What Is a State Space?

A state space $X$ equipped with a transition structure $T: X \to X$ captures the complete information needed to determine a system's future. The general form is:

where $\theta$ are parameters, $u_t$ are control inputs, and $\varepsilon_t$ is noise. Every science studies some version of this structure. What varies is the geometry of $X$, the character of $T$, and the accessibility of $\theta$ and $\varepsilon_t$.

The Classification Axes

Ten orthogonal dimensions characterize any state space. Geometry gives dimensionality. Dynamics gives stochasticity, nonlinearity, and predictability. Epistemics gives observability and controllability. Systems theory gives openness and adaptation. Social structure gives endogeneity and reflexivity. No single axis determines the "difficulty" of a science — it is the combination that matters.

The Developmental Ladder

Fixed → Adaptive → Endogenous → Reflexive. Chemistry occupies mostly-fixed state spaces: the laws of thermodynamics and kinetics are exogenous to the reactions they govern. Biology is adaptive: immune systems learn, neural circuits rewire. Economics is endogenous: the rules of the market emerge from the behavior of market participants. Finance and politics are reflexive: participants' models of the system feed back into the system itself.

This is not a value judgment. It describes the kind of regularity each domain can discover and the style of explanation that works.

Why Contingency Doesn't Disqualify a Science

The boundary conditions of chemistry are contingent on planetary history. The rules of economics are contingent on institutions. Both are still sciences if they identify stable, testable structure within their state spaces. The question is not "are the laws arbitrary?" but "given these constraints, do disciplined regularities emerge?"

Prediction, Explanation, Intervention

Pure prediction is too weak a criterion for science. A black-box correlation may predict without explaining. Science requires robustness under perturbation — which is precisely what the controllability and observability axes capture. A system that is observable and controllable admits experiments; one that is neither admits only observation and narrative.

This Table Is a Synthesis

No single canonical "periodic table of state spaces" exists in the literature. This playground merges ideas from: Poincaré and Gibbs (phase spaces), Bertalanffy (open systems), Ashby (cybernetic feedback), Kalman (observability and controllability), Lucas (endogenous policy regimes), Soros (reflexivity in finance), and second-order cybernetics (observer inclusion). The result is not a final taxonomy but a tool for thinking about what kind of knowledge is possible in what kind of domain.