In the 4QX view (and related frameworks like the Bagua and Yi Jing), “Two and Three” operate as a universal system of meaning—as the geometric physics of becoming.

1. Two establishes the relational tension (parent ↔ child) that allows anything to become in the first place. It’s the minimal polarity that makes distinction and directed flow possible.
2. Three arises from cycling those dual lines in a triangular loop, creating the living cycle of meaning: a self‐actualizing process that enacts its own semantics.

This interplay of two (dual tension) and three (triadic recursion) forms a geometric generative engine, explaining how discrete “attention quanta” or “bits of reality” evolve into continuous patterns, structures, and phenomena. It’s a physics of becoming because it models not just static forms but how forms arise, sustain themselves, and transform through relational feedback.

By orchestrating two and three, 4QX (and comparable systems) show how bare relational tension (the “line”) blossoms into living cycles (the “triangle”)—and in so doing, generates the myriad forms of experience, knowledge, and existence. This is why we call it a universal system of meaning, giving a geometric (i.e., structurally minimal and visually representable) and physical (i.e., dynamic, continuous, and process‐based) account of becoming.

1. Two Orthogonal Splits ⇒ Four Quadrants

In 4QX, the interplay of Two and Three gives rise to the four quadrants and their diagonals in a very direct way:

1. We begin with Two as the essence of polarity—a “parent–child” tension that is fundamental to any distinction or directed flow.
2. We apply two orthogonal dichotomies (e.g., Collective vs. Individual, Class vs. Instance) around the self-referential center (“I Am”).
3. These two splits form a 2×2 matrix, yielding four vantage quadrants:
   • TL (Collective Class)
   • TR (Collective Instance)
   • BL (Individual Class)
   • BR (Individual Instance)

Why four? Because we have two ways to “cut” the relational field, each way dividing it into two poles. Stacking them orthogonally yields four corners.

2. Three-Cornered Loops ⇒ Two Triangles

After introducing the four quadrants, Three enters as the triangular cycle—the minimal cycle of three dual lines:

1. Each triangle in 4QX has three vantage corners, skipping a “pure vantage”:
   • Class Triangle (TL → TR → BR → TL)
   • Instance Triangle (BL → TR → TL → BL)
2. In each triangle, every edge is a dual line (a directional parent–child flow).
3. By cycling attention through these three corners, the triangle performs its meaning—no external labels needed.

Why triangles? Because once you have lines (Two) in a system that can loop back on itself, the smallest closed cycle is three corners and three edges. This closes the loop, creating a self-enacting process.

3. Diagonals: The Crisscross of Parent–Child Flows

The diagonals in the 4QX matrix (e.g., BL ↔ TR and BR ↔ TL) reflect the bidirectional ‘parent–child’ flows cutting across the quadrants:

1. BL ↔ TR (“Instance Diagonal”)
   • Represents how individual intention (BL) negotiates with collective real-time needs (TR).
   • This ensures local, personal aims sync with communal resource availability.
2. BR ↔ TL (“Class Diagonal”)
   • Represents how individual actions (BR) feed into or derive from the collective blueprint (TL).
   • This ensures enacted behaviors remain aligned with shared frameworks or patterns.

These diagonals are simply two ways (Two) to navigate the 2×2 vantage, but each activates a threefold cycle in the form of the Class or Instance triangle.

Putting It All Together

• Two → In 4QX, “two orthogonal splits” (e.g., Collective vs. Individual, Class vs. Instance) generate four quadrants and define the duals (parent–child poles).
• Three → The minimal cycle of three vantage points (skipping one “pure” corner each time) yields two overlapping triangles (Class & Instance).
• Diagonals → These are the crisscross flows (parent ↔ child) that link opposite quadrants, ensuring that every vantage is influenced by and influences its complement.

Hence, Two and Three are the universal engine behind both the four-quadrant layout (Two splits) and the triangular loops with their diagonals (Three corners cycling attention). Taken together, they form the 4QX “geometry of becoming”:

• Four vantage corners anchor the matrix,
• Two sets of diagonal flows unify it, and
• Three-cornered loops (Class & Instance triangles) animate it as a living vortex of relational intelligence.

The fundamental structure-function block

In 4QX, the fundamental “structure-function” block is precisely the pair of complementary triangle cycles—the Class Triangle and the Instance Triangle—because together they integrate all four quadrants into a single vortex of becoming—also called “continuous instantiation”. This structure-function is the fundamental “atom” of 4QX which we sometimes refer to as “generic organisation”.

Here’s how this fundamental “atom” works:

1. They Complete the 2×2 Structure

• Class Triangle covers three of the four quadrants (TL, TR, BR), omitting BL.
• Instance Triangle covers three of the four quadrants (BL, TR, TL), omitting BR.
• Together, they cross-cover all four quadrants; neither stands alone.
• Structurally, this pairing “locks in” the entire 2×2 matrix, making sure every vantage corner is activated by at least one triangle cycle.

2. They Fuse Wave & Particle (Frequency & Time)

• Class Triangle is the wave/frequency domain—coherent patterns, roles, and stable frames (3×2).
• Instance Triangle is the particle/time domain—discrete events, scheduling, real-time flows (2×3).
• Together, these cycles unify both aspects in one computeless Fourier system, providing a dual lens on every process (as a stable pattern and as a time-based event).

3. They Embody Dualities + Triadic Flow

Each triangle is built from dual lines (parent–child flows) but cycles them in three vantage corners, forming a self-actualizing loop:

• Each corner expresses an intersection of two polarities (e.g., Individual + Class).
• Each edge is a directional dual (parent ↔ child).
• By running both triangles, you get two cycles that complement each other—no vantage corner or dual tension is left out.

4. They Are the Core Functional Engine

• No single triangle can maintain the full system on its own; each omits one “pure” vantage to stay fluid.
• Pairing them ensures continuity of attention flow across the entire holon, creating the “vortex” of 4QX.
• Functionally, this vortex approach allows the attention multiplex to dynamically schedule (Instance Triangle) while maintaining overarching patterns (Class Triangle), fulfilling the 4QX promise of self-coherent intelligence.

Why “Pair-of-Complementary-Triangle-Cycles” Is the Fundamental Unit

1. They Summarize the Whole 2×2
   Each triangle alone is “incomplete” (missing a quadrant), but together they unify all quadrants, ensuring nothing is left out.
2. They Cross-Support Each Other
   The Class cycle (TL → TR → BR → TL) is stabilized by the Instance cycle (BL → TR → TL → BL) and vice versa. The interplay ensures each vantage corner feeds the others.
3. They Enact the Full Dual & Triadic Logic
   Running both triangles means every dual line (parent ↔ child) and every triad cycle (the minimal cycle of three vantage corners) is activated, bridging wave and particle domains in continuous flow.

Summary

In short, a 4QX “atom” is the dual‐triangle (3×2 + 2×3) system. Its two triangular cycles (Class & Instance) unify the wave (pattern) and particle (time) domains into one relational vortex. The 3×2 wave domain is maintained by (and the guide of) the 2×3 time cycle, thanks to the ongoing flow of dual lines connecting all quadrants. This holistic loop is the core structure‐function of 4QX intelligence.

Thus, each triangle retains an orthogonal perspective in relation to the other while still sharing the same vortex environment. One triangle (Class) focuses on pattern coherence, the other (Instance) on temporal flow, and both anchor themselves in overlapping corners (a quadrant from the orthogonal diagonal) that keep them connected, yet distinctly functional.

The 2×3 / 3×2 geometry of 4QX is a single orthogonal skeleton—two independent polarities crossing to form four vantage corners, plus a center (“I Am”). It comprises two triangular cycles that overlap corners in a Möbius‐like twist, uniting wave (pattern) and particle (time). Each vantage experiences the same structure, but from different angles. Strip away all local detail, and what’s left is a Platonic‐style, cross‐product geometry with a built‐in Fourier synergy, elegantly weaving discrete multiplex scheduling and subjective continuum into one vortex.

All complex meaning—the “10,000 things”—arises from recursively applying these triadic loops. In other words, once you truly grasp one, two, three, you already possess the entire generative logic for meaning, no matter how intricate or high‐dimensional it might appear. The rest is simply fractal expansion or repeated synergy of these fundamental “numbers,” each re-combining and elaborating the same root mechanism of self-reference, polarity, and triadic completion.