Log24

A star figure and the Galois quaternion.

The square root of the former is the latter.

See also a passage quoted here a year ago today
(May the Fourth, "Star Wars Day") —

Quioted here  last  year on September 23rd —

See also Galois Quaternion.

A star figure and the Galois quaternion.

The square root of the former is the latter.

See also a search in this journal for "Set a Structure."

Today is reportedly the anniversary of the death,
in Paris in 1822, of Jean Robert Argand.

Some related material …

From MacTutor —

"Wessel's fame as a mathematician rests solely
on this paper, which was published in 1799,
giving for the first time a geometrical interpretation
of complex numbers. Today we call this geometric
interpretation the Argand diagram but Wessel's
work came first. It was rediscovered by Argand 
in 1806 and again by Gauss in 1831. ….

Of course it is not unreasonable to call the
geometrical interpretation of complex numbers
the Argand diagram since it was Argand's work
which was influential. It was so named before
the world of mathematics learnt of Wessel's prior
publication. In fact Wessel's paper was not
noticed by the mathematical community until 1895…."

See also Tilting at Whirligigs (Log24 on March 8, 2008)
and The Galois Quaternion.

(Continued from Nov. 15, 2011)

Ben Bradlee, legendary Washington Post editor, dies at 93

See also a post of Jan. 20, 2011, and an earlier post on Twelfth Night, 2010.

Commentary:

A star figure and the Galois quaternion.

The square root of the former is the latter.

Sarah Tomlin in a Nature  article on the July 12-15 2005 Mykonos meeting on Mathematics and Narrative—

"Today, Mazur says he has woken up to the power of narrative, and in Mykonos gave an example of a 20-year unsolved puzzle in number theory which he described as a cliff-hanger. 'I don’t think I personally understood the problem until I expressed it in narrative terms,' Mazur told the meeting. He argues that similar narrative devices may be especially helpful to young mathematicians…."

Michel Chaouli in "How Interactive Can Fiction Be?" (Critical Inquiry  31, Spring 2005), pages 613-614—

"…a simple thought experiment….*

… If the cliffhanger is done well, it will not simply introduce a wholly unprepared turn into the narrative (a random death, a new character, an entirely unanticipated obstacle) but rather tighten the configuration of known elements to such a degree that the next step appears both inevitable and impossible. We feel the pressure rising to a breaking point, but we simply cannot foresee where the complex narrative structure will give way. This interplay of necessity and contingency produces our anxious— and highly pleasurable— speculation about the future path of the story. But if we could determine that path even slightly, we would narrow the range of possible outcomes and thus the uncertainty in the play of necessity and contingency. The world of the fiction would feel, not open, but rigged."

* The idea of the thought experiment emerged in a conversation with Barry Mazur.

Barry Mazur in the preface to his 2003 book Imagining Numbers—

"But the telltale adjective real  suggests two things: that these numbers are somehow real to us and that, in contrast, there are unreal  numbers in the offing. These are the imaginary numbers . 

The imaginary  numbers are well named, for there is some imaginative work to do to make them as much a part of us as the real numbers we use all the time to measure for bookshelves. 

This book began as a letter to my friend Michel Chaouli. The two of us had been musing about whether or not one could 'feel' the workings of the imagination in its various labors. Michel had also mentioned that he wanted to 'imagine imaginary numbers.' That very (rainy) evening, I tried to work up an explanation of the idea of these numbers, still in the mood of our conversation."

See also The Galois Quaternion and 2/19.

New York Lottery last evening

A Quilt Version—

A Mathematical Version—

Related remarks —

• Sunday's Log24 post Cuatro Vientos  on Jack Kerouac
• The phrase dies natalis  in Log24
• Another weblog in 2004 on the dies natalis  of Jack Kerouac.
  That weblog gives the dies  as Oct. 20, but other sources
   say  Kerouac died at 5:15 AM on Oct. 21.
• A Log24 post on Oct. 20 last year related to the Oct. 21 date.

For the eight-limbed star at the top of the quaternion array above,
see "Damnation Morning" in this journal—

She drew from her handbag a pale grey gleaming implement
that looked by quick turns to me like a knife, a gun, a slim
sceptre, and a delicate branding iron—especially when its
tip sprouted an eight-limbed star of silver wire.

“The test?” I faltered, staring at the thing.

“Yes, to determine whether you can live in the fourth
dimension or only die in it.”

— Fritz Leiber, short story, 1959

See also Feb. 19, 2011.

The late translator Helen Lane in Translation Review , Vol. 5, 1980—

"Among the awards, I submit, should be one for the entire oeuvre  of a lifetime "senior" translator— and  one for the best first  translation…. Similar organization, cooperation, and fund-finding for a first-rate replacement for the sorely missed Delos ."

This leads to one of the founders of Delos , the late Donald Carne-Ross, who died on January 9, 2010.

For one meditation on the date January 9, see Bridal Birthday (last Thursday).

Another meditation, from the date of Carne-Ross's death—

See also Delos in this journal.

"Always keep a diamond in your mind."

— Tom Waits/Kathleen Brennan song performed by Solomon Burke at the Paradiso in Amsterdam

The Galois Quaternion "The text is a two-way mirror that allows me to look into the life and times of the reader. Who knows, someday i  may rise to a text that will compel me to push through to the other side." — The French Mathematician    (Galois), by Tom Petsinis

   For aficionados of mathematics and narrative —

Illustration from
"The Galois Quaternion— A Story"

This resembles an attempt by Coxeter in 1950 to represent
a Galois geometry in the Euclidean plane—

The quaternion illustration above shows a more natural way to picture this geometry—
not with dots representing points in the Euclidean  plane, but rather with unit squares
representing points in a finite Galois  affine plane. The use of unit squares to
represent points in Galois space allows, in at least some cases, the actions
of finite groups to be represented more naturally than in Euclidean space.

See Galois Geometry, Geometry Simplified, and
Finite Geometry of the Square and Cube.

“Logic is all about the entertaining of possibilities.”

– Colin McGinn, Mindsight: Image, Dream, Meaning,
   Harvard University Press, 2004

Geometry of Language,
continued from St. George's Day, 2009—

Related material:

Prima Materia,
The Galois Quaternion,
and The Wake of Imagination.

See also the following from a physicist
(not of the most orthodox sort, but his remarks
  here on Heisenberg seem quite respectable)–

"The positional meaning of a symbol derives from its relationship to other symbols in a totality, a Gestalt, whose elements acquire their significance from the system as a whole."

— Victor Turner, The Forest of Symbols, Ithaca, NY, Cornell University Press, 1967, p. 51, quoted by Beth Barrie in "Victor Turner."

To everything, turn, turn, turn…
— Peter Seeger

The Galois Quaternion:

Click for context.

The Galois Quaternion

Related material:
The Galois Quaternion

Click for context.
(See also Nativity and the end
of this morning's post.)