Log24

Venn's Trinity

Today is the birthday of logician John Venn.

From the St. Andrews History of Mathematics site:

"Venn considered three discs R, S, and T as typical subsets of a set U. The intersections of these discs and their complements divide U into 8 non-overlapping regions, the unions of which give 256 different Boolean combinations of the original sets R, S, T." 

Last night's entry, "A Queer Religion," gave a Catholic view of the Trinity.  Here are some less interesting but more fruitful thoughts inspired by Venn's diagram of the Trinity (or, indeed, of any three entities):

"To really know a subject you've got to learn a bit of its history…."
— John Baez, August 4, 2002

"We both know what memories can bring;
They bring diamonds and rust."
— Joan Baez, April 1975

For the "diamonds" brought by memories of the 2⁸ combinations described above, consider how the symmetric group S₈ is related to the symmetries of the finite projective space PG(3,2).  (See Diamond Theory.) 

For the "rust," consider the following:

"Lay not up for yourselves treasures upon earth, where moth and rust doth corrupt…."
— Matthew 6:19

The letters R, U, S, T in the Venn diagram above are perhaps relevant here, symbolizing, if you will, the earthly confusion of language, as opposed to the heavenly clarity of mathematics.

As for MOTH, see the article Hometown Zeroes (which brings us yet again to the Viper Room, scene of River Phoenix's death) and the very skillfully designed website MOTHEMATICS.