The Source —
Some similar notions from my own work . . .
The "Digraph" of Mazzola might correspond to a directed graph
indicating the structure of a permutation, as at right below —
Mazzola's "Formula" might correpond to a matrix and translation that
transform the above "Space" of eight coordinates, and his "Gesture"
to a different way of generating affine transformations of that space . . .
as in my webpage "Cube Space, 1984-2003."
See also earlier references to Mazzola in this journal.
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From Gilles Châtelet, Introduction to Figuring Space Metaphysics does have a catalytic effect, which has been described in a very beautiful text by the mathematician André Weil: Nothing is more fertile, all mathematicians know, than these obscure analogies, these murky reflections of one theory in another, these furtive caresses, these inexplicable tiffs; also nothing gives as much pleasure to the researcher. A day comes when the illusion vanishes: presentiment turns into certainty … Luckily for researchers, as the fogs clear at one point, they form again at another.4 André Weil cuts to the quick here: he conjures these 'murky reflections', these 'furtive caresses', the 'theory of Galois that Lagrange touches … with his finger through a screen that he does not manage to pierce.' He is a connoisseur of these metaphysical 'fogs' whose dissipation at one point heralds their reforming at another. It would be better to talk here of a horizon that tilts thereby revealing a new space of gestures which has not as yet been elucidated and cut out as structure. 4 A. Weil, 'De la métaphysique aux mathématiques', (Oeuvres, vol. II, p. 408.) |
For gestures as fogs, see the oeuvre of Guerino Mazzola.
For some clearer remarks, see . . .
Illustrations of object and gestures
from finitegeometry.org/sc/ —
Object
Gestures
An earlier presentation
of the above seven partitions
of the eightfold cube:
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Related material: Galois.space .
"Let me say this about that." — Richard Nixon
Interpenetration in Weyl's epistemology —
Interpenetration in Mazzola's music theory —
Interpenetration in the eightfold cube — the three midplanes —
A deeper example of interpenetration:
Aitchison has shown that the Mathieu group M24 has a natural
action on the 24 center points of the subsquares on the eightfold
cube's six faces (four such points on each of the six faces). Thus
the 759 octads of the Steiner system S(5, 8, 24) interpenetrate
on the surface of the cube.
Source citation for an article quoted here last night —
“Hegel’s Conceptual Group Action” —
A check of that source yields the seal of the University of Torino —
Related material —
From https://www.mathunion.org/outreach/logos/versions-all-logos —
Click the logo for some IMU history.
Related bullshit —
“Hegel’s Conceptual Group Action” —
Click the banner below for the background of the logo —
Continued from Music Box – The Theory (April 21)
in memory of jazz enthusiast Ann Sneed,
who reportedly died in Las Vegas at 87 on that date.
Hollywood homicide detective Harry Bosch at home.
See also Mother of Beauty (April 7, 2004).
… A Scottish Play suggested by …
"The Hegel action is applied to understand creative processes
in two classical compositions — Beethoven’s Hammerklavier
Sonata op. 106, and Liszt’s Mephisto Walzer — but also to
the creation of a small model composition."
— From the abstract of "Hegel’s Conceptual
Group Action on Creative Dynamics in Music," by
Guerino Mazzola and Maria Mannone
http://toomuchhorrorfiction.blogspot.com/
2014/04/go-waltzing-mephisto-with-me.html
Wednesday, April 23, 2014
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Illustration —
Connoisseurs of bullshit who enjoyed the previous post
might also enjoy the following:
The previous two posts introduced Mazzola's noxious combination of
category theory and Hegel. The current version (Rev. 254) of the above
nLab "Science of Logic" article, though not by Mazzola, displays this
combination in its full hideous splendor.
Some posts in this journal that might be viewed as leading up to
the original Sept. 2, 2012, "Science of Logic" article are now tagged
Death Warmed Over.
For the music box of the title, see the previous post.
See also Mazzola on the Glass Bead Game
(Facebook date June 7, 2016)
and the Log24 post Symmetry (May 3, 2016).
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