Friday, April 4, 2014
From a Huffington Post discussion of aesthetics by Colm Mulcahy
of Spelman College, Atlanta:
"The image below on the left… is… overly simplistic, and lacks reality:
It's all a matter of perspective: the problem here is that opposite sides
of the cube, which are parallel in real life, actually look parallel in the
left image! The image on the right is better…."
A related discussion: Eight is a Gate.
Comments Off on Eight Gate
Tuesday, June 4, 2013
(Continued)
A review of Beautiful Mathematics for 8 PM.
The corrected index the reviewer links to is here.
As a June 1 post shows, it is not corrected enough .
The review is dated March 16, 2012.
See this journal on that date.
See also Good Bye, Marty.
Comments Off on Eight is a Gate
Wednesday, December 7, 2011
For Saint Irving
* For one interpretation of this phrase, see
Sicilian Reflections (from this year's Feast
of St. Irving Berlin on his dies natalis ).
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Thursday, August 5, 2010
"Eight is a gate."
— This journal, December 2002
Tralfamadorian Structure
in Slaughterhouse-Five
includes the following passage:
“…the nonlinear characterization of Billy Pilgrim
emphasizes that he is not simply an established
identity who undergoes a series of changes but
all the different things he is at different times.”
This suggests that the above structure be viewed
as illustrating not eight parts but rather
8! = 40,320 parts.
See also April 2, 2003.
Happy birthday to John Huston and
happy dies natalis to Richard Burton.
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Thursday, November 19, 2009
Comments Off on Eight is a Gate, continued
Monday, March 18, 2024
" 'The S[elf] is invariant, origin, locus or field, it’s a functional property of consciousness' (C, 15:170 [2: 315]). Just as in transformational geometry, something remains fixed in all the projective transformations of the mind’s momentary systems, and that something is the Self (le Moi, or just M, as Valéry notates it so that it will look like an algebraic variable)."
C Valéry, Cahiers, 29 vols. (Paris: Centre National de le Recherche Scientifique, 1957-61)
This is from page 157 of . . .
Flight from Eden: The Origins of
Modern Literary Criticism and Theory,
by Steven Cassedy, U. of California Press, 1990.
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"Time for you to see the field." — Bagger Vance.
Comments Off on At the Gate
Thursday, August 12, 2021
Filed under: General, Geometry —
Tags: Plato in China, The Church in Philadelphia —
m759 @ 12:00 PM
Women's History Month continues…
Ontology Alignment
"He had with him a small red book of Mao's poems, and as he talked he squared it on the table, aligned it with the table edge first vertically and then horizontally. To understand who Michael Laski is you must have a feeling for that kind of compulsion."
— Joan Didion in the Saturday Evening Post,
Nov. 18, 1967 (reprinted in Slouching Towards Bethlehem)
"Or were you," I said.
He said nothing.
"Raised a Catholic," I said.
He aligned a square crystal paperweight with the edge of his desk blotter.
— Joan Didion in The Last Thing He Wanted, Knopf, 1996
"It was Plato who best expressed– who veritably embodied– the tension between the narrative arts and mathematics….
Plato clearly loved them both, both mathematics and poetry. But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry. Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto. Let none ignorant of geometry enter. This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge. Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason. Mathematics is the threshold we cross to pass into the ideal, the truly real."
— Rebecca Goldstein,
Mathematics and the Character of Tragedy
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Comments Off on A Square Crystal Paperweight
Sunday, January 3, 2021
Comments Off on The Salomon Gate
Monday, June 25, 2018
<title data-rh="true">Frank Heart, Who Linked Computers Before the Internet, Dies at 89 – The New York Times</title>
. . . .
<meta data-rh="true" name="description" itemprop="description" content="Mr. Heart’s team built the gateway device for the Arpanet, the precursor to the internet. Data networking was so new then, they made it up as they went."/>
. . . .
<meta data-rh="true" property="article:published" itemprop="datePublished" content="2018-06-25T19:16:17.000Z"/>
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See also yesterday's "For 6/24" and …
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Thursday, July 3, 2014
The Los Alamos Vision
“Gates said his foundation is an advocate for the Common Core State Standards
that are part of the national curriculum and focus on mathematics and language
arts. He said learning ‘needs to be on the edge’ where it is challenging but not
too challenging, and that students receive the basics through Common Core.
‘It’s great to teach other things, but you need that foundation,’ he said.”
— T. S. Last in the Albuquerque Journal , 12:05 AM Tuesday, July 1, 2014
See also the previous post (Core Mathematics: Arrays) and, elsewhere
in this journal,
“Eight is a Gate.” — Mnemonic rhyme:
Comments Off on Gates and Windows:
Monday, November 18, 2013
In the spirit of Beckett:
"Bobbies on bicycles two by two…" — Roger Miller, 1965
The Literary Field
A mathematics weblog in Australia today—
Clearly, the full symmetric group contains elements
with no regular cycles, but what about other groups?
Siemons and Zalesskii showed that for any group G
between PSL(n,q) and PGL(n,q) other than for
(n,q)=(2,2) or (2,3), then in any action of G, every
element of G has a regular cycle, except G=PSL(4,2)
acting on 8 points. The exceptions are due to
isomorphisms with the symmetric or alternating groups.
Comments Off on The Four-Gated Song
Thursday, June 13, 2013
"Eight is a Gate." — Mnemonic rhyme
Today's previous post, Window, showed a version
of the Chinese character for "field"—
This suggests a related image—
The related image in turn suggests…
Unlike linear perspective, axonometry has no vanishing point,
and hence it does not assume a fixed position by the viewer.
This makes axonometry 'scrollable'. Art historians often speak of
the 'moving' or 'shifting' perspective in Chinese paintings.
Axonometry was introduced to Europe in the 17th century by
Jesuits returning from China.
— Jan Krikke
As was the I Ching. A related structure:
Comments Off on Gate
Friday, December 7, 2012
In today's New York Times :
The late film executive Steven Bach on
the late literary agent Robert Lescher —
Mr. Bach’s 1985 book about film, “Final Cut:
Dreams and Disaster in the Making of ‘Heaven’s Gate’ ”—
a crow’s-nest view of the cultural and personal tensions
on the set— became a best seller and a Hollywood-insider
classic. In his acknowledgments, Mr. Bach said Mr. Lescher
“was the spiritual father to the book and to its author as well.”
See also "The rest is the madness of art" and Eight Gate.
Comments Off on Bach Gate
Tuesday, April 10, 2012
Comments Off on Turing Gate
Wednesday, February 14, 2024
RHYMES for Bergen Feb. 13-14, 2024
one fun
two crew
three see
four core
five live
six tricks
seven heaven
eight gate
nine line
core line crew
see live heaven
gate fun tricks
This post was suggested by the
"Night of Lunacy" post of May 5, 2013.
Comments Off on Live Poet Society
Sunday, November 17, 2024
Some historical background for a new book by Robert T. Curtis,
The Art of Working with the Mathieu Group M24 —
"Space is another example of an entity endowed with a structure.
Here the elements are points, and the structure is established
in terms of certain basic relations between points such as:
A, B, C lie on a straight line, AB is congruent CD, and the like.
What we learn from our whole discussion and what has indeed
become a guiding principle in modern mathematics is this lesson:
Whenever you have to do with a structure endowed entity Σ
try to determine its group of automorphisms, the group of those
element-wise transformations which leave all structural relations
undisturbed. You can expect to gain a deep insight into the
constitution of Σ in this way. After that you may start to investigate
symmetric configurations of elements, i.e. configurations which are
invariant under a certain subgroup of the group of all automorphisms;
and it may be advisable, before looking for such configurations,
to study the subgroups themselves, e.g. the subgroup of those
automorphisms which leave one element fixed, or leave two distinct
elements fixed, and investigate what discontinuous or finite subgroups
there exist, and so forth."
— Hermann Weyl, Symmetry, Princeton University Press, 1952.
(Page 144 in the Princeton Science Library edition of 1989.)
This square's automorphism group
has 322,560 transformations.
— The diamond theorem of Steven H. Cullinane.
This rectangle's automorphism group
has 244,823,040 transformations.
— The Miracle Octad Generator (MOG) of Robert T. Curtis.
The rectangle's automorphism group contains the
square's as a subgroup. The square's automorphism
group leaves invariant a set of 30 eight-subsquare sets
called affine hyperplanes. The rectangle's automorphism
group leaves invariant a set of 759 eight-subsquare sets
called octads.
View this post as a PDF.
Tuesday, April 23, 2024
“Chess problems are the
hymn-tunes of mathematics.”
— G. H. Hardy,
A Mathematician’s Apology
“The key is the cocktail that begins the proceedings.”
– Brian Harley, Mate in Two Moves
"I named this script ocode and chmod 755'd it to make it executable…"
— Software forum post on the OCR program Tesseract
From the author of
The Pearly Gates of Cyberspace:
"Like so many other heroes
who have seen the light
of a higher order…."
Comments Off on Golden Keys
Wednesday, December 6, 2023
Introduction
In the present article, the research work of many years is summarized in an interim report concerning the connection between logic, space, time and matter. The author always had in mind two things, namely 1. The discovery/construction of an interface between matter and mind, and 2. some entry points for the topos view that concern graphs, grade rotations and contravariant involutions in geometric Boolean lattices. In this part of the MiTopos theme I follow the historic approach to mathematical physics and remain with the Clifford algebra of the Minkowski space. It turns out that this interface is a basic morphogenetic structure inherent in both matter and thought. It resides in both oriented spaces and logic, and most surprisingly is closely linked to the symmetries of elementary particle physics.
— "MiTopos: Space Logic I,"
by Bernd Schmeikal,
23rd of January 2023
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Sunday, November 26, 2023
"Play Stella by Starlight for Lady Macbeth" — Bob Dylan
A variation for Macbeth —
For enthusiasts of arithmetic rather than geometry —
"4 + 12 = 16."
And for fans of Christoper Nolan — Window Panes :
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Tuesday, October 10, 2023
Comments Off on Exploring Color Space: Pinkie and Blue Boy
Friday, June 30, 2023
Margaret Atwood on Lewis Hyde's
Trickster Makes This World: Mischief, Myth, and Art—
"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)
What is "the next world"? It might be the Underworld….
The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation and art all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254) If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist. Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.
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"Drop me a line" — Request attributed to Emma Stone
Comments Off on Trickster Fuge (German for Joint)
Monday, October 17, 2022
"Geometric Group Theory" by Matt Clay, U. of Arkansas
"This article is intended to give an idea about how
the topology and geometry of a space influences
the algebraic structure of groups that act on it and
how this can be used to investigate groups."
— Notices homepage summary
A more precise description of the subject . . .
"The key idea in geometric group theory is to study
infinite groups by endowing them with a metric and
treating them as geometric spaces."
— AMS description of the 2018 treatise
Geometric Group Theory , by Drutu and Kapovich
See also "Geometric Group Theory" in this journal.
The sort of thing that most interests me, finite groups
acting on finite structures, is not included in the above
description of Clay's article. That description only
applies to topological spaces. Topology is of little use
for finite structures … unless they are embedded* in
larger spaces that are continuous, not discrete.
* As, for instance, the fifty-six 3-subsets of an 8-set are
embedded in the continuous space of The Eightfold Way .
Comments Off on From the November 2022 Notices of the A.M.S.
Saturday, September 3, 2022
Cube Bricks 1984 —
Related material —
Note the three quadruplets of parallel edges in the 1984 figure above.
Further Reading —
The above Gates article appeared earlier, in the June 2010 issue of
Physics World , with bigger illustrations. For instance —
Exercise: Describe, without seeing the rest of the article,
the rule used for connecting the balls above.
Wikipedia offers a much clearer picture of a (non-adinkra) tesseract —
And then, more simply, there is the Galois tesseract —
For parts of my own world in June 2010, see this journal for that month.
The above Galois tesseract appears there as follows:
See also the Klein correspondence in a paper from 1968
in yesterday's 2:54 PM ET post.
Comments Off on 1984 Revisited
Saturday, February 5, 2022
Shown below is an illustration from "The Puzzle Layout Problem" —
Exercise: Using the above numerals 1 through 24
(with 23 as 0 and 24 as ∞) to represent the points
∞, 0, 1, 2, 3 … 22 of the projective line over GF(23),
reposition the labels 1 through 24 in the above illustration
so that they appropriately* illustrate the cube-parts discussed
by Iain Aitchison in his March 2018 Hiroshima slides on
cube-part permutations by the Mathieu group M24.
A note for Northrop Frye —
Interpenetration in the eightfold cube — the three midplanes —
A deeper example of interpenetration:
Aitchison has shown that the Mathieu group M24 has a natural
action on the 24 center points of the subsquares on the eightfold
cube's six faces (four such points on each of the six faces). Thus
the 759 octads of the Steiner system S(5, 8, 24) interpenetrate
on the surface of the cube.
* "Appropriately" — I.e. , so that the Aitchison cube octads correspond
exactly, via the projective-point labels, to the Curtis MOG octads.
Comments Off on Mathieu Cube Labeling
Tuesday, August 10, 2021
Margaret Atwood on Lewis Hyde's
Trickster Makes This World: Mischief, Myth, and Art—
"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)
What is "the next world"? It might be the Underworld….
The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation and art all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254) If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist. Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.
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"As a Chinese jar . . . ."
— Four Quartets
Rosalind Krauss
in "Grids," 1979:
"If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit. From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.
Or, to take a more up-to-date example…."
"He was looking at the nine engravings and at the circle,
checking strange correspondences between them."
– The Club Dumas , 1993
"And it's whispered that soon if we all call the tune
Then the piper will lead us to reason."
– Robert Plant, 1971
The nine engravings of The Club Dumas
(filmed as "The Ninth Gate") are perhaps more
an example of the concrete than of the universal.
An example of the universal— or, according to Krauss,
a "staircase" to the universal— is the ninefold square:
"This is the garden of Apollo,
the field of Reason…."
– John Outram, architect
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The "Katz" of the August 7 post Art Angles
is a product of Princeton's
Department of Art and Archaeology.
ART —
ARCHAEOLOGY —
"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."
– The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71
Comments Off on Ex Fano Apollinis
Sunday, March 21, 2021
Continues from March 17.
See as well some remarks on Chinese perspective
in the Log24 post “Gate” of June 13, 2013.
Comments Off on Mind the Gaps…
Saturday, March 13, 2021
According to Lt. Col. Wayne M. McDonnell in June 1983 —
“… it is accurate to observe that when a person experiences
the out-of- body state he is, in fact, projecting that eternal spark
of consciousness and memory which constitutes the ultimate
source of his identity….”
— Section 27, “Consciousness in Perspective,” of
“Analysis and Assessment of Gateway Process.”
A related quotation —
“In truth, the physical AllSpark is but a shell….”
— https://tfwiki.net/wiki/AllSpark
From the post Ghost in the Shell (Feb. 26, 2019) —
See also, from posts tagged Ogdoad Space —
“Like the Valentinian Ogdoad— a self-creating theogonic system
of eight Aeons in four begetting pairs— the projected eightfold work
had an esoteric, gnostic quality; much of Frye’s formal interest lay in
the ‘schematosis’ and fearful symmetries of his own presentations.”
— From p. 61 of James C. Nohrnberg’s “The Master of the Myth
of Literature: An Interpenetrative Ogdoad for Northrop Frye,”
Comparative Literature , Vol. 53 No. 1, pp. 58-82, Duke University
Press (quarterly, January 2001)
— as well as . . .
Related illustration from posts tagged with
the quilt term Yankee Puzzle —
Comments Off on Eternal Spark
Friday, March 12, 2021
See Trinity Cube in this journal and . . .
McDonnell’s illustration is from 9 June 1983.
See as well a less official note from later that June.
Comments Off on Grid
Saturday, August 15, 2020
“Don’t forget the portcullis, Dutch Boy!”
Comments Off on Hidden Figures Matter
Wednesday, April 1, 2020
Comments Off on Adventures in the Matrix
Sunday, September 29, 2019
"The 15 Puzzle and the Magic Cube
are spiritual kin …."
— "Metamagical Themas" column,
Douglas R. Hofstadter, Scientific American ,
Vol. 244, No. 3 (March 1981), pp. 20-39
As are the 15 Schoolgirls and the Eightfold Cube.
Comments Off on Spiritual Kin
Friday, September 27, 2019
"… Max Black, the Cornell philosopher, and others have pointed out
how 'perhaps every science must start with metaphor and end with
algebra, and perhaps without the metaphor there would never have
been any algebra' …."
— Max Black, Models and Metaphors, Cornell U. Press, 1962,
page 242, as quoted in Dramas, Fields, and Metaphors, by
Victor Witter Turner, Cornell U. Press, paperback, 1975, page 25
Metaphor —
Algebra —
The 16 Dirac matrices form six anticommuting sets of five matrices each (Arfken 1985, p. 214):
1. , , , , ,
2. , , , , ,
3. , , , , ,
4. , , , , ,
5. , , , , ,
6. , , , , .
SEE ALSO: Pauli Matrices
REFERENCES:
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 211-217, 1985.
Berestetskii, V. B.; Lifshitz, E. M.; and Pitaevskii, L. P. "Algebra of Dirac Matrices." §22 in Quantum Electrodynamics, 2nd ed. Oxford, England: Pergamon Press, pp. 80-84, 1982.
Bethe, H. A. and Salpeter, E. Quantum Mechanics of One- and Two-Electron Atoms. New York: Plenum, pp. 47-48, 1977.
Bjorken, J. D. and Drell, S. D. Relativistic Quantum Mechanics. New York: McGraw-Hill, 1964.
Dirac, P. A. M. Principles of Quantum Mechanics, 4th ed. Oxford, England: Oxford University Press, 1982.
Goldstein, H. Classical Mechanics, 2nd ed. Reading, MA: Addison-Wesley, p. 580, 1980.
Good, R. H. Jr. "Properties of Dirac Matrices." Rev. Mod. Phys. 27, 187-211, 1955.
Referenced on Wolfram|Alpha: Dirac Matrices
CITE THIS AS:
Weisstein, Eric W. "Dirac Matrices."
From MathWorld— A Wolfram Web Resource.
http://mathworld.wolfram.com/DiracMatrices.html
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Desiring the exhilarations of changes:
The motive for metaphor, shrinking from
The weight of primary noon,
The A B C of being,
The ruddy temper, the hammer
Of red and blue, the hard sound—
Steel against intimation—the sharp flash,
The vital, arrogant, fatal, dominant X.
— Wallace Stevens, "The Motive for Metaphor"
Comments Off on The Black List
Sunday, May 26, 2019
Compare and contrast with . . .
The Brightburn Logo:
Related material from the May 12 post
"The Collective Unconscious
in a Cartoon Graveyard" —
"When they all finally reach their destination —
a deserted field in the Florida Panhandle…."
" When asked about the film's similarities to the 2015 Disney movie Tomorrowland , which also posits a futuristic world that exists in an alternative dimension, Nichols sighed. 'I was a little bummed, I guess,' he said of when he first learned about the project. . . . 'Our die was cast. Sometimes this kind of collective unconscious that we're all dabbling in, sometimes you're not the first one out of the gate.' "
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Comments Off on Burning Bright
Wednesday, November 28, 2018
Einstein, "Geometry and Experience," lecture before the
Prussian Academy of Sciences, January 27, 1921–
… This view of axioms, advocated by modern axiomatics, purges mathematics of all extraneous elements, and thus dispels the mystic obscurity, which formerly surrounded the basis of mathematics. But such an expurgated exposition of mathematics makes it also evident that mathematics as such cannot predicate anything about objects of our intuition or real objects. In axiomatic geometry the words "point," "straight line," etc., stand only for empty conceptual schemata. That which gives them content is not relevant to mathematics.
Yet on the other hand it is certain that mathematics generally, and particularly geometry, owes its existence to the need which was felt of learning something about the behavior of real objects. The very word geometry, which, of course, means earth-measuring, proves this. For earth-measuring has to do with the possibilities of the disposition of certain natural objects with respect to one another, namely, with parts of the earth, measuring-lines, measuring-wands, etc. It is clear that the system of concepts of axiomatic geometry alone cannot make any assertions as to the behavior of real objects of this kind, which we will call practically-rigid bodies. To be able to make such assertions, geometry must be stripped of its merely logical-formal character by the coordination of real objects of experience with the empty conceptual schemata of axiomatic geometry. To accomplish this, we need only add the proposition: solid bodies are related, with respect to their possible dispositions, as are bodies in Euclidean geometry of three dimensions. Then the propositions of Euclid contain affirmations as to the behavior of practically-rigid bodies.
Geometry thus completed is evidently a natural science; we may in fact regard it as the most ancient branch of physics. Its affirmations rest essentially on induction from experience, but not on logical inferences only. We will call this completed geometry "practical geometry," and shall distinguish it in what follows from "purely axiomatic geometry." The question whether the practical geometry of the universe is Euclidean or not has a clear meaning, and its answer can only be furnished by experience. ….
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Later in the same lecture, Einstein discusses "the theory of a finite
universe." Of course he is not using "finite" in the sense of the field
of mathematics known as "finite geometry " — geometry with only finitely
many points.
Nevertheless, his remarks seem relevant to the Fano plane , an
axiomatically defined entity from finite geometry, and the eightfold cube ,
a physical object embodying the properties of the Fano plane.
I want to show that without any extraordinary difficulty we can illustrate the theory of a finite universe by means of a mental picture to which, with some practice, we shall soon grow accustomed.
First of all, an observation of epistemological nature. A geometrical-physical theory as such is incapable of being directly pictured, being merely a system of concepts. But these concepts serve the purpose of bringing a multiplicity of real or imaginary sensory experiences into connection in the mind. To "visualize" a theory therefore means to bring to mind that abundance of sensible experiences for which the theory supplies the schematic arrangement. In the present case we have to ask ourselves how we can represent that behavior of solid bodies with respect to their mutual disposition (contact) that corresponds to the theory of a finite universe.
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Comments Off on Geometry and Experience
Wednesday, August 22, 2018
See the title in a TV review* from io9 this morning and in
this journal.
* Spoiler alert
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Thursday, July 12, 2018
Three hidden keys open three secret gates
Wherein the errant will be tested for worthy traits
And those with the skill to survive these straits
Will reach The End where the prize awaits
— Ready Player One , by Ernest Cline
“Look, my favorite expression is,
‘When you go up to the bell, ring it,
or don’t go up to the bell.’ …
We’ve gone too far. We have to ring the bell.”
— Mel Brooks on “The Producers”
in The New York Times today.
A 2016 Scribner edition of Stephen King’s IT —
Related material —
Mystery box merchandise from the 2011 J. J. Abrams film Super 8
Comments Off on The Bell
Tuesday, March 27, 2018
Related material on automorphism groups —
The "Eightfold Cube" structure shown above with Weyl
competes rather directly with the "Eightfold Way" sculpture
shown above with Bryant. The structure and the sculpture
each illustrate Klein's order-168 simple group.
Perhaps in part because of this competition, fans of the Mathematical
Sciences Research Institute (MSRI, pronounced "Misery') are less likely
to enjoy, and discuss, the eight-cube mathematical structure above
than they are an eight-cube mechanical puzzle like the one below.
Note also the earlier (2006) "Design Cube 2x2x2" webpage
illustrating graphic designs on the eightfold cube. This is visually,
if not mathematically, related to the (2010) "Expert's Cube."
Comments Off on Compare and Contrast
Monday, September 4, 2017
(A sequel to the previous post, Up to Date)
"Dr. Sekler lectured around the world, but one trip proved life-changing.
In 1962, the year he married, Dr. Sekler made his first trip to Nepal.
'It was the way it had been for centuries — a beautiful valley filled with
happy, peaceful people. It seemed like Shangri-La,' he told the Harvard
Gazette in 2004."
— Bryan Marquard in The Boston Globe today
See also "Eight is a gate" in this journal.
Comments Off on Labor Date
Tuesday, November 15, 2016
The half-hour referred to here was from 12 PM ET
to 12:30 PM ET on Friday, April 4, 2014 …
12 PM at Log24 —
12:30 PM at Princeton —
The New York Times on an art lecturer who died on Nov. 9 —
She became a Vogue correspondent in postwar Paris
and worked for art magazines before starting her own,
the celebrated L’Oeil (The Eye).
See also Obituary Metaphysics from November 11th —
Comments Off on A Paris Review
Saturday, July 2, 2016
Wednesday, June 22, 2016
Comments Off on Fragments Against My Ruins, by Odd Thomas
Sunday, April 17, 2016
The New York Times philosophy column yesterday —
The Times's philosophy column "The Stone" is named after the legendary
"philosophers' stone." The column's name, and the title of its essay yesterday
"Is that even a thing?" suggest a review of the eightfold cube as "The object
most closely resembling a 'philosophers' stone' that I know of" (Page 51 of
the current issue of a Norwegian art quarterly, KUNSTforum.as).
The eightfold cube —
Definition of Epiphany
From James Joyce’s Stephen Hero , first published posthumously in 1944. The excerpt below is from a version edited by John J. Slocum and Herbert Cahoon (New York: New Directions Press, 1959).
Three Times:
… By an epiphany he meant a sudden spiritual manifestation, whether in the vulgarity of speech or of gesture or in a memorable phase of the mind itself. He believed that it was for the man of letters to record these epiphanies with extreme care, seeing that they themselves are the most delicate and evanescent of moments. He told Cranly that the clock of the Ballast Office was capable of an epiphany. Cranly questioned the inscrutable dial of the Ballast Office with his no less inscrutable countenance:
— Yes, said Stephen. I will pass it time after time, allude to it, refer to it, catch a glimpse of it. It is only an item in the catalogue of Dublin’s street furniture. Then all at once I see it and I know at once what it is: epiphany.
— What?
— Imagine my glimpses at that clock as the gropings of a spiritual eye which seeks to adjust its vision to an exact focus. The moment the focus is reached the object is epiphanised. It is just in this epiphany that I find the third, the supreme quality of beauty.
— Yes? said Cranly absently.
— No esthetic theory, pursued Stephen relentlessly, is of any value which investigates with the aid of the lantern of tradition. What we symbolise in black the Chinaman may symbolise in yellow: each has his own tradition. Greek beauty laughs at Coptic beauty and the American Indian derides them both. It is almost impossible to reconcile all tradition whereas it is by no means impossible to find the justification of every form of beauty which has ever been adored on the earth by an examination into the mechanism of esthetic apprehension whether it be dressed in red, white, yellow or black. We have no reason for thinking that the Chinaman has a different system of digestion from that which we have though our diets are quite dissimilar. The apprehensive faculty must be scrutinised in action.
— Yes …
— You know what Aquinas says: The three things requisite for beauty are, integrity, a wholeness, symmetry and radiance. Some day I will expand that sentence into a treatise. Consider the performance of your own mind when confronted with any object, hypothetically beautiful. Your mind to apprehend that object divides the entire universe into two parts, the object, and the void which is not the object. To apprehend it you must lift it away from everything else: and then you perceive that it is one integral thing, that is a thing. You recognise its integrity. Isn’t that so?
— And then?
— That is the first quality of beauty: it is declared in a simple sudden synthesis of the faculty which apprehends. What then? Analysis then. The mind considers the object in whole and in part, in relation to itself and to other objects, examines the balance of its parts, contemplates the form of the object, traverses every cranny of the structure. So the mind receives the impression of the symmetry of the object. The mind recognises that the object is in the strict sense of the word, a thing , a definitely constituted entity. You see?
— Let us turn back, said Cranly.
They had reached the corner of Grafton St and as the footpath was overcrowded they turned back northwards. Cranly had an inclination to watch the antics of a drunkard who had been ejected from a bar in Suffolk St but Stephen took his arm summarily and led him away.
— Now for the third quality. For a long time I couldn’t make out what Aquinas meant. He uses a figurative word (a very unusual thing for him) but I have solved it. Claritas is quidditas . After the analysis which discovers the second quality the mind makes the only logically possible synthesis and discovers the third quality. This is the moment which I call epiphany. First we recognise that the object is one integral thing, then we recognise that it is an organised composite structure, a thing in fact: finally, when the relation of the parts is exquisite, when the parts are adjusted to the special point, we recognise that it is that thing which it is. Its soul, its whatness, leaps to us from the vestment of its appearance. The soul of the commonest object, the structure of which is so adjusted, seems to us radiant. The object achieves its epiphany.
Having finished his argument Stephen walked on in silence. He felt Cranly’s hostility and he accused himself of having cheapened the eternal images of beauty. For the first time, too, he felt slightly awkward in his friend’s company and to restore a mood of flippant familiarity he glanced up at the clock of the Ballast Office and smiled:
— It has not epiphanised yet, he said.
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Comments Off on The Thing and I
Wednesday, March 23, 2016
From a post of August 3, 2013 —
Note, on the map of Wyoming, Devil's Gate.
There are, of course, many such gates.
* A character from the recent film "The Hateful Eight."
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Sunday, March 20, 2016
"Where indeed might the literary scholar expect to find,
if not in literature, the measure of modern thought?"
— "Ruins of the Ogdoad," by Michael Keefer
"Seven is Heaven, Eight is a Gate, Nine is a Vine."
— Mnemonic rhyme; author anonymous
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Friday, November 6, 2015
"Eight is a gate." — Mnemonic rhyme
Girard reportedly died at 91 on Wednesday, Nov. 4, 2015.
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Saturday, April 18, 2015
Kyle Smith on April 15 in the New York Post —
"The ludicrous action thriller 'Beyond the Reach'
fails to achieve the Southwestern noir potency
of 'No Country for Old Men,' but there’s no denying
it brings to mind another Southwestern classic
about malicious pursuit: the Road Runner cartoons."
Related material:
-
Legespiel Meets Würfelspiel in…
Gift of the Third Kind
(April 7, 2007), featuring Ellen Yi-Luen Do —
-
the current home page of Ellen Yi-Luen Do,
now at Georgia Tech, and…
-
a page about her ACME Lab —
Welcome to ACME lab!
A Creativity Machine Environment!
aka ACME Creativity Machine Environment –
ACME Lab
Yes, the name is both confusing and has
many meanings. We like the acronym of ACME,
since it means the highest point, and also refers to
the fictional company in Looney Tunes, which is
A Company that Makes Everything!
We call it ACME Creativity Machine Environment –
yes, the acronym of this is ACME.
We like recursive ideas.
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Saturday, September 27, 2014
“One must proceed cautiously, for this road— of truth and falsehood
in the realm of fiction— is riddled with traps and any enticing oasis
is usually a mirage.”
– “Is Fiction the Art of Lying?” by Mario Vargas Llosa,
New York Times essay of October 7, 1984
For the title plan, see Sisteen in this journal.
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Saturday, September 20, 2014
See “Seven is Heaven, Eight is a Gate” in this journal.
For greater detail, see “Seven is Heaven” and “Eight is a Gate” separately.
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Friday, May 2, 2014
” ‘Harriet Burden has been really great to me,’
Rune says in an interview, ‘not only as a collector
of my work but as a true supporter. And I think of her
as a muse for the project … ‘ “
— In The Blazing World , the artist known as Rune
(See also Rune + Muse in this journal.)
Lily Collins in a Log24 post of Jan. 15, 2014— “Entertainment Theory“—
Related material from Trish Mayo—
The tulips are from today,
the gate is from April 27.
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Friday, February 14, 2014
“… the object sets up a kind of
frame or space or field
within which there can be epiphany.”
— Charles Taylor
A frame or space or field —
Related material —
Star Wars (January 11, 2014),
The Lyche Gate Asterisk , from 10:31 AM ET on May 22, 2010,
the date of Martin Gardner's death —
— and the March 2014 issue of the
Notices of the American Mathematical Society —
See as well Epiphany 2014 (Jan. 6) in this journal and the
March Notices on the Shaw prize —
"Established under the auspices of Run Run Shaw
in November 2002, the prize is managed and
administered by the Shaw Prize Foundation
based in Hong Kong."
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Wednesday, January 22, 2014
Hexagonale Unwesen
Einstein and Thomas Mann, Princeton, 1938
See also the life of Diogenes Allen, a professor at Princeton
Theological Seminary, a life that reportedly ended on the date—
January 13, 2013— of the above Log24 post.
January 13 was also the dies natalis of St. James Joyce.
Some related reflections —
"Praeterit figura huius mundi " — I Corinthians 7:31 —
Conclusion of of "The Dead," by James Joyce—
The air of the room chilled his shoulders. He stretched himself cautiously along under the sheets and lay down beside his wife. One by one, they were all becoming shades. Better pass boldly into that other world, in the full glory of some passion, than fade and wither dismally with age. He thought of how she who lay beside him had locked in her heart for so many years that image of her lover's eyes when he had told her that he did not wish to live.
Generous tears filled Gabriel's eyes. He had never felt like that himself towards any woman, but he knew that such a feeling must be love. The tears gathered more thickly in his eyes and in the partial darkness he imagined he saw the form of a young man standing under a dripping tree. Other forms were near. His soul had approached that region where dwell the vast hosts of the dead. He was conscious of, but could not apprehend, their wayward and flickering existence. His own identity was fading out into a grey impalpable world: the solid world itself, which these dead had one time reared and lived in, was dissolving and dwindling.
A few light taps upon the pane made him turn to the window. It had begun to snow again. He watched sleepily the flakes, silver and dark, falling obliquely against the lamplight. The time had come for him to set out on his journey westward. Yes, the newspapers were right: snow was general all over Ireland. It was falling on every part of the dark central plain, on the treeless hills, falling softly upon the Bog of Allen and, farther westward, softly falling into the dark mutinous Shannon waves. It was falling, too, upon every part of the lonely churchyard on the hill where Michael Furey lay buried. It lay thickly drifted on the crooked crosses and headstones, on the spears of the little gate, on the barren thorns. His soul swooned slowly as he heard the snow falling faintly through the universe and faintly falling, like the descent of their last end, upon all the living and the dead.
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Monday, September 30, 2013
(Continued from High White Noon,
Finishing Up at Noon, and A New York Jew.)
Above: Frank Langella in "Starting Out in the Evening"
Below: Frank Langella and Johnny Depp in "The Ninth Gate"
"Not by the hair on your chinny-chin-chin."
Above: Detail from a Wikipedia photo.
For the logo, see Lostpedia.
For some backstory, see Noether.
Those seeking an escape from the eightfold nightmare
represented by the Dharma logo above may consult
the remarks of Heisenberg (the real one, not the
Breaking Bad version) to the Bavarian Academy
of Fine Arts.
Those who prefer Plato's cave to his geometry are
free to continue their Morphean adventures.
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Thursday, September 5, 2013
Underworld and Evolution
This journal on 9/11, 2009 —
Poster for Kate Beckinsale in a film
released on 9/11, 2009 —
For Qohen Leth — A quotation from
this journal on 9/11, 2009 —
"Time and chance
happeneth to them all."
— Ecclesiastes 9:11
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Tuesday, August 27, 2013
For Fans of Bad Movies*
This post was suggested by my viewing last night
the 1995 horror film Species , and by news that
Scarlett Johansson will be starring in a similar
production at the Venice Film Festival, which
opens tomorrow.
The new Johansson film, Under the Skin ,
is based on a novel by one Michel Faber.
Faber on books that have influenced him—
"Most influential has possibly been John Berger's Ways of Seeing —
not a novel at all (although Berger has written fiction) but a book of
art criticism. The influence of these wonderfully perceptive and
thought-provoking essays peeps out everywhere in my own work."
An excerpt from the Berger book—
Click image for a better view of the original.
Related material: Johansson in this journal, Sunday's NY Times
teaser for a piece on Saturday Night Live, and a more serious
approach to the geometry of perspective.
* And of Ben Kingsley, who starred both in Species and in
a previous film by the director of Under the Skin .
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Saturday, August 3, 2013
By chance, the latest* remarks in philosopher Colin McGinn's
weblog were posted (yesterday) at 10:04 AM.
Checking, in my usual mad way, for synchronicity, I find
the following from this weblog on the date 10/04 (2012)—
Note too the time of this morning's previous post here
(on McGinn)— 9:09 AM. Another synchronistic check
yields Log24 posts from 9/09 (2012):
Related to this last post:
Detail from a stock image suggested by the web page of
a sociologist (Harvard '64) at the University of Washington in Seattle—
Note, on the map of Wyoming, Devil's Gate.
There are, of course, many such gates.
* Correction (of about 11:20 AM Aug. 3):
Later remarks by McGinn were posted at 10:06 AM today.
They included the phrase "The devil is in the details."
Yet another check for synchronicity leads to
10/06 (2012) in this journal with its post related to McGinn's
weblog remarks yesterday on philosophy and art.
That 10/06 Log24 post is somewhat in the spirit of other
remarks by McGinn discussed in a 2009 Harvard Crimson review.
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Sunday, April 28, 2013
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Let's do the twist.
The image at left
is from a poster
for a film released
on March 28, 2003.
See this journal
on that date.
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A phrase from yesterday's noon post:
Sinking the Magic 8-Ball .
A scene from the above film is related to this phrase.
Another image from the film poster:
A review of the film:
"The final 'twist' seems to negate the entire story,
like a bad shaggy-dog joke."
Such a joke:
“Words and numbers are of equal value,
for, in the cloak of knowledge,
one is warp and the other woof.”
— The princesses Rhyme and Reason
in The Phantom Tollbooth
"A core component in the construction
is a 3-dimensional vector space V over F2 ."
— Page 29 of "A twist in the M24 moonshine story,"
by Anne Taormina and Katrin Wendland.
(Submitted to the arXiv on 13 Mar 2013.)
The number of points in such a space is, of course, 8.
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Saturday, January 12, 2013
Saturday January 12, 2013,
8:00 a.m.-10:50 a.m. Pacific Standard Time
MAA Invited Paper Session on
Writing, Talking, and Sharing Mathematics
Room 2, Upper Level, San Diego
Convention Center
9:30 a.m.
Mathematics, Meaning, and Misunderstanding.
Gerald B. Folland, University of Washington
(1086-AH-1058)
Abstract:
Mathematicians develop habits of thought and employ
ways of expressing their ideas that are not always
shared by others who wish to learn mathematics or
use mathematics in their own disciplines. We shall
comment on various aspects of this phenomenon
and the (often amusing) pitfalls it creates for effective
communication. (Received September 18, 2012)
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Remarks for a dead mathematician—
Click on the above image for the original post.
Then click on the Harmonic Analysis link for
some exposition by Folland.
* As opposed to concrete —
See yesterday morning's Grapevine Hill and…
SFGate 1/12/13 —
Californians bring out gloves, hats
for cold spell
http://www.sfgate.com/news/us/article/
Zookeepers-growers-prepare-for-
California-freeze-4185448.php
A 40-mile stretch of a major highway north of
Los Angeles reopened some 17 hours after snow
shut the route and forced hundreds of truckers
to spend the cold night in their rigs.
The California Highway Patrol shut the Grapevine
segment of Interstate 5 on Thursday afternoon,
severing a key link between the Central Valley
and Los Angeles.
"There must have been 1,000 Mack trucks lined up,"
said traveler Heidi Blood, 40. |
Comments Off on Abstract*
Sunday, December 9, 2012
"Now the serpent was more subtle
than any beast of the field…."
— Genesis 3:1
"“The serpent’s eyes shine
As he wraps around the vine….”
– Don Henley
"Nine is a vine."
— Folk rhyme
Part I
Part II
Part III
Halloween 2005—
Click images for some background.
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Friday, November 2, 2012
"Seven is Heaven, Eight is a Gate" — Memory rhyme
For Rebekah Gay—
Click for image source.
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Friday, October 5, 2012
(Continued)
The Hallowed Crucible—
Some related symbolism—
See also Stallion Gate (a novel) in this journal.
For some related nonfiction, see interviews with
Los Alamos physicist Robert F. Christy, who died
at 96 on Wednesday, October 3, 2012.
Comments Off on The Hallowed Crucible
Monday, July 16, 2012
(Continued.)
Jaws for Frank
Part I: October 8, 2010
Part II: Noon Today
"The rest is the madness of art."
See also Patterns in the Carpets
and Saturday's Shadows.
Comments Off on Finishing Up at Noon
Thursday, April 5, 2012
Presidential candidate Mitt Romney on Monday, April 2, 2012—
"I think there is in this country a war on religion.
I think there is a desire to establish a religion
in America known as secularism."
Nancy Haught of The Oregonian on Leap Day, Feb. 29, 2012—
William Hamilton, the retired theologian who declared in the 1960s that God was dead, died Tuesday [Feb. 28, 2012] in his downtown Portland apartment at 87. Hamilton said he'd been haunted by questions about God since he was a teenager. Years later, when his conclusion was published in the April 8, 1966, edition of Time Magazine, he found himself in a hornet's nest.
Time christened the new movement "radical theology" and Hamilton, one of its key figures, received death threats and inspired angry letters to the editor in newspapers that carried the story. He encountered hostility at Colgate Rochester Crozer Divinity School, where he had been teaching theology, and lost his endowed chair in 1967.
Hamilton moved on to teach religion at New College in Sarasota, Fla.
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(See also this journal on Leap Day.)
From New College: The Honors College of Florida—
History Highlights
Oct. 11, 1960: New College is founded as a private college
1961: Trustees obtain options to purchase the former Charles Ringling estate on Sarasota Bay and 12 acres of airport land facing U.S. 41 held by private interests. The two pieces form the heart of the campus
Nov. 18, 1962: the campus is dedicated. Earth from Harvard is mixed with soil from New College as a symbol of the shared lofty ideals of the two institutions.
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See also, in this journal, "Greatest Show on Earth" and The Harvard Crimson—
The Harvard Crimson,
Online Edition |
Sunday,
Oct. 8, 2006 |
POMP AND
CIRCUS-STANCE
CRIMSON/ MEGHAN T. PURDY
Friday, Oct. 6:
The Ringling Bros. Barnum & Bailey Circus has come to town, and yesterday the animals were disembarked near MIT and paraded to their temporary home at the Banknorth Garden.
|
OPINION
At Last, a
Guiding Philosophy
The General Education report is a strong cornerstone, though further scrutiny is required.
By THE CRIMSON STAFF
After four long years, the Curricular Review has finally found its heart.
The Trouble
With the Germans
The College is a little under-educated these days.
By SAHIL K. MAHTANI
Harvard College– in the best formulation I’ve heard– promulgates a Japanese-style education, where the professoriate pretend to teach, the students pretend to learn, and everyone is happy.
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Comments Off on Leap Day of Faith
Friday, January 20, 2012
Saturday, November 12, 2005
— m759 @ 8:00 PM
(continued)
“… problems are the poetry of chess.
They demand from the composer
the same virtues that characterize
all worthwhile art:
originality, invention,
harmony, conciseness,
complexity, and
splendid insincerity.”
—Vladimir Nabokov
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Sunday, January 8, 2012
“…the nonlinear characterization of Billy Pilgrim
emphasizes that he is not simply an established
identity who undergoes a series of changes but
all the different things he is at different times.”
This suggests that the above structure
be viewed as illustrating not eight parts
but rather 8! = 40,320 parts.
"The Cardinal seemed a little preoccupied today."
The New Yorker , May 13, 2002
See also a note of May 14 , 2002.
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Wednesday, November 2, 2011
A search today, All Souls Day, for relevant learning
at All Souls College, Oxford, yields the person of
Sir Michael Dummett and the following scholarly page—
(Click to enlarge.)
My own background is in mathematics rather than philosophy.
From a mathematical point of view, the cells discussed above
seem related to some "universals" in an example of Quine.
In Quine's example,* universals are certain equivalence classes
(those with the "same shape") of a family of figures
(33 convex regions) selected from the 28 = 256 subsets
of an eight-element set of plane regions.
A smaller structure, closer to Wright's concerns above,
is a universe of 24 = 16 subsets of a 4-element set.
The number of elements in this universe of Concepts coincides,
as it happens, with the number obtained by multiplying out
the title of T. S. Eliot's Four Quartets .
For a discussion of functions that map "cells" of the sort Wright
discusses— in the quartets example, four equivalence classes,
each with four elements, that partition the 16-element universe—
onto a four-element set, see Poetry's Bones.
For some philosophical background to the Wright passage
above, see "The Concept Horse," by Harold W. Noonan—
Chapter 9, pages 155-176, in Universals, Concepts, and Qualities ,
edited by P. F. Strawson and Arindam Chakrabarti,
Ashgate Publishing, 2006.
For a different approach to that concept, see Devil's Night, 2011.
* Admittedly artificial. See From a Logical Point of View , IV, 3
Comments Off on The Poetry of Universals
Monday, October 24, 2011
Last evening's New York Lottery numbers were 123 and 5597.
The 123 suggests page 123 of DeLillo's Underworld .
(For some context, see searches in this journal for Los Muertos and for Pearly Gates of Cyberspace .)
The 5597 suggests the birth date of literary theorist Kenneth Burke— May 5, 1897.
These two topics—
- the afterlife (in the Latin-American rhythms context of yesterday's Shine On, Edmundo)
- and Kenneth Burke
are combined in Heaven's Gate, a post from April 11, 2003—
Babylon = Bab-ilu, “gate of God,” Hebrew: Babel or Bavel.”
Modern rendition
of “Bab-ilu“
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Kenneth
Burke
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The above observations on lottery hermeneutics, on a ridiculously bad translation, and on Latin rhythms did not seem worth recording until…
The New York Times Book Review for Sunday, October 30, arrived this morning.
From page 22, an extract from the opening paragraph of a review titled…
Making Sense of It
David Bellos offers a new approach to translation.
BY ADAM THIRLWELL
The theory of translation is very rarely— how to put this?— comical. Its mode is elegy, and severe admonishment…. You can never, so runs the elegiac argument, precisely reproduce a line of poetry in another language…. And this elegiac argument has its elegiac myth: the Tower of Babel, where the world's multiplicity of languages is seen as mankind's punishment— condemned to the howlers, the faux amis , the foreign menu apps. Whereas the ideal linguistic state would be the lost universal language of Eden.
See also Saturday's Edenville.
Comments Off on The Lottery of Babalu
Saturday, September 10, 2011
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Thursday, September 1, 2011
“Design is how it works.” — Steven Jobs (See Symmetry and Design.)
“By far the most important structure in design theory is the Steiner system S(5, 8, 24).”
— “Block Designs,” by Andries E. Brouwer
The name Carmichael is not to be found in Booher’s thesis. A book he does cite for the history of S(5,8,24) gives the date of Carmichael’s construction of this design as 1937. It should be dated 1931, as the following quotation shows—
From Log24 on Feb. 20, 2010—
“The linear fractional group modulo 23 of order 24•23•11 is often represented as a doubly transitive group of degree 24 on the symbols ∞, 0, 1, 2,…, 22. This transitive group contains a subgroup of order 8 each element of which transforms into itself the set ∞, 0, 1, 3, 12, 15, 21, 22 of eight elements, while the whole group transforms this set into 3•23•11 sets of eight each. This configuration of octuples has the remarkable property that any given set of five of the 24 symbols occurs in one and just one of these octuples. The largest permutation group Γ on the 24 symbols, each element of which leaves this configuration invariant, is a five-fold transitive group of degree 24 and order 24•23•22•21•20•48. This is the Mathieu group of degree 24.”
– R. D. Carmichael, “Tactical Configurations of Rank Two,” in American Journal of Mathematics, Vol. 53, No. 1 (Jan., 1931), pp. 217-240
Epigraph from Ch. 4 of Design Theory , Vol. I:
“Es is eine alte Geschichte,
doch bleibt sie immer neu ”
—Heine (Lyrisches Intermezzo XXXIX)
See also “Do you like apples?“
Comments Off on How It Works
Saturday, August 20, 2011
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
Comments Off on Castle Rock
Wednesday, July 13, 2011
From The Da Vinci Code,
by Dan Brown
Chapter 56
Sophie stared at Teabing a long moment and then turned to Langdon. “The Holy Grail is a person?”
Langdon nodded. “A woman, in fact.” From the blank look on Sophie’s face, Langdon could tell they had already lost her. He recalled having a similar reaction the first time he heard the statement. It was not until he understood the symbology behind the Grail that the feminine connection became clear.
Teabing apparently had a similar thought. “Robert, perhaps this is the moment for the symbologist to clarify?” He went to a nearby end table, found a piece of paper, and laid it in front of Langdon.
Langdon pulled a pen from his pocket. “Sophie are you familiar with the modern icons for male and female?” He drew the common male symbol ♂ and female symbol ♀.
“Of course,” she said.
“These,” he said quietly, are not the original symbols for male and female. Many people incorrectly assume the male symbol is derived from a shield and spear, while the female represents a mirror reflecting beauty. In fact, the symbols originated as ancient astronomical symbols for the planet-god Mars and the planet-goddess Venus. The original symbols are far simpler.” Langdon drew another icon on the paper.
∧
“This symbol is the original icon for male ,” he told her. “A rudimentary phallus.”
“Quite to the point,” Sophie said.
“As it were,” Teabing added.
Langdon went on. “This icon is formally known as the blade , and it represents aggression and manhood. In fact, this exact phallus symbol is still used today on modern military uniforms to denote rank.”
“Indeed.” Teabing grinned. “The more penises you have, the higher your rank. Boys will be boys.”
Langdon winced. “Moving on, the female symbol, as you might imagine, is the exact opposite.” He drew another symbol on the page. “This is called the chalice .”
∨
Sophie glanced up, looking surprised.
Langdon could see she had made the connection. “The chalice,” he said, “resembles a cup or vessel, and more important, it resembles the shape of a woman’s womb. This symbol communicates femininity, womanhood, and fertility.” Langdon looked directly at her now. “Sophie, legend tells us the Holy Grail is a chalice—a cup. But the Grail’s description as a chalice is actually an allegory to protect the true nature of the Holy Grail. That is to say, the legend uses the chalice as a metaphor for something far more important.”
“A woman,” Sophie said.
“Exactly.” Langdon smiled. “The Grail is literally the ancient symbol for womankind, and the Holy Grail represents the sacred feminine and the goddess, which of course has now been lost, virtually eliminated by the Church. The power of the female and her ability to produce life was once very sacred, but it posed a threat to the rise of the predominantly male Church, and so the sacred feminine was demonized and called unclean. It was man , not God, who created the concept of ‘original sin,’ whereby Eve tasted of the apple and caused the downfall of the human race. Woman, once the sacred giver of life, was now the enemy.”
“I should add,” Teabing chimed, “that this concept of woman as life-bringer was the foundation of ancient religion. Childbirth was mystical and powerful. Sadly, Christian philosophy decided to embezzle the female’s creative power by ignoring biological truth and making man the Creator. Genesis tells us that Eve was created from Adam’s rib. Woman became an offshoot of man. And a sinful one at that. Genesis was the beginning of the end for the goddess.”
“The Grail,” Langdon said, “is symbolic of the lost goddess. When Christianity came along, the old pagan religions did not die easily. Legends of chivalric quests for the lost Grail were in fact stories of forbidden quests to find the lost sacred feminine. Knights who claimed to be “searching for the chalice” were speaking in codes as a way to protect themselves from a Church that had subjugated women, banished the Goddess, burned nonbelievers, and forbidden pagan reverence for the sacred feminine.”
|
Happy birthday to Harrison Ford.
One for my baby…
∧
One more for the road.
∨
Comments Off on The Sinatra Code
Saturday, June 18, 2011
Tracking Shot
Related material—
See also this journal's September 2009 posts.
This post was suggested by today's previous post and by today's NY Lottery.
For some background to the ioncinema.com post numbered 4210 above,
see, in conjunction with the page headed "Azazel" linked to here earlier today,
the ioncinema.com post numbered 5601.
“Stranger, dreams verily are baffling and unclear of meaning,
and in no wise do they find fulfillment in all things for men.
For two are the gates of shadowy dreams,
and one is fashioned of horn and one of ivory.
Those dreams that pass through the gate of sawn ivory
deceive men, bringing words that find no fulfillment.
But those that come forth through the gate of polished horn
bring true issues to pass, when any mortal sees them.
But in my case it was not from thence, methinks,
that my strange dream came.”
Homer, Odyssey , Book 19
Translation by A.T. Murray, in two volumes.
Harvard University Press, 1919
Quoted in a press release for the film "Two Gates of Sleep."
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From the post numbered 460 in this journal—
At the still point… from the film "Absolute Power" :
Photo credit – Graham Kuhn
I’ve heard of affairs that are strictly plutonic,
But diamonds are a girl’s best friend!
— Marilyn Monroe, modeling a Freudian slip
Comments Off on Midnight in the Garden (continued)–
Sunday, April 10, 2011
From last October—
A stitch in time…
Related material—
This journal on April 8—
See also "Putting Mental Health on the Map at Harvard"—
Harvard Crimson , Friday, April 8, 2011, 2:09 AM—
They're outside the Science Center with their signs, their cheer, and their smiles. They've been introducing themselves over House lists, and they want you to ask questions. They're here for you. They're the Student Mental Heath Liaisons.
Harvard's SMHL crew—they pronounce it smile—have recently launched a new website and recruited more members in their effort to foster an informed and understanding environment on campus….
Mental Health Services, SMHL said, are not meant for "students who are really 'crazy.'" Everyone is entitled to a little help smiling.
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Friday, April 8, 2011
Roberta Smith in today's New York Times —
"… the argument that painting may ultimately be about
little more than the communication of some quality of
light and space, however abstract or indirect."
— Review of "Rooms With a View" at the Met
Lowry —
Malcolm Lowry, author of Under the Volcano
Hollywood —
Related material —
"You've got to pick up every stitch…"
Comments Off on Windows
Tuesday, April 5, 2011
(A sequel to last night's "For Taylor")
On Joan Tewkesbury, who wrote the script for the 1975 film "Nashville"—
She urges writers to continue to generate new ideas
and new material. "Keep writing. The hardest thing
is to sell one script and not have another to follow it with."
One script— Yesterday's link titled "An Ordinary Evening in Tennessee"
Another— "A Point of Central Arrival"
Related material from last October—
"You've got to pick up every stitch…"
* A former governor of Tennessee who died at 80 yesterday in Nashville
Comments Off on For Ned*
Saturday, January 8, 2011
"Rosetta Stone" as a Metaphor
in Mathematical Narratives
For some backgound, see Mathematics and Narrative from 2005.
Yesterday's posts on mathematics and narrative discussed some properties
of the 3×3 grid (also known as the ninefold square ).
For some other properties, see (at the college-undergraduate, or MAA, level)–
Ezra Brown, 2001, "Magic Squares, Finite Planes, and Points of Inflection on Elliptic Curves."
His conclusion:
When you are done, you will be able to arrange the points into [a] 3×3 magic square,
which resembles the one in the book [5] I was reading on elliptic curves….
This result ties together threads from finite geometry, recreational mathematics,
combinatorics, calculus, algebra, and number theory. Quite a feat!
5. Viktor Prasolov and Yuri Solvyev, Elliptic Functions and Elliptic Integrals ,
American Mathematical Society, 1997.
Brown fails to give an important clue to the historical background of this topic —
the word Hessian . (See, however, this word in the book on elliptic functions that he cites.)
Investigation of this word yields a related essay at the graduate-student, or AMS, level–
Igor Dolgachev and Michela Artebani, 2009, "The Hesse Pencil of Plane Cubic Curves ."
From the Dolgachev-Artebani introduction–
In this paper we discuss some old and new results about the widely known Hesse
configuration of 9 points and 12 lines in the projective plane P2(k ): each point lies
on 4 lines and each line contains 3 points, giving an abstract configuration (123, 94).
PlanetMath.org on the Hesse configuration—
A picture of the Hesse configuration–
(See Visualizing GL(2,p), a note from 1985).
Related notes from this journal —
From last November —
From 2006 —
Also from 2006 —
Sunday November 26, 2006
m759 @ 7:26 AM
Rosalind Krauss
in "Grids," 1979:
"If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit. From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.
Or, to take a more up-to-date example…."
"He was looking at the nine engravings and at the circle,
checking strange correspondences between them."
– The Club Dumas ,1993
"And it's whispered that soon if we all call the tune
Then the piper will lead us to reason."
– Robert Plant ,1971
The nine engravings of The Club Dumas
(filmed as "The Ninth Gate") are perhaps more
an example of the concrete than of the universal.
An example of the universal*– or, according to Krauss,
a "staircase" to the universal– is the ninefold square:
"This is the garden of Apollo, the field of Reason…."
– John Outram, architect
For more on the field of reason, see
Log24, Oct. 9, 2006.
A reasonable set of "strange correspondences"
in the garden of Apollo has been provided by
Ezra Brown in a mathematical essay (pdf).
Unreason is, of course, more popular.
* The ninefold square is perhaps a "concrete universal" in the sense of Hegel:
"Two determinations found in all philosophy are the concretion of the Idea and the presence of the spirit in the same; my content must at the same time be something concrete, present. This concrete was termed Reason, and for it the more noble of those men contended with the greatest enthusiasm and warmth. Thought was raised like a standard among the nations, liberty of conviction and of conscience in me. They said to mankind, 'In this sign thou shalt conquer,' for they had before their eyes what had been done in the name of the cross alone, what had been made a matter of faith and law and religion– they saw how the sign of the cross had been degraded."
– Hegel, Lectures on the History of Philosophy ,
"Idea of a Concrete Universal Unity"
"For every kind of vampire,
there is a kind of cross."
– Thomas Pynchon
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And from last October —
"You've got to pick up every stitch…"
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Tuesday, November 9, 2010
A Theory of Pure Design
by Denman Waldo Ross
Lecturer on the Theory of Design
in Harvard University
Boston and New York
Houghton, Mifflin and Company, 1907
PREFACE
"My purpose in this book is to elucidate, so far as I can, the
principles which underlie the practice of drawing and painting
as a Fine Art. Art is generally regarded as the expression of
feelings and emotions which have no explanation except per-
haps in such a word as inspiration , which is expletive rather
than explanatory. Art is regarded as the one activity of man
which has no scientific basis, and the appreciation of Art is
said to be a matter of taste in which no two persons can be
expected to agree. It is my purpose in this book to show how,
in the practice of Art, as in all other practices, we use certain
terms and follow certain principles. Being defined and ex-
plained, these terms and principles may be known and under-
stood by everybody. They are, so to speak, the form of the
language.
While an understanding of the terms and principles of Art
will not, in itself, enable any one to produce important works,
such works are not produced without it. It must be understood,
however, that the understanding of terms and principles
is not, necessarily, an understanding in words. It may lie in
technical processes and in visual images and may never rise,
or shall I say fall, to any formulation in words, either spoken
or written."
_________________________________________________
One of Ross's protégés, Jack Levine, died yesterday at 95. He
is said to have remarked, "I want to paint with the dead ones."
Related material: This journal on the day of Levine's death
and on the day of Martin Gardner's death.
The latter post has an image illustrating Ross's remarks on
formulations in words—
For further details, see Finale, Darkness Visible, and Packed.
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Saturday, October 16, 2010
Benoît Mandelbrot died on Oct. 14.
— New York Lottery on Thursday, Oct. 14, 2010
Related material on 109: See 1/09, 2009.
Related material on 060: See Hexagram 60 of the I Ching and…
Margaret Atwood on Lewis Hyde's Trickster Makes This World: Mischief, Myth, and Art—
"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)
What is "the next world"? It might be the Underworld….
The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation and art all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254) If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist. Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.
Comments Off on The Mandelbrot Numbers
Saturday, October 9, 2010
Seven is Heaven, Eight is a Gate, Nine is a Vine…
"And the serpent's eyes shine…."
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Saturday, May 22, 2010
Comments Off on But seriously…
Thursday, November 19, 2009
“Orthodox Jews are disappearing from Jerusalem. One moment they are praying at the Western Wall, and in the blink of an eye, they seem to evaporate…. In order to build the Third Temple while being respectful of the Islamic structures on the Temple Mount, the Jews have discovered a way to access a fourth spatial dimension. They will build the Third Temple invisibly ‘above’ the Temple Mount and ‘above’ the Mosque in the direction of the fourth dimension.”
— Clifford Pickover, description of his novel Jews in Hyperspace
“If you have built castles in the air, your work need not be lost; that is where they should be. Now put the foundations under them.”
— Henry David Thoreau, conclusion of Walden
Related material: Log24 entries, morning and evening of June 11, 2009, “Text” (June 22, 2009), and Salomon Bochner‘s remarks on space in “Eight is a Gate” (Feb. 26, 2008).
Comments Off on Walden for Jews
Monday, August 3, 2009
“Who knows where madness lies?”
— Quoted here July 29, 2009
(the day the keeper of
the Oscars died)
Possible clues:
From Google News at about
7 AM ET Mon., Aug. 3, 2009:
CHILMARK – Black scholar Henry Louis Gates Jr. has received numerous death threats since he accused a white officer of …
The Daily Inquirer – 4 hours ago
Henry Louis Gates Jr. said yesterday that Harvard University suggested he move after receiving numerous death threats since he accused a white officer of …
NECN – 9 hours ago
… Gates spoke at a book signing on Martha’s Vineyard. He also said that he has received death and bomb threats after the incident at his Cambridge home. …
Gates said he received numerous threats after the incident, including an e-mail that read, “You should die, you’re a racist.” Gates has changed his e-mail …
As a result of death threats and bomb threats, he hasn’t returned to his Cambridge home, leased from Harvard University. The university has encouraged him …
Gates, who spoke at a book signing on Martha’s Vineyard Sunday, says there also have been some serious moments. He says he received death and bomb threats …
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Comments Off on Monday August 3, 2009
Thursday, July 30, 2009
Academy Awards
for Cambridge
“First of all, I’d like
to thank the Academy.”
— Remark attributed to Plato
“A poem cannot exhaust reality,
but it can arrest it.“
— At War with the Word:
Literary Theory and
Liberal Education,
by R. V. Young,
Chapter One
For one such poem, see
“Life and Death United:
An Intimate Portrait of
a Man Named Miles Davis,”
from a seminar’s weblog
at DePauw University on
Sunday, November 21, 2004.
See also the four Log24
entries on that date as well
as yesterday’s entry on Davis
and the entries preceding it.
Comments Off on Thursday July 30, 2009
Friday, June 26, 2009
Apocatastasis Now
I give you the end of a golden string,
Only wind it into a ball:
It will lead you in at Heavens gate,
Built in Jerusalems wall.
— WILLIAM BLAKE
"In 'Apocatastasis Now: A Very Condensed Reading of William Blake's Jerusalem' (JBSSJ [Journal of the Blake Society at St James's] 6 [2001] 18–25), Susanne Sklar argues that Blake is not apocalyptic but apocatastatic, that is (following a doctrine of Origen and Gregory of Nyssa) he believes that all free creatures will be redeemed by God's universal love."
— The Year's Work in English Studies, 2003: Vol. 82, No. 1, pp. 493-547
Related material:
From the website of Philip Pullman,
president of The Blake Society:
"I must create a System…"
The Blake Society, 25 October 2005: St James’s Church, Piccadilly
I see that the title of this lecture is given as BLAKE'S DARK MATERIALS. Now in the lecturer's handbook, the second rule says "You need take no obsessive notice of the title that has been announced in advance." Whether Blake's materials are dark or not I couldn't really say, but I am going to talk about Blake, partly, and partly about religion. Appropriate, perhaps, in a place like this, but you might think not appropriate from someone whose reputation is that of a scoffer or mocker or critic of religion; but I haven't come here to scoff or mock. Nor have I come here to recant, as a matter of fact. I'm profoundly interested in religion, and I think it's extremely important to understand it. I've been trying to understand it all my life, and every so often it's useful to put one's thoughts in order; but I shall never like God.
|
For more dark materials
from the Halloween season
of 2005 — in fact, from the
very date of Pullman's lecture–
see
Darkness Doubled.
Comments Off on Friday June 26, 2009
Monday, June 22, 2009
Text
Today’s birthday:
Kris Kristofferson
Online Etymology Dictionary
-
-
1369, “wording of anything written,” from O.Fr. texte, O.N.Fr. tixte (12c.), from M.L. textus “the Scriptures, text, treatise,” in L.L. “written account, content, characters used in a document,” from L. textus “style or texture of a work,” lit. “thing woven,” from pp. stem of texere “to weave,” from PIE base *tek- “make” (see texture).
“An ancient metaphor: thought is a thread, and the raconteur is a spinner of yarns– but the true storyteller, the poet, is a weaver. The scribes made this old and audible abstraction into a new and visible fact. After long practice, their work took on such an even, flexible texture that they called the written page a textus, which means cloth.” [Robert Bringhurst, “The Elements of Typographic Style”]
Text-book is from 1779.
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“Discuss the geometry
underlying the above picture.”
— Log24, June 11, 2009
Comments Off on Monday June 22, 2009
Wednesday, March 11, 2009
Found (sort of)
in translation
The Associated Press, “Today in History” March 11– On this date…
“In 1959, the Lorraine Hansberry drama ‘A Raisin in the Sun’ opened at New York’s Ethel Barrymore Theater.”
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Thursday, January 15, 2009
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Wednesday, January 14, 2009
Eight is a Gate
From the most highly
rated negative review:
“I never did figure out
what ‘The Eight’ was.”
Various approaches
to this concept
(click images for details):
Comments Off on Wednesday January 14, 2009
Sunday, December 7, 2008
Space and
the Soul
On a book by Margaret Wertheim:
“She traces the history of space beginning with the cosmology of Dante. Her journey continues through the historical foundations of celestial space, relativistic space, hyperspace, and, finally, cyberspace.” –Joe J. Accardi, Northeastern Illinois Univ. Lib., Chicago, in Library Journal, 1999 (quoted at Amazon.com)
There are also other sorts of space.
© 2005 The Institute for Figuring
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Thursday, December 4, 2008
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Sunday, November 16, 2008
Art and Lies
Observations suggested by an article on author Lewis Hyde– "What is Art For?"– in today's New York Times Magazine:
Margaret Atwood (pdf) on Lewis Hyde's
Trickster Makes This World: Mischief, Myth, and Art —
"Trickster," says Hyde, "feels no anxiety when he deceives…. He… can tell his lies with creative abandon, charm, playfulness, and by that affirm the pleasures of fabulation." (71) As Hyde says, "… almost everything that can be said about psychopaths can also be said about tricksters," (158), although the reverse is not the case. "Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)
What is "the next world"? It might be the Underworld….
The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation and art all come from the same ancient root, a word meaning to join, to fit, and to make. (254) If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist. Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.
"What happened to that… cube?"
Apollinax laughed until his eyes teared. "I'll give you a hint, my dear. Perhaps it slid off into a higher dimension."
"Are you pulling my leg?"
"I wish I were," he sighed. "The fourth dimension, as you know, is an extension along a fourth coordinate perpendicular to the three coordinates of three-dimensional space. Now consider a cube. It has four main diagonals, each running from one corner through the cube's center to the opposite corner. Because of the cube's symmetry, each diagonal is clearly at right angles to the other three. So why shouldn't a cube, if it feels like it, slide along a fourth coordinate?"
— "Mr. Apollinax Visits New York," by Martin Gardner, Scientific American, May 1961, reprinted in The Night is Large
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Comments Off on Sunday November 16, 2008
Sunday, November 9, 2008
“Beauty is a riddle.”
— Dostoevsky
“Seven is Heaven
Eight is a Gate
Nine is a Vine”
— Folk rhyme
Comments Off on Sunday November 9, 2008
Tuesday, August 19, 2008
Three Times
"Credences of Summer," VII,
by Wallace Stevens, from
Transport to Summer (1947)
"Three times the concentred
self takes hold, three times
The thrice concentred self,
having possessed
The object, grips it
in savage scrutiny,
Once to make captive,
once to subjugate
Or yield to subjugation,
once to proclaim
The meaning of the capture,
this hard prize,
Fully made, fully apparent,
fully found." |
Stevens does not say what object he is discussing.
One possibility —
Bertram Kostant, Professor Emeritus of Mathematics at MIT, on an object discussed in a recent New Yorker:
"A word about E(8). In my opinion, and shared by others, E(8) is the most magnificent 'object' in all of mathematics. It is like a diamond with thousands of facets. Each facet offering a different view of its unbelievable intricate internal structure."
Another possibility —
A more modest object —
the 4×4 square.
Update of Aug. 20-21 —
Symmetries and Facets
Kostant's poetic comparison might be applied also to this object.
The natural rearrangements (symmetries) of the 4×4 array might also be described poetically as "thousands of facets, each facet offering a different view of… internal structure."
More precisely, there are 322,560 natural rearrangements– which a poet might call facets*— of the array, each offering a different view of the array's internal structure– encoded as a unique ordered pair of symmetric graphic designs. The symmetry of the array's internal structure is reflected in the symmetry of the graphic designs. For examples, see the Diamond 16 Puzzle.
For an instance of Stevens's "three times" process, see the three parts of the 2004 web page Ideas and Art.
* For the metaphor of rearrangements as facets, note that each symmetry (rearrangement) of a Platonic solid corresponds to a rotated facet: the number of symmetries equals the number of facets times the number of rotations (edges) of each facet–
The metaphor of rearrangements as facets breaks down, however, when we try to use it to compute, as above with the Platonic solids, the
number of natural rearrangements, or symmetries, of the 4×4 array. Actually, the true analogy is between the 16 unit squares of the 4×4 array, regarded as the 16 points of a finite 4-space (which has finitely many symmetries), and the infinitely many points of Euclidean 4-space (which has infinitely many symmetries).
If Greek geometers had started with a finite space (as in The Eightfold Cube), the history of mathematics might have dramatically illustrated Halmos's saying (Aug. 16) that
"The problem is– the genius is– given an infinite question, to think of the right finite question to ask. Once you thought of the finite answer, then you would know the right answer to the infinite question."
The Greeks, of course, answered the infinite questions first– at least for Euclidean space. Halmos was concerned with more general modern infinite spaces (such as Hilbert space) where the intuition to be gained from finite questions is still of value.
Comments Off on Tuesday August 19, 2008
Friday, June 27, 2008
Comments Off on Friday June 27, 2008
Saturday, June 21, 2008
From Notre-Dame de Paris:
"Un cofre de gran riqueza
Hallaron dentro un pilar,
Dentro del, nuevas banderas
Con figuras de espantar."
"A coffer of great richness
In a pillar's heart they found,
Within it lay new banners,
With figures to astound."
For some further details, see
the brief Log24 narrative
"Indiana Jones and
the Hidden Coffer" as well as
Symmetry Framed and
the design of the doors
to Rick's Cafe Americain:
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Everyone comes to Rick's.
Comments Off on Saturday June 21, 2008
Wednesday, April 16, 2008
Poetry for Physicists:
The Gates of Hell
From the obituary of physicist John Archibald Wheeler at Princeton:
In the fall of 1967, he was invited to give a talk…. As he spoke, he… [mentioned] something strange… what he called a gravitationally completely collapsed object. But such a phrase was a mouthful, he said, wishing aloud for a better name. "How about black hole?" someone shouted from the audience.
That was it. "I had been searching for just the right term for months, mulling it over in bed, in the bathtub, in my car, wherever I had quiet moments," he later said. "Suddenly this name seemed exactly right." He kept using the term, in lectures and on papers, and it stuck.
From Log24 last year on this date ("Happy Birthday, Benedict XVI"):
"Know the one about the Demiurge and the Abridgment of Hope?"
— Robert Stone, A Flag for Sunrise, Knopf, 1981, the final page, 439
From Dante, The Inferno, inscription on the gates of Hell:
"Abandon all hope, ye who enter."
From Psychoshop, an unfinished novel by Alfred Bester completed by Roger Zelazny:
His manner was all charm and grace; pure cafe society….
He purred a chuckle. "My place. If you want to come, I'll show you."
"Love to. The Luogo Nero? The Black Place?"
"That's what the locals call it. It's really Buoco Nero, the Black Hole."
"Like the Black Hole of Calcutta?"
"No. Black Hole as in astronomy. Corpse of a dead star, but also channel between this universe and its next-door neighbor."
"Here? In Rome?"
"Sure. They drift around in space until they run out of gas and come to a stop. This number happened to park here."
"How long ago?"
"No one knows," he said. "It was there six centuries before Christ, when the Etruscans took over a small town called Roma and began turning it into the capital of the world."
Comments Off on Wednesday April 16, 2008
Tuesday, April 8, 2008
Comments Off on Tuesday April 8, 2008
Sunday, March 2, 2008
Thursday, February 28, 2008
Comments Off on Thursday February 28, 2008
Tuesday, February 26, 2008
Eight is a Gate (continued)
"To begin at the beginning: Is God?…" [very long pause]
|
From "Space," by Salomon Bochner
Makom. Our term “space” derives from the Latin, and is thus relatively late. The nearest to it among earlier terms in the West are the Hebrew makom and the Greek topos (τόπος). The literal meaning of these two terms is the same, namely “place,” and even the scope of connotations is virtually the same (Theol. Wörterbuch…, 1966). Either term denotes: area, region, province; the room occupied by a person or an object, or by a community of persons or arrangements of objects. But by first occurrences in extant sources, makom seems to be the earlier term and concept. Apparently, topos is attested for the first time in the early fifth century B.C., in plays of Aeschylus and fragments of Parmenides, and its meaning there is a rather literal one, even in Parmenides. Now, the Hebrew book Job is more or less contemporary with these Greek sources, but in chapter 16:18 occurs in a rather figurative sense:
O earth, cover not thou my blood, and let my cry have no place (makom).
Late antiquity was already debating whether this makom is meant to be a “hiding place” or a “resting place” (Dhorme, p. 217), and there have even been suggestions that it might have the logical meaning of “occasion,” “opportunity.” Long before it appears in Job, makom occurs in the very first chapter of Genesis, in:
And God said, Let the waters under the heaven be gathered together unto one place (makom) and the dry land appear, and it was so (Genesis 1:9).
This biblical account is more or less contemporary with Hesiod's Theogony, but the makom of the biblical account has a cosmological nuance as no corresponding term in Hesiod. Elsewhere in Genesis (for instance, 22:3; 28:11; 28:19), makom usually refers to a place of cultic significance, where God might be worshipped, eventually if not immediately. Similarly, in the Arabic language, which however has been a written one only since the seventh century A.D., the term makām designates the place of a saint or of a holy tomb (Jammer, p. 27). In post-biblical Hebrew and Aramaic, in the first centuries A.D., makom became a theological synonym for God, as expressed in the Talmudic sayings: “He is the place of His world,” and “His world is His place” (Jammer, p. 26). Pagan Hellenism of the same era did not identify God with place, not noticeably so; except that the One (τὸ ἕν) of Plotinus (third century A.D.) was conceived as something very comprehensive (see for instance J. M. Rist, pp. 21-27) and thus may have been intended to subsume God and place, among other concepts. In the much older One of Parmenides (early fifth century B.C.), from which the Plotinian One ultimately descended, the theological aspect was only faintly discernible. But the spatial aspect was clearly visible, even emphasized (Diels, frag. 8, lines 42-49).
BIBLIOGRAPHY
Paul Dhorme, Le livre de Job (Paris, 1926).
H. Diels and W. Kranz, Die Fragmente der Vorsokratiker, 6th ed. (Berlin, 1938).
Max Jammer, Concepts of Space… (Cambridge, Mass., 1954).
J. M. Rist, Plotinus: The Road to Reality (Cambridge, 1967).
Theologisches Wörterbuch zum Neuen Testament (1966), 8, 187-208, esp. 199ff.
— SALOMON BOCHNER
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Related material: In the previous entry — "Father Clark seizes at one place (page eight)
upon the fact that…."
Father Clark's reviewer (previous entry) called a remark by Father Clark "far fetched."
This use of "place" by the reviewer is, one might say, "near fetched."
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Monday, February 25, 2008
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Wednesday, October 24, 2007
Adieu:
A Story for Dobbs
Internet Movie Database on screenwriter Lem Dobbs:
"Trivia:
Son of painter R.B. (Ron) Kitaj.
Took his pseudonym from the character Humphrey Bogart played
in 'The Treasure of the Sierra Madre.'"
Click for details.
October 21 was the day
that R. B. Kitaj died.
For what Kitaj called
"midrashic glosses"
on the numbers and
the lucky sums, see
4/30, 5/12, and
Eight is a Gate.
Screenwriter Joan Didion:
"We tell ourselves stories in order to live….
We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the 'ideas' with which we have learned to freeze the shifting phantasmagoria which is our actual experience.
Or at least we do for a while. I am talking here about a time when I began to doubt the premises of all the stories I had ever told myself, a common condition but one I found troubling."
David Cohen on R. B. Kitaj:
"He has come to be fascinated… by the kabbalah, finding in it parallels to the world of art and ideas. Every morning, after a long walk, he winds up at a Westwood café surrounded by pretty UCLA students where he studies the writings of Emmanuel Levinas, before working for an hour on his memoirs."
Levinas Adieu:
Click for source.
"There is no teacher
but the enemy."
— Orson Scott Card,
Ender's Game
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Monday, October 1, 2007
Bright as Magnesium
"Definitive"
— The New York Times,
Sept. 30, 2007, on
Blade Runner:
The Final Cut
Institute for Advanced Study, Princeton, N.J.—
"The art historian Kirk Varnedoe died on August 14, 2003, after a long and valiant battle with cancer. He was 57. He was a faculty member in the Institute for Advanced Study’s School of Historical Studies, where he was the fourth art historian to hold this prestigious position, first held by the German Renaissance scholar Erwin Panofsky in the 1930s."
Hal Crowther—
"His final lecture was an eloquent, prophetic flight of free association….
Varnedoe chose to introduce his final lecture with the less-quoted last words of the android Roy Batty (Rutger Hauer) in Ridley Scott's film Blade Runner: 'I've seen things you people wouldn't believe– attack ships on fire off the shoulder of Orion, bright as magnesium; I rode on the back decks of a blinker and watched C-beams glitter in the dark near the Tannhauser Gate. All those moments will be lost in time, like tears in the rain. Time to die.'"
Related material:
tears in the rain–
Game Over
(Nov. 5, 2003):
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Monday, August 6, 2007
The Place of the Lion, by Charles Williams, 1931, Chapter Eight:
"Besides, if this fellow were right, what harm would the Divine Universals do us? I mean, aren't the angels supposed to be rather gentle and helpful and all that?"
"You're doing what Marcellus warned you against… judging them by English pictures. All nightgowns and body and a kind of flacculent sweetness. As in cemeteries, with broken bits of marble. These are Angels– not a bit the same thing. These are the principles of the tiger and the volcano and the flaming suns of space."
Under the Volcano, Chapter Two:
"But if you look at that sunlight there, then perhaps you'll get the answer, see, look at the way it falls through the window: what beauty can compare to that of a cantina in the early morning? Your volcanoes outside? Your stars– Ras Algethi? Antares raging south southeast? Forgive me, no."
A Spanish-English dictionary:
lucero m.
morning or evening star:
any bright star….
hole in a window panel
for the admission of light….
Look at the way it
falls through the window….
— Malcolm Lowry
How art thou fallen from heaven,
O Lucifer, son of the morning!
— Isaiah 14:12
For more on Spanish
and the evening star,
see Plato, Pegasus, and
the Evening Star.
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Symmetry axes
of the square:
(See Damnation Morning.)
From the cover of the
Martin Cruz Smith novel
Stallion Gate:
"That old Jew
gave me this here."
— Dialogue from the
Robert Stone novel
A Flag for Sunrise.
Related material:
A Mass for Lucero,
Log24, Sept. 13, 2006—
— and this morning's online
New York Times obituaries:
The above image contains summary obituaries for Cardinal Lustiger, Archbishop of Paris, 1981-2005, and for Sal Mosca, jazz pianist and teacher. In memory of the former, see all of the remarks preceding the image above. In memory of the latter, the remarks of a character in Martin Cruz Smith's Stallion Gate on jazz piano may have some relevance:
"I hate arguments. I'm a coward. Arguments are full of words, and each person is sure he's the only one who knows what the words mean. Each word is a basket of eels, as far as I'm concerned. Everybody gets to grab just one eel and that's his interpretation and he'll fight to the death for it…. Which is why I love music. You hit a C and it's a C and that's all it is. Like speaking clearly for the first time. Like being intelligent. Like understanding. A Mozart or an Art Tatum sits at the piano and picks out the undeniable truth."
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Saturday, July 7, 2007
Seven is Heaven
John Lahr, review of a production of Tom Stoppard’s “Jumpers”–
The play is about a philosophy professor, George, and his wife, Dotty, who “exudes a sumptuous sexuality…. She has a pert round head, high cheekbones, and a deep voice, which, like her acting, is full of playfulness and longing. George is lost in thought; Dotty is just lost. ‘Heaven, how can I believe in Heaven?’ she sings at the finale. ‘Just a lying rhyme for seven!’ She is promise and heartbreak in one.”
“With a name like Frigo…”
Related material:
Eight is a Gate
Comments Off on Saturday July 7, 2007
Wednesday, June 27, 2007
Juneteenth Revisited:
A Long and Strange Day
Time and chance
yesterday:
Pennsylvania Lottery
June 26, 2007–
Mid-day 040
Evening 810
040:
A discussion of the work of Ralph Ellison:
"… why do you think he did not finish these novels? He wrote on them for many, many years– 40 years, I think."
"Yes, he worked for 40 years."
See Ellison's novel Juneteenth (New York Times review, 1999)
810:
August 10 (8/10), 2004 —
"But all things then were oracle and secret.
Remember the night when,
lost, returning, we turned back
Confused, and our headlights
singled out the fox?
Our thoughts went with it then,
turning and turning back
With the same terror,
into the deep thicket
Beside the highway,
at home in the dark thicket.
I say the wood within is the dark wood…."
— Donald Justice, "Sadness"
John Baez, Diary, entry of June 22, 2007:
"On Tuesday the 19th….
I hiked down the completely dark but perfectly familiar gravel road with my suitcase in hand, listening to the forest creatures. But then, I couldn't find my parents' driveway! It was embarrassing: I could see their house perfectly well, off in the distance, but it was so darn dark I couldn't spot the driveway. It felt like a dream: after a long flight with many delays, one winds up walking to ones parents house, lost in a spooky forest….
… I sort of enjoy this kind of thing, as long as there's no real danger. It's also sort of scary. The well-lit grid of civilization slowly falls away, and you're out there alone in the night…
Anyway: I considered hiking straight through the woods to my parents' house, but I decided things were already interesting enough, so instead I called my mom and ask her to drive down the driveway a bit, just so I could see where it was. And so she did, and then it was obvious.
So, I got home shortly before midnight. A long and strange day. My dad was already in bed, but I said hi to him anyway."
Related material:
Juneteenth through
Midsummer Night
Comments Off on Wednesday June 27, 2007
Monday, June 25, 2007
Object Lesson
"… the best definition
I have for Satan
is that it is a real
spirit of unreality."
M. Scott Peck,
People of the Lie
"Far in the woods they sang
their unreal songs,
Secure. It was difficult
to sing in face
Of the object. The singers
had to avert themselves
Or else avert the object."
— Wallace Stevens,
"Credences of Summer"
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Today is June 25,
anniversary of the
birth in 1908 of
Willard Van Orman Quine.
Quine died on
Christmas Day, 2000.
Today, Quine's birthday, is,
as has been noted by
Quine's son, the point of the
calendar opposite Christmas–
i.e., "AntiChristmas."
If the Anti-Christ is,
as M. Scott Peck claims,
a spirit of unreality, it seems
fitting today to invoke
Quine, a student of reality,
and to borrow the title of
Quine's Word and Object…
Word:
An excerpt from
"Credences of Summer"
by Wallace Stevens:
"Three times the concentred
self takes hold, three times
The thrice concentred self,
having possessed
The object, grips it
in savage scrutiny,
Once to make captive,
once to subjugate
Or yield to subjugation,
once to proclaim
The meaning of the capture,
this hard prize,
Fully made, fully apparent,
fully found."
— "Credences of Summer," VII,
by Wallace Stevens, from
Transport to Summer (1947)
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Object:
From Friedrich Froebel,
who invented kindergarten:
From Christmas 2005:
Click on the images
for further details.
For a larger and
more sophisticaled
relative of this object,
see yesterday's entry
At Midsummer Noon.
The object is real,
not as a particular
physical object, but
in the way that a
mathematical object
is real — as a
pure Platonic form.
"It's all in Plato…."
— C. S. Lewis
Comments Off on Monday June 25, 2007
Thursday, June 14, 2007
A Time
for Remembering
June 9, the birthday of
Aaron Sorkin, a writer
mentioned in recent
Log24 entries, was also
the birthday of writer
Patricia Cornwell.
An illustration
from that date:
Cornwell's first book was
a biography of
Ruth Bell Graham,
A Time for Remembering.
"Seven is heaven,
Eight is a gate,
Nine is a vine."
Comments Off on Thursday June 14, 2007
Friday, February 16, 2007
“The much-borrowed Brown formula involves some very specific things. The name of a great artist, artifact or historical figure must be in the book’s story, not to mention on its cover. The narrative must start in the present day with a bizarre killing, then use that killing as a reason to investigate the past. And the past must yield a secret so big, so stunning, so saber-rattling that all of civilization may be changed by it. Probably not for the better.
This formula is neatly summarized….”
Cover illustration
for
The Judas Seat:
The Narrative:
The Secret:
Part I
“Little ‘Jack’ Horner was actually Thomas Horner, steward to the Abbot of Glastonbury during the reign of King Henry VIII…. Always keen to raise fresh funds, Henry had shown a interest in Glastonbury (and other abbeys). Hoping to appease the royal appetite, the nervous Abbot, Richard Whiting, allegedly sent Thomas Horner to the King with a special gift. This was a pie containing the title deeds to twelve manor houses in the hope that these would deflect the King from acquiring Glastonbury Abbey. On his way to London, the not so loyal courier Horner apparently stuck his thumb into the pie and extracted the deeds for Mells Manor, a plum piece of real estate. The attempted bribe failed and the dissolution of the monasteries (including Glastonbury) went ahead from 1536 to 1540. Richard Whiting was subsequently executed, but the Horner family kept the house, so the moral of this one is: treachery and greed pay off, but bribery is a bad idea.” –Chris Roberts, Heavy Words Lightly Thrown: The Reason Behind the Rhyme
“In medieval romance, the grail was said to have been brought to
Glastonbury in Britain by Joseph of Arimathea and his followers. In the time of Arthur, the quest for the Grail was the highest spiritual pursuit.” —
The Camelot Project
Part III
The Log24 entry for the date–
February 13, 2007–
of the above Bible scholar’s death,
and the three entries preceding it:
“And what the dead had no speech for, when living,
they can tell you, being dead:
the communication of the dead is tongued with fire
beyond the language of the living.”
— T. S. Eliot, Four Quartets
Comments Off on Friday February 16, 2007
Tuesday, February 6, 2007
The Poetics of Space
The title is from Bachelard.
I prefer Stevens:
The rock is the habitation of the whole,
Its strength and measure, that which is near, point A
In a perspective that begins again
At B: the origin of the mango's rind.
It is the rock where tranquil must adduce
Its tranquil self, the main of things, the mind,
The starting point of the human and the end,
That in which space itself is contained, the gate
To the enclosure, day, the things illumined
By day, night and that which night illumines,
Night and its midnight-minting fragrances,
Night's hymn of the rock, as in a vivid sleep.
— Wallace Stevens,
"The Rock," 1954
Joan Ockman in Harvard Design Magazine (Fall 1998):
"'We are far removed from any reference to simple geometrical forms,' Bachelard wrote…."
No, we are not. See Log24, Christmas 2005:
Compare and contrast:
(Click on pictures for details.)
More on Bachelard from Harvard Design Magazine:
"The project of discerning a loi des quatre éléments would preoccupy him until his death…."
For such a loi, see Theme and Variations and…
(Click on design for details.)
Thought for Today:
"If you can talk brilliantly
about a problem, it can create
the consoling illusion that
it has been mastered."
— Stanley Kubrick, American
movie director (1928-1999).
(AP, "Today in History,"
February 6, 2007)
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Thursday, February 1, 2007
Change
The above is from
Feb. 15, 2006.
"I don't believe in an afterlife, so I think this is it, and I'm trying to spend my time as best I can, and I'm trying to spend my time so I'm proud of what I've done, and I try not to do any things that I'm not proud of."
—Jim Gray, 2002 interview (pdf)
Commencement Address (doc)
to Computer Science Division,
College of Letters and Science,
University of California, Berkeley,
by Jim Gray,
May 25, 2003:
"I was part of Berkeley's class of 1965. Things have changed a lot since then….
So, what's that got to do with you? Well, there is going to be MORE change…. Indeed, change is accelerating– Vernor Vinge suggests we are approaching singularities when social, scientific and economic change are so rapid that we cannot imagine what will happen next. These futurists predict humanity will become post-human. Now, THAT! is change– a lot more than I have seen.
If it happens, the singularity will happen in your lifetime– and indeed, you are likely to make it happen."
For other singular
sci-fi tales, click on
the above hexagram.
More from Gray's speech:
"I am an optimist. Science is a Faustian bargain– and I am betting on mankind muddling through. I grew up under the threat of atomic war; we've avoided that so far. Information Technology is a Faustian bargain. I am optimistic that we can have the good parts and protect ourselves from the worst part– but I am counting on your help in that."
Comments Off on Thursday February 1, 2007
Friday, November 10, 2006
Livingstone
On this date:
In 1871, journalist-explorer Henry M. Stanley found Scottish missionary David Livingstone, who had not been heard from for years, near Lake Tanganyika in central Africa.
— AP “Today in History,” Nov. 10
“Counter-change is
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Monday, October 9, 2006
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Sunday, October 8, 2006
Today’s Birthday:
Matt Damon
“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
See also works by the late Arthur Loeb of Harvard’s Department of Visual and Environmental Studies.
“I don’t want to be a product of my environment. I want my environment to be a product of me.” — Frank Costello in The Departed
For more on the Harvard environment,
see today’s online Crimson:
The Harvard Crimson, Online Edition |
Sunday, Oct. 8, 2006 |
POMP AND CIRCUS-STANCE
CRIMSON/ MEGHAN T. PURDY
Friday, Oct. 6:
The Ringling Bros. Barnum & Bailey Circus has come to town, and yesterday the animals were disembarked near MIT and paraded to their temporary home at the Banknorth Garden.
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OPINION
At Last, a Guiding Philosophy The General Education report is a strong cornerstone, though further scrutiny is required.
By THE CRIMSON STAFF After four long years, the Curricular Review has finally found its heart.
The Trouble With the Germans The College is a little under-educated these days.
By SAHIL K. MAHTANI Harvard College– in the best formulation I’ve heard– promulgates a Japanese-style education, where the professoriate pretend to teach, the students pretend to learn, and everyone is happy.
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Monday, July 31, 2006
For the feast of
St. Ignatius Loyola…
Final Arrangements,
continued:
“Now you has jazz.”
– High Society, 1956
— Today’s online New York Times
Also from today’s New York Times:
Kurt Kreuger
in the 1945 film “Paris Underground.”
Kurt Kreuger,
a German-born actor
who reluctantly played
Nazi soldiers
in many films
about World War II,
died July 12 in
Beverly Hills, Calif.
He was 89.
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Log24, Wednesday, July 12, 2006:
Band Numbers
“Some friends of mine are in this band…”
— David Auburn, Proof
Seven is Heaven, Eight is a Gate, Nine is a Vine.
— The Prime Powers
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Related material:
A Log24 entry commemorating
the murder of six Jesuits
in El Salvador.
Wednesday, July 12, 2006
Band Numbers
“Some friends of mine
are in this band…”
— David Auburn, Proof
Seven is Heaven,
Eight is a Gate,
Nine is a Vine.
— The Prime Powers
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Monday, July 10, 2006
An obituary in this morning's New York Times suggests a flashback. The Times says that Paul Nelson, 69, a music critic once famously ripped off by the young Bobby Zimmerman, was found dead in his Manhattan apartment last Wednesday. Here is a Log24 entry for that date. (The obituary, by Jon Pareles, notes that Nelson "prized hard-boiled detective novels and film noir.")
Comments Off on Monday July 10, 2006
Wednesday, July 5, 2006
Sunday, June 4, 2006
Images
and Words
for Baccalaureate
Day at Princeton
From Hermann Weyl’s
Symmetry,
Princeton University
Press, page 140
Adapted from the
cover of Alan Watts’s
The Spirit of Zen
Romani flag, courtesy of
myspace.com/RomArmando
Related material:
“The Scholar Gypsy”
in The Oxford Book
of English Prose, 1923,
edited by
Sir Arthur Quiller-Couch
This is available online:
From The Vanity of Dogmatizing,
by Joseph Glanvill
(London, printed by E.C. for
Henry Eversden at the Grey-Hound
in St.Pauls-Church-Yard, 1661)
Pages 195-201:
That one man should be able to bind the thoughts of another, and determine them to their particular objects; will be reckon’d in the first rank of Impossibles: Yet by the power of advanc’d Imagination it may very probably be effected; and story abounds with Instances. I’le trouble the Reader but with one; and the hands from which I had it, make me secure of the truth on’t. There was very lately a Lad in the University of Oxford, who being of very pregnant and ready parts, and yet wanting the encouragement of preferment; was by his poverty forc’d to leave his studies there, and to cast himself upon the wide world for a livelyhood. Now, his necessities growing dayly on him, and wanting the help of friends to relieve him; he was at last forced to joyn himself to a company of Vagabond Gypsies, whom occasionally he met with, and to follow their Trade for a maintenance. Among these extravagant people, and by the insinuating subtilty of his carriage, he quickly got so much of their love, and esteem; as that they discover’d to him their Mystery: in the practice of which, by the pregnancy of his wit and parts he soon grew so good a proficient, as to be able to out-do his Instructors. After he had been a pretty while exercis’d in the Trade; there chanc’d to ride by a couple of Scholars who had formerly bin of his acquaintance. The Scholars had quickly spyed out their old friend, among the Gypsies; and their amazement to see him among such society, had well-nigh discover’d him: but by a sign he prevented their owning him before that Crew: and taking one of them aside privately, desired him with his friend to go to an Inn, not far distant thence, promising there to come to them. They accordingly went thither, and he follows: after their first salutations, his friends enquire how he came to lead so odd a life as that was, and to joyn himself with such a cheating beggarly company. The Scholar-Gypsy having given them an account of the necessity, which drove him to that kind of life; told them, that the people he went with were not such Impostours as they were taken for, but that they had a traditional kind of learning among them, and could do wonders by the power of Imagination, and that himself had learnt much of their Art, and improved in further than themselves could. And to evince the truth of what he told them, he said, he’d remove into another room, leaving them to discourse together; and upon his return tell them the sum of what they had talked of: which accordingly he perform’d, giving them a full acount of what had pass’d between them in his absence. The Scholars being amaz’d at so unexpected a discovery, ernestly desir’d him to unriddle the mystery. In which he gave them satisfaction, by telling them, that what he did was by the power of Imagination, his Phancy binding theirs; and that himself had dictated to them the discourse, they held together, while he was from them: That there were warrantable wayes of heightening the Imagination to that pitch, as to bind anothers; and that when he had compass’d the whole secret, some parts of which he said he was yet ignorant of, he intended to give the world an account of what he had learned.
Now that this strange power of the Imagination is no Impossibility; the wonderful signatures in the Foetus caus’d by the Imagination of the Mother, is no contemptible Item. The sympathies of laughing & gaping together, are resolv’d into this Principle: and I see not why the phancy of one man may not determine the cogitation of another rightly qualified, as easily as his bodily motion. This influence seems to be no more unreasonable, then [sic] that of one string of a Lute upon another; when a stroak on it causeth a proportionable motion in the sympathizing confort, which is distant from it and not sensibly touched. Now if this notion be strictly verifiable; ’twill yeeld us a good account of how Angels inject thoughts into our minds, and know our cogitations: and here we may see the source of some kinds of fascination. If we are prejudic’d against the speculation, because we cannot conceive the manner of so strange an operation; we shall indeed receive no help from the common Philosophy: But yet the Hypothesis of a Mundane soul, lately reviv’d by that incomparable Platonist and Cartesian, Dr. H. More, will handsomely relieve us. Or if any would rather have a Mechanical account; I think it may probably be made out some such way as follow. Imagination is inward Sense. To Sense is required a motion of certain Filaments of the Brain; and consequently in Imagination there’s the like: they only differing in this, that the motion of the one proceeds immediately from external objects; but that of the other hath its immediate rise within us. Now then, when any part of the Brain is stringly agitated; that, which is next and most capable to receive the motive Impress, must in like manner be moved. Now we cannot conceive any thing more capable of motion, then the fluid matter, that’s interspers’d among all bodies, and contiguous to them. So then, the agitated parts of the Brain begetting a motion in the proxime Aether; it is propagated through the liquid medium, as we see the motion is which is caus’d by a stone thrown into the water. Now, when the thus moved matter meets with anything like that, from which it received its primary impress; it will proportionably move it, as it is in Musical strings tuned Unisons. And thus the motion being convey’d, from the Brain of one man to the Phancy of another; it is there receiv’d from the instrument of conveyance, the subtil matter; and the same kind of strings being moved, and much of whay after the same manner as in the first Imaginant; the Soul is awaken’d to the same apprehensions, as were they that caus’d them. I pretend not to any exactness or infallibility in this account, fore-seeing many scruples that must be removed to make it perfect: ‘Tis only a hint of the possibility of mechanically solving the Phaenomenon; though very likely it may require many other circumstances completely to make it out. But ’tis not my business here to follow it: I leave it therefore to receive accomplishment from maturer Inventions.
Comments Off on Sunday June 4, 2006
Friday, April 14, 2006
Last Temptation:
Click on picture for details.
“Little Red Ridin’ Hood,
You sure are lookin’ good….”
See also today’s Log24
guestbook entries.
Comments Off on Friday April 14, 2006
Sunday, April 2, 2006
Comments Off on Sunday April 2, 2006
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