichen? " — Wittgenstein, Zettel , § 273 Antwort— Accomplished in Steps and For 34th Street. See also Boundary Method. |
The "Boundary Method" link above leads to a Christmas Day obituary
for Maurice Jaswon, co-author of a book on color symmetry.
Those who prefer entertainment may consult the previous Christmas.
Tony Award Nominations
"The losers? 'Spider-Man: Turn Off the Dark,'
the $75 million blockbuster that received just
two nominations. 'Seminar' and 'Godspell,'
which have some strong fans but were
shut out of the nominations."
— Patrick Healy in this morning's New York Times
A thought for Max Bialystock—
The Spider-Man Godspell Seminar!
Jeff Goldblum in "Seminar"
Update of 12:25 PM —
The reviews are in!
"A version of this article appeared in print on May 1, 2012, on page A1 of the New York edition…."
(Continued from Part I and Part II.)
The paper excerpted below supplies some badly needed technical
background for the Wikipedia article on functional decomposition.
The preprint above gives the precise definitions and technical references
that are completely absent from Wikipedia's Functional decomposition.
For some related material on 4×4 arrays like those in the above figure
see Decomposition Part I and Geometry of the 4×4 Square.
Compare and contrast
1. The following excerpt from Wikipedia—
2. A webpage subtitled "Function Decomposition Over a Finite Field."
Related material—
“Birthday, death-day — what day is not both?”
— John Updike, The New Yorker dated August 5, 2002, page 63
Today's date— Poincaré's birth, Wittgenstein's death.
A Saint for Clark University—
Today is also the birth date of William Edward Story,
a mathematician who taught at Clark University
in Worcester, Mass.
Story's date of death was April 10, 1930.
See the Log24 posts for that date in 2012.
“Oh, Sara!” she whispered joyfully. “It is like a story!”
“It is a story,” said Sara. “Everything's a story.
You are a story— I am a story.”
— Frances Hodgson Burnett, A Little Princess
The last paragraph of the previous post
(as updated at about 7:20 PM today)
suggests a search for the phrase
"play and interplay" that yields…
"He had accepted the world as the world,
but now he was comprehending the
organization of it, the play and interplay
of force and matter."
— Martin Eden by Jack London
This in turn suggests a review of the film "Queen to Play" —
(Background: Nabokov + Patterns.)
The review announces showings of the film at Clark University
in Worcester, Mass., on Sunday, October 30, 2011.
See also this journal on that date— "The Idea Idea"— and
references to a knight figure from today's date in 1985.
A Log24 post, "Bridal Birthday," one year ago today linked to
"The Discrete and the Continuous," a brief essay by David Deutsch.
From that essay—
"The idea of quantization—
the discreteness of physical quantities—
turned out to be immensely fruitful."
Deutsch's "idea of quantization" also appears in
the April 12 Log24 post Mythopoetic—
|
"Is Space Digital?" — Cover story, Scientific American "The idea that space may be digital — Physicist Sabine Hossenfelder "A quantization of space/time — Peter Woit in a comment |
It seems some clarification is in order.
Hossenfelder's "The idea that space may be digital"
and Woit's "a quantization of space/time" may not
refer to the same thing.
Scientific American on the concept of digital space—
"Space may not be smooth and continuous.
Instead it may be digital, composed of tiny bits."
Wikipedia on the concept of quantization—
Causal sets, loop quantum gravity, string theory,
and black hole thermodynamics all predict
a quantized spacetime….
For a purely mathematical approach to the
continuous-vs.-discrete issue, see
Finite Geometry and Physical Space.
The physics there is somewhat tongue-in-cheek,
but the geometry is serious.The issue there is not
continuous-vs.-discrete physics , but rather
Euclidean-vs.-Galois geometry .
Both sorts of geometry are of course valid.
Euclidean geometry has long been applied to
physics; Galois geometry has not. The cited
webpage describes the interplay of both sorts
of geometry— Euclidean and Galois, continuous
and discrete— within physical space— if not
within the space of physics.
This post was suggested by Paradigms Lost
(a post cited here a year ago today),
by David Weinberger's recent essay "Shift Happens,"
and by today's opening of "The Raven."
David Weinberger in The Chronicle of Higher Education , April 22—
"… Kuhn was trying to understand how Aristotle could be such a brilliant natural scientist except when it came to understanding motion. Aristotle's idea that stones fall and fire rises because they're trying to get to their natural places seems like a simpleton's animism.
Then it became clear to Kuhn all at once. Ever since Newton, we in the West have thought movement changes an object's position in neutral space but does not change the object itself. For Aristotle, a change in position was a change in a quality of the object, and qualitative change tended toward an asymmetric actualization of potential: an acorn becomes an oak, but an oak never becomes an acorn. Motion likewise expressed a tendency for things to actualize their essence by moving to their proper place. With that, 'another initially strange part of Aristotelian doctrine begins to fall into place,' Kuhn wrote in The Road Since Structure ."
Dr. John Raven (of Raven's Progressive Matrices)—
"… these tools cannot be immediately applied within our current workplaces, educational systems, and public management systems because the operation of these systems is determined, not by personal developmental or societal needs, but by a range of latent, rarely discussed, and hard to influence sociological forces.
But this is not a cry of despair: It points to another topic which has been widely neglected by psychologists: It tells us that human behaviour is not mainly determined by internal properties— such as talents, attitudes, and values— but by external social forces. Such a transformation in psychological thinking and theorising is as great as the transformation Newton introduced into physics by noting that the movement of inanimate objects is not determined by internal, 'animistic,' properties of the objects but by invisible external forces which act upon them— invisible forces that can nevertheless be mapped, measured, and harnessed to do useful work for humankind.
So this brings us to our fourth conceptualisation and measurement topic: How are these social forces to be conceptualised, mapped, measured, and harnessed in a manner analogous to the way in which Newton made it possible to harness the destructive forces of the wind and the waves to enable sailing boats to get to their destinations?"
Before Newton, boats never arrived?
"These lowbrow, popular cultural references bring the possibilities
of interpretation down to an everyday level, forcing us to acknowledge
that not every painting that looks like a splatter is necessarily a
homage/anti-homage to Jackson Pollock."
— Stina Högqvist, review of the art of Josefine Lyche
The 3×3×3 Galois Cube
Backstory— The Talented, from April 26 last year,
and Atlas Shrugged, from April 27 last year.
(Mythopoetic continued)
Voice of America today—
Thousands of Norwegians Defy Confessed Killer Breivik in Song
"The demonstrators waved roses and flags
Thursday as they and Norwegian folk singer
Lillebjoern Nilsen sang an adaptation
of the children's song, 'My Rainbow Race,'
which Breivik in court last week called
an example of Marxist brainwashing."
[See also PETE SEEGER AND LILLEBJØRN NILSEN.
Click on the image below for Seeger's original version.]
Liberia Reacts to Taylor Conviction With Mixed Emotions
"As the verdict was read out, a rainbow was seen
in the sky, encircling the sun. For many Liberians,
superstition is a part of life. The rainbow heralded
a new era, they said, beginning with the verdict of Taylor."
["You're not the only one… with mixed emotions."]
Two narratives in memory of my seventh-grade
history teacher, who died on January 27, 2012—
1. On the history of Liberia
(subject of a paper I wrote in seventh grade), and
2. Comic-book history (from the above date)
A meditation suggested by the April 20 post Complex Reflection
and by the life and April 20 death of a scientist who worked
at Los Alamos (home of the Monte Carlo method) and at
the Santa Fe Institute (home of complexity theory).
A search for 286 in this journal yields "Yet Another Cartoon Graveyard."
That June 1, 2008, post linked to poem 286 in a 1919 anthology.
Here is that poem, together with poem 823.
Together, these poems may be regarded as a meditation on
Simone Weil and her brother André Weil or,
more abstractly, on Love and Death.
Happy birthday to Al Pacino.
(Not Olympus )
(Continued from Mythopoetic, a post of April 12)
This post was suggested by a 2010 film about fictional Olympians,
by today's New York Times obituaries, and by a bar brawl at the Olympian
New York Athletic Club in "the wee hours of April 13."
Rick Riordan in the image below advertises another large
"Demigod Gathering" on October 12, 2010.
The Riordan image is from a post at ComposersCave.com
made on October 3, 2010.
Applying Jung's principle of synchronicity to this demigod material,
we find the October 3, 2010, Log24 post Search for the Basic Picture
and the October 12, 2010, Log24 post King Solomon's Mind.
Note that the latter October date is that of the traditional
Columbus Day, and that the 2010 film of The Lightning Thief
was directed by Chris Columbus of 1492 Pictures.
The film's release was earlier in 2010, on February 12.
See also —
"Pardon me. J'adoube."
— The Consul as he fastens his fly in Under the Volcano ,
the Garden of Eden scene
Suggested by a piece in the
Melbourne Herald Sun dated August 1, 2007—
A link from Log24 on that date—
Show Business
according to Fritz Leiber:
“Sid thinks you’re ready for
some of the smaller parts.”
In memory of Mike Wallace—
See also Knight Moves.
"… this notion of ‘depth’ is an elusive one
even for a mathematician who can recognize it…."
— G. H. Hardy, A Mathematician's Apology
In Geometry and the Imagination , Hilbert and Cohn-Vossen
describe the Brianchon-Pascal configuration of 9 points
and 9 lines, with 3 points on each line and 3 lines through
each point, as being "the most important configuration of all geometry."
The Brianchon-Pascal configuration is also known as the Pappus configuration—
Some background …
"The Theorem of Pappus: A Bridge Between Algebra and Geometry"
Elena Anne Marchisotto
The American Mathematical Monthly
Vol. 109, No. 6 (Jun. – Jul., 2002), pp. 497-516
Click image for some context from MIT.
Background from The New York Times— "Can You Make Yourself Smarter?"
See also "Plan 9" in this journal.
"Every multiplayer game, both free-for-all and team based,
will begin with a Mexican standoff." —Wikipedia
"The Cardinal seemed a little preoccupied today."
In "Contact," Dr. Arroway is shown the key to the Primer—
In this journal, fictional symbologist Robert Langdon is shown a cube—
"Confusion is nothing new." — Song lyric
"So the sundering we sense between nature and culture
lies not like a canyon outside us, but splits our being
at its most intimate depths the way mind breaks off from body.
It is still another version of that bitter bifurcation
long ago decreed— our expulsion from Eden…."
— William H. Gass in Finding a Form ,
Cornell U. Press paperback, 1997, page 138
See also…
For another bitter bifurcation, see La Despedida .
— Title of a 1975 film. The late Martin Poll (previous post)
was the executive producer.
See also "A Corpse Will Be Transported by Express."
Related material—
From Deadline Hollywood—
A film producer's death "between Friday night and early Saturday morning,"
April 13-14, 2012—
| R.I.P. Martin Poll
By THE DEADLINE TEAM | Sunday April 15, 2012 @ 7:36 pm PDT Veteran movie and TV producer Martin Poll died between Friday night and early Saturday morning of natural causes at a care facility on the Upper Westside in New York City. He was 89. |
See also the post linked to on the afternoon of Friday the 13th of April—
"All the saints have powers." — Cardinal Marchisano.
Happy birthday, James McAvoy (at left below in X-Men: First Class ).
(Continued from October First, 2010)
Today's Birthdays:
Britain's Queen Elizabeth II is 86.
Actress-comedian-writer Elaine May is 80.
Actor Charles Grodin is 77.
— AP, Today in History, April 21, 2012
Found in a Google search today—
(Click image for videos.)
I hadn't known until today that youtube.com/blogs/m759 exists.
The Arduino link under "More Channels" suggests a site
that may interest some future Arroway or Hadden.
Yesterday's post in memory of Octavio Paz—
|
… the free-standing, two-sided “Life-Death Figure,” |
An earlier post yesterday, Fashion Notes, linked to a Sting video—
|
From "Loo Ree," by Zenna Henderson "It's so hard to explain–" "Oh, foof!" I cried defiantly, taking off my glasses and, smearing the tears across both lenses with a tattered Kleenex. "So I'm a dope, a moron! If I can explain protective coloration to my six-year-olds and the interdependence of man and animals, you can tell me something of what the score is!" I scrubbed the back of my hand across my blurry eyes. "If you have to, start out 'Once upon a time."' I sat down– hard. Loo Ree smiled and sat down, too. "Don't cry, teacher. Teachers aren't supposed to have tears." "I know it," I sniffed. "A little less than human-that's us." "A little more than human, sometimes." Loo Ree corrected gently. "Well then, you must understand that I'll have to simplify. You will have to dress the bare bones of the explanation according to your capabilities. "Once upon a time there was a classroom. Oh, cosmic in size, but so like yours that you would smile in recognition if you could see it all. And somewhere in the classroom something was wrong. Not the whispering and murmuring– that's usual. Not the pinching and poking and tattling that goes on until you get so you don't even hear it." I nodded. How well I knew. "It wasn't even the sudden blow across the aisle or the unexpected wrestling match in the back of the room. That happens often, too. But something else was wrong. It was an undercurrent, a stealthy, sly sort of thing that has to be caught early or it disrupts the whole classroom and tarnishes the children with a darkness that will never quite rub off. "The teacher could feel it –as all good teachers can– and she spoke to the principal. He, being a good principal, immediately saw the urgency of the matter and also saw that it was beyond him, so he called in an Expert." "You?" I asked, feeling quite bright because I had followed the analogy so far. Loo Ree smiled. "Well, I'm part of the Expert." |
"If you have to, start out 'Once upon a time.'"
Yesterday's Paz post was at 6:48 PM EDT.
For the autistic, here is some related mathematics.
Yesterday's Fashion Notes post was at 1:06 PM EDT.
A related chronological note from Rolling Stone yesterday—
"Levon Helm, singer and drummer for the Band,
died on April 19th in New York of throat cancer.
He was 71.
"He passed away peacefully at 1:30 this afternoon…."
Helm and The Band performing "The Weight"—
"I pulled into Nazareth, I was a-feelin' 'bout half past dead…"
Suggested by two posts today at other weblogs—
"The Ariel Thread" and "Spring in the Virgin Islands."
Background— Beach with Palms, One Story and Descanse .
For Octavio Paz, who died on this date in 1998
|
… the free-standing, two-sided “Life-Death Figure,” — Holland Cotter, New York Times online today |
…. and John Golding, an authority on Cubism who "courted abstraction"—
"Adam in Eden was the father of Descartes." — Wallace Stevens
Fictional symbologist Robert Langdon and a cube—
From a Log24 post, "Eightfold Cube Revisited,"
on the date of Golding's death—
A related quotation—
"… quaternions provide a useful paradigm
for studying the phenomenon of 'triality.'"
— David A. Richter's webpage Zometool Triality
See also quaternions in another Log24 post
from the date of Golding's death— Easter Act.
"… he continued to make brief appearances
on the show, including the one this past
New Year's Eve.* "
— Bruce Weber, New York Times
"The only stars Clark coveted
for his show in those early years
but could not get were
the Beatles and Ricky Nelson…."
— Geoff Boucher, Los Angeles Times
"I don't know why you say goodbye"
"There was … magic in the air"
„Ein formal stimmiges Produkt braucht keine Verzierung,
es soll durch die reine Form erhöht werden.“
"My friends all drive Porsches,
I must make amends."
— Janis Joplin, Pearl Sessions CD
reissue released today at Amazon.co.uk
|
|
Gary Gutting, "Arguing About Language," in "The Stone,"
The New York Times philosophy column, yesterday—
There's a sense in which we speak language
and a sense in which, in Mallarmé's famous phrase,
“language itself speaks.”
Famous? A Google Book Search for
"language itself speaks" Mallarmé
yields 2 results, neither helpful.
But a Google Book Search for
"language itself speaks" Heidegger
yields "about 312 results."
A related search yields the following—
Paul Valéry, encountering Un Coup de Dés in Mallarmé’s worksheets in 1897, described the text as tracing the pattern of thought itself:
It seemed to me that I was looking at the form and pattern of a thought, placed for the first time in finite space. Here space itself truly spoke, dreamed, and gave birth to temporal forms….
… there in the same void with them, like some new form of matter arranged in systems or masses or trailing lines, coexisted the Word! (Leonardo 309*)
* The page number is apparently a reference to The Collected Works of Paul Valéry: Leonardo, Poe, Mallarmé , translated by Malcolm Cowley and James R. Lawler, Princeton University Press, 1972. (As a temporal form, "309" might be interpreted as a reference to 3/09, March 9, the date of a webpage on the Void.)
For example—
Background:
Deconstructing Alice
and Symbology.
This afternoon's post Tally quotes "Day-O,"
a song performed, notably, in the 1988 film
"Beetlejuice"—
More merriment —
Tummler Lou Goldstein died at 90 on April 2, 2012,
according to this evening's online New York Times .
In his honor, figures from a Sept. 17, 2009, post—
See also "Boo Boo Boo."
Those not amused by tummler humor may prefer
a post from the date of Goldstein's death
related to the object viewed above by the fictional
symbologist Robert Langdon.
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