Why Three Must Emerge

There's a remarkable paper by Luis Cisneros which shows that when anything differentiates, it follows an inevitable three-stage pattern:

1. Binary Opposition: The initial split. A quantum state collapses into one outcome or another. A stem cell divides into two daughter cells. Matter separates from antimatter. This creates maximum tension with two things pulling apart and nothing between them.
2. Triadic Closure: The system can't stay binary. Almost instantaneously, a third element emerges, forming the first stable configuration. Three quarks bind into a proton. Three primary colors span our visual perception. A triangle is the first closed shape.
3. Circular Enclosure: As differentiation continues recursively, the system approaches circular or spherical organization: electron orbitals, cell membranes, planetary orbits. This is the limit structure, the most efficient possible configuration.

Why Binary Systems Fail

At the most elementary physical level, binary differentiation already reveals its own insufficiency. A two-state quantum system prepared in superposition:

$$\lvert \Psi \rangle = \frac{\lvert \uparrow \rangle + \lvert \downarrow \rangle}{\sqrt{2}}$$

carries one full bit of unresolved information prior to measurement. When measurement occurs, the system undergoes irreversible decoherence through coupling with the environment. Tracing out the environmental degrees of freedom produces an entropy increase which corresponds to a real energetic cost by the Landauer bound:

$$\Delta E_{\text{diss}} \ge k_B T \Delta S.$$

After environmental degrees of freedom are traced out, this dissipated energy does not disappear; it reappears as an increase in the system’s internal interaction energy:

$$\Delta E_{\text{diss}} \equiv \Delta E_{\text{int}}.$$

For a two-particle system with no internal structure, the Hamiltonian must reduce to a pairwise interaction term. Generically:

$$H_{\text{int}} = \lambda \, V(A,B)$$

The simplest, rotationally invariant choice is quadratic separation:

$$V(A,B) = \lVert A - B \rVert^2$$

So the only possible place for the irreversibly generated energy to live is

$$E_{\text{int}} = E_{\text{binary}} = \lambda \lVert A - B \rVert^2$$

where one bond carries all the potential energy.

But three particles following the Fermat-Torricelli point (where each angle is 120° distribute that same force across three bonds:

$$E_{\text{triadic}} = J(\sigma_1 \cdot \sigma_2 + \sigma_2 \cdot \sigma_3 + \sigma_3 \cdot \sigma_1)$$

For equal total constraints, the optimization gives:

$$E_{\text{triadic}} = 3J \cdot \cos(120^\circ) = 3J \cdot (-1/2) = -3J/2$$

versus binary:

$$E_{\text{binary}} = \lambda$$

The coupling constants relate as: $$J \approx 0.53\lambda$$ due to geometric distribution, yielding:

$$E_{\text{triadic}}/E_{\text{binary}} = (-3 \times 0.53\lambda/2)/\lambda \approx 0.8$$

$$E_{\text{triadic}} \approx 0.8E_{\text{binary}}$$

A 20% reduction in energy, which comes from three bonds sharing the load at optimal angles versus one bond bearing it all.

The Physics of Love

Augustine (354–430 AD) spent decades trying to understand love, and in his masterwork De Trinitate, he realized that love itself requires three:

1. The Lover (the one who loves)
2. The Beloved (the one loved)
3. Love itself (the relationship between them)

You can't have love with just one person as there's no one to love. But you can't have it with just two either. Binary relationships without a shared third often become toxic because all the energy of the relationship becomes concentrated in one bond.

Augustine saw that perfect, truly generous love cannot be just the lover and beloved, but that the love between them must have its own reality. Lovers A and B must love each other through their shared love of C.

Here, the stress distributes across three relationships and thus the lovers find their love strengthened not despite the third, but because of it.

And this is exactly what happens in physics. Energy concentrated is unstable. Energy distributed is stable.

Why Three Specifically?

Because the universe was created by the Trinity.

Not just in some abstract sense, but through the Logos, the Second Person of the Trinity, the Word through whom “all things were made” (John 1:3). And the Logos is inherently relational: He's the Son proceeding from the Father, breathing forth the Spirit. His very being is triadic communion.

When the Logos creates, He imposes His own relational structure on matter.

The Christological Center

The infinite-finite gap is unbridgeable in binary terms:

$$ \text{God (infinite)} \;\xleftrightarrow{\text{impossible}}\; \text{Humanity (finite)} $$

But the Incarnation itself is triadic:

$$ \text{God (infinite)} \;\xleftrightarrow{\text{Christ}}\; \text{Humanity (finite)} $$

This is why Aquinas says the Incarnation was “fitting.” It follows the pattern God has written into creation itself. And this is why Christ's saving work succeeds.

The energy of divine life flows to us through the Mediator. Not in one impossible leap (infinite voltage would destroy us), but mediated through the God-Man who distributes the “stress” across His two natures.

Binary theology fails. Attempts to relate directly to transcendent deity without mediation collapse into either rationalism (claiming self-sufficiency) or despair (recognizing impossibility).

Triadic theology works. The Father sends the Son in the Spirit. We approach the Father through the Son in the Spirit. Circulation. Mediation. Stable communion.

The Eschatological Circle

Finally, Cisneros shows the progression ends in circular enclosure, spherical organization, maximal symmetry, optimal flow:

$$\lim_{n \to \infty} \delta_e^n(\Omega) \to S^2$$

As differentiation recurses infinitely, it approaches spherical topology. This isn't arbitrary.

This is the Beatific Vision.

In City of God (XXII.29), Augustine describes the blessed in heaven arranged in perfect fellowship all facing the center (God), all facing each other (communion of saints), perfect circulation of love with minimal loss.

The universe begins from the Trinity (undivided whole), differentiates through triadic structures (creation), and returns to Trinitarian communion (eschatological completion).

$$\text{Binary → Triadic → Circular}$$

isn't just physics. It's salvation history.

Conclusion: The Universe is a Love Letter

What Cisneros has shown mathematically, and what Augustine and Aquinas knew theologically, is that the structure of stable being is the structure of perfect love, and both are triadic because God is Trinity.

The universe isn't just created by the Triune God. The universe is patterned on the Triune God. The thermodynamics of love are the thermodynamics of physics because the God who is Love created physics as a reflection of His own nature.

So next time you see a triangle, notice three people sharing a moment, or think about quarks binding in triplets, remember: you're seeing the Trinity.

For since the creation of the world God’s invisible qualities have been clearly seen, being understood from what has been made, so that people are without excuse.

— Romans 1:20 (NIV)