The Shining of May 29
by S. H. Cullinane on Wednesday, May 29, 2002
Commentary on Hexagram 29: "K'an represents...
the principle of light inclosed in the dark."
-- Richard Wilhelm, Translation of the I Ching
"How do we explain the mathematical
if not by mathematics?"
-- Rhetorical question of Martin Heidegger,
page 273 of Heidegger's Basic Writings,
edited by David Farrell Krell,
Harper Collins paperback, 1993
Part I: Truth and Beauty
"We acknowledge a theorem's beauty when we see how the theorem 'fits' in its place, how it sheds light around itself, like a Lichtung, a clearing in the woods."
-- Gian-Carlo Rota, page 132 of Indiscrete Thoughts, Birkhauser Boston, 1997
Rota fails to cite the source of his metaphor. It is Heidegger's 1964 essay, "The End of Philosophy and the Task of Thinking" --
"The forest clearing [Lichtung] is experienced in contrast to dense forest, called Dickung in our older language."
-- Heidegger's Basic Writings, cited above, page 441
Part II: An Example
As a mathematical example of Lichtung, we have a volume from the series of books so highly praised by Rota in Indiscrete Thoughts: namely, Schaum's Outline of Combinatorics, by V. K. Balakrishnan, McGraw-Hill, 1995.
As a mathematical example of Dickung, we have Dissemination, by Jacques Derrida (1972), translated and edited by Barbara Johnson, University of Chicago Press paperback, 1981.
Page 342 of the Derrida/Johnson Dickung contains the following assertion, quoted from Numbers, a work by Philippe Sollers (see http://www.obscurantist.net/numbers.html):
"The minimum number of rows -- lines or columns -- that contain all the zeros in a matrix is equal to the maximum number of zeros located in any individual line or column."
When we isolate and destroy this obviously false statement, along with some damned nonsense about Jewish theology that surrounds it, we create (as Heidegger recommends) an opening for truth to appear.
Specifically, the Derrida/Johnson/Sollers falsehood should be replaced by the following truths from Balakrishnan's text:
- Theorem 2.7, pp. 48-49, Philip Hall's marriage theorem
- Problem 2.108, p. 86, The Konig-Egervary theorem
- Problem 2.109, p. 86, Konig's theorem
- Problem 2.129, pp. 95-96, Dilworth's theorem
- Problem 2.130, p. 96, Mirsky's dual of Dilworth's theorem
- Problem 2.135, p. 98, Equivalence of the Konig, Konig-Egervary, Dilworth, and Hall theorems
- Theorem A.10, pp. 186-187, The Ford-Fulkerson theorem
- Theorem A.12, pp. 187-188, Menger's theorem
- Theorem A.13, p. 188, Equivalence of Dilworth's theorem, the Ford-Fulkerson theorem, Hall's marriage theorem, Konig's theorem, and Menger's theorem
Part III: Further Reading
"And the light shineth in darkness;
and the darkness comprehended it not."
-- The Gospel according to St. John,
Chapter 1, Verse 5
For more on the role of mathematics in the ongoing struggle between Light and Darkness, Good and Evil, see Chapter 5, "The Tesseract," in A Wrinkle in Time, by Madeleine L'Engle.
For more on the concept of Lichtung, or "shining," see
- The etymology of the proper noun Phaeton, the suffix -phany, the prefix phen-, the nouns phenomenon and phenomenology, and the proper noun Phoebus.
- The (corrected) etymology of the name Phaedrus in the introduction to the twenty-fifth anniversary edition of Zen and the Art of Motorcycle Maintenance, by Robert M. Pirsig (Morrow paperback, 1999)
- The etymology of the name Adolf (in the context of Pirsig's book, Derrida's book, and philosophy at the University of Chicago)
- The Shining, by Stephen King
"By groping toward the light we are made to realize
how deep the darkness is around us."
-- Arthur Koestler, The Call Girls: A Tragi-Comedy,
Random House, 1973, page 118