See as well a search in this journal for Frost at Wanganui.
Saturday, February 17, 2018
Frosties: A Sequel to “Frozen”
God’s Dice
On a Trinity classmate of Ian Macdonald (see previous post)—
Atiyah's eulogy of Shaw in Trinity Annual Record 2017
is on pages 137 through 146. The conclusion —
Friday, February 16, 2018
Two Kinds of Symmetry
The Institute for Advanced Study (IAS) at Princeton in its Fall 2015 Letter
revived "Beautiful Mathematics" as a title:
This ugly phrase was earlier used by Truman State University
professor Martin Erickson as a book title. See below.
In the same IAS Fall 2015 Letter appear the following remarks
by Freeman Dyson —
". . . a special case of a much deeper connection that Ian Macdonald
discovered between two kinds of symmetry which we call modular and affine.
The two kinds of symmetry were originally found in separate parts of science,
modular in pure mathematics and affine in physics. Modular symmetry is
displayed for everyone to see in the drawings of flying angels and devils
by the artist Maurits Escher. Escher understood the mathematics and got the
details right. Affine symmetry is displayed in the peculiar groupings of particles
created by physicists with high-energy accelerators. The mathematician
Robert Langlands was the first to conjecture a connection between these and
other kinds of symmetry. . . ." (Wikipedia link added.)
The adjective "modular" might aptly be applied to . . .
The adjective "affine" might aptly be applied to . . .
The geometry of the 4×4 square combines modular symmetry
(i.e., related to theta functions) with the affine symmetry above.
Hudson's 1905 discussion of modular symmetry (that of Rosenhain
tetrads and Göpel tetrads) in the 4×4 square used a parametrization
of that square by the digit 0 and the fifteen 2-subsets of a 6-set, but
did not discuss the 4×4 square as an affine space.
For the connection of the 15 Kummer modular 2-subsets with the 16-
element affine space over the two-element Galois field GF(2), see my note
of May 26, 1986, "The 2-subsets of a 6-set are the points of a PG(3,2)" —
— and the affine structure in the 1979 AMS abstract
"Symmetry invariance in a diamond ring" —
For some historical background on the symmetry investigations by
Dyson and Macdonald, see Dyson's 1972 article "MIssed Opportunities."
For Macdonald's own use of the words "modular" and "affine," see
Macdonald, I. G., "Affine Lie algebras and modular forms,"
Séminaire N. Bourbaki , Vol. 23 (1980-1981), Talk no. 577, pp. 258-276.
Nicht Spielerei
"What of the night
That lights and dims the stars?
Do you know, Hans Christian,
Now that you see the night?"
— The concluding lines of
"Sonatina to Hans Christian,"
by Wallace Stevens
(in Harmonium (second edition, 1931))
". . . in the end the space itself is the star. . . ."
Related material — The death Tuesday night
of Prince Consort Henrik of Denmark, and the
New Year's Eve speech on Dec. 31, 2015, of
Queen Margrethe II of Denmark.
Distantly related material — Yesterday morning's
post The Search for Child's Play.
Thursday, February 15, 2018
The Search for Child’s Play
Yesterday morning's post "Child's Play" suggests . . .
— "Love is an Open Door," from Disney's "Frozen"
Wednesday, February 14, 2018
Child’s Play
From a search for Child's Play in this journal —
See also the previous post.
Tuesday, February 13, 2018
Babble On
Symbology for Tom Hanks and for a Latin teacher
who reportedly died on Saturday, Feb. 10, 2018 —
Click the image below to search Log24 for "green fields."
See also Space Cross.
Attention Must Be Paid
For the late Anne M. Treisman, who reportedly died Friday, Feb. 9:
From "A Feature-Integration Theory of Attention" —
"The controversy between analytic and synthetic theories
of perception goes back many years: the Associationists
asserted that the experience of complex wholes is built
by combining more elementary sensations, while the
Gestalt psychologists claimed that the whole precedes
its parts, that we initially register unitary objects and
relationships, and only later, if necessary, analyze these
objects into their component parts or properties. This view
is still active now . . . ."
— Anne M. Treisman, University of British Columbia,
and Garry Gelade, Oxford University, in
Cognitive Psychology 12, 97-136 (1980)
"Before time began, there was the Cube." — Optimus Prime
A Titan of the Field
On the late Cambridge astronomer Donald Lynden-Bell — "As an academic at a time when students listened and lecturers lectured, he had the disconcerting habit of instead picking on a random undergraduate and testing them on the topic. One former student, now a professor, remembered how he would 'ask on-the-spot questions while announcing that his daughter would solve these problems at the breakfast table'. He got away with it because he was genuinely interested in the work of his colleagues and students, and came to be viewed with great affection by them. He also got away with it because he was well established as a titan of the field." — The London Times on Feb. 8, 2018, at 5 PM (British time) |
Related material —
Two Log24 posts from yesteday, Art Wars and The Void.
See as well the field GF(9) …
… and the 3×3 grid as a symbol of Apollo
(an Olympian rather than a Titan) —
Monday, February 12, 2018
The Void
In memory of Professor Donald Lynden-Bell,
Emeritus Professor of Astrophysics at the University of Cambridge
Lynden-Bell with colleagues at Meteor Crater, Arizona, reportedly in 1960 —
Lynden-Bell was one of the subjects of the 2015 film "Star Men."
Related material —
"After peering into the void from a perch
outside the visitor center, young Henry, 9,
said he liked the rugged landscape.
'It’s a good place to film a space movie,' he said.
Funny he should mention that —
the crater was the setting for the climactic scenes
of the 1984 sci-fi film 'Starman,' with Jeff Bridges
and Karen Allen arriving for a rendezvous with
an alien mother ship."
— Henry Fountain in The New York Times , Jan. 22, 2009
Lynden-Bell reportedly died at 82 on Feb. 5, 2018 (British time).
See as well this journal on that date.
Sunday, February 11, 2018
Visions of Hell
In memory of a Manhattan art figure
who reportedly died on
Wednesday, February Seventh, 2018 —
ABOUT 'ASCENSION VARIATIONS'
“Ascension Variations is a magical adventure
woven from grand and pedestrian touches, and
in the end the space itself is the star —
or Ms. Monk's transformation of it.
For an hour, we've lived in a spiral,
where up is down and down is up.
It's a sacred place.”
— Gia Kourlas, The New York Times , March 6, 2009
See also the previous post — yesterday's Into the Upside Down —
and two posts of February Seventh:
Conceptual Art and Conceptual Minimalism.
For some related artistic remarks, see this journal on March 6-7, 2009.
Saturday, February 10, 2018
Into the Upside Down
(Title suggested by the TV series Stranger Things )
" 'Untitled' (2016) is the most recent painting in the show
and includes one of Mr. Johns’s recurring images of a ruler."
— Image caption in an article by Deborah Solomon
in The New York Times online, Feb. 7, 2018
From a Log24 search for "Ruler" —
Related art —
See also, in this journal, Magic Mountain and Davos.
Wednesday, February 7, 2018
Village Voices
Conceptual Minimalism
"At the point of convergence by Octavio Paz, translated by Helen Lane
|
See also AS IS.
Conceptual Art
Related conceptual art —
Tom Wolfe in The Painted Word :
Click the automat image above to enlarge.
See as well a new retrospective at Facebook.
Tuesday, February 6, 2018
For Times Square Church*
The metaphor for metamorphosis no keys unlock.
— Steven H. Cullinane, "Endgame"
* See Times Square Church in this journal and
the posts of July 2010. Related material:
A Monday night death —
Monday, February 5, 2018
Stranger Things than Pulp Fiction
Click on the image for a
relevant Wallace Stevens poem.
A new Facebook page will describe
some background for the above image.
Sunday, February 4, 2018
Logos for Sunday, February 4
"The walls in the back of the room show geometric shapes
that remind us of the logos on a space shuttle. "
— Web page on an Oslo art installation by Josefine Lyche.
See also Subway Art posts.
The translation above was obtained via Google.
The Norwegian original —
"På veggene bakerst i rommer vises geometriske former
som kan minne om logoene på en romferge."
Related logos — Modal Diamond Box in this journal:
Logos for Philosophers
(Suggested by Modal Logic) —
Friday, February 2, 2018
For 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
Friday, January 26, 2018
Shadows and Reflections
From the post "For Guy Noir" of Wednesday morning, January 24 —
"as privileged viewers of the shadows and reflections"
Related material —
The death on January 24 of a famed ski film maker,
and the Sun Valley icon below (one of a pair of ski
location icons by Wink, a Minneapolis design firm).
Thursday, January 25, 2018
Our Class
See earlier posts now also tagged O.C.D. .
Related material —
Beware of Analogical Extension
"By an archetype I mean a systematic repertoire
of ideas by means of which a given thinker describes,
by analogical extension , some domain to which
those ideas do not immediately and literally apply."
— Max Black in Models and Metaphors
(Cornell, 1962, p. 241)
"Others … spoke of 'ultimate frames of reference' …."
— Ibid.
A "frame of reference" for the concept four quartets —
A less reputable analogical extension of the same
frame of reference —
Madeleine L'Engle in A Swiftly Tilting Planet :
"… deep in concentration, bent over the model
they were building of a tesseract:
the square squared, and squared again…."
See also the phrase Galois tesseract .
Wednesday, January 24, 2018
The Pentagram Papers
From a Log24 post of March 4, 2008 —
SINGER, ISAAC:
"Sets forth his own aims in writing for children and laments
— An Annotated Listing of Criticism
"She returned the smile, then looked across the room to
— A Swiftly Tilting Planet,
For "the dimension of time," see A Fold in Time, Time Fold,
A Swiftly Tilting Planet is a fantasy for children |
Ibid. —
The pen's point:
John Trever, Albuquerque Journal, 2/29/08
Note the figure on the cover of National Review above —
A related figure from Pentagram Design —
See, more generally, Isaac Singer in this journal.
For Guy Noir
From a search for Limerick in this journal —
"C A V E S is an exhibition of three large scale works,
each designed to immerse the viewer, and then to
confront the audience with a question regarding how far
they, as privileged viewers of the shadows and reflections
being played out upon the walls, are willing to allow
themselves to believe what they know to be a false reality."
Tuesday, January 23, 2018
Spielfeld
For the original Davos icon by Wink-Minneapolis,
see the previous post.
For related geometry, see posts tagged Barth Art.
Monday, January 22, 2018
Hollywood Moment
A death on the date of the above symmetry chat,
Wednesday, August 17, 2016 —
An Hispanic Hollywood moment:
Ojo de Dios —
Click for related material.
For further Hispanic entertainment,
see Ben Affleck sing
"Aquellos Ojos Verdes "
in "Hollywoodland."
Sunday, January 21, 2018
At Which Point
"In 'Sophistry,' a new play by Jonathan Marc Sherman
at the Playwrights Horizons Studio, a popular tenured
professor stands accused of sexual harassment
by a male student."
— Frank Rich in The New York Times , theater review
on October 12, 1993
"At which point another play, inchoate but arresting,
edges into view." — Rich, ibid.
"Johansson began acting during childhood,
after her mother started taking her to auditions.
She made her professional acting debut
at the age of eight in the off-Broadway production
of 'Sophistry' with Ethan Hawke, at New York's
Playwrights Horizons."
— IMDb Mini Biography by: Pedro Borges
" 'Suddenly, I was 19 again and I started to remember
all the men I'd known who had taken advantage of
the fact that I was a young woman who didn't yet have
the tools to say no, or to understand the value of
my own self-worth,' the Avengers star described.
'I had many relationships both personal and professional
where the power dynamic was so off that I had to create
a narrative in which I was the cool girl who could hang in
and hang out, and that sometimes meant compromising
what felt right for me . . . . ' "
— Scarlett Johansson yesterday at the 2018 Women's March
in Los Angeles, as reported in E! News .
Image in a Log24 post
of March 12, 2009.
Spiritual Memoir
In her new spiritual memoir . . . .
Armies of the Night —
Armies of the Day —
Cole Porter —
Night and Day —
Saturday, January 20, 2018
The Chaos Symbol of Dan Brown
In the following passage, Dan Brown claims that an eight-ray star
with arrowheads at the rays’ ends is “the mathematical symbol for
entropy.” Brown may have first encountered this symbol at a
questionable “Sacred Science” website. Wikipedia discusses
some even less respectable uses of the symbol.
Related news —
Related symbolism —
A star figure and the Galois quaternion.
The square root of the former is the latter.
Friday, January 19, 2018
The Pentagram Papers
Jodie Foster in a Dec. 15, 2017, sketch with Stephen Colbert —
"People invest in and take ownership of brands,
and they wonder why the brand didn’t
ask their permission to change."
— Michael Bierut of Pentagram Design
in a Design Week article of Jan. 17, 2018
Thursday, January 18, 2018
A Phrase That Might Have Been
The online New York Times reports this afternoon
the death of a production designer on January 9th —
"In addition to the two Oscars Mr. Marsh won
(which he shared with others), he was nominated
for two more: for 'Scrooge' (1970), with Albert Finney and
Alex [sic ] Guinness, and 'Mary, Queen of Scots' (1971),
with Vanessa Redgrave and Glenda Jackson."
"… The Little Broomstick by Mary Stewart,
illustrated by Shirley Hughes, published Brockhampton 1971.
The story is about Mary, staying at Great-Aunt Charlotte's house,
bored until she meets the black cat Tib and finds the purple flower
fly-by-night that makes the little broomstick fly. In chapter 10
'gay go up and gay go down' Mary hides in Endor College,
the witch school, after hours and finds Tib transformed into a frog
(Madame Mumblechook had taken him from her as her entry fee).
She recites the Master Spell to release him. ' It was a simple,
gay little rhyme, and it ended on a phrase that might have been
(but wasn't) "the dancing ring of days".' "
"Bah, humbug!" — A Christmas Carol
Wednesday, January 17, 2018
Language Game
Continued from Zen and Language Games
(a post of May 2, 2003, written on March 1, 2002)
From The Harvard Crimson on St. Andrew's Day 2017 —
See also a larger, clearer view of the titles in the above file photo.
Dialogue suggested by the above Harvard Crimson line
"I am a book today . . . . I know it all." —
A problem child* of sorts in the 2017 film "Gifted" —
Mary- "Maybe this school isn't as great as you think it is." Mary is returned to the place of her examination. Professor- "Mary, you knew that the problem was incorrect, why didn't you say anything?" Mary- "Frank says I'm not supposed to correct older people. Nobody likes a smart-ass."
* "Problem Child" was a working title related to a novel
Heinlein wrote in 1941, Beyond This Horizon —
“Before Time Began, There Was the Cube”
See Eightfold Froebel.
At Heaven’s Gate
(Continued from September 12, 2005)
The previous post contrasted the number-triple 11-7-8 below
with number triples 12-9-5 and 12-5-9.
A perhaps more logical counterpart of the triple 11-7-8, based
on opposite locations of star-points or cube-edges, is
the triple 9-12-5. For a theological interpretation, see 9/12/05.
Tuesday, January 16, 2018
An Orison for Ha-Why
Lines from characters played in the film by Tom Hanks and Halle Berry —
— Cloud Atlas , by David Mitchell (2004).
An orison of sorts from a post on Martin Scorsese's
birthday, Sunday, Nov. 18, 2007 —
Displayed on the BlackBerry are parts
of Log24 posts from October 25, 2007,
and October 24, 2007.
Related pattern geometry
From a Log24 search for Angleton + Brotherhood:
A photo of Angleton in a post from 12/9/5 —
From a post of 11/7/8 —
A cryptic note for Dan Brown:
The above dates 11/7/8 and 12/9/5 correspond to the corner-labels
(read clockwise and counter-clockwise) of the two large triangles
in the Finkelstein Talisman —
Above: More symbology for Tom Hanks from
this morning's post The Pentagram Papers.
The above symbology is perhaps better suited to Hanks in his
role as Forrest Gump than in his current role as Ben Bradlee.
For Hanks as Dan Brown's Harvard symbologist
Robert Langdon, see the interpretation 12/5/9, rather
than 12/9/5, of the above triangle/cube-corner label.
The Pentagram Papers
Other intersection-points-counting material —
See also Hanks + Cube in this journal —
Game
"There was a game we used to play . . . ."
— The Cranberries on "Charmed,"
Season 2, Episode 5 (aired Nov. 4, 1999)
Monday, January 15, 2018
Boston News
Related material in this journal —
The final link in a post of 8:07 AM ET on Friday, June 27, 2008,
pointed to http://www.gateofheavenparish.com. That 2008 link
now leads to a more recent, quite different, webpage.
The page that the link led to in 2008 is now archived at
https://web.archive.org/web/20080509125920/
http://www.gateofheavenparish.com/.
Sunday, January 14, 2018
Horizon
Plea
Ken Yuszkus, Salem News staff photo
SALEM — The former MIT professor from Hamilton
accused of trying to swindle his son’s widow and children
out of nearly $5 million pleaded not guilty to the charges
on Friday in Salem Superior Court.
John Donovan Sr., 75, was clutching a set of rosary beads
as he entered his plea before Judge Timothy Feeley.
Donovan was indicted last month by an Essex County grand jury
on 13 counts, including larceny, forgery and witness intimidation.
. . . .
— Julie Manganis, Salem News staff writer, Jan. 13, 2018
See also other posts tagged Systems Programming.
Saturday, January 13, 2018
Charmed
From an obituary in this morning's online New York Times —
"John Tunney seemed to have a charmed political life until 1976,
when at age 42 he lost his Senate seat after just one term
to the unlikeliest of Republican challengers, a former Democrat
named Samuel I. Hayakawa."
Topology punchline —
"Sorry, but A is closed."
For more tasteless mathematical humor, see . . .
Friday, January 12, 2018
Twelfth Tradition for San Diego
From The New York Times online last October —
"A version of this article appears in print on October 6, 2017,
on Page A1 of the New York edition with the headline:
Genre-Spanning Author of ‘The Remains of the Day’
Wins Nobel."
From The San Diego Union-Tribune on that October 6th —
"UC San Diego is mourning the loss of mathematician Jeff Remmel,
who died unexpectedly on Sept. 29th."
From Log24 on that Sept. 29th —
Principles Before Personalities:
Some Remarks for Science Addicts.
Thursday, January 11, 2018
The Bourne Report
From the Hannah Goldfield link in today's 7 AM ET
post "In the Bag" —
"… the bride . . . . is a daughter of Gaylord Bourne and
Carl Goldfield of New Haven."
— Wedding story, New York Times , Oct. 18, 2015
A search indicates that Bourne may be the person of that name
associated with Achievement First charter schools.
Here is a related story from today's online New York Times —
"Can a ‘No Excuses’ Charter Teach Students
to Think for Themselves?" (11:40 AM ET)
Upper West Side Story Continues
In memory of a resident of the Upper West Side
who reportedly died on Twelfth Night 2018 —
“… the horizon is not the limit of meaning,
but that which extends meaning
from what is directly given
to the whole context in which it is given,
including a sense of a world.”
— David Vessey, Department of Philosophy,
Grand Valley State University,
Gadamer and the Fusion of Horizons,
International Journal of Philosophical Studies,
17/4 (2009), 531-42.
In the Bag
See as well Hannah Goldfield as Pennywise the Dancing Clown
in this morning's online New York Times —
<meta property="og:description" content="Life doesn’t present us
with many opportunities to put to use the facts that we know
for no other reason than that we know them." />
<meta property="article:published" itemprop="datePublished"
content="2018-01-11T05:00:26-05:00" />
Grab-Bag
In a new film, "The Commuter," Liam Neeson fights
a conspiracy …
"so vast and preposterous that it becomes
nothing more than a grab-bag of plot twists."
— A. O. Scott in The New York Times , 5 AM Jan. 11
Update of 6:29 AM —
Wednesday, January 10, 2018
Logos
Updates of 9:40 PM ET Jan. 10
to 5:45 AM ET the next day:
See a letter from the AMS on their new logo.
Recent revision (pre-2018) of the former AMS logo
The Society's letter describes perceptions of the pre-2018 logo —
"… market research on our current logo revealed that
the connection between a Greek temple and
a mathematical society has become increasingly tenuous
among non-members and younger mathematicians, who
associate the Greek temple with a financial institution."
The omission of the alleged motto of Plato's Academy,
AGEOMETRETOS ME EISITO, in the recent (pre-2018)
revision of the logo was part of the Society's ongoing
process of politically correct dumbing-down. That omission
may have influenced the perception of the logo as picturing
a Greek temple rather than the Academy.
Some related remarks from 2005 —
Tuesday, January 9, 2018
Unpleasantly Discursive
Background for the remarks of Koen Thas in the previous post —
Schumacher and Westmoreland, "Modal Quantum Theory" (2010).
Related material —
" 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
The whole truth may require an unpleasantly discursive treatment.
Example —
1. The reported death on Friday, Jan. 5, 2018, of a dancer
closely associated with George Balanchine
2. This journal on Friday, Jan. 5, 2018:
3. Illustration from a search related to the above dancer:
4. "Per Mare Per Terras" — Clan slogan above, illustrated with
what looks like a cross-dagger.
"Unsheathe your dagger definitions." — James Joyce.
5. Discursive remarks on quantum theory by the above
Schumacher and Westmoreland:
6. "How much story do you want?" — George Balanchine
Koen Thas and Quantum Theory
This post supplies some background for earlier posts tagged
Quantum Tesseract Theorem.
Monday, January 8, 2018
Raiders of the Lost Theorem
The Quantum Tesseract Theorem —
Raiders —
A Wrinkle in Time
starring Storm Reid,
Reese Witherspoon,
Oprah Winfrey &
Mindy Kaling
Time Magazine December 25, 2017 – January 1, 2018
The Overnight Case
The previous post suggests a look at a baggage tale
from this evening's New York Times —
"Domestic airlines hoped to reunite all bags at the airport
with their owners by the end of Monday."
Sunday, January 7, 2018
Saturday, January 6, 2018
Report from Red Mountain
Tom Wolfe in The Painted Word (1975):
“It is important to repeat that Greenberg and Rosenberg
did not create their theories in a vacuum or simply turn up
with them one day like tablets brought down from atop
Green Mountain or Red Mountain (as B. H. Friedman once
called the two men). As tout le monde understood, they
were not only theories but … hot news,
straight from the studios, from the scene.”
Harold Rosenberg in The New Yorker (click to enlarge)—
See also Interality and the Eightfold Cube .
Yale News
The Yale of the title is not the university, but rather the
mathematician Paul B. Yale. Yale's illustration of the Fano
plane is below.
A different illustration from a mathematician named Greenberg —
This illustration of the ominous phrase "line at infinity"
may serve as a sort of Deathly Hallows for Greenberg.
According to the AMS website yesterday, he died on
December 12, 2017:
A search of this journal for Greenberg yields no mention of
the dead mathematician, but does yield some remarks
on art that are pehaps less bleak than the above illustration.
For instance —
Art adapted from the Google search screen. Discuss.
Friday, January 5, 2018
Tamagawa
Wikipedia — "Tamagawa's doctoral students included
Doris Schattschneider and Audrey Terras."
See also Schattschneider and Terras in this journal.
Subway Art for Plato’s Ghost
Subway Art Continues
Subway art related to an event of January 3, 2018 —
Monday, November 7, 2016
|
Types of Ambiguity
From "The Principle of Sufficient Reason," by George David Birkhoff,
in "Three Public Lectures on Scientific Subjects,"
delivered at the Rice Institute, March 6, 7, and 8, 1940 —
From the same lecture —
Up to the present point my aim has been to consider a variety of applications of the Principle of Sufficient Reason, without attempting any precise formulation of the Principle itself. With these applications in mind I will venture to formulate the Principle and a related Heuristic Conjecture in quasi-mathematical form as follows: PRINCIPLE OF SUFFICIENT REASON. If there appears in any theory T a set of ambiguously determined ( i e . symmetrically entering) variables, then these variables can themselves be determined only to the extent allowed by the corresponding group G. Consequently any problem concerning these variables which has a uniquely determined solution, must itself be formulated so as to be unchanged by the operations of the group G ( i e . must involve the variables symmetrically). HEURISTIC CONJECTURE. The final form of any scientific theory T is: (1) based on a few simple postulates; and (2) contains an extensive ambiguity, associated symmetry, and underlying group G, in such wise that, if the language and laws of the theory of groups be taken for granted, the whole theory T appears as nearly self-evident in virtue of the above Principle. The Principle of Sufficient Reason and the Heuristic Conjecture, as just formulated, have the advantage of not involving excessively subjective ideas, while at the same time retaining the essential kernel of the matter. In my opinion it is essentially this principle and this conjecture which are destined always to operate as the basic criteria for the scientist in extending our knowledge and understanding of the world. It is also my belief that, in so far as there is anything definite in the realm of Metaphysics, it will consist in further applications of the same general type. This general conclusion may be given the following suggestive symbolic form:
While the skillful metaphysical use of the Principle must always be regarded as of dubious logical status, nevertheless I believe it will remain the most important weapon of the philosopher. |
Related remarks by a founding member of the Metaphysical Club:
See also the previous post, "Seven Types of Interality."
Seven Types of Interality*
* See the term interality in this journal.
For many synonyms, see
“The Human Seriousness of Interality,”
by Peter Zhang, Grand Valley State University,
China Media Research 11(2), 2015, 93-103.
Thursday, January 4, 2018
Perspectives from a Chinese Jar
" . . . Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness."
— T. S. Eliot, Four Quartets
"The Grand Valley spirit never dies."
— Adapted from the Tao Te Ching
For T. S. Eliot
“I need a photo opportunity, I want a shot at redemption.
Don’t want to end up a cartoon in a cartoon graveyard.”
— Paul Simon
For a Cartoon Graveyard
“… the horizon is not the limit of meaning,
but that which extends meaning
from what is directly given
to the whole context in which it is given,
including a sense of a world.”
— David Vessey,
Gadamer and the Fusion of Horizons
(Quoted here on Saturday, June 4, 2005.)
Tuesday, January 2, 2018
Hell and Easter
This post was suggested by the reported Monday, Jan. 1, 2018,
death of the Juilliard String Quartet founding violinist and by the
reported Thursday, Feb. 25, 2016 death of his brother, a
biotech entrepreneur.
Details from Feb. 25-26, 2016 —
Related material from this evening's New York Times —
The archaeologist above reportedly died on Friday, Dec. 29, 2016.
See too a Log24 post from that date, On Becket's Day.
Debs and Redhead
The above images were suggested in part by the birthdays
on Sept. 21, 2011, of Bill Murray and Stephen King.
More seriously, also in this journal on that date, from a post
titled Symmetric Generation —
Monday, January 1, 2018
Diamond Theory 1976
The first 12 pages of my 1976 preprint "Diamond Theory" are
now scanned and uploaded. See a slideshow.
For downloading, all 12 pages are combined in a PDF.
Sunday, December 31, 2017
Where Parallels Meet
The previous post, together with a New York Times report on
an Upper West Side figure's death on Friday, suggests a review . . .
Related material —
Illustrations from a post of Oct. 11, 2010 —
Ich, Du, etc., etc.
Recent posts involving the English pronoun IT referred to
classic tales of horror by Madeleine L'Engle and Stephen King.
Those posts suggest some further remarks by Martin Buber:
THE WORLD IS TWOFOLD for man
in accordance with his twofold attitude.
The attitude of man is twofold
in accordance with the two basic words he can speak.
The basic words are not single words but word pairs.
One basic word is the word pair I-You.
The other basic word is the word pair I-It;
but this basic word is not changed when
He or She takes the place of It.
Thus the I of man is also twofold.
For the I of the basic word I-You is different from
that in the basic word I-It.
— Buber, Martin. I and Thou, Trans. Kaufmann
(p. 53). Kindle Edition.
Four German pronouns from the above passage
by Martin Buber lead to six pronoun pairs:
ich-du, ich-es, ich-sie, du-es, du-sie, es-sie.
This is in accordance with some 1974 remarks by
Marie-Louise von Franz —
The following passage by Buber may confuse readers of
L'Engle and King with its use, in translation, of "it" instead of
the original German "sie" ("she," corresponding to "die Welt") —
Here, for comparison, are the original German and the translation.
As for "that you in which the lines of relation, though parallel,
intersect," and "intimations of eternity," see Log24 posts on
the concept "line at infinity" as well as "Lost Horizon."
Saturday, December 30, 2017
Aliveness*
"It was a dark and stormy night . . ."
* See also other posts using this word.
A Dream
Say You, Say Me
Lionel Richie
. . . .
"I had a dream,
I had an awesome dream
People in the park
playing games in the dark
And what they played
was a masquerade
And from behind walls of doubt
a voice was crying out"
. . . .
"Something else was behind this . . .
because it makes no sense.”
— The author reviewed in today's previous post,
as quoted yesterday in The Boston Globe
Say you, say me, say IT . . .
A comment on Sean Kelly's Christmas Morning column on "aliveness"
in the New York Times philosophy series The Stone —
About IT
Background: See Wrinkle in this journal and a post,
Field of Manifestation, from the above 2015 date.
See as well the Goodreads page below.
The six books reviewed by this user were written or
co-written by the author in the review shown above.
Each review gave the highest rating, five stars.
Friday, December 29, 2017
On Becket’s Day
Thursday, December 28, 2017
Rocky Start
The above prose suggests a musical alternative to the Dec. 21
Camazotz song in the posts tagged Quantum Tesseract Theorem . . .
Memorandum of Misunderstanding
Harrison Ford in "Blade Runner 2049" —
Click the above quote for a scholium.
See also the previous post and . . .
Wednesday, December 27, 2017
On Fiction and Mathematics
"There is always an awareness in her fiction
of the subjectivity of perception, and
the kaleidoscopic permutations
that memory can work on reality."
This is from a New York Times article subtitled
"Alice Munro, Nobel Winner, Mines the Inner Lives
of Girls and Women" …
The New York Times article was linked to by Marjorie Senechal
in a Huffington Post article of All Saints' Day 2013.
Further material on kaleidoscopic permutations —
See the Log24 post Symmetry of May 3, 2016.
For further material on mining, see Diamond-Mine:
"SEE HEAR READ" — Walt Disney Productions
For Day 27 of December 2017
See the 27-part structure of
the 3x3x3 Galois cube
as well as Autism Sunday 2015.
Tuesday, December 26, 2017
Raiders of the Lost Stone
Two Students of Structure
A comment on Sean Kelly's Christmas Morning column on "aliveness"
in the New York Times philosophy series The Stone —
Diana Senechal's 1999 doctoral thesis at Yale was titled
"Diabolical Structures in the Poetics of Nikolai Gogol."
Her mother, Marjorie Senechal, has written extensively on symmetry
and served as editor-in-chief of The Mathematical Intelligencer .
From a 2013 memoir by Marjorie Senechal —
"While I was in Holland my enterprising student assistant at Smith had found, in Soviet Physics – Crystallography, an article by N. N. Sheftal' on tetrahedral penetration twins. She gave it to me on my return. It was just what I was looking for. The twins Sheftal' described had evidently begun as (111) contact twins, with the two crystallites rotated 60o with respect to one another. As they grew, he suggested, each crystal overgrew the edges of the other and proceeded to spread across the adjacent facet. When all was said and done, they looked like they'd grown through each other, but the reality was over-and-around. Brilliant! I thought. Could I apply this to cubes? No, evidently not. Cube facets are all (100) planes. But . . . these crystals might not have been cubes in their earliest stages, when twinning occurred! I wrote a paper on "The mechanism of certain growth twins of the penetration type" and sent it to Martin Buerger, editor of Neues Jarbuch für Mineralogie. This was before the Wrinch symposium; I had never met him. Buerger rejected it by return mail, mostly on the grounds that I hadn't quoted any of Buerger's many papers on twinning. And so I learned about turf wars in twin domains. In fact I hadn't read his papers but I quickly did. I added a reference to one of them, the paper was published, and we became friends.[5]
After reading Professor Sheftal's paper I wrote to him in Moscow; a warm and encouraging correspondence ensued, and we wrote a paper together long distance.[6] Then I heard about the scientific exchanges between the Academies of Science of the USSR and USA. I applied to spend a year at the Shubnikov Institute for Crystallography, where Sheftal' worked. I would, I proposed, study crystal growth with him, and color symmetry with Koptsik. To my delight, I was accepted for an 11-month stay. Of course the children, now 11 and 14, would come too and attend Russian schools and learn Russian; they'd managed in Holland, hadn't they? Diana, my older daughter, was as delighted as I was. We had gone to Holland on a Russian boat, and she had fallen in love with the language. (Today she holds a Ph.D. in Slavic Languages and Literature from Yale.) . . . . |
Philosophy professors and those whose only interest in mathematics
is as a path to the occult may consult the Log24 posts tagged Tsimtsum.
Stoned: A Reading for St. Stephen’s Day
See also Log24 posts now tagged Apperception.
Monday, December 25, 2017
New Kids on a Block:
A Midnight Special for Charles Wallace
Old Kid on Peter Block —
See the remarks today of Harvard philosophy professor Sean D. Kelly
in The New York Times :
Alexander's "15 properties that create the wholeness and aliveness" —
This is the sort of bullshit that seems to go over well at Harvard.
See Christopher Alexander in this journal.
Every Picture Tells a Story
The movie marquee below
("Batman" and "Lethal Weapon 2")
indicates that the recent film "IT"
is set in the summer of 1989.
The marquee suggests a review. Also . . . .
"… the thing that has shown up every twenty-seven years
or so . . . . It always comes back, you see. It."
— King, Stephen. IT (p. 151). Scribner. Kindle Edition.
Note that the flashback summer in King's book,
1958… plus 27 is 1985… plus 27 is 2012.
Sunday, December 24, 2017
Saturday, December 23, 2017
The Right Stuff
A figure related to the general connecting theorem of Koen Thas —
See also posts tagged Dirac and Geometry in this journal.
Those who prefer narrative to mathematics may, if they so fancy, call
the above Thas connecting theorem a "quantum tesseract theorem ."
The Patterning
Friday, December 22, 2017
Thursday, December 21, 2017
Wrinkles
TIME magazine, issue of December 25th, 2017 —
" In 2003, Hand worked with Disney to produce a made-for-TV movie.
Thanks to budget constraints, among other issues, the adaptation
turned out bland and uninspiring. It disappointed audiences,
L’Engle and Hand. 'This is not the dream,' Hand recalls telling herself.
'I’m sure there were people at Disney that wished I would go away.' "
Not the dream? It was, however, the nightmare, presenting very well
the encounter in Camazotz of Charles Wallace with the Tempter.
From a trailer for the latest version —
Detail:
From the 1962 book —
"There's something phoney in the whole setup, Meg thought.
There is definitely something rotten in the state of Camazotz."
Song adapted from a 1960 musical —
"In short, there's simply not
A more congenial spot
For happy-ever-aftering
Than here in Camazotz!"
Wednesday, December 20, 2017
A Snow Ball for Clifford Irving (1930-2017)
William Grimes in The New York Times this evening —
"Clifford Irving, who perpetrated one of the biggest literary hoaxes
of the 20th century in the early 1970s when he concocted a
supposedly authorized autobiography of the billionaire Howard Hughes
based on meetings and interviews that never took place, died on Tuesday
at a hospice facility near his home in Sarasota, Fla. He was 87."
A figure reproduced here on Tuesday —
A related figure —
See too the 1973 Orson Welles film "F for Fake."
Some background on the second figure above —
posts tagged April 8-11, 2016.
Some background on the first figure above —
today's previous post, January 2018 AMS Notices.
January 2018 AMS Notices
Update of 9:29 PM ET Dec. 20, 2017 —
See in particular, in the above Notices , the article
"Algebraic Structures on Polytopes," by Federico Ardila,
within the 2018 Joint Mathematics Meeting Lecture Sampler.
Related reading:
arXiv:1711.09102v1 [hep-th] 24 Nov 2017,
"Scattering Forms and the Positive Geometry of
Kinematics, Color and the Worldsheet," by
Nima Arkani-Hamed, Yuntao Bai, Song He, Gongwang Yan
(Submitted to the arXiv on 24 Nov. 2017).
Tuesday, December 19, 2017
A Mythologem for Meletinsky
The word "mythologem" on page 55 of The Burning Fountain
by Philip Wheelwright, revised edition of 1968 (p. 91 in the 1954
edition), suggests a Web search for that word. It was notably often
used in the 1998 English translation of a book by Eleazar Meletinsky
first published in Russian in 1976 —
Meletinsky reportedly died on December 17, 2005.
In his memory, Log24 posts from that date are now tagged Mythologem Day.
"And we may see the meadow in December,
icy white and crystalline" — Johnny Mercer
Monday, December 18, 2017
Mathematics and Art
From the American Mathematical Society homepage today —
From concinnitasproject.org —
"Concinnitas is the title of a portfolio of fine art prints. . . .
The portfolio draws its name from a word famously used
by the Renaissance scholar, artist, architect, and philosopher
Leon Battista Alberti (1404-1472) to connote the balance of
number, outline, and position (in essence, number, geometry,
and topology) that he believed characterize a beautiful work of art."
The favicon of the Concinnitas Project —
The structure of the Concinnitas favicon —
This structure is from page 15 of
"Diamond Theory," a 1976 preprint —
Wheelwright and the Dance
The page preceding that of yesterday's post Wheelwright and the Wheel —
See also a Log24 search for
"Four Quartets" + "Four Elements".
A graphic approach to this concept:
"The Bounded Space" —
"The Fire, Air, Earth, and Water" —
Sunday, December 17, 2017
Wheelwright and the Wheel
From the 1968 "new and revised edition" —
See also the previous post.
For the phrase "burning fountain," see Shelley's "Adonais,"
as well as Logos (a post of Dec. 4) and The Crimson Abyss.
Concrete Universals
The remarks on universals in the previous post linked to the following
note by James Hillman:
James Hillman, Re-Visioning Psychology ,
Harper Collins, 1977, p. 155 —
"Myths also make concrete particulars into universals,
so that each image, name, thing in my life when
experienced mythically takes on universal sense,
and all abstract universals, the grand ideas of
human fate, are presented as concrete actions."
[See note 48.]
Note 48: Cf. P. Wheelwright's discussion of concrete universality
in The Burning Fountain (Bloomington, Ind.: Indiana University
Press, 1968), pp. 52-54.
For Wheelwright's discussion, see the following excerpts from his book:
Saturday, December 16, 2017
Dagger Definitions (Review)
The previous post suggests a review of
the philosophical concept of universals —
A part of the above-mentioned 2011 "Saturday evening's post" that is
relevant to the illustration at the end of today's previous post —
Note the whatness of Singer's dagger definitions —
Triptychs
Two readings by James Parker —
From next year’s first Atlantic issue
From last month’s Atlantic issue
“Let’s return to that hillside where Clayton exited his Mercedes.
In the gray light, he climbs the pasture. Halfway up the slope,
three horses are standing: sculpturally still, casually composed
in a perfect triptych of horsitude.”
— James Parker in The Atlantic , Nov. 2017 issue
Logos-related material
Friday, December 15, 2017
Matter
The previous post, "Mind," suggests a search for "n+1" in this journal.
From that search —
The above psychoanalytic remarks suggest . . .
See also "Transformers" (2007).
"Before time began, there was the Cube."
— Optimus Prime
Thursday, December 14, 2017
Philosophy
The above reading was suggested by a post of
New Year's Day, Jan. 1, 2013 — The Simplest Situation.
See also Ahem (Sunday morning, Dec. 10, 2017).
Wednesday, December 13, 2017
Portland News
An obituary from this afternoon suggests a review of
a Log24 post from last year —
See also today's earlier post Once in a Lullaby and yesterday's
London Daily Mail — "Kristen Stewart Cuts a Cool Figure" —