A very brief introduction:
Tuesday, May 31, 2016
In memory of CBS TV programmer Michael Dann,
who reportedly died at 94 on Friday, May 27 —
Don't Forget Hoss
Judy Carne and Hoss in NBC's "Bonanza," a nemesis
of CBS Sunday programming.
In other entertainment news …
Cartoonist Frank Modell reportedly died at 98,
also on Friday, May 27.
In his memory, part of a Weird Tale from 1948 that is
illustrated (sort of) by a more recent Modell drawing —
"No one ever found out who the dead man was.
He had no luggage and no identification;
he had been hitchhiking, and he had
over ninety dollars in his pocket.
He might have been anybody—
someone from show business, or a writer perhaps,
on a haywire vacation of his own wild devising.
I suppose that doesn't matter either.
What does matter is that he died while
Grace was in a very close communion
with what he was doing, and her mind was
wide open for his fantasy. …. "
— Theodore Stugeon, "The Perfect Host,"
Weird Tales , November 1948, page 15
Some context: This morning's post
"Entertainment in Plato's Cave," and
a few titles from my Kindle library —
"Plato's allegory of the cave describes prisoners,
inhabiting the cave since childhood, immobile,
facing an interior wall. A large ﬁre burns behind
the prisoners, and as people pass this ﬁre their
shadows are cast upon the cave's wall, and
these shadows of the activity being played out
behind the prisoner become the only version of
reality that the prisoner knows."
— From the Occupy Space gallery in Ireland
Monday, May 30, 2016
(A sequel to the previous post, Perfect Number)
Since antiquity, six has been known as
"the smallest perfect number." The word "perfect"
here means that a number is the sum of its
proper divisors — in the case of six: 1, 2, and 3.
The properties of a six-element set (a "6-set")
divided into three 2-sets and divided into two 3-sets
are those of what Burkard Polster, using the same
adjective in a different sense, has called
"the smallest perfect universe" — PG(3,2), the projective
3-dimensional space over the 2-element Galois field.
A Google search for the phrase "smallest perfect universe"
suggests a turnaround in meaning , if not in finance,
that might please Yahoo CEO Marissa Mayer on her birthday —
The semantic turnaround here in the meaning of "perfect"
is accompanied by a model turnaround in the picture of PG(3,2) as
Polster's tetrahedral model is replaced by Cullinane's square model.
Further background from the previous post —
See also Kirkman's Schoolgirl Problem.
"Ageometretos me eisito."—
"Let no one ignorant of geometry enter."—
Said to be a saying of Plato, part of the
seal of the American Mathematical Society—
For the birthday of Marissa Mayer, who turns 41 today —
AUGUST 16, 2013 12:01 AM
by JACOB WEISBERG —
"As she works to reverse the fortunes of a failing Silicon Valley
giant, Yahoo’s Marissa Mayer has fueled a national debate
about the office life, motherhood, and what it takes to be the
CEO of the moment.
'I really like even numbers, and
I like heavily divisible numbers.
Twelve is my lucky number—
I just love how divisible it is.
I don’t like odd numbers, and
I really don’t like primes.
When I turned 37,
I put on a strong face, but
I was not looking forward to 37.
But 37 turned out to be a pretty amazing year.
Especially considering that
36 is divisible by twelve!'
A few things may strike you while listening to Marissa Mayer
deliver this riff . . . . "
Yes, they may.
A smaller number for Marissa's meditations:
Six has been known since antiquity as the first "perfect" number.
Why it was so called is of little interest to anyone but historians
of number theory (a discipline that is not, as Wikipedia notes,
to be confused with numerology .)
What part geometry , on the other hand, played in Marissa's education,
I do not know.
Here, for what it's worth, is a figure from a review of posts in this journal
on the key role played by the number six in geometry —
Sunday, May 29, 2016
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 as A is to B so is C to D. AB:CD.
It can see AB relations. But relations in four terms are still
verboten. This amounts to deep occultation of nearly all
human thought for the U.S.A.
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)
A relation in four terms —
A : B :: C : D as Model : Crutch :: Metaphor : Ornament —
Saturday, May 28, 2016
Friday, May 27, 2016
The above passage suggests a meditation on this morning's
New York Times * —
"When shall we three meet again?" — William Shakespeare
“We three have scattered, leaving only me behind
to clean up the scene,” Ms. Yang wrote.
“I am alone, missing us three.” — Amy Qin
A review of the phrase "Innermost Kernel" in this journal
suggests the following meditation …
"Who am I?" — Existential cry
in "Zoolander" and "Zoolander 2."
A similar question occurs in "Peer Gynt" —
Ben Brantley in yesterday morning's print New York Times *
expressed a nihilistic view of Peer as an onion-peeler —
"Toward the end of Ibsen’s 'Peer Gynt,' a saga of self
under siege, the title character is discovered peeling
an onion, finding in the layers of that humble vegetable
a symbol for the chapters of an eventful life . . . .
… [the director’s] approach is the same one that Peer
applies to the onion: Keep stripping until you find the core.
Of course in Peer’s case what is finally found is
plenty of nothing, an apt conclusion for a man
for whom a solid self remains elusive."
I prefer a view from what Fitzgerald called
"the dark fields of the republic" — the Dordt College view —
* The Times — "A version of this review appears in print on May 26, 2016,
on page C3 of the New York edition with the headline:
'A Saga of Self-Identity, Stripped to Its Core, Still Provokes.' "
Thursday, May 26, 2016
Images suggested by the previous post —
Note the name "Dorje" in the first image above.
Remarks related to the name "Dorje," as well as to
"Projective Geometry and PT-Symmetric Dirac Hamiltonian,"
a 2009 paper by Y. Jack Ng and the late Hendrik van Dam —
Remarks for the Church of Synchronology from December 16, 2015,
the date of the above Dorje arXiv upload —
The physicist Hendrik van Dam was mentioned in recent posts.
He reportedly died at 78 on February 11, 2013.
A post from that date, and a followup —
Wednesday, May 25, 2016
"Studies of spin-½ theories in the framework of projective geometry
have been undertaken before." — Y. Jack Ng and H. van Dam,
February 20, 2009
For one such framework,* see posts from that same date
four years earlier — February 20, 2005.
Update of 10:42 PM ET on Sunday, June 19, 2016 —
The above images are precursors to …
Conway and Sloane, 1988
Update of 10 AM ET Sept. 16, 2016 — The excerpt from the
1977 "Diamond Theory" article was added above.
For the Church of Synchronology
From "Projective Geometry and PT-Symmetric Dirac Hamiltonian,"
Y. Jack Ng and H. van Dam,
Physics Letters B , Volume 673, Issue 3,
23 March 2009, Pages 237–239
(http://arxiv.org/abs/0901.2579v2, last revised Feb. 20, 2009)
" Studies of spin-½ theories in the framework of projective geometry
have been undertaken before. See, e.g., Ref. . 1 "
" 1 These papers are rather mathematical and technical.
The authors of the first two papers discuss the Dirac equation
in terms of the Plucker-Klein correspondence between lines of
a three-dimensional projective space and points of a quadric
in a five-dimensional projective space. The last paper shows
that the Dirac equation bears a certain relation to Kummer’s
surface, viz., the structure of the Dirac ring of matrices is
related to that of Kummer’s 166 configuration . . . ."
Proc. Natl. Acad. Sci. USA , 19 (1933), p. 503
Full Text via CrossRef
Proc. Nederl. Akad. Wetensch. , 52 (1949), p. 1135
F.C. Taylor Jr., Master thesis, University of North Carolina
at Chapel Hill (1968), unpublished
A remark of my own on the structure of Kummer’s 166 configuration . . . .
See as well yesterday morning's post.
See also "Box of Nothing" in this journal.
Tuesday, May 24, 2016
The authors Taormina and Wendland in the previous post
discussed some mathematics they apparently did not know was
related to a classic 1905 book by R. W. H. T. Hudson, Kummer's
Quartic Surface .
"This famous book is a prototype for the possibility
of explaining and exploring a many-faceted topic of
research, without focussing on general definitions,
formal techniques, or even fancy machinery. In this
regard, the book still stands as a highly recommendable,
unparalleled introduction to Kummer surfaces, as a
permanent source of inspiration and, last but not least,
as an everlasting symbol of mathematical culture."
— Werner Kleinert, Mathematical Reviews ,
as quoted at Amazon.com
Some 4×4 diagrams from that book are highly relevant to the
discussion by Taormina and Wendland of the 4×4 squares within
the 1974 Miracle Octad Generator of R. T. Curtis that were later,
in 1987, described by Curtis as pictures of the vector 4-space over
the two-element Galois field GF(2).
Hudson did not think of his 4×4 diagrams as illustrating a vector space,
but he did use them to picture certain subsets of the 16 cells in each
diagram that he called Rosenhain and Göpel tetrads .
Some related work of my own (click images for related posts)—
Rosenhain tetrads as 20 of the 35 projective lines in PG(3,2)
Göpel tetrads as 15 of the 35 projective lines in PG(3,2)
Related terminology describing the Göpel tetrads above
Monday, May 23, 2016
A Talking Horse —
What the horse says: "First online: 28 August 2013."
Sunday, May 22, 2016
"(CBS News) Two decades after Morley Safer took
a critical look at contemporary art in his 60 Minutes
story 'Yes…But is it Art?' he has found the definitive
answer to his snide question . . . ."
— March 30, 2012, introduction to a "60 Minutes" piece
dated April 1, 2012
A less metaphysical approach to a "pre-form" —
From Wallace Stevens, "The Man with the Blue Guitar":
And the color, the overcast blue
Of the air, in which the blue guitar
Is a form, described but difficult,
And I am merely a shadow hunched
Above the arrowy, still strings,
The maker of a thing yet to be made . . . .
"Arrowy, still strings" from the diamond theorem
See also "preforming" and the blue guitar
in a post of May 19, 2010.
Update of 7:11 PM ET:
More generally, see posts tagged May 19 Gestalt.
Saturday, May 21, 2016
The previous post suggests two images …
The date of the above Promoted Tweet is October 19, 2015.
"So we beat on, boats against the current …" — F. Scott Fitzgerald
Three reflections suggested by the previous post —
1. A Whit Stillman film mentions favorably Scrooge McDuck —
2. A "promoted tweet" at the Twitter of the previous post's author leads to …
3. The above phrase "New Base" suggests a related literary note —
Friday, May 20, 2016
Updated 10:46 PM ET, Fri., May 20, 2016
" (CNN) Alan Young, who played the hapless yet protective
owner of a talking horse on the popular television comedy
'Mister Ed,' has died at age 96, according to officials at the
Motion Picture & Television Home in Woodland Hills, California.
He died Thursday of natural causes with his children at his side,
the organization said.
Young also was a well-received voice actor, with appearances
as Scrooge McDuck in many Disney productions . . . ."
[McDuck link added.]
For Galatea 2.2 on Eliza Doolittle Day
My Google searches are set to ignore my own private
search history. Still, I am not sure whether others would
see the same results as those below, which do seem to
reflect rather closely my own interests. Google-as-Galatea
perhaps based the search results partly on associations
from this weblog. An exception: the "Family Circus " novel
in the list below. I have not heard of this book before, but
it seems to be a tale analogous to Stephen King's It ,
from which the searched-for quotation below is drawn.
I prefer a different Family Circus.
"… Thursday morning at 7:30 a.m. at a hospice
in Danvers, Massachusetts."
"Danvers is a town in Essex County, Massachusetts,
In a world gone mad it's hard to think right
Read more: Beastie Boys – In A World Gone Mad Lyrics
Illustrations: Thursday's 3:28 AM ET post and …
Thursday, May 19, 2016
The title is a quote from Sir Galahad in
"Monty Python and the Holy Grail."
Immediately following these words …
Note also posts on The Hourglass Code .
This post was suggested by an album cover
mentioned in tonight's New York Times story
on the May 11 death at 73 in London of one
David King , a graphic designer and design historian —
"For the third Hendrix album, 'Electric Ladyland,'
Mr. King commissioned a photograph of 19
nude women, in various sizes and shapes, which
he intended as a rebuttal to the Playboy image of
women. In the United States, it was regarded as
risqué and was replaced with a head shot of Hendrix."
— William Grimes
From a check tonight of The New York Review of Books —
These NYRB stories from May 15 and May 13 suggest a
review of images on Ratner's Star and on the Eye of God.
Above image reposted from Jan. 10, 2014
I. The structures in the Diamond Puzzle…
Click on image for Jungian background.
II: The structure on a recent cover of Semiotica…
Above images reposted from May 5, 2016
Related material: The previous post, Dueling Formulas.
Wednesday, May 18, 2016
Note the echo of Jung's formula in the diamond theorem.
An attempt by Lévi-Strauss to defend his formula —
"… reducing the life of the mind to an abstract game . . . ." —
For a fictional version of such a game, see Das Glasperlenspiel .
Tuesday, May 17, 2016
The originator of the phrase 'Fab Four' reportedly
died at 80 on Saturday, May 14, 2016.
This suggests a review of another noted four-set.
The above image is from a study of Lévi-Strauss's "Canonical Formula" …
[Above photo of Lévi-Strauss and formula added June 6, 2016.]
Monday, May 16, 2016
Click the tweets below for a related news story.
See also this journal on the same weekend —
A sample —
From the Wikipedia article Bauhaus (band) —
(A companion-piece to Fake Eliot.)
"Point number one:
When you hear someone longing for the 'good old days,'
take it with a grain of salt. (Laughter and applause.)
Take it with a grain of salt."
Boris Karloff as a modernist architect in a 1934 horror film —
Sunday, May 15, 2016
The New Yorker
Poems | September 3, 2012 issue
. . . .
"I remember everything.
I remember nothing.
I remember ancient Greek sparkles like a diamond ring."
. . . .
And no fact of Alain Resnais’s life seemed to strike a stranger note than his assertion that the films which first inspired his ambition to become a film director were those in which Fred Astaire and Ginger Rogers danced. Or was it Dick Powell and Ruby Keeler? He could never be sure. “I wondered if I could find the equivalent of that exhilaration,” he recalled.
If he never did it was perhaps because of his highly cultivated attitude to serious cinema. His character and temperament were more attuned to the theory of film and a kind of intellectual square dance* which was far harder to bring to the screen with “exhilaration” than the art of Astaire and Rogers.
*See today's 11 AM ET Sermon.
Saturday, May 14, 2016
From a New York Times obituary this evening —
"She entered Reed College in Portland as a philosophy major.
'I enjoyed it until I ran aground in an aesthetics class,'
Ms. Dunn told Wired magazine. 'I went in thinking, yeah,
art, beauty — my meat, drink and air. But on the first day,
I didn’t understand a word that was said in class, so I
marched out and changed my major to psychology.' "
Could have marched out and bought a dictionary .
A version of the I Ching’s Hexagram 19:
From Katherine Neville's The Eight , a book on the significance
of the date April 4 — the author's birthday —
The Eight by Katherine Neville —
“What does this have to do with why we’re here?”
Related material: Posts now tagged Hourglass Code.
See also the hourglass in a search for Pilgrim's Progress Illustration.
Friday, May 13, 2016
"Just as both tragedy and comedy can be written
by using the same letters of the alphabet, the vast
variety of events in this world can be realized by
the same atoms through their different arrangements
and movements. Geometry and kinematics, which
were made possible by the void, proved to be still
more important in some way than pure being."
— Werner Heisenberg in Physics and Philosophy
For more about geometry and kinematics, see (for instance)
"An introduction to line geometry with applications,"
by Helmut Pottmann, Martin Peternell, and Bahram Ravani,
Computer-Aided Design 31 (1999), 3-16.
The concepts of line geometry (null point, null plane, null polarity,
linear complex, Klein quadric, etc.) are also of interest in finite geometry.
Some small finite spaces have as their natural models arrays of cubes .
Sixties conspiracy theorist Mark Lane reportedly
died at 89 on Tuesday night.
From the previous post, But Seriously . . . —
"Today, we are excited to share the fruits of our research
with the broader community . . . ."
Thursday, May 12, 2016
Google today released on GitHub an English parser,
Parsey McParseface . From Google Research Blog —
"Today, we are excited to share the fruits of our research
with the broader community by releasing SyntaxNet,
an open-source neural network framework implemented in
TensorFlow that provides a foundation for
Natural Language Understanding (NLU) systems.
Our release includes all the code needed to train new
SyntaxNet models on your own data, as well as
Parsey McParseface , an English parser that we have
trained for you and that you can use to analyze English text."
"While the accuracy is not perfect, it’s certainly high enough
to be useful in many applications. The major source of errors
at this point are examples such as the prepositional phrase
attachment ambiguity described above, which require real
world knowledge (e.g. that a street is not likely to be located
in a car) and deep contextual reasoning. Machine learning
(and in particular, neural networks) have made significant
progress in resolving these ambiguities. But our work is still
cut out for us: we would like to develop methods that can
learn world knowledge and enable equal understanding of
natural language across all languages and contexts."
But seriously …
For some historical background, see (for instance) a book by
Ekaterina Ovchinnikova —
Integration of World Knowledge for
Natural Language Understanding ,
Atlantis Press, Springer, 2012.
A PDF of Chapter 2, "Natural Language Understanding
and World Knowledge," is available for download.
The philosophical background is the distinction between
syntax and semantics . See (for instance) …
Wednesday, May 11, 2016
A title I prefer: that of this post, Null Point. *
For related mathematics, see Zero System .
* Wikipedia —
The Kelvin scale is an absolute,
thermodynamic temperature scale
using as its null point absolute zero,
the temperature at which
all thermal motion ceases in the
classical description of thermodynamics.
See also Trinkets.
Continued from Saturday, May 7, 2016 .
From an obituary in yesterday evening's online New York Times —
"I was writing plays, one-acters, about musicians
who were speakers of the idiom I loved most:
black American male speech, full of curse words,"
he wrote in an autobiographical essay. . . .
The obituary is for a poet who reportedly died on Saturday, May 7.
Backstory from Wikipedia — See Black Speech —
"The only example of 'pure' Black Speech is
the inscription upon the One Ring . . .
One Ring to rule them all,
One Ring to find them,
One Ring to bring them all
And in the darkness bind them. "
Tuesday, May 10, 2016
The following passage appeared in this journal
on the night of May 23-24, 2015.
Monday, May 9, 2016
Today's online New York Times describes an authority
figure who reportedly died on Sunday (May 8, 2016) —
"With his preternaturally mature, intelligent but
(by Hollywood standards) unremarkable looks,
he was cast almost from the beginning as an
authority figure — a father or a teacher, a doctor
or a scientist, a mayor or a judge."
This journal on Sunday —
From the online Harvard Crimson this afternoon —
"It's just another manic Monday
I wish it was Sunday
'Cause that's my fun day"
"1975–1977 war Schinz bei UNDP im Irak engagiert,
1977–1980 im Auftrag von Speer-Plan in Saudi-Arabien."
Some backstory —
The three Solomons of the previous post (LeWitt,
Marcus, and Golomb) suggest the three figures
-1, 0, and 1 … symbols for the three elements
of the Galois field GF(3). This in turn suggests a
Search for The Lost Theorem. Some cross-cultural
context: The First of May, 2010.
Sunday, May 8, 2016
Earlier posts have dealt with Solomon Marcus and Solomon Golomb,
both of whom died this year — Marcus on Saint Patrick's Day, and
Golomb on Orthodox Easter Sunday. This suggests a review of
Solomon LeWitt, who died on Catholic Easter Sunday, 2007.
A quote from LeWitt indicates the depth of the word "conceptual"
in his approach to "conceptual art."
From Sol LeWitt: A Retrospective , edited by Gary Garrels, Yale University Press, 2000, p. 376:
THE SQUARE AND THE CUBE
"The best that can be said for either the square or the cube is that they are relatively uninteresting in themselves. Being basic representations of two- and three-dimensional form, they lack the expressive force of other more interesting forms and shapes. They are standard and universally recognized, no initiation being required of the viewer; it is immediately evident that a square is a square and a cube a cube. Released from the necessity of being significant in themselves, they can be better used as grammatical devices from which the work may proceed."
"Reprinted from Lucy R. Lippard et al ., “Homage to the Square,” Art in America 55, No. 4 (July-August 1967): 54. (LeWitt’s contribution was originally untitled.)"
See also the Cullinane models of some small Galois spaces —
„Ich begriff plötzlich, daß in der Sprache oder doch
mindestens im Geist des Glasperlenspiels tatsächlich
alles allbedeutend sei, daß jedes Symbol und jede
Kombination von Symbolen nicht hierhin oder dorthin,
nicht zu einzelnen Beispielen, Experimenten und
Beweisen führe, sondern ins Zentrum, ins Geheimnis
und Innerste der Welt, in das Urwissen. Jeder Übergang
von Dur zu Moll in einer Sonate, jede Wandlung eines
Mythos oder eines Kultes, jede klassische, künstlerische
Formulierung sei, so erkannte ich im Blitz jenes
Augenblicks, bei echter meditativer Betrachtung,
nichts andres als ein unmittelbarer Weg ins Innere
des Weltgeheimnisses, wo im Hin und Wider zwischen
Ein- und Ausatmen, zwischen Himmel und Erde,
zwischen Yin und Yang sich ewig das Heilige vollzieht.“
Saturday, May 7, 2016
Friday, May 6, 2016
Thanks to some British computer foul-up, today's Telegraph 's
"Latest obituaries by syndication" include election results—
"Again, in spite of that, we call this Friday good."
— T. S. Eliot, Four Quartets
From this journal on Orthodox Good Friday, 2016,
an image from New Scientist on St. Andrew's Day, 2015 —
From an old Dick Tracy strip —
" There is a pleasantly discursive treatment
of Pontius Pilate’s unanswered question
‘What is truth?’ ”
— Coxeter, 1987, introduction to Trudeau’s
The Non-Euclidean Revolution
Thursday, May 5, 2016
Excerpt from a post of November 4, 2009 —
I. The structures in the Diamond Puzzle…
Click on image for Jungian background.
II: The structure on a recent cover of Semiotica…
For some related material, see a search
for Solomon Marcus in this journal.
Wednesday, May 4, 2016
"Kroto is believed to have died on Saturday, April 30.
Responding to the news on Twitter, Prof Brian Cox
tweeted: 'RIP Harry Kroto – brilliant scientist and a
strong, passionate advocate for science as a vital
part of our culture.' — The Guardian
See also Walpurgisnacht 2016 in this journal.
Update of 10:45 PM — Some related pure mathematics :
"Stencil’s entire existence is focused on the hunt for V.,
a classic novelistic quest-without-resolution (in fact, V.
might be fiction’s greatest example of a MacGuffin). V.
may be a person, or may be a place, though it could
also be neither: Pynchon calls it, at one point,
'a remarkably scattered concept' and, at another,
'the ultimate Plot Which Has No Name.' "
— Alexander Nazaryan in The New Yorker ,
article dated March 29, 2013
How about a date ?
From this journal on Good Friday, March 29, 2013 —
From the webpage Diamond Theory Bibliography —
Golomb, Solomon W.
Shift register sequences (Revised edition)
Aegean Park Press, Laguna Hills, CA, 1982
The fifteen "stencils" in Golomb's Fig. VIII-8, page 219,
are the same as the fifteen affine hyperplanes that
account for patterns' symmetry in diamond theory.
This figure occurs in a discussion of Rademacher-
Material related to the previous post, "Symmetry" —
This is the group of "8 rigid motions
generated by reflections in midplanes"
of "Solomon's Cube."
Material from this journal on May 1, the date of Golomb's death —
"Weitere Informationen zu diesem Themenkreis
finden sich unter http://www.encyclopediaofmath.org/
Tuesday, May 3, 2016
“"I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”
A less poetic meditation on the above web page* —
"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."
Update of Sept. 5, 2016 — See also a related remark
by Lévi-Strauss in 1955: "…three different readings
become possible: left to right, top to bottom, front
* For the underlying mathematics, see a June 21, 1983, research note.
Monday, May 2, 2016
The previous post, on subjective and objective quality,
suggests a review of Pirsig —
"And finally: Phaedrus, following a path
that to his knowledge had never been taken before
in the history of Western thought,
went straight between the horns of
the subjectivity-objectivity dilemma and said
Quality is neither a part of mind, nor is it a part of matter.
It is a third entity which is independent of the two.
He was heard along the corridors
and up and down the stairs of Montana Hall
singing softly to himself, almost under his breath,
'Holy, holy, holy…blessed Trinity.' "
Siobhan Roberts recently wrote a book about the first of these
authors, Conway. I just discovered that last fall she also had an
article about the second author, Sloane, published:
"How to Build a Search Engine for Mathematics,"
Nautilus , Oct 22, 2015.
Meanwhile, in this journal …
Log24 on that same date, Oct. 22, 2015 —
Roberts's remarks on Conway and later on Sloane are perhaps
examples of subjective quality, as opposed to the objective quality
sought, if not found, by Alexander, and exemplified by the
above bijection discussed here last October.
Sunday, May 1, 2016
“What would an organic Christian Sabbath look like today?”
The 2015 German edition of Beautiful Mathematics ,
a 2011 Mathematical Association of America (MAA) book,
was retitled Mathematische Appetithäppchen —
Mathematical Appetizers . The German edition mentions
the author's source, omitted in the original American edition,
for his section 5.17, "A Group of Operations" (in German,
5.17, "Eine Gruppe von Operationen") —
Autor: Erickson, Martin —
"Weitere Informationen zu diesem Themenkreis finden sich
That source was a document that has been on the Web
since 2002. The document was submitted to the MAA
in 1984 but was rejected. The German edition omits the
document's title, and describes it as merely a source for
"further information on this subject area."
The title of the document, "Binary Coordinate Systems,"
is highly relevant to figure 11.16c on page 312 of a book
published four years after the document was written: the
1988 first edition of Sphere Packings, Lattices and Groups ,
by J. H. Conway and N. J. A. Sloane —
A passage from the 1984 document —