Saturday, November 26, 2011

Innermost Kernel (continued*)

Filed under: General — m759 @ 12:00 PM

A search on the word "innermost" in a PDF copy of a book
by Suzanne Gieser on Jung and Pauli yields no definite meaning
for the book's title, The Innermost Kernel  (Springer, 2005).

The author does, however, devote a section (pp. 36-41) to the
influence of Schopenhauer on Jung and Pauli, and that section at least
suggests that the historical  origin of her title is in Schopenhauer's
reformulation of Kant's "Ding an sich."

The Innermost Kernel , p. 37—

"… an expression of an underlying invisible world,
the one that forms the innermost essence of reality,
the thing-in-itself. This is the will, a blind existence
that forms an omnipresent entity beyond time, space
and individuality." *

* Arthur Schopenhauer, "Über die Vierfache Wurzel
  des Satzes vom zureichenden Grunde" (1813),
  Kleinere Schriften, SämtlicheWerke III 
  (Stuttgart, 1962), 805–806.

* See also Mann on Schopenhauer and an "innermost kernel."

Friday, November 25, 2011

The Innermost Kernel and Physics

Filed under: General — m759 @ 12:00 PM

"Letzen Endes wird also der Materiebegriff in beiden Fällen auf Mathematik zurückgefürt. Der innerste Kern alles Stofflichen ist für uns wie für Plato eine Form, nicht irgendein materieller Inhalt."

"In the final analysis, in both cases [Plato and modern physics] the notion of matter is essentially a mathematical concept. The most fundamental kernel of all that is material is for us, as well as for Plato, a [mathematical] form, and not some material content."

— W. Heisenberg, "Platons Vorstellungen von den kleinsten Bausteinen der Materie und die Elementarteilchen der modernen Physik," Im Umkreis der Kunst. Eine Festschrift für Emil Preetorius , Wiesbaden 1953, pp. 137-140, as cited by Luc Brisson and F. Walter Meyerstein in Inventing the Universe , SUNY Press, 1995.

See also remarks by Pauli in For All Hallows Day.

Update of 1 PM

Related material —

IMAGE- Schopenhauer, 'innermost kernel,' and atman

"Zweiteilung und Symmetrieverminderung, das ist des Pudels Kern. Zweiteilung ist ein sehr altes Attribut des Teufels."

—Pauli to Heisenberg

Here "the poodle's kernel" is a reference to Faust , where the devil appears as a poodle.

On Schopenhauer's later years—

"In Frankfurt he spent the remaining years of his life, living quietly in two rooms with his pipe and his flute but with no friends or companions except a small poodle, the only creature to which Schopenhauer ever seems to have felt any real attachment. He named the dog Atman, a term taken from the pessimistic religion of India, in which Schopenhauer had become more and more interested in his later years."

— Robert F. Davidson, "Pessimism: Arthur Schopenhauer" in Philosophies Men Live By , New York, The Dryden Press, 1952

Innermost Kernel

Filed under: General — m759 @ 5:01 AM

Thomas Mann on an innermost kernel


"Denn um zu wiederholen, was ich anfangs sagte:
in dem Geheimnis der Einheit von Ich und Welt,
Sein und Geschehen, in der Durchschauung des
scheinbar Objectiven und Akzidentellen als
Veranstaltung der Seele glaube ich den innersten Kern
der analytischen Lehre zu erkennen." (GW IX 488)

See also previous quotations here of the phrase "innermost kernel."

Friday, May 27, 2016

Raiders of the Lost Crucible…

Filed under: General — m759 @ 8:00 AM

Continues .

Number and Time, by Marie-Louise von Franz

For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.

The above passage suggests a meditation on this morning's
New York Times * —

"When shall we three meet again?" — William Shakespeare

“We three have scattered, leaving only me behind
to clean up the scene,” Ms. Yang wrote.
“I am alone, missing us three.” — Amy Qin

Peer Review

Filed under: General — m759 @ 7:00 AM

A review of the phrase "Innermost Kernel" in this journal
suggests the following meditation

"Who am I?" — Existential cry
in "Zoolander" and "Zoolander 2."

A similar question occurs in "Peer Gynt" —

Ben Brantley in yesterday morning's print New York Times *
expressed a nihilistic view of Peer as an onion-peeler —

"Toward the end of Ibsen’s 'Peer Gynt,' a saga of self
under siege, the title character is discovered peeling
an onion, finding in the layers of that humble vegetable
a symbol for the chapters of an eventful life . . . .

[the director’s] approach is the same one that Peer
applies to the onion: Keep stripping until you find the core.
Of course in Peer’s case what is finally found is
plenty of nothing, an apt conclusion for a man
for whom a solid self remains elusive."

I prefer a view from what Fitzgerald called
"the dark fields of the republic" — the Dordt College view —

* The Times — "A version of this review appears in print on May 26, 2016, 
on page C3 of the New York edition with the headline:
'A Saga of Self-Identity, Stripped to Its Core, Still Provokes.' "

Wednesday, December 16, 2015

Soul Notes

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

See pages 36 and 37 of Suzanne Gieser's The Innermost Kernel 
as well as PyrE in The Stars My Destination  and Old St. Patrick's*
in "Gangs of New York."

For some related aesthetic remarks, see a New Yorker  essay
published onlne today and this  journal's previous post.

* The older  version of the "Old St. Patrick's"
    of The Stars My Destination . (Update of 4/21/16.)

Saturday, March 30, 2013

Realm of the Mothers

Filed under: General — m759 @ 3:33 AM

See Jung on Archetypes and The Innermost Kernel.

For some backstory, see Christmas Eve, 2012.

Saturday, December 22, 2012

For Larry L. King…

Filed under: General — m759 @ 3:26 AM

… author of "The Best Little Whorehouse in Texas,"
who reportedly died on Thursday

IMAGE- Harper's magazine, Oct. 1970, pp. 94-95: John Berryman poem and Larry L. King Harvard article

Sunday, November 18, 2012


Filed under: General,Geometry — Tags: — m759 @ 11:00 AM

Happy birthday to

IMAGE- Margaret Atwood, Kim Wilde, Peta Wilson

Today's sermon, by Marie-Louise von Franz

Number and Time, by Marie-Louise von Franz

For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.

Another modern physicist, Niels Bohr, died
on this date in 1962

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

The circle above is marked with a version
of the classic Chinese symbol
adopted as a personal emblem
by Danish physicist Niels Bohr,
leader of the Copenhagen School.

For the square, see the diamond theorem.

"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"

Tuesday, September 18, 2012

Simple Skill

Filed under: General — m759 @ 10:18 AM

But with good Will
To show our simple skill…

( Continued from Midsummer Eve, 1993 )

The "Black Diamond" search from Holy Cross Day 
leads to Talk Amongst Yourselves, which in turn
leads to PyrE in the Book, with Alfred Bester's
version of "Will and Idea."

This phrase may be regarded as a version of 
Schopenhauer's "Will and Representation."

Related material—

"Schopenhauer's notion of the will comes from the Kantian thing-in-itself, which Kant believed to be the fundamental reality behind the representation that provided the matter of perception, but lacked form. Kant believed that space, time, causation, and many other similar phenomena belonged properly to the form imposed on the world by the human mind in order to create the representation, and these factors were absent from the thing-in-itself. Schopenhauer pointed out that anything outside of time and space could not be differentiated, so the thing-in-itself must be one and all things that exist, including human beings, must be part of this fundamental unity. Our inner-experience must be a manifestation of the noumenal realm and the will is the inner kernel* of every being. All knowledge gained of objects is seen as self-referential, as we recognize the same will in other things as is inside us." —Wikipedia

* "Die Schrecken des Todes beruhen großentheils auf dem falschen Schein, daß jetzt das Ich verschwinde, und die Welt bleibe, Vielmehr aber ist das Gegentheil wahr: die Welt verschwindet; hingegen der innerste Kern des Ich, der Träger und Hervorbringer jenes Subjekts, in dessen Vorstellung allein die Welt ihr Daseyn hatte, beharrt." 

— Schopenhauer, Die Welt als Wille und Vorstellung , Kapitel 41

Added Nov. 16, 2012, a translation by E. F. J. Payne—

"The terrors of death rest for the most part on the false illusion that then the I or ego vanishes, and the world remains. But rather is the opposite true, namely that the world vanishes; on the other hand, the innermost kernel of the ego endures, the bearer and producer of that subject in whose representation alone the world had its existence."


by Arthur Schopenhauer
Translated from the German by E. F. J. Payne
In two volumes
© 1969 Dover Publications, Inc.
© 1958 by The Falcon's Wing Press

Volume Two: Supplements to the Fourth Book, 
XLI. On Death and Its Relation to the Indestructibility of Our Inner Nature

Saturday, March 28, 2009

Saturday March 28, 2009

Filed under: General,Geometry — m759 @ 11:07 PM

The Rest
of the Story

Today's previous entry discussed the hermeneutics of the midday NY and PA lottery numbers.

The rest of the story:

The Revelation Game
(continued from 7/26, 2008)

on Reba's
(No revelation)
New York
(No belief)
No belief,
no revelation

without belief

Belief without

Belief and


Interpretations of the evening numbers–

The PA evening number, 006, may be viewed as a followup to the PA midday 726 (or 7/26, the birthday of Kate Beckinsale and Carl Jung). Here 006 is the prestigious "00" number assigned to Beckinsale.

Will: Do you like apples?     
Clark: Yeah.                       
Will: Well, I got her number.
 How do you like them apples?

— "Good Will Hunting

Kate Beckinsale in 'Underworld: Evolution'

The NY evening number, 091, may be viewed as a followup to the NY midday 378 (the number of pages in The Innermost Kernel by Suzanne Gieser, published by Springer, 2005)–

Page 91: The entire page is devoted to the title of the book's Part 3– "The Copenhagen School and Psychology"–

Page 91 of 'The Innermost Kernel' by Suzanne Gieser, Springer 2005

The next page begins: "With the crisis of physics, interest in epistemological and psychological questions grew among many theoretical physicists. This interest was particularly marked in the circle around Niels Bohr."

A particularly
marked circle
 from March 15:

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

The circle above is
marked with a version of
the classic Chinese symbol
adopted as a personal emblem
by Danish physicist Niels Bohr,
leader of the Copenhagen School.

"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"

The square above is marked
with a graphic design
related to the four-diamond
figure of Jung's Aion.

Saturday March 28, 2009

Filed under: General — m759 @ 3:28 PM
The Dance
of Chance

Today’s midday

NY 378
PA 726


The 378 pages of
a book on Pauli and Jung,
The Innermost Kernel

The date, 7/26, of
birth for Jung and for
Kate Beckinsale,
star of

See also today’s previous entry
and “Bright Star and Dark Lady”
from 7/26, 2003.

Thursday, March 19, 2009

Thursday March 19, 2009

Filed under: General — m759 @ 4:00 AM
An image from
A Glass Bead Game

by Charles Cameron

Christ and the four elements, 1495

Christ and the Four Elements

This 1495 image is found in
The Janus Faces of Genius:
The Role of Alchemy
in Newton's Thought

by B. J. T. Dobbs,
Cambridge U. Press,
2002, p. 85

Kernel of Eternity:

Pauli's Dream Square from 'The Innermost Kernel'

Sacerdotal Jargon
at Harvard

The Klein Four-Group: The four elements in four colors, with black points representing the identity

From "The Fifth Element"
(1997, Milla Jovovich
    and Bruce Willis) —

The crossing of the beams:

The Fifth Element, crossing of the beams

Happy birthday, Bruce Willis.

Tuesday, April 29, 2008

Tuesday April 29, 2008

Filed under: General,Geometry — Tags: , , — m759 @ 11:09 AM
Sacerdotal Jargon
at Harvard:

Thomas Wolfe

Thomas Wolfe
(Harvard M.A., 1922)


Rosalind Krauss

Rosalind Krauss
(Harvard M.A., 1964,
Ph.D., 1969)


The Kernel of Eternity

"No culture has a pact with eternity."
George Steiner, interview in  
The Guardian of April 19

"At that instant he saw,
in one blaze of light, an image
of unutterable conviction….
the core of life, the essential
pattern whence all other things
proceed, the kernel of eternity."

— Thomas Wolfe, Of Time
and the River, quoted in
Log24 on June 9, 2005


From today's online Harvard Crimson:

"… under the leadership of Faust,
Harvard students should look forward
to an ever-growing opportunity for
international experience
and artistic endeavor."


Wolfgang Pauli as Mephistopheles

Pauli as Mephistopheles
in a 1932 parody of
Faust at Niels Bohr's
institute in Copenhagen

From a recent book
on Wolfgang Pauli,
The Innermost Kernel:

Pauli's Dream Square (square plus the two diagonals)

A belated happy birthday
to the late
Felix Christian Klein
  (born on April 25) —

The Klein Group: The four elements in four colors, with black points representing the identity

Another Harvard figure quoted here on Dec. 5, 2002:

"The theory of poetry, that is to say, the total of the theories of poetry, often seems to become in time a mystical theology or, more simply, a mystique. The reason for this must by now be clear. The reason is the same reason why the pictures in a museum of modern art often seem to become in time a mystical aesthetic, a prodigious search of appearance, as if to find a way of saying and of establishing that all things, whether below or above appearance, are one and that it is only through reality, in which they are reflected or, it may be, joined together, that we can reach them. Under such stress, reality changes from substance to subtlety, a subtlety in which it was natural for Cézanne to say: 'I see planes bestriding each other and sometimes straight lines seem to me to fall' or 'Planes in color…. The colored area where shimmer the souls of the planes, in the blaze of the kindled prism, the meeting of planes in the sunlight.' The conversion of our Lumpenwelt went far beyond this. It was from the point of view of another subtlety that Klee could write: 'But he is one chosen that today comes near to the secret places where original law fosters all evolution. And what artist would not establish himself there where the organic center of all movement in time and space– which he calls the mind or heart of creation– determines every function.' Conceding that this sounds a bit like sacerdotal jargon, that is not too much to allow to those that have helped to create a new reality, a modern reality, since what has been created is nothing less."

— Wallace Stevens, Harvard College Class of 1901, "The Relations between Poetry and Painting" in The Necessary Angel (Knopf, 1951)

From a review of Rosalind Krauss's The Optical Unconscious  (MIT Press hardcover, 1993):

Krauss is concerned to present Modernism less in terms of its history than its structure, which she seeks to represent by means of a kind of diagram: "It is more interesting to think of modernism as a graph or table than a history." The "table" is a square with diagonally connected corners, of the kind most likely to be familiar to readers as the Square of Opposition, found in elementary logic texts since the mid-19th century. The square, as Krauss sees it, defines a kind of idealized space "within which to work out unbearable contradictions produced within the real field of history." This she calls, using the inevitable gallicism, "the site of Jameson's Political Unconscious" and then, in art, the optical unconscious, which consists of what Utopian Modernism had to kick downstairs, to repress, to "evacuate… from its field."

— Arthur C. Danto in ArtForum, Summer 1993

Rosalind Kraus in The Optical Unconscious (MIT Press paperback, 1994):

For a presentation of the Klein Group, see Marc Barbut, "On the Meaning of the Word 'Structure' in Mathematics," in Introduction to Structuralism, ed. Michael Lane (New York: Basic Books, 1970). Claude Lévi-Strauss uses the Klein group in his analysis of the relation between Kwakiutl and Salish masks in The Way of the Masks, trans. Sylvia Modelski (Seattle: University of Washington Press, 1982), p. 125; and in relation to the Oedipus myth in "The Structural Analysis of Myth," Structural Anthropology, trans. Claire Jackobson [sic] and Brooke Grundfest Schoepf (New York: Basic Books, 1963). In a transformation of the Klein Group, A. J. Greimas has developed the semiotic square, which he describes as giving "a slightly different formulation to the same structure," in "The Interaction of Semiotic Constraints," On Meaning (Minneapolis: University of Minnesota Press, 1987), p. 50. Jameson uses the semiotic square in The Political Unconscious (see pp. 167, 254, 256, 277) [Fredric Jameson, The Political Unconscious: Narrative as a Socially Symbolic Act (Ithaca: Cornell University Press, 1981)], as does Louis Marin in "Disneyland: A Degenerate Utopia," Glyph, no. 1 (1977), p. 64.

For related non-sacerdotal jargon, see…

Wikipedia on the Klein group (denoted V, for Vierergruppe):

In this representation, V is a normal subgroup of the alternating group A4 (and also the symmetric group S4) on 4 letters. In fact, it is the kernel of a surjective map from S4 to S3. According to Galois theory, the existence of the Klein four-group (and in particular, this representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals.

For radicals of another sort, see A Logocentric Meditation, A Mass for Lucero, and [update of 7 PM] Steven Erlanger in today's New York Times— "France Still Divided Over Lessons of 1968 Unrest."

For material related to Klee's phrase mentioned above by Stevens, "the organic center of all movement in time and space," see the following Google search:

April 29, 2008, Google search on 'penrose space time'

Click on the above
 image for details.

See also yesterday's
Religious Art.

Monday, August 13, 2007

Monday August 13, 2007

Filed under: General,Geometry — Tags: — m759 @ 11:07 AM

Adam Gopnik in
The New Yorker of
August 20, 2007–

On Philip K. Dick:

"… the kind of guy who can't drink one cup of coffee without drinking six, and then stays up all night to tell you what Schopenhauer really said and how it affects your understanding of Hitchcock and what that had to do with Christopher Marlowe."

Modernity: A Film by
Alfred Hitchcock

"… the most thoroughgoing modernist design element in Hitchcock's films arises out of geometry, as Francois Regnault has argued, identifying 'a global movement for each one, or a "principal geometric or dynamic form," which can appear in the pure state in the credits….'" –Peter J. Hutchings (my italics)

More >>


Adam Gopnik is also the author
of The King in the Window, a tale
of the Christian feast of Epiphany
and a sinister quantum computer.

For more on Epiphany, see
the Log24 entries of August 1.

For more on quantum computing,
see What is Quantum Computation?.

See also
the previous entry.

Thursday, June 21, 2007

Thursday June 21, 2007

Filed under: General,Geometry — m759 @ 12:07 PM
Let No Man
Write My Epigraph

(See entries of June 19th.)

“His graceful accounts of the Bach Suites for Unaccompanied Cello illuminated the works’ structural logic as well as their inner spirituality.”

Allan Kozinn on Mstislav Rostropovich in The New York Times, quoted in Log24 on April 29, 2007

“At that instant he saw, in one blaze of light, an image of unutterable conviction…. the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”

— Thomas Wolfe, Of Time and the River, quoted in Log24 on June 9, 2005

“… the stabiliser of an octad preserves the affine space structure on its complement, and (from the construction) induces AGL(4,2) on it. (It induces A8 on the octad, the kernel of this action being the translation group of the affine space.)”

— Peter J. Cameron, “The Geometry of the Mathieu Groups” (pdf)

“… donc Dieu existe, réponse!

— Attributed, some say falsely,
to Leonhard Euler

“Only gradually did I discover
what the mandala really is:
‘Formation, Transformation,
Eternal Mind’s eternal recreation'”

(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)

Wolfgang Pauli as Mephistopheles

“Pauli as Mephistopheles
in a 1932 parody of
Goethe’s Faust at Niels Bohr’s
institute in Copenhagen.
The drawing is one of
many by George Gamow
illustrating the script.”
Physics Today

“Borja dropped the mutilated book on the floor with the others. He was looking at the nine engravings and at the circle, checking strange correspondences between them.

‘To meet someone’ was his enigmatic answer. ‘To search for the stone that the Great Architect rejected, the philosopher’s stone, the basis of the philosophical work. The stone of power. The devil likes metamorphoses, Corso.'”

The Club Dumas, basis for the Roman Polanski film “The Ninth Gate” (See 12/24/05.)

“Pauli linked this symbolism
with the concept of automorphism.”

The Innermost Kernel
 (previous entry)

And from
Symmetry in Mathematics
and Mathematics of Symmetry

(pdf), by Peter J. Cameron,
a paper presented at the
International Symmetry Conference,
Edinburgh, Jan. 14-17, 2007,
we have

The Epigraph–

Weyl on automorphisms
(Here “whatever” should
of course be “whenever.”)

Also from the
Cameron paper:

Local or global?

Among other (mostly more vague) definitions of symmetry, the dictionary will typically list two, something like this:

• exact correspondence of parts;
• remaining unchanged by transformation.

Mathematicians typically consider the second, global, notion, but what about the first, local, notion, and what is the relationship between them?  A structure M is homogeneous if every isomorphism between finite substructures of M can be extended to an automorphism of M; in other words, “any local symmetry is global.”

Some Log24 entries
related to the above politically
(women in mathematics)–

Global and Local:
One Small Step

and mathematically–

Structural Logic continued:
Structure and Logic

This entry cites
Alice Devillers of Brussels–

Alice Devillers

“The aim of this thesis
is to classify certain structures
which are, from a certain
point of view, as homogeneous
as possible, that is which have
  as many symmetries as possible.”

“There is such a thing
as a tesseract.”

Madeleine L’Engle 

Wednesday, June 20, 2007

Wednesday June 20, 2007

Filed under: General,Geometry — Tags: — m759 @ 1:06 AM


Mathematical Reviews citation:

MR2163497 (2006g:81002) 81-03 (81P05)
Gieser, Suzanne The innermost kernel. Depth psychology and quantum physics. Wolfgang Pauli's dialogue with C. G. Jung. Springer-Verlag, Berlin, 2005. xiv+378 pp. ISBN: 3-540-20856-9

A quote from MR at Amazon.com:

"This revised translation of a Swedish Ph. D. thesis in philosophy offers far more than a discussion of Wolfgang Pauli's encounters with the psychoanalyst Carl Gustav Jung…. Here the book explains very well how Pauli attempted to extend his understanding beyond superficial esotericism and spiritism…. To understand Pauli one needs books like this one, which… seems to open a path to a fuller understanding of Pauli, who was seeking to solve a quest even deeper than quantum physics." (Arne Schirrmacher, Mathematical Reviews, Issue 2006g)

An excerpt:


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

I do not yet know what Gieser means by "the innermost kernel." The following is my version of a "kernel" of sorts– a diagram well-known to students of anthropologist Claude Levi-Strauss and art theorist Rosalind Krauss:

The four-group is also known as the Vierergruppe or Klein group.  It appears, notably, as the translation subgroup of A, the group of 24 automorphisms of the affine plane over the 2-element field, and therefore as the kernel of the homomorphism taking A to the group of 6 automorphisms of the projective line over the 2-element field. (See Finite Geometry of the Square and Cube.)

Related material:

The "chessboard" of
   Nov. 7, 2006
(as revised Nov. 7, 2012)–

I Ching chessboard. Previous version replaced on Nov. 7, 2012, by original 1989 chessboard arrangement

I Ching chessboard

None of this material really has much to do with the history of physics, except for its relation to the life and thought of physicist Wolfgang Pauli— the "Mephistopheles" of the new book Faust in Copenhagen. (See previous entry.)

"Only gradually did I discover
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"

(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)

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