What Is a Model?
A clarification of structure, representation, and explanatory function
The previous essays have emphasized that both understanding and control require models. This raises an apparently simple but conceptually dense question: what, precisely, counts as a model? The term is used across scientific practice, cognitive science, cybernetics, and philosophy, often with subtle differences in meaning. A clear account helps unify these domains and situates the Axio framework within a broader landscape of representational theory.
Models as structured representations
At the most general level, a model is a structured representation of some domain. The structure preserves distinctions and relations that are relevant to a particular explanatory or regulatory task. A model need not resemble the domain visually or materially; it must simply encode enough structure to support correct inferences about the domain’s behavior.
This understanding encompasses a wide range of representational forms:
Mathematical formulations (e.g., Newtonian mechanics)
Computational simulations
State–transition systems
Statistical or probabilistic models
Neural representations
Conceptual frameworks used in cognitive interpretation
What unifies these cases is not their format but their function: each provides a mapping from situations to expectations.
Fidelity, abstraction, and purpose
A model is not required to duplicate every aspect of the system it represents. Instead, it abstracts away irrelevant detail while preserving the features needed for the task at hand. The London Underground map preserves connectivity rather than geography. Classical mechanics preserves predictive accuracy for moderate speeds but not for relativistic conditions.
Thus, the adequacy of a model is always relative to a purpose. A model may be adequate for short-term prediction yet inadequate for long-term inference; adequate for coarse-grained regulation but inadequate for fine-grained control. Models earn their status by enabling appropriate action or explanation within their domain of use.
Implicit and explicit models
Not all models are explicit. A biological organizm may embody a model in its structure without representing it conceptually. Enzyme pathways regulate cellular processes according to the chemical regularities they have evolved to exploit. Neural circuits encode regularities of the sensory world without expressing them symbolically. These are implicit models, realized physically rather than linguistically.
Explicit models, by contrast, are constructed deliberately: mathematical theories, simulations, and conceptual frameworks. Scientific modelling often involves refining explicit models to achieve greater explanatory coherence or predictive accuracy.
Generative and predictive structure
A defining feature of a model is its ability to generate expectations. Given a hypothetical or observed state of the system, the model yields predictions—probabilistic or deterministic—about how that state will evolve or how the system will respond to interventions. This functions as a generative mechanism: a set of rules or relations that map inputs to outputs.
This criterion distinguishes models from mere lists of observations. A dataset, by itself, has no generative capacity. A model, however, supplies the relational structure that enables prediction and explanation.
Compression and generalization
Models often compress information, capturing regularities in a more compact form. Compression facilitates generalization: the ability to apply learned structure to novel cases. Although compression is not strictly necessary—lookup tables can function as minimal models—it is typically advantageous in complex environments where the state space is large.
The absence of compression limits generalization. A lookup table can only respond to states it has already encoded. A compressed model that captures underlying patterns can extend its predictions beyond observed cases.
The role of interpretation
When discussing agents, models also appear in an interpretive role. Attributing beliefs, desires, or intentions involves constructing a model of the agent’s behavior at a conceptual level. These interpretive models are not part of the agent but guide our understanding of it. They belong to a different representational layer than the agent’s own regulatory architecture.
Models in the Axio framework
Within Axio, models serve as the foundational apparatus for understanding, regulating, and interpreting systems. Conditionalism treats all empirical claims as conditional on background models. The Quantum Branching Universe framework uses models to define vantage, measure, and expectation. The study of agency relies on models to understand how agents act coherently within environments.
Conclusion
To ask what a model is, in this context, is to recognize that models are the means by which structure is extracted, organized, and used. They are representational frameworks—implicit or explicit—that preserve relevant distinctions and enable prediction or control. Their adequacy is measured by their coherence, their capacity for generalization, and their success in guiding action or explanation.
Understanding what a model is clarifies why cognition, science, and agency all depend on them. A system without a model cannot anticipate, explain, or regulate; a system with a model gains the ability to interpret and act within the world.