The phrase "cultural correlations" from the previous post suggests . . .
From this journal on Bloomsday 2008 —
The holy image
denoting belief and revelation
may be interpreted as
a black hole or as a
symbol by James Joyce :
|
When? Going to dark bed there was a square round Sinbad the Sailor roc’s auk’s egg in the night of the bed of all the auks of the rocs of Darkinbad the Brightdayler. Where?
— Ulysses , conclusion of Chapter 17. |
"Read something that means something."
— New Yorker ad
.
http://m759.net/wordpress/?s="Correlation"
http://m759.net/wordpress/?tag=correlative
Related literary reference —
"The only way of expressing emotion in the form of art
is by finding an 'objective correlative'; in other words,
a set of objects, a situation, a chain of events which
shall be the formula of that particular emotion; such that
when the external facts, which must terminate in sensory
experience, are given, the emotion is immediately evoked.
If you examine any of Shakespeare’s more successful
tragedies, you will find this exact equivalence…."
— T. S. Eliot, "Hamlet and His Problems" (1919)
Click image for a larger, clearer version.
"That in which space itself is contained"
— Wallace Stevens
In the ninefold square,
projective-perspectivity duality
corresponds to
projective-correlation duality.
Illustrations —
From The Man Who Knew Infinity to The Man Who Knew Zero.
Related mathematics: The Diamond Theorem Correlation, which
results from interchanging infinity and zero in the figure below.
"Read something that means something."
— New Yorker ad
.
Click image for
related posts.
Background — Relativity Problem in Log24.
The above New Yorker art illustrates the 2×4 structure of
an octad in the Miracle Octad Generator of R. T. Curtis.
Enthusiasts of simplicity may note how properties of this eight-cell
2×4 grid are related to those of the smaller six-cell 3×2 grid:
See Nocciolo in this journal and . . .
Further reading on the six-set – eight-set relationship:
In the spirit of the Linz website in the previous post,
the title refers to New Yorker writer Adam Gopnik:
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Tuesday, November 7, 2017
Polarities and Correlation
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See also a search in this journal for Polarity + Correlation.
"This outer automorphism can be regarded as
the seed from which grow about half of the
sporadic simple groups…." — Noam Elkies
Closely related material —
The top two cells of the Curtis "heavy brick" are also
the key to the diamond-theorem correlation.
See also "Overarching + Tesseract" in this journal. From the results
of that search, some context for the "inscape" of the previous post —
A phrase from the previous post —
"a size-eight dame in a size-six dress" —
suggests a review . . .
See as well the diamond-theorem correlation and . . .
.gif)
A clue to the relationship between the Kummer (16, 6)
configuration and the large Mathieu group M24 —
Related material —
See too the diamond-theorem correlation.
". . . dance, fueled by music, opens up space."
— Alastair Macaulay in the online New York Times today
Putting aside the unfortunate fuel metaphor, this suggests a review —
A video published on the above date —
The video has six-plus-two dancers, a more concise arrangement
than the eight-plus-two discussed by Macaulay.
Another approach to six plus two: the diamond-theorem correlation.
A figure related to the general connecting theorem of Koen Thas —
See also posts tagged Dirac and Geometry in this journal.
Those who prefer narrative to mathematics may, if they so fancy, call
the above Thas connecting theorem a "quantum tesseract theorem ."
See also Symplectic in this journal.
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….”
The above symplectic figure appears in remarks on
the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2). See also
related remarks on the notion of linear (or line ) complex
in the finite projective space PG(3,2) —
Part I: Black Magician
"Schools of criticism create their own canons, elevating certain texts,
discarding others. Yet some works – Malcolm Lowry’s Under the Volcano
is one of them – lend themselves readily to all critical approaches."
— Joan Givner, review of
A Darkness That Murmured: Essays on Malcolm Lowry and the Twentieth Century
by Frederick Asals and Paul Tiessen, eds.
The Asals-Tiessen book (U. of Toronto Press, 2000) was cited today
by Margaret Soltan (in the link below) as the source of this quotation —
"When one thinks of the general sort of snacky
under-earnest writers whose works like wind-chimes
rattle in our heads now, it is easier to forgive Lowry
his pretentious seriousness, his old-fashioned ambitions,
his Proustian plans, [his efforts] to replace the reader’s
consciousness wholly with a black magician’s."
A possible source, Perle Epstein, for the view of Lowry as black magician —
Part II: Mythos and Logos
Part I above suggests a review of Adam Gopnik as black magician
(a figure from Mythos ) —
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Tuesday, November 7, 2017
Polarities and Correlation
|
— and of an opposing figure from Logos ,
Paul B. Yale, in the references below:
Scholia on the title — See Quantum + Mystic in this journal.
"In Vol. I of Structural Anthropology , p. 209, I have shown that
this analysis alone can account for the double aspect of time
representation in all mythical systems: the narrative is both
'in time' (it consists of a succession of events) and 'beyond'
(its value is permanent)." — Claude Lévi-Strauss, 1976
I prefer the earlier, better-known, remarks on time by T. S. Eliot
in Four Quartets , and the following four quartets (from
The Matrix Meets the Grid) —
.
From a Log24 post of June 26-27, 2017:
A work of Eddington cited in 1974 by von Franz —
See also Dirac and Geometry and Kummer in this journal.
Ron Shaw on Eddington's triads "associated in conjugate pairs" —
For more about hyperbolic and isotropic lines in PG(3,2),
see posts tagged Diamond Theorem Correlation.
For Shaw, in memoriam — See Contrapuntal Interweaving and The Fugue.
The Linotype Fixer
( Sequel to "The Typewriter Fixer" * )
From The Hollywood Reporter on Tuesday, Nov. 7, 2017 —
* "The Typewriter Fixer" refers to a typewriter repair shop
on New York's Upper West Side —
The Hollywood Reporter 's promotional piece above is from
Tuesday, November 7, 2017. For another meditation suited to
the Upper West Side, see this journal on that date —
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Tuesday, November 7, 2017
Polarities and Correlation
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This post was suggested by the previous post — Four Dots —
and by the phrase "smallest perfect" in this journal.
Related material (click to enlarge) —
Detail —
From the work of Eddington cited in 1974 by von Franz —
See also Dirac and Geometry and Kummer in this journal.
Updates from the morning of June 27 —
Ron Shaw on Eddington's triads "associated in conjugate pairs" —
For more about hyperbolic and isotropic lines in PG(3,2),
see posts tagged Diamond Theorem Correlation.
For Shaw, in memoriam — See Contrapuntal Interweaving and The Fugue.
Pinterest boards uploaded to the new m759.net/piwigo —
Update of May 2 —
Update of May 3 —
Update of May 8 —
Art Space board created at Pinterest
See, too, this evening's A Common Space
and earlier posts on Raiders of the Lost Crucible.
Also not without relevance —
Space —
Space structure —
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….”
The above symplectic figure appears in remarks on
the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2).
Space shuttle —
Related ethnic remarks —
… As opposed to Michael Larsen —
Funny, you don't look Danish.
From the American Mathematical Society (AMS) webpage today —
From the current AMS Notices —
Related material from a post of Aug. 6, 2014 —
(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….”
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.
|
Abstract: "Protection of digital content from being tapped by intruders is a crucial task in the present generation of Internet world. In this paper, we proposed an implementation of new visual secret sharing scheme for gray level images using diamond theorem correlation. A secret image has broken into 4 × 4 non overlapped blocks and patterns of diamond theorem are applied sequentially to ensure the secure image transmission. Separate diamond patterns are utilized to share the blocks of both odd and even sectors. Finally, the numerical results show that a novel secret shares are generated by using diamond theorem correlations. Histogram representations demonstrate the novelty of the proposed visual secret sharing scheme." — "New visual secret sharing scheme for gray-level images using diamond theorem correlation pattern structure," by V. Harish, N. Rajesh Kumar, and N. R. Raajan.
Published in: 2016 International Conference on Circuit, Power and Computing Technologies (ICCPCT). |
Excerpts —
Related material — Posts tagged Diamond Theorem Correlation.
1. Tom Wolfe has a new book on Chomsky, "The Kingdom of Speech."
2. This suggests a review of a post of Aug. 11, 2014, Syntactic/Symplectic.
To paraphrase Wittgenstein, sentence 1 above is about "correlating in real life"
(cf. Crooked House and Wolfe's From Bauhaus to Our House ), and may be
compared to sentence 2 above, which links to a sort of "correlating in
mathematics" that is a particular example of the more general sort of
mathematical correlating mentioned by Wittgenstein in 1939.
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.
Note that the six anticommuting sets of Dirac matrices listed by Arfken
correspond exactly to the six spreads in the above complex of 15 projective
lines of PG(3,2) fixed under a symplectic polarity (the diamond theorem
correlation ). As I noted in 1986, this correlation underlies the Miracle
Octad Generator of R. T. Curtis, hence also the large Mathieu group.
References:
Arfken, George B., Mathematical Methods for Physicists , Third Edition,
Academic Press, 1985, pages 213-214
Cullinane, Steven H., Notes on Groups and Geometry, 1978-1986
Related material:
The 6-set in my 1986 note above also appears in a 1996 paper on
the sixteen Dirac matrices by David M. Goodmanson —
Background reading:
Ron Shaw on finite geometry, Clifford algebras, and Dirac groups
(undated compilation of publications from roughly 1994-1995)—
The title is a phrase from R. D. Laing's book The Politics of Experience .
(Published in the psychedelic year 1967. The later "contrapuntal interweaving"
below is of a less psychedelic nature.)
An illustration of the "interweaving' part of the title —
The "deep structure" of the diamond theorem:
.
The word "symplectic" from the end of last Sunday's (Oct. 11) sermon
describes the "interwoven" nature of the above illustration.
An illustration of the "contrapuntal" part of the title (click to enlarge):
Some context for yesterday's post on a symplectic polarity —
This 1986 note may or may not have inspired some remarks
of Wolf Barth in his foreword to the 1990 reissue of Hudson's
1905 Kummer's Quartic Surface .
See also the diamond-theorem correlation.
The words: "symplectic polarity"—
The images:
The Natural Symplectic Polarity in PG(3,2)
Symmetry Invariance in a Diamond Ring
The Diamond-Theorem Correlation
Steven Pressfield on April 25, 2012:
What exactly is High Concept?
Let’s start with its opposite, low concept.
Low concept stories are personal,
idiosyncratic, ambiguous, often European.
“Well, it’s a sensitive fable about a Swedish
sardine fisherman whose wife and daughter
find themselves conflicted over … ”
ZZZZZZZZ.
Fans of Oslo artist Josefine Lyche know she has
valiantly struggled to find a high-concept approach
to the diamond theorem. Any such approach must,
unfortunately, reckon with the following low
(i.e., not easily summarized) concept —
The Diamond Theorem Correlation:
From left to right …
http://www.log24.com/log/pix14B/140824-Diamond-Theorem-Correlation-1202w.jpg
http://www.log24.com/log/pix14B/140731-Diamond-Theorem-Correlation-747w.jpg
http://www.log24.com/log/pix14B/140824-Picturing_the_Smallest-1986.gif
http://www.log24.com/log/pix14B/140806-ProjPoints.gif
For some backstory, see ProjPoints.gif and "Symplectic Polarity" in this journal.
In the Miracle Octad Generator (MOG):
The above details from a one-page note of April 26, 1986, refer to the
Miracle Octad Generator of R. T. Curtis, as it was published in 1976:
From R. T. Curtis (1976). A new combinatorial approach to M24,
Mathematical Proceedings of the Cambridge Philosophical Society ,
79, pp 25-42. doi:10.1017/S0305004100052075.
The 1986 note assumed that the reader would be able to supply, from the
MOG itself, the missing top row of each heavy brick.
Note that the interchange of the two squares in the top row of each
heavy brick induces the diamond-theorem correlation.
Note also that the 20 pictured 3-subsets of a 6-set in the 1986 note
occur as paired complements in two pictures, each showing 10 of the
3-subsets.
This pair of pictures corresponds to the 20 Rosenhain tetrads among
the 35 lines of PG(3,2), while the picture showing the 2-subsets
corresponds to the 15 Göpel tetrads among the 35 lines.
See Rosenhain and Göpel tetrads in PG(3,2). Some further background:
(Continued from August 9, 2014.)
Syntactic:
Symplectic:
"Visual forms— lines, colors, proportions, etc.— are just as capable of
articulation , i.e. of complex combination, as words. But the laws that govern
this sort of articulation are altogether different from the laws of syntax that
govern language. The most radical difference is that visual forms are not
discursive . They do not present their constituents successively, but
simultaneously, so the relations determining a visual structure are grasped
in one act of vision."
– Susanne K. Langer, Philosophy in a New Key
For examples, see The Diamond-Theorem Correlation
in Rosenhain and Göpel Tetrads in PG(3,2).
This is a symplectic correlation,* constructed using the following
visual structure:
.
* Defined in (for instance) Paul B. Yale, Geometry and Symmetry ,
Holden-Day, 1968, sections 6.9 and 6.10.
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…."
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:
* 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
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):
See also the 10 AM ET post of Sunday, June 8, 2014, on this topic.
Profile picture of "Jo Lyxe" (Josefine Lyche) at Vimeo—
Compare to an image of Vril muse Maria Orsitsch.
From the catalog of a current art exhibition
(25 May – 31 August, 2013) in Norway,
I DE LANGE NÆTTER —
|
Josefine Lyche
Keywords (to help place my artwork in the (See also the original catalog page.) |
Clearly most of this (the non-highlighted parts) was taken
from my webpage Diamond Theory. I suppose I should be
flattered, but I am not thrilled to be associated with the
(apparently fictional) Vril Society.
For some background, see (for instance)
Conspiracy Theories and Secret Societies for Dummies .
Happy birthday to Amy Adams
(actress from Castle Rock, Colorado)
"The metaphor for metamorphosis…" —Endgame
Related material:
"The idea that reality consists of multiple 'levels,' each mirroring all others in some fashion, is a diagnostic feature of premodern cosmologies in general…."
— Scholarly paper on "Correlative Cosmologies"
"How many layers are there to human thought? Sometimes in art, just as in people’s conversations, we’re aware of only one at a time. On other occasions, though, we realize just how many layers can be in simultaneous action, and we’re given a sense of both revelation and mystery. When a choreographer responds to music— when one artist reacts in detail to another— the sensation of multilayering can affect us as an insight not just into dance but into the regions of the mind.
The triple bill by the Mark Morris Dance Group at the Rose Theater, presented on Thursday night as part of the Mostly Mozart Festival, moves from simple to complex, and from plain entertainment to an astonishingly beautiful and intricate demonstration of genius….
'Socrates' (2010), which closed the program, is a calm and objective work that has no special dance excitement and whips up no vehement audience reaction. Its beauty, however, is extraordinary. It’s possible to trace in it terms of arithmetic, geometry, dualism, epistemology and ontology, and it acts as a demonstration of art and as a reflection of life, philosophy and death."
— Alastair Macaulay in today's New York Times
SOCRATES: Let us turn off the road a little….
— Libretto for Mark Morris's 'Socrates'
See also Amy Adams's new film "On the Road"
in a story from Aug. 5, 2010 as well as a different story,
Eightgate, from that same date:
The above reference to "metamorphosis" may be seen,
if one likes, as a reference to the group of all projectivities
and correlations in the finite projective space PG(3,2)—
a group isomorphic to the 40,320 transformations of S8
acting on the above eight-part figure.
See also The Moore Correspondence from last year
on today's date, August 20.
For some background, see a book by Peter J. Cameron,
who has figured in several recent Log24 posts—
"At the still point, there the dance is."
— Four Quartets
From the previous entry:
“If it’s a seamless whole you want,
pray to Apollo, who sets the limits
within which such a work can exist.”
— Margaret Atwood,
author of Cat’s Eye
Happy birthday
to the late
Eugene Wigner
… and a belated
Merry Christmas
to Paul Newman:
— Eugene Wigner, Nobel Prize Lecture, December 12, 1963
Upscale Realism
or, "Have some more
wine and cheese, Barack."
Allyn Jackson on Rebecca Goldstein
in the April 2006 AMS Notices (pdf)
|
"Rebecca Goldstein’s 1983 novel The Mind-Body Problem has been widely admired among mathematicians for its authentic depiction of academic life, as well as for its exploration of how philosophical issues impinge on everyday life. Her new book, Incompleteness: The Proof and Paradox of Kurt Gödel, is a volume in the 'Great Discoveries' series published by W. W. Norton….
In March 2005 the Mathematical Sciences Research Institute (MSRI) in Berkeley held a public event in which its special projects director, Robert Osserman, talked with Goldstein about her work. The conversation, which took place before an audience of about fifty people at the Commonwealth Club in San Francisco, was taped…. A member of the audience posed a question that has been on the minds of many of Goldstein’s readers: Is The Mind-Body Problem based on her own life? She did indeed study philosophy at Princeton, finishing her Ph.D. in 1976 with a thesis titled 'Reduction, Realism, and the Mind.' She said that while there are correlations between her life and the novel, the book is not autobiographical…. She… talked about the relationship between Gödel and his colleague at the Institute for Advanced Study, Albert Einstein. The two were very different: As Goldstein put it, 'Einstein was a real mensch, and Gödel was very neurotic.' Nevertheless, a friendship sprang up between the two. It was based in part, Goldstein speculated, on their both being exiles– exiles from Europe and intellectual exiles. Gödel's work was sometimes taken to mean that even mathematical truth is uncertain, she noted, while Einstein's theories of relativity were seen as implying the sweeping view that 'everything is relative.' These misinterpretations irked both men, said Goldstein. 'Einstein and Gödel were realists and did not like it when their work was put to the opposite purpose.'" |
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"'What is this Stone?' Chloe asked…. 'It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'"
— Many Dimensions,
For more on this theme
appropriate to Passion Week — Jews playing God — see
Rebecca Goldstein
Wine and cheese |
From
UPSCALE,
a website of the
physics department at
the University of Toronto:
|
Mirror Symmetry
"The image [above]
The caption of the
'That most divine and beautiful
The caption of the
'A shadow, likeness, or * Sic. The original is incomprehensibilis, a technical theological term. See Dorothy Sayers on the Athanasian Creed and John 1:5. |
For further iconology of the
above equilateral triangles,
see Star Wars (May 25, 2003),
Mani Padme (March 10, 2008),
Rite of Sping (March 14, 2008),
and
Art History: The Pope of Hope
(In honor of John Paul II
three days after his death
in April 2005).
Happy Shakespeare's Birthday.
An Epiphany
for the Birthday
of E. L. Doctorow,
Author of
City of God
(Doctorow wrote about
New York. A city more
closely associated with
God is Jerusalem.)
On the morning of January 2 this year, inspired by Sambin’s “basic picture,” I considered an entry dealing with Galois lattices (pdf). This train of thought was halted by news of the death earlier that morning of Teddy Kollek, 95, a founder of the Israeli intelligence service and six-term mayor of Jerusalem. (This led later to the entry “Damnation Morning“– a reference to the Fritz Leiber short story.)
This morning’s entry reboards the Galois train of thought.
Here are some relevant links:
Galois Connections (a French weblog entry providing an brief overview of Galois theory and an introduction to the use of Galois lattices in “formal concept analysis“)
Ontology (an introduction to formal concept analysis linked to on 3/31/06)
One motive for resuming consideration of Galois lattices today is to honor the late A. Richard Newton, a pioneer in engineering design who died at 55– also on Tuesday, Jan. 2, the date of Kollek’s death. Today’s New York Times obituary for Newton says that “most recently, Professor Newton championed the study of synthetic biology.”
A check of syntheticbiology.org leads to a web page on– again– ontology.
For the relationship between ontology (in the semantic-web sense) and Galois lattices, see (for instance)
“Knowledge Organisation and Information Retrieval Using Galois Lattices” (ps) and its references.
An epiphany within all this that Doctorow might appreciate is the following from Wikipedia, found by following a link to “upper ontology” in the syntheticbiology.org ontology page:
- There is no self-evident way of dividing the world up into concepts.
- There is no neutral ground that can serve as a means of translating between specialized (lower) ontologies.
- Human language itself is already an arbitrary approximation of just one among many possible conceptual maps. To draw any necessary correlation between English words and any number of intellectual concepts we might like to represent in our ontologies is just asking for trouble.
Related material:
The intellectual concepts
mentioned by Richard Powers
at the end of tomorrow’s
New York Times Book Review.
(See the links on these concepts
in yesterday’s “Goldberg Variation.”)
See also Old School Tie.
Serious
"I don't think the 'diamond theorem' is anything serious, so I started with blitzing that."
— Charles Matthews at Wikipedia, Oct. 2, 2006
"The 'seriousness' of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. We may say, roughly, that a mathematical idea is 'significant' if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas."
— G. H. Hardy, A Mathematician's Apology
Matthews yesterday deleted references to the diamond theorem and related material in the following Wikipedia articles:
Affine group
Reflection group
Symmetry in mathematics
Incidence structure
Invariant (mathematics)
Symmetry
Finite geometry
Group action
History of geometry
This would appear to be a fairly large complex of mathematical ideas.
See also the following "large complex" cited, following the above words of Hardy, in Diamond Theory:
Affine geometry, affine planes, affine spaces, automorphisms, binary codes, block designs, classical groups, codes, coding theory, collineations, combinatorial, combinatorics, conjugacy classes, the Conwell correspondence, correlations, design theory, duads, duality, error correcting codes, exceptional groups, finite fields, finite geometry, finite groups, finite rings, Galois fields, generalized quadrangles, generators, geometry, GF(2), GF(4), the (24,12) Golay code, group actions, group theory, Hadamard matrices, hypercube, hyperplanes, hyperspace, incidence structures, invariance, Karnaugh maps, Kirkman's schoolgirl problem, Latin squares, Leech lattice, linear groups, linear spaces, linear transformations, Mathieu groups, matrix theory, Meno, Miracle Octad Generator, MOG, multiply transitive groups, octads, the octahedral group, orthogonal arrays, outer automorphisms, parallelisms, partial geometries, permutation groups, PG(3,2), polarities, Polya-Burnside theorem, projective geometry, projective planes, projective spaces, projectivities, Reed-Muller codes, the relativity problem, Singer cycle, skew lines, sporadic simple groups, Steiner systems, symmetric, symmetry, symplectic, synthemes, synthematic, tesseract, transvections, Walsh functions, Witt designs.
STAR WARS
opened on this date in 1977.
From the web page Amande:
Le Christ et la Vierge apparurent souvent entourés d’une auréole en forme d’amande: la mandorle.
Étymologiquement, le mot amande est une altération de amandala, qui dérive lui-même du latin classique amygdala….
L’amande a… une connotation symbolique, celle du sexe féminin. Elle figure souvent la vulve. Elle est alors en analogie avec la yoni du vocabulaire de l’hindouisme, la vulve ou la matrice, représentée par une amande ou une noix coupée en deux.
Screenshot of the online
New York Times, May 25, 2003:
Ariel the Hutt and Princess Amygdala
|
by Horia Cristescu and
The intersection of two geometric forms (lines, triangles, circles, etc.) represents forces that are even more intense than those generated by the simple forms. Such an interpenetration indicates a high level in the dynamic interaction of the correspondent energies. The empty spaces generated by such combinations are described as very efficient operational fields of the forces emanating from the central point of the YANTRA. That is why we can very often encounter representations of MANTRAS in such spaces. YANTRA and MANTRA are complementary aspects of SHIVA and their use together is much more efficient than the use of one alone.
|
AMEN.
Symmetries…. May 15, 1998
The following journal note, from the day after Sinatra died, was written before I heard of his death. Note particularly the quote from Rilke. Other material was suggested, in part, by Alasdair Gray's Glasgow novel 1982 Janine. The "Sein Feld" heading is a reference to the Seinfeld final episode, which aired May 14, 1998. The first column contains a reference to angels — apparently Hell's Angels — and the second column provides a somewhat more serious look at this theological topic.
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Sein Feld
1984 Janine
"But Angels love their own
"Logos means above all relation."
"Gesang ist Dasein…. |
Geometry and Theology
PA lottery May 14, 1998: |
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Tape purchased 12/23/97:
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"In the middle of 1982 Janine there are pages in which Jock McLeish is fighting with drugs and alcohol, attempting to either die or come through and get free of his fantasies. In his delirium, he hears the voice of God, which enters in small print, pushing against the larger type of his ravings. Something God says is repeated on the first and last pages of Unlikely Stories, Mostly, complete with illustration and the words 'Scotland 1984' beside it. God's statement is 'Work as if you were in the early days of a better nation.' It is the inherent optimism in that statement that perhaps best captures the strength of Aladair Gray's fiction, its straightforwardness and exuberance." |
For another look at angels, see "Winging It," by Christopher R. Miller, The New York Times Book Review Bookend page for Sunday, May 24, 1998. May 24 is the feast day of Sara (also known by the Hindu name Kali), patron saint of Gypsies.
For another, later (July 16, 1998) reply to Dyson, from a source better known than myself, see Why Religion Matters, by Huston Smith, Harper Collins, 2001, page 66.
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The Triangle (TRIKONA)
The group of all projectivities and correlations of 
