Poster from Walpurgisnacht 2012
Raven’s Progressive Matrices problem:
Click the problem for a related story.
Poster from Walpurgisnacht 2012
Raven’s Progressive Matrices problem:
Click the problem for a related story.
“To say more is to say less.”
― Harlan Ellison, as quoted at goodreads.com
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….
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
The books pictured above are From Discrete to Continuous ,
by Katherine Neal, and Geometrical Landscapes , by Amir Alexander.
“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
‘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.
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.
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—
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.
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),
Today is commencement day at College of the Desert.
(from a poem by Jorie Graham)
Click either passage above for some commentary.
For The Hunger Games
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.
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.
(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
From this date in 2010—
"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.'"
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.
* 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."
"Here I am, stuck in the middle with you."
we are just like a couple of tots…
Born 1973 in Bergen. Lives and works in Oslo.
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 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…"
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.
(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."
For some context, see Saints Have Powers in this journal.
Related material —
"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.
38, 23, 7B
May 19, 2012 9:06 AM
(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)—
"… 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
"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)
Six PM EDT is midnight in Paris.
Así Que Pasen Cinco Años
" '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."
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—
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
* 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."
A search for material that is more entertaining—
Odin 's Tesseract.
See also a related Hollywood story in The Washington Post .
"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—
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
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.
"In the end… [spoiler details omitted]…
children… 'don’t know they play
on a graveyard'…."
"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"—
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."
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.
"In this context, triality manifests itself
as the symmetry that cyclically permutes
the Hurwitz integers i , j , and k ."
“… 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….."
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
|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—
"There is a pleasantly discursive treatment of
Pontius Pilate's unanswered question 'What is truth?'"
— H. S. M. Coxeter, 1987
Some further background…
(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.
From this journal last Christmas—
Sunday, December 25, 2011
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."
A thought for Max Bialystock—
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…."
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