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Monday, December 29, 2014

Dodecahedron Model of PG(2,5)

Filed under: General,Geometry — Tags: , , — m759 @ 2:28 PM

Recent posts tagged Sagan Dodecahedron 
mention an association between that Platonic
solid and the 5×5 grid. That grid, when extended
by the six points on a "line at infinity," yields
the 31 points of the finite projective plane of
order five.  

For details of how the dodecahedron serves as
a model of this projective plane (PG(2,5)), see
Polster's A Geometrical Picture Book , p. 120:

For associations of the grid with magic rather than
with Plato, see a search for 5×5 in this journal.

Sunday, December 28, 2014

Tyson’s Cosmos

Filed under: General — Tags: — m759 @ 1:00 PM

Related material

See also Cosmos + Sagan in this journal.

Thursday, December 25, 2014

Design

Filed under: General — Tags: , , — m759 @ 12:00 AM

Click image for some related posts.

Wednesday, December 24, 2014

More-Nuanced Realities

Filed under: General — Tags: , — m759 @ 11:32 PM

This evening's NY Times  wire:

Mabee reportedly died on December 18, 2014.

The cover of Harvard Design Magazine , Spring/Summer 2014:

See also Sigla (Dec. 22, 2014):
"Everyword for oneself but Code for us all."
— James Joyce in Scribbledehobble

What hath Joyce wrought?

Tuesday, December 23, 2014

Stoicheia*

Filed under: General — Tags: — m759 @ 2:02 PM

See also Derrida + Serpent in this journal.

* See Stoicheia (Elements) in this journal.

Friday, December 19, 2014

Colorful Tale

Filed under: General — Tags: , — m759 @ 11:30 AM

Wikipedia on a tale about one Hippasus of Metapontum,
who supposedly was drowned by Pythagoreans for his
discovery of irrational numbers and/or of the dodecahedron —

"In the hands of modern writers this combination of vague
ancient reports and modern guesswork has sometimes
evolved into a much more emphatic and colourful tale."

See, for instance, a tale told by the late Carl Sagan,
who was bitterly anti-Pythagorean (and anti-Platonic):

IMAGE- Sagan in 'Cosmos' on the Pythagoreans

For a related colorful tale, see "Patrick Blackburn" in this journal.

Thursday, December 18, 2014

Platonic Analogy

Filed under: General,Geometry — Tags: , , — m759 @ 2:23 PM

(Five by Five continued)

As the 3×3 grid underlies the order-3 finite projective plane,
whose 13 points may be modeled by
the 13 symmetry axes of the cube,
so the 5×5 grid underlies the order-5 finite projective plane,
whose 31 points may be modeled by
the 31 symmetry axes of the dodecahedron.

See posts tagged Galois-Plane Models.

Five by Five

Filed under: General — Tags: , — m759 @ 12:00 AM

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"This is Control. Do you copy?"
"Reading you five by five…"

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