Saturday, October 24, 2020


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

Wikipedia on what has been called “the doily” —

“The smallest non-trivial generalized quadrangle
is GQ(2,2), whose representation* has been dubbed
‘the doily’ by Stan Payne in 1973.”

A later publication relates the doily to grids.

From Finite Generalized Quadrangles , by Stanley E. Payne
and J. A. Thas, December 1983, at researchgate.net, pp. 81-82—

“Then the lines … define a 3×3 grid G  (i.e. a grid
consisting of 9 points and 6 lines).”
. . . .
“So we have shown that the grid G  can completed [sic ]
in a unique way to a grid with 8 lines and 16 points.”
. . . .
“A 4×4 grid defines a linear subspace
of  the 2−(64,4,1) design, i.e. a 4×4 grid
together with the affine lines on it is AG(2,4).”

A more graphic approach from this journal —

Seven is Heaven...

Click the image for further details.

* This wording implies that GQ(2,2) has a unique
visual representation. It does not. See inscape .

Sunday, March 15, 2020

Moriarty Songs

Filed under: General — m759 @ 2:09 PM

In memory of mathematician Richard K. Guy
and of songwriter Eric Taylor
who each reportedly died on March 9.

For Guy, some small numbers:

The image “http://www.log24.com/log/pix06/060407-Heaven.gif” cannot be displayed, because it contains errors.

For Taylor, a link to the lyrics of his song "Dean Moriarty."

See as well this journal on March 9.

(More backstory — Posts on Nanci Griffith.)

Tuesday, May 31, 2016

Galois Space —

Filed under: General,Geometry — Tags: — m759 @ 7:00 PM

A very brief introduction:

Seven is Heaven...

Sunday, July 19, 2015

Lying Rhyme

Filed under: General,Geometry — m759 @ 6:45 PM

Tom Stoppard, Jumpers —

“Heaven, how can I believe in Heaven?” 
she sings at the finale.
“Just a lying rhyme for seven!”

“To begin at the beginning: Is God?…”
[very long pause]

Leave a space.”

See as well a search for "Heaven.gif" in this journal.

For the more literate among us —

     … and the modulation from algebra to space.

Monday, April 25, 2011

The Apollo* Meme

Filed under: General — m759 @ 9:00 PM

In the May Smithsonian  magazine— "What Defines a Meme?"

Related — Seven is Heaven

Seven is Heaven...

* For the connection to Apollo, see Oct. 9, 2006.

Thursday, July 9, 2009

Thursday July 9, 2009

Filed under: General — m759 @ 8:00 AM
and Poetry

Click on the image for
some background related
to yesterday’s The Aleph
 and its  link  to  a 2003
 entry, At Mt. Sinai.

A related entry on Mt. Sinai
mentions the monumental
treatise by Leonard Shlain

The Alphabet Versus
the Goddess: The Conflict
Between Word and Image

Monday, July 30, 2007

Monday July 30, 2007

Filed under: General,Geometry — m759 @ 7:00 PM
The Deathly Hallows Symbol

'Deathly Hallows symbol, related to the 'Snakes on a Plane' cartoon.

Some fear that the Harry Potter books introduce children to the occult; they are not entirely mistaken.

According to Wikipedia, the “Deathly Hallows” of the final Harry Potter novel are “three fictional magical objects that appear in the book.”

The vertical line, circle, and triangle in the symbol pictured above are said to refer to these three magical objects.

One fan relates the “Deathly Hallows” symbol above, taken from the spine of a British children’s edition of the book, to a symbol for “the divine (or sacred, or secret) fire” of alchemy. She relates this fire in turn to “serpent power” and the number seven:

Kristin Devoe at a Potter fan site:

“We know that seven is a powerful number in the novels. Tom Riddle calls it ‘the most powerfully magic number.‘ The ability to balance the seven chakras within oneself allows the person to harness the secret fire. This secret fire in alchemy is the same as the kundalini or coiled snake in yogic philosophy. It is also known as ‘serpent power’ or the ‘dragon’ depending on the tradition. The kundalini is polar in nature and this energy, this internal fire, is very powerful for those who are able to harness it and it purifies the aspirant allowing them the knowledge of the universe. This secret fire is the Serpent Power which transmutes the base metals into the Perfect Gold of the Sun.

It is interesting that the symbol of the caduceus in alchemy is thought to have been taken from the symbol of the kundalini. Perched on the top of the caduceus, or the staff of Hermes, the messenger of the gods and revealer of alchemy, is the golden snitch itself! Many fans have compared this to the scene in The Order of the Phoenix where Harry tells Dumbledore about the attack on Mr. Weasley and says, ‘I was the snake, I saw it from the snake’s point of view.

The chapter continues with Dumbledore consulting ‘one of the fragile silver instruments whose function Harry had never known,’ tapping it with his wand:

The instrument tinkled into life at once with rhythmic clinking noises. Tiny puffs of pale green smoke issued from the minuscule silver tube at the top. Dumbledore watched the smoke closely, his brow furrowed, and after a few seconds, the tiny puffs became a steady stream of smoke that thickened and coiled into he air… A serpent’s head grew out of the end of it, opening its mouth wide. Harry wondered whether the instrument was confirming his story; He looked eagerly at Dumbledore for a sign that he was right, but Dumbledore did not look up.

“Naturally, Naturally,” muttered Dumbledore apparently to himself, still observing the stream of smoke without the slightest sign of surprise. “But in essence divided?”

Harry could make neither head not tail of this question. The smoke serpent, however split instantly into two snakes, both coiling and undulating in the dark air. With a look of grim satisfaction Dumbledore gave the instrument another gentle tap with his wand; The clinking noise slowed and died, and the smoke serpents grew faint, became a formless haze, and vanished.

Could these coiling serpents of smoke be foreshadowing events to come in Deathly Hallows where Harry learns to ‘awaken the serpent’ within himself? Could the snake’s splitting in two symbolize the dual nature of the kundalini?”

Related material

The previous entry

“And the serpent’s eyes shine    
As he wraps around the vine
In The Garden of Allah” —

and the following
famous illustration of
the double-helix
structure of DNA:

 Odile Crick, drawing of DNA structure in the journal Nature, 1953
This is taken from
a figure accompanying
an obituary, in today’s
New York Times, of the
artist who drew the figure

The double helix
is not a structure
from magic; it may,
however, as the Rowling
quote above shows, have
certain occult uses,
better suited to
Don Henley’s
Garden of Allah
than to the
  Garden of Apollo.

Seven is Heaven...

Similarly, the three objects
above (Log24 on April 9)
are from pure mathematics–
the realm of Apollo, not
of those in Henley’s song.

The similarity of the
top object of the three —
the “Fano plane” — to
the “Deathly Hallows”
symbol is probably
entirely coincidental.

Friday, May 11, 2007

Friday May 11, 2007

Filed under: General — m759 @ 6:29 AM
Two-Part Invention

“O for a muse of fire,
that would ascend
The brightest heaven
of invention”
Henry V, Prologue  

The image “http://www.log24.com/log/pix07/070511-Fire2.jpg” cannot be displayed, because it contains errors.


“The man who lives in contact with what he believes to be a living Church is a man always expecting to meet Plato and Shakespeare to-morrow at breakfast.” –G. K. Chesterton, Orthodoxy, Ch. IX

The image “http://www.log24.com/log/pix06/060407-Heaven.gif” cannot be displayed, because it contains errors.

“Going Up.”

— “Love at the  
 Five and Dime
Nanci Griffith

Monday, April 9, 2007

Monday April 9, 2007

Filed under: General — m759 @ 1:00 PM
Continued from last April:

in Poetry Month

Seven is Heaven...

Related Log24
entries from
last April:


Related Log24
entry from
this April

Monday, April 2, 2007

Monday April 2, 2007

Filed under: General — m759 @ 4:00 AM
in Poetry Month

The image �http://www.log24.com/log/pix06/060407-Heaven.gif� cannot be displayed, because it contains errors.

Related Log24
entries from
last April:


Related story:
April 1 PA
  numbers —
407, 214.

Friday, April 7, 2006

Friday April 7, 2006

Filed under: General — m759 @ 9:27 AM
in Poetry Month

The image “http://www.log24.com/log/pix06/060407-Heaven.gif” cannot be displayed, because it contains errors.

Tomorrow is the final day
for the Liza Lou exhibit at
  London’s White Cube gallery.

For related material, see
Log24, March 24-26, and
the entries culminating
on Pi Day.

Wednesday, June 4, 2003

Wednesday June 4, 2003

Filed under: General — m759 @ 5:24 PM

Fearful Meditation, Part II
The Four Last Things

“Where is Evelyn Waugh when you need him?”
Roger Kimball, “Minimalist Fantasies” 

Death, Judgment, Heaven, Hell
known collectively in the Catholic world as
the Four Last Things. They would have
formed the basis for a course of
uncomfortable meditations….”
A Companion to Evelyn Waugh’s
Brideshead Revisited
, by David Cliffe

Death, Judgment, Heaven, and Hell.

Click on pictures for details.

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