Tuesday, May 29, 2018

The Schwartz Meme

Filed under: General — m759 @ 1:33 PM

IMAGE- The matrix Omega from notes of Richard Evan Schwartz. See also earlier versions (1977-1979) by Steven H. Cullinane.

Aficionados of the preposterous joke 
(see yesterday's post Epstein on Art
may consult a Google Image Search for
Schwartz Meme.

I prefer Schwartz même —

Wednesday, June 1, 2011

The Schwartz Notes

Filed under: General,Geometry — Tags: , — m759 @ 2:00 PM

A Google search today for material on the Web that puts the diamond theorem
in context yielded a satisfyingly complete list. (See the first 21 results.)
(Customization based on signed-out search activity was disabled.)

The same search limited to results from only the past month yielded,
in addition, the following—


This turns out to be a document by one Richard Evan Schwartz,
Chancellor's Professor of Mathematics at Brown University.

Pages 12-14 of the document, which is untitled, undated, and
unsigned, discuss the finite-geometry background of the R.T.
Curtis Miracle Octad Generator (MOG) . As today's earlier search indicates,
this is closely related to the diamond theorem. The section relating
the geometry to the MOG is titled "The MOG and Projective Space."
It does not mention my own work.

See Schwartz's page 12, page 13, and page 14.

Compare to the web pages from today's earlier search.

There are no references at the end of the Schwartz document,
but there is this at the beginning—

These are some notes on error correcting codes. Two good sources for
this material are
From Error Correcting Codes through Sphere Packings to Simple Groups ,
by Thomas Thompson.
Sphere Packings, Lattices, and Simple Groups  by J. H. Conway and N.
Planet Math (on the internet) also some information.

It seems clear that these inadequate remarks by Schwartz on his sources
can and should be expanded.

Monday, December 2, 2019

Gray Space

Filed under: General — Tags: , — m759 @ 3:00 PM

See as well a search for Gray Space in this journal.

Related material:  The Schwartz Omega .

“Looking carefully at Golay’s code
  is like staring into the sun.”

— Richard Evan Schwartz

Friday, December 14, 2018

Small Space Odyssey

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 11:00 AM

References in recent posts to physical space and 
to mathematical space suggest a comparison.

Physical space is well known, at least in the world
of mass entertainment.

Mathematical space, such as the 12-dimensional
finite space of the Golay code, is less well known.

A figure from each space —

The source of the Conway-Sloane brick —

Quote from a mathematics writer —

“Looking carefully at Golay’s code is like staring into the sun.”

— Richard Evan Schwartz

The former practice yields reflections like those of Conway and Sloane.
The latter practice is not recommended.

Monday, May 28, 2018


Filed under: General,Geometry — m759 @ 1:16 PM

A piece co-written by Ivanov, the author noted in the previous post, was cited
in my "Geometry of the 4×4 Square."

Also cited there —  A paper by Pasini and Van Maldeghem that mentions
the Klein quadric.

Those sources suggested a search —

The link is to some geometry recently described by Tabachnikov
that seems rather elegant:

For another, more direct, connection to the geometry of the 4×4 square,
see Richard Evan Schwartz in this  journal.

This same Schwartz appears also in the above Tabachnikov paper:

Tuesday, March 7, 2017

Signature Backdrop

Filed under: General — Tags: — m759 @ 9:00 PM

"The Bitter End’s signature stage backdrop —
a bare 150-year-old brick wall — helped distinguish it from
other popular bohemian hangouts like the Village Gate  
and the Village Vanguard. It appeared on the cover of
Peter, Paul and Mary’s first album."

The New York Times  this evening on a Sunday death


“Looking carefully at Golay’s code is like staring into the sun.”

— Richard Evan Schwartz

See also Schwartz in "The Omega Matrix," a post of 5 PM ET Sunday:

Sunday, March 5, 2017

The Omega Matrix

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

Richard Evan Schwartz on
the mathematics of the 4×4 square

See also Priority in this journal.

Monday, November 28, 2016


Filed under: General — Tags: — m759 @ 3:00 PM

Or:  A Candle for Sunrise  


Commentary —

“Looking carefully at Golay’s code is like staring into the sun.”

— Richard Evan Schwartz

Thursday, August 7, 2014

The Omega Mystery

Filed under: General — Tags: — m759 @ 11:00 PM

See a post,  The Omega Matrix, from the date of her death.

Related material:

"When Death tells a story, you really have to listen."
— Cover of The Book Thief

A scene from the film of the above book —

“Looking carefully at Golay’s code is like staring into the sun.”

— Richard Evan Schwartz

Some context — "Mathematics, Magic, and Mystery" —
See posts tagged April Awareness 2014.

Tuesday, August 5, 2014

The Omega Story

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

"We tell ourselves stories in order to live…. We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the 'ideas' with which we have learned to freeze the shifting phantasmagoria which is our actual experience."

Joan Didion

See also a post from May 4, 2011 (the date, according to a Google
search, of untitled notes regarding a matrix called Omega).

Sunday, August 3, 2014

The Omega Matrix

Filed under: General,Geometry — Tags: , , — m759 @ 10:31 PM

Shown below is the matrix Omega from notes of Richard Evan Schwartz.
See also earlier versions (1976-1979) by Steven H. Cullinane.

IMAGE- The matrix Omega from notes of Richard Evan Schwartz. See also earlier versions (1977-1979) by Steven H. Cullinane.

Backstory:  The Schwartz Notes (June 1, 2011), and Schwartz on
the American Mathematical Society's current home page:

(Click to enlarge.)

Thursday, March 13, 2014


Filed under: General — m759 @ 12:00 PM

A Presbyterian meditation —

A scene from the film of the above book —

“Looking carefully at Golay’s code is like staring into the sun.”

Richard Evan Schwartz

For more of the story, see Golay in this journal.

Tuesday, June 21, 2011

Piracy Project

Filed under: General,Geometry — Tags: , — m759 @ 2:02 AM

Recent piracy of my work as part of a London art project suggests the following.


           From http://www.trussel.com/rls/rlsgb1.htm

The 2011 Long John Silver Award for academic piracy
goes to ….

Hermann Weyl, for the remark on objectivity and invariance
in his classic work Symmetry  that skillfully pirated
the much earlier work of philosopher Ernst Cassirer.

And the 2011 Parrot Award for adept academic idea-lifting
goes to …

Richard Evan Schwartz of Brown University, for his
use, without citation, of Cullinane’s work illustrating
Weyl’s “relativity problem” in a finite-geometry context.

For further details, click on the above names.

Monday, December 9, 2019

Lost in Translation

Filed under: General — Tags: — m759 @ 12:26 PM

See as well hypokeimenon  in this journal.

Friday, December 6, 2019

Cezanne’s Greetings

Filed under: General — Tags: — m759 @ 12:18 PM

David Corfield on "Aesthetic Theory and Artistic Practice" —

" British naturalism of the nineteenth century is seen to be
based on a theory of art whose origin lies in eighteenth century
philosophy. Collingwood believes this to be a false theory,
as first made clear artistically by Cezanne. Note also that
Collingwood should feel the need to depart from abstract
argument to include the case study.

Exercise: with minimal changes make the above true for
the philosophy of mathematics. Once done, we see how
we should expect to find a philosophy of mathematics
in each mathematician, even if it only functions implicitly.
See Philosophy as Normative or Descriptive.

Last revised on July 12, 2010 at 11:02:44."

See as well some philosophical remarks by the late
William J. Richardson, S.J., quoted here  on July 12, 2010.

For Saint Nicholas

Filed under: General — Tags: — m759 @ 12:44 AM

In memory of William J. Richardson, S.J., who reportedly
died at 97 on 10 December 2016

This journal on that date

Wednesday, December 4, 2019


Filed under: General — Tags: , , — m759 @ 7:18 PM

(See the title in this journal.)

Also on the above YouTube date — July 12, 2010 —


Monday, December 2, 2019

D8: The Black Queen’s Square

Filed under: General — Tags: , — m759 @ 3:45 AM

The previous post quoted some dialogue from Victor Hugo's
novel about the French Revolution, Ninety-Three.

This suggests a look at the following non-fiction book:

Compare and contrast with the novel The Eight , by Katherine Neville,
about chess and the French Revolution.

Neville's birthday, April 4, plays a major role in her novel. The dies natalis 
(in the Roman Catholic sense) of the above Birth of the Chess Queen 
author, on the other hand, was reportedly November 20, 2019.

Following a link in this journal from November 20 leads to remarks 
that might interest the subjects of an upcoming film, "The Two Popes."

Monday, July 12, 2010

Lying Forth

Filed under: General — Tags: — m759 @ 12:00 PM


Related material:

Heidegger and Aristotle: The Twofoldness of Being,
by Walter A. Brogan, (SUNY Press, 2005)—

Pages 96-97

Heidegger: Through Phenomenology to Thought,
by William J. Richardson, S.J., (Springer, 1974)—

Pages  492493494495,  and  501

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