May 7, 2009

Thought of Triad

In the previous post, I tried to categorize my approaches into just three. Here, I shall write why I choose three-fold division.

This kind of triad is sometimes used in order to categorize something important, simply because the triad works out. Trichotomy, which is three-fold division, is known to often work out rather than dichotomy, because it can capture the complex relations. But you may wonder why three is special than other numbers like two, four, or five.

As an answer, Charles S. Peirce, who was an American philosopher and emphasized the significance of trichotomy, pointed out as follows;

"The reason is that while it is impossible to form a genuine three by any modification of the pair, without introducing something of a different nature from the unit and the pair, four, five and every higher number can be formed by mere complications of threes."
* Charles Sanders Peirce, "A Guess at the Riddle" in The Essential Peirce: Selected Philosophical Writings Volume 1 (1867-1893), Edited by Nathan Houser and Christian Kloesel, Indiana University Press, 1992. p.251

Borrowing the metaphor by Peirce, dyadic relation is similar to direct unforked road. It is impossible to obtain third termination by extending the existing termination of dyad. It can provide only the extension as a chain. The extension of triad, however, can increase the number of termination, then  we can make the relation more complex like a network.

Recall also the three-body motion discussed by Henri Poncare. Although two bodies shows periodic motion, the motion of three-bodies becomes chaotic. It means, so to speak, three is the minimum number to bring complex dynamism into the world. This seems to be a quite interesting idea about the source of creativity. Creativity must need a kind of dynamism rather than equilibrium. Of course, this is just an intuition, so it wants more discussions. I want to keep considering three-fold division as a source of creative dynamism.

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