Log24

Friday, April 16, 2021

Zero System*

Filed under: General — m759 @ 1:28 pm

See  Lying at the Axis .

* A mathematical term. This post was suggested
by the image link to posts tagged Gainesville at
the end of the previous post.

Saturday, November 21, 2015

The Zero System

Filed under: General,Geometry — Tags: — m759 @ 12:00 am

For the title phrase, see Encyclopedia of Mathematics .
The zero system  illustrated in the previous post*
should not be confused with the cinematic Zero Theorem .

* More precisely, in the part showing the 15 lines fixed under
   a zero-system polarity in PG(3,2).  For the zero system 
   itself, see diamond-theorem correlation.

Thursday, July 31, 2014

Zero System

Filed under: General,Geometry — Tags: , , — m759 @ 6:11 pm

The title phrase (not to be confused with the film 'The Zero Theorem')
means, according to the Encyclopedia of Mathematics,
a null system , and

"A null system is also called null polarity,
a symplectic polarity or a symplectic correlation….
it is a polarity such that every point lies in its own
polar hyperplane."

See Reinhold Baer, "Null Systems in Projective Space,"
Bulletin of the American Mathematical Society, Vol. 51
(1945), pp. 903-906.

An example in PG(3,2), the projective 3-space over the
two-element Galois field GF(2):

IMAGE- The natural symplectic polarity in PG(3,2), illustrating a symplectic structure

See also the 10 AM ET post of Sunday, June 8, 2014, on this topic.

Thursday, September 19, 2024

The Zen of Brick Space:
Embedding the Null Brick

Filed under: General — Tags: — m759 @ 2:21 am


The "Brick Space" model of PG(5,2) —

Brick space: The 2x4 model of PG(5,2)

Related reading . . .

See also "Zero System."

Wednesday, November 23, 2016

Yogiism

Filed under: General,Geometry — Tags: , — m759 @ 12:31 pm

From the American Mathematical Society (AMS) webpage today —

From the current AMS Notices

Related material from a post of Aug. 6, 2014

http://www.log24.com/log/pix10B/100915-SteinbergOnChevalleyGroups.jpg

(Here "five point sets" should be "five-point sets.")

From Gotay and Isenberg, “The Symplectization of Science,”
Gazette des Mathématiciens  54, 59-79 (1992):

“… what is the origin of the unusual name ‘symplectic’? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure ‘line complex group’ the ‘symplectic group.’
… the adjective ‘symplectic’ means ‘plaited together’ or ‘woven.’
This is wonderfully apt….”

IMAGE- A symplectic structure -- i.e. a structure that is symplectic (meaning plaited or woven)

The above symplectic  structure* now appears in the figure
illustrating the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2).

* The phrase as used here is a deliberate 
abuse of language .  For the real definition of 
“symplectic structure,” see (for instance) 
“Symplectic Geometry,” by Ana Cannas da Silva
(article written for Handbook of Differential
Geometry 
, Vol 2.) To establish that the above
figure is indeed symplectic , see the post 
Zero System of July 31, 2014.

Wednesday, May 11, 2016

Null Point

Filed under: General — Tags: — m759 @ 7:59 pm

This evening's previous post links to an earlier post
on a book by DeLillo.  This suggests a review
of DeLillo's most recent book, Zero K .

A title I prefer: that of this post, Null Point. *
For related mathematics, see Zero System .

Wikipedia — 

The Kelvin scale is an absolute, 
thermodynamic temperature scale 
using as its null point  absolute zero,
the temperature at which
all thermal motion ceases in the
classical description of thermodynamics.

Friday, July 3, 2015

Crunching Entities*

Filed under: General — m759 @ 9:19 pm

A figure I prefer to the "Golden Tablet" of Night at the Museum —

IMAGE- The natural symplectic polarity in PG(3,2), illustrating a symplectic structure

The source — The Log24 post "Zero System" of July 31, 2014.

* For the title, see The New Yorker  of Sept. 22, 2014.

Monday, December 8, 2014

Language Game

Filed under: General — m759 @ 12:01 pm

Continued from December 5 .

The previous post dealt with video game pioneer Ralph Baer. 
Here is a link in honor of mathematician Reinhold  Baer 
(see Baer in  Zero System , a post from the feast of St. Ignatius
Loyola in 2014.)

The posts in Reinhold 's link (those tagged "Yankee Puzzle")
include a reference to the Zero System post. The link tag was
suggested in part by the devil's claws in yesterday morning's post 
The Kernel Conundrum and in part by last night's 
Kennedy Center Honors tribute to Tom Hanks.

Hanks as the Harvard "symbologist" from the
novels of Dan Brown —

Wednesday, November 19, 2014

The Eye/Mind Conflict

Filed under: General,Geometry — Tags: — m759 @ 10:25 am

Harold Rosenberg, "Art and Words," 
The New Yorker , March 29, 1969. From page 110:

"An advanced painting of this century inevitably gives rise
in the spectator to a conflict between his eye and his mind; 
as Thomas Hess has pointed out, the fable of the emperor's 
new clothes is echoed at the birth of every modemist art 
movement. If work in a new mode is to be accepted, the 
eye/mind conflict must be resolved in favor of the mind; 
that is, of the language absorbed into the work. Of itself, 
the eye is incapable of breaking into the intellectual system 
that today distinguishes between objects that are art and 
those that are not. Given its primitive function of 
discriminating among things in shopping centers and on 
highways, the eye will recognize a Noland as a fabric
design, a Judd as a stack of metal bins— until the eye's 
outrageous philistinism has been subdued by the drone of 
formulas concerning breakthroughs in color, space, and 
even optical perception (this, too, unseen by the eye, of 
course). It is scarcely an exaggeration to say that paintings 
are today apprehended with the ears. Miss Barbara Rose, 
once a promoter of striped canvases and aluminum boxes, 
confesses that words are essential to the art she favored 
when she writes, 'Although the logic of minimal art gained 
critical respect, if not admiration, its reductiveness allowed
for a relatively limited art experience.' Recent art criticism 
has reversed earlier procedures: instead of deriving principles 
from what it sees, it teaches the eye to 'see' principles; the 
writings of one of America's influential critics often pivot on 
the drama of how he failed to respond to a painting or 
sculpture the first few times he saw it but, returning to the 
work, penetrated the concept that made it significant and
was then able to appreciate it. To qualify as a member of the 
art public, an individual must be tuned to the appropriate 
verbal reverberations of objects in art galleries, and his 
receptive mechanism must be constantly adjusted to oscillate 
to new vocabularies."

New vocabulary illustrated:

Graphic Design and a Symplectic Polarity —

Background: The diamond theorem
and a zero system .

Wednesday, August 6, 2014

Symplectic Structure*

Filed under: General,Geometry — Tags: — m759 @ 1:00 pm

From Gotay and Isenberg, "The Symplectization of Science,"
Gazette des Mathématiciens  54, 59-79 (1992):

"… what is the origin of the unusual name 'symplectic'? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure 'line complex group' the 'symplectic group.'
… the adjective 'symplectic' means 'plaited together' or 'woven.'
This is wonderfully apt…."

IMAGE- A symplectic structure -- i.e. a structure that is symplectic (meaning plaited or woven)

The above symplectic  structure** now appears in the figure
illustrating the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2).

Some related passages from the literature:

http://www.log24.com/log/pix10B/100915-SteinbergOnChevalleyGroups.jpg

* The title is a deliberate abuse of language .
For the real definition of "symplectic structure," see (for instance)
"Symplectic Geometry," by Ana Cannas da Silva (article written for
Handbook of Differential Geometry, vol 2.) To establish that the
above figure is indeed symplectic , see the post Zero System of
July 31, 2014.

** See Steven H. Cullinane, Inscapes III, 1986

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