Thursday, March 7, 2019

In Reality

Filed under: General — m759 @ 11:45 AM

The previous post, quoting a characterization of the R. T. Curtis
Miracle Octad Generator , describes it as a "hand calculator ."

Other views 

A "natural diagram " —


A geometric object

Counting symmetries with the orbit-stabilizer theorem.

Sunday, January 20, 2019

Scope Resolution

Filed under: General — Tags: , — m759 @ 9:00 AM

Wikipedia on a programming term

The scope resolution operator helps to identify
and specify the context to which an identifier refers,
particularly by specifying a namespace. The specific
uses vary across different programming languages
with the notions of scoping.  In many languages
the scope resolution operator is written


In a completely different context, these four dots might represent
a geometric object  — the four-point plane .

Friday, January 18, 2019

The Woke Grids …

Filed under: General — Tags: , — m759 @ 10:45 AM

… as opposed to The Dreaming Jewels .

A July 2014 Amsterdam master's thesis on the Golay code
and Mathieu group —

"The properties of G24 and M24 are visualized by
four geometric objects:  the icosahedron, dodecahedron,
dodecadodecahedron, and the cubicuboctahedron."

Some "geometric objects"  — rectangular, square, and cubic arrays —
are even more fundamental than the above polyhedra.

A related image from a post of Dec. 1, 2018

Wednesday, January 16, 2019

Permutahedron Dream

Filed under: General — Tags: , , , — m759 @ 3:21 PM

The geometric object of the title appears in a post mentioning Bourgain 
in this journal.  Bourgain appears also in today's online New York Times —


Bourgain reportedly died on December 22.

An image from this journal on that date

Related poetic meditations —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

Monday, July 29, 2013

St. Walter’s Day

Filed under: General,Geometry — m759 @ 5:05 PM

Today is the dies natalis  of group theorist  Walter Feit.

     "The Steiner systems (5,6,12) and (5,8,24) are remarkable combinatorial
configurations unlike any others. Their automorphism groups are the Mathieu
groups M12 and M24. These are the only 5-transitive permutation groups other
than symmetric and alternating groups: (a fact long conjectured but only
proved as a consequence of the classification). The Leech lattice is a blown up
version of (5,8,24).
It is the unique even unimodular lattice in 24 dimensions
with no vectors of weight 2. This uniqueness is an essential reason why it is a
geometric object of fundamental importance. The automorphism group Co.O
of the Leech lattice involves about half of the sporadic groups and generally it
is felt that these are well understood."

— Walter Feit, book review, Bulletin of the American Mathematical Society ,
     Vol. 8 (1983), 120-124, page 123

Saturday, December 20, 2003

Saturday December 20, 2003

Filed under: General,Geometry — Tags: — m759 @ 5:00 PM

White, Geometric, and Eternal

This afternoon's surfing:

Prompted by Edward Rothstein's own Fides et Ratio encyclical in today's NY Times, I googled him.

At the New York Review of Books, I came across the following by Rothstein:

"… statements about TNT can be represented within TNT: the formal system can, in a precise way, 'talk' about itself."

This naturally prompted me to check what is on TNT on this, the feast day of St. Emil Artin.  At 5 PM this afternoon, we have Al Pacino in "The Devil's Advocate" — a perfect choice for the festival of an alleged saint.

Preparing for Al, I meditated on the mystical significance of the number 373, as explained in Zen and Language Games: the page number 373 in Robert Stone's theological classic A Flag for Sunrise conveys the metaphysical significance of the phrase "diamonds are forever" — "the eternal in the temporal," according to Stone's Catholic priest.  This suggests a check of another theological classic, Pynchon's Gravity's RainbowPage 373 there begins with the following description of prewar Berlin:

"white and geometric."

This suggests the following illustration of a white and geometric object related to yesterday's entry on Helmut Wielandt:

From antiquark.com

Figure 1

(This object, which illustrates the phrase "makin' the changes," also occurs in this morning's entry on the death of a jazz musician.)

A further search for books containing "white" and "geometric" at Amazon.com yields the following:

Figure 2

From Mosaics, by
Fassett, Bahouth, and Patterson:

"A risco fountain in Mexico city, begun circa 1740 and made up of Mexican pottery and Chinese porcelain, including Ming.

The delicate oriental patterns on so many different-sized plates and saucers [are] underlined by the bold blue and white geometric tiles at the base."

Note that the tiles are those of Diamond Theory; the geometric object in figure 1 above illustrates a group that plays a central role in that theory.

Finally, the word "risco" (from Casa del Risco) associated with figure 2 above leads us to a rather significant theological site associated with the holy city of Santiago de Compostela:

Figure 3

Vicente Risco's
Dedalus in Compostela.

Figure 3 shows James Joyce (alias Dedalus), whose daughter Lucia inspired the recent entry Jazz on St. Lucia's Day — which in turn is related, by last night's 2:45 entry and by Figure 1, to the mathematics of group theory so well expounded by the putative saint Emil Artin.

"His lectures are best described as
polished diamonds."
Fine Hall in its Golden Age,
by Gian-Carlo Rota

If Pynchon plays the role of devil's advocate suggested by his creation, in Gravity's Rainbow, of the character Emil Bummer, we may hope that Rota, no longer in time but now in eternity, can be persuaded to play the important role of saint's advocate for his Emil.

Update of 6:30 PM 12/20/03:


The Absolutist Faith
of The New York Times

White and Geometric, but not Eternal.

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