Monday, December 18, 2017

Wheelwright and the Dance

Filed under: G-Notes,General,Geometry — m759 @ 1:00 PM

The page preceding that of yesterday's post  Wheelwright and the Wheel —

See also a Log24 search for 
"Four Quartets" + "Four Elements".

A graphic approach to this concept:

"The Bounded Space" —

'Space Cross' from the Cullinane diamond theorem

"The Fire, Air, Earth, and Water" —

Logo for 'Elements of Finite Geometry'

Sunday, September 9, 2012

Decomposition Sermon

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

(Continued from Walpurgisnacht 2012)

Wikipedia article on functional decomposition

"Outside of purely mathematical considerations,
perhaps the greatest value of functional decomposition
is the insight it provides into the structure of the world."

Certainly this is true for the sort of decomposition
known as harmonic analysis .

It is not, however, true of my own decomposition theorem,
which deals only with structures made up of at most four
different sorts of elementary parts.

But my own approach has at least some poetic value.

See the four elements of the Greeks in (for instance)
Eliot's Four Quartets  and in Auden's For the Time Being .

Wednesday, May 9, 2012

Geometry of the Dance

Filed under: General,Geometry — m759 @ 9:00 PM

Peter Pesic uses a dance metaphor to explain
finite group theory, with permutations of four elements
represented by symmetries of a tetrahedron—

IMAGE- 'The geometry of the dance' is that of a tetrahedron, according to Peter Pesic

For a different approach to the dance metaphor, see
the dance in Four Quartets and Poetry's Bones.

                                             In that open field
If you do not come too close, if you do not come too close,
On a summer midnight, you can hear the music
Of the weak pipe and the little drum
And see them dancing around the bonfire
The association of man and woman
In daunsinge, signifying matrimonie—
A dignified and commodiois sacrament.
Two and two, necessarye coniunction….

Wednesday, November 2, 2011

The Poetry of Universals

Filed under: General,Geometry — m759 @ 7:59 PM

A search today, All Souls Day, for relevant learning
at All Souls College, Oxford, yields the person of
Sir Michael Dummett and the following scholarly page—

(Click to enlarge.)


My own background is in mathematics rather than philosophy.
From a mathematical point of view, the cells discussed above
seem related to some "universals" in an example of Quine.

In Quine's example,* universals are certain equivalence classes
(those with the "same shape") of a family of figures
(33 convex regions) selected from the 28 = 256 subsets
of an eight-element set of plane regions.

A smaller structure, closer to Wright's concerns above,
is a universe of 24 = 16 subsets of a 4-element set.

The number of elements in this universe of Concepts  coincides,
as it happens, with the number obtained by multiplying out
the title of T. S. Eliot's Four Quartets .

For a discussion of functions that map "cells" of the sort Wright
discusses— in the quartets example, four equivalence classes,
each with four elements, that partition the 16-element universe—
onto a four-element set, see Poetry's Bones.

For some philosophical background to the Wright passage
above, see "The Concept Horse," by Harold W. Noonan—
Chapter 9, pages 155-176, in Universals, Concepts, and Qualities ,
edited by P. F. Strawson and Arindam Chakrabarti,
Ashgate Publishing, 2006.

For a different approach to that concept, see Devil's Night, 2011.

* Admittedly artificial. See From a Logical Point of View , IV, 3

Wednesday, June 3, 2009

Wednesday June 3, 2009

Filed under: General,Geometry — m759 @ 4:00 AM
to Four Quartets:

Epigraphs to Eliot's 'Four Quartets'-- Heraclitus on the common logos and on the way up and the way down

The Dissertations of Maximus Tyrius
, translated from the Greek by Thomas Taylor, printed by C. Whittingham, London, for the translator, 1804, Vol. II, p. 55:

“You see the mutation of bodies, and the transition of generation, a path upwards and downwards according to Heraclitus; and again, as he says, one thing living the death, but dying the life of another. Thus fire lives the death of earth, and air lives the death of fire; water lives the death of air, and earth lives the death of water. You see a succession of life, and a mutation of bodies, both of which are the renovation of the whole.”

Eight-rayed star of Venus (also the symmetry axes of the square)

For an interpretation
of the above figure
in terms of the classical
four elements discussed
in Four Quartets,
in Dissertations, and
in Angels & Demons,
Notes on Mathematics
 and Narrative.

For a more entertaining
interpretation, see Fritz Leiber’s
classic story “Damnation Morning.”

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