Saturday Mourning
Part I:
Part II:
Click on images for details.
Part I:
Part II:
Click on images for details.
Posted 5/30/2009 at 9:29 AM
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Saturday Mourning Part I: Part II: Click on images for details. Posted 5/30/2009 at 9:29 AM |
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Spelling
"There comes a time when you have learned enough to decide whether the way of the Craft is for you.... First you will need to prepare your sacred space.... Calling the Corners (or Quarters) is something you will always do." Happy birthday, Kylie. Posted 5/28/2009 at 9:00 PM |
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For Daedalus "Some writers describe the first draft as 'making clay'...." -- Janet Burroway Quoted here a year ago today: "... she explores -- Janet Burroway
Amy Adams in Doubt
Amy Adams and Meryl Streep
Above: Posted 5/26/2009 at 12:00 PM |
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One More for the Road "Angel eyes that old Devil sent, they glow unbearably bright...." -- Sinatra Posted 5/24/2009 at 2:45 AM |
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Release Date: 23 May 1984 (USA) Plot: "After arriving in India, Indiana Jones is asked by a desperate village to find a mystical stone...." Posted 5/23/2009 at 1:00 PM |
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Steiner System New York Times banner this morning:  Click to enlarge. Related material from July 11, 2008: 
Related material suggested by an ad last night on ABC's Ugly Betty season finale:   Diamond from last night's Log24 entry, with four colored pencils from Diane Robertson Design:  See also A Four-Color Theorem. Posted 5/22/2009 at 9:29 AM |
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Diamonds  Posted 5/21/2009 at 8:14 PM |
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Posted 5/21/2009 at 8:00 PM |
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Die Cast:
From "Secondary Structures," by Tom Moody, Sculpture Magazine, June 2000: "By the early '90s, the perception of Minimalism as a 'pure' art untouched by history lay in tatters. The coup de grâce against the movement came not from an artwork, however, but from a text. Shortly after the removal of Richard Serra's Tilted Arc from New York City's Federal Plaza, Harvard art historian Anna Chave published 'Minimalism and the Rhetoric of Power' (Arts Magazine, January 1990), a rousing attack on the boys' club that stops just short of a full-blown ad hominem rant. Analyzing artworks (Walter de Maria's aluminum swastika, Morris's 'carceral images,' Flavin's phallic 'hot rods'), critical vocabulary (Morris's use of 'intimacy' as a negative, Judd's incantatory use of the word 'powerful'), even titles (Frank Stella's National Socialist-tinged Arbeit Macht Frei and Reichstag), Chave highlights the disturbing undercurrents of hypermasculinity and social control beneath Minimalism's bland exterior. Seeing it through the eyes of the ordinary viewer, she concludes that 'what [most] disturbs [the public at large] about Minimalist art may be what disturbs them about their own lives and times, as the face it projects is society's blankest, steeliest face; the impersonal face of technology, industry and commerce; the unyielding face of the father: a face that is usually far more attractively masked.'" For a more attractively masked father figure, see the Terminator series:
For further religious background, Posted 5/21/2009 at 8:28 AM |
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From Quilt Blocks to the Mathieu Group M24 Click on illustrations for details. The connection: The four-diamond figure is related to the finite geometry PG(3,2). (See "Symmetry Invariance in a Diamond Ring," AMS Notices, February 1979, A193-194.) PG(3,2) is in turn related to the 759 octads of the Steiner system S(5,8,24). (See "Generating the Octad Generator," expository note, 1985.) The relationship of S(5,8,24) to the finite geometry PG(3,2) has also been discussed in--
Abstract: "The Steiner system S(4,7,23) is constructed from the geometry of PG(3,2)."
Abstract: "The Steiner system S(5,8,24) is constructed from the geometry of PG(3,2)." For the connection of S(5,8,24) with the Mathieu group M24, see the references in The Miracle Octad Generator. Posted 5/20/2009 at 4:00 PM |
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Exquisite Geometries "By far the most important structure in design theory is the Steiner system -- "Block Designs," 1995, by Andries E. Brouwer "The Steiner system S(5, 8, 24) is a set S of 759 eight-element subsets ('octads') of a twenty-four-element set T such that any five-element subset of T is contained in exactly one of the 759 octads. Its automorphism group is the large Mathieu group M24." -- The Miracle Octad Generator (MOG) of R.T. Curtis (webpage) "... in 1861 Mathieu... discovered five multiply transitive permutation groups.... In a little-known 1931 paper of Carmichael... they were first observed to be automorphism groups of exquisite finite geometries." -- William M. Kantor, 1981 The 1931 paper of Carmichael is now available online from the publisher for $10. Posted 5/19/2009 at 7:20 PM |
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The Sign of the Double Cross Scott Carnahan at Secret Blogging Seminar, December 14, 2007: "... my advisor once told me, 'If you ever find yourself drawing one of those meaningless diagrams with arrows connecting different areas of mathematics, it’s a good sign that you’re going senile.'"Steven Cullinane at Log24, May 19, 2004:
Google search, May 17, 2009:  Related material: Log24, Feb. 16, 2008 Posted 5/17/2009 at 10:00 PM |
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Scott Carnahan at Secret Blogging Seminar, December 14, 2007 "... my advisor once told me, 'If you ever find yourself drawing one of those meaningless diagrams with arrows connecting different areas of mathematics, it’s a good sign that you’re going senile.'" Steven Cullinane at Log24.com, May 19, 2004:
Posted 5/17/2009 at 9:49 PM |
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Scott Carnahan at Secret Blogging Seminar, December 14, 2007 "... my advisor once told me, 'If you ever find yourself drawing one of those meaningless diagrams with arrows connecting different areas of mathematics, it’s a good sign that you’re going senile.'" Steven Cullinane at Log24.com, May 19, 2004:
Posted 5/17/2009 at 9:38 PM |
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Design Theory Laura A. Smit, Calvin College, "Towards an Aesthetic Teleology: Romantic Love, Imagination and the Beautiful in the Thought of Simone Weil and Charles Williams"-- "My work is motivated by a hope that there may be a way to recapture the ancient and medieval vision of both Beauty and purpose in a way which is relevant to our own century. I even dare to hope that the two ideas may be related, that Beauty is actually part of the meaning and purpose of life." Hans Ludwig de Vries, "On Orthogonal Resolutions of the Classical Steiner Quadruple System SQS(16)," Designs, Codes and Cryptography Vol. 48, No. 3 (Sept. 2008) 287-292 (DOI 10.1007/s10623-008-9207-5)-- "The Reverend T. P. Kirkman knew in 1862 that there exists a group of degree 16 and order 322560 with a normal, elementary abelian, subgroup of order 16 [1, p. 108]. Frobenius identified this group in 1904 as a subgroup of the Mathieu group M24 [4, p. 570]...."Olli Pottonen, "Classification of Steiner Quadruple Systems" (Master's thesis, Helsinki, 2005)--1. Biggs N.L., "T. P. Kirkman, Mathematician," Bulletin of the London Mathematical Society 13, 97–120 (1981). "The concept of group actions is very useful in the study of isomorphisms of combinatorial structures."  "Simplify, simplify." "Beauty is bound up
Pottonen's thesis is For some remarks on Click on the above image Posted 5/17/2009 at 7:59 AM |
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Thanks to Jillian's Specials for the following quotation: "... faith is.... validated by individual experience and inspired by epiphanies." -- "Where Physics Meets Faith," by , Oct. 21, 2004 Individual Experience: See, for instance, the link in last Sunday's entry to a remarkable group-theoretic map. Epiphanies: Part I: For Jillian --  (with a nod to Matthew McConaughey and his films Contact and, more recently, Ghosts of Girlfriends Past). Part II: For a mountaineer-- In this morning's news:  (with a nod to Tom Hanks and to Gian-Carlo Rota and the Black Hole of Rome (cf. Psychoshop) as well as to the mountains, both real and imagined, in last Sunday's link "a remarkable group-theoretic map"). Posted 5/15/2009 at 6:29 AM |
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Feds Rescue Mathematical Ponzi Victims     Amen. Posted 5/13/2009 at 10:31 AM |
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Mother's Day at MAA Rick’s Tricky Six Puzzle: Abstract. Rick Wilson identified a sliding block puzzle, the Tricky Six puzzle, in which a uniquely small fraction of the possible scrambled arrangements of the six moving pieces can be restored to the solved state. The permutations one can perform form the abstract group S5, the symmetric group on five letters, but surprisingly they aren't any of the "obvious" copies of S5 in S6 that fix a single point and allow the other five to be permuted arbitrarily. This special S5 comes from the outer automorphism of S6, a remarkable group-theoretic map whose presence is felt in several combinatorial objects. We track down this outer automorphism in the Tricky Six puzzle as well as the projective plane of order 4, the Hoffman-Singleton graph, the Steiner system S(5,6,12), and a couple of error-correcting codes. Meanwhile:
Background: A pair of matronly women
the MAA's Carriage House Posted 5/10/2009 at 6:29 PM |
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Joke "My pursuits are a joke in that the universe is a joke. One has to reflect the universe faithfully." -- John Frederick Michell Feb. 9, 1933 - April 24, 2009 "I laugh because I dare not cry. This is a crazy world and the only way to enjoy it is to treat it as a joke." -- Robert A. Heinlein, The Number of the Beast For Marisa Tomei (born Dec. 4, 1964) -- on the day that Bob Seger turns 64 -- A Joke: Points All Her Own Points All Her Own, Part I: (For the backstory, see the Log24 entries and links on Marisa Tomei's birthday last year.)  Points All Her Own, Part II: (For the backstory, see Galois Geometry: The Simplest Examples.)  Points All Her Own, Part III: (For the backstory, see Geometry of the I Ching and the history of Chinese philosophy.)  In simpler terms: Smackdown!  Posted 5/6/2009 at 11:07 AM |
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Annals of Sacred Geometry (The phrase "sacred geometry" is of course anathema to most mathematicians, to whom nothing is sacred.) From "The Geometric Art of John Michell":  From this morning's New York Times:
Michell, who wrote on Glastonbury (a site associated with King Arthur) and on sacred geometry, seems to have had a better education than most sacred-geometry enthusiasts. He is said to have studied at Eton and at Trinity College, Cambridge. He is not to be confused with an earlier Trinity figure, mathematician John Henry Michell, who died at 76 on the third day of February in 1940. Related material: See the Log24 entry from the date of death of the later Michell -- April 24 -- and, in light of the later Michell's interest in geometry and King Arthur, the Log24 remarks for Easter Sunday this year (April 12). These remarks include the following figure by Sebastian Egner related, if only through myth, to Arthur's round table --  -- and the classic Delmore Schwartz poem "Starlight Like Intuition Pierced the Twelve." Which of the two John Michells (each a Merlin figure of sorts) would be more welcome in Camelot is open to debate. Posted 5/3/2009 at 7:59 AM |
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