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") —
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") —
In the following passage, Dan Brown claims that an eight-ray star
with arrowheads at the rays' ends is "the mathematical symbol for
entropy." Brown may have first encountered this symbol at a
questionable "Sacred Science" website. Wikipedia discusses
some even less respectable uses of the symbol.
Related news —
Related symbolism —
A star figure and the Galois quaternion.
The square root of the former is the latter.
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 …
"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.
A star figure and the Galois quaternion.
The square root of the former is the latter.
For the late mathematics educator Zoltan Dienes.
"There comes a time when the learner has identified
the abstract content of a number of different games
and is practically crying out for some sort of picture
by means of which to represent that which has been
gleaned as the common core of the various activities."
— Article by "Melanie" at Zoltan Dienes's website
Dienes reportedly died at 97 on Jan. 11, 2014.
From this journal on that date —
A star figure and the Galois quaternion.
The square root of the former is the latter.
Update of 5:01 PM ET Feb. 6, 2014 —
An illustration by Dienes related to the diamond theorem —
See also the above 15 images in …
… and versions of the 4×4 coordinatization in The 4×4 Relativity Problem
(Jan. 17, 2014).
From "Entertainment," a 1981 story by M. A. Foster—
"For some time, Cormen had enjoyed a peculiar suspicion, which he had learned from his wanderings around the city, and cultivated with a little notebook, in which he had made a detailed series of notes and jottings, as well as crude, but effective, charts and maps of certain districts. 'Cormen's Problem,' as it was known, was familiar to the members of the circle in which he moved; in fact, if he had not been so effective with his productions and so engaging in his personality, they might have considered him a bore. It seemed, so the suspicion went, that the city was slowly shrinking, as evidenced by abandoned districts along the city edges. Beyond the empty houses were ruins, and beyond that, traces of foundations and street lines. Moreover, it had recently dawned on him that there were no roads out of the city, although there were no restraints. One hardly noticed this—it was the norm. But like many an easy assumption, once broken it became increasingly obvious. Cormen's acquaintances were tolerant of his aberration, but generally unsympathetic. What he needed was proof, something he could demonstrate in black and white—and color if required. But the city was reluctant, so it appeared, to give up its realities so easily. The Master Entertainment Center, MEC, would not answer direct queries about this, even though it would obediently show him presentations, pictorial or symbolic as he required, of the areas in question. But it was tiresome detail work, in which he had to proceed completely on his own." |
Lily Collins in City of Bones (2013)—
American Folk Art (see August 23, 2011) —
See as well Ballet Blanc .
The premiere of the Lily Collins film Abduction
(see previous post) was reportedly in Sydney, Australia,
on August 23, 2011.
From that date in this journal—
For the eight-limbed star at the top of the quaternion array above, 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 |
Related material from Wikipedia, suggested by the reference quoted
in this morning's post to "a four-dimensionalist (perdurantist) ontology"—
"… perdurantism also applies if one believes there are temporal
but non-spatial abstract entities (like immaterial souls…)."
A star figure and the Galois quaternion.
The square root of the former is the latter.
"… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte."
"… the human will cannot be simultaneously
triumphant and imaginary."
— Ross Douthat, Defender of the Faith,
in this afternoon's New York Times at 3:25* PM ET
Some— even some Catholics— might say the will
cannot be triumphant unless imaginary.
Related material: The Galois Quaternion: A Story.
See also C. S. Lewis on enchantment.
* Cf., in this journal, the most recent 3/25 ,
and a bareword —
Click image for some context.
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
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
Related remarks —
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—
Saturday, January 9, 2010
Positional Meaning"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 … |
See also Delos in this journal.
From Epiphany Revisited —
A star figure and the Galois quaternion.
The square root of the former is the latter.
… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.
"Always keep a diamond in your mind."
— Tom Waits/Kathleen Brennan song performed by Solomon Burke at the Paradiso in Amsterdam
"The text is a two-way mirror — The French Mathematician |
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
I had foreseen it all in precise detail. i = an imaginary being Here, on this complex space, |
Related material:
The Galois Quaternion
Click for context.
(See also Nativity and the end
of this morning's post.)
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