Angel Bayona: 🌰🐿️ The Seed of MetaOntdy

The Seed of MetaOntdy | Tensorial Approach to Systems

I brief first story about MetaOntdy - It will be an accumulative notebook

Context

Before of this articles:

Symbols Are All You Need — A Bridge Between MetaOntdy Part 1 and Part 2

https://angel-bayona.blogspot.com/2026/03/symbols-are-all-you-need.html

The MetaOntdy Lens: Internal Mechanics and Ecosystemic Pressures — Re-Engineering Specialization

https://angel-bayona.blogspot.com/2026/03/the-metaontdy-lens-internal-mechanics.html

It was this:

🤯 Abordaje Tensorial de Sistemas Complicados, Híbridos y Complejos: Ontología, Epistemología y Modelado Cognitivo (October 2025)

https://angel-bayona.blogspot.com/2025/10/abordaje-tensorial-de-los-sistemas.html

Disclaimer: this article is just divulgative, some error or horrors could be presented, anyway..

This article from October 2025 was the first serious attempt to build a language for what would later become MetaOntdy (back then at some point, I called it Ontodynamics). The goal was ambitious: to find a unified way to talk about any system—a rock, a cell, a human, an AI—without collapsing their differences, but also without treating them as completely separate universes.

The tool I reached for was tensorial notation. Not because systems are literally tensors in the physics sense, but because tensors offer a way to represent structured relationships between different kinds of properties. It was an attempt to give ontology a semi-formal handle.

Looking back now, after the work on symbols, narrative resilience, and the AGI 0.25/0.5/1.0 distinction, I can see exactly where the seed was planted.

The Core Intuition: Systems Have Layers of Being

The article proposed that any system could be understood through a combination of fundamental "tensors." For a Complicated System (like a machine or a rock), the definition was simple:

$S_{c} = (T_{1}) + D \otimes (T_{2})$

$T_{1}$ (Structural Configuration Tensor): The physical "what it is." Its components, its hardware.
$T_{2}$ (Latent Emergent Properties Tensor): The potential "what it could do." Its capacity to couple with other systems.
$D$ (Design Intentionality Factor): The "why" or "for what purpose" it was made. This could be human design, evolutionary pressure, or even a synergistic pattern.

The key was the Categorical-Gradient Cascade for $D$ : first, you classify the kind of intentionality (ontological category), and then you measure its degree or sophistication (epistemic gradient). This was an early attempt to handle the fuzzy boundary between what a system is and how we know it.

For a Hybrid System (a living being, a society, a sophisticated AI), the notation exploded in complexity to account for life, symbols, order, and chaos:

$S_{h} = (T_{3}) + (D_{h}) \otimes (T_{4}) + (C_{1}) + (L_{b} \otimes C_{2}) + (L_{s} \otimes C_{3}) + α (C_{2} \otimes C_{3}) + p (C_{4}) + κ (C_{5}) + β (C_{4} \otimes C_{5})$

This messy equation was trying to say something important: a hybrid system is not just a complicated one plus a "soul." It's a layered integration of:

A material base ( $T_{3}, T_{4}$ ).
Internal states ( $C_{1}$ ).
Biological and symbolic life ( $L_{b} \otimes C_{2}, L_{s} \otimes C_{3}$ ) and their synergy ( $α$ ).
Order and predictability ( $C_{4}, p$ ).
Chaos and creativity ( $C_{5}, κ$ ).
And the deep coupling of order and chaos ( $β \cdot C_{4} \otimes C_{5}$ )—which I called Deep Agency and Ontological Resilience.

What This Early Framework Got Right (The Seed)

The Hybrid is Universal: The article insisted that "hybrid" isn't just for humans. An ecosystem, a culture, even a cosmological model could be analyzed as an $S_{h}$ . Agency, it argued, is a phenomenon of integrating vitalities, not a property of a specific substrate. This is a cornerstone of MetaOntdy.
Agency as Order- Chaos Coupling: The idea that resilience and deep agency emerge from the dynamic interaction between predictable patterns ( $C_{4}$ ) and creative novelty/chaos ( $C_{5}$ ) is directly ancestral to my later work on narrative resilience and the function $ρ$ (rigidity). A system that is all order is rigid; one that is all chaos is incoherent. The magic is in the coupling, $β \cdot (C_{4} \otimes C_{5})$ .
Multiple Epistemologies: The article listed many ways to know a system (structural, emergent, hermeneutic, transitional...). This was an early acknowledgment of the onto-epistemic gap that became the starting point for Part 1 of MetaOntdy. We don't have one single window into reality; we have many, each revealing a different aspect of the system's being.
The Complex as a Limit Case: It defined the "Pure Complex System" ( $S_{c p}$ ) not as a separate category, but as a limit case of the hybrid—a system where the material base ( $T_{3}$ ) becomes minimal or distributed, but never disappears. This echoes the "polygon" metaphor: complexity is an approximation that never reaches a perfect, disembodied circle (Symbols Are All You Need thesis).

What Was Missing (And Why Symbols Are All You Need thesis Was Necessary)

Reading this now, I see the ambition and the flaw. The framework was too heavy. It tried to model everything with tensors, but it didn't have a clear operator—a fundamental unit of cognitive work.

The tensors described what was there, but not how a system actually navigated its own complexity.

That's where the symbol came in.

The "Movil Vegetalt" exercise was the stress test that revealed this gap. To model the plant's decision to move, I didn't need a tensor for every possible property. I needed to understand how it represented its world (with symbols as compression), how it strung those symbols together into a narrative of threat or opportunity, and how it used that narrative to act.

The symbols became the missing first-order operator ( $L_{1}$ ) that makes all the higher-order complexity ( $L_{2}$ models, $L_{3}$ theories) possible. The tensors from 2025 were trying to describe $L_{2}$ and $L_{3}$ without first grounding them in $L_{1}$ . The tensors were polygons without a clear circle.

The Evolution into MetaOntdy

So, the journey from this October 2025 post to the March 2026 formalization was one of finding the right primitive.

From $C_{4} \otimes C_{5}$ (Order-Chaos coupling) to $ρ$ (Rigidity function): The intuition about resilience being a dynamic between stability and change became a formal, measurable property of symbols. $ρ (σ)$ tells you how crystallized or revisable a symbol is.
From $L_{s} \otimes C_{3}$ (Symbolic Life) to $Σ$ (Operative Symbols): The vague notion of "symbolic life" became the concrete set of symbols $Σ$ that an agent actually uses to operate.
From $D$ (Design Intentionality) to $ϵ_{g r o u n d i n g}$ (Grounding Error): The question of a system's origin (human-designed vs. self-built) became a quantifiable part of its epistemic error. This is the heart of the AGI 0.5 vs. 1.0 distinction.
From Multiple Epistemologies to Categorical Functors ( $F_{δ}, F_{E}$ ): The different "ways of knowing" are now elegantly mapped as transformations between the internal level-structures of different cognitive agents.

The 2025 article was me trying to build a map of the territory.
The 2026 formalization, via the plant, realizes that what we need is a theory of the mapmaker—and the mapmaker operates with symbols.

Why This Seed Matters

This old article, in its dense and slightly chaotic notation, contains the DNA of everything that came later. It shows that the core questions have been consistent for months:

How do we model systems that mix hardware and "wetware," structure and meaning?
What is the nature of agency and resilience?
How do we bridge the gap between what a system is and how we know it?

The "Tensorial Approach" was the first pass. It was too complicated because the problem is complicated. The breakthrough was finding the right level of simplicity—the symbol—from which the complexity could be rebuilt in a cleaner, more powerful way.

The tensors were the scaffolding. The symbol is the foundation.

Updates:

Next on April 2026