Wednesday, June 8, 2011

… And Rosetta Stone

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

Halle Berry as Rosetta Stone

Halle Berry as Rosetta Stone

Friday, May 11, 2018

A Pure Geometry

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

From posts tagged Modernism

Sunday, December 10, 2006

m759 @ 9:00 PM

A Miniature Rosetta Stone:

The 3x3 grid

“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

Tuesday, August 7, 2012

The Space of Horizons

Filed under: General,Geometry — m759 @ 4:00 AM

“In the space of horizons that neither love nor hate”
— Wallace Stevens, “Things of August”

Seven years ago yesterday—

IMAGE- 3x3 grid related to Borofsky's 'Four Gods'

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.

Friday, January 27, 2012


Filed under: General — Tags: — m759 @ 12:21 PM


Notices of the American Mathematical Society

See also Rosetta Stone in this  journal.

Sunday, December 4, 2011

Code Wars

Filed under: General — m759 @ 2:00 PM

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"



In related news…


"Her name drives me insane."

Rosetta Stone, 1978 cover of "Sheila," Tommy Roe's 1962 classic


Click image for sketch.

Saturday, January 8, 2011

True Grid (continued)

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

"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 college-undergraduate, 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 graduate-student, or AMS, level–
Igor Dolgachev and Michela Artebani, 2009, "The Hesse Pencil of Plane Cubic Curves ."

From the Dolgachev-Artebani introduction–

In this paper we discuss some old and new results about the widely known Hesse
  of 9 points and 12 lines in the projective plane P2(k ): each point lies
on 4 lines and each line contains 3 points, giving an abstract configuration (123, 94).

PlanetMath.org on the Hesse configuration


A picture of the Hesse configuration–

The image “http://www.log24.com/log/pix05B/grid3x3med.bmp” cannot be displayed, because it contains errors.

(See Visualizing GL(2,p), a note from 1985).

Related notes from this journal —

From last November —

Saturday, November 13, 2010


m759 @ 10:12 PM

From the December 2010 American Mathematical Society Notices


Related material from this  journal—

Mathematics and Narrative and

Consolation Prize (August 19, 2010)

From 2006 —

Sunday December 10, 2006


 m759 @ 9:00 PM

A Miniature Rosetta Stone:

The image “http://www.log24.com/log/pix05B/grid3x3med.bmp” cannot be displayed, because it contains errors.

“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

Also from 2006 —

Sunday November 26, 2006


m759 @ 7:26 AM

Rosalind Krauss
in "Grids," 1979:

"If we open any tract– Plastic Art and Pure Plastic Art  or The Non-Objective 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 up-to-date example…."

"He was looking at the nine engravings and at the circle,
checking strange correspondences between them."
The Club Dumas ,1993

"And it's whispered that soon if we all call the tune
Then the piper will lead us to reason."
Robert Plant ,1971

The nine engravings of The Club Dumas
(filmed as "The Ninth Gate") are perhaps more
an example of the concrete than of the universal.

An example of the universal*– or, according to Krauss,
a "staircase" to the universal– is the ninefold square:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

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

For more on the field of reason, see
Log24, Oct. 9, 2006.

A reasonable set of "strange correspondences"
in the garden of Apollo has been provided by
Ezra Brown in a mathematical essay (pdf).

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 ,
   "Idea of a Concrete Universal Unity"

"For every kind of vampire,
there is a kind of cross."
– Thomas Pynchon   

And from last October —

Friday, October 8, 2010


m759 @ 12:00 PM

Starting Out in the Evening
… and Finishing Up at Noon

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



Above: Frank Langella in
"Starting Out in the Evening"

Right: Johnny Depp in
"The Ninth Gate"


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

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

* The Web version's title has a misprint—
   "living" instead of "lying."

"You've got to pick up every stitch…"

Thursday, September 30, 2010


Filed under: General — Tags: — m759 @ 11:02 AM

"Here was finality indeed, and cleavage!"
— Malcolm Lowry, Under the Volcano

Related— Rosetta Stone, today's Google Doodle, and Rock of Ages.

See also the New York daily numbers in yesterday's lottery.

Saturday, August 2, 2008

Saturday August 2, 2008

Filed under: General,Geometry — m759 @ 6:23 AM

There is an article in today’s Telegraph on mathematician Simon Phillips Norton– co-author, with John Horton Conway, of the rather famous paper “Monstrous Moonshine” (Bull. London Math. Soc. 11, 308–339, 1979).
“Simon studies one of the most complicated groups of all: the Monster. He is, still, the world expert on it ….

Simon tells me he has a quasi-religious 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 self-curiosity. 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 Twenty-Five Years” (pdf) and book– Moonshine Beyond the Monster— may also be of interest.

Thursday, July 31, 2008

Thursday July 31, 2008

Filed under: General,Geometry — m759 @ 12:00 PM
Symmetry in Review

“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 —

Pavarotti takes a bow
Related material:

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:

Cover of '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 Four-Color Conjecture

6. Geometry of the 4×4 Square

7. Yesterday’s entry,
Theories of Everything


There is such a thing

     as a tesseract.

— Madeleine L’Engle

Cover of The New Yorker, April 12, 2004-- Roz Chast, Easter Eggs

For a profile of
L’Engle, click on
the Easter eggs.

Tuesday, December 19, 2006

Tuesday December 19, 2006

Filed under: General — Tags: — m759 @ 9:00 AM
Joseph Barbera
at the Apollo

The 3x3 Grid

Click on picture
for related symbolism.

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

I need a photo-opportunity
I want a shot at redemption
Don’t want to end up a cartoon
In a cartoon graveyard
— Paul Simon

In memory of Joseph Barbera–
co-creator ot the Flintstones–
who died yesterday, a photo
from today’s Washington Post:

Joseph Barbera in Washington Post

Playing the role of
recording angel —

Halle Berry as
Rosetta Stone:

Halle Berry as Rosetta Stone

Related material:

Citizen Stone
Putting the X in Xmas.”

Sunday, December 10, 2006

Sunday December 10, 2006

Filed under: General,Geometry — Tags: — m759 @ 9:00 PM
The Librarian
on Nobel Prize Day

"Time and chance
happeneth to them all."
— Ecclesiastes  

PA Lottery Dec. 10, 2006: Mid-day 569, Evening 048

Timeline Index:

Pythagoras, born ca. 569 B.C.

The number 048
may be interpreted
as referring to…

A Miniature
Rosetta Stone

The image “http://www.log24.com/log/pix05B/grid3x3med.bmp” cannot be displayed, because it contains errors.

"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

Monday, October 9, 2006

Monday October 9, 2006

Filed under: General,Geometry — m759 @ 9:00 AM
To Apollo
The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

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

To Apollo (10/09/02)
Art Wars: Apollo and Dionysus
Balanchine's Birthday

Art Theory for Yom Kippur

A Form

A Form, continued

Deep Game
Gameplayers of Zen
And So To Bed
Translation Plane for Rosh Hashanah
Derrida Dead
The Nine
From Tate to Plato
Art History
A Miniature Rosetta Stone
High Concept
High Concept, Continued
Analogical Train of Thought
Today's Sermon: Magical Thinking
Seven is Heaven, Eight is a Gate
Nine is a Vine
Apollo and Christ
Hamilton's Whirligig
On Beauty
Sunday Morning
New Haven
Washington Ballet
Catholic Schools Sermon
The Logic of Apollo
Game Boy
Art Wars Continued: The Krauss Cross
Art Wars Continued: Pandora's Box
The Pope in Plato's Cave
Today's Birthdays
Symbology 101

Friday, June 23, 2006

Friday June 23, 2006

Filed under: General,Geometry — m759 @ 2:56 PM

Binary Geometry

There is currently no area of mathematics named “binary geometry.” This is, therefore, a possible name for the geometry of sets with 2n elements (i.e., a sub-topic of Galois geometry and of algebraic geometry over finite fields– part of Weil’s “Rosetta stone” (pdf)).


Saturday, December 24, 2005

Saturday December 24, 2005

Filed under: General — m759 @ 9:00 PM
Nine is a Vine

The image “http://www.log24.com/log/pix05B/051224-Stars.jpg” cannot be displayed, because it contains errors.

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?
To Graves at the Winter Solstice,

and, finally, a more
down-to-earth symbol,
adapted from a snowflake in

The image “http://www.log24.com/log/pix05B/051224-RebaCard2.jpg” cannot be displayed, because it contains errors.

an online Christmas card.

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.

Saturday, August 6, 2005

Saturday August 6, 2005

Filed under: General,Geometry — Tags: — m759 @ 9:00 AM
For André Weil on
the seventh anniversary
of his death:

 A Miniature
Rosetta Stone

The image “http://www.log24.com/log/pix05B/grid3x3med.bmp” cannot be displayed, because it contains errors.

In a 1940 letter to his sister Simone,  André Weil discussed a sort of “Rosetta stone,” or trilingual text of three analogous parts: classical analysis on the complex field, algebraic geometry over finite fields, and the theory of number fields.  

John Baez discussed (Sept. 6, 2003) the analogies of Weil, and he himself furnished another such Rosetta stone on a much smaller scale:

“… a 24-element group called the ‘binary tetrahedral group,’ a 24-element group called ‘SL(2,Z/3),’ and the vertices of a regular polytope in 4 dimensions called the ’24-cell.’ The most important fact is that these are all the same thing!”

For further details, see Wikipedia on the 24-cell, 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 48-element 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

Thursday, June 23, 2005

Thursday June 23, 2005

Filed under: General,Geometry — m759 @ 3:00 PM

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 Rosetta-stone 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 (“algebraico-geometric,” over finite fields), and arithmetic (i.e., number-theoretic).
From Fermat’s Enigma, by Simon Singh, Anchor paperback, Sept. 1998, pp. 190-191:

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 Taniyama-Shimura 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 Taniyama-Shimura 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 Taniyama-Shimura 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 Taniyama-Shimura 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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