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From
Peter J. Cameron's review notes for
his new course in group
theory—
From Log24 on June 24—
Geometry
Simplified
(an affine
space with subsquares as points
and sets
of subsquares as hyperplanes)
(a projective
space with, as points, sets
of line segments that separate subsquares)
Exercise—
Show
that the above geometry is a model
for the algebra discussed by Cameron.
Tuesday, July 6, 2010
Thoreau on Group Theory
"Instead
of a million count half a dozen." —Walden
"Of
all the symmetric groups, S6 is
perhaps the most remarkable."
– Notes 2 (Autumn
2008), apparently by Robert A. Wilson,
for Group Theory, MTH714U
For a connection of MTH714U with Walden, see "Window, continued."
For a connection of "Window" with the remarkable S6, see Inscapes.
For some deeper background, see Wilson's "Exceptional Simplicity."
Tuesday, July 6, 2010
What “As” Is
or: Combinatorics
(Rota) as Philosophy (Heidegger) as Geometry (Me)
"Dasein’s
full existential structure is constituted by
the 'as-structure'
or 'well-joined structure' of the rift-design*…"
– Gary Williams, post of January 22, 2010
Background—
Gian-Carlo Rota on Heidegger…
"… The universal as is given various names in Heidegger's writings….
The discovery of the universal as is Heidegger's contribution to philosophy….
The universal 'as' is the surgence of sense in Man, the shepherd of Being.
The
disclosure of the primordial as
is the end of a search that began with Plato….
This search comes to its conclusion with Heidegger."
– "Three Senses of 'A is B' in Heideggger," Ch. 17 in Indiscrete Thoughts
… and points as separating rifts—
* rift-design— Definition by Deborah Levitt—
"Rift. The stroke or rending by which a world worlds, opening both the 'old' world and the self-concealing earth to the possibility of a new world. As well as being this stroke, the rift is the site— the furrow or crack— created by the stroke. As the 'rift design' it is the particular characteristics or traits of this furrow."
– "Heidegger and the Theater of Truth," in Tympanum: A Journal of Comparative Literary Studies, Vol. 1, 1998
Tuesday, July 6, 2010
A Serious Artist
Today's
Google logo
honors a serious artist:
Related
material:
That
post quotes the words of another serious artist,
Malcolm Lowry, on a barranca,
or deep ravine.
(See also Heidegger's "rift" concept.)
For a less serious rift, see the art of Kylie Minogue.
Tuesday, July 6, 2010
Bright Star
A room by the architect Luis Barragán.