See also "The Unfolding" in this journal.
Thursday, April 4, 2019
Tuesday, April 5, 2005
Tuesday April 5, 2005
“Bingo!”
| Part I | On Linguistic Creation |
| Part II | Saul Bellow |
| Part III | Sequel |
“Call the Vatican.
Ask them if anything’s missing.”
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Sunday, February 2, 2025
Eric Temple Bell on Solomon’s Seal
From pp. 322 ff. of The Development of Mathematics, by Eric Temple Bell, Second Edition, McGraw-Hill, 1945, at https://archive.org/stream/in.ernet.dli.2015.133966/2015.133966. The-Development-Of-Mathematics-Second-Edition_djvu.txt — Rising to a considerably higher level of difficulty, we may instance what the physicist Maxwell called “Solomon’s seal in space of three dimensions,” the twenty-seven real or imaginary straight lines which lie wholly on the general cubic surface, and the forty-five triple tangent planes to the surface, all so curiously related to the twenty-eight bitangents of the general plane quartic curve. If ever there was a fascinating snarl of interlaced theories, Solomon’s seal is one. Synthetic and analytic geometry, the Galois theory of equations, the trisection of hyperelliptic functions, the algebra of invariants and covariants, geometric-algebraic algorithms specially devised to render the tangled configurations of Solomon’s seal more intuitive, the theory of finite groups — all were applied during the second half of the nineteenth century by scores of geometers who sought to break the seal. Some of the most ingenious geometers and algebraists in history returned again and again to this highly special topic. The result of their labors is a theory even richer and more elaborately developed than Klein’s (1884) of the icosahedron. Yet it was said by competent geometers in 1945 that a serious student need never have heard of the twenty-seven lines, the forty-five triple tangent planes, and the twenty-eight bitangents in order to be an accomplished and productive geometer; and it was a fact that few in the younger generation of creative CONTRIBUTIONS FROM GEOMETRY 323 geometers had more than a hazy notion that such a thing as tiie Solomon’s seal of the nineteenth century ever existed. Those rvho could recall from personal experience the last glow of living appreciation that lighted this obsolescent master- piece of geometry and others in the same fading tradition looked back with regret on the dying past, and wished that mathe- matical progress were not always so ruthless as it is. They also sympathized with those who still found the modern geometry of the triangle and the circle worth cultivating. For the differ- ence between the geometry of the twenty-seven lines and that of, say, Tucker, Lemoine, and Brocard circles, is one of degree, not of kind. The geometers of the twentieth century long since piously removed all these treasures to the museum of geometry, where the dust of history quickly dimmed their luster. For those who may be interested in the unstable esthetics rather than the vitality of geometry, we cite a concise modern account1 (exclusive of the connection with hyperclliptic func- tions) of Solomon’s seal. The twenty-seven lines were discovered in 1849 by Cayley and G. Salmon2 (1819-1904, Ireland); the application of transcendental methods originated in Jordan’s work (1869-70) on groups and algebraic equations. Finally, in the 1870’s L. Cremona (1830-1903), founder of the Italian school of geometers, observed a simple connection between the twenty-one distinct straight lines which lie on a cubic surface with a node and the ‘cat’s cradle’ configuration of fifteen straight lines obtained by joining six points on a conic in all possible ways. The ‘mystic hexagram’ of Pascal and its dual (1806) in C. J. Brianchon’s (1783-1864, French) theorem were thus related to Solomon’s seal; and the seventeenth century met the nineteenth in the simple, uniform deduc- tion of the geometry of the plane configuration from that of a corresponding configuration in space by the method of projection. The technique here had an element of generality that was to prove extremely powerful in the discovery and proof of cor- related theorems by projection from space of a given number of dimensions onto a space of lower dimensions. Before Cremona applied this technique to the complete Pascal hexagon, his countryman G. Veronese had investigated the Pascal configura- tion at great length by the methods of plane geometry, as had also several others, including Steiner, Cayley, Salmon, and Kirkman. All of these men were geometers of great talent; 324 THE DEVELOPMENT OF MATHEMATICS Cremona’s flash of intuition illuminated the massed details of all his predecessors and disclosed their simple connections. That enthusiasm for this highly polished masterwork of classical geometry is by no means extinct is evident from the appearance as late as 1942 of an exhaustive monograph (xi + 180 pages) by B. Segre (Italian, England) on The nonsingular cubic surface. Solomon’s seal is here displayed in all its “complicated and many-sided symmetry” — in Cayley’s phrase — as never before. The exhaustive enumeration of special configurations provides an unsurpassed training ground or ‘boot camp’ for any who may wish to strengthen their intuition in space of three dimensions. The principle of continuity, ably seconded by the method of degeneration, consistently applied, unifies the multi- tude of details inherent in the twenty-seven lines, giving the luxuriant confusion an elusive coherence which was lacking in earlier attempts to “bind the sweet influences” of the thirty- six possible double sixes (or ‘double sixers,’ as they were once called) into five types of possible real cubic surfaces, containing respectively 27, 15, 7, 3, 3 real lines. A double six is two sextuples of skew lines such that each line of one is skew to precisely one corresponding line of the other. A more modern touch appears in the topology of these five species. Except for one of the three-line surfaces, all are closed, connected manifolds, while the other three-line is two connected pieces, of which only one is ovoid, and the real lines of the surface are on this second piece. The decompositions of the nonovoid piece into generalized polyhedra by the real lines of the surface are painstakingly classified with respect to their number of faces and other char- acteristics suggested by the lines. The nonovoid piece of one three-line surface is homeomorphic to the real projective plane, as also is the other three-line surface. The topological interlude gives way to a more classical theme in space of three dimensions, which analyzes the group in the complex domain of the twenty- seven lines geometrically, either through the intricacies of the thirty-six double sixes, or through the forty triads of com- plementary Steiner sets. A Steiner set of nine lines is three sets of three such that each line of one set is incident with precisely two lines of each other set. The geometrical significance of permutability of operations in the group is rather more com- plicated than its algebraic equivalent. The group is of order 51840. There is an involutorial transformation in the group for each double six; the transformation permutes corresponding CONTRIBUTIONS FROM GEOMETRY 325 lines of the complementary sets of six of the double six, and leaves each of the remaining fifteen lines invariant. If the double sixes corresponding to two such transformations have four common lines, the transformations are permutable. If the transformations are not permutable, the corresponding double sixes have six common lines, and the remaining twelve lines form a third double six. Although the geometry of the situation may be perspicuous to those gifted with visual imagination, others find the underlying algebraic identities, among even so impressive a number of group operations as 51840, somewhat easier to see through. But this difference is merely one of ac- quired taste or natural capacity, and there is no arguing about it. However, it may be remembered that some of this scintillating pure geometry was subsequent, not antecedent, to many a dreary page of laborious algebra. The group of the twenty- seven lines alone has a somewhat forbidding literature in the tradition of the late nineteenth and early twentieth centuries which but few longer read, much less appreciate. So long as geometry — of a rather antiquated kind, it may be — can clothe the outcome of intricate calculations in visualizable form, the Solomon’s seal of the nineteenth century will attract its de- votees, and so with other famous classics of the geometric imagination. But in the meantime, the continually advancing front of creative geometry will have moved on to unexplored territory of fresher and perhaps wider interest. The world some- times has sufficient reason to be weary of the past in mathe- matics as in everything else. |
See as well a figure from yesterday's Matrix Geometry post —
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Saturday, January 25, 2025
Supplement to “The Most Powerful Diagram in Mathematics”
The diagram description in the title is from a YouTube video about
the Miracle Octad Generator of R. T. Curtis.
Supplemental AI-generated reading . . .
|
Diamond Theorem and Miracle Octad Generator
An “AI Overview” Google Search response to the ___________________________________________________ In mathematics, the "diamond theorem" refers to a geometric concept related to finite projective geometry, which is used to explain the surprising symmetry properties observed in the "Miracle Octad Generator" (MOG), a tool developed by mathematician R.T. Curtis for studying the Mathieu groups and binary Golay code; essentially, the diamond theorem helps analyze the patterns within the MOG, revealing a hidden structure based on geometric principles. [1, 2, 3, 4, 5] Key points about the connection: [1, 2, 3]
Generative AI is experimental. [1] http://finitegeometry.org/sc/16/dtheorem.html [2] https://encyclopediaofmath.org/wiki/Cullinane_diamond_theorem [3] https://arxiv.org/abs/1308.1075 [4] https://en.wikipedia.org/wiki/Miracle_Octad_Generator [5] http://xenon.stanford.edu/~hwatheod/mog/mog.html |
"Generative AI is experimental." . . .
Exercise: Correct errors in the text, using the links.
A more concise presentation —
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Tuesday, January 21, 2025
The Cullinane Diamond Theorem
and the Miracle Octad Generator
|
The Cullinane Diamond Theorem Document created on Jan. 21. 2025, by Google’s Gemini Advanced 1.5 Pro with Deep Research, in response to the following prompt:
“Research how the Cullinane diamond theorem and The Cullinane diamond theorem and the Miracle Octad Generator (MOG) are two seemingly disparate mathematical concepts that find a surprising connection through the realm of finite projective geometry. This report delves into the relationship between these two concepts, exploring their definitions, properties, and historical context to illuminate their interconnectedness. Cullinane Diamond Theorem The Cullinane diamond theorem, developed by Steven H. Cullinane, is a mathematical concept that explores the symmetrical properties of certain geometric patterns. It focuses on a 4×4 square pattern with alternating colors arranged in a diamond shape, referred to as the "diamond figure".4 The theorem states that every permutation of the 16 tiles within this diamond figure, generated by mixing rows, columns, and quadrants, will result in a pattern with some form of ordinary or color-interchange symmetry.5 This "invariance of symmetry" is a remarkable property that highlights the inherent order within seemingly random arrangements.3 The theorem has deep roots in group theory, with the group of permutations (G) being isomorphic to the affine group A on the linear 4-space over the finite field GF(2).6 This group has an order of 322,560 and plays a crucial role in understanding the symmetry of both the diamond-theorem figures and the square patterns of the MOG.5 A key result used in the proof of the theorem states that every 4-coloring (i.e., every map into a 4-set) can be expressed as a sum of three 2-colorings.1 Interestingly, the Cullinane diamond theorem can be extended to higher dimensions. For instance, extending the action of A to a 4x4x4 array yields a way of generating the 1.3 trillion transformations natural to the 64 hexagrams of the I Ching, an ancient Chinese divination text.1 This connection suggests potential applications of the theorem in diverse fields beyond geometry. Another interesting concept that arises from the Cullinane diamond theorem is that of "diamond rings." These rings are algebraic structures generated by the G-images of the diamond figure, and they are isomorphic to rings of matrices over GF(4).5 This algebraic formulation provides a deeper understanding of the symmetry properties explored by the theorem. Miracle Octad Generator The Miracle Octad Generator (MOG), conceived by R.T. Curtis, is a mathematical tool used to study the symmetries and properties of the Mathieu group M24, a sporadic simple group of significant importance in group theory and coding theory.7 It is a 4×6 array of combinations that can describe any point in 24-dimensional space.7 More precisely, each element in the array represents a combination of coordinates or symbols that contribute to defining a point in this 24-dimensional space. Properties The MOG preserves all the symmetries and maximal subgroups of M24, including the monad, duad, triad, octad, octern, sextet, trio, and duum groups.7 It can be used to visualize partitions of the 24 points, which is important for characterizing these maximal subgroups of M24.8 One of the key applications of the MOG lies in its ability to quickly verify codewords of the binary Golay code, a highly efficient error-correcting code used in various communication systems.7 Each element in the MOG can store a '1' or a '0', and by analyzing the counts (number of '1's) in each column and the top row, one can determine if a set of 24 coordinates forms a valid codeword.7 The MOG achieves this by projecting the 24 Golay code onto a code called the hexacode.8 The MOG is also closely related to the concept of octads and sextets. Any 5 elements of the MOG lie in a unique octad, which is a set of 8 elements.9 A sextet is a set of 6 tetrads (sets of 4 elements) where the union of any two tetrads forms an octad.9 Every tetrad lies in a unique sextet. Furthermore, the MOG is a pairing of the 35 partitions of an 8-set into two 4-sets with the 35 partitions of AG(4,2) (the affine 4-space over GF(2)) into 4 affine planes.10 This pairing preserves specific incidence properties, which refer to the relationships between points, lines, and planes in a geometric space. It's worth noting that there are two competing definitions of the MOG. Curtis originally defined it as a pairing of two 35-member sets.11 However, many sources now define it as a rectangular array based on Conway's hexacode.11 Finally, the MOG helps in understanding the octad stabilizer, a subgroup of M24 that leaves an octad invariant as a set.10 This subgroup is isomorphic to the automorphism group of the affine 4-space over GF(2), highlighting the deep connection between the MOG and finite geometry. Relationship Between the Cullinane Diamond Theorem and the Miracle Octad Generator The relationship between the Cullinane diamond theorem and the MOG emerges from their shared foundation in finite projective geometry. The 35 square patterns within the MOG have an underlying structure based on finite projective geometry.5 These patterns, composed of two-color diagonally-divided square tiles, exhibit surprising symmetry properties that can be explained using the Cullinane diamond theorem.5 A crucial link between the Cullinane diamond theorem and the MOG is the fact that the same symmetry group, of order 322,560, underlies both concepts.5 This shared symmetry group highlights a deep connection between the seemingly different patterns studied by these two concepts. The line diagrams used to visualize the Cullinane diamond theorem also play a crucial role in understanding the symmetry of the square patterns in the MOG.5 These line diagrams, based on the three partitions of the four-set of square tiles, correspond to the 35 lines in the 3-dimensional projective space over GF(2).5 In essence, the Cullinane diamond theorem provides a way to understand and visualize the symmetry properties inherent in the MOG. Furthermore, the underlying geometry of the 4×4 patterns in the Cullinane diamond theorem is closely related to the MOG, which is used in the construction of the Steiner system S(5,8,24).5 This connection extends to the Leech lattice, a highly symmetrical mathematical structure in 24 dimensions, which Walter Feit described as a "blown up version of S(5,8,24)".5 The Leech lattice is a dense sphere-packing in 24 dimensions with remarkable symmetry properties and connections to various areas of mathematics and physics. Interestingly, the Cullinane diamond theorem also sheds light on the relationship between orthogonality of Latin squares and skewness of lines in a finite projective 3-space.12 Latin squares are square arrays filled with symbols, and orthogonality between two Latin squares means that when they are superimposed, each possible pair of symbols appears exactly once. Skewness of lines in projective geometry refers to lines that do not intersect. The Cullinane diamond theorem helps establish a connection between these seemingly unrelated concepts. Another interesting connection is to Beutelspacher's model of the 15 points of PG(3,2).1 This model provides a way to visualize the points of this projective space, and it relates to the Cullinane diamond theorem and the MOG through their shared foundation in finite projective geometry. Applications The relationship between the Cullinane diamond theorem and the MOG has potential applications in various fields, including coding theory and cryptography. The MOG's ability to verify codewords of the binary Golay code is particularly relevant in coding theory, where efficient error-correcting codes are essential for reliable data transmission.7 The Cullinane diamond theorem, with its focus on symmetry and permutations, could potentially contribute to the development of new coding schemes or cryptographic algorithms. For example, the theorem's insights into the structure of finite projective spaces could be used to design codes with specific properties or to analyze the security of existing cryptographic systems. Beyond coding theory, the Cullinane diamond theorem has applications in visualizing various mathematical concepts. For instance, it provides a way to visualize Walsh functions, which are a set of orthogonal functions used in signal processing and other areas of mathematics.1 The theorem also helps visualize the finite projective plane PG(2,4), a fundamental object in finite geometry with connections to various combinatorial structures.12 Additionally, the theorem has connections to the outer automorphisms of S6, the symmetric group on 6 letters, which are transformations that preserve the group structure but are not inner automorphisms.12 Visualizations Visualizations play a crucial role in understanding the connection between the Cullinane diamond theorem and the MOG. The 35 square patterns within the original (1976) MOG, as defined by R. T. Curtis, provide a visual representation of this connection.5 These patterns, along with the line diagrams used to illustrate the Cullinane diamond theorem, offer a tangible way to grasp the interplay between these concepts.5 Here are some examples of visualizations that illustrate this connection:
Historical Connections Historically, the development of the Cullinane diamond theorem and the MOG stemmed from explorations in finite projective geometry and group theory.5 While the exact historical connections between their development remain unclear, both concepts emerged from a desire to understand the symmetries and properties of mathematical structures in finite spaces. Conclusion The Cullinane diamond theorem and the Miracle Octad Generator, while seemingly distinct, are intricately linked through the principles of finite projective geometry. The theorem's focus on symmetry invariance and the MOG's ability to capture the symmetries of the Mathieu group M24 highlight their shared foundation. This connection extends to higher-dimensional structures like the Leech lattice and has potential applications in coding theory, cryptography, and the visualization of various mathematical concepts. The relationship between these two concepts exemplifies the interconnectedness of mathematical ideas. Often, seemingly unrelated areas of mathematics converge in unexpected ways, revealing hidden symmetries and relationships. The Cullinane diamond theorem and the MOG provide a compelling example of this phenomenon, demonstrating the power of finite projective geometry in unifying and illuminating diverse mathematical structures. Works cited 1. Diamond Theory: Symmetry in Binary Spaces, accessed January 21, 2025, https://m759.tripod.com/theory/dtheory.html 2. The Diamond Theorem in Finite Geometry, accessed January 21, 2025, http://finitegeometry.org/sc/16/dtheorem.html 3. finitegeometry.org, accessed January 21, 2025, http://finitegeometry.org/sc/gen/dtcas.html#:~:text=Cullinane,have%20some%20sort%20of%20symmetry. 4. Speak, Memory « Log24 – Home page of m759.net, a domain used by Steven H. Cullinane for a WordPress weblog., accessed January 21, 2025, http://m759.net/wordpress/?p=112809 5. Cullinane diamond theorem – Encyclopedia of Mathematics, accessed January 21, 2025, https://encyclopediaofmath.org/wiki/Cullinane_diamond_theorem 6. What is the Cullinane diamond theorem? – Log24, accessed January 21, 2025, http://log24.com/log24/240303-You.com-Cullinane_Diamond_Theorem-research-paper.pdf 7. Miracle Octad Generator – Wikipedia, accessed January 21, 2025, https://en.wikipedia.org/wiki/Miracle_Octad_Generator 8. Mathieu groups, the Golay code and Curtis' Miracle Octad Generator, accessed January 21, 2025, https://vrs.amsi.org.au/wp-content/uploads/sites/6/2014/09/UWA-Kelly.pdf 9. MOG (Miracle Octad Generator) – Stanford, accessed January 21, 2025, http://xenon.stanford.edu/~hwatheod/mog/mog.html 10. The Miracle Octad Generator (MOG) of R T. Curtis – Elements of Finite Geometry, accessed January 21, 2025, http://finitegeometry.org/sc/24/MOG.html 11. Competing Definitions of the Miracle Octad Generator – Elements of Finite Geometry, accessed January 21, 2025, http://finitegeometry.org/sc/24/mogdefs.html 12. Diamond Theory: Symmetry in Binary Spaces – Elements of Finite Geometry, accessed January 21, 2025, http://finitegeometry.org/sc/gen/dth/DiamondTheory.html 13. arxiv.org, accessed January 21, 2025, https://arxiv.org/abs/1308.1075 |
View this post as a standalone web page at
http://log24.com/log25/DTandMOG.html.
and as a PDF at
http://log24.com/log25/DTandMOG.pdf.
For a more elementary introduction to the MOG, see a YouTube video,
"The Most Powerful Diagram in Mathematics."
For a PDF of the video's metadata and comments, click here.
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and the Miracle Octad Generator
and the Miracle Octad Generator
Tuesday, January 30, 2024
Sunday, January 28, 2024
For Loki at the Disney Wormhole
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Thursday, December 28, 2023
Basque Country Art Book
Book description at Amazon.com, translated by Google —
|
Las matemáticas como herramienta
Mathematics as a tool by Raúl Ibáñez Torres Kindle edition in Spanish, 2023 Although the relationship between mathematics and art can be traced back to ancient times, mainly in geometric and technical aspects, it is with the arrival of the avant-garde and abstract art at the beginning of the 20th century that mathematics takes on greater and different relevance: as a source of inspiration and as a tool for artistic creation. Let us think, for example, of the importance of the fourth dimension for avant-garde movements or, starting with Kandisnky and later Max Bill and concrete art, the vindication of mathematical thinking in artistic creation. An idea that would have a fundamental influence on currents such as constructivism, minimalism, the fluxus movement, conceptual art, systematic art or optical art, among others. Following this approach, this book analyzes, through a variety of examples and activities, how mathematics is present in contemporary art as a creative tool. And it does so through five branches and the study of some of its mathematical topics: geometry (the Pythagorean theorem), topology (the Moebius strip), algebra (algebraic groups and matrices), combinatorics (permutations and combinations) and recreational mathematics (magic and Latin squares). |
From the book ("Cullinane Diamond Theorem" heading and picture of
book's cover added) —
Publisher: Los Libros de La Catarata (October 24, 2023)
Author: Raúl Ibáñez Torres, customarily known as Raúl Ibáñez
(Ibáñez does not mention Cullinane as the author of the above theorem
in his book (except indirectly, quoting Josefine Lyche), but he did credit
him fully in an earlier article, "The Truchet Tiles and the Diamond Puzzle"
(translation by Google).)
About Ibáñez (translated from Amazon.com by Google):
Mathematician, professor of Geometry at the University of the Basque Country
and scientific disseminator. He is part of the Chair of Scientific Culture of the
UPV/EHU and its blog Cuaderno de Cultura Cientifica. He has been a scriptwriter
and presenter of the program “Una de Mates” on the television program Órbita Laika.
He has collaborated since 2005 on the programs Graffiti and La mechanica del caracol
on Radio Euskadi. He has also been a collaborator and co-writer of the documentary
Hilos de tiempo (2020) about the artist Esther Ferrer. For 20 years he directed the
DivulgaMAT portal, Virtual Center for the Dissemination of Mathematics, and was a
member of the dissemination commission of the Royal Spanish Mathematical Society.
Author of several books, including The Secrets of Multiplication (2019) and
The Great Family of Numbers (2021), in the collection Miradas Matemáticas (Catarata).
He has received the V José María Savirón Prize for Scientific Dissemination
(national modality, 2010) and the COSCE Prize for the Dissemination of Science (2011).
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Sunday, December 17, 2023
Speak, Memory
"Unsocratic Dialogue" with Google DeepMind's Gemini AI continues . . .
|
Do you remember a previous conversation about the question "What is the Cullinane diamond theorem?" If so, how would you answer the question now?
|
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Monday, August 9, 2021
Harvard Elegy
Bryan Marquard in The Boston Globe yesterday
on a professor who died on 7 July, 2021 —
" A Harvard Medical School professor emeritus in psychiatry,
Dr. Hobson told the Globe in 2011 that he didn’t 'feel bad about
taking on Sigmund Freud. I think Sigmund Freud has become
politically correct. Psychoanalysis has become the bible, and
I think that’s crazy.'
He also forcefully set aside the theories of Carl Jung, the Swiss
psychiatrist who analyzed dreams and saw them as important
messages sent from the psyche.
'If you’re a pure scientist, Jung is just deadly,' Dr. Hobson said
in [a] 2005 interview. 'The collective unconscious, the anima …
these are literary constructs. You can’t do any science on that
kind of stuff.' ”
See as well this journal on 7 July 2021 —
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Saturday, April 17, 2021
Tuesday, February 13, 2018
Attention Must Be Paid
For the late Anne M. Treisman, who reportedly died Friday, Feb. 9:
From "A Feature-Integration Theory of Attention" —
"The controversy between analytic and synthetic theories
of perception goes back many years: the Associationists
asserted that the experience of complex wholes is built
by combining more elementary sensations, while the
Gestalt psychologists claimed that the whole precedes
its parts, that we initially register unitary objects and
relationships, and only later, if necessary, analyze these
objects into their component parts or properties. This view
is still active now . . . ."
— Anne M. Treisman, University of British Columbia,
and Garry Gelade, Oxford University, in
Cognitive Psychology 12, 97-136 (1980)
"Before time began, there was the Cube." — Optimus Prime
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Friday, May 19, 2017
In the Service of Narrative
Quoted here on St. Stephen's Day, 2008 —
“Wayne C. Booth’s lifelong
study of the art of rhetoric
illuminated the means
by which authors seduce,
cajole and lie to their readers
in the service of narrative.”
— New York Times, Oct. 11, 2005
Booth was a native of American Fork, Utah.
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Friday, May 27, 2016
Raiders of the Lost Crucible…
For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.
The above passage suggests a meditation on this morning's
New York Times * —
"When shall we three meet again?" — William Shakespeare
“We three have scattered, leaving only me behind
to clean up the scene,” Ms. Yang wrote.
“I am alone, missing us three.” — Amy Qin
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Thursday, May 12, 2016
But Seriously …
Google today released on GitHub an English parser,
Parsey McParseface . From Google Research Blog —
"Today, we are excited to share the fruits of our research
with the broader community by releasing SyntaxNet,
an open-source neural network framework implemented in
TensorFlow that provides a foundation for
Natural Language Understanding (NLU) systems.
Our release includes all the code needed to train new
SyntaxNet models on your own data, as well as
Parsey McParseface , an English parser that we have
trained for you and that you can use to analyze English text."
"While the accuracy is not perfect, it’s certainly high enough
to be useful in many applications. The major source of errors
at this point are examples such as the prepositional phrase
attachment ambiguity described above, which require real
world knowledge (e.g. that a street is not likely to be located
in a car) and deep contextual reasoning. Machine learning
(and in particular, neural networks) have made significant
progress in resolving these ambiguities. But our work is still
cut out for us: we would like to develop methods that can
learn world knowledge and enable equal understanding of
natural language across all languages and contexts."
But seriously …
For some historical background, see (for instance) a book by
Ekaterina Ovchinnikova —
Integration of World Knowledge for
Natural Language Understanding ,
Atlantis Press, Springer, 2012.
A PDF of Chapter 2, "Natural Language Understanding
and World Knowledge," is available for download.
The philosophical background is the distinction between
syntax and semantics . See (for instance) …
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Saturday, March 19, 2016
To Sum It
"To sum it all up I see mathematical activity as
a jumping ahead and then plodding along
to chart a path by rational toil."
— Verena Huber-Dyson, Feb. 15, 1998
"VERENA HUBER-DYSON, mathematician and logician,
died yesterday [March 12, 2016] in Bellingham, Washington,
at the age of 92. She was Emeritus Professor of the
Philosophy Department, University of Calgary, Alberta."
— John Brockman at edge.org, March 13, 2016
Some posts from earlier this month are related to mathematical
activity, Bellingham, jumping ahead, and plodding along:
"The process of plodding is being analyzed by proof theory,
a prolific branch of meta mathematics. Still riddled with questions
is the jumping." — Huber-Dyson, loc. cit.
Still riddled — "Why IS a raven like a writing desk?"
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Tuesday, August 11, 2015
Saturday, November 29, 2014
Mountain, Fountain
For the late Vladimir Nabokov, author of Pale Fire :
He took his article from a steel file:
"It's accurate. I have not changed her style.
There's one misprint–not that it matters much:
Mountain, not fountain. The majestic touch."
Click for a related Hollywood Reporter story.
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Sunday, November 18, 2012
Sermon
Happy birthday to…
Today's sermon, by Marie-Louise von Franz—
For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.
Another modern physicist, Niels Bohr, died
on this date in 1962…
|
The circle above is marked with a version For the square, see the diamond theorem. "Two things of opposite natures seem to depend — Wallace Stevens, |
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Saturday, September 22, 2012
Occupy Space
"The word 'space' has, as you suggest, a large number of different meanings."
— Nanavira Thera in [Early Letters. 136] 10.xii.1958
From that same letter (links added to relevant Wikipedia articles)—
|
Space (ākāsa) is undoubtedly used in the Suttas
Your second letter seems to suggest that the space |
A simpler metaphysical system along the same lines—
|
The theory, he had explained, was that the persona
— The Gameplayers of Zan , |
"I am glad you have discovered that the situation is comical:
ever since studying Kummer I have been, with some difficulty,
refraining from making that remark."
— Nanavira Thera, [Early Letters, 131] 17.vii.1958
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Monday, December 12, 2011
X o’ Jesus
Religion for stoners,♦ in memory of Horselover Fat
Amazon.com gives the publication date of a condensed
version* of Philip K. Dick's Exegesis as Nov. 7, 2011.
The publisher gives the publication date as Nov. 8, 2011.
Here, in memory of the author, Philip K. Dick (who sometimes
called himself, in a two-part pun, "Horselover Fat"), is related
material from the above two dates in this journal—
|
Tuesday, November 8, 2011 m759 @ 12:00 PM …. Update of 9:15 PM Nov. 8, 2011— From a search for the word "Stoned" in this journal—
See also Monday's post "The X Box" with its illustration
Monday, November 7, 2011
"Design is how it works." — Steve Jobs, quoted in
For some background on this enigmatic equation,
|
Merry Xmas.
♦ See also last night's post and the last words of Steve Jobs.
* Houghton Mifflin Harcourt, the publisher, has, deliberately or not, sown confusion
about whether this is only the first of two volumes.
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Tuesday, November 8, 2011
Stoned*
From "The Stone" in Sunday's online New York Times—
Cosmic Imagination
By William Egginton
Do the humanities need to be defended from hard science?
Illustration of hard science —
Illustration of the humanities —
(The above illustrations from Sunday's "The Stone" are by Leif Parsons.)
Midrash by the Coen brothers— "The Dude Abides."
See also 10/10/10— The Day of the Tetractys—
* Update of 9:15 PM Nov. 8, 2011—
From a search for the word "Stoned" in this journal—
|
Sunday, January 2, 2011
m759 @ 6:40 PM Simon Critchley today in the New York Times series "The Stone"— Philosophy, among other things, is that living activity of critical reflection in a specific context, by which human beings strive to analyze the world in which they find themselves, and to question what passes for common sense or public opinion— what Socrates called doxa— in the particular society in which they live. Philosophy cuts a diagonal through doxa. It does this by raising the most questions of a universal form: “What is X?”
Actually, that's two diagonals. See Kulturkampf at the Times and Geometry of the
[Here the "Stoned" found by the search |
See also Monday's post "The X Box" with its illustration
.
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Sunday, October 23, 2011
Starting Out in the Evening (continued)
(This post's title was appropriated from a novel by Brian Morton.)
Yesterday's evening New York Lottery— 229 and 9294.
Alex Ross in the online New Yorker quotes a bad essay he wrote in college titled…
“The Grand Hotel Abyss: History and Violence in ‘The Shining,’”
which purports to analyze the famous scene in which Jack Nicholson
types the phrase “All work and no play makes Jack a dull boy”:
Nicholson has become a chomping-machine of language,
recycling stock phrases, appropriating whatever
drifts into his path. His words are nothing but echoes….
The lottery's 229 may be interpreted as "2/29." See a post from that date in 2008
involving echoes and the abyss.
The lottery's 9294 may be interpreted as "9/2/94." A search for that date yields
an article from Pacific Stars and Stripes—
That article is echoed by a later Doonesbury caricature
of a professor discussing echoes in black rhetoric. That
caricature is from the 2/29 post—
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Sunday, January 2, 2011
A Universal Form
Simon Critchley today in the New York Times series "The Stone"—
Philosophy, among other things, is that living activity of critical reflection in a specific context, by which human beings strive to analyze the world in which they find themselves, and to question what passes for common sense or public opinion— what Socrates called doxa— in the particular society in which they live. Philosophy cuts a diagonal through doxa. It does this by raising the most questions of a universal form: “What is X?”
Actually, that's two diagonals. See Kulturkampf at the Times and Geometry of the I Ching .
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Saturday, June 26, 2010
Bold and Brilliant Emergence
"Rosemary Desjardins argues boldly and brilliantly that the Theaetetus contains not only an answer to the question of the character of knowledge, but considerably more besides — an outline of a Platonic ontology. That ontology is neither materialist nor idealist (it is not a theory of forms), but like the twentieth century theory known as generative emergence holds that beings are particular interactive combinations of material elements. On this view, while wholes (for example, words, to use a Platonic model) may be analyzed into their elemental parts (letters), each whole has a property or quality separate from the aggregated properties of its parts."
— Stephen G. Salkever, 1991 review of The Rational Enterprise : Logos in Plato's Theaetetus (SUNY Press, 1990)
See also "strong emergence" in this journal.
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Wednesday, April 28, 2010
Eightfold Geometry
Related web pages:
Miracle Octad Generator,
Generating the Octad Generator,
Geometry of the 4×4 Square
Related folklore:
"It is commonly known that there is a bijection between the 35 unordered triples of a 7-set [i.e., the 35 partitions of an 8-set into two 4-sets] and the 35 lines of PG(3,2) such that lines intersect if and only if the corresponding triples have exactly one element in common." –"Generalized Polygons and Semipartial Geometries," by F. De Clerck, J. A. Thas, and H. Van Maldeghem, April 1996 minicourse, example 5 on page 6
The Miracle Octad Generator may be regarded as illustrating the folklore.
Update of August 20, 2010–
For facts rather than folklore about the above bijection, see The Moore Correspondence.
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Sunday, March 14, 2010
Joplin at the Lapin Blanc
From Google News this evening–
Now Showing- “Alice in Wonderland”
Red and Black – Michael Prochaska
Tim Burton receives praise for his imaginative constructions
(“Nightmare Before Christmas” was inspired by a dream),
but if you analyze his work on adaptations of classic
children-oriented escapism, whimsical surrealism bears
a ball and chain.
A serenade for Einstein's birthday–
If you got it today you don't want it tomorrow, man,
'cause you don't need it, 'cause as a matter of fact,
as we discovered in the train,
tomorrow never happens, man.
It's all the same fucking day, man.
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Friday, September 11, 2009
Friday September 11, 2009
Theology
in memory of
physicist Aage Bohr,
who died at 87 on
Tuesday, Sept. 8, 2009
From the perspective of one inside the jewel, one might ask 'Why is this section blue while this section is black?,' and from within the jewel, one could not formulate an answer since one could not see the entire picture projected on the jewel; however, from outside the jewel, an observer (some analogue of Newton's God, perhaps, looking down on his 'sensorium' from the 5th dimension) could easily see the pattern and understand that all of the 'genuinely fortuitous' events inside the space-time jewel are, in fact, completely determined by the pattern in the projector."
in memory of
physicist Aage Bohr,
who died at 87 on
Tuesday, Sept. 8, 2009
Swarthmore physics honors thesis, 136 pp., 2007–
Abstract:
"Quantum mechanics, which has no completely accepted interpretation but many seemingly strange physical results, has been interpreted in a number of bizarre and fascinating ways over the years. The two interpretations examined in this paper, [Aage] Bohr and [Ole] Ulfbeck's 'Genuine Fortuitousness' and Stuckey, Silberstein, and Cifone's 'Relational Blockworld,' seem to be two such strange interpretations; Genuine Fortuitousness posits that causality is not fundamental to the universe, and Relational Blockworld suggests that time does not act as we perceive it to act. In this paper, I analyze these two interpretations…."
Footnote 55, page 114:
"Thus far, I have been speaking in fairly abstract terms, which can sometimes be unhelpful on the issue of explaining anything about the structure of space-time. I want to pause for a moment to suggest a new potential view of the blockworld within a 'genuinely fortuitous' universe in more visual terms. Instead of the 'static spacetime jewel' of blockworld that is often invoked by eternalists to help their readers conceptualize of what a blockworld would 'look like' from the outside, now imagine that a picture on a slide is being projected onto the surface of this space-time jewel."
From the perspective of one inside the jewel, one might ask 'Why is this section blue while this section is black?,' and from within the jewel, one could not formulate an answer since one could not see the entire picture projected on the jewel; however, from outside the jewel, an observer (some analogue of Newton's God, perhaps, looking down on his 'sensorium' from the 5th dimension) could easily see the pattern and understand that all of the 'genuinely fortuitous' events inside the space-time jewel are, in fact, completely determined by the pattern in the projector."
— "Genuine Fortuitousness, Relational Blockworld, Realism, and Time" (pdf), by Daniel J. Peterson, Honors Thesis, Swarthmore College, December 13, 2007
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Thursday, June 4, 2009
Thursday June 4, 2009
New collection release:
|
The above prose illustrates
the institutional mind at work.
the institutional mind at work.
Those who actually try to view
the Wade collection will
encounter the following warning:
| To access the images in the ARTstor Digital Library you need to be affiliated with a participating institution (university, college, museum, public library or K-12 school). |
Comments Off on Thursday June 4, 2009
Sunday, February 15, 2009
Sunday February 15, 2009
| From April 28, 2008:
Religious Art
The black monolith of One artistic shortcoming The following One approach to "Transformations play See 4/28/08 for examples |
Related material:
| From Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, pp. 117-118:
"… his point of origin is external nature, the fount to which we come seeking inspiration for our fictions. We come, many of Stevens's poems suggest, as initiates, ritualistically celebrating the place through which we will travel to achieve fictive shape. Stevens's 'real' is a bountiful place, continually giving forth life, continually changing. It is fertile enough to meet any imagination, as florid and as multifaceted as the tropical flora about which the poet often writes. It therefore naturally lends itself to rituals of spring rebirth, summer fruition, and fall harvest. But in Stevens's fictive world, these rituals are symbols: they acknowledge the real and thereby enable the initiate to pass beyond it into the realms of his fictions. Two counter rituals help to explain the function of celebration as Stevens envisions it. The first occurs in 'The Pediment of Appearance,' a slight narrative poem in Transport to Summer. A group of young men enter some woods 'Hunting for the great ornament, The pediment of appearance.' Though moving through the natural world, the young men seek the artificial, or pure form, believing that in discovering this pediment, this distillation of the real, they will also discover the 'savage transparence,' the rude source of human life. In Stevens's world, such a search is futile, since it is only through observing nature that one reaches beyond it to pure form. As if to demonstrate the degree to which the young men's search is misaligned, Stevens says of them that 'they go crying/The world is myself, life is myself,' believing that what surrounds them is immaterial. Such a proclamation is a cardinal violation of Stevens's principles of the imagination. For in 'Notes Toward a Supreme Fiction' he tells us that ... the first idea was not to shape the clouds In imitation. The clouds preceded us. There was a muddy centre before we breathed. There was a myth before the myth began, Venerable and articulate and complete. From this the poem springs: that we live in a place That is not our own and, much more, not ourselves And hard it is in spite of blazoned days. We are the mimics. (Collected Poems, 383-84) Believing that they are the life and not the mimics thereof, the world and not its fiction-forming imitators, these young men cannot find the savage transparence for which they are looking. In its place they find the pediment, a scowling rock that, far from being life's source, is symbol of the human delusion that there exists a 'form alone,' apart from 'chains of circumstance.' A far more productive ritual occurs in 'Sunday Morning.'…." |
For transformations of a more
specifically religious nature,
see the remarks on
Richard Strauss,
"Death and Transfiguration,"
(Tod und Verklärung, Opus 24)
in Mathematics and Metaphor
on July 31, 2008, and the entries
of August 3, 2008, related to the
death of Alexander Solzhenitsyn.
Comments Off on Sunday February 15, 2009
Friday, May 23, 2008
Friday May 23, 2008
The Idea
of Identity
of Identity
“Philosophers ponder the idea
of identity: what it is to give
something a name on Monday
and have it respond to
that name on Friday….”
Conclusion of “Analyze That” —
“There’s a place for us….”
New York Times
on Friday, May 23:
“A poem should not mean
But be”
— Archibald MacLeish,
quoted in a Friday comment
on a Thursday night column
by Rosanne Cash
Thursday evening photo
by Josh Haner for Friday’s
online New York Times:
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Monday, April 28, 2008
Monday April 28, 2008
Religious Art
The black monolith of
Kubrick's 2001 is, in
its way, an example
of religious art.
One artistic shortcoming
(or strength– it is, after
all, monolithic) of
that artifact is its
resistance to being
analyzed as a whole
consisting of parts, as
in a Joycean epiphany.
The following
figure does
allow such
an epiphany.
One approach to
the epiphany:
"Transformations play
a major role in
modern mathematics."
– A biography of
Felix Christian Klein
The above 2×4 array
(2 columns, 4 rows)
furnishes an example of
a transformation acting
on the parts of
an organized whole:
For other transformations
acting on the eight parts,
hence on the 35 partitions, see
"Geometry of the 4×4 Square,"
as well as Peter J. Cameron's
"The Klein Quadric
and Triality" (pdf),
and (for added context)
"The Klein Correspondence,
Penrose Space-Time, and
a Finite Model."
For a related structure–
not rectangle but cube–
see Epiphany 2008.
Comments Off on Monday April 28, 2008
Sunday, July 29, 2007
Sunday July 29, 2007
| Nordic Truth: | Jewish Fiction: |
| Snowball | In Hell |
| From The New York Times in 2005:
 “HE’S the hottest conductor you’ve never heard of…. In music, as in most other pursuits, one person’s misfortune can be another’s opportunity. Many a podium career has been built on successful substitutions…. typically, the process is cumulative and measured. In Mr. Remmereit’s case, it seems a sort of spontaneous combustion…. he seems destined for big things, and soon. Regarding his sudden change in stature, he spoke as if from afar. ‘The snowball has reached such a size that it has started to roll,’ he said matter-of-factly…. ‘It’s terrifying when it happens,’ he said, ‘but I can’t tell you how naively happy I am when it goes well. These are such major steps that I wasn’t even hoping for a few weeks ago.’ ARILD REMMEREIT (pronounced AHR-eeld REMM-uh-right, with the r’s heavily rolled) was born in a village in Norway, between Bergen and Trondheim, and has lived in Vienna since 1987. Slim and fresh-faced at 43, he has had a busy but low-level career in Europe…. So here he was, on April 15, conducting the Pittsburgh Symphony… in a vintage… Germanic program…. Wagner’s ‘Siegfried Idyll,’ Schumann’s Fourth Symphony and Brahms’s Second Piano Concerto….” Württemberg Philharmonic February 2004 Arild Remmereit as a guest conductor: ‘As when the sun rises in the North.’ The Philharmonics and their brilliant guest conductor fetched the mind-blowing, tempting and exciting Scandinavia. It was like a lucky strike to see the Norwegian conductor on stage with the Philharmonic. When he conducts the Dane Nielsen, the Finn Sibelius and the Norwegian Grieg, one can really feel that this man has the locally marked music floating in his blood.” |
From The New York Times today: Discussion of
a new novel: 
Variations on An interview with Henry Grinberg conducted by James R. Oestreich: “For those who find inspiration and edification in great art, it is always painful to be reminded that artists are not necessarily admirable as people and that art is powerless in the face of great evil. That truth was baldly evident in Nazi Germany and in the way the regime used and abused music and musicians, to say nothing of the way it used and abused human beings of all kinds. [A new novel touches on] these issues…. In Variations on the Beast (Dragon Press), Henry Grinberg, a psychoanalyst, posits Hermann Kapp-Dortmunder, a powerful maestro, as a fictional rival of Wilhelm Furtwängler (whose qualms about working under the regime he does not share) and Herbert von Karajan (whose vaulting ambition he does).” GRINBERG: “And it soon occurred to me… that, my God, a lot of the famous, the notable, the moving, the magnificent composers in the 18th and 19th centuries and earlier were Germans. And I tried to understand, how did such a nation turn out to be so bestial and cruel, so indifferent to the suffering of others? And I have no explanation for it. As a practicing psychoanalyst, I can see individual expressions of rage and their causes and their so-called justifications. But for a whole nation to be consumed, to be seduced by an overwhelming idea– well, there are rationalizations, I guess, but not explanations. There’s no forgiveness for this. And I tried to put together a story of a person who was a participant and a causer of these kinds of things…. So I sort of poured my feelings of contempt and rage into the character I was devising. And I have to admit, after having been psychoanalyzed myself in preparation for the training, that something of Hermann Kapp-Dortmunder exists in me. I shudder to think that this may be so, but I have to accept the possibility. Murderous thoughts may have occurred to me, but, thank God, I’ve never killed anyone.” |
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Sunday, March 27, 2005
Sunday March 27, 2005
From
The Mother Ship
The Mother Ship
Camille Paglia, The Magic of Images:
“Young people today are flooded with disconnected images but lack a sympathetic instrument to analyze them as well as a historical frame of reference in which to situate them…. The new generation, raised on TV and the personal computer but deprived of a solid primary education, has become unmoored from the mother ship of culture.”
Saturday, July 31, 2004
Saturday July 31, 2004
It’s Alive!
“People once worried about the boundary between the living and the nonliving. Today, the boundary seems meaningless….”
— Attributed to Francis Crick
(now among the nonliving)
Opening of
the above novel:
“My name is David Tennant, M.D.
I’m professor of ethics at the
University of Virginia Medical School,
and if you’re watching
this tape, I’m dead.”
From a public-relations newsletter
of the University of Southern California’s
Health Sciences Campus
dated April 20, 2001:
| of Frankenstein W. French Anderson, the physician and scientist who carried out the first human gene therapy clinical trial, will discuss the ethical issues involved in human genetic engineering and how science fiction has shaped the public’s perception of this budding new technology, Thursday, May 3, at noon, in USC’s Mayer Auditorium. The lecture, titled “Frankenstein, GATTACA and Gene Therapy,” is free and open to the public. Mayer Auditorium is located on USC’s Health Sciences campus. In his talk, Anderson will analyze the book Frankenstein and its filmic progeny and discuss how the Frankenstein story has captured the public’s imagination. He will also examine the ethical and moral issues raised by the book and movies and address the charge that, like Dr. Frankenstein, today geneticists are attempting to play God. Anderson will evaluate the 1997 movie GATTACA, a cautionary tale about injustice in a 21st century society run by genetically “superior” elites. Anderson, who was a scientific consultant for the movie and is now proposing to carry out the first in utero gene therapy trial, will discuss the impact of GATTACA on the public’s understanding of genetic engineering. |
See also the previous entry,
on Anderson’s arrest Friday
on charges of child molestation.
For the origin of the title GATTACA,
see The Diamond Code.
Comments Off on Saturday July 31, 2004
Wednesday, March 19, 2003
Wednesday March 19, 2003
A Look at the Rat
In memory of Herbert Aptheker, theoretician of the American Communist Party, who died on St. Patrick’s Day, 2003 —
From The New Yorker, issue dated March 24, 2003, Louis Menand on Edmund Wilson’s To the Finland Station:
“Wilson did know what was going on in the Soviet Union in the nineteen-thirties, as his pages on Stalin in To the Finland Station make clear. The problem wasn’t with Stalin; the problem was with Lenin, the book’s ideal type of the intellectual as man of action. Wilson admitted that he had relied on publications controlled by the Party for his portrait of Lenin. (Critical accounts were available; for example, the English translation of the émigré Mark Landau-Aldanov’s Lenin was published, by Dutton, in 1922.) Lenin could create an impression of selfless humanitarianism; he was also a savage and ruthless politician—a ‘pail of milk of human kindness with a dead rat at the bottom,’ as Vladimir Nabokov put it to Wilson in 1940, after reading To the Finland Station. In the introduction to the 1972 edition, Wilson provided a look at the rat. He did not go on to explain in that introduction that the most notorious features of Stalin’s regime—the use of terror, the show trials, and the concentration camps—had all been inaugurated by Lenin. To the Finland Station begins with Napoleon’s betrayal of the principles of the French Revolution; it should have ended with Lenin’s betrayal of European socialism.”
From Herbert Aptheker, “More Comments on Howard Fast“:
“We observe that in the list of teachers whom Howard Fast names as most influential in his own life there occur the names of fourteen individuals from Jefferson to Bernard Shaw, Upton Sinclair to Marx, Douglass to Engels, but there is no room for Lenin.
He is, I think, an important teacher, too; indeed, in my view, Lenin is the greatest figure in the whole galaxy of world revolutionary leaders. He is, certainly, the greatest analyzer of and fighter against imperialism.”
For more on Howard Fast, see my entry
“Death Knell” of March 13, 2003.
For a look at the pail of milk, see
the New Yorker cover in Geometry for Jews.
For a more cheerful look at geometry
on this St. Joseph’s Day, see
Harry J. Smith’s
“There is such a thing as a tesseract.”
— A Wrinkle in Time
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Wednesday, November 27, 2002
Wednesday November 27, 2002
Waiting for Logos
Searching for background on the phrase "logos and logic" in yesterday's "Notes toward a Supreme Fact," I found this passage:
"…a theory of psychology based on the idea of the soul as the dialectical, self-contradictory syzygy of a) soul as anima and b) soul as animus. Jungian and archetypal psychology appear to have taken heed more or less of only one half of the whole syzygy, predominantly serving an anima cut loose from her own Other, the animus as logos and logic (whose first and most extreme phenomenological image is the killer of the anima, Bluebeard). Thus psychology tends to defend the virginal innocence of the anima and her imagination…"
— Wolfgang Giegerich, "Once More the Reality/Irreality Issue: A Reply to Hillman's Reply," website
The anima and other Jungian concepts are used to analyze Wallace Stevens in an excellent essay by Michael Bryson, "The Quest for the Fiction of an Absolute." Part of Bryson's motivation in this essay is the conflict between the trendy leftist nominalism of postmodern critics and the conservative realism of more traditional critics:
"David Jarraway, in his Stevens and the Question of Belief, writes about a Stevens figured as a proto-deconstructionist, insisting on 'Steven's insistence on dismantling the logocentric models of belief' (311) in 'An Ordinary Evening in New Haven.' In opposition to these readings comes a work like Janet McCann's Wallace Stevens Revisited: 'The Celestial Possible', in which the claim is made (speaking of the post-1940 period of Stevens' life) that 'God preoccupied him for the rest of his career.'"
Here "logocentric" is a buzz word for "Christian." Stevens, unlike the postmodernists, was not anti-Christian. He did, however, see that the old structures of belief could not be maintained indefinitely, and pondered what could be found to replace them. "Notes toward a Supreme Fiction" deals with this problem. In his essay on Stevens' "Notes," Bryson emphasizes the "negative capability" of Keats as a contemplative technique:
"The willingness to exist in a state of negative capability, to accept that sometimes what we are seeking is not that which reason can impose…."
For some related material, see Simone Weil's remarks on Electra waiting for her brother Orestes. Simone Weil's brother was one of the greatest mathematicians of the past century, André Weil.
"Electra did not seek Orestes, she waited for him…"
— Simone Weil
"…at the end, she pulls it all together brilliantly in the story of Electra and Orestes, where the importance of waiting on God rather than seeking is brought home forcefully."
— Tom Hinkle, review of Waiting for God
Compare her remarks on waiting for Orestes with the following passage from Waiting for God:
"We do not obtain the most precious gifts by going in search of them but by waiting for them. Man cannot discover them by his own powers, and if he sets out to seek for them he will find in their place counterfeits of which he will be unable to discern falsity.
The solution of a geometry problem does not in itself constitute a precious gift, but the same law applies to it because it is the image of something precious. Being a little fragment of particular truth, it is a pure image of the unique, eternal, and living Truth, the very Truth that once in a human voice declared: "I am the Truth."
Every school exercise, thought of in this way, is like a sacrament.
In every school exercise there is a special way of waiting upon truth, setting our hearts upon it, yet not allowing ourselves to go out in search of it. There is a way of giving our attention to the data of a problem in geometry without trying to find the solution…."
— Simone Weil, "Reflections on the Right Use of School Studies with a View to the Love of God"
Weil concludes the preceding essay with the following passage:
"Academic work is one of those fields containing a pearl so precious that it is worth while to sell all of our possessions, keeping nothing for ourselves, in order to be able to acquire it."
This biblical metaphor is also echoed in the work of Pascal, who combined in one person the theological talent of Simone Weil and the mathematical talent of her brother. After discussing how proofs should be written, Pascal says
"The method of not erring is sought by all the world. The logicians profess to guide to it, the geometricians alone attain it, and apart from their science, and the imitations of it, there are no true demonstrations. The whole art is included in the simple precepts that we have given; they alone are sufficient, they alone afford proofs; all other rules are useless or injurious. This I know by long experience of all kinds of books and persons.
And on this point I pass the same judgment as those who say that geometricians give them nothing new by these rules, because they possessed them in reality, but confounded with a multitude of others, either useless or false, from which they could not discriminate them, as those who, seeking a diamond of great price amidst a number of false ones, but from which they know not how to distinguish it, should boast, in holding them all together, of possessing the true one equally with him who without pausing at this mass of rubbish lays his hand upon the costly stone which they are seeking and for which they do not throw away the rest."
— Blaise Pascal, The Art of Persuasion
Comments Off on Wednesday November 27, 2002