Saturday, July 27, 2019
“Design Is How It Works.” — Steve Jobs
Wednesday, November 22, 2017
“Design is how it works” — Steve Jobs
News item from this afternoon —
The above phrase "mapping systems" suggests a review
of my own very different "map systems." From a search
for that phrase in this journal —
See also "A Four-Color Theorem: Function Decomposition
Over a Finite Field."
Wednesday, June 28, 2017
In Memory of Steve Jobs …
And his June 12, 2005, "Connecting the Dots" address at Stanford —
Monday, September 7, 2015
Saturday, June 22, 2013
Stevens and the Rock
Passage quoted in A Philosopher's Stone (April 4, 2013)—
This passage from Heidegger suggested the lexicon excerpt on
to hypokeimenon (the underlying) in yesterday's post Lexicon.
A related passage:
The Eliade passage was quoted in a 1971 Ph.D. thesis
on Wallace Stevens.
Some context— Stevens's Rock in this journal.
Sunday, November 18, 2018
Space Music
Thursday, April 5, 2018
Easter Fantasy
From this journal at midnight (12 AM ET) on April 4 —
Related material —
From the weblog of Ready Player One author Ernest Cline —
"Recently, a lot of people have asked me if a real person
inspired the character of James Halliday, the eccentric
billionaire video game designer in my book. Steve Jobs
and Steve Wozniak are both mentioned in the text,
because their world changing partnership inspired the
relationship between James Halliday and Ogden Morrow,
with Morrow being a charismatic tech industry leader like
Jobs, and Halliday being the computer geek genius of the
duo like Woz. But the character of James Halliday was
inspired by two other very different people.
As I told Wired magazine earlier this year, from the
beginning, I envisioned James Halliday’s personality as
a cross between Howard Hughes and Richard Garriott.
If I had to break it down mathematically, I’d estimate that
about 15% of Halliday’s character was inspired by
Howard Hughes (the crazy reclusive millionaire part), with
most of the other 85% being inspired by Richard Garriott."
See as well Log24 posts tagged "Space Writer"
and the classic tune "Midnight at the Oasis."
Saturday, October 22, 2016
Magis
From "The Magis way: Notes on the publishing culture,"
by Giampiero Bosoni, at http://www.magisdesign.com/magis-world/ —
"… perhaps it is interesting to reflect further on the relationship between a design object and a literary work, by reading (in whatever interpretative key you choose) the illuminating definition given by the great semiologist Roland Barthes of the act of writing and of the literary value of a text. 'Writing,' Barthes tells us, 'is historically an action that involves constant contradiction, based on dual expectations. One aspect of writing is essentially commercial, a means of control and segregation, steeped in the most materialistic aspect of society. The other is an act of pleasure, connected to the deepest urges of the body and to the subtlest and most successful products of art. This is how the written text is woven. All I have done is to arrange and reveal the threads. Now each can add his own warp to the weft.' [3] Magis’ long and highly advanced experience has given evidence, further confirmed by this latest publishing catalogue, of an ever-growing awareness of this necessary interweaving between warp and weft, between the culture of craftsmanship and that of industry, between design culture and business culture, between form and technique, between symbolic codes and practical functions, between poetry and everyday life." — Giampiero Bosoni [3] Barthes R., Variations sur l’écriture (1972), Editions du Seuil, Paris 1994, published in the second volume of the Oeuvres complètes 1966-1975 (freely translated from the Italian translation, Variazioni sulla scrittura seguite da Il piacere del testo , Ossola C. (editor) Einaudi, Turin 1999). |
See as well "Interweaving" in this journal.
"Design is how it works." — Steve Jobs
Sunday, December 27, 2015
Rigorous
Symbol —
Monday, November 7, 2011
|
Thursday, December 3, 2015
Design Wars
"… if your requirement for success is to be like Steve Jobs,
good luck to you."
— "Transformation at Yahoo Foiled by Marissa Mayer’s
Inability to Bet the Farm," New York Times online yesterday
"Design is how it works." — Steve Jobs
Related material: Posts tagged Ambassadors.
Friday, October 2, 2015
Letters
"The close of trading today will spell a new era for Google
as the search giant becomes a part of new holding company
Alphabet Inc." — ABC News, 1:53 PM ET today
From an Aug. 10, 2015, letter by Larry Page announcing the change:
Other business philosophy:
Strategy Rules: Five Timeless Lessons from
Bill Gates, Andy Grove, and Steve Jobs
by David B. Yoffie, Michael A. Cusumano
On Sale: 04/14/2015
A not-so-timeless lesson: a synchronicity check
(of this journal, not of the oeuvre of Joseph Jaworski) —
04/14/2015 — Sacramental Geometry.
Sunday, February 15, 2015
Inside the White Square
Review:
Monday, November 7, 2011
|
See also the phrase "a dance results" in the original
source and in yesterday's Valentine Dance.
Thursday, December 26, 2013
How It Works
“Design is how it works.” — Steve Jobs
“By far the most important structure in design theory
is the Steiner system S(5, 8, 24).”
— “Block Designs,” by Andries E. Brouwer (Ch. 14 (pp. 693-746),
Section 16 (p. 716) of Handbook of Combinatorics, Vol. I ,
MIT Press, 1995, edited by Ronald L. Graham, Martin Grötschel,
and László Lovász)
For some background on that Steiner system, see the footnote to
yesterday’s Christmas post.
Wednesday, June 20, 2012
Flash Job
For those who prefer a cinematic approach…
"I was alone, I took a ride…"
— Sound track of the 2010 film Steve Jobs on Flash
Tuesday, June 19, 2012
Last Words
In memory of Victor Spinetti, who died today—
— Courtesy of Steve Jobs and Aldous Huxley—
Saturday, March 3, 2012
Decomposition
A search tonight for material related to the four-color
decomposition theorem yielded the Wikipedia article
Functional decomposition.
The article, of more philosophical than mathematical
interest, is largely due to one David Fass at Rutgers.
(See the article's revision history for mid-August 2007.)
Fass's interest in function decomposition may or may not
be related to the above-mentioned theorem, which
originated in the investigation of functions into the
four-element Galois field from a 4×4 square domain.
Some related material involving Fass and 4×4 squares—
A 2003 paper he wrote with Jacob Feldman—
"Design is how it works." — Steve Jobs
An assignment for Jobs in the afterlife—
Discuss the Fass-Feldman approach to "categorization under
complexity" in the context of the Wikipedia article's
philosophical remarks on "reductionist tradition."
The Fass-Feldman paper was assigned in an MIT course
for a class on Walpurgisnacht 2003.
Monday, January 23, 2012
How Stuff Works
"Design is how it works." —Steve Jobs
Website logo—
Screenshot from How Stuff Works—
(Click image for details.)
From "A Device Worthy of a Gothic Novel,"
Chapter XVI of The Club Dumas,
by Arturo Perez-Reverte (1993),
Vintage International, April 1998….
the basis of the 1999 Roman Polanski film
The Ninth Gate —
Aren't you going to give me a document to sign?"
"A document?"
"Yes. It used to be called a pact. Now it would be a contract
with lots of small print, wouldn't it? 'In the event of litigation,
the parties are to submit to the jurisdiction of the courts of…'
That's a funny thing. I wonder which court covers this."
Saturday, December 31, 2011
The Uploading
"Design is how it works." — Steve Jobs
From a commercial test-prep firm in New York City—
From the date of the above uploading—
|
From a New Year's Day, 2012, weblog post in New Zealand—
From Arthur C. Clarke, an early version of his 2001 monolith—
"So they left a sentinel, one of millions they have scattered
throughout the Universe, watching over all worlds with the
promise of life. It was a beacon that down the ages has been
patiently signaling the fact that no one had discovered it.
Perhaps you understand now why that crystal pyramid was set…."
The numerical (not crystal) pyramid above is related to a sort of
mathematical block design known as a Steiner system.
For its relationship to the graphic block design shown above,
see the webpages Block Designs and The Diamond Theorem
as well as The Galois Tesseract and R. T. Curtis's classic paper
"A New Combinatorial Approach to M24," which contains the following
version of the above numerical pyramid—
For graphic block designs, I prefer the blocks (and the parents)
of Grand Rapids to those of New York City.
For the barbed tail of Clarke's "Angel" story, see the New Zealand post
of New Year's Day mentioned above.
Monday, December 12, 2011
X o’ Jesus
Religion for stoners,♦ in memory of Horselover Fat
Amazon.com gives the publication date of a condensed
version* of Philip K. Dick's Exegesis as Nov. 7, 2011.
The publisher gives the publication date as Nov. 8, 2011.
Here, in memory of the author, Philip K. Dick (who sometimes
called himself, in a two-part pun, "Horselover Fat"), is related
material from the above two dates in this journal—
Tuesday, November 8, 2011 m759 @ 12:00 PM …. Update of 9:15 PM Nov. 8, 2011— From a search for the word "Stoned" in this journal—
See also Monday's post "The X Box" with its illustration
Monday, November 7, 2011
"Design is how it works." — Steve Jobs, quoted in
For some background on this enigmatic equation,
|
Merry Xmas.
♦ See also last night's post and the last words of Steve Jobs.
* Houghton Mifflin Harcourt, the publisher, has, deliberately or not, sown confusion
about whether this is only the first of two volumes.
Sunday, December 11, 2011
Nine is a Vine
Flirtations
"We need a Steve Jobs of religion. Someone (or ones) who can invent not a new religion but, rather, a new way of being religious. Like Mr. Jobs’s creations, this new way would be straightforward and unencumbered and absolutely intuitive. Most important, it would be highly interactive. I imagine a religious space that celebrates doubt, encourages experimentation and allows one to utter the word God without embarrassment. A religious operating system for the Nones[*] among us. And for all of us."
— Eric Weiner , the author, most recently, of Man Seeks God: My Flirtations with the Divine .
[* A term for the religiously unaffiliated. See also the 3 PM hour of prayer.]
For highly interactive flirtations, I prefer Rebecca Larue. ("Skyrockets in flight…")
Saturday, December 3, 2011
Wednesday, November 16, 2011
Apple Meets Pumpkin
The reported last words of
Apple founder Steve Jobs were
"Oh wow. Oh wow. Oh wow."
In the spirit of these words, a
Google search from today—
See also…
- Lemniscate in this journal as well as
- Stone Junction and
- Infinite Jest .
Monday, November 7, 2011
The X Box
"Design is how it works." — Steve Jobs, quoted in
The New York Times Magazine on St. Andrew's Day, 2003
.
For some background on this enigmatic equation,
see Geometry of the I Ching.
Sunday, November 6, 2011
Design Sermon
''Most people make the mistake of thinking design is what it looks like,''
says Steve Jobs, Apple's C.E.O. ''People think it's this veneer—
that the designers are handed this box and told, 'Make it look good!'
That's not what we think design is. It's not just what it looks like and feels like.
Design is how it works.''
— "The Guts of a New Machine," by Rob Walker,
New York Times Magazine , Sunday, Nov. 30, 2003
![]() |
See also, from the day of the above Anything Box review—
St. Peter's Day, 2011— two Log24 posts—
The Shattered Mind and Rome After Dark.
Related boxes… Cosmic Cube and Design Cube.
Thursday, October 6, 2011
What’s NeXT?
(Click logo for details.)
NeXT in action:
This morning's post Opening Act suggests the following scholium—
To Purgatory fire you'll come at last;
And Christ receive your soul.
If ever you gave meat or drink,
Every night and all,
The fire will never make you shrink;
And Christ receive your soul.
See also The Wall Street Journal 's Ice Water in Hell story.
Followup scholium — "Vague but exciting …" —
Sunday, January 5, 2020
The Vulgate of Experience
"The eye’s plain version is a thing apart,
The vulgate of experience."
— Wallace Stevens, opening lines of
"An Ordinary Evening in New Haven"
Real architectural detail from a New Year's
Netflix fiction —
Click for context.
See as well a similar architectural detail in
a Log24 post of June 21, 2010.
Tuesday, September 12, 2017
Think Different
The New York Times online this evening —
"Mr. Jobs, who died in 2011, loomed over Tuesday’s
nostalgic presentation. The Apple C.E.O., Tim Cook,
paid tribute, his voice cracking with emotion, Mr. Jobs’s
steeple-fingered image looming as big onstage as
Big Brother’s face in the classic Macintosh '1984' commercial."
Review —
Thursday, September 1, 2011
How It Works
|
See also 1984 Bricks in this journal.
Chin Music
Saturday, September 9, 2017
How It Works
Del Toro and the History of Mathematics ,
Or: Applied Bullshit Continues
For del Toro —
For the history of mathematics —
Thursday, September 1, 2011
How It Works
|
Sunday, April 3, 2016
The Cruelest Month
Continued from the April 1 posts
Apple Gate and Wonders of the Invisible World
Background music: "Like a rose under the April snow…." — Streisand
The Emergence of Harlan Kane continues from yesterday —
Friday, April 1, 2016
Wonders of the Invisible World
Saturday, February 27, 2016
Pontifex ex Machina…
This time it's personal.
"Mr. Clark's designs built a bridge … ."
— The New York Times today on a computer designer
who reportedly died on Monday, Feb. 22, 2016.
From Log24 on the reported date of Mr. Clark's death —
Monday, February 22, 2016
Schoolgirl Problems…
and versions of "Both Sides Now"
See a New York Times version of "Both Sides Now."
I prefer a version by Umberto Eco.
Related material for storytellers and the Church of Synchronology —
This journal on the date of the above shooting script, 03/19/15.
Monday, December 7, 2015
Neon Joe, Werewolf Hunter
For the title, see The New York Times and the oeuvre of Joseph Kosuth.
From The Dreaming Jewels , by Theodore Sturgeon: "Oh. And the crystals make things — even complete things — like Tin Pan Alley makes songs." "Something like it." Zena smiled. It was the first smile in a long while. "Sit down, honey; I'll bring the toast. Now — this is my guess — when two crystals mate, something different happens. They make a whole thing. But they don't make it from just anything the way the single crystals do. First they seem to die together. For weeks they lie like that. After that they begin a together-dream. They find something near them that's alive, and they make it over. They replace it, cell by cell. You can't see the change going on in the thing they're replacing. It might be a dog; the dog will keep on eating and running around; it will howl at the moon and chase cats. But one day — I don't know how long it takes — it will be completely replaced, every bit of it." "Then what?" "Then it can change itself — if it ever thinks of changing itself. It can be almost anything if it wants to be." Bunny stopped chewing, thought, swallowed, and asked, "Change how?" "Oh, it could get bigger or smaller. Grow more limbs. Go into a funny shape — thin and flat, or round like a ball. If it's hurt it can grow new limbs. And it could do things with thought that we can't even imagine. Bunny, did you ever read about werewolves?" "Those nasty things that change from wolves to men and back again?" Zena sipped coffee. "Mmm. Well, those are mostly legends, but they could have started when someone saw a change like that." |
See as well The Dreaming Jewels
and "Steven Universe" in this journal.
You can't make this stuff up.
McGinn Illustrated
Monday, November 9, 2015
A Particular Mind
"The old, slow art of the eye and the hand, united in service
to the imagination, is in crisis. It’s not that painting is 'dead'
again—no other medium can as yet so directly combine
vision and touch to express what it’s like to have a particular
mind, with its singular troubles and glories, in a particular
body. But painting has lost symbolic force and function in a
culture of promiscuous knowledge and glutting information."
— Peter Schjeldahl in The New Yorker ,
issue dated Jan. 5, 2015
Cover of a 1980 book on computer music that contains a
helpful article on Walsh functions —
See, in this book, "Walsh Functions: A Digital Fourier Series,"
by Benjamin Jacoby (BYTE , September 1977). Some context:
Symmetry of Walsh Functions.
Excerpts from a search for Steve + Jobs in this journal —
Friday, October 9, 2015
Cube Design
For Aaron Sorkin and Walter Isaacson —
Related material —
Bauhaus Cube, Design Cube, and
Nabokov's Transparent Things .
Thursday, October 1, 2015
Cartoon Graveyard
The following horrific images —
— were suggested by two pieces I read yesterday in
The Harvard Crimson —
"On Belonging and 'Steven Universe'" and
"Wise Words from the King."
See also a more realistic daydream, starring Amy Adams,
in the previous post, Ornamental Language.
Tuesday, August 4, 2015
To Fuse Words with Things
A passage suggested by the previous post —
— Catholic Resistance in Elizabethan England :
Robert Persons's Jesuit Polemic, 1580–1610
by Victor Houliston (Ashgate Publishing, 2007)
Boundary Value Problem
"'The Owl in the Sarcophagus,' for all its incantatory
elegiac power, consists almost entirely of
a self-generated and self-generating rhetoric.
It points up one of the limits of poetic composition itself,
the boundary where technique turns into technology."
— Bart Eeckhout in Wallace Stevens and the Limits
of Reading and Writing , University of Missouri Press,
2002, p. 210
See as well this morning's previous post.
Block That Metaphor
"In theory, a robot could be the cloud-connecting Charon
that ushers us into the Internet of Things."
— Bryan Lufkin at Gizmodo.com, July 29, 2015
Related material —
The death of MIT computability theorist Hartley Rogers, Jr.
at 89 on July 17, and this journal on July 17.
Monday, August 3, 2015
Text and Context*
"The ORCID organization offers an open and
independent registry intended to be the de facto
standard for contributor identification in research
and academic publishing. On 16 October 2012,
ORCID launched its registry services… and
started issuing user identifiers." — Wikipedia
This journal on the above date —
A more recent identifier —
Related material —
See also the recent posts Ein Kampf and Symplectic.
* Continued.
Sunday, August 2, 2015
Symplectic
See "Symplectic" in this journal. Some illustrations —
Midrash —
"Adorned with cryptic stones and sliding shines,
An immaculate personage in nothingness,
With the whole spirit sparkling in its cloth,
Generations of the imagination piled
In the manner of its stitchings, of its thread,
In the weaving round the wonder of its need,
And the first flowers upon it, an alphabet
By which to spell out holy doom and end,
A bee for the remembering of happiness."
— Wallace Stevens, "The Owl in the Sarcophagus"
Friday, February 21, 2014
Night’s Hymn of the Rock
One way of interpreting the symbol
at the end of yesterday's post is via
the phrase "necessary possibility."
See that phrase in (for instance) a post
of July 24, 2013, The Broken Tablet .
The Tablet post may be viewed in light
of a Tom Wolfe passage quoted here on
the preceding day, July 23, 2013—
On that day (July 23) another weblog had
a post titled
Wallace Stevens: Night's Hymn of the Rock.
Some related narrative —
I prefer the following narrative —
Part I: Stevens's verse from "The Rock" (1954) —
"That in which space itself is contained"
Part II: Mystery Box III: Inside, Outside (2014)
Monday, February 10, 2014
Mystery Box III: Inside, Outside
(Continued from Mystery Box, Feb. 4, and Mystery Box II, Feb. 5.)
The Box
Inside the Box
Outside the Box
For the connection of the inside notation to the outside geometry,
see Desargues via Galois.
(For a related connection to curves and surfaces in the outside
geometry, see Hudson's classic Kummer's Quartic Surface and
Rosenhain and Göpel Tetrads in PG(3,2).)
Tuesday, June 25, 2013
Big Rock
From the LA Times online obituaries today:
Michael Feran Baigent was born in Nelson, New Zealand,
From 1998 he lectured on and led tours of the temples and Elliott Reid Longtime film, TV actor with a comic touch
Elliott "Ted" Reid, 93, a longtime character actor in films |
From a post last Saturday, June 22, and the earlier
post last Friday, June 21, that preceded it:
The Eliade passage was quoted in a 1971 Ph.D. thesis Some context— Stevens's Rock in this journal. Friday, June 21, 2013
Lexicon
|
"… a fundamental language
"… the questions raised by R. Lowell |
See also, in this journal, Big Rock.
Wednesday, April 24, 2013
Title
Google search result at 1 PM ET April 24, 2013:
New York Stage and Film 2013 Musicals – EPA – Playbill
www.playbill.com/jobs/find/job_detail/51922.html
14 hours ago – BRIGHT STAR
Casting: Howie Cherpakov
Music by Edie Brickell and Steve Martin
Lyrics by Edie Brickell Book by Steve Martin…
The musical is set in North Carolina.
From Howie Cherpakov:
From North Carolina:
Archibald Henderson monument, Chestnut Hill Cemetery, Salisbury, NC
Henderson died in 1963 on the Feast of St. Nicholas.
Related material: Santa vs. the Obelisk.
Sunday, April 14, 2013
Space Itself
From The Cambridge Companion to Wallace Stevens ,
John N. Serio, ed., "Stevens's Late Poetry," by B.J. Leggett,
pp. 62-75, an excerpt from page 70:
Click the above image for further details.
See also Nothingness and "The Rock" in this journal.
Further readings along these lines:
For pure mathematics, rather than theories of the physical world,
see the properties of the cube illustrated on the second (altered)
book cover above.
Monday, November 19, 2012
Sunday, October 9, 2011
Beautiful Failure
"Design is how it works." — Steven Jobs
A comment on the life of Jobs —
Paola Antonelli
Photo Credit: Andrea Ciotti
Paola Antonelli, senior curator of architecture and design
at the Museum of Modern Art in New York—
“NeXT was a risk and a beautiful failure."
Related material—
and 2008 posts of
Thursday, September 1, 2011
How It Works
“Design is how it works.” — Steven Jobs (See Symmetry and Design.)
“By far the most important structure in design theory is the Steiner system S(5, 8, 24).”
— “Block Designs,” by Andries E. Brouwer
The name Carmichael is not to be found in Booher’s thesis. A book he does cite for the history of S(5,8,24) gives the date of Carmichael’s construction of this design as 1937. It should be dated 1931, as the following quotation shows—
From Log24 on Feb. 20, 2010—
“The linear fractional group modulo 23 of order 24•23•11 is often represented as a doubly transitive group of degree 24 on the symbols ∞, 0, 1, 2,…, 22. This transitive group contains a subgroup of order 8 each element of which transforms into itself the set ∞, 0, 1, 3, 12, 15, 21, 22 of eight elements, while the whole group transforms this set into 3•23•11 sets of eight each. This configuration of octuples has the remarkable property that any given set of five of the 24 symbols occurs in one and just one of these octuples. The largest permutation group Γ on the 24 symbols, each element of which leaves this configuration invariant, is a five-fold transitive group of degree 24 and order 24•23•22•21•20•48. This is the Mathieu group of degree 24.”
– R. D. Carmichael, “Tactical Configurations of Rank Two,” in American Journal of Mathematics, Vol. 53, No. 1 (Jan., 1931), pp. 217-240
Epigraph from Ch. 4 of Design Theory , Vol. I:
“Es is eine alte Geschichte,
doch bleibt sie immer neu ”
—Heine (Lyrisches Intermezzo XXXIX)
See also “Do you like apples?“
Thursday, August 25, 2011
Design
"Design is how it works." — Steven Jobs (See yesterday's Symmetry.)
Today's American Mathematical Society home page—
Some related material—
The above Rowley paragraph in context (click to enlarge)—
"We employ Curtis's MOG …
both as our main descriptive device and
also as an essential tool in our calculations."
— Peter Rowley in the 2009 paper above, p. 122
And the MOG incorporates the
Geometry of the 4×4 Square.
For this geometry's relation to "design"
in the graphic-arts sense, see
Block Designs in Art and Mathematics.
Wednesday, June 29, 2011
The Shattered Mind
For St. Peter's Day
"For Stevens, the poem 'makes meanings of the rock.'
In the mind, 'its barrenness becomes a thousand things/
And so exists no more.' In fact, in a peculiar irony
that only a poet with Stevens's particular notion
of the imagination's function could develop,
the rock becomes the mind itself, shattered
into such diamond-faceted brilliance
that it encompasses all possibilities for human thought…."
—A discussion of Stevens's late poem "The Rock" (1954)
in Wallace Stevens: A World of Transforming Shapes,
by Alan D. Perlis, Bucknell University Press, 1976, p. 120
Related material on transforming shapes:
Thursday, May 5, 2011
Beyond Forgetfulness
From this journal on July 23, 2007—
It is not enough to cover the rock with leaves.
Of the ground, a cure beyond forgetfulness.
And if we ate the incipient colorings – Wallace Stevens, "The Rock" |
This quotation from Stevens (Harvard class of 1901) was posted here on when Daniel Radcliffe (i.e., Harry Potter) turned 18 in July 2007.
Other material from that post suggests it is time for a review of magic at Harvard.
On September 9, 2007, President Faust of Harvard
"encouraged the incoming class to explore Harvard’s many opportunities.
'Think of it as a treasure room of hidden objects Harry discovers at Hogwarts,' Faust said."
That class is now about to graduate.
It is not clear what "hidden objects" it will take from four years in the Harvard treasure room.
Perhaps the following from a book published in 1985 will help…
The March 8, 2011, Harvard Crimson illustrates a central topic of Metamagical Themas , the Rubik's Cube—
Hofstadter in 1985 offered a similar picture—
Hofstadter asks in his Metamagical introduction, "How can both Rubik's Cube and nuclear Armageddon be discussed at equal length in one book by one author?"
For a different approach to such a discussion, see Paradigms Lost, a post made here a few hours before the March 11, 2011, Japanese earthquake, tsunami, and nuclear disaster—
Whether Paradigms Lost is beyond forgetfulness is open to question.
Perhaps a later post, in the lighthearted spirit of Faust, will help. See April 20th's "Ready When You Are, C.B."
Sunday, April 24, 2011
Romancing the Metaphor
Background —
- Gerard Manley Hopkins on "the comfort of the Resurrection" and
- "immortal diamond" in this journal.
From a 1990 novel —
Monday, June 21, 2010
Test
From a post by Ivars Peterson, Director
of Publications and Communications at
the Mathematical Association of America,
at 19:19 UTC on June 19, 2010—
Exterior panels and detail of panel,
Michener Gallery at Blanton Museum
in Austin, Texas—
Peterson associates the four-diamond figure
with the Pythagorean theorem.
A more relevant association is the
four-diamond view of a tesseract shown here
on June 19 (the same date as Peterson's post)
in the "Imago Creationis" post—
This figure is relevant because of a
tesseract sculpture by Peter Forakis—
This sculpture was apparently shown in the above
building— the Blanton Museum's Michener gallery—
as part of the "Reimagining Space" exhibition,
September 28, 2008-January 18, 2009.
The exhibition was organized by
Linda Dalrymple Henderson, Centennial Professor
in Art History at the University of Texas at Austin
and author of The Fourth Dimension and
Non-Euclidean Geometry in Modern Art
(Princeton University Press, 1983;
new ed., MIT Press, 2009).
For the sculptor Forakis in this journal,
see "The Test" (December 20, 2009).
"There is such a thing
as a tesseract."
— A Wrinkle in TIme
Saturday, June 19, 2010
Imago Creationis
In the above view, four of the tesseract's 16
vertices are overlaid by other vertices.
For views that are more complete and
moveable, see Smith's tesseract page.
Four-Part Tesseract Divisions—
The above figure shows how four-part partitions
of the 16 vertices of a tesseract in an infinite
Euclidean space are related to four-part partitions
of the 16 points in a finite Galois space
Euclidean spaces versus Galois spaces in a larger context—
Infinite versus Finite The central aim of Western religion —
"Each of us has something to offer the Creator...
the bridging of
masculine and feminine,
life and death.
It's redemption.... nothing else matters."
-- Martha Cooley in The Archivist (1998)
The central aim of Western philosophy —
Dualities of Pythagoras
as reconstructed by Aristotle:
Limited Unlimited
Odd Even
Male Female
Light Dark
Straight Curved
... and so on ....
"Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited [man, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy." |
Another picture related to philosophy and religion—
Jung's Four-Diamond Figure from Aion—
This figure was devised by Jung
to represent the Self. Compare the
remarks of Paul Valéry on the Self—
Flight from Eden: The Origins of Modern Literary Criticism and Theory, by Steven Cassedy, U. of California Press, 1990, pages 156-157—
Valéry saw the mind as essentially a relational system whose operation he attempted to describe in the language of group mathematics. "Every act of understanding is based on a group," he says (C, 1:331). "My specialty— reducing everything to the study of a system closed on itself and finite" (C, 19: 645). The transformation model came into play, too. At each moment of mental life the mind is like a group, or relational system, but since mental life is continuous over time, one "group" undergoes a "transformation" and becomes a different group in the next moment. If the mind is constantly being transformed, how do we account for the continuity of the self? Simple; by invoking the notion of the invariant. And so we find passages like this one: "The S[elf] is invariant, origin, locus or field, it's a functional property of consciousness" (C, 15:170 [2:315]). Just as in transformational geometry, something remains fixed in all the projective transformations of the mind's momentary systems, and that something is the Self (le Moi, or just M, as Valéry notates it so that it will look like an algebraic variable). Transformation theory is all over the place. "Mathematical science… reduced to algebra, that is, to the analysis of the transformations of a purely differential being made up of homogeneous elements, is the most faithful document of the properties of grouping, disjunction, and variation in the mind" (O, 1:36). "Psychology is a theory of transformations, we just need to isolate the invariants and the groups" (C, 1:915). "Man is a system that transforms itself" (C, 2:896). O Paul Valéry, Oeuvres (Paris: Pléiade, 1957-60) C Valéry, Cahiers, 29 vols. (Paris: Centre National de le Recherche Scientifique, 1957-61) |
Note also the remarks of George David Birkhoff at Rice University
in 1940 (pdf) on Galois's theory of groups and the related
"theory of ambiguity" in Galois's testamentary letter—
… metaphysical reasoning always relies on the Principle of Sufficient Reason, and… the true meaning of this Principle is to be found in the “Theory of Ambiguity” and in the associated mathematical “Theory of Groups.” If I were a Leibnizian mystic, believing in his “preestablished harmony,” and the “best possible world” so satirized by Voltaire in “Candide,” I would say that the metaphysical importance of the Principle of Sufficient Reason and the cognate Theory of Groups arises from the fact that God thinks multi-dimensionally* whereas men can only think in linear syllogistic series, and the Theory of Groups is the appropriate instrument of thought to remedy our deficiency in this respect. * That is, uses multi-dimensional symbols beyond our grasp. |
Related material:
A medal designed by Leibniz to show how
binary arithmetic mirrors the creation by God
of something (1) from nothing (0).
Another array of 16 strings of 0's and 1's, this time
regarded as coordinates rather than binary numbers—
Some context by a British mathematician —
Imago by Wallace Stevens Who can pick up the weight of Britain, Who can move the German load Or say to the French here is France again? Imago. Imago. Imago. It is nothing, no great thing, nor man Of ten brilliancies of battered gold And fortunate stone. It moves its parade Of motions in the mind and heart, A gorgeous fortitude. Medium man In February hears the imagination's hymns And sees its images, its motions And multitudes of motions And feels the imagination's mercies, In a season more than sun and south wind, Something returning from a deeper quarter, A glacier running through delirium, Making this heavy rock a place, Which is not of our lives composed . . . Lightly and lightly, O my land, Move lightly through the air again. |
Tuesday, February 24, 2009
Tuesday February 24, 2009
Meets
Pantheistic Solipsism
Tina Fey to Steve Martin
at the Oscars:
"Oh, Steve, no one wants
to hear about our religion
… that we made up."
From Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 117:
… in 'The Pediment of Appearance,' a slight narrative poem in Transport to Summer… A group of young men enter some woods 'Hunting for the great ornament, The pediment of appearance.' Though moving through the natural world, the young men seek the artificial, or pure form, believing that in discovering this pediment, this distillation of the real, they will also discover the 'savage transparence,' the rude source of human life. In Stevens's world, such a search is futile, since it is only through observing nature that one reaches beyond it to pure form. As if to demonstrate the degree to which the young men's search is misaligned, Stevens says of them that 'they go crying/The world is myself, life is myself,' believing that what surrounds them is immaterial. Such a proclamation is a cardinal violation of Stevens's principles of the imagination. |
Superficially the young men's philosophy seems to resemble what Wikipedia calls "pantheistic solipsism"– noting, however, that "This article has multiple issues."
As, indeed, does pantheistic solipsism– a philosophy (properly called "eschatological pantheistic multiple-ego solipsism") devised, with tongue in cheek, by science-fiction writer Robert A. Heinlein.
Despite their preoccupation with solipsism, Heinlein and Stevens point, each in his own poetic way, to a highly non-solipsistic topic from pure mathematics that is, unlike the religion of Martin and Fey, not made up– namely, the properties of space.
"Sharpie, we have condensed six dimensions into four, then we either work by analogy into six, or we have to use math that apparently nobody but Jake and my cousin Ed understands. Unless you can think of some way to project six dimensions into three– you seem to be smart at such projections."
I closed my eyes and thought hard. "Zebbie, I don't think it can be done. Maybe Escher could have done it."
A discussion of Stevens's late poem "The Rock" (1954) in Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 120:
For Stevens, the poem "makes meanings of the rock." In the mind, "its barrenness becomes a thousand things/And so exists no more." In fact, in a peculiar irony that only a poet with Stevens's particular notion of the imagination's function could develop, the rock becomes the mind itself, shattered into such diamond-faceted brilliance that it encompasses all possibilities for human thought:
The rock is the gray particular of man's life,
The stone from which he rises, up—and—ho,
The step to the bleaker depths of his descents ...
The rock is the stern particular of the air,
The mirror of the planets, one by one,
But through man's eye, their silent rhapsodist,
Turquoise the rock, at odious evening bright
With redness that sticks fast to evil dreams;
The difficult rightness of half-risen day.
The rock is the habitation of the whole,
Its strength and measure, that which is near,
point A
In a perspective that begins again
At B: the origin of the mango's rind.
(Collected Poems, 528)
|
Stevens's rock is associated with empty space, a concept that suggests "nothingness" to one literary critic:
B. J. Leggett, "Stevens's Late Poetry" in The Cambridge Companion to Wallace Stevens— On the poem "The Rock":"… the barren rock of the title is Stevens's symbol for the nothingness that underlies all existence, 'That in which space itself is contained'…. Its subject is its speaker's sense of nothingness and his need to be cured of it."
More positively…
Space is, of course, also a topic
in pure mathematics…
For instance, the 6-dimensional
affine space (or the corresponding
5-dimensional projective space)
over the two-element Galois field
can be viewed as an illustration of
Stevens's metaphor in "The Rock."
Cara:
Here the 6-dimensional affine
space contains the 63 points
of PG(5, 2), plus the origin, and
the 3-dimensional affine
space contains as its 8 points
Conwell's eight "heptads," as in
Generating the Octad Generator.
Tuesday, February 17, 2009
Tuesday February 17, 2009
Diamond-Faceted:
Transformations
of the Rock
A discussion of Stevens's late poem "The Rock" (1954) in Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 120:
For Stevens, the poem "makes meanings of the rock." In the mind, "its barrenness becomes a thousand things/And so exists no more." In fact, in a peculiar irony that only a poet with Stevens's particular notion of the imagination's function could develop, the rock becomes the mind itself, shattered into such diamond-faceted brilliance that it encompasses all possibilities for human thought:
The rock is the gray particular of man's life,
The stone from which he rises, up—and—ho,
The step to the bleaker depths of his descents ...
The rock is the stern particular of the air,
The mirror of the planets, one by one,
But through man's eye, their silent rhapsodist,
Turquoise the rock, at odious evening bright
With redness that sticks fast to evil dreams;
The difficult rightness of half-risen day.
The rock is the habitation of the whole,
Its strength and measure, that which is near,
point A
In a perspective that begins again
At B: the origin of the mango's rind.
(Collected Poems, 528)
|
A mathematical version of
this poetic concept appears
in a rather cryptic note
from 1981 written with
Stevens's poem in mind:
For some explanation of the
groups of 8 and 24
motions referred to in the note,
see an earlier note from 1981.
For the Perlis "diamond facets,"
see the Diamond 16 Puzzle.
For a much larger group
of motions, see
Solomon's Cube.
As for "the mind itself"
and "possibilities for
human thought," see
Geometry of the I Ching.
Monday, July 23, 2007
Monday July 23, 2007
is 18 today.

Greetings.
“The greatest sorcerer (writes Novalis memorably)
would be the one who bewitched himself to the point of
taking his own phantasmagorias for autonomous apparitions.
Would not this be true of us?”
–Jorge Luis Borges, “Avatars of the Tortoise”
“El mayor hechicero (escribe memorablemente Novalis)
sería el que se hechizara hasta el punto de
tomar sus propias fantasmagorías por apariciones autónomas.
¿No sería este nuestro caso?”
–Jorge Luis Borges, “Los Avatares de la Tortuga“
At Midsummer Noon:“In Many Dimensions (1931)
Williams sets before his reader the
mysterious Stone of King Solomon,
an image he probably drew from
a brief description in Waite’s
The Holy Kabbalah (1929) of
a supernatural cubic stone
on which was inscribed
‘the Divine Name.’”
![]() Related material:
|
It is not enough to cover the rock with leaves. We must be cured of it by a cure of the ground Or a cure of ourselves, that is equal to a cure Of the ground, a cure beyond forgetfulness. And if we ate the incipient colorings – Wallace Stevens, “The Rock” |
Gödel and Escher and Bach
were only shadows
cast in different directions by
some central solid essence.
I tried to reconstruct
the central object, and
came up with this book.”

“shadows” of a sort,
derived from a different
“central object”:
Tuesday, February 6, 2007
Tuesday February 6, 2007
The title is from Bachelard.
I prefer Stevens:
The rock is the habitation of the whole, Its strength and measure, that which is near, point A In a perspective that begins again At B: the origin of the mango's rind. It is the rock where tranquil must adduce Its tranquil self, the main of things, the mind, The starting point of the human and the end, That in which space itself is contained, the gate To the enclosure, day, the things illumined By day, night and that which night illumines, Night and its midnight-minting fragrances, Night's hymn of the rock, as in a vivid sleep.
— Wallace Stevens,
"The Rock," 1954
Joan Ockman in Harvard Design Magazine (Fall 1998):
"'We are far removed from any reference to simple geometrical forms,' Bachelard wrote…."
No, we are not. See Log24, Christmas 2005:
More on Bachelard from Harvard Design Magazine:
"The project of discerning a loi des quatre éléments would preoccupy him until his death…."
For such a loi, see Theme and Variations and…
Saturday, August 26, 2006
Saturday August 26, 2006
"Alcatraz, Spanish for pelican, was named Isla de los Alcatraces after the birds that were the island's only inhabitants." —Bay City Guide
Related material
Thomas Kuhn's "Pelican Brief":
"… the Philosopher’s Stone was a psychic rather than a physical product. It symbolized one’s Self…."
"The formula presents a symbol of the self…."
"… Jung presents a diagram to illustrate the dynamic movements of the self…."
…the movement of
a self in the rock…
— Wallace Stevens:
The Poems of Our Climate,
by Harold Bloom,
Cornell U. Press, 1977
Wednesday, January 11, 2006
Wednesday January 11, 2006
Time in the Rock
"a world of selves trying to remember the self
before the idea of self is lost–
Walk with me world, upon my right hand walk,
speak to me Babel, that I may strive to assemble
of all these syllables a single word
before the purpose of speech is gone."
— Conrad Aiken, "Prelude" (1932),
later part of "Time in the Rock,
or Preludes to Definition, XIX" (1936),
in Selected Poems, Oxford U. Press
paperback, 2003, page 156
"The rock is the habitation of the whole,
Its strength and measure, that which is near, point A
In a perspective that begins again
At B: the origin of the mango's rind.
It is the rock where tranquil must adduce
Its tranquil self, the main of things, the mind,
The starting point of the human and the end,
That in which space itself is contained, the gate
To the enclosure, day, the things illumined
By day, night and that which night illumines,
Night and its midnight-minting fragrances,
Night's hymn of the rock, as in a vivid sleep."
— Wallace Stevens in The Rock (1954)
"Poetry is an illumination of a surface,
the movement of a self in the rock."
— Wallace Stevens, introduction to
The Necessary Angel, 1951
Jung's Imago and Solomon's Cube.
The following may help illuminate the previous entry:
"I want, as a man of the imagination, to write poetry with all the power of a monster equal in strength to that of the monster about whom I write. I want man's imagination to be completely adequate in the face of reality."
— Wallace Stevens, 1953 (Letters 790)
The "monster" of the previous entry is of course not Reese Witherspoon, but rather Vox Populi itself.
Friday, December 10, 2004
Friday December 10, 2004
Gray Particular
in Hartford
From Wallace Stevens,
"The Rock, Part III:
Forms of the Rock in a Night-Hymn" —
The rock is
the gray particular of man's life,
The stone from which
he rises, up–and–ho,
The step to
the bleaker depths of his descents…
From this morning's
New York Times obituaries—
leve Gray, a painter admired for his large-scale, vividly colorful and lyrically gestural abstract compositions, died on Wednesday in Hartford. He was 86.
The cause was a massive subdural hematoma suffered after he fell on ice and hit his head on Tuesday outside his home in Warren, Conn., said his wife, the writer Francine du Plessix Gray.
*******************************
Jackson Mac Low, a poet, composer and performance artist whose work reveled in what happens when the process of composition is left to carefully calibrated chance, died on Wednesday….
… in 1999 [he] received the Wallace Stevens Award, which carries a $100,000 prize, from the Academy of American Poets.
A Wallace Stevens Award,
in Seven Parts:
I. From a page linked to in
Tuesday's entry White Christmas:
"A bemused Plato reasoned that nonbeing must in some sense be, otherwise what is it that there is not? In our own day Martin Heidegger ventured that das Nichts nichtet — 'the nothing nothings' — evidently still sensing a problem."
— W. V. Quine in Quiddities
II. "As if nothingness
contained a métier…"
— Wallace Stevens, "The Rock"
III. "Massive subdural hematoma"
— Three-word poem
performed on Tuesday
in Connecticut
IV. mé·tier n.
- An occupation, a trade, or a profession.
- Work or activity for which a person is particularly suited; one's specialty.
[French, from Old French mestier, from Vulgar Latin misterium, from Latin ministerium. See ministry.]
Source: The American Heritage® Dictionary of the English Language, Fourth Edition
V. "ho"
— Wallace Stevens, "The Rock"
VI. Francine du Plessix Gray…
From the
Archives of the
New York Review of Books:
July 16, 1992: Splendor and Miseries, review of
Women for Hire: Prostitution and Sexuality in France after 1850 by Alain Corbin, translated by Alan Sheridan
La Vie quotidienne dans les maisons closes, 1830–1930 by Laure Adler
Figures of Ill Repute: Representing Prostitution in Nineteenth-Century France by Charles Bernheimer
Painted Love: Prostitution in French Art of the Impressionist Era by Hollis Clayson
VII. From an entry of April 29, 2004:
"… a 'dead shepherd who brought
tremendous chords from hell
And bade the sheep carouse' "
as quoted by Michael Bryson
(p. 227, The Palm
at the End of the Mind:
Selected Poems and a Play.
Ed. Holly Stevens.
New York: Vintage Books, 1990)
Sunday, December 5, 2004
Sunday December 5, 2004
Chorus from
The Rock
Author Joan Didion is 70 today.
On Didion’s late husband, John Gregory Dunne:
“His 1989 memoir Harp includes Dunne’s early years in Hartford and his Irish-Catholic family’s resentment of WASP social superiority: ‘Don’t stand out so that the Yanks can see you,’ he wrote, ‘don’t let your pretensions become a focus of Yank merriment and mockery.'”
— The Hartford Courant, August 4, 2002
From a Hartford Protestant:
The American Sublime
How does one stand
To behold the sublime,
To confront the mockers,
The mickey mockers
And plated pairs?When General Jackson
Posed for his statue
He knew how one feels.
Shall a man go barefoot
Blinking and blank?But how does one feel?
One grows used to the weather,
The landscape and that;
And the sublime comes down
To the spirit itself,The spirit and space,
The empty spirit
In vacant space.
What wine does one drink?
What bread does one eat?— Wallace Stevens
A search of the Internet for “Wallace Stevens” + “The Rock” + “Seventy Years Later” yields only one quotation…
Log24 entries of Aug. 2, 2002:
From “Seventy Years Later,” Section I of “The Rock,” a poem by Wallace Stevens:
A theorem proposed
between the two —
Two figures in a nature
of the sun….
From page 63 of The New Yorker issue dated August 5, 2002:
“Birthday, death-day —
what day is not both?”
— John Updike
From Didion’s Play It As It Lays:
Everything goes. I am working very hard at not thinking about how everything goes. I watch a hummingbird, throw the I Ching but never read the coins, keep my mind in the now.
— Page 8
From Play It As It Lays:
I lie here in the sunlight, watch the hummingbird. This morning I threw the coins in the swimming pool, and they gleamed and turned in the water in such a way that I was almost moved to read them. I refrained.
— Page 214
And the sublime comes down
To the spirit itself,
The spirit and space,
The empty spirit
In vacant space.
One heart will wear a Valentine.
— Sinatra, 1954
Saturday, February 14, 2004
Saturday February 14, 2004
Export Janet.
“… on behalf of the
Entertainment Industry Coalition
for Free Trade (EIC),
we appreciate the opportunity
to appear before you….”
— Testimony before the
U. S. International
Trade Commission
at mpaa.org
From the CNN transcript of Lou Dobbs Tonight, Friday the 13th of February, 2004…
DOBBS: Joining us tonight… Steve Forbes, the editor and chief of “Forbes”…. Mark Morrison, managing editor of “Businessweek”……..
MORRISON: We’d all like to see more job creation and less exporting of jobs. But coming to the right answer as to achieving that, what policy changes, can we make? We don’t want to go down a protectionist road.
DOBBS: Why not?
MORRISON: What would you suggest?
DOBBS: Why not?
You want to know what I would suggest? You go first.
FORBES: I don’t want another depression.
DOBBS: You don’t want a Great Depression. Do you think Smoot-Hawley caused the depression?
FORBES: It certainly contributed to it.
DOBBS: Oh, for crying out loud. The fact of the matter is, that…
FORBES: Do you want to go to North Carolina and say to the BMW workers send the jobs back to Germany?
DOBBS: I haven’t made a proposal yet and Forbes is all over me here.
FORBES: You want to have a lively show, keep your ratings up.
(LAUGHTER)
DOBBS: Yes, we’ll do that talking about Smoot-Hawley.
The fact of the matter is…
FORBES: Culture… Janet Jackson Act.
DOBBS: The fact of the matter is, we’re exporting our wealth at an alarming rate. We simply cannot continue this. And we’ve got 3 trillion dollars in IOUs. You tell me, at some point you are going to have to make a decision, either you are going to have free trade that has mindlessly led us to this point, or you are going to have fair, managed, mutual trade and build the economy back up.
FORBES: The trouble with managed trade it’s managed by politicians.
DOBBS: Well, I’d rather it be managed by politicians…
FORBES: Managing anything is something to be avoided and deplored. There — our economy today.
DOBBS: There are politicians who care about working men and women in this country. Who care about long-term wealth of this economy [more] than heads of multinationals who are indifferent.
FADE OUT; BACKGROUND SOUND:
Monday, January 20, 2003
Monday January 20, 2003
Shine On, Robinson Jeffers
"…be in nothing so moderate as in love of man,
a clever servant, insufferable master.
There is the trap that catches noblest spirits,
that caught — they say — God, when he walked on earth."
— Shine, Perishing Republic, by Robinson Jeffers
Robinson Jeffers died at Big Sur, California, on January 20, 1962 — a year to the day after Robert Frost spoke at the Kennedy inauguration.
"The poetry of Robinson Jeffers shines with a diamond's brilliance when he depicts Nature's beauty and magnificence. His verse also flashes with a diamond's hardness when he portrays human pain and folly."
— Gary Suttle
"Praise Him, He hath conferred aesthetic distance
Upon our appetites, and on the bloody
Mess of our birthright, our unseemly need,
Imposed significant form. Through Him the brutes
Enter the pure Euclidean kingdom of number…."
— Howard Nemerov,
Grace To Be Said at the Supermarket
"Across my foundering deck shone
A beacon, an eternal beam. | Flesh fade, and mortal trash
Fáll to the resíduary worm; | world's wildfire, leave but ash:
In a flash, at a trumpet crash,
I am all at once what Christ is |, since he was what I am, and
Thís Jack, jóke, poor pótsherd, | patch, matchwood,
immortal diamond,
Is immortal diamond."
— Gerard Manley Hopkins,
That Nature is a Heraclitean Fire and of the Comfort of the Resurrection
"In the last two weeks, I've been returning to Hopkins. Even in the 'world's wildfire,' he asserts that 'this Jack, joke, poor potsherd, patch, matchwood, immortal diamond,/Is immortal diamond.' A comfort."
— Michael Gerson, head White House speechwriter,
in Vanity Fair, May 2002, page 162
"There's none but truth can stead you. Christ is truth."
— Gerard Manley Hopkins
"The rock cannot be broken. It is the truth."
— Wallace Stevens
"My ghost you needn't look for; it is probably
Here, but a dark one, deep in the granite…."
— Robinson Jeffers, Tor House
On this date in 1993, the inauguration day of William Jefferson Clinton, Audrey Hepburn died.
"…today, the Rock cries out to us, clearly, forcefully…."
— Maya Angelou, January 20, 1993
"So, purposing each moment to retire,
She linger'd still. Meantime, across the moors,
Had come young Porphyro, with heart on fire"
— John Keats, The Eve of St. Agnes (January 20), IX
Top view of |
Top view of |
What you see with a Hearts On Fire diamond is an unequalled marriage of math and physics, resulting in the world's most perfectly cut diamond. |
"Eightpointed symmetrical signs are ancient symbols for the Venus goddess or the planet Venus as either the Morning star or the Evening star."
— Symbols.com
"Set me as a seal upon your heart, as a seal upon your arm; for love is strong as death, passion fierce as the grave. Its flashes are flashes of fire, a raging flame."
— Song of Solomon
"The last words from the people in the towers and on the planes, over and over again, were 'I love you.' Over and over again, the message was the same, 'I love you.' …. Perhaps this is the loudest chorus from The Rock: we are learning just how powerful love really is, even in the face of death."
— The Rev. Kenneth E. Kovacs
"Then I'll get on my knees and pray
We don't get fooled again."
— The Who
See also my note, "Bright Star," of October 23, 2002.