Triad or Tetrad?


Difference emphases on either the three or the four can be found within varying cultures, the beginnings of which are lost in the sands of time.

Although scientists move away from the quantitative view toward the qualitative view and acknowledge the validity of both positions, the dilemma of three and four is by no means resolved – its beginning is lost in antiquity and its end is not yet in sight. As to its beginning, Jung says that number helps more than anything else to bring order into “the chaos of appearances…primitive patterns of order are mostly triads or tetrads,” and he points to I Ching, Book of Changes:

“…the experimental basis of classical Chinese philosophy…one of the oldest known methods for grasping a situation as a whole and thus placing the details against a cosmic background – the interplay of Yin and Yang… there is also a Western method of very ancient origin which is based on the same general principle as the I Ching, the only difference being that in the West this principle is not triadic but, significantly enough, tetradic…”

He refers also to the alchemists’ tackling of the problem of three and four, seeing the dilemma stated in the story that serves as a setting for the Timeaus and extending all the way to the “Cabiri scene in Faust, Part II…recognized by a sixteenth-century alchemist, Gerhard Dorn, as the decision between the Christian Trinity and the serpens quadricornutus, the four-horned serpent who is the Devil.”

Of course western religion and culture has been based on the tension between the three and the four, both being primary factors in the Holy Scriptures. The four is stated outright: YHVH, even translated into English as a four-letter word, LORD. The three is implied in the three visitors to Abrahm, the Christian Trinity, etc. Returning to alchemy’s approach of the problem, Preston Harold says:

Wolfgang Pauli discusses the controversy between Johannes Kepler, discoverer of the three famous laws of planetary motion, and Robert Fludd, in his day a famous alchemist and Rosicrucian. Pauli says that Kepler’s ideas “represent a remarkable intermediary stage between the earlier, magical-symbolical and the modern, quantitive-mathematical descriptions of nature,” indicating a way of thinking that produced the natural science which today is called classical. Kepler, a devotee of Euclid’s geometry, insisted upon strict mathematical methods of proof. His premise was that “Mathematical reasoning is ‘inborn in the human soul’…” His is a trinity-concept, his symbol “contains no hint of the number four or quaternity.” Fludd, however, was a mystic with great aversion to all quantitative mensuration: “It is significant for the psychological contrast between Kepler and Fludd that for Fludd the number four has a special symbolical character, which, as we have seen, is not true of Kepler.” Fludd drew his inspiration from Moses, and he brilliantly defends his stand on the nature of the soul. Kepler, however, appears to best him in all scientific argument until one realizes that Kepler considered the quantitative relations of the parts to be essential while Fludd considered the qualitative indivisibility of the whole. Pauli says, “modern quantum physics again stresses the factor of the disturbance of phenomena through measurement,” as Fludd (and Goethe) insisted upon. He concludes that the only acceptable point of view appears to be one that recognizes both the quantitative and the qualitative, “the physical and the psychical” as compatible, embracing them simultaneously.

This attitude eases the argument, but it does not resolve the dilemma of three and four, as may be seen in a mathematician’s explanation of continua.

We will explore this mathematical explanation in our next post. Until then, peace.


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