Log24

Wednesday, February 9, 2022

8!

Filed under: General — Tags: , , , — m759 @ 12:03 am

Conwell, 1910 — 

(In modern notation, Conwell is showing that the complete
projective group of collineations and dualities of the finite
3-space PG (3,2) is of order 8 factorial, i.e. "8!"
In other words, that any  permutation of eight things may be
regarded as a geometric transformation of PG (3,2).)

Later discussion of this same "Klein correspondence"
between Conwell's 3-space and 5-space . . .

A somewhat simpler toy model —

Page from 'The Paradise of Childhood,' 1906 edition

Related fiction —  "The Bulk Beings" of the film "Interstellar."

Thursday, December 2, 2004

Thursday December 2, 2004

Filed under: General,Geometry — Tags: — m759 @ 8:23 pm

The Poem of Pure Reality

                                       "We seek
The poem of pure reality, untouched
By trope or deviation,
    straight to the word,
Straight to the transfixing object,
    to the object
At the exactest point at which it is itself,
Transfixing by being purely what it is…."

Wallace Stevens (1879-1955)
"An Ordinary Evening in New Haven" IX,
from The Auroras of Autumn (1950)
(Collected Poems, pp. 465-489)

I have added new material to Geometry of the 4×4 Square, including links to a new commentary on a paper by Burkard Polster.

"It is a good light, then, for those
That know the ultimate Plato,
Tranquillizing with this jewel
The torments of confusion."

— Wallace Stevens,
Collected Poetry and Prose, page 21,
The Library of America, 1997

Powered by WordPress