Craig Feinstein
Registered: Nov 2004
Posts: 36 
The Fano Plane, Numerology, Physics, and NKS
When I was first introduced to the Fano Plane http://en.wikipedia.org/wiki/Fano_plane
in college, it seemed to me that there was something about this abstract object that is very beautiful and special. A beautiful symmetry seems to be optimally compressed into the Fano plane.
7 points.
7 lines.
3 lines per point.
3 points per line.
Every two lines intersect in one point.
Every two points intersect in one line.
Also, there are 168 ways of permuting the points so that none of the lines are disturbed and 168 ways of permuting the lines so that none of the points are disturbed.
The number 168 is special in that 168 = 7 x 24, the number of hours in the week. The Babylonian Talmud describes a popular system of ancient Babylonian astrology in which each of these 168 hours gets assigned one of the seven planets known to man in ancient times (Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn) See http://math.ucr.edu/home/baez/week214.html for a demonstration of how this astrological system explains the origin of the modern English names of our sevenday week.
The ancient book, Sefer Yetzirah, separates the letters of the Hebrew alphabet into three categories: 3 Mothers, 7 Doubles and 12 Elementals. Multiply these numbers together and you come up with 7 x 12. Multiply this by two (because the seven _Doubles_) and you get 168 = 7 x 24.
These three numbers 3, 7, and 12 seem to play a special role in Western Civilization. In music, a chord is composed of 3 notes, a scale is composed of 7 notes, and the number of notes is 12. (Other cultures have a different system, for instance there are Oriental cultures which use scales of 5 notes.)
I have a guess that the Ancients were familiar with the Fano plane and their numerology and astrology was somehow based upon the Fano plane, but I cannot prove this; it's just a hunch.
So why am I posting this here in a science forum? Because I am wondering if anyone has tried NKS experiments which make use of the Fano plane. Wolfram's idea that the universe can be explained by very simple rules in a discrete universe seem very intriguing. And because our universe is a naturally esthetically beautiful universe (with lots of symmetry, which in my opinion is the reason for its esthetic beauty), I propose that the simple rules of the universe which Wolfram hypothesizes about in NKS should also be esthetically beautiful.
So because the Fano plane is so esthetically beautiful, would not the Fano plane be a good place to look for the basic rules of our universe? What have we got to lose?
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Craig
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