Log24

Monday, December 26, 2016

Fanciful (continued)

Filed under: General — m759 @ 1:00 PM

From "Plato Thanks the Academy," March 19, 2014 —

IMAGE- Art Jeffries (Bruce Willis) and Simon Lynch (Miko Hughes), 'Mercury Rising' (1998)

“Click on fanciful .”

A possible result —

See also "Triple Cross."

Saturday, July 2, 2016

Fanciful

Filed under: General — m759 @ 12:00 PM

IMAGE- Art Jeffries (Bruce Willis) and Simon Lynch (Miko Hughes), 'Mercury Rising' (1998)

"Search for the title."

Friday, May 16, 2014

Fanciful

Filed under: General — m759 @ 12:21 AM

From this journal last March:

Wednesday, April 17, 2019

The Royal Society Diamond

Filed under: General — Tags: — m759 @ 9:34 AM

The phrase "pattern recognition" in a news story about the
April 13 death of Princeton neuroscientist Charles Gross,
and yesterday's post about a fanciful "purloined diamond,"
suggest a review of a less fanciful diamond.

See also earlier posts tagged Fitch
and my own, much  earlier and very
different, approach to such patterns —

Thursday, August 9, 2018

True Grids

Filed under: General,Geometry — Tags: , — m759 @ 7:59 PM

From a search in this journal for "True Grid,"
a fanciful description of  the 3×3 grid —

"This is the garden of Apollo,
the field of Reason…."
John Outram, architect    

A fanciful instance of the 4×2 grid in
a scene from the film "The Master" —

IMAGE- Joaquin Phoenix, corridor scene in 'The Master'

A fanciful novel referring to the number 8,
and a not -so-fanciful reference:

http://www.log24.com/log/pix18/180809-The_EIght-and-coordinates-for-PSL(2,7)-actions-500w.jpg

Illustrated above are Katherine Neville's novel The Eight  and the
"knight" coordinatization of the 4×2 grid from a page on the exceptional
isomorphism between PSL(3,2) (alias GL(3,2)) and PSL(2,7) — groups
of, respectively, degree 7 and degree 8.

Literature related to the above remarks on grids:

Ross Douthat's New York Times  column yesterday purported, following
a 1946 poem by Auden, to contrast students of the humanities with
technocrats by saying that the former follow Hermes, the latter Apollo.

I doubt that Apollo would agree.

Wednesday, August 8, 2018

Annals of Phenomenology

Filed under: General — Tags: — m759 @ 4:44 PM

The Return of Purple Man
Or:  This Just In

Detail from a post of yesterday morning taken from
the laptop of private investigator Jessica Jones —

http://www.log24.com/log/pix18/180808-Jessica_Jones-laptop-detail-256w.jpg

The above image, together with yesterday's date, suggested, rather
fancifully, yesterday morning's later post on just intonation, "Seventh."

The nemesis of Jessica Jones, the Purple Man

http://www.log24.com/log/pix18/180808-comicbook.com-purplemandavidtennant-127648-500w.jpg

A New York Times  piece today* is related to both just intonation and
the color purple —

http://www.log24.com/log/pix18/180808-Purple_Piano_Tuning-NYT.jpg

* Published at 1:50 PM ET —
itemprop="datePublished" content="2018-08-08T17:50:30.000Z"

Thursday, June 14, 2018

Link, Not Wand.

Filed under: General — m759 @ 12:25 AM

"How frail the wand, but how profound the spell !"

— Clarence R. Wylie, Jr., "Paradox" (1948)

The above fanciful PlayStation symbols suggest an etymology

See also Kipnis.

Sunday, May 7, 2017

Art Space

Filed under: General,Geometry — Tags: — m759 @ 1:00 PM

Detail of an image in the previous post

This suggests a review of a post on a work of art by fashion photographer
Peter Lindbergh, made when he was younger and known as "Sultan."

The balls in the foreground relate Sultan's work to my own.

Linguistic backstory —

The art space where the pieces by Talman and by Lindbergh
were displayed is Museum Tinguely in Basel.

As the previous post notes, the etymology of "glamour" (as in
fashion photography) has been linked to "grammar" (as in 
George Steiner's Grammars of Creation ). A sculpture by 
Tinguely (fancifully representing Heidegger) adorns one edition
of Grammars .

Yale University Press, 2001:

Tinguely, "Martin Heidegger,
Philosopher," sculpture, 1988

Tuesday, December 27, 2016

Bright Star

Filed under: General,Geometry — m759 @ 8:15 AM

See instances of the title in this journal.

Material related to yesterday evening's post
"Bright and Dark at Christmas" —

The Buddha of Rochester:

See also the Gelman (i.e., Gell-Mann) Prize
in the film "Dark Matter" and the word "Eightfold"
in this journal.

" A fanciful mark is a mark which is invented
for the sole purpose of functioning as a trademark,
e.g., 'Kodak.' "

"… don't take my Kodachrome away." — Paul Simon

Monday, December 26, 2016

Old News

Filed under: General — m759 @ 12:00 PM

From IndieWire on November 11, 2016 —

"Bleecker Street has announced it has acquired
U.S. and select territory rights to 'The Man Who
Invented Christmas
,' to be directed by Bharat
Nalluri. The film will start shooting next month
and is targeting a holiday 2017 release date."

This  journal on November 11, 2016 —

On Christmas 2015, Log24 featured
the Bleecker Street favicon

in the post 'Dark Symbol.'

Here is the dark symbol again —

The apparent symbols for "times" and "plus"
in the above screenshot are, of course, icons for
browser functions. Readers who prefer the
fanciful  may regard them instead as symbols for
"a gateway to another realm," that of number theory.

Friday, July 15, 2016

Autistic Enchantment*

Filed under: General,Geometry — m759 @ 10:29 AM

Robert Nye, author of the novel Falstaffreportedly died
at 77 on July 2, 2016.

Harvey D. Heinz, expert on magic squares, cubes,
tesseracts, etc., reportedly died at 82 on July 6, 2013.

In memoriam —

From the date of Nye's death:

From Nye's book:

From the date of Heinz's death:

* See also a search for the title in this journal.

Sunday, June 14, 2015

Autistic Enchantments

Filed under: General — m759 @ 12:45 PM

Continued )

Log24  on January 31, 2015 —
 

Spellbound (continued)

Filed under: Uncategorized — m759 @ 3:33 AM 

The New York Times  this morning, in an
obituary for a maker of crossword puzzles :

"… the first known crossword puzzle appeared in
an American newspaper. (Called a 'word-cross'
and shaped like a diamond, it was published in
The New York World  on Sunday, Dec. 21, 1913.)"

See St. Nicholas  magazine, November 1874, p. 59 :

For the answer, see this  journal on Aug. 29, 2002
(with a scene from Spellbound ) and on July 15, 2004.

On that same date 

The Seattle Times , Feb. 8, 2015, updated Feb. 12—

How to solve the puzzle:

"… you begin by filling in the missing words 
for the limericks. 

Dice, yAhtzee, woN, yahTzee, twicE; 
Wall, dRawl, geOrgia’s, staTe, minnEsota; 
Truck, rEd, fiReman’s, blaZe, hydrAnt; 
Bob, sLob, prAy, saiNt, thanK. 

The capital letters help to show what comes next, 
as clued by the 1,2,3,4,5 in the title. 

You take the first letter of the first inserted word, 
the second of the second and so on. The resulting 
message is ‘Dante wrote terza blank.’ The blank 
is RIMA, as terza rima was the rhyme scheme 
Dante used in the Divine Comedy."

See also two other dates, June 3, 2015, and June 10, 2015,
in this  journal and in the life of the puzzle author.

The date of the puzzle's answer, Feb. 8, 2015, is also
not without interest.

IMAGE- Art Jeffries (Bruce Willis) and Simon Lynch (Miko Hughes), 'Mercury Rising' (1998)

“Click on fanciful .”

Wednesday, March 19, 2014

Plato Thanks the Academy

Filed under: General — Tags: — m759 @ 9:00 PM

(Continued)

IMAGE- Art Jeffries (Bruce Willis) and Simon Lynch (Miko Hughes), 'Mercury Rising' (1998)

“Click on fanciful .”

Tuesday, March 11, 2014

Dark Fields of the Republic

Filed under: General,Geometry — Tags: , — m759 @ 10:00 PM

This post was suggested by today's previous post, Depth,
by Plato's Diamond, and by Rebecca Newberger Goldstein's
recent fanciful fiction about Plato.

Plato, Republic , Book II, Paul Shorey translation at Perseus

“Consider,” [382a] said I; “would a god wish to deceive, or lie, by presenting in either word or action what is only appearance?” “I don’t know,” said he. “Don’t you know,” said I, “that the veritable lie, if the expression is permissible, is a thing that all gods and men abhor?” “What do you mean?” he said. “This,” said I, “that falsehood in the most vital part of themselves, and about their most vital concerns, is something that no one willingly accepts, but it is there above all that everyone fears it.” “I don’t understand yet either.” “That is because you suspect me of some grand meaning,” [382b] I said; “but what I mean is, that deception in the soul about realities, to have been deceived and to be blindly ignorant and to have and hold the falsehood there, is what all men would least of all accept, and it is in that case that they loathe it most of all.” “Quite so,” he said.

Related material —

A meditation from the Feast of St. Francis, 2012 —

A post from Sept. 30, 2012, the reported date of  death
for British children's author Helen Nicoll —

The New Criterion  on the death of Hilton Kramer —

This uncredited translation of Plato is, Google Books tells us,
by "Francis MacDonald Cornfield."  The name is an error,
but the error is illuminating —

Signs Movie Stills: Mel Gibson, Joaquin Phoenix, Patricia Kalember, M. Night Shyamalan

Sunday, March 2, 2014

Plato Thanks the Academy…

Filed under: General — Tags: — m759 @ 12:00 PM

(Continued)

… With a trip to yesteryear suggested by
the Feb. 28 New York Times  article 
"Casting Shadows on a Fanciful World"

("Wes Anderson Evokes Nostalgia in 
'The Grand Budapest Hotel' ").

Tuesday, March 19, 2013

Mathematics and Narrative (continued)

Filed under: General,Geometry — Tags: , — m759 @ 10:18 AM

Angels & Demons meet Hudson Hawk

Dan Brown's four-elements diamond in Angels & Demons :

IMAGE- Illuminati Diamond, pp. 359-360 in 'Angels & Demons,' Simon & Schuster Pocket Books 2005, 448 pages, ISBN 0743412397

The Leonardo Crystal from Hudson Hawk :

Hudson:

Mathematics may be used to relate (very loosely)
Dan Brown's fanciful diamond figure to the fanciful
Leonardo Crystal from Hudson Hawk 

"Giving himself a head rub, Hawk bears down on
the three oddly malleable objects. He TANGLES 
and BENDS and with a loud SNAP, puts them together,
forming the Crystal from the opening scene."

— A screenplay of Hudson Hawk

Happy birthday to Bruce Willis.

Saturday, March 16, 2013

The Crosswicks Curse

Filed under: General,Geometry — Tags: , — m759 @ 4:00 PM

Continues.

From the prologue to the new Joyce Carol Oates
novel Accursed

"This journey I undertake with such anticipation
is not one of geographical space but one of Time—
for it is the year 1905 that is my destination.

1905!—the very year of the Curse."

Today's previous post supplied a fanciful link
between the Crosswicks Curse of Oates and
the Crosswicks tesseract  of Madeleine L'Engle.

The Crosswicks Curse according to L'Engle
in her classic 1962 novel A Wrinkle in Time —

"There is  such a thing as a tesseract."

A tesseract is a 4-dimensional hypercube that
(as pointed out by Coxeter in 1950) may also 
be viewed as a 4×4 array (with opposite edges
identified).

Meanwhile, back in 1905

For more details, see how the Rosenhain and Göpel tetrads occur naturally
in the diamond theorem model of the 35 lines of the 15-point projective
Galois space PG(3,2).

See also Conwell in this journal and George Macfeely Conwell in the
honors list of the Princeton Class of 1905.

Sunday, April 17, 2011

Sunday School

Filed under: General,Geometry — Tags: — m759 @ 7:00 AM

Apollo and the Tricksters

From The Story of N (Oct. 15, 2010)—

Roberta Smith on what she calls "endgame art"—

"Fear of form above all means fear of compression— of an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible."

Margaret Atwood on tricksters and art—

"If it’s a seamless whole you want, pray to Apollo."

Here is some related material In memory of CIA officer Clare Edward Petty, who died at 90 on March 18—

A review of a sort of storyteller's MacGuffin — the 3×3 grid. This is, in Smith's terms, an "artistic focus" that appears  to be visually comprehensible but is not as simple as it seems.

The Hesse configuration can serve as more than a sort of Dan Brown MacGuffin. As a post of January 14th notes, it can (rather fancifullly) illustrate the soul—

http://www.log24.com/log/pix11/110417-AlderTilleyColoredSm.jpg

" … I feel I understand
Existence, or at least a minute part
Of my existence, only through my art,
In terms of combinational delight…."

— Vladimir Nabokov, Pale Fire

Friday, January 14, 2011

Ironic Butterfly

Filed under: General,Geometry — Tags: — m759 @ 11:07 AM

David Brooks's column today quotes Niebuhr. From the same source—
Reinhold Niebuhr, The Irony of American History

Chapter 8: The Significance of Irony

Any interpretation of historical patterns and configurations raises the question whether the patterns, which the observer discerns, are "objectively" true or are imposed upon the vast stuff of history by his imagination. History might be likened to the confusion of spots on the cards used by psychiatrists in a Rorschach test. The patient is asked to report what he sees in these spots; and he may claim to find the outlines of an elephant, butterfly or frog. The psychiatrist draws conclusions from these judgments about the state of the patient’s imagination rather than about the actual configuration of spots on the card. Are historical patterns equally subjective?
….
The Biblical view of human nature and destiny moves within the framework of irony with remarkable consistency. Adam and Eve are expelled from the Garden of Eden because the first pair allowed "the serpent" to insinuate that, if only they would defy the limits which God had set even for his most unique creature, man, they would be like God. All subsequent human actions are infected with a pretentious denial of human limits. But the actions of those who are particularly wise or mighty or righteous fall under special condemnation. The builders of the Tower of Babel are scattered by a confusion of tongues because they sought to build a tower which would reach into the heavens.

Niebuhr's ironic butterfly may be seen in the context of last
Tuesday's post Shining and of last Saturday's noon post True Grid

http://www.log24.com/log/pix11/110114-AlderTilleyColored.gif

The "butterfly" in the above picture is a diagram showing the 12 lines* of the Hesse configuration from True Grid.

It is also a reference to James Hillman's classical image (see Shining) of the psyche, or soul, as a butterfly.

Fanciful, yes, but this is in exact accordance with Hillman's remarks on the soul (as opposed to the spirit— see Tuesday evening's post).

The 12-line butterfly figure may be viewed as related to the discussions of archetypes and universals in Hillman's Re-Visioning Psychology  and in Charles Williams's The Place of the Lion . It is a figure intended here to suggest philosophy, not entertainment.

Niebuhr and Williams, if not the more secular Hillman, might agree that those who value entertainment above all else may look forward to a future in Hell (or, if they are lucky, Purgatory). Perhaps such a future might include a medley of Bob Lind's "Elusive Butterfly" and Iron Butterfly's "In-a-Gadda-da-Vida."

* Three horizontal, three vertical, two diagonal, and four arc-shaped.

Tuesday, December 7, 2010

The Tiffany Puzzle

Filed under: General,Geometry — Tags: — m759 @ 5:00 AM

Suggested by Dan Brown's remarks in today's Science Times  special section on puzzles—

http://www.log24.com/log/pix10B/101202-DreidelAndStoneSm.jpg

For a fanciful linkage of the dreidel 's concept of chance
to The Stone 's concept of invariant law, note that the
New York Lottery evening number on Dec. 1 (the
beginning of Hanukkah) was 840. See also the number
840 in the final post (July 20, 2002) of a search for
Solomon's Cube.

http://www.log24.com/log/pix10B/101207-FifthAve5AM.jpg

Thursday, December 2, 2010

Caesarian

Filed under: General,Geometry — m759 @ 8:00 AM

The Dreidel Is Cast

The Nietzschean phrase "ruling and Caesarian spirits" occurred in yesterday morning's post "Novel Ending."

That post was followed yesterday morning by a post marking, instead, a beginning— that of Hanukkah 2010. That Jewish holiday, whose name means "dedication," commemorates the (re)dedication of the Temple in Jerusalem in 165 BC.

The holiday is celebrated with, among other things, the Jewish version of a die—  the dreidel . Note the similarity of the dreidel  to an illustration of The Stone*  on the cover of the 2001 Eerdmans edition of  Charles Williams's 1931 novel Many Dimensions

http://www.log24.com/log/pix10B/101202-DreidelAndStone.jpg

For mathematics related to the dreidel , see Ivars Peterson's column on this date fourteen years ago.
For mathematics related (if only poetically) to The Stone , see "Solomon's Cube" in this journal.

Here is the opening of Many Dimensions

http://www.log24.com/log/pix10B/101202-WilliamsChOne.jpg

For a fanciful linkage of the dreidel 's concept of chance to The Stone 's concept of invariant law, note that the New York Lottery yesterday evening (the beginning of Hanukkah) was 840. See also the number 840 in the final post (July 20, 2002) of the "Solomon's Cube" search.

Some further holiday meditations on a beginning—

Today, on the first full day of Hanukkah, we may or may not choose to mark another beginning— that of George Frederick James Temple, who was born in London on this date in 1901. Temple, a mathematician, was President of the London Mathematical Society in 1951-1953. From his MacTutor biography

"In 1981 (at the age of 80) he published a book on the history of mathematics. This book 100 years of mathematics (1981) took him ten years to write and deals with, in his own words:-

those branches of mathematics in which I had been personally involved.

He declared that it was his last mathematics book, and entered the Benedictine Order as a monk. He was ordained in 1983 and entered Quarr Abbey on the Isle of Wight. However he could not stop doing mathematics and when he died he left a manuscript on the foundations of mathematics. He claims:-

The purpose of this investigation is to carry out the primary part of Hilbert's programme, i.e. to establish the consistency of set theory, abstract arithmetic and propositional logic and the method used is to construct a new and fundamental theory from which these theories can be deduced."

For a brief review of Temple's last work, see the note by Martin Hyland in "Fundamental Mathematical Theories," by George Temple, Philosophical Transactions of the Royal Society, A, Vol. 354, No. 1714 (Aug. 15, 1996), pp. 1941-1967.

The following remarks by Hyland are of more general interest—

"… one might crudely distinguish between philosophical and mathematical motivation. In the first case one tries to convince with a telling conceptual story; in the second one relies more on the elegance of some emergent mathematical structure. If there is a tradition in logic it favours the former, but I have a sneaking affection for the latter. Of course the distinction is not so clear cut. Elegant mathematics will of itself tell a tale, and one with the merit of simplicity. This may carry philosophical weight. But that cannot be guaranteed: in the end one cannot escape the need to form a judgement of significance."

— J. M. E. Hyland. "Proof Theory in the Abstract." (pdf)
Annals of Pure and Applied Logic 114, 2002, 43-78.

Here Hyland appears to be discussing semantic ("philosophical," or conceptual) and syntactic ("mathematical," or structural) approaches to proof theory. Some other remarks along these lines, from the late Gian-Carlo Rota

http://www.log24.com/log/pix10B/101202-RotaChXII-sm.jpg

    (Click to enlarge.)

See also "Galois Connections" at alpheccar.org and "The Galois Connection Between Syntax and Semantics" at logicmatters.net.

* Williams's novel says the letters of The Stone  are those of the Tetragrammaton— i.e., Yod, He, Vau, He  (cf. p. 26 of the 2001 Eerdmans edition). But the letters on the 2001 edition's cover Stone  include the three-pronged letter Shin , also found on the dreidel .  What esoteric religious meaning is implied by this, I do not know.

Saturday, November 6, 2010

A Better Story

Filed under: General,Geometry — m759 @ 6:00 PM

Continued from June 4, 2010

http://www.log24.com/log/pix10B/101106-GardnerGalois.jpg

See also Jon Han's fanciful illustration in today's New York Times  and "Galois Cube" in this journal.

http://www.log24.com/log/pix10B/101106-JonHanCube.jpg

Friday, October 8, 2010

Starting Out in the Evening

Filed under: General,Geometry — Tags: , — m759 @ 12:00 PM

… and Finishing Up at Noon

This post was suggested by last evening’s post on mathematics and narrative
and by Michiko Kakutani on Vargas Llosa in this morning’s New York Times.

http://www.log24.com/log/pix10B/101008-StartingOut.jpg

Above: Frank Langella in
Starting Out in the Evening

Right: Johnny Depp in
The Ninth Gate

http://www.log24.com/log/pix10B/101008-NinthGate.jpg

“One must proceed cautiously, for this road— of truth and falsehood in the realm of fiction— is riddled with traps and any enticing oasis is usually a mirage.”

— “Is Fiction the Art of Lying?”* by Mario Vargas Llosa, New York Times  essay of October 7, 1984

My own adventures in that realm— as reader, not author— may illustrate Llosa’s remark.

A nearby stack of paperbacks I haven’t touched for some months (in order from bottom to top)—

  1. Pale Rider by Alan Dean Foster
  2. Franny and Zooey by J. D. Salinger
  3. The Hobbit by J. R. R. Tolkien
  4. Le Petit Prince by Antoine de Saint Exupéry
  5. Literary Reflections by James A. Michener
  6. The Ninth Configuration by William Peter Blatty
  7. A Streetcar Named Desire by Tennessee Williams
  8. Nine Stories by J. D. Salinger
  9. A Midsummer Night’s Dream by William Shakespeare
  10. The Tempest by William Shakespeare
  11. Being There by Jerzy Kosinski
  12. What Dreams May Come by Richard Matheson
  13. Zen and the Art of Motorcycle Maintenance by Robert M. Pirsig
  14. A Gathering of Spies by John Altman
  15. Selected Poems by Robinson Jeffers
  16. Hook— Tinkerbell’s Challenge by Tristar Pictures
  17. Rising Sun by Michael Crichton
  18. Changewar by Fritz Leiber
  19. The Painted Word by Tom Wolfe
  20. The Hustler by Walter Tevis
  21. The Natural by Bernard Malamud
  22. Truly Tasteless Jokes by Blanche Knott
  23. The Man Who Was Thursday by G. K. Chesterton
  24. Under the Volcano by Malcolm Lowry

What moral Vargas Llosa might draw from the above stack I do not know.

Generally, I prefer the sorts of books in a different nearby stack. See Sisteen, from May 25. That post the fanciful reader may view as related to number 16 in the above list. The reader may also relate numbers 24 and 22 above (an odd couple) to By Chance, from Thursday, July 22.

* The Web version’s title has a misprint— “living” instead of “lying.”

Saturday, January 26, 2008

Saturday January 26, 2008

Filed under: General — m759 @ 2:22 AM
Working Backward

Those who have followed the links here recently may appreciate a short story told by yesterday’s lottery numbers in Pennsylvania: mid-day 096, evening 513.

The “96” may be regarded as a reference to the age at death of geometer H.S.M. Coxeter (see yesterday morning’s links). The “513” may be regarded as a reference to the time of yesterday afternoon’s entry, 5:01, plus the twelve minutes discussed in that entry by presidential aide Richard Darman, who died yesterday.

These references may seem less fanciful in the light of other recent Log24 material: a verse quoted here on Jan. 18

… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.


Rubén Darío,
born January 18, 1867

— and a link on Jan. 19 to the following:

The Lion, the Witch
and the Wardrobe:

 

“But what does it all mean?” asked Susan when they were somewhat calmer.

“It means,” said Aslan, “that though the Witch knew the Deep Magic, there is a magic deeper still which she did not know. Her knowledge goes back only to the dawn of Time. But if she could have looked a little further back, into the stillness and the darkness before Time dawned, she would have read there a different incantation. She would have known that when a willing victim who had committed no treachery was killed in a traitor’s stead, the Table would crack and Death itself would start working backward.”

Tuesday, May 22, 2007

Tuesday May 22, 2007

Filed under: General,Geometry — m759 @ 7:11 AM
 
Jewel in the Crown

A fanciful Crown of Geometry

The Crown of Geometry
(according to Logothetti
in a 1980 article)

The crown jewels are the
Platonic solids, with the
icosahedron at the top.

Related material:

"[The applet] Syntheme illustrates ways of partitioning the 12 vertices of an icosahedron into 3 sets of 4, so that each set forms the corners of a rectangle in the Golden Ratio. Each such rectangle is known as a duad. The short sides of a duad are opposite edges of the icosahedron, and there are 30 edges, so there are 15 duads.

Each partition of the vertices into duads is known as a syntheme. There are 15 synthemes; 5 consist of duads that are mutually perpendicular, while the other 10 consist of duads that share a common line of intersection."

— Greg Egan, Syntheme

Duads and synthemes
(discovered by Sylvester)
also appear in this note
from May 26, 1986
(click to enlarge):

 

Duads and Synthemes in finite geometry

The above note shows
duads and synthemes related
to the diamond theorem.

See also John Baez's essay
"Some Thoughts on the Number 6."
That essay was written 15 years
ago today– which happens
to be the birthday of
Sir Laurence Olivier, who,
were he alive today, would
be 100 years old.

Olivier as Dr. Christian Szell

The icosahedron (a source of duads and synthemes)

"Is it safe?"

Wednesday, October 25, 2006

Wednesday October 25, 2006

Filed under: General,Geometry — m759 @ 9:00 AM

Conceit
at Harvard

conceit (See definition.)
“c.1374, from conceiven (see conceive). An Eng. formation based on deceit and receipt. Sense evolved from ‘something formed in the mind,’ to ‘fanciful or witty notion’ (1513), to ‘vanity’ (1605)….”

Online Eytmology Dictionary

“… there is some virtue in tracking cultural trends in terms of their relation to the classic Trinitarian framework of Christian thought.”

Description of lectures to be given Monday, Tuesday, and Wednesday of this week (on Father, Son, and Holy Spirit, respectively, and their relationship to “cultural trends”) at Harvard’s Memorial Church

I prefer more-classic trinitarian frameworks– for example,

the classic Pythagorean
trinity of 4, 3, and 5


The image “http://www.log24.com/log/pix06A/061025-Pyth2.gif” cannot be displayed, because it contains errors.

and the structural trinity
underlying
classic quilt patterns:

The image “http://www.log24.com/theory/images/TradBlocks.gif” cannot be displayed, because it contains errors.

Click on pictures for further details.

These mathematical trinities are
conceits in the sense of concepts
or notions; examples of the third
kind of conceit are easily
found, especially at Harvard.

For a possible corrective to
examples of the third kind,
see
To Measure the Changes.

Friday, May 27, 2005

Friday May 27, 2005

Filed under: General,Geometry — m759 @ 12:25 PM
Drama of the Diagonal,
Part Deux

Wednesday’s entry The Turning discussed a work by Roger Cooke.  Cooke presents a

fanciful story (based on Plato’s dialogue Meno).”

The History of Mathematics is the title of the Cooke book.

Associated Press thought for today:

“History is not, of course, a cookbook offering pretested recipes. It teaches by analogy, not by maxims. It can illuminate the consequences of actions in comparable situations, yet each generation must discover for itself what situations are in fact comparable.”
 — Henry Kissinger (whose birthday is today)

For Henry Kissinger on his birthday:
a link to Geometry for Jews.

This link suggests a search for material
on the art of Sol LeWitt, which leads to
an article by Barry Cipra,
The “Sol LeWitt” Puzzle:
A Problem in 16 Squares
(ps),
a discussion of a 4×4 array
of square linear designs.
  Cipra says that

“If you like, there are three symmetry groups lurking within the LeWitt puzzle:  the rotation/reflection group of order 8, a toroidal group of order 16, and an ‘existential’* group of order 16.  The first group is the most obvious.  The third, once you see it, is also obvious.”

* Jean-Paul Sartre,
  Being and Nothingness,
  Philosophical Library, 1956
  [reference by Cipra]

For another famous group lurking near, if not within, a 4×4 array, click on Kissinger’s birthday link above.

Kissinger’s remark (above) on analogy suggests the following analogy to the previous entry’s (Drama of the Diagonal) figure:
 

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Logos Alogos II:
Horizon

This figure in turn, together with Cipra’s reference to Sartre, suggests the following excerpts (via Amazon.com)–

From Sartre’s Being and Nothingness, translated by Hazel E. Barnes, 1993 Washington Square Press reprint edition:

1. on Page 51:
“He makes himself known to himself from the other side of the world and he looks from the horizon toward himself to recover his inner being.  Man is ‘a being of distances.'”
2. on Page 154:
“… impossible, for the for-itself attained by the realization of the Possible will make itself be as for-itself–that is, with another horizon of possibilities.  Hence the constant disappointment which accompanies repletion, the famous: ‘Is it only this?’….”
3. on Page 155:
“… end of the desires.  But the possible repletion appears as a non-positional correlate of the non-thetic self-consciousness on the horizon of the  glass-in-the-midst-of-the-world.”
4. on Page 158:
“…  it is in time that my possibilities appear on the horizon of the world which they make mine.  If, then, human reality is itself apprehended as temporal….”
5. on Page 180:
“… else time is an illusion and chronology disguises a strictly logical order of  deducibility.  If the future is pre-outlined on the horizon of the world, this can be only by a being which is its own future; that is, which is to come….”
6. on Page 186:
“…  It appears on the horizon to announce to me what I am from the standpoint of what I shall be.”
7. on Page 332:
“… the boat or the yacht to be overtaken, and the entire world (spectators, performance, etc.) which is profiled on the horizon.  It is on the common ground of this co-existence that the abrupt revelation of my ‘being-unto-death’….”
8. on Page 359:
“… eyes as objects which manifest the look.  The Other can not even be the object aimed at emptily at the horizon of my being for the Other.”
9. on Page 392:
“… defending and against which he was leaning as against a wail, suddenly opens fan-wise and becomes the foreground, the welcoming horizon toward which he is fleeing for refuge.”
10.  on Page 502:
“… desires her in so far as this sleep appears on the ground of consciousness. Consciousness therefore remains always at the horizon of the desired body; it makes the meaning and the unity of the body.”
11.  on Page 506:
“… itself body in order to appropriate the Other’s body apprehended as an organic totality in situation with consciousness on the horizon— what then is the meaning of desire?”
12.  on Page 661:
“I was already outlining an interpretation of his reply; I transported myself already to the four corners of the horizon, ready to return from there to Pierre in order to understand him.”
13.  on Page 754:
“Thus to the extent that I appear to myself as creating objects by the sole relation of appropriation, these objects are myself.  The pen and the pipe, the clothing, the desk, the house– are myself.  The totality of my possessions reflects the totality of my being.  I am what I have.  It is I myself which I touch in this cup, in this trinket.  This mountain which I climb is myself to the extent that I conquer it; and when I am at its summit, which I have ‘achieved’ at the cost of this same effort, when I attain this magnificent view of the valley and the surrounding peaks, then I am the view; the panorama is myself dilated to the horizon, for it exists only through me, only for me.”

Illustration of the
last horizon remark:

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The image “http://www.log24.com/log/pix05/050527-CIPRAview.jpg” cannot be displayed, because it contains errors.
 
From CIPRA – Slovenia,
the Institute for the
Protection of the Alps

For more on the horizon, being, and nothingness, see

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