Log24

Thursday, December 21, 2023

Mutternacht

Filed under: General — Tags: , — m759 @ 1:31 am
 
"Ich bin ein Teil des Teils, der anfangs alles war
Ein Teil der Finsternis, die sich das Licht gebar
Das stolze Licht, das nun der Mutter Nacht
Den alten Rang, den Raum ihr streitig macht,
Und doch gelingt’s ihm nicht, da es, so viel es strebt,
Verhaftet an den Körpern klebt.
Von Körpern strömt’s, die Körper macht es schön,
Ein Körper hemmt’s auf seinem Gange;
So, hoff ich, dauert es nicht lange,
Und mit den Körpern wird’s zugrunde gehn."
 
Goethe, Faust
 

"The title of the book … is taken from a speech by Mephistopheles in Goethe’s Faust. As translated by Carlyle F. MacIntyre (New Directions, 1941), the speech is this:

I am a part of the part that at first was all, part of the darkness that gave birth to light, that supercilious light which now disputes with Mother Night her ancient rank and space, and yet can not succeed; no matter how it struggles, it sticks to matter and can’t get free. Light flows from substance, makes it beautiful; solids can check its path, so I hope it won’t be long till light and the world’s stuff are destroyed together."

— Vonnegut, Kurt. Mother Night: A Novel 
     (Gold Medal Books, 1962).

Mutternacht , as opposed to Mutter Nacht , is tonight,
the night of December 20-21, Winter Solstice Eve.

Sunday, October 8, 2023

Today’s Science Sermon

Filed under: General — Tags: , — m759 @ 12:54 pm

"Quantum accidents happen all the time.
Why haven’t I simply vanished into a quantum fizz
like Schrodinger’s cat, both dead and alive
at the same time? I can only conclude that
there is safety and stability in the astronomical
numbers of which we are composed.
Perhaps the large numbers constitute a bulwark
against quantum uncertainty. So I am here — I think."

Dennis Overbye in the New York Times ,

Update of 1:20 p.m. ET the same day —

"And what is your bulwark against the Heisenberg  group?"

Sunday, November 20, 2022

The Passenger

Tags: — m759 @ 9:00 am
 

See as well The Passenger  in this journal.

Saturday, July 10, 2021

Transformers

Filed under: General — Tags: , — m759 @ 11:33 am

Memories, Dreams, Reflections
by C. G. Jung

Recorded and edited By Aniela Jaffé,
translated from the German
by Richard and Clara Winston, 
Vintage Books edition of April 1989

From pages 195-196:

“Only gradually did I discover what the mandala really is:
‘Formation, Transformation, Eternal Mind’s eternal recreation.’*
And that is the self, the wholeness of the personality,
which if all goes well is harmonious,
but which cannot tolerate self-deceptions.”

Faust , Part Two, trans. by Philip Wayne (Harmondsworth,
England, Penguin Books Ltd., 1959), p. 79. The original:

                   … Gestaltung, Umgestaltung, 
  Des ewigen Sinnes ewige Unterhaltung….

Jung’s “Formation, Transformation” quote is from
the realm of the Mothers (Faust Part Two, Act 1, Scene 5:
A Dark Gallery).

The speaker is Mephistopheles.

"I have too much backstory" — Bryan Cranston, 2012

Or not enough.

Wednesday, October 19, 2016

The Intelligent User:

Filed under: General — m759 @ 7:59 pm

A Meditation on Two Dates

The dates are October 14, 2016, the release date of
the new film "The Accountant" —

"… clearer, more economical and formal, more liturgical."
     — David Remnick on lyrics of Leonard Cohen
     vs. those of Bob Dylan, quoted here on Oct. 14

— and May 12, 2016, the publication date of 
a YouTube trailer for "The Accountant."

Also quoted in the May 12 post

See as well the Ape with Skull (Affe mit Schädel) statue in
the Oct. 17 post Memorial Encounter. The version of the statue
pictured there omits the inscription "ERITIS SICUT DEUS"
in a book at the statue's base. There are related  remarks on
Mephistopheles and Faust at a different weblog.

Saturday, March 26, 2016

Crucible, Cauldron, Whatever

Filed under: General — m759 @ 2:45 am

Readings for the morning of Holy Saturday —

Crucible,  Cauldron,  Whatever.

Tuesday, February 23, 2016

White Mischief

Filed under: General — m759 @ 11:29 am

From a post of Christmas Eve, 2012 —

Memories, Dreams, Reflections
by C. G. Jung

Recorded and edited By Aniela Jaffé,
translated from the German
by Richard and Clara Winston, 
Vintage Books edition of April 1989

From pages 195-196:

“Only gradually did I discover what the mandala really is:
‘Formation, Transformation, Eternal Mind’s eternal recreation.’*
And that is the self, the wholeness of the personality,
which if all goes well is harmonious,
but which cannot tolerate self-deceptions.”

Faust , Part Two, trans. by Philip Wayne (Harmondsworth,
England, Penguin Books Ltd., 1959), p. 79. The original:

                   … Gestaltung, Umgestaltung, 
  Des ewigen Sinnes ewige Unterhaltung….

Jung’s “Formation, Transformation” quote is from
the realm of the Mothers (Faust Part Two, Act 1, Scene 5:
A Dark Gallery).

The speaker is Mephistopheles.

"Mephistopheles is not your name…" — Sting lyric

"You see, technically, chemistry is the study of matter,
but I prefer to see it as the study of change :

Electrons change their energy levels.
Molecules change their bonds.
Elements combine and change into compounds.

But that's all of life, right? It's the constant, it's the cycle.

It's solution, dissolution. Just over and over and over.

It is growth, then decay, then transformation! .

It is fascinating, really."

— Walter White, Season 1, Ep. 1, "Pilot"
more or less as quoted in huffingtonpost.com

See also Gestaltung  in this journal.

Monday, December 24, 2012

Eternal Recreation

Memories, Dreams, Reflections
by C. G. Jung

Recorded and edited By Aniela Jaffé, translated from the German
by Richard and Clara Winston, Vintage Books edition of April 1989

From pages 195-196:

"Only gradually did I discover what the mandala really is:
'Formation, Transformation, Eternal Mind's eternal recreation.'*
And that is the self, the wholeness of the personality, which if all
goes well is harmonious, but which cannot tolerate self-deceptions."

* Faust , Part Two, trans. by Philip Wayne (Harmondsworth,
England, Penguin Books Ltd., 1959), p. 79. The original:

                   … Gestaltung, Umgestaltung, 
  Des ewigen Sinnes ewige Unterhaltung….

Jung's "Formation, Transformation" quote is from the realm of
the Mothers (Faust Part Two, Act 1, Scene 5: A Dark Gallery).
The speaker is Mephistopheles.

See also Prof. Bruce J. MacLennan on this realm
in a Web page from his Spring 2005 seminar on Faust:

"In alchemical terms, F is descending into the dark, formless
primary matter from which all things are born. Psychologically
he is descending into the deepest regions of the
collective unconscious, to the source of life and all creation.
Mater (mother), matrix (womb, generative substance), and matter
all come from the same root. This is Faust's next encounter with
the feminine, but it's obviously of a very different kind than his
relationship with Gretchen."

The phrase "Gestaltung, Umgestaltung " suggests a more mathematical
approach to the Unterhaltung . Hence

Part I: Mothers

"The ultimate, deep symbol of motherhood raised to
the universal and the cosmic, of the birth, sending forth,
death, and return of all things in an eternal cycle,
is expressed in the Mothers, the matrices of all forms,
at the timeless, placeless originating womb or hearth
where chaos is transmuted into cosmos and whence
the forms of creation issue forth into the world of
place and time."

— Harold Stein Jantz, The Mothers in Faust:
The Myth of Time and Creativity 
,
Johns Hopkins Press, 1969, page 37

Part II: Matrices

        

Part III: Spaces and Hypercubes

Click image for some background.

Part IV: Forms

Forms from the I Ching :

Click image for some background.

Forms from Diamond Theory :

Click image for some background.

Tuesday, November 1, 2011

For All Hallows Day

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

The following was suggested by the Sermon
of October 30 (the day preceding Devil's Night)
and by yesterday's Beauty, Truth, Halloween.

"The German language has itself been influenced by Goethe's Faust , particularly by the first part. One example of this is the phrase 'des Pudels Kern ,' which means the real nature or deeper meaning of something (that was not evident before). The literal translation of 'des Pudels Kern ' is 'the core of the poodle,' and it originates from Faust's exclamation upon seeing the poodle (which followed him home) turn into Mephistopheles." —Wikipedia

See also the following readings (click to enlarge)—

Hans Primas on Pauli's 'des Pudels Kern'

Suzanne Gieser on Pauli's 'des Pudels Kern'

Note particularly…

"The main enigma of any description of a patternless
unus mundus  is to find appropriate partitions which
create relevant patterns." —Hans Primas, above

"In general, the partition of into right cosets
can differ from its partition into left cosets. Galois
was the first to recognize the importance of when
these partitions agree. This happens when the
subgroup is normal." — David A. Cox,
Galois Theory , Wiley, 2004, p. 510

Thursday, January 15, 2009

Thursday January 15, 2009

Filed under: General — Tags: — m759 @ 6:00 pm
Harvard, Magic,
and The New York Times

The New York Times Magazine for next Sunday:

The Edge of the Mystery, by Matt Bai–

“Weeks before the election of 1960, Norman Mailer, already an accomplished novelist, sat down to write his first major work of political journalism, an essay for Esquire in which he argued that only John F. Kennedy could save America… the only kind of leader who could rescue it, who could sweep in an era of what Mailer called ‘existential’ politics, was a ‘hipster’ hero– someone who welcomed risk and adventure, someone who sought out new experience, both for himself and for the country….

… Mailer essentially created a new genre for a generation of would-be literary philosophers covering politics….  By 1963, Mailer and other idealists were crushed to discover that Kennedy was in fact a fairly conventional and pragmatic politician, more Harvard Yard than Fortress of Solitude.”

The New York Times today:

Magic and Realism, by Roger Cohen–

“… what I want from the Obama administration is something more than Harvard-to-the-Beltway smarts. I want magical realism.”

Mailer and Cohen, taken together, suggest I should review two authors– Picard and Hesse– I encountered as a Harvard freshman in 1960.

Max Picard:

“In the ‘Prologue in Heaven’ in Goethe’s Faust a powerful silence is produced by the powerful word after each verse. There is an active, audible silence after every verse. The things that were moved into position by the word stand motionless in the silence, as if they were waiting to be called back into the silence and to disappear therein. The word not only brings the things out of silence; it also produces the silence in which they can disappear again.”

Goethe:

DER HERR:
Kennst du den Faust?

MEPHISTOPHELES:
Den Doktor?

DER HERR:
Meinen Knecht!

Online Etymology Dictionary:

knight
O.E. cniht “boy, youth, servant,” common W.Gmc. (cf. O.Fris. kniucht, Du. knecht, kneht “boy, youth, lad,” Ger. Knecht “servant, bondsman, vassal”), of unknown origin. Meaning “military follower of a king or other superior” is from c.1100. Began to be used in a specific military sense in Hundred Years War, and gradually rose in importance through M.E. period until it became a rank in the nobility 16c. The verb meaning “to make a knight of (someone)” is from c.1300. Knighthood is O.E. cnihthad M.H.G. “the period between childhood and manhood;” sense of “rank or dignity of a knight” is from c.1300. The chess piece so called from c.1440.

Further background on the word “Knecht”–

'Magister Ludi,' or 'The Glass Bead Game,' by Hermann Hesse

Epigraph to Magister Ludi
(Joseph Knecht’s translation):


“… For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.”

Tuesday, April 29, 2008

Tuesday April 29, 2008

Sacerdotal Jargon
at Harvard:

Thomas Wolfe

Thomas Wolfe
(Harvard M.A., 1922)

versus

Rosalind Krauss

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

on

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
Goethe's
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.

Thursday, June 21, 2007

Thursday June 21, 2007

Filed under: General,Geometry — Tags: , , , , — 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
(4/30/07):

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

Kernel

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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