"It's the system that matters.
How the data arrange themselves inside it."
— Gravity's Rainbow
"Examples are the stainedglass windows of knowledge."
— Vladimir Nabokov
"It's the system that matters.
How the data arrange themselves inside it."
— Gravity's Rainbow
"Examples are the stainedglass windows of knowledge."
— Vladimir Nabokov
News item from this afternoon —
The above phrase "mapping systems" suggests a review
of my own very different "map systems." From a search
for that phrase in this journal —
See also "A FourColor Theorem: Function Decomposition
Over a Finite Field."
The previous post discussed some art related to the
deceptively simple concept of "four colors."
For other related material, see posts that contain a link
to "…mapsys.html."
(A review)
For geeks* —
" Domain, Domain on the Range , "
where Domain = the Galois tesseract and
Range = the fourelement Galois field.
This post was suggested by the previous post,
by a Log24 search for Knight + Move, and by
the phrase "discouraging words" found in that search.
* A term from the 1947 film "Nightmare Alley."
Structured gray matter:
Graphic symmetries of Galois space:
The reason for these graphic symmetries in affine Galois space —
symmetries of the underlying projective Galois space:
* For related remarks, see posts of May 2628, 2012.
My webpage "The Order4 Latin Squares" has a rival—
"Latin squares of order 4: Enumeration of the
24 different 4×4 Latin squares. Symmetry and
other features."
The author — Yp de Haan, a professor emeritus of
materials science at Delft University of Technology —
The main difference between de Haan's approach and my own
is my use of the fourcolor decomposition theorem, a result that
I discovered in 1976. This would, had de Haan known it, have
added depth to his "symmetry and other features" remarks.
The Philosopher's Gaze , by David Michael Levin, The postmetaphysical question—question for a postmetaphysical phenomenology—is therefore: Can the perceptual field, the ground of perception, be released from our historical compulsion to represent it in a way that accommodates our will to power and its need to totalize and reify the presencing of being? In other words: Can the ground be experienced as ground? Can its hermeneutical way of presencing, i.e., as a dynamic interplay of concealment and unconcealment, be given appropriate respect in the receptivity of a perception that lets itself be appropriated by the ground and accordingly lets the phenomenon of the ground be what and how it is? Can the comingtopass of the ontological difference that is constitutive of all the local figureground differences taking place in our perceptual field be made visible hermeneutically, and thus without violence to its withdrawal into concealment? But the question concerning the constellation of figure and ground cannot be separated from the question concerning the structure of subject and object. Hence the possibility of a movement beyond metaphysics must also think the historical possibility of breaking out of this structure into the spacing of the ontological difference: différance , the primordial, sensuous, ekstatic écart . As Heidegger states it in his Parmenides lectures, it is a question of "the way historical man belongs within the bestowal of being (Zufügung des Seins ), i.e., the way this order entitles him to acknowledge being and to be the only being among all beings to see the open" (PE* 150, PG** 223. Italics added). We might also say that it is a question of our responseability, our capacity as beings gifted with vision, to measure up to the responsibility for perceptual responsiveness laid down for us in the "primordial decision" (Entscheid ) of the ontological difference (ibid.). To recognize the operation of the ontological difference taking place in the figureground difference of the perceptual Gestalt is to recognize the ontological difference as the primordial Riß , the primordial Urteil underlying all our perceptual syntheses and judgments—and recognize, moreover, that this rift, this division, decision, and scission, an ekstatic écart underlying and gathering all our socalled acts of perception, is also the only "norm" (ἀρχή ) by which our condition, our essential deciding and becoming as the ones who are gifted with sight, can ultimately be judged. * PE: Parmenides of Heidegger in English— Bloomington: Indiana University Press, 1992 ** PG: Parmenides of Heidegger in German— Gesamtausgabe , vol. 54— Frankfurt am Main: Vittorio Klostermann, 1992 
Examples of "the primordial Riß " as ἀρχή —
For an explanation in terms of mathematics rather than philosophy,
see the diamond theorem. For more on the Riß as ἀρχή , see
Function Decomposition Over a Finite Field.
The concept of "deep structure," once a popular meme,
has long been abandoned by Chomskians.
It still applies, however, to the 1976 mathematics, diamond theory ,
underlying the formal patterns discussed in a Royal Society paper
this year.
A review of deep structure, from the Wikipedia article Cartesian linguistics—
[Numbers in parentheses refer to pages in the original 1966 Harper edition of Chomsky's book Cartesian Linguistics .] Deep structure vs. surface structure "Pursuing the fundamental distinction between body and mind, Cartesian linguistics characteristically assumes that language has two aspects" (32). These are namely the sound/character of a linguistic sign and its significance (32). Semantic interpretation or phonetic interpretation may not be identical in Cartesian linguistics (32). Deep structures are often only represented in the mind (a mirror of thought), as opposed to surface structures, which are not. Deep structures vary less between languages than surface structures. For instance, the transformational operations to derive surface forms of Latin and French may obscure common features of their deep structures (39). Chomsky proposes, "In many respects, it seems to me quite accurate, then, to regard the theory of transformational generative grammar, as it is developing in current work, as essentially a modern and more explicit version of the PortRoyal theory" (39). Summary of Port Royal Grammar The Port Royal Grammar is an often cited reference in Cartesian Linguistics and is considered by Chomsky to be a more than suitable example of Cartesian linguistic philosophy. "A sentence has an inner mental aspect (a deep structure that conveys its meaning) and an outer, physical aspect as a sound sequence"***** This theory of deep and surface structures, developed in Port Royal linguistics, meets the formal requirements of language theory. Chomsky describes it in modern terms as "a base system that generates deep structures and a transformational system that maps these into surface structures", essentially a form of transformational grammar akin to modern studies (42). 
The corresponding concepts from diamond theory are…
"Deep structure"— The line diagrams indicating the underlying
structure of varying patterns
"A base system that generates deep structures"—
Group actions on square arrays… for instance, on the 4×4 square
"A transformational system"— The decomposition theorem
that maps deep structure into surface structure (and viceversa)
( Continued from yesterday's post FLT )
Context Part I —
"In 1957, George Miller initiated a research programme at Harvard University to investigate rulelearning, in situations where participants are exposed to stimuli generated by rules, but are not told about those rules. The research program was designed to understand how, given exposure to some finite subset of stimuli, a participant could 'induce' a set of rules that would allow them to recognize novel members of the broader set. The stimuli in question could be meaningless strings of letters, spoken syllables or other sounds, or structured images. Conceived broadly, the project was a seminal first attempt to understand how observers, exposed to a set of stimuli, could come up with a set of principles, patterns, rules or hypotheses that generalized over their observations. Such abstract principles, patterns, rules or hypotheses then allow the observer to recognize not just the previously seen stimuli, but a wide range of other stimuli consistent with them. Miller termed this approach 'pattern conception ' (as opposed to 'pattern perception'), because the abstract patterns in question were too abstract to be 'truly perceptual.'….
…. the 'grammatical rules' in such a system are drawn from the discipline of formal language theory (FLT)…."
— W. Tecumseh Fitch, Angela D. Friederici, and Peter Hagoort, "Pattern Perception and Computational Complexity: Introduction to the Special Issue," Phil. Trans. R. Soc. B (2012) 367, 19251932
Context Part II —
Context Part III —
A fourcolor theorem describes the mathematics of
general structures, not just symbolstrings, formed from
four kinds of things— for instance, from the four elements
of the finite Galois field GF(4), or the four bases of DNA.
Context Part IV —
A quotation from William P. Thurston, a mathematician
who died on Aug. 21, 2012—
"It may sound almost circular to say that
what mathematicians are accomplishing
is to advance human understanding of mathematics.
I will not try to resolve this
by discussing what mathematics is,
because it would take us far afield.
Mathematicians generally feel that they know
what mathematics is, but find it difficult
to give a good direct definition.
It is interesting to try. For me,
'the theory of formal patterns'
has come the closest, but to discuss this
would be a whole essay in itself."
Related material from a literate source—
"So we moved, and they, in a formal pattern"
Formal Patterns—
Not formal language theory but rather
finite projective geometry provides a graphic grammar
of abstract design—
See also, elsewhere in this journal,
Crimson Easter Egg and Formal Pattern.
(Continued from Walpurgisnacht 2012)
Wikipedia article on functional decomposition—
"Outside of purely mathematical considerations,
perhaps the greatest value of functional decomposition
is the insight it provides into the structure of the world."
Certainly this is true for the sort of decomposition
known as harmonic analysis .
It is not, however, true of my own decomposition theorem,
which deals only with structures made up of at most four
different sorts of elementary parts.
But my own approach has at least some poetic value.
See the four elements of the Greeks in (for instance)
Eliot's Four Quartets and in Auden's For the Time Being .
(Continued from July 19, 2008)
From the Diamond 16 Puzzle —
The resemblance between the "quadrants" part of
the above picture and the new Microsoft symbol—
— is of course purely coincidental, as is the fact
that the new symbol illustrates four colors.
Compare and contrast
1. The following excerpt from Wikipedia—
2. A webpage subtitled "Function Decomposition Over a Finite Field."
Related material—
A search tonight for material related to the fourcolor
decomposition theorem yielded the Wikipedia article
Functional decomposition.
The article, of more philosophical than mathematical
interest, is largely due to one David Fass at Rutgers.
(See the article's revision history for midAugust 2007.)
Fass's interest in function decomposition may or may not
be related to the abovementioned theorem, which
originated in the investigation of functions into the
fourelement Galois field from a 4×4 square domain.
Some related material involving Fass and 4×4 squares—
A 2003 paper he wrote with Jacob Feldman—
"Design is how it works." — Steve Jobs
An assignment for Jobs in the afterlife—
Discuss the FassFeldman approach to "categorization under
complexity" in the context of the Wikipedia article's
philosophical remarks on "reductionist tradition."
The FassFeldman paper was assigned in an MIT course
for a class on Walpurgisnacht 2003.
Pentagram design agency on the new Windows 8 logo—
"… the logo reimagines the familiar fourcolor symbol
as a modern geometric shape"—
Sam Moreau, Principal Director of User Experience for Windows,
yesterday—
On Redesigning the Windows Logo—
"To see what is in front of one's nose
needs a constant struggle." —George Orwell
That is the feeling we had when Paula Scher
(from the renowned Pentagram design agency)
showed us her sketches for the new Windows logo.
Related material:
On the Complexity of Combat—
The above article (see original pdf), clearly of more
theoretical than practical interest, uses the concept
of "symmetropy" developed by some Japanese
researchers.
For some background from finite geometry, see
Symmetry of Walsh Functions. For related posts
in this journal, see Smallest Perfect Universe.
Update of 7:00 PM EST Feb. 9, 2012—
Background on Walshfunction symmetry in 1982—
(Click image to enlarge. See also original pdf.)
Note the somewhat confusing resemblance to
a fourcolor decomposition theorem
used in the proof of the diamond theorem.
(Continued from Epiphany and from yesterday.)
Detail from the current American Mathematical Society homepage—
Further detail, with a comparison to Dürer's magic square—
The three interpenetrating planes in the foreground of Donmoyer's picture
provide a clue to the structure of the the magic square array behind them.
Group the 16 elements of Donmoyer's array into four 4sets corresponding to the
four rows of Dürer's square, and apply the 4color decomposition theorem.
Note the symmetry of the set of 3 line diagrams that result.
Now consider the 4sets 14, 58, 912, and 1316, and note that these
occupy the same positions in the Donmoyer square that 4sets of
like elements occupy in the diamondpuzzle figure below—
Thus the Donmoyer array also enjoys the structural symmetry,
invariant under 322,560 transformations, of the diamondpuzzle figure.
Just as the decomposition theorem's interpenetrating lines explain the structure
of a 4×4 square , the foreground's interpenetrating planes explain the structure
of a 2x2x2 cube .
For an application to theology, recall that interpenetration is a technical term
in that field, and see the following post from last year—
Saturday, June 25, 2011
— m759 @ 12:00 PM
"… the formula 'Three Hypostases in one Ousia '
Ousia

Richard J. Trudeau, a mathematics professor and Unitarian minister, published in 1987 a book, The NonEuclidean Revolution , that opposes what he calls the Story Theory of truth [i.e., Quine, nominalism, postmodernism] to what he calls the traditional Diamond Theory of truth [i.e., Plato, realism, the Roman Catholic Church]. This opposition goes back to the medieval "problem of universals" debated by scholastic philosophers.
(Trudeau may never have heard of, and at any rate did not mention, an earlier 1976 monograph on geometry, "Diamond Theory," whose subject and title are relevant.)
From yesterday's Sunday morning New York Times—
"Stories were the primary way our ancestors transmitted knowledge and values. Today we seek movies, novels and 'news stories' that put the events of the day in a form that our brains evolved to find compelling and memorable. Children crave bedtime stories…."
— Drew Westen, professor at Emory University
From May 22, 2009—
The above ad is by Diamond from last night’s

For further details, see Saturday's correspondences 
Comme de longs échos qui de loin se confondent
Dans une ténébreuse et profonde unité….
— Baudelaire, "Correspondances "
From "A FourColor Theorem"—
Figure 1
Note that this illustrates a natural correspondence
between
(A) the seven highly symmetrical fourcolorings
of the 4×2 array at the left of Fig. 1, and
(B) the seven points of the smallest
projective plane at the right of Fig. 1.
To see the correspondence, add, in binary
fashion, the pairs of projective points from the
"points" section that correspond to likecolored
squares in a fourcoloring from the left of Fig. 1.
(The correspondence can, of course, be described
in terms of cosets rather than of colorings.)
A different correspondence between these 7 fourcoloring
structures and these 7 projectiveline structures appears in
a structural analysis of the Miracle Octad Generator
(MOG) of R.T. Curtis—
Figure 2
Here the correspondence between the 7 fourcoloring structures (left section) and the 7 projectiveline structures (center section) is less obvious, but more fruitful. It yields, as shown, all of the 35 partitions of an 8element set (an 8set ) into two 4sets. The 7 fourcolorings in Fig. 2 also appear in the 35 4×4 parts of the MOG that correspond, in a way indicated by Fig. 2, to the 35 8set paritions. This larger correspondence— of 35 4×2 arrays with 35 4×4 arrays— is the MOG, at least as it was originally defined. See The MOG, Generating the Octad Generator, and Eightfold Geometry.
For some applications of the Curtis MOG, see 
The following is from the weblog of a high school mathematics teacher—
This is related to the structure of the figure on the cover of the 1976 monograph Diamond Theory—
Each small square pattern on the cover is a Latin square,
with elements that are geometric figures rather than letters or numerals.
All orderfour Latin squares are represented.
For a deeper look at the structure of such squares, let the highschool
chart above be labeled with the letters A through X, and apply the
fourcolor decomposition theorem. The result is 24 structural diagrams—
Some of the squares are structurally congruent under the group of 8 symmetries of the square.
This can be seen in the following regrouping—
(Image corrected on Jan. 25, 2011– "seven" replaced "eight.")
* Retitled "The Order4 (i.e., 4×4) Latin Squares" in the copy at finitegeometry.org/sc.
"Human perception is a saga of created reality. But we were devising entities beyond the agreedupon limits of recognition or interpretation…."
– Don DeLillo, Point Omega
Capitalized, the letter omega figures in the theology of two Jesuits, Teilhard de Chardin and Gerard Manley Hopkins. For the former, see a review of DeLillo. For the latter, see James Finn Cotter's Inscape and "Hopkins and Augustine."
The lowercase omega is found in the standard symbolic representation of the Galois field GF(4)—
A representation of GF(4) that goes beyond the standard representation—
Here the four diagonallydivided twocolor squares represent the four elements of GF(4).
The graphic properties of these design elements are closely related to the algebraic properties of GF(4).
This is demonstrated by a decomposition theorem used in the proof of the diamond theorem.
To what extent these theorems are part of "a saga of created reality" may be debated.
I prefer the Platonist's "discovered, not created" side of the debate.
"You ain't been blue; no, no, no.
You ain't been blue,
Till you've had that mood indigo."
— Song lyrics, authorship disputed
Indigo (web color) (#4B0082)
"Pigment indigo (web color indigo) represents
the way the color indigo was always reproduced
in pigments, paints, or colored pencils in the 1950s."
Related mythology:
Indigo Children and the classic
1964 film Children of the Damned
Related nonmythology:
Towards a Philosophy of Real Mathematics, by David Corfield, Cambridge U. Press, 2003, p. 206:
"Now, it is no easy business defining what one means by the term conceptual…. I think we can say that the conceptual is usually expressible in terms of broad principles. A nice example of this comes in the form of harmonic analysis, which is based on the idea, whose scope has been shown by George Mackey (1992) to be immense, that many kinds of entity become easier to handle by decomposing them into components belonging to spaces invariant under specified symmetries."
For a simpler example of this idea, see the entities in The Diamond Theorem, the decomposition in A FourColor Theorem, and the space in Geometry of the 4×4 Square. The decomposition differs from that of harmonic analysis, although the subspaces involved in the diamond theorem are isomorphic to Walsh functions— wellknown as discrete analogues of the trigonometric functions of traditional harmonic analysis.
Old Year, Raus!
Also in today’s New York Times obituaries index:
John T. Elson, Editor Who Asked
“Is God Dead?” at Time, Dies at 78
Wikipedia article on George Polya:
From the date of Elson’s death:
Magic Boxes
"Somehow it seems to fill my head with ideas– only I don't exactly know what they are!…. Let's have a look at the garden first!"
— A passage from Lewis Carroll's Through the LookingGlass. The "garden" part– but not the "ideas" part– was quoted by Jacques Derrida in Dissemination in the epigraph to Chapter 7, "The Time before First."
Commentary
on the passage:
Part I "The Magic Box," shown on Turner Classic Movies earlier tonight
Part II: "Mimsy Were the Borogoves," a classic science fiction story:
"… he lifted a square, transparent crystal block, small enough to cup in his palm– much too small to contain the maze of apparatus within it. In a moment Scott had solved that problem. The crystal was a sort of magnifying glass, vastly enlarging the things inside the block. Strange things they were, too. Miniature people, for example– They moved. Like clockwork automatons, though much more smoothly. It was rather like watching a play."
Part III: A Crystal Block —
Image of pencils is by
Diane Robertson Design.
Related material:
"A FourColor Theorem."
Part IV:
Part I: “The Magic Box,” shown on Turner Classic Movies tonight
Part II: “Mimsy Were the Borogoves,” a classic science fiction story:
“… he lifted a square, transparent crystal block, small enough to cup in his palm– much too small to contain the maze of apparatus within it. In a moment Scott had solved that problem. The crystal was a sort of magnifying glass, vastly enlarging the things inside the block. Strange things they were, too. Miniature people, for example–
They moved. Like clockwork automatons, though much more smoothly. It was rather like watching a play.”
Image of pencils is by
Diane Robertson Design.
Related material:
“A FourColor Theorem.”
New York Times
banner this morning:
Related material from
July 11, 2008:
The HSBC Logo Designer — Henry Steiner He is an internationally recognized corporate identity consultant. Based in Hong Kong, his work for clients such as HongkongBank, IBM and Unilever is a major influence in Pacific Rim design. Born in Austria and raised in New York, Steiner was educated at Yale under Paul Rand and attended the Sorbonne as a Fulbright Fellow. He is a past President of Alliance Graphique Internationale. Other professional affiliations include the American Institute of Graphic Arts, Chartered Society of Designers, Design Austria, and the New York Art Directors' Club. His CrossCultural Design: Communicating in the Global Marketplace was published by Thames and Hudson (1995). 
Charles Taylor,
"Epiphanies of Modernism," Chapter 24 of Sources of the Self (Cambridge U. Press, 1989, p. 477):
"… the object sets up
See also Talking of Michelangelo.

Related material suggested by
an ad last night on
ABC's Ugly Betty season finale:
Diamond from last night's
Log24 entry, with
four colored pencils from
Diane Robertson Design:
See also
A FourColor Theorem.
The Kohs Block Design
Intelligence Test
Samuel Calmin Kohs, the designer (but not the originator) of the above intelligence test, would likely disapprove of the "Aryan Youth types" mentioned in passing by a film reviewer in today's New York Times. (See below.) The Aryan Youth would also likely disapprove of Dr. Kohs.
1. Wechsler Cubes (intelligence testing cubes derived from the Kohs cubes shown above). See…
Harvard psychiatry and…
The Montessori Method;
The Crimson Passion;
The Lottery Covenant.
2. Wechsler Cubes of a different sort (Log24, May 25, 2008)
3. Manohla Dargis in today's New York Times:
"… 'Momma’s Man' is a touchingly true film, part weepie, part comedy, about the agonies of navigating that slippery slope called adulthood. It was written and directed by Azazel Jacobs, a native New Yorker who has set his modestly scaled movie with a heart the size of the Ritz in the same downtown warren where he was raised. Being a child of the avantgarde as well as an A student, he cast his parents, the filmmaker Ken Jacobs and the artist Flo Jacobs, as the puzzled progenitors of his centerpiece, a wayward son of bohemia….
In American movies, growing up tends to be a job for either Aryan Youth types or the oddballs and outsiders…."
"… I think that the deeper opportunity, the greater opportunity film can offer us is as an exercise of the mind. But an exercise, I hate to use the word, I won't say 'soul,' I won't say 'soul' and I won't say 'spirit,' but that it can really put our deepest psychological existence through stuff. It can be a powerful exercise. It can make us think, but I don't mean think about this and think about that. The very, very process of powerful thinking, in a way that it can afford, is I think very, very valuable. I basically think that the mind is not complete yet, that we are working on creating the mind. Okay. And that the higher function of art for me is its contribution to the making of mind."
— Interview with Ken Jacobs, UC Berkeley, October 1999
5. For Dargis's "Aryan Youth types"–
From a Manohla Dargis
New York Times film review
of April 4, 2007
(Spy Wednesday) —
See also, from August 1, 2008
(anniversary of Hitler's
opening the 1936 Olympics) —
For Sarah Silverman —
and the 9/9/03 entry
Doonesbury,
August 2122, 2008:
… we know that we use
Only the eye as faculty, that the mind
Is the eye, and that this landscape of the mind
Is a landscape only of the eye; and that
We are ignorant men incapable
Of the least, minor, vital metaphor….
— Wallace Stevens, “Crude Foyer”
… So, so,
O son of man, the ignorant night, the travail
Of early morning, the mystery of the beginning
Again and again,
while history is unforgiven.
— Delmore Schwartz,
“In the Naked Bed, in Plato’s Cave“
— Susan Sontag,
"Against Interpretation"
"An introductory wall panel tells us that in the Jewish mystical tradition the four letters [in Hebrew] of pardes each stand for a level of biblical interpretation: very roughly, the literal, the allusive, the allegorical and the hidden. Pardes, we are told, became the museum’s symbol because it reflected the museum’s intention to cultivate different levels of interpretation: 'to create an environment for exploring multiple perspectives, encouraging openmindedness' and 'acknowledging diverse backgrounds.' Pardes is treated as a form of mystical multiculturalism.
But even the most elaborate interpretations of a text or tradition require more rigor and must begin with the literal. What is being said? What does it mean? Where does it come from and where else is it used? Yet those are the types of questions– fundamental ones– that are not being asked or examined […].
"Examples are the stained
glass windows of knowledge."
Click on image to enlarge.
“It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy.”
— Simon Blackburn, Think (Oxford, 1999)
Michael Harris, mathematician at the University of Paris:
“… three ‘parts’ of tragedy identified by Aristotle that transpose to fiction of all types– plot (mythos), character (ethos), and ‘thought’ (dianoia)….”
— paper (pdf) to appear in Mathematics and Narrative, A. Doxiadis and B. Mazur, eds.
Mythos —
A visitor from France this morning viewed the entry of Jan. 23, 2006: “In Defense of Hilbert (On His Birthday).” That entry concerns a remark of Michael Harris.
A check of Harris’s website reveals a new article:
“Do Androids Prove Theorems in Their Sleep?” (slighly longer version of article to appear in Mathematics and Narrative, A. Doxiadis and B. Mazur, eds.) (pdf).
From that article:
“The word ‘key’ functions here to structure the reading of the article, to draw the reader’s attention initially to the element of the proof the author considers most important. Compare E.M. Forster in Aspects of the Novel:
[plot is] something which is measured not be minutes or hours, but by intensity, so that when we look at our past it does not stretch back evenly but piles up into a few notable pinnacles.”
Ethos —
“Forster took pains to widen and deepen the enigmatic character of his novel, to make it a puzzle insoluble within its own terms, or without. Early drafts of A Passage to India reveal a number of false starts. Forster repeatedly revised drafts of chapters thirteen through sixteen, which comprise the crux of the novel, the visit to the Marabar Caves. When he began writing the novel, his intention was to make the cave scene central and significant, but he did not yet know how:
When I began a A Passage to India, I knew something important happened in the Malabar (sic) Caves, and that it would have a central place in the novel– but I didn’t know what it would be… The Malabar Caves represented an area in which concentration can take place. They were to engender an event like an egg.”
— E. M. Forster: A Passage to India, by Betty Jay
Dianoia —
“Despite the flagrant triviality of the proof… this result is the key point in the paper.”
— Michael Harris, op. cit., quoting a mathematical paper
Online Etymology Dictionary:
flagrant c.1500, “resplendent,” from L. flagrantem (nom. flagrans) “burning,” prp. of flagrare “to burn,” from L. root *flag, corresponding to PIE *bhleg– (cf. Gk. phlegein “to burn, scorch,” O.E. blæc “black”). Sense of “glaringly offensive” first recorded 1706, probably from common legalese phrase in flagrante delicto “redhanded,” lit. “with the crime still blazing.”
A related use of “resplendent”– applied to a Trinity, not a triviality– appears in the Liturgy of Malabar:
— The Liturgies of SS. Mark, James, Clement, Chrysostom, and Basil, and the Church of Malabar, by the Rev. J.M. Neale and the Rev. R.F. Littledale, reprinted by Gorgias Press, 2002
Judy Davis in the Marabar Caves
In mathematics
(as opposed to narrative),
somewhere between
a flagrant triviality and
a resplendent Trinity we
have what might be called
“a resplendent triviality.”
For further details, see
“A FourColor Theorem.”
An earlier entry today ("Hollywood Midrash continued") on a father and son suggests we might look for an appropriate holy ghost. In that context…
A search for further background on Emmanuel Levinas, a favorite philosopher of the late R. B. Kitaj (previous two entries), led (somewhat indirectly) to the following figures of Descartes:
Compare and contrast:
The harmonicanalysis analogy suggests a review of an earlier entry's
link today to 4/30– Structure and Logic— as well as
reexamination of Symmetry and a Trinity
(Dec. 4, 2002).
See also —
A FourColor Theorem,
The Diamond Theorem, and
The Most Violent Poem,
ART WARS:
Readings for Bach’s Birthday
Larry J. Solomon:
Symmetry as a Compositional Determinant,
Chapter VIII: New Transformations
In Solomon’s work, a sequence of notes is represented as a set of positions within a Latin square:
Transformations of the Latin square correspond to transformations of the musical notes. For related material, see The Glass Bead Game, by Hermann Hesse, and Charles Cameron’s sites on the Game.
Steven H. Cullinane:
Dorothy Sayers:
“The function of imaginative speech is not to prove, but to create–to discover new similarities, and to arrange them to form new entities, to build new selfconsistent worlds out of the universe of undifferentiated mindstuff.” (Christian Letters to a PostChristian World, Grand Rapids: Eerdmans, 1969, p. xiii)
— Quoted by Timothy A. Smith, “Intentionality and Meaningfulness in Bach’s Cyclical Works“
Edward Sapir:
“…linguistics has also that profoundly serene and satisfying quality which inheres in mathematics and in music and which may be described as the creation out of simple elements of a selfcontained universe of forms. Linguistics has neither the sweep nor the instrumental power of mathematics, nor has it the universal aesthetic appeal of music. But under its crabbed, technical, appearance there lies hidden the same classical spirit, the same freedom in restraint, which animates mathematics and music at their purest.”
— “The Grammarian and his Language,”
American Mercury 1:149155, 1924


Example:





Initial Xanga entry. Updated Nov. 18, 2006.
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