From Dichotomy to Complementarity

Yin–Yang, Circular Theory, and the Geometry of Reality

Sungchul Ji, Ph.D. (with ChatGPT assistance)
Emeritus Professor of Theoretical Cell Biology
Ernest Mario School of Pharmacy, Rutgers University, Piscataway, NJ
September 6, 2025

1. The Problem of False Dualisms

Across philosophy, science, and spirituality, we often encounter diagrams or theories that appear dyadic—framed around two irreducible opposites. The yin–yang symbol, for example, is frequently interpreted as a simple dualism: light versus dark, male versus female, yin versus yang.

But here lies a subtle danger. If we stop at two, we risk mistaking dichotomy (opposition without reconciliation) for complementarity (opposition mediated by a unifying third). This distinction is rarely made explicit, yet it profoundly shapes how we think about nature, consciousness, and reality itself.

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2. Two Versions of Yin–Yang [1]

Consider the two most common depictions of the yin–yang symbol [1]:

• Version 1 (Dyadic) (left panel, Figure 1): Two teardrop-like halves—black and white—dividing the circle cleanly. This figure stresses dichotomy: each half is pure, absolute, and wholly opposed.

• Version 2 (Triadic) (right panel, Figure 1): The same two halves, but with a small dot of the opposite color inside each. Suddenly, yin contains the seed of yang, and yang the seed of yin. This introduces a third element—the relational insight that each pole depends on and carries the other within itself.

The first symbol represents dichotomy. The second represents complementarity.

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3. Ilexa Yardley’s Circular Theory

Ilexa Yardley’s Circular Theory [2] provides a parallel. She identifies two elemental states:

• Zero ↔ Circumference (wholeness, potential, boundary)

• One ↔ Diameter (linearity, actuality, definition)

At first glance, this seems dyadic—a simple opposition. But Yardley insists that neither circumference nor diameter can exist independently. Their relationship is embedded in the circle itself, which unites them.

Thus, Circular Theory too moves from dichotomy (0 vs. 1, circumference vs. diameter) toward complementarity (both bound together in the circle).

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4. Mapping Circular Theory into the Irreducible Triadic Relation (ITR)

Your Irreducible Triadic Relation (ITR) [3], inspired by Charles Sanders Peirce, has three roles:

1. Sign – the representation (form, potential)

2. Object – the represented (actual content)

3. Interpretant – the mediating third that unites them in meaning

Seen this way:

• Circumference (0) → Sign

• Diameter (1) → Object

• Circle (relation) → Interpretant

Circular Theory [2] is therefore not dyadic but triadic: the circle itself functions as the indispensable third term.

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5. Mapping into the Geometry of Reality (GOR)

The same holds in the Geometry of Reality (GOR) framework [4], where Reality is projected along three axes:

• Matter/Energy (X-axis)

• Mind/Information (Y-axis)

• Spirit/Consciousness (Z-axis)

Here:

• Circumference (0) → Mind/Information (delimitation, possibility)

• Diameter (1) → Matter/Energy (actualization, linearity)

• Circle (relation) → Spirit/Consciousness (the unifying whole that binds them)

Thus, the circle is not just a shape—it represents the third axis of Reality that prevents collapse into pure opposition.

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6. The Lesson: Always Three, Never Just Two

When scholars fail to distinguish between dichotomy and complementarity, they risk reducing triadic unity to binary opposition. The yin–yang without dots, or Circular Theory [2] seen as “just circumference vs. diameter,” are examples of this flattening.

But the deeper truth is triadic:

• Yin–yang requires the dot of the opposite.

• Circular Theory requires the circle as mediator.

• Reality itself, as articulated in ITR [3] and GOR [4], requires the irreducible triad of sign–object–interpretant, or matter–mind–spirit.

In short: Dichotomy divides. Complementarity unites. Triadicity explains.

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7. Conclusion

The apparent struggle between opposites—yin and yang, zero and one, circumference and diameter—does not resolve within a dyadic frame. Resolution comes only when we recognize the third element: the mediating relation that makes opposition meaningful.

The challenge for contemporary philosophy and science is to move beyond false dichotomies and embrace the triadic structures that underlie nature, mind, and reality itself.

In doing so, we rediscover an ancient truth: the whole is more than two.

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References:

[1] The Taoist philosophy. https://en.wikipedia.org/wiki/Taoist_philosophy.
[2] The Circular Theory. https://philpapers.org/rec/YARTCT-4.
[3] Ji, S. (2018). The Universality of the Irreducible Triadic Relation. In: The Cell Language Theory: Connecting Mind and Matter. World Scientific Publishing, New Jersey. Pp. 377-393.
[4] Ji, S. (2025). Miracle as coupled processes. https://622622.substack.com/p/miracles-as-coupled-processes