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"As though their knowledge of the quantum secrets came with the power of
prophecy, some three dozen of Europe's best physicists ended their 1932
meeting in Copenhagen with a parody of Goethe’s 'Faust.'....
It was only in retrospect that the silliness became profound. The
players were becoming possessors of 'a truth with implicit powers of
good and evil,' Gino Segrè writes in 'Faust in Copenhagen,' his
inventive new book about the era. And 'the devil... was in the
details.'" --George Johnson
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"Ich
aber, hier auf dem objektiven Wege, bin jetzt bemüht, das Positive der
Sache nachzuweisen, daß nämlich das Ding an sich von der Zeit und Dem,
was nur durch sie möglich ist, dem Entstehen und Vergehen, unberührt
bleibt, und daß die Erscheinungen in der Zeit sogar jenes rastlos
flüchtige, dem Nichts zunächst stehende Dasein nicht haben könnten,
wenn nicht in ihnen ein Kern aus der Ewigkeit*
wäre. Die Ewigkeit ist freilich ein Begriff, dem keine Anschauung zum
Grunde liegt: er ist auch deshalb bloß negativen Inhalts, besagt
nämlich ein zeitloses Dasein. Die Zeit ist demnach ein bloßes Bild der
Ewigkeit, ho chronos eikôn tou aiônos,**
wie es Plotinus*** hat: und ebenso ist unser zeitliches Dasein das bloße
Bild unsers Wesens an sich. Dieses muß in der Ewigkeit liegen, eben
weil die Zeit nur die Form unsers Erkennens ist: vermöge dieser allein
aber erkennen wir unser und aller Dinge Wesen als vergänglich, endlich
und der Vernichtung anheimgefallen."
* "a kernel of eternity"
** "Time is the image of eternity."
*** "wie es Plotinus hat"--
Actually, not Plotinus, but Plato,
according to Diogenes Laertius.
Related material:
Time Fold,
J. N. Darby,
"On the Greek Words for
Eternity and Eternal
(aion and aionios),"
Carl Gustav Jung, Aion,
which contains the following
four-diamond figure,
and Jung and the Imago Dei.
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"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!"
"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)
"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--
(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."
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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--
"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
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