My last post made me realize that I had written about six-fold things several times before. The first time was about Richard McKeon’s Aspects of Knowing, the second was about Vaughan Pratt’s Duality of Information and Time, and now we have Edward de Bono’s Six Thinking Hats.
For each of these schema, three pairs of opposites can be shown on the edges of a tetrahedron. I have previously written about the Alchemical Marriage of Opposites, where I imagined two pairs of opposites being in a fourfold. With this new common design, I see that three pairs of opposites can label the vertices of a tetrahedron. In fact, this may be at least as common as double dualities, and I have found several triple dualities to write about in the near future.
In algebraic notation this triple marriage of opposites yields:
(A + A’)(B + B’)(C + C’) = (ABC + A’B’C’) + (AB’C’ + A’BC) + (A’BC’ + AB’C) + (A’B’C + ABC’)
I might even call this diagram a “Ménage of Opposites”, but ménage of course merely means household. Appropriate, nonetheless.
This diagram also represents four pairs of opposites.