Log24

Saturday, November 10, 2012

Descartes Field of Dreams

Filed under: General,Geometry — m759 @ 2:01 PM

(A prequel to Galois Field of Dreams)

The opening of Descartes' Dream ,
by Philip J. Davis and Reuben Hersh—

"The modern world,
our world of triumphant rationality,
began on November 10, 1619,
with a revelation and a nightmare."

For a revelation, see Battlefield Geometry.

For a nightmare, see Joyce's Nightmare.

Some later work of Descartes

From "What Descartes knew of mathematics in 1628,"
by David Rabouin, CNRS-Univ. Paris Diderot,
Historia Mathematica , Volume 37, Issue 3,
Contexts, emergence and issues of Cartesian geometry,
August 2010, pages 428–459 —

Fig. 5. How to represent the difference between white, blue, and red
according to Rule XII [from Descartes, 1701, p. 34].

A translation —

The 4×4 array of Descartes appears also in the Battlefield Geometry posts.
For its relevance to Galois's  field of dreams, see (for instance) block designs.

Saturday, September 5, 2020

Poetry 101: “Do Not Block Intersection”

Filed under: General — m759 @ 3:15 PM

The title is from a post of July 27.

From earlier posts (Feb. 20, 2009) —

Emblematizing the Modern

The Cross of Descartes: coordinate axes

The Cross of Descartes

Note that in applications, the vertical axis of
the Cross of Descartes often symbolizes the timeless
(money, temperature, etc.) while the horizontal axis
often symbolizes time.

T.S. Eliot:

“Men’s curiosity searches past and future
And clings to that dimension. But to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint….”

Midrash for LA —

Friday, April 20, 2018

Time and Money

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

Emblematizing the Modern

The Cross of Descartes: coordinate axes

The Cross of Descartes 

Note that in applications, the vertical axis of the Cross of Descartes often symbolizes the timeless (money, temperature, etc.) while the horizontal axis often symbolizes time.

T.S. Eliot

“Men’s curiosity searches past and future
And clings to that dimension. But to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint….”

Thursday, September 1, 2016

Requiem for a Professor

Filed under: General — Tags: — m759 @ 2:00 PM

The professor of the title is David Lavery,
who reportedly died Tuesday, August 30.

Lavery is the author of, among other things, the website
Evil Genius, which contains notes toward a fiction based
on a concept by Descartes.

In memoriam

Sunday, January 24, 2016

Long Line

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

"The ideal of a complete mathematical theory of beauty
lies on the same long line of distinguished fantasies of
mathematical wisdom as the number mysticism of
Pythagoras and Plato, the Ars Magna  of Ramon Llull
(whom Agrippa studied) and Giordano Bruno
(who studied Llull and Agrippa), the vision of Mathesis
Universalis
  that Descartes and Leibniz shared, and the
Ars Combinatoria  of Leibniz. Dürer does not deny the
existence of absolute beauty but despairs of knowing it."

— The late David Ritz Finkelstein in 2007.
     He reportedly died today.

Tuesday, August 5, 2014

Verhexung

Filed under: General — Tags: — m759 @ 8:15 PM

"Philosophy is a battle against the bewitchment [Verhexung ]
of our intelligence by means of our language."

— Wittgenstein, Philosophical Investigations , Section 109

"The philosophy of logic speaks of sentences and words
in exactly the sense in which we speak of them in ordinary life
when we say e.g. 'Here is a Chinese sentence,' or 'No, that only
looks like writing; it is actually just an ornament' and so on."

— Wittgenstein, Philosophical Investigations , Section 108

Monday, June 30, 2014

High Concept

Tags:  — m759 @ 5:24 PM

For the title, see a post of Nov. 4, 2007.

Related material:

Hexagram 29, Water, and a pattern resembling
the symbol for Aquarius:

http://www.log24.com/images/IChing/hexagram29.gif          .

For some backstory about the former,
see the June 21 post Hallmark.

For some backstory about the latter,
see today’s post Toward Evening.

Tom Wolfe has supplied some scaffolding*
to support the concept.

* A reference to Grossman and Descartes.

Tuesday, July 1, 2014

Latin Word:

Filed under: General — Tags: , — m759 @ 4:36 AM

Aqua

Version 1:

(See the June 30 posts Toward Evening,
Joke, and High Concept.)

Version 2:

Version 3:

Monday, June 30, 2014

High Concept

Filed under: General — Tags: , — m759 @ 5:24 PM

For the title, see a post of Nov. 4, 2007.

Related material:

Hexagram 29, Water, and a pattern resembling
the symbol for Aquarius:

http://www.log24.com/images/IChing/hexagram29.gif          .

For some backstory about the former,
see the June 21 post Hallmark.

For some backstory about the latter,
see today’s post Toward Evening.

Tom Wolfe has supplied some scaffolding*
to support the concept.

* A reference to Grossman and Descartes.

Toward Evening

Filed under: General — Tags: , — m759 @ 7:29 AM

(Friday’s Latin Club  posts, continued)

The poet Allen Grossman reportedly died in
the morning on Friday, June 27, 2014.

IMAGE- 'Descartes' Loneliness,' by Allen Grossman, from a book published in December, 2007

Log24 post of Aug. 31, 2010, 'Page Mark'

Saturday, April 12, 2014

Art Wars

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

For the late Allen E. Puckett, Hughes Aircraft engineer and CEO,
who reportedly died at 94 on March 31 (the birthday of René Descartes) —

Friday, October 18, 2013

Mathematical Epistemology

Filed under: General,Geometry — m759 @ 2:07 PM

Yesterday's post on epistemology and geometry
suggests an Amazon customer review of Descartes's
Rules for the Direction of the Mind —

Quoted in that review —

"… we must make use of every assistance 
of the intellect, the imagination, the senses,
and the memory" (Descartes, Rules, XII)

One such assistance is the calendar.
See the date of the Blasjo review, Dec. 20, 2009,
in this journal. See also Descartes.

Monday, June 10, 2013

Brightness at Noon (continued)

Filed under: General — m759 @ 12:00 PM

A book review, a coordinate system, a post.

Click images for details.

Sunday, December 9, 2012

Adam in Eden

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

(Continued)

"… we have taken the first steps
in decoding the uniquely human
fascination with visual patterns…."

W. Tecumseh Fitch et al. ,  July 2012

Fitch cites the following as a reference:

IMAGE- Washburn and Crowe, 'Symmetries of Culture' (1988)

Washburn and Crowe discuss symmetries in general, but
not the Galois geometry underlying patterns like some of
those shown on their book's cover.

Wednesday, April 18, 2012

Adam in Eden

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

…. and John Golding, an authority on Cubism who "courted abstraction"—

"Adam in Eden was the father of Descartes." — Wallace Stevens

Fictional symbologist Robert Langdon and a cube

Symbologist Robert Langdon views a corner of Solomon's Cube

From a Log24 post, "Eightfold Cube Revisited,"
on the date of Golding's death—

Dynkin diagram D4 for triality

A related quotation—

"… quaternions provide a useful paradigm
  for studying the phenomenon of 'triality.'"

  — David A. Richter's webpage Zometool Triality

See also quaternions in another Log24 post
from the date of Golding's death— Easter Act.

Thursday, January 20, 2011

Trinity

Filed under: General — Tags: — m759 @ 8:00 PM

Reynolds Price died today. See Lore of the Manhattan Project in this journal.

In memoriam : Descartes's Twelfth Step and Symmetry and a Trinity.

Tuesday, February 16, 2010

Mysteries of Faith

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

From today's NY Times

http://www.log24.com/log/pix10/100216-NYTobits.jpg

Obituaries for mystery authors
Ralph McInerny and Dick Francis

From the date (Jan. 29) of McInerny's death–

"…although a work of art 'is formed around something missing,' this 'void is its vanishing point, not its essence.'"

Harvard University Press on Persons and Things (Walpurgisnacht, 2008), by Barbara Johnson

From the date (Feb. 14) of Francis's death–

2x2x2 cube

The EIghtfold Cube

The "something missing" in the above figure is an eighth cube, hidden behind the others pictured.

This eighth cube is not, as Johnson would have it, a void and "vanishing point," but is instead the "still point" of T.S. Eliot. (See the epigraph to the chapter on automorphism groups in Parallelisms of Complete Designs, by Peter J. Cameron. See also related material in this journal.) The automorphism group here is of course the order-168 simple group of Felix Christian Klein.

For a connection to horses, see
a March 31, 2004, post
commemorating the birth of Descartes
  and the death of Coxeter–

Putting Descartes Before Dehors

     Binary coordinates for a 4x2 array  Chess knight formed by a Singer 7-cycle

For a more Protestant meditation,
see The Cross of Descartes

Descartes

Descartes's Cross

"I've been the front end of a horse
and the rear end. The front end is better."
— Old vaudeville joke

For further details, click on
the image below–

Quine and Derrida at Notre Dame Philosophical Reviews

Notre Dame Philosophical Reviews

Tuesday, March 3, 2009

Tuesday March 3, 2009

Filed under: General — m759 @ 11:32 AM
Straight

“For every kind of vampire,
there is a kind of cross.”

— Thomas Pynchon in  
Gravity’s Rainbow

This entry is continued
from yesterday evening,
from midnight last night,
and from an entry of
 February 20 (the date
four years ago of
 Hunter Thompson’s death)–
  “Emblematizing the Modern“–

Emblematizing the Modern

Note that in applications, the vertical axis of the Cross of Descartes often symbolizes the timeless (money, temperature, etc.) while the horizontal axis often symbolizes time.

T.S. Eliot:


“Men’s curiosity searches past and future
And clings to that dimension. But to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint….”

“I played ‘Deathmaster’ straight….
 The best villains are the ones who are
 both protagonist and antagonist.”
The late Robert Quarry

“Selah.”
The late Hunter Thompson

'Deathmaster' Robert Quarry and gonzo journalist Hunter Thompson, who both died on a February 20

Yesterday afternoon’s online
New York Times:

NY Times online front page, 5 PM March 2, 2009-- graph of stock market plunge

Today’s online New York Times:

Footnote

Descending financial graph's arrow strikes man's pants cuff, immobilizing him

Friday, February 20, 2009

Friday February 20, 2009

Filed under: General — Tags: , — m759 @ 6:00 PM
A Kind of Cross

Descartes portrait

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

— Thomas Pynchon in  
Gravity's Rainbow

Descartes's Cross

Click for source.

Related material:

A memorial service
held at 2 PM today at the
U.S. Space & Rocket Center
in Huntsville, Alabama, and
 today's previous entry.

Friday February 20, 2009

Filed under: General,Geometry — Tags: , — m759 @ 2:01 PM
Emblematizing
 the Modern
 

The following meditation was
inspired by the recent fictional
recovery, by Mira Sorvino
in "The Last Templar,"

of a Greek Cross —
"the Cross of Constantine"–
and by the discovery, by
art historian Rosalind Krauss,
of a Greek Cross in the
art of Ad Reinhardt.

http://www.log24.com/log/pix09/090220-CrossOfDescartes.jpg

The Cross of Descartes  

Note that in applications, the vertical axis
of the Cross of Descartes often symbolizes
the timeless (money, temperature, etc.)
while the horizontal axis often symbolizes time.


T.S. Eliot:

"Men’s curiosity searches past and future
And clings to that dimension. But to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint…."


There is a reason, apart from her ethnic origins, that Rosalind Krauss (cf. 9/13/06) rejects, with a shudder, the cross as a key to "the Pandora's box of spiritual reference that is opened once one uses it." The rejection occurs in the context of her attempt to establish not the cross, but the grid, as a religious symbol:
 

"In suggesting that the success [1] of the grid
is somehow connected to its structure as myth,
I may of course be accused of stretching a point
beyond the limits of common sense, since myths
are stories, and like all narratives they unravel
through time, whereas grids are not only spatial
to start with, they are visual structures
that explicitly reject a narrative
or sequential reading of any kind.

[1] Success here refers to
three things at once:
a sheerly quantitative success,
involving the number of artists
in this century who have used grids;
a qualitative success through which
the grid has become the medium
for some of the greatest works
of modernism; and an ideological
success, in that the grid is able–
in a work of whatever quality–
to emblematize the Modern."

— Rosalind Krauss, "Grids" (1979)

Related material:

Time Fold and Weyl on
objectivity and frames of reference.

See also Stambaugh on
The Formless Self
as well as
A Study in Art Education
and
Jung and the Imago Dei.

Thursday, October 25, 2007

Thursday October 25, 2007

Filed under: General,Geometry — Tags: — m759 @ 9:19 AM

Something Anonymous

From this date–
Picasso's birthday–
five years ago:
 
"A work of art has an author
and yet,
when it is perfect,
it has something
which is
essentially anonymous about it."

Simone Weil, Gravity and Grace   

 
Michelangelo's birthday, 2003

4x4 square grid

Yesterday:

The color-analogy figures of Descartes

Nineteenth-century quilt design:

Tents of Armageddon quilt design

Related material:

Battlefield Geometry
 

Wednesday, October 24, 2007

Wednesday October 24, 2007

Filed under: General,Geometry — Tags: , , — m759 @ 11:11 PM
Descartes’s Twelfth Step

An earlier entry today (“Hollywood Midrash continued“) on a father and son suggests we might look for an appropriate holy ghost. In that context…

Descartes

A search for further background on Emmanuel Levinas, a favorite philosopher of the late R. B. Kitaj (previous two entries), led (somewhat indirectly) to the following figures of Descartes:

The color-analogy figures of Descartes
This trinity of figures is taken from DescartesRule Twelve in Rules for the Direction of the Mind. It seems to be meant to suggest an analogy between superposition of colors and superposition of shapes.Note that the first figure is made up of vertical lines, the second of vertical and horizontal lines, and the third of vertical, horizontal, and diagonal lines. Leon R. Kass recently suggested that the Descartes figures might be replaced by a more modern concept– colors as wavelengths. (Commentary, April 2007). This in turn suggests an analogy to Fourier series decomposition of a waveform in harmonic analysis. See the Kass essay for a discussion of the Descartes figures in the context of (pdf) Science, Religion, and the Human Future (not to be confused with Life, the Universe, and Everything).

Compare and contrast:

The harmonic-analysis analogy suggests a review of an earlier entry’s
link today to 4/30–  Structure and Logic— as well as
re-examination of Symmetry and a Trinity


(Dec. 4, 2002).

See also —

A Four-Color Theorem,
The Diamond Theorem, and
The Most Violent Poem,

Emma Thompson in 'Wit'

from Mike Nichols’s birthday, 2003.

Tuesday, August 7, 2007

Tuesday August 7, 2007

Filed under: General — m759 @ 8:00 AM
The Horse Whisperer

Scarlett Johansson and friend in The Horse Whisperer

Scarlett Johansson and friend
in “The Horse Whisperer” (1998)

Thanks to University Diaries (Aug. 6) for the following:

“‘The University of Sydney has ordered an independent review into allegations that the dean of the Conservatorium of Music hired a horse whisperer to conduct management workshops.’ [Are you, like UD, a bit vague on exactly what a horse whisperer is? And are you having trouble figuring out what a horse whisperer would have to offer a management workshop? But then, what exactly is a management workshop? Read on.]”

For some background on horse whispering and management workshops, see IABC Steal Sheet, March 2004.

Related material:

The recent Log24 entries

University Diaries:
“God, isn’t there already
enough crap in this story?”

See also Log24,
Dec. 10, 2003:

Putting Descartes Before Dehors

      

Descartes déclare que
c’est en moi, non hors de moi,
en moi, non dans le monde,
que je pourrais voir
si quelque chose existe
hors de moi.”

ATRIUM, Philosophie     

For further details,
see ART WARS.

Sunday, June 17, 2007

Sunday June 17, 2007

Filed under: General — Tags: — m759 @ 3:00 PM
No Place Like Home:
A Father's Day Special
for Stephen King

The image “http://www.log24.com/log/pix07/070617-Shining2.jpg” cannot be displayed, because it contains errors.

"… the poet's search
for the same exterior
made / Interior"
— Wallace Stevens  

"Imago. Imago. Imago."
— Wallace Stevens
(See previous entry.)

Stevens's phrase was
the epigraph to
The Imago Sequence,
a novella published
in May 2005.

From a review
(containing a spoiler)
of the novella:

"The Imago Sequence are three notable photographs taken by an otherwise unnotable photographer. They are photographs taken underground, location a well kept secret, and show either a bizarre rock formation carved out over millenia, or perhaps the imprint of a fossiled hominid in an anguished pose.

The photographs can have an impact on the viewer, and have had a history of having a major impact on the owners. One has changed hands, and the new owner shows off his new prized objet d'art, and sets one of his employees the tasks [sic] of identifying the location of the third in the sequence…."


Greensburg, Kansas

prior to
May 4, 2007:

The image “http://www.log24.com/log/pix07/070617-WellSign.jpg” cannot be displayed, because it contains errors.

This may be taken
as a reference to
today's previous entry.

That entry, like
the novella
The Imago Sequence,
contains a sequence
of three photographs.
The sequence was made
a month or so after the
novella was published,
but I was unaware
until this afternoon
that the novella existed.

Besides
"Imago Imago Imago,"
two other phrases
come to mind…

The real estate motto

"Location, Location, Location"

and Stevens again

"Adam in Eden was the
father of Descartes."

Happy Father's Day.
 

Friday, June 15, 2007

Friday June 15, 2007

Filed under: General,Geometry — Tags: , — m759 @ 1:00 PM
A Study in
Art Education

Rudolf Arnheim, a student of Gestalt psychology (which, an obituary notes, emphasizes "the perception of forms as organized wholes") was the first Professor of the Psychology of Art at Harvard.  He died at 102 on Saturday, June 9, 2007.

The conclusion of yesterday's New York Times obituary of Arnheim:

"… in The New York Times Book Review in 1986, Celia McGee called Professor Arnheim 'the best kind of romantic,' adding, 'His wisdom, his patient explanations and lyrical enthusiasm are those of a teacher.'"

A related quotation:

"And you are teaching them a thing or two about yourself. They are learning that you are the living embodiment of two timeless characterizations of a teacher: 'I say what I mean, and I mean what I say' and 'We are going to keep doing this until we get it right.'"

Tools for Teaching

Here, yet again, is an illustration that has often appeared in Log24– notably, on the date of Arnheim's death:
 

The 3x3 square

Related quotations:

"We have had a gutful of fast art and fast food. What we need more of is slow art: art that holds time as a vase holds water: art that grows out of modes of perception and whose skill and doggedness make you think and feel; art that isn't merely sensational, that doesn't get its message across in 10 seconds, that isn't falsely iconic, that hooks onto something deep-running in our natures. In a word, art that is the very opposite of mass media. For no spiritually authentic art can beat mass media at their own game."

Robert Hughes, speech of June 2, 2004

"Whether the 3×3 square grid is fast art or slow art, truly or falsely iconic, perhaps depends upon the eye of the beholder."

Log24, June 5, 2004

If the beholder is Rudolf Arnheim, whom we may now suppose to be viewing the above figure in the afterlife, the 3×3 square is apparently slow art.  Consider the following review of his 1982 book The Power of the Center:

"Arnheim deals with the significance of two kinds of visual organization, the concentric arrangement (as exemplified in a bull's-eye target) and the grid (as exemplified in a Cartesian coordinate system)….

It is proposed that the two structures of grid and target are the symbolic vehicles par excellence for two metaphysical/psychological stances.  The concentric configuration is the visual/structural equivalent of an egocentric view of the world.  The self is the center, and all distances exist in relation to the focal spectator.  The concentric arrangement is a hermetic, impregnable pattern suited to conveying the idea of unity and other-worldly completeness.  By contrast, the grid structure has no clear center, and suggests an infinite, featureless extension…. Taking these two ideal types of structural scaffold and their symbolic potential (cosmic, egocentric vs. terrestrial, uncentered) as given, Arnheim reveals how their underlying presence organizes works of art."

— Review of Rudolf Arnheim's The Power of the Center: A Study of Composition in the Visual Arts (Univ. of Calif. Press, 1982). Review by David A. Pariser, Studies in Art Education, Vol. 24, No. 3 (1983), pp. 210-213

Arnheim himself says in this book (pp. viii-ix) that "With all its virtues, the framework of verticals and horizontals has one grave defect.  It has no center, and therefore it has no way of defining any particular location.  Taken by itself, it is an endless expanse in which no one place can be distinguished from the next.  This renders it incomplete for any mathematical, scientific, and artistic purpose.  For his geometrical analysis, Descartes had to impose a center, the point where a pair of coordinates [sic] crossed.  In doing so he borrowed from the other spatial system, the centric and cosmic one."

Students of art theory should, having read the above passages, discuss in what way the 3×3 square embodies both "ideal types of structural scaffold and their symbolic potential."

We may imagine such a discussion in an afterlife art class– in, perhaps, Purgatory rather than Heaven– that now includes Arnheim as well as Ernst Gombrich and Kirk Varnedoe.

Such a class would be one prerequisite for a more advanced course– Finite geometry of the square and cube.

Sunday, October 1, 2006

Sunday October 1, 2006

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

Recipe for Disaster
 
according to Jerome Kagan,
Harvard psychologist emeritus
 

From Log24 —
 

The Line

The image “http://www.log24.com/theory/images/GridCube165C3.jpg” cannot be displayed, because it contains errors.

The Cube

From Harvard's
Jerome Kagan —
"'Humans demand that there be a clear right and wrong,' he said. 'You've got to believe that the track you've taken is the right track. You get depressed if you're not certain as to what it is you're supposed to be doing or what's right and wrong in the world.'" "People need to divide the world into good and evil, us and them, Kagan continued. To do otherwise– to entertain the possibility that life is not black and white, but variously shaded in gray– is perhaps more honest, rational and decent. But it's also, psychically, a recipe for disaster."
The image “http://www.log24.com/log/pix06A/061001-epi3-w156.jpg” cannot be displayed, because it contains errors.

Black and White:

Log24 in
May 2005

The image “http://www.log24.com/log/pix06A/061001-Grays.jpg” cannot be displayed, because it contains errors.

Shades of Gray:

An affine space
and 
Harvard's
Jerome Kagan

 

The above Kagan quotes are taken
from a New York Times essay by
Judith Warner as transcribed by
Mark Finkelstein on Sept. 29.

See also Log24 on
Sept. 29 and 30.

Related material:

Kagan's book

The image “http://www.log24.com/log/pix06A/SurpriseUncertainty.jpg” cannot be displayed, because it contains errors.

Surprise, Uncertainty,
and Mental Structures

(Harvard U. Press, April 2002)

and Werner Heisenberg–
discoverer of the
uncertainty principle
as Anakin Skywalker
being tempted by
the Dark Side:

The image “http://www.log24.com/log/pix05/050519-Anakin.jpg” cannot be displayed, because it contains errors.

(From Log24, May 2005)
 
George Lucas, who has profited
enormously from public depictions
of the clash between
good and evil, light and dark,
may in private life be inclined
to agree with Hercule Poirot:
 
"It is the brain, the little gray cells
on which one must rely.
One must seek the truth
within– not without."
 
(This is another version of the
"Descartes before dehors" principle–
See "A Table," Sept. 28.)
 

Thursday, September 28, 2006

Thursday September 28, 2006

Filed under: General,Geometry — m759 @ 9:15 AM
A Table

From the diary
of John Baez:

September 22, 2006

… Meanwhile, the mystics beckon:

Out beyond ideas of wrongdoing and rightdoing, there is a field. I’ll meet you there. – Rumi

September 23, 2006

I’m going up to San Rafael (near the Bay in Northern California) to visit my college pal Bruce Smith and his family. I’ll be back on Wednesday the 27th, just in time to start teaching the next day.

A check on the Rumi quote yields
this, on a culinary organization:

“Out beyond rightdoing and wrongdoing there is a field.  I’ll meet you there.”

This is the starting place of good spirit for relationship healing and building prescribed centuries ago in the Middle East by Muslim Sufi teacher and mystic, Jelaluddin Rumi (1207-1273).

Even earlier, the Psalmists knew such a meeting place of adversaries was needed, sacred and blessed:

“Thou preparest a table before me in the presence of mine enemies….” (23rd Psalm)

A Field and a Table:

The image “http://www.log24.com/theory/GF8-Table.gif” cannot be displayed, because it contains errors.

From “Communications Toolbox”
at MathWorks.com

For more on this field
in a different context, see
Generating the Octad Generator
and
“Putting Descartes Before Dehors”
in my own diary for December 2003.

The image “http://www.log24.com/log/pix06A/060928-Descartes.jpg” cannot be displayed, because it contains errors.
Descartes



Après l’Office à l’Église
de la Sainte-Trinité, Noël 1890

(After the Service at Holy Trinity Church,
Christmas 1890), Jean Béraud

Let us pray to the Holy Trinity that
San Rafael guides the teaching of John Baez
this year.  For related material on theology
and the presence of enemies, see Log24 on
  the (former) Feast of San Rafael, 2003.

Saturday, April 8, 2006

Saturday April 8, 2006

Filed under: General — Tags: — m759 @ 4:06 PM

April 6 two years ago:

Ideas and Art

The first idea was not our own.  Adam
In Eden was the father of Descartes

— Wallace Stevens, from
   Notes Toward a Supreme Fiction

Thursday, March 31, 2005

Thursday March 31, 2005

Filed under: General — m759 @ 3:16 AM

“In collage, juxtaposition is everything.”

    April 2, 2004

The above material may be regarded
as commemorating the March 31
birth of René Descartes
 and death of H. S. M. Coxeter.

For material related to Descartes,
see The Line.
For material related to Coxeter,
see Art Wars.

Thursday, April 29, 2004

Thursday April 29, 2004

Filed under: General — m759 @ 5:12 PM

X

Tonight on PBS:
The Jesus Factor

From Good Friday:

3 PM
Good
Friday

For an explanation
of this icon, see

Art Wars
and
To Be.

From Eternity:

Red Hook! Jesus!

From Holy Saturday:

“There is a suggestion of Christ descending into the abyss for the harrowing of Hell.  But it is the Consul whom we think of here, rather than of Christ.  The Consul is hurled into this abyss at the end of the novel.”

— Introduction to
Under the Volcano

Couleurs

In memory of
René Descartes
(born March 31)
and
René Gruau
(died March 31)

On the former:

“The predominant use
of the letter

x
to represent
an unknown value
came about in
an interesting way.”

On the latter:

“The women he drew
often seemed
to come alive.”

“…a ‘dead shepherd who brought
tremendous chords from hell
And bade the sheep carouse’ “

(p. 227, The Palm at the End of the Mind: Selected Poems and a Play. Ed. Holly Stevens. New York: Vintage Books, 1990)
— Wallace Stevens
    as quoted by Michael Bryson

See also the entries of 5/12.

Sunday, April 18, 2004

Sunday April 18, 2004

Filed under: General — m759 @ 2:00 AM

Dream of Youth Revisited

For some material related to the entry Dream of Youth of last Dec. 8 (the feast day of St. Hermann Weyl), see the recently updated A Mathematical Lie.

See, too, a “comedy of errors” from

7 rue René Descartes in Strasbourg (pdf)

on what Hilbert reportedly called “the most beautiful part of mathematics.”

Sunday, April 11, 2004

Sunday April 11, 2004

Filed under: General,Geometry — m759 @ 3:28 PM

Good Friday and
Descartes’s Easter Egg

“The use of z, y, x . . . to represent unknowns is due to René Descartes, in his La géometrie (1637)…. In a paper on Cartesian ovals, prepared before 1629, x alone occurs as unknown…. This is the earliest place in which Descartes used one of the last letters of the alphabet to represent an unknown.”

— Florian Cajori, A History of Mathematical Notations. 2 volumes. Lasalle, Illinois: The Open Court Publishing Co., 1928-1929. (Vol. 1, page 381)

This is from

http://members.aol.com/jeff570/variables.html.

Descartes’s Easter Egg is found at

EggMath: The Shape of an Egg —
Cartesian Ovals
 

An Easter Meditation
on Humpty Dumpty

The following is excerpted from a web page headed “Catholic Way.”  It is one of a series of vicious and stupid Roman Catholic attacks on Descartes.  Such attacks have been encouraged by the present Pope, who today said “may the culture of life and love render vain the logic of death.”

The culture of life and love is that of the geometry (if not the philosophy) of Descartes.  The logic of death is that of Karol Wojtyla, as was made very clear in the past century by the National Socialist Party, which had its roots in Roman Catholicism.

Humpty Dumpty sat on a wall.
Humpty Dumpty had a great fall

“In the century just completed, the human race found itself in a position not unlike the scrambled mess at the base of an imaginary English wall….

… we are heirs to a humanity that is broken, fractured, confused, unsure of what to make of itself….

 … ‘postmodernism’ is merely the articulation of the fractured, dissipated state of the human being…. 

Without relating a history of modern philosophy, our unfortunate human shell has suffered a continual fragmentation for a period of roughly 500 years. (You philosophers out there will recognize immediately that I am referring to the legacy of René Descartes.) And this fragmentation has been a one-way street: one assault after another on the integrity and dignity of the human person until you have, well, the 20th Century.

But now it’s the 21st Century.

The beauty … the marvel … the miracle of our time is the possibility that gravity will reverse itself: Humpty Dumpty may be able, once again, to assume his perch.”

—  Ted Papa,
Raising Humpty Dumpty

Voilà.

The upper part
of the above icon
is from EggMath.
For the lower part,
see Good Friday.

Saturday, April 10, 2004

Saturday April 10, 2004

Filed under: General — m759 @ 3:19 PM

Couleurs

In memory of
René Descartes
(born March 31)
and
René Gruau
(died March 31)

On the former:

“The predominant use of the letter x
to represent an unknown value
came about in an interesting way.”

On the latter:

“The women he drew
often seemed to come alive.”

Tuesday, April 6, 2004

Tuesday April 6, 2004

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

Ideas and Art, Part III

The first idea was not our own.  Adam
In Eden was the father of Descartes

— Wallace Stevens, from
Notes Toward a Supreme Fiction

“Quaedam ex his tanquam rerum imagines sunt, quibus solis proprie convenit ideae nomen: ut cùm hominem, vel Chimaeram, vel Coelum, vel Angelum, vel Deum cogito.”

Descartes, Meditationes III, 5

“Of my thoughts some are, as it were, images of things, and to these alone properly belongs the name idea; as when I think [represent to my mind] a man, a chimera, the sky, an angel or God.”

Descartes, Meditations III, 5

Begin, ephebe, by perceiving the idea
Of this invention, this invented world,
The inconceivable idea of the sun.

You must become an ignorant man again
And see the sun again with an ignorant eye
And see it clearly in the idea of it.

— Wallace Stevens, from
Notes Toward a Supreme Fiction

“… Quinimo in multis saepe magnum discrimen videor deprehendisse: ut, exempli causâ, duas diversas solis ideas apud me invenio, unam tanquam a sensibus haustam, & quae maxime inter illas quas adventitias existimo est recensenda, per quam mihi valde parvus apparet, aliam verò ex rationibus Astronomiae desumptam, hoc est ex notionibus quibusdam mihi innatis elicitam, vel quocumque alio modo a me factam, per quam aliquoties major quàm terra exhibetur; utraque profecto similis eidem soli extra me existenti esse non potest, & ratio persuadet illam ei maxime esse dissimilem, quae quàm proxime ab ipso videtur emanasse.”

Descartes, Meditationes III, 11

“… I have observed, in a number of instances, that there was a great difference between the object and its idea. Thus, for example, I find in my mind two wholly diverse ideas of the sun; the one, by which it appears to me extremely small draws its origin from the senses, and should be placed in the class of adventitious ideas; the other, by which it seems to be many times larger than the whole earth, is taken up on astronomical grounds, that is, elicited from certain notions born with me, or is framed by myself in some other manner. These two ideas cannot certainly both resemble the same sun; and reason teaches me that the one which seems to have immediately emanated from it is the most unlike.”

Descartes, Meditations III, 11

“Et quamvis forte una idea ex aliâ nasci possit, non tamen hîc datur progressus in infinitum, sed tandem ad aliquam primam debet deveniri, cujus causa sit in star archetypi, in quo omnis realitas formaliter contineatur, quae est in ideâ tantùm objective.”

Descartes, Meditationes III, 15

“And although an idea may give rise to another idea, this regress cannot, nevertheless, be infinite; we must in the end reach a first idea, the cause of which is, as it were, the archetype in which all the reality [or perfection] that is found objectively [or by representation] in these ideas is contained formally [and in act].”

Descartes, Meditations III, 15

Michael Bryson in an essay on Stevens’s “Notes Toward a Supreme Fiction,”

The Quest for the Fiction of the Absolute:

“Canto nine considers the movement of the poem between the particular and the general, the immanent and the transcendent: “The poem goes from the poet’s gibberish to / The gibberish of the vulgate and back again. / Does it move to and fro or is it of both / At once?” The poet, the creator-figure, the shadowy god-figure, is elided, evading us, “as in a senseless element.”  The poet seeks to find the transcendent in the immanent, the general in the particular, trying “by a peculiar speech to speak / The peculiar potency of the general.” In playing on the senses of “peculiar” as particular and strange or uncanny, these lines play on the mystical relation of one and many, of concrete and abstract.”

Brian Cronin in Foundations of Philosophy:

“The insight is constituted precisely by ‘seeing’ the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete. We pivot back and forth between images and ideas as we search for the correct insight.”

— From Ch. 2, Identifying Direct Insights

Michael Bryson in an essay on Stevens’s “Notes Toward a Supreme Fiction“:

“The fourth canto returns to the theme of opposites. ‘Two things of opposite natures seem to depend / On one another . . . . / This is the origin of change.’  Change resulting from a meeting of opposities is at the root of Taoism: ‘Tao produced the One. / The One produced the two. / The two produced the three. / And the three produced the ten thousand things’ (Tao Te Ching 42) ….”

From an entry of March 7, 2004

From the web page

Introduction to the I Ching–
By Richard Wilhelm
:

“He who has perceived the meaning of change fixes his attention no longer on transitory individual things but on the immutable, eternal law at work in all change. This law is the tao of Lao-tse, the course of things, the principle of the one in the many. That it may become manifest, a decision, a postulate, is necessary. This fundamental postulate is the ‘great primal beginning’ of all that exists, t’ai chi — in its original meaning, the ‘ridgepole.’ Later Chinese philosophers devoted much thought to this idea of a primal beginning. A still earlier beginning, wu chi, was represented by the symbol of a circle. Under this conception, t’ai chi was represented by the circle divided into the light and the dark, yang and yin,

.

This symbol has also played a significant part in India and Europe. However, speculations of a gnostic-dualistic character are foreign to the original thought of the I Ching; what it posits is simply the ridgepole, the line. With this line, which in itself represents oneness, duality comes into the world, for the line at the same time posits an above and a below, a right and left, front and back-in a word, the world of the opposites.”

The t’ai chi symbol is also illustrated on the web page Cognitive Iconology, which says that

“W.J.T. Mitchell calls ‘iconology’
a study of the ‘logos’
(the words, ideas, discourse, or ‘science’)
of ‘icons’ (images, pictures, or likenesses).
It is thus a ‘rhetoric of images’
(Iconology: Image, Text, Ideology, p. 1).”

A variation on the t’ai chi symbol appears in a log24.net entry for March 5:

The Line,
by S. H. Cullinane

See too my web page Logos and Logic, which has the following:

“The beautiful in mathematics resides in contradiction. Incommensurability, logoi alogoi, was the first splendor in mathematics.”

— Simone Weil, Oeuvres Choisies, ed. Quarto, Gallimard, 1999, p. 100

 Logos Alogos,
by S. H. Cullinane 

In the conclusion of Section 3, Canto X, of “Notes,” Stevens says

“They will get it straight one day
at the Sorbonne.
We shall return at twilight
from the lecture
Pleased that
the irrational is rational….”

This is the logoi alogoi of Simone Weil.

In “Notes toward a Supreme Fiction,”
Wallace Stevens lists three criteria
for a work of the imagination:

It Must Be Abstract

The Line,
by S.H. Cullinane 

It Must Change

 The 24,
by S. H. Cullinane

It Must Give Pleasure

Puzzle,
by S. H. Cullinane

Related material:

Logos and Logic.

 

Tuesday April 6, 2004

Filed under: General — m759 @ 2:45 AM

Ideas and Art, Part II

"We do not, of course, see  ideas."

— Roger Kimball, Minimalist Fantasies, 2003

"Idea (Lat. idea , forma , species ; Gk. idea , eidos , from idein , to see; Fr. idée ; Ger. Bild ; Begriff )

Probably to no other philosophical term have there been attached so many different shades of meaning as to the word idea. Yet what this word signifies is of much importance. Its sense in the minds of some philosophers is the key to their entire system. But from Descartes onwards usage has become confused and inconstant. Locke, in particular, ruined the term altogether in English philosophical literature…."

The Catholic Encylopedia, 1910  

James Hillman, A Blue Fire , p. 53:

"For us ideas are ways of regarding things (modi res considerandi ), perspectives.  Ideas give us eyes, let us see …. Ideas are ways of seeing and knowing….

Our word idea  comes from the Greek eidos , which meant originally in early Greek thought, and as Plato used it, both that which one sees — an appearance or shape in a concrete sense — and that by means of which one sees.  We see them, and by means of them.  Ideas are both the shape of events, their constellation in this or that archetypal pattern, and the modes that make possible our ability to see through events into their pattern.  By means of an idea we can see the idea cloaked in the passing parade.  The implicit connection between having ideas to see with  and seeing ideas themselves suggests that the more ideas we have, the more we see, and the deeper the ideas we have, the deeper we see.  It also suggests that ideas engender other ideas, breeding new perspectives for viewing ourselves and world.

Moreover, without them we cannot 'see' even what we sense with the eyes in our heads, for our perceptions are shaped according to particular ideas …. And our ideas change as changes take place in the soul, for as Plato said, soul and idea refer to each other, in that an idea is the 'eye of the soul,' opening us through its insight and vision."

Hillman does not say where in Plato this extraordinary saying, that an idea is the eye of the soul, occurs.  He is probably wrong.

Both Kimball and Hillman seem confused.

A more sensible approach to these matters is available in Brian Cronin's Foundations of Philosophy:

"3.4 An Insight Pivots between the Abstract and the Concrete

On the one hand, an insight is dealing with data and images which are concrete and particular: Archimedes had one chalice, one King, and one particular problem to solve. On the other hand, what the insight grasps is an idea, a relation, a universal, a law; and that is abstract. The laws that Archimedes eventually formulated were universal, referring not only to this chalice but also to any other material body immersed in any other liquid at any time or any place. The insight is constituted precisely by 'seeing' the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete. We pivot back and forth between images and ideas as we search for the correct insight. First let us now clarify the difference between images, ideas and concepts…."

— From Ch. 2, Identifying Direct Insights

Wednesday, March 31, 2004

Wednesday March 31, 2004

Filed under: General — Tags: , — m759 @ 12:25 AM

To Be

A Jesuit cites Quine:

"To be is to be the value of a variable."

— Willard Van Orman Quine, cited by Joseph T. Clark, S. J., in Conventional Logic and Modern Logic: A Prelude to Transition,  Woodstock, MD: Woodstock College Press, 1952, to which Quine contributed a preface.

Quine died in 2000 on Xmas Day.

From a July 26, 2003, entry,
The Transcendent Signified,
on an essay by mathematician
Michael Harris:

Kubrick's
monolith

Harris's
slab

From a December 10, 2003, entry:

Putting Descartes Before Dehors

      

"Descartes déclare que c'est en moi, non hors de moi, en moi, non dans le monde, que je pourrais voir si quelque chose existe hors de moi."

ATRIUM, Philosophie

For further details, see ART WARS.

The above material may be regarded as commemorating the March 31 birth of René Descartes and death of H. S. M. Coxeter.

For further details, see

Plato, Pegasus, and the Evening Star.

Wednesday, March 10, 2004

Wednesday March 10, 2004

Filed under: General — m759 @ 6:01 PM

Split

The first idea was not our own. Adam
in Eden was the father of Descartes.

— Wallace Stevens,
Notes Toward a Supreme Fiction

A very interesting web site at
Middle Tennessee State University
relates the Stevens quote
to two others:

“The sundering we sense, between nature and culture, lies not like a canyon outside us but splits our being at its most intimate depths the way mind breaks off from body. It is still another version of that bitter bifurcation long ago decreed: our expulsion from Eden. It differs from the apparently similar Cartesian crease across things in the fact that the two halves of us once were one; that we did not always stand askance like molasses and madness–logically at odds–but grew apart over the years like those husbands and wives who draw themselves into different corners of contemplation.”

— William Gass,
“The Polemical Philosopher”

“The experiment [to make rationality primary] reached the reductio ad absurdum following the attempt by Descartes to solve problems of human knowledge by giving ontological status to the dichotomy of thinking substance and extended substance, that is subject and object. Not only were God and man, sacred and secular, being and becoming, play and seriousness severed, but now also the subject which wished to unite these fragmented dichotomies was itself severed from that which it would attempt to reconcile.”

— David Miller, God and Games

“Which is it then? For Gass, the Cartesian schism is a post- lapsarian divorce-in progress, only apparently similar to the expulsion from paradise. For Stevens the fault is primordial and Descartes only its latter-day avatar. For Miller, Descartes is the historical culprit, the patriarch of the split.”

The Evil Genius Notebook,
by
David Lavery

Wednesday, December 10, 2003

Wednesday December 10, 2003

Filed under: General — m759 @ 6:13 PM

Putting Descartes Before Dehors

      

Descartes déclare que c’est en moi, non hors de moi, en moi, non dans le monde, que je pourrais voir si quelque chose existe hors de moi.”

ATRIUM, Philosophie

For further details, see ART WARS.

Tuesday, December 9, 2003

Tuesday December 9, 2003

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

Street of the Fathers

From Bruce Wagner’s Wild Palms —

Robert Morse sings in Kyoto
as negotiators discuss
the Go chip
:

In My Room

Coordinates for a 4×4 space:

A Small Go Board Study:


A 4×4
Go Board

From
Université René Descartes,
45 rue des Saints Pères,
Paris

Today’s birthdays:

Kirk Douglas
Buck Henry
John Malkovich

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