Log24

Tuesday, September 20, 2016

Savage Logic

Filed under: General,Geometry — m759 @ 9:29 PM

From "The Cerebral Savage," by Clifford Geertz —

(Encounter, Vol. 28 No. 4 (April 1967), pp. 25-32.)

From http://www.diamondspace.net/about.html

The diamond theorem

Monday, February 6, 2012

Savage Logic

Filed under: General — m759 @ 1:00 PM

(Continued)

Saturday, October 16, 2010

Quaternion Day

m759 @ 12:00 PM

Brightness at Noon continued

i2 = j2 = k2 = ijk = -1

– Sir William Rowan Hamilton,
   
Oct. 16, 1843

See also this journal on 1/09, 2010.

This post was suggested by the date
of a user comment in Wikipedia.

Monday, November 28, 2011

Savage Logic

Filed under: General — m759 @ 9:29 AM

A search in memory of Ken Russell, who died Sunday.

Russell directed, among many other films, "Savage Messiah"—

http://www.log24.com/log/pix11C/111128-savage_messiah.jpg

Tuesday, October 19, 2010

Savage Logic continued…

Filed under: General,Geometry — m759 @ 9:36 AM

CHAPTER V

THE KALEIDOSCOPE

"This is an account of the discrete groups generated by reflections…."

Regular Polytopes , by H.S.M. Coxeter (unabridged and corrected 1973 Dover reprint of the 1963 Macmillan second edition)

"In this article, we begin a theory linking hyperplane arrangements and invariant forms for reflection groups over arbitrary fields…. Let V  be an n-dimensional vector space over a field F, and let G ≤ Gln (F) be a finite group…. An element of finite order in Gl(V ) is a reflection if its fixed point space in V  is a hyperplane, called the reflecting hyperplane. There are two types of reflections: the diagonalizable reflections in Gl(V ) have a single nonidentity eigenvalue which is a root of unity; the nondiagonalizable reflections in Gl(V ) are called transvections and have determinant 1 (note that they can only occur if the characteristic of F is positive)…. A reflection group is a finite group G  generated by reflections."

— Julia Hartmann and Anne V. Shepler, "Reflection Groups and Differential Forms," Mathematical Research Letters , Vol. 14, No. 6 (Nov. 2007), pp. 955-971

"… the class of reflections is larger in some sense over an arbitrary field than over a characteristic zero field. The reflections in Gl(V ) not only include diagonalizable reflections (with a single nonidentity eigenvalue), but also transvections, reflections with determinant 1 which can not be diagonalized. The transvections in Gl(V ) prevent one from developing a theory of reflection groups mirroring that for Coxeter groups or complex reflection groups."

— Julia Hartmann and Anne V. Shepler, "Jacobians of Reflection Groups," Transactions of the American Mathematical Society , Vol. 360, No. 1 (2008), pp. 123-133 (Pdf available at CiteSeer.)

See also A Simple Reflection Group of Order 168 and this morning's Savage Logic.

Savage Logic

Filed under: General,Geometry — Tags: — m759 @ 2:22 AM

and the New York Lottery

IMAGE-- NY Lottery Oct. 18, 2010-- Midday 069, Evening 359

A search in this journal for yesterday's evening number in the New York Lottery, 359, leads to…

The Cerebral Savage: 
On the Work of Claude Lévi-Strauss

by Clifford Geertz

Shown below is 359, the final page of Chapter 13 in
The Interpretation of Cultures: Selected Essays by Clifford Geertz,
New York, 1973: Basic Books, pp. 345-359 —

http://www.log24.com/log/pix10B/101019-Geertz359.gif

This page number 359 also appears in this journal in an excerpt from Dan Brown's novel Angels & Demons

See this journal's entries for March 1-15, 2009, especially…

Sunday, March 15, 2009  5:24 PM

Philosophy and Poetry:

The Origin of Change

A note on the figure
from this morning's sermon:

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

"Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined

On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come."

-- Wallace Stevens,
  "Notes Toward a Supreme Fiction,"
   Canto IV of "It Must Change"

Sunday, March 15, 2009  11:00 AM

Ides of March Sermon:

Angels, Demons,
"Symbology"

"On Monday morning, 9 March, after visiting the Mayor of Rome and the Municipal Council on the Capitoline Hill, the Holy Father spoke to the Romans who gathered in the square outside the Senatorial Palace…

'… a verse by Ovid, the great Latin poet, springs to mind. In one of his elegies he encouraged the Romans of his time with these words:

"Perfer et obdura: multo graviora tulisti."

 "Hold out and persist:
  you have got through
  far more difficult situations."

 (Tristia, Liber  V, Elegia  XI, verse 7).'"
 

This journal
on 9 March:

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

Note the color-interchange
symmetry
of each symbol
under 180-degree rotation.

Related material:
The Illuminati Diamond:

IMAGE- Illuminati Diamond, pp. 359-360 in 'Angels & Demons,' Simon & Schuster Pocket Books 2005, 448 pages, ISBN 0743412397

The symmetry of the yin-yang symbol, of the diamond-theorem symbol, and of Brown's Illuminati Diamond is also apparent in yesterday's midday New York lottery number (see above).

"Savage logic works like a kaleidoscope…." — Clifford Geertz on Lévi-Strauss

Wednesday, March 13, 2019

The Origin of Change . . .

Filed under: General — m759 @ 10:00 PM

According to Wallace Stevens:

From Savage Logic

Sunday, March 15, 2009  5:24 PM

The Origin of Change

A note on the figure
from this morning's sermon:

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

"Two things of opposite natures seem to depend
On one another, as a man depends 
On a woman, day on night, the imagined 
On the real. This is the origin of change. 
Winter and spring, cold copulars, embrace 
And forth the particulars of rapture come."

— Wallace Stevens,   
"Notes Toward a Supreme Fiction,"
Canto IV of "It Must Change"

This  post was suggested by the following passage —

" the Fano plane ,
a set of seven points
grouped into seven lines
that has been called
'the combinatorialist’s coat of arms.' "

— Blake Stacey in a post with tomorrow's date:

and by Stacey at another weblog, in a post dated Jan. 29, 2019, 

"(Yes, Bohr was the kind of guy who would choose
the yin-yang symbol as his coat of arms.)"

Yes, Stacey is the kind of guy who would casually dismiss
Bohr's coat of arms. 

Related material — 

(See also Faust in Copenhagen in this  journal)—

» more

Thursday, October 29, 2015

A Word in Your Delicate Ear

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

☯

Saturday, May 28, 2011

Savage Detectives

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

IMAGE- Rubeus Hagrid and Jorn Barger


IMAGE- Cover of 'The Savage and Beautiful Country'

   Alan McGlashan

From Savage Logic

Sunday, March 15, 2009  5:24 PM

The Origin of Change

A note on the figure
from this morning's sermon:

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

"Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined
On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come."

Wallace Stevens,  
"Notes Toward a Supreme Fiction,"
Canto IV of "It Must Change"

Thursday, April 28, 2011

Crimson Tide…

Filed under: General — m759 @ 3:59 PM

A sequel to Wednesday afternoon's post on The Harvard Crimson ,
Atlas Shrugged (illustrated below) —

http://www.log24.com/log/pix11A/110427-CrimsonAtlas500w.jpg

Related material found today in Wikipedia—

A defense of Rubik by 'Pazouzou'

See also Savage Logic (Oct. 19, 2010), as well as
Stellan Skarsgård in Lie Groups for Holy Week (March 30, 2010)
and in Exorcist: The Beginning (2004).

Wednesday, February 2, 2011

Rite of Change

Filed under: General — m759 @ 11:32 PM

An image suggested by the date July 19, 2010

the day that abstract painter Alan Uglow (see this morning's Origin) turned 69—

http://www.log24.com/log/pix11/110202-FocusingRite.jpg

Some background — In the Details and Savage Logic.

Tuesday, December 21, 2010

Savage Solstice

Filed under: General,Geometry — Tags: — m759 @ 7:20 PM

In memory of kaleidoscope enthusiast Cozy Baker, who died at 86, according to Saturday's Washington Post , on October 19th.

http://www.log24.com/log/pix10B/101221-BrewsterSociety.jpg

This journal on that date — Savage Logic and Savage Logic continued.

See this journal on All Saints' Day 2006 for some background to those posts—

Savage logic works like a kaleidoscope whose chips can fall into a variety of patterns while remaining unchanged in quantity, form, or color. The number of patterns producible in this way may be large if the chips are numerous and varied enough, but it is not infinite. The patterns consist in the disposition of the chips vis-a-vis one another (that is, they are a function of the relationships among the chips rather than their individual properties considered separately). And their range of possible transformations is strictly determined by the construction of the kaleidoscope, the inner law which governs its operation. And so it is too with savage thought. Both anecdotal and geometric, it builds coherent structures out of ‘the odds and ends left over from psychological or historical process.’

These odds and ends, the chips of the kaleidoscope, are images drawn from myth, ritual, magic, and empirical lore. (How, precisely, they have come into being in the first place is one of the points on which Levi-Strauss is not too explicit, referring to them vaguely as the ‘residue of events… fossil remains of the history of an individual or a society.’) Such images are inevitably embodied in larger structures– in myths, ceremonies, folk taxonomies, and so on– for, as in a kaleidoscope, one always sees the chips distributed in some pattern, however ill-formed or irregular. But, as in a kaleidoscope, they are detachable from these structures and arrangeable into different ones of a similar sort. Quoting Franz Boas that ‘it would seem that mythological worlds have been built up, only to be shattered again, and that new worlds were built from the fragments,’ Levi-Strauss generalizes this permutational view of thinking to savage thought in general.”

– Clifford Geertz, “The Cerebral Savage: the Structural Anthropology of Claude Levi-Strauss,” in Encounter, Vol. 28 No. 4 (April 1967), pp. 25-32.

Related material  —

http://www.log24.com/log/pix10B/101221-TristesTropiques.jpg

See also "Levi-Strauss" in this journal and "At Play in the Field."

Friday, November 26, 2010

Shining Forth

Filed under: General — Tags: — m759 @ 3:00 PM

continued from 2001

A quotation from Robert Lowell in this journal —

From “Epilogue,” in Robert Lowell’s Day by Day , 1977:

The painter’s vision is not a lens,
it trembles to caress the light.

….
All’s misalliance.
Yet why not say what happened?
Pray for the grace of accuracy
Vermeer gave to the sun’s illumination….

Lowell’s stepdaughter published a memoir, Why Not Say What Happened? , on October 19th, 2010.

What happened in this journal on that date was “Savage Logic and the New York Lottery.”

That post includes the quoted rhetorical question

“Is it a genuine demolition of the walls which seem to separate mind from mind…?”

Here is the context of October 19th—

http://www.log24.com/log/pix10B/101019-Geertz359.gif

For a different, and to me more interesting, context for the “walls” question, see Party Phone  (August 31st, 2006).

Saturday, March 24, 2007

Saturday March 24, 2007

Filed under: General,Geometry — m759 @ 2:09 AM
Savage Scrutiny

“They sang desiring an object that was near,
In face of which desire no longer moved,
Nor made of itself that which it could not find…
Three times the concentred self takes hold, three times
The thrice concentred self, having possessed

The object, grips it in savage scrutiny,
Once to make captive, once to subjugate
Or yield to subjugation, once to proclaim
The meaning of the capture, this hard prize,
Fully made, fully apparent, fully found.”

— “Credences of Summer,” VII,
    by Wallace Stevens, from
    Transport to Summer (1947)

Clifford Geertz on Levi-Strauss, from The Cerebral Savage:

Savage logic works like a kaleidoscope whose chips can fall into a variety of patterns…. “

Related material:

The kaleidoscope puzzle and “Claude Levi-Strauss and the Aesthetic Object,” a videotaped interview with Dr. Boris Wiseman.

Wednesday, November 1, 2006

Wednesday November 1, 2006

Filed under: General,Geometry — Tags: — m759 @ 8:24 AM

The image “http://www.log24.com/log/pix06B/061101-Geertz2.jpg” cannot be displayed, because it contains errors.

Clifford Geertz 

Professor Emeritus,
Institute for Advanced Study

Savage Logic

"Savage logic works like a kaleidoscope whose chips can fall into a variety of patterns while remaining unchanged in quantity, form, or color. The number of patterns producible in this way may be large if the chips are numerous and varied enough, but it is not infinite. The patterns consist in the disposition of the chips vis-a-vis one another (that is, they are a function of the relationships among the chips rather than their individual properties considered separately). And their range of possible transformations is strictly determined by the construction of the kaleidoscope, the inner law which governs its operation. And so it is too with savage thought. Both anecdotal and geometric, it builds coherent structures out of 'the odds and ends left over from psychological or historical process.'

These odds and ends, the chips of the kaleidoscope, are images drawn from myth, ritual, magic, and empirical lore. (How, precisely, they have come into being in the first place is one of the points on which Levi-Strauss is not too explicit, referring to them vaguely as the 'residue of events… fossil remains of the history of an individual or a society.') Such images are inevitably embodied in larger structures– in myths, ceremonies, folk taxonomies, and so on– for, as in a kaleidoscope, one always sees the chips distributed in some pattern, however ill-formed or irregular. But, as in a kaleidoscope, they are detachable from these structures and arrangeable into different ones of a similar sort. Quoting Franz Boas that 'it would seem that mythological worlds have been built up, only to be shattered again, and that new worlds were built from the fragments,' Levi-Strauss generalizes this permutational view of thinking to savage thought in general."

— Clifford Geertz, "The Cerebral Savage: the Structural Anthropology of Claude Levi-Strauss," in Encounter, Vol. 28 No. 4 (April 1967), pp. 25-32.

Today's New York Times
reports that
Geertz died on Monday,
October 30, 2006.

Related material:

Kaleidoscope Puzzle,

Being Pascal Sauvage,

and Up the River:
 

 

 
The Necessity For Story

by Frederick Zackel

While it's a story that's never been written, a suggested title– Indiana Jones Sails Up The River Of Death–

The image “http://www.log24.com/log/pix04B/041016-Poster2.jpg” cannot be displayed, because it contains errors.

shows how readily we as individuals or we as a culture can automatically visualize a basic story motif. We may each see the particular elements of the story differently, but almost instantaneously we catch its drift.

The hero sails up the river of death to discover what lies within his own heart: i.e., how much moral and physical strength he has.

Indiana Jones sails up the River of Death.

We are following Indiana Jones up the River of Death. We're going to visit with Colonel Kurtz. (You may not want to get off the boat.)

No, I am not mixing up metaphors.

These are the Story.

 

Amen.

Thursday, August 11, 2005

Thursday August 11, 2005

Filed under: General,Geometry — m759 @ 8:16 AM

Kaleidoscope, continued

From Clifford Geertz, The Cerebral Savage:

"Savage logic works like a kaleidoscope whose chips can fall into a variety of patterns while remaining unchanged in quantity, form, or color. The number of patterns producible in this way may be large if the chips are numerous and varied enough, but it is not infinite. The patterns consist in the disposition of the chips vis-a-vis one another (that is, they are a function of the relationships among the chips rather than their individual properties considered separately).  And their range of possible transformations is strictly determined by the construction of the kaleidoscope, the inner law which governs its operation. And so it is too with savage thought.  Both anecdotal and geometric, it builds coherent structures out of 'the odds and ends left over from psychological or historical process.'

These odds and ends, the chips of the kaleidoscope, are images drawn from myth, ritual, magic, and empirical lore….  as in a kaleidoscope, one always sees the chips distributed in some pattern, however ill-formed or irregular.   But, as in a kaleidoscope, they are detachable from these structures and arrangeable into different ones of a similar sort….  Levi-Strauss generalizes this permutational view of thinking to savage thought in general.  It is all a matter of shuffling discrete (and concrete) images–totem animals, sacred colors, wind directions, sun deities, or whatever–so as to produce symbolic structures capable of formulating and communicating objective (which is not to say accurate) analyses of the social and physical worlds.

…. And the point is general.  The relationship between a symbolic structure and its referent, the basis of its meaning,  is fundamentally 'logical,' a coincidence of form– not affective, not historical, not functional.  Savage thought is frozen reason and anthropology is, like music and mathematics, 'one of the few true vocations.'

Or like linguistics."

Edward Sapir on Linguistics, Mathematics, and Music:

"… linguistics has also that profoundly serene and satisfying quality which inheres in mathematics and in music and which may be described as the creation out of simple elements of a self-contained universe of forms.  Linguistics has neither the sweep nor the instrumental power of mathematics, nor has it the universal aesthetic appeal of music.  But under its crabbed, technical, appearance there lies hidden the same classical spirit, the same freedom in restraint, which animates mathematics and music at their purest."

— Edward Sapir, "The Grammarian and his Language,"
  American Mercury 1:149-155,1924

From Robert de Marrais, Canonical Collage-oscopes:

"…underwriting the form languages of ever more domains of mathematics is a set of deep patterns which not only offer access to a kind of ideality that Plato claimed to see the universe as created with in the Timaeus; more than this, the realm of Platonic forms is itself subsumed in this new set of design elements– and their most general instances are not the regular solids, but crystallographic reflection groups.  You know, those things the non-professionals call . . . kaleidoscopes! *  (In the next exciting episode, we'll see how Derrida claims mathematics is the key to freeing us from 'logocentrism' **— then ask him why, then, he jettisoned the deepest structures of mathematical patterning just to make his name…)

* H. S. M. Coxeter, Regular Polytopes (New York: Dover, 1973) is the great classic text by a great creative force in this beautiful area of geometry  (A polytope is an n-dimensional analog of a polygon or polyhedron.  Chapter V of this book is entitled 'The Kaleidoscope'….)

** … contemporary with the Johns Hopkins hatchet job that won him American marketshare, Derrida was also being subjected to a series of probing interviews in Paris by the hometown crowd.  He first gained academic notoriety in France for his book-length reading of Husserl's two-dozen-page essay on 'The Origin of Geometry.'  The interviews were collected under the rubric of Positions (Chicago: U. of Chicago Press, 1981…).  On pp. 34-5 he says the following: 'the resistance to logico-mathematical notation has always been the signature of logocentrism and phonologism in the event to which they have dominated metaphysics and the classical semiological and linguistic projects…. A grammatology that would break with this system of presuppositions, then, must in effect liberate the mathematization of language…. The effective progress of mathematical notation thus goes along with the deconstruction of metaphysics, with the profound renewal of mathematics itself, and the concept of science for which mathematics has always been the model.'  Nice campaign speech, Jacques; but as we'll see, you reneged on your promise not just with the kaleidoscope (and we'll investigate, in depth, the many layers of contradiction and cluelessness you put on display in that disingenuous 'playing to the house'); no, we'll see how, at numerous other critical junctures, you instinctively took the wrong fork in the road whenever mathematical issues arose… henceforth, monsieur, as Joe Louis once said, 'You can run, but you just can't hide.'…."

Powered by WordPress