Halle Berry as Rosetta Stone
From posts tagged Modernism —
m759 @ 9:00 PM
“Function defined form, expressed in a pure geometry
– J. G. Ballard on Modernism
“The greatest obstacle to discovery is not ignorance –
— Daniel J. Boorstin, 
“In the space of horizons that neither love nor hate”
— Wallace Stevens, “Things of August”
Seven years ago yesterday—
For some context, see Rosetta Stone as a Metaphor.
Related material from the University of Western Australia—
Projective plane of order 3
(The four points on the curve
at the right of the image are
the points on the line at infinity.)
Art critic Robert Hughes, who nearly died in Western
Australia in a 1999 car crash, actually met his death
yesterday at Calvary Hospital in the Bronx.
See also Hughes on “slow art” in this journal.
Steve Buscemi last night on Saturday Night Live
describing Christmas tree ornaments with his mate Sheila—
"This one's a little computer."
"Beep Boop Beep"
"This one's a little pinecone. … Beep Boop Beep"
Meanwhile…
In related news…
"Her name drives me insane."
— Rosetta Stone, 1978 cover of "Sheila," Tommy Roe's 1962 classic
Click image for sketch.
"Rosetta Stone" as a Metaphor
in Mathematical Narratives
For some backgound, see Mathematics and Narrative from 2005.
Yesterday's posts on mathematics and narrative discussed some properties
of the 3×3 grid (also known as the ninefold square ).
For some other properties, see (at the collegeundergraduate, or MAA, level)–
Ezra Brown, 2001, "Magic Squares, Finite Planes, and Points of Inflection on Elliptic Curves."
His conclusion:
When you are done, you will be able to arrange the points into [a] 3×3 magic square,
which resembles the one in the book [5] I was reading on elliptic curves….
This result ties together threads from finite geometry, recreational mathematics,
combinatorics, calculus, algebra, and number theory. Quite a feat!
5. Viktor Prasolov and Yuri Solvyev, Elliptic Functions and Elliptic Integrals ,
American Mathematical Society, 1997.
Brown fails to give an important clue to the historical background of this topic —
the word Hessian . (See, however, this word in the book on elliptic functions that he cites.)
Investigation of this word yields a related essay at the graduatestudent, or AMS, level–
Igor Dolgachev and Michela Artebani, 2009, "The Hesse Pencil of Plane Cubic Curves ."
From the DolgachevArtebani introduction–
In this paper we discuss some old and new results about the widely known Hesse
configuration of 9 points and 12 lines in the projective plane P^{2}(k ): each point lies
on 4 lines and each line contains 3 points, giving an abstract configuration (12_{3}, 9_{4}).
PlanetMath.org on the Hesse configuration—
A picture of the Hesse configuration–
(See Visualizing GL(2,p), a note from 1985).
Related notes from this journal —
From last November —
From the December 2010 American Mathematical Society Notices—
Related material from this journal— Consolation Prize (August 19, 2010) 
From 2006 —
Sunday December 10, 2006
“Function defined form, expressed in a pure geometry
– J. G. Ballard on Modernism
“The greatest obstacle to discovery is not ignorance –
— Daniel J. Boorstin, 
Also from 2006 —
Sunday November 26, 2006
Rosalind Krauss "If we open any tract– Plastic Art and Pure Plastic Art or The NonObjective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit. From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete. Or, to take a more uptodate example…."
"He was looking at the nine engravings and at the circle,
"And it's whispered that soon if we all call the tune
The nine engravings of The Club Dumas
An example of the universal*– or, according to Krauss,
"This is the garden of Apollo, the field of Reason…."
For more on the field of reason, see
A reasonable set of "strange correspondences" Unreason is, of course, more popular. * The ninefold square is perhaps a "concrete universal" in the sense of Hegel: "Two determinations found in all philosophy are the concretion of the Idea and the presence of the spirit in the same; my content must at the same time be something concrete, present. This concrete was termed Reason, and for it the more noble of those men contended with the greatest enthusiasm and warmth. Thought was raised like a standard among the nations, liberty of conviction and of conscience in me. They said to mankind, 'In this sign thou shalt conquer,' for they had before their eyes what had been done in the name of the cross alone, what had been made a matter of faith and law and religion– they saw how the sign of the cross had been degraded."
– Hegel, Lectures on the History of Philosophy ,
"For every kind of vampire, 
And from last October —
Friday, October 8, 2010
Starting Out in the Evening 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 .
"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,
* The Web version's title has a misprint— 
"Here was finality indeed, and cleavage!"
— Malcolm Lowry, Under the Volcano
Related— Rosetta Stone, today's Google Doodle, and Rock of Ages.
Simon tells me he has a quasireligious faith in the Monster. One day, he says, … the Monster will expose the structure of the universe.
… although Simon says he is keen for me to write a book about him and his work on the Monster and his obsession with buses, he doesn’t like talking, has no sense of anecdotes or extended conversation, and can’t remember (or never paid any attention to) 90 per cent of the things I want him to tell me about in his past. It is not modesty. Simon is not modest or immodest: he just has no selfcuriosity. To Simon, Simon is a collection of disparate facts and no interpretative glue. He is a man without adjectives. His speech is made up almost entirely of short bursts of grunts and nouns.
This is the main reason why we spent three weeks together …. I needed to find a way to make him prattle.”
Those in search of prattle and interpretive glue should consult Anthony Judge’s essay ““Potential Psychosocial Significance of Monstrous Moonshine: An Exceptional Form of Symmetry as a Rosetta Stone for Cognitive Frameworks.” This was cited here in Thursday’s entry “Symmetry in Review.” (That entry is just a list of items related in part by synchronicity, in part by mathematical content. The list, while meaningful to me and perhaps a few others, is also lacking in prattle and interpretive glue.)
Those in search of knowledge, rather than glue and prattle, should consult Symmetry and the Monster, by Mark Ronan. If they have a good undergraduate education in mathematics, Terry Gannon‘s survey paper “Monstrous Moonshine: The First TwentyFive Years” (pdf) and book– Moonshine Beyond the Monster— may also be of interest.
“Put bluntly, who is kidding whom?”
— Anthony Judge, draft of
“Potential Psychosocial Significance
of Monstrous Moonshine:
An Exceptional Form of Symmetry
as a Rosetta Stone for
Cognitive Frameworks,”
dated September 6, 2007.
Good question.
Also from
September 6, 2007 —
the date of
Madeleine L’Engle‘s death —

1. The performance of a work by
Richard Strauss,
“Death and Transfiguration,”
(Tod und Verklärung, Opus 24)
by the Chautauqua Symphony
at Chautauqua Institution on
July 24, 2008
2. Headline of a music review
in today’s New York Times:
Welcoming a Fresh Season of
Transformation and Death
3. The picture of the R. T. Curtis
Miracle Octad Generator
on the cover of the book
Twelve Sporadic Groups:
4. Freeman Dyson’s hope, quoted by
Gorenstein in 1986, Ronan in 2006,
and Judge in 2007, that the Monster
group is “built in some way into
the structure of the universe.”
5. Symmetry from Plato to
the FourColor Conjecture
7. Yesterday’s entry,
“Theories of Everything“
Coda:
as a tesseract.“
— Madeleine L’Engle
For a profile of
L’Engle, click on
the Easter eggs.
Click on picture
for related symbolism.
“This is the garden of Apollo,
the field of Reason….”
John Outram, architect
I need a photoopportunity
I want a shot at redemption
Don’t want to end up a cartoon
In a cartoon graveyard
— Paul Simon
In memory of Joseph Barbera–
cocreator ot the Flintstones–
who died yesterday, a photo
from today’s Washington Post:
Playing the role of
recording angel —
Halle Berry as
Rosetta Stone:
Related material:
“Citizen Stone“
and
“Putting the X in Xmas.”
"Time and chance
happeneth to them all."
— Ecclesiastes
The number 048
may be interpreted
as referring to…
"Function defined form,
expressed in a pure geometry
that the eye could easily grasp
in its entirety."
— J. G. Ballard on Modernism
(The Guardian, March 20, 2006)
"The greatest obstacle to discovery
is not ignorance —
it is the illusion of knowledge."
— Daniel J. Boorstin,
Librarian of Congress,
quoted in Beyond Geometry
"This is the garden of Apollo,
the field of Reason…."
John Outram, architect
To Apollo (10/09/02)
Art Wars: Apollo and Dionysus (10/09/02)
Balanchine's Birthday (01/09/03)
Art Theory for Yom Kippur (10/05/03)
A Form (05/22/04)
Ineluctable (05/27/04)
A Form, continued (06/05/04)
Parallelisms (06/06/04)
Ado (06/25/04)
Deep Game (06/26/04)
Gameplayers of Zen (06/27/04)
And So To Bed (06/29/04)
Translation Plane for Rosh Hashanah (09/15/04)
Derrida Dead (10/09/04)
The Nine (11/09/04)
From Tate to Plato (11/19/04)
Art History (05/11/05)
A Miniature Rosetta Stone (08/06/05)
High Concept (8/23/05)
High Concept, Continued (8/24/05)
Analogical Train of Thought (8/25/05)
Today's Sermon: Magical Thinking (10/09/05)
Balance (10/31/05)
Matrix (11/01/05)
Seven is Heaven, Eight is a Gate (11/12/05)
Nine is a Vine (11/12/05)
Apollo and Christ (12/02/05)
Hamilton's Whirligig (01/05/06)
Cross (01/06/06)
On Beauty (01/26/06)
Sunday Morning (01/29/06)
Centre (01/29/06)
New Haven (01/29/06)
Washington Ballet (02/05/06)
Catholic Schools Sermon (02/05/06)
The Logic of Apollo (02/05/06)
Game Boy (08/06/06)
Art Wars Continued: The Krauss Cross (09/13/06)
Art Wars Continued: Pandora's Box (09/16/06)
The Pope in Plato's Cave (09/16/06)
Today's Birthdays (09/26/06)
Symbology 101 (09/26/06)
Binary Geometry
There is currently no area of mathematics named “binary geometry.” This is, therefore, a possible name for the geometry of sets with 2^{n} elements (i.e., a subtopic of Galois geometry and of algebraic geometry over finite fields– part of Weil’s “Rosetta stone” (pdf)).
Examples:
The figures are:
A symbol of Apollo from
Balanchine’s Birthday and
A Minature Rosetta Stone,
a symbol of pure reason from
Visible Mathematics and
Analogical Train of Thought,
a symbol of Venus from
Why Me? and
To Graves at the Winter Solstice,
and, finally, a more
downtoearth symbol,
adapted from a snowflake in
Those who prefer their
theological art on the scary side
may enjoy the
Christian Snowflake
link in the comments on
the “Logos” entry of
Orthodox Easter (May 1), 2005.
A Miniature
Rosetta Stone
John Baez discussed (Sept. 6, 2003) the analogies of Weil, and he himself furnished another such Rosetta stone on a much smaller scale:
“… a 24element group called the ‘binary tetrahedral group,’ a 24element group called ‘SL(2,Z/3),’ and the vertices of a regular polytope in 4 dimensions called the ’24cell.’ The most important fact is that these are all the same thing!”
For further details, see Wikipedia on the 24cell, on special linear groups, and on Hurwitz quaternions,
The group SL(2,Z/3), also known as “SL(2,3),” is of course derived from the general linear group GL(2,3). For the relationship of this group to the quaternions, see the Log24 entry for August 4 (the birthdate of the discoverer of quaternions, Sir William Rowan Hamilton).
The 3×3 square shown above may, as my August 4 entry indicates, be used to picture the quaternions and, more generally, the 48element group GL(2,3). It may therefore be regarded as the structure underlying the miniature Rosetta stone described by Baez.
“The typical example of a finite group is GL(n,q), the general linear group of n dimensions over the field with q elements. The student who is introduced to the subject with other examples is being completely misled.”
— J. L. Alperin, book review,
Bulletin (New Series) of the American
Mathematical Society 10 (1984), 121
Mathematics and Metaphor
The current (June/July) issue of the Notices of the American Mathematical Society has two feature articles. The first, on the vulgarizer Martin Gardner, was dealt with here in a June 19 entry, Darkness Visible. The second is related to a letter of André Weil (pdf) that is in turn related to mathematician Barry Mazur’s attempt to rewrite mathematical history and to vulgarize other people’s research by using metaphors drawn, it would seem, from the Weil letter.
A Mathematical Lie conjectures that Mazur’s revising of history was motivated by a desire to dramatize some arcane mathematics, the Taniyama conjecture, that deals with elliptic curves and modular forms, two areas of mathematics that have been known since the nineteenth century to be closely related.
Mazur led author Simon Singh to believe that these two areas of mathematics were, before Taniyama’s conjecture of 1955, completely unrelated —
“Modular forms and elliptic equations live in completely different regions of the mathematical cosmos, and nobody would ever have believed that there was the remotest link between the two subjects.” — Simon Singh, Fermat’s Enigma, 1998 paperback, p. 182
This is false. See Robert P. Langlands, review of Elliptic Curves, by Anthony W. Knapp, Bulletin of the American Mathematical Society, January 1994.
It now appears that Mazur’s claim was in part motivated by a desire to emulate the great mathematician André Weil’s manner of speaking; Mazur parrots Weil’s “bridge” and “Rosetta stone” metaphors —
From Peter Woit’s weblog, Feb. 10, 2005:
“The focus of Weil’s letter is the analogy between number fields and the field of algebraic functions of a complex variable. He describes his ideas about studying this analogy using a third, intermediate subject, that of function fields over a finite field, which he thinks of as a ‘bridge‘ or ‘Rosetta stone.'”
In “A 1940 Letter of André Weil on Analogy in Mathematics,” (pdf), translated by Martin H. Krieger, Notices of the A.M.S., March 2005, Weil writes that
“The purely algebraic theory of algebraic functions in any arbitrary field of constants is not rich enough so that one might draw useful lessons from it. The ‘classical’ theory (that is, Riemannian) of algebraic functions over the field of constants of the complex numbers is infinitely richer; but on the one hand it is too much so, and in the mass of facts some real analogies become lost; and above all, it is too far from the theory of numbers. One would be totally obstructed if there were not a bridge between the two. And just as God defeats the devil: this bridge exists; it is the theory of the field of algebraic functions over a finite field of constants….
On the other hand, between the function fields and the ‘Riemannian’ fields, the distance is not so large that a patient study would not teach us the art of passing from one to the other, and to profit in the study of the first from knowledge acquired about the second, and of the extremely powerful means offered to us, in the study of the latter, from the integral calculus and the theory of analytic functions. That is not to say that at best all will be easy; but one ends up by learning to see something there, although it is still somewhat confused. Intuition makes much of it; I mean by this the faculty of seeing a connection between things that in appearance are completely different; it does not fail to lead us astray quite often. Be that as it may, my work consists in deciphering a trilingual text {[cf. the Rosetta Stone]}; of each of the three columns I have only disparate fragments; I have some ideas about each of the three languages: but I know as well there are great differences in meaning from one column to another, for which nothing has prepared me in advance. In the several years I have worked at it, I have found little pieces of the dictionary. Sometimes I worked on one column, sometimes under another.”
Here is another statement of the Rosettastone metaphor, from Weil’s translator, Martin H. Krieger, in the A.M.S. Notices of November 2004, “Some of What Mathematicians Do” (pdf):
“Weil refers to three columns, in analogy with the Rosetta Stone’s three languages and their arrangement, and the task is to ‘learn to read Riemannian.’ Given an ability to read one column, can you find its translation in the other columns? In the first column are Riemann’s transcendental results and, more generally, work in analysis and geometry. In the second column is algebra, say polynomials with coefficients in the complex numbers or in a finite field. And in the third column is arithmetic or number theory and combinatorial properties.”
For greater clarity, see Armand Borel (pdf) on Weil’s Rosetta stone, where the three columns are referred to as Riemannian (transcendental), Italian (“algebraicogeometric,” over finite fields), and arithmetic (i.e., numbertheoretic).
From Fermat’s Enigma, by Simon Singh, Anchor paperback, Sept. 1998, pp. 190191:
Barry Mazur: “On the one hand you have the elliptic world, and on the other you have the modular world. Both these branches of mathematics had been studied intensively but separately…. Than along comes the TaniyamaShimura conjecture, which is the grand surmise that there’s a bridge between these two completely different worlds. Mathematicians love to build bridges.”
Simon Singh: “The value of mathematical bridges is enormous. They enable communities of mathematicians who have been living on separate islands to exchange ideas and explore each other’s creations…. The great potential of the TaniyamaShimura conjecture was that it would connect two islands and allow them to speak to each other for the first time. Barry Mazur thinks of the TaniyamaShimura conjecture as a translating device similar to the Rosetta stone…. ‘It’s as if you know one language and this Rosetta stone is going to give you an intense understanding of the other language,’ says Mazur. ‘But the TaniyamaShimura conjecture is a Rosetta stone with a certain magical power.'”
If Mazur, who is scheduled to speak at a conference on Mathematics and Narrative this July, wants more material on stones with magical powers, he might consult The Blue Matrix and The Diamond Archetype.
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