Bleecker Street logo —
Click image for some background.
Related remarks on mathematics:
The title of the previous post, "Ground Omega," suggests a related nightmare . . .
A writer of fiction in the previous post —
"When we say a thing is unreal, we mean it is too real…."
Old joke —
"What you mean 'we,' paleface?"
At Ground Omega in the above My Hero Academia site —
"The twenty-four students are split into six groups of four…."
I prefer the similar splittings of the Curtis Omega —
The title phrase, paraphrased without quotes in
the previous post, is from Christopher Alexander's book
The Timeless Way of Building (Oxford University Press, 1979).
A quote from the publisher:
"Now, at last, there is a coherent theory
which describes in modern terms
an architecture as ancient as
human society itself."
Three paragraphs from the book (pp. xiii-xiv):
19. Within this process, every individual act
of building is a process in which space gets
differentiated. It is not a process of addition,
in which preformed parts are combined to
create a whole, but a process of unfolding,
like the evolution of an embryo, in which
the whole precedes the parts, and actualy
gives birth to then, by splitting.
20. The process of unfolding goes step by step,
one pattern at a time. Each step brings just one
pattern to life; and the intensity of the result
depends on the intensity of each one of these
individual steps.
21. From a sequence of these individual patterns,
whole buildings with the character of nature
will form themselves within your thoughts,
as easily as sentences.
Compare to, and contrast with, these illustrations of "Boolean space":
(See also similar illustrations from Berkeley and Purdue.)
Detail of the above image —
Note the "unfolding," as Christopher Alexander would have it.
These "Boolean" spaces of 1, 2, 4, 8, and 16 points
are also Galois spaces. See the diamond theorem —
From the current index to obituaries at Telegraph.co.uk—
Teufel is also featured in today's New York Times—
"Mr. Teufel became a semicelebrity, helped in no small part by his last name, which means 'devil' in German."
From Group Analysis , June 1993, vol. 26 no. 2, 203-212—
by Ronald Sandison, Ledbury, Herefordshire HR8 2EY, UK
In my contribution to the Group Analysis Special Section: "Aspects of Religion in Group Analysis" (Sandison, 1993) I hinted that any consideration of a spiritual dimension to the group involves us in a discussion on whether we are dealing with good or evil spirits. But if we say that God is in the group, why is not the Devil there also? Can good and evil coexist in the same group matrix? Is the recognition of evil "nothing but" the ability to distinguish between good and bad? If not, then what is evil? Is it no more than the absence of good?
These and other questions were worked on at a joint Institute of Group Analysis and Group-Analytic Society (London) Workshop entitled "The Problem of Good and Evil." We considered the likelihood that good and evil coexist in all of us, as well as in the whole of the natural world, not only on earth, but in the cosmos and in God himself What we actually do with good and evil is to split them apart, thereby shelving the problem but at the same time creating irreconcilable opposites. This article examines this splitting and how we can work with it psychoanalytically.
This suggests a biblical remark—
"Now there was a day… when the sons of God
came to present themselves before the Lord,
and Satan came also among them."
— Job 1:6, quoted by Chesterton in The Man Who Was Thursday
Sandison died on June 18. See the Thursday, August 5, Log24 post "The Matrix."
Teufel died on July 6. See the Log24 posts for that day.
The title of this post, "rift designs," refers to a recurring theme in the July 6 posts. It is taken from Heidegger.
From a recent New Yorker review of Absence of Mind by Marilynne Robinson—
"Robinson is eloquent in her defense of the mind’s prerogatives, but her call for a renewed metaphysics might be better served by rereading Heidegger than by dusting off the Psalms."
Following this advice, we find—
"Propriation gathers the rift-design of the saying and unfolds it in such a way that it becomes the well-joined structure of a manifold showing."
— p. 415 of Heidegger's Basic Writings , edited by David Farrell Krell, HarperCollins paperback, 1993
"Das Ereignis versammelt den Aufriß der Sage und entfaltet ihn zum Gefüge des vielfältigen Zeigens."
— Heidegger, Weg zur Sprache
John Allen Paulos yesterday at Twitter—
"Plato's code cracked? http://bit.ly/ad6k1S
Fascinating if not a hoax or hype."
The story that Paulos linked to is about a British
academic who claims to have found some
symbolism hidden in Plato's writings by
splitting each into 12 parts and correlating
the 12 parts with semitones of a musical scale.
I prefer a different approach to Plato that is
related to the following hoax and hype—
HOAX:
From Dan Brown's novel Angels & Demons (2000)—
HYPE:
This four-elements diamond summarizes the classical
four elements and four qualities neatly, but some scholars
might call the figure "hype" since it deals with an academically
disreputable subject, alchemy, and since its origin is unclear.
For the four elements' role in some literature more respectable
than Dan Brown's, see Poetry's Bones.
Although an author like Brown might spin the remarks
below into a narrative— The Plato Code — they are
neither hoax nor hype.
NOT HOAX:
NOT HYPE:
For related non-hoax, non-hype remarks, see
The Rational Enterprise: Logos in Plato's Theaetetus,
by Rosemary Desjardins.
Those who prefer hoax and hype in their philosophy may consult
the writings of, say, Barbara Johnson, Rosalind Krauss, and—
in yesterday's NY Times's "The Stone" column— Nancy Bauer.
— The New York Times
Some fear that the Harry Potter books introduce children to the occult; they are not entirely mistaken.
According to Wikipedia, the “Deathly Hallows” of the final Harry Potter novel are “three fictional magical objects that appear in the book.”
The vertical line, circle, and triangle in the symbol pictured above are said to refer to these three magical objects.
One fan relates the “Deathly Hallows” symbol above, taken from the spine of a British children’s edition of the book, to a symbol for “the divine (or sacred, or secret) fire” of alchemy. She relates this fire in turn to “serpent power” and the number seven:
Kristin Devoe at a Potter fan site:
“We know that seven is a powerful number in the novels. Tom Riddle calls it ‘the most powerfully magic number.‘ The ability to balance the seven chakras within oneself allows the person to harness the secret fire. This secret fire in alchemy is the same as the kundalini or coiled snake in yogic philosophy. It is also known as ‘serpent power’ or the ‘dragon’ depending on the tradition. The kundalini is polar in nature and this energy, this internal fire, is very powerful for those who are able to harness it and it purifies the aspirant allowing them the knowledge of the universe. This secret fire is the Serpent Power which transmutes the base metals into the Perfect Gold of the Sun.
It is interesting that the symbol of the caduceus in alchemy is thought to have been taken from the symbol of the kundalini. Perched on the top of the caduceus, or the staff of Hermes, the messenger of the gods and revealer of alchemy, is the golden snitch itself! Many fans have compared this to the scene in The Order of the Phoenix where Harry tells Dumbledore about the attack on Mr. Weasley and says, ‘I was the snake, I saw it from the snake’s point of view.‘
The chapter continues with Dumbledore consulting ‘one of the fragile silver instruments whose function Harry had never known,’ tapping it with his wand:
The instrument tinkled into life at once with rhythmic clinking noises. Tiny puffs of pale green smoke issued from the minuscule silver tube at the top. Dumbledore watched the smoke closely, his brow furrowed, and after a few seconds, the tiny puffs became a steady stream of smoke that thickened and coiled into he air… A serpent’s head grew out of the end of it, opening its mouth wide. Harry wondered whether the instrument was confirming his story; He looked eagerly at Dumbledore for a sign that he was right, but Dumbledore did not look up.
“Naturally, Naturally,” muttered Dumbledore apparently to himself, still observing the stream of smoke without the slightest sign of surprise. “But in essence divided?”
Harry could make neither head not tail of this question. The smoke serpent, however split instantly into two snakes, both coiling and undulating in the dark air. With a look of grim satisfaction Dumbledore gave the instrument another gentle tap with his wand; The clinking noise slowed and died, and the smoke serpents grew faint, became a formless haze, and vanished.
Could these coiling serpents of smoke be foreshadowing events to come in Deathly Hallows where Harry learns to ‘awaken the serpent’ within himself? Could the snake’s splitting in two symbolize the dual nature of the kundalini?”
and the following
famous illustration of
the double-helix
structure of DNA:
This is taken from
a figure accompanying
an obituary, in today’s
New York Times, of the
artist who drew the figure.
The double helix
is not a structure
from magic; it may,
however, as the Rowling
quote above shows, have
certain occult uses,
better suited to
Don Henley’s
Garden of Allah
than to the
Garden of Apollo.
Similarly, the three objects
above (Log24 on April 9)
are from pure mathematics–
the realm of Apollo, not
of those in Henley’s song.
The similarity of the
top object of the three —
the “Fano plane” — to
the “Deathly Hallows”
symbol is probably
entirely coincidental.
Leventhal recently appeared in the American Masters Bob Dylan documentary on PBS. According to today’s NYT obituary, “Mr. Leventhal was… widely, if tacitly, acknowledged to have been the inspiration for Irving Steinbloom, the folk impresario whose memorial concert sets in motion the plot of the 2003 film comedy ‘A Mighty Wind.'”
From a Rosh Hashana sermon by Devra Felder Noily:
“Throughout these Holy Days we will chant Unetaneh Tokef, a liturgical poem more than a thousand years old. In it we find the words:
U-ve shofar gadol yi-ta-ka. V’ kol d’ma-ma da-kah yi-shama. The great shofar is sounded. And a still small voice is heard….
The prayer quotes from the book of Kings. There, the prophet Elijah has reached his breaking point, and God reaches out to him. The text tells us:
Then the Eternal passed by. There was a great and mighty wind, splitting mountains and shattering rocks by the power of God, but God was not in the wind. After the wind, an earthquake– but God was not in the earthquake. After the earthquake, fire– but God was not in the fire. And after the fire, a still small voice.”
or, The Eightfold Cube
Every permutation of the plane's points that preserves collinearity is a symmetry of the plane. The group of symmetries of the Fano plane is of order 168 and is isomorphic to the group PSL(2,7) = PSL(3,2) = GL(3,2). (See Cameron on linear groups (pdf).)
The above model indicates with great clarity six symmetries of the plane– those it shares with the equilateral triangle. It does not, however, indicate where the other 162 symmetries come from.
Shown below is a new model of this same projective plane, using partitions of cubes to represent points:
The second model is useful because it lets us generate naturally all 168 symmetries of the Fano plane by splitting a cube into a set of four parallel 1x1x2 slices in the three ways possible, then arbitrarily permuting the slices in each of the three sets of four. See examples below.
(Note that this procedure, if regarded as acting on the set of eight individual subcubes of each cube in the diagram, actually generates a group of 168*8 = 1,344 permutations. But the group's action on the diagram's seven partitions of the subcubes yields only 168 distinct results. This illustrates the difference between affine and projective spaces over the binary field GF(2). In a related 2x2x2 cubic model of the affine 3-space over GF(2) whose "points" are individual subcubes, the group of eight translations is generated by interchanges of parallel 2x2x1 cube-slices. This is clearly a subgroup of the group generated by permuting 1x1x2 cube-slices. Such translations in the affine 3-space have no effect on the projective plane, since they leave each of the plane model's seven partitions– the "points" of the plane– invariant.)
To view the cubes model in a wider context, see Galois Geometry, Block Designs, and Finite-Geometry Models.
For another application of the points-as-partitions technique, see Latin-Square Geometry: Orthogonal Latin Squares as Skew Lines.
For more on the plane's symmetry group in another guise, see John Baez on Klein's Quartic Curve and the online book The Eightfold Way. For more on the mathematics of cubic models, see Solomon's Cube.
Summary:
Aug 31 2004 07:31:01 PM |
Early Evening, Shining Star |
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Sep 01 2004 09:00:35 AM |
Words and Images |
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Sep 01 2004 12:07:28 PM |
Whale Rider |
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Sep 02 2004 11:11:42 AM |
Heaven and Earth |
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Sep 02 2004 07:00:23 PM |
Whale Road |
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Cinderella’s Slipper |
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Sep 03 2004 10:01:56 AM |
Another September Morn |
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Noon |
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De Nada | ||
Ite, Missa Est |
Symmetry and Change, Part 1…
Early Evening,
Shining Star
Hexagram 01
The Creative:
The movement of heaven
is full of power.
Click on picture
for details.
The Clare Lawler Prize
for Literature goes to…
For the thoughts on time |
Symmetry and Change, Part 2…
Words and Images
Hexagram 35
Progress:
The Image
The sun rises over the earth.
“Oh, my Lolita. I have only words “This is the best toy train set “As the quotes above by Nabokov and Welles suggest, we need to be able to account for the specific functions available to narrative in each medium, for the specific elements that empirical creators will ‘play with’ in crafting their narratives.” |
For
James Whale
and
William French Anderson —
Words
In the Spirit of
Dave Barry’s Book of Bad Songs:
Stay for just a while…
Stay, and let me look at you.
It’s been so long, I hardly knew you.
Standing in the door…
Stay with me a while.
I only want to talk to you.
We’ve traveled halfway ’round the world
To find ourselves again.
September morn…
We danced until the night
became a brand new day,
Two lovers playing scenes
from some romantic play.
September morning still can
make me feel this way.
Look at what you’ve done…
Why, you’ve become a grown-up girl…
— Neil Diamond
Images
In the Spirit of
September Morn:
The Last Day of Summer:
Photographs by Jock Sturges
“In 1990, the FBI entered Sturges’s studio and seized his work, claiming violation of child pornography laws.”
Related material:
and
Log24 entries of
Aug. 15, 2004.
Those interested in the political implications of Diamond’s songs may enjoy Neil Performs at Kerry Fundraiser.
I personally enjoyed this site’s description of Billy Crystal’s remarks, which included “a joke about former President Clinton’s forthcoming children’s
“Puff, puff, woo, woo, off we go!”
Symmetry and Change, Part 3…
Hexagram 28
Preponderance of
the Great:
The Image
The lake rises
above the trees.
“Congratulations to Clare Lawler, who participated very successfully in the recently held Secondary Schools Judo Championships in Wellington.”
For an explanation of this entry’s title, see the previous two entries and
Oxford Word
(Log24, July 10, 2004)
Symmetry and Change, Part 4…
Heaven and Earth
Hexagram 42
Increase:
Wind and thunder:
the image of Increase.
“This time resembles that of
the marriage of heaven and earth”
|
|
“What it all boiled down to really was everybody giving everybody else a hard time for no good reason whatever… You just couldn’t march to your own music. Nowadays, you couldn’t even hear it… It was lost, the music which each person had inside himself, and which put him in step with things as they should be.”
— The Grifters, Ch. 10, 1963, by
James Myers Thompson
“The Old Man’s still an artist
with a Thompson.”
— Terry in “Miller’s Crossing”
For some of “the music which
each person had inside,”
click on the picture
with the Thompson.
It may be that Kylie is,
in her own way, an artist…
with a 357:
(Hits counter at
The Quality of Diamond
as of 11:05 AM Sept. 2, 2004)
For more on
“the marriage of heaven and earth,”
see
Plato, Pegasus, and the Evening Star.
Symmetry and Change, Part 5…
Whale Road
Hexagram 23
Splitting Apart:
The Image
The mountain rests
on the earth.
“… the plot is different but the monsters, names, and manner of speaking will ring a bell.”
— Frank Pinto, Jr., review of Seamus Heaney’s translation of Beowulf
Other recommended reading, found during a search for the implications of today’s previous entry, “Hexagram 42”:
This excellent meditation
on symmetry and change
comes from a site whose
home page
has the following image:
Symmetry and Change, Part 6…
Cinderella’s Slipper
Hexagram 54
The Marrying Maiden:
Symmetry and Change, Part 7…
Another September Morn
Hexagram 56:
The Wanderer
Fire on the mountain,
Run boys run…
Devil’s in the House of
The Rising Sun!
Symmetry and Change, Part 8…
Hexagram 25
Innocence:
Symmetry and Change, Part 9…
Hexagram 49
Revolution:
“I sit now in a little room off the bar at four-thirty in the morning drinking ochas and then mescal and writing this on some Bella Vista notepaper I filched the other night…. But this is worst of all, to feel your soul dying. I wonder if it is because to-night my soul has really died that I feel at the moment something like peace. Or is it because right through hell there is a path, as Blake well knew, and though I may not take it, sometimes lately in dreams I have been able to see it? …And this is how I sometimes think of myself, as a great explorer who has discovered some extraordinary land from which he can never return to give his knowledge to the world: but the name of this land is hell. It is not Mexico of course but in the heart.”
— Malcolm Lowry, Under the Volcano
Symmetry and Change, conclusion…
Ite, Missa Est
Hexagram 13
Fellowship With Men:
“A pretty girl —
is like a melody —- !”
For details, see
A Mass for Lucero.
Symmetry and Change, Part 5…
Whale Road
Hexagram 23
Splitting Apart:
The Image
The mountain rests
on the earth.
“… the plot is different but the monsters, names, and manner of speaking will ring a bell.”
— Frank Pinto, Jr., review of Seamus Heaney’s translation of Beowulf
Other recommended reading, found during a search for the implications of today’s previous entry, “Hexagram 42”:
This excellent meditation
on symmetry and change
comes from a site whose
home page
has the following image:
Diablo Ballet
Thanks to Meghan for the following:
not going, not coming,
rooted, deep and still
not reaching out, not reaching in
just resting, at the center
a single jewel, the flawless crystal drop
in the blaze of its brilliance
the way beyond.
— Shih Te (c. 730)
It turns out that Shih Te ("Foundling") was the sidekick of Han Shan ("Cold Mountain"). Here are some relevant links:
Thoughts of Robert Frost (see past two days' entries) lead to "Two Tramps in Mud Time," which in turn leads to Jack Kerouac and Gary Snyder splitting wood in The Dharma Bums.
This in turn leads, via a search on "Kerouac" and "axe," to the sentence
"There's the grace of an axe handle
as good as an Eglevsky ballet,"
in Big Sur.
Kerouac taught me when I was 16 and he is still teaching me now that I am 60.
Searching for "Eglevsky ballet" leads to this site on André Eglevsky, his work, his life, and his children. A further search leads to his daughter Marina Eglevsky, who stages dance for the Diablo Ballet.
Marina Eglevsky and |
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Those who feel the above is too "arty" for them may nevertheless appreciate the movie by the same name: "Born to Dance" (1936), starring Eleanor Powell and James Stewart.
In the larger metaphorical sense, of course, Powell and Eglevsky are both part of the same dance… at the "still point" described so well by Shih Te.
"just resting, at the center
a single jewel…"
"At the still point, |
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From Marshall's Jewelers, Tucson — The ideal cut is a mathematical formula for cutting diamonds to precise angles and proportions to maximize the reflection and refraction of light. In addition to these ideal proportions, the polish and symmetry of the diamond is done to the highest standards also. Only then does it qualify to receive the American Gem Society (AGS) "triple zero" rating. A "zero" rating is the most perfect rating that the AGS gives evaluating the cut, polish, and symmetry of the diamond. When a diamond receives the "zero" rating for each of these areas, (cut, polish, and symmetry), it gets three "zeros," hence the "triple zero" rating. Because of this attention to detail, it takes up to four times longer to cut a diamond to these standards than an "average" diamond. You may choose to compromise on color or clarity but to ensure the most brilliant diamond you should not compromise on cut…. The "triple zero" ideal cut guarantees you a magnificent balance of brilliance, sparkle, and fire. |
Postscript of 1/25/03:
See also the obituary of Irene Diamond, ballet patron, for whom the New York City Ballet's "Diamond Project" is named. Diamond died on January 21, 2003, the date of the above weblog entry.
Great Simplicity
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|
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is the day that Daisetsu Suzuki attained satori,
according to the Zen Calendar. “Daisetsu” is
said to mean “Great Simplicity.”
For those who prefer Harry Potter and
Diagon Alley, here is another calendar:
To Have and Have Not
Those who prefer traditional Western religions may like a site on the Trinity that contains this:
“Zen metaphysics is perhaps most succinctly set forth in the words ‘not-two.” But even when he uses this expression, Suzuki is quick to assert that it implies no monism. Not-two, it is claimed, is not the same as one.* But when Suzuki discusses the relationship of Zen with Western mysticism, it is more difficult to escape the obvious monistic implications of his thinking. Consider the following:
We are possessed of the habit of looking at Reality by dividing it into two… It is all due to the human habit of splitting one solid Reality into two, and the result is that my ‘have’ is no ‘have’ and my ‘have not’ is no ‘have not.’ While we are actually passing, we insist that the gap is impassable.**”
*See: Daisetz T. Suzuki, ‘Basic Thoughts Underlying Eastern Ethical and Social Practice’ in Philosophy and Culture — East and West: East-West Philosophy in Practical Perspective, ed. Charles A. Moore (Honolulu: University of Hawaii Press, 1968), p. 429
** Daisetsu Teitaro Suzuki, Mysticism Christian and Buddhist (London: George Allen & Unwin, 1957, Unwin paperback, 1979), p. 57.
Personally, I am reminded by Suzuki’s satori on this date that today is the eve of the anniversary of Pearl Harbor. I am also reminded by the rather intolerant tract on the Trinity quoted above that the first atomic bomb was exploded in the New Mexico desert at a test site named Trinity. Of course, sometimes intolerance is justified.
Concluding unscientific postscript:
On the same day in 1896 that D. T. Suzuki attained satori,
lyricist Ira Gershwin was born.
Dies irae, dies illa.
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