A very brief introduction:
Tuesday, May 31, 2016
Und Dann …
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 —
Wild Devising
"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 —
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Entertainment in Plato’s Cave
"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
See also the number 6 in yesterday's posts,
Perfect Number and Perfect Universe.
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Monday, May 30, 2016
Perfect Universe
(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.
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Perfect Number
"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 —
VOGUE Magazine,
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 —
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Sunday, May 29, 2016
The Ideogram Principle …
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 —
See also Dueling Formulas and Symmetry.
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Saturday, May 28, 2016
Friday, May 27, 2016
Raiders of the Lost Crucible…
For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.
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
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Peer Review
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.' "
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Thursday, May 26, 2016
Dorje
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 —
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Expanding the Spielraum
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 —
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Wednesday, May 25, 2016
Framework
"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.
* A 4×4 array. See the 1977, 1978, and 1986 versions by
Steven H. Cullinane, the 1987 version by R. T. Curtis, and
the 1988 Conway-Sloane version illustrated below —
Cullinane, 1977
Cullinane, 1978
Cullinane, 1986
Curtis, 1987
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.
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Crucifers
For the Church of Synchronology
Marissa Mayer, as illustrated on the cover
of the current issue of Variety , and
Mira Sorvino, as discussed in posts of
Feb. 20, 2009 (a date suggested by the
arXiv upload date in the previous post).
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Kummer and Dirac
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. [4]. 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 . . . ."
[4]
O. Veblen
Proc. Natl. Acad. Sci. USA , 19 (1933), p. 503
Full Text via CrossRef
E.M. Bruins
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.
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Nothing Illustrated
Illustration by Javier Jaén
See also "Box of Nothing" in this journal.
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Tuesday, May 24, 2016
Rosenhain and Göpel Revisited
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
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Monday, May 23, 2016
Springer
In memory of the late mathematician John Nash
and of the late actor Alan Young ...
A Talking Horse —
What the horse says: "First online: 28 August 2013."
See also Overarching, Psychonauts, and Spider Tale in this journal.
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Sunday, May 22, 2016
Definitive
"(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
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Sunday School
A less metaphysical approach to a "pre-form" —
From Wallace Stevens, "The Man with the Blue Guitar":
IX
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.
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Saturday, May 21, 2016
Fitzgerald and Paris
The previous post suggests two images …
The date of the above Promoted Tweet is October 19, 2015.
For the Church of Synchronology, an image from Log24 on that date:
"So we beat on, boats against the current …" — F. Scott Fitzgerald
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New Base
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 —
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Friday, May 20, 2016
Well Received
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.]
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It from Bit*
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.
* A phrase coined by the late John Archibald Wheeler.
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20
"… Thursday morning at 7:30 a.m. at a hospice
in Danvers, Massachusetts."
Read more: http://www.rollingstone.com/music/news/
original-beastie-boys-member-john-berry-dead-at-52-20160519
From a search for Danvers in this journal, two quotations
for Stephen King fans …
|
"Danvers is a town in Essex County, Massachusetts, |
[CHORUS]
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 …
THE HOURGLASS CODE
(Sketch for a favicon)
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