Log24

Wednesday, May 28, 2003

Wednesday May 28, 2003

Filed under: General,Geometry — Tags: — m759 @ 5:55 AM

Mental Health Month, Day 28:

The Eightfold Way and
Solomon's Seal

For a continuation of the mathematical and religious themes in yesterday's entry, click on the figure below.

 

Tuesday, May 27, 2003

Tuesday May 27, 2003

Filed under: General,Geometry — Tags: — m759 @ 5:01 AM

Mental Health Month, Day 27:

Conspiracy Theory and
Solomon's Seal

In our journey through Mental Health Month, we have now arrived at day 27. This number, the number of lines on a non-singular cubic surface in complex projective 3-space, suggests it may be time to recall the following note (a sort of syllabus for an imaginary course) from August 1997, the month that the Mel Gibson film "Conspiracy Theory" was released.

Conspiracy Theory 101
August 13, 1997

Fiction:

(A) Masks of the Illuminati, by Robert Anton Wilson, Pocket Books, New York, 1981.  Freemasonry meets The Force (starring James Joyce and Albert Einstein).
(B) The Number of the Beast, by Robert A. Heinlein, Ballantine Books, New York, 1980.  "Pantheistic multiple solipsism" and transformation groups in n-dimensional space combine to yield "the ultimate total philosophy." (p. 438). 
(C) The Essential Blake, edited by Stanley Kunitz, MJF Books, New York, 1987.  "Fearful symmetry" in context.

Fact:

(1) The Cosmic Trigger, by Robert Anton Wilson, Falcon Press, Phoenix, 1986 (first published 1977).  Page 245 reveals that "the most comprehensive conspiracy theory," that of the physicist Sir Arthur Eddington, is remarkably similar to Heinlein's theory in (B) above.
(2) The Development of Mathematics, by E. T. Bell, 2nd. ed., McGraw-Hill, New York, 1945.  See the discussion of "Solomon's seal," a geometric configuration in complex projective 3-space.  This is as good a candidate as any for Wilson's "Holy Guardian Angel" in (A) above.
(3) Finite Projective Spaces of Three Dimensions, by J. W. P. Hirschfeld, Clarendon Press, Oxford, 1985.  Chapter 20 shows how to represent Solomon's seal in the 63-point 5-dimensional projective space over the 2-element field.  (The corresponding 6-dimensional affine space, with 64 points, is reminiscent of Heinlein's 6-dimensional space.)
 

See also China's 3,000-year-old "Book of Transformations," the I Ching, for more philosophy and lore of the affine 6-dimensional space over the binary field.

© 1997 S. H. Cullinane 

For a more up-to-date and detailed look at the mathematics mentioned above, see

Abstract Configurations
in Algebraic Geometry
,

by Igor Dolgachev.

"Art isn't easy." — Stephen Sondheim

Powered by WordPress