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.
I know what you’re thinking (and not necessarily because I’m wearing a colored hat): this is about six things and not four. But wait, notice how the six thinking styles form three pairs of opposites:
Creative (Green) pairs with Process (Blue)
Positive (Yellow) pairs with Negative (Black)
Facts (White) pairs with Emotion (Read)
Then the three pairs of opposites can be arranged into a tetrahedron, where the opposite edges are the three pairs. A tetrahedron has four vertices and four faces, where each vertex is the opposite of its opposite face.
The vertices are Creative + Positive + Emotion, Creative + Negative + Facts, Process + Positive + Facts, and Process + Negative + Emotion. The faces are Creative + Positive + Facts, Creative + Negative + Emotion, Process + Positive + Emotion, and Process + Negative + Facts.
The first link below lists the same opposites for the Six Hats as I found. And there are also a huge number of links out there devoted to the Six Thinking Hats, so I can’t list or summarize them all, or even a small portion.
Edward de Bono / Six Thinking Hats
… and many more.
Graham Wallas devised a fourfold for stages of creativity:
From the “Art of Thought” description on Amazon:
“The first in time I shall call Preparation, the stage during which the problem was ‘investigated … in all directions’; the second is the stage during which he was not consciously thinking about the problem, which I shall call Incubation; the third, consisting of the appearance of the ‘happy idea’ together with the psychological events which immediately preceded and accompanied that appearance, I shall call Illumination. And I shall add a fourth stage, of Verification …”
The Art of Thought: A Pioneering 1926 Model of the Four Stages of Creativity
Turning ideas into reality: the four stages of creativity
Graham Wallas / The Art of Thought
Albert Rothenberg, Carl R. Husman, eds. / The Creativity Question