Consciousness as the intrinsic nature of physical structure. A formal framework connecting conscious agents, Markov blankets, and information geometry.
Two influential frameworks address consciousness from opposite directions:
Both describe similar structures — perception-action loops, internal/external boundaries — but no formal bridge connects them.
The functor Θ: Con → MB is a mathematically precise, structure-preserving map between the two frameworks. It shows that:
The position: consciousness is the intrinsic nature of physical structure. Not emergent from it, not separate from it — identical to it, viewed from the inside.
Both frameworks are formalized as monoidal categories. Θ preserves this structure (a monoidal functor).
The consciousness manifold carries a Fisher-Rao metric. Agent configurations are points; transformations are geodesics.
Tononi's Φ measures irreducibility. Zero Φ corresponds to dissociability in the categorical framework.
A structure-preserving map from conscious agents to Markov blanket systems.
Objects are conscious agents $\alpha = (X, G, W, P, D, A)$ — perception, decision, action Markov kernels operating on internal states $X$, actions $G$, and world states $W$.
Objects are Markov blanket systems $M = (\Omega, \mu, B, \eta, K)$ — internal states $\mu$ conditionally independent of external states $\eta$ given blanket $B$.
Click objects and morphisms to explore how consciousness maps to Markov blankets. The functor preserves composition and tensor products.
Particles self-organize into internal, blanket (sensory + active), and external zones. Internal states are conditionally independent of external states given the blanket.
The consciousness manifold $\mathcal{C} = \mathcal{K}(W \times X, X) \times \mathcal{K}(X, G) \times \mathcal{K}(G \times W, W)$ with Fisher-Rao metric. Agent configurations as points, geodesics as natural transformations.
Integrated information $\Phi$ measures irreducibility. The minimum information partition (MIP) is shown as a dashed line. Higher connectivity leads to higher $\Phi$.
Philosophical paper arguing that consciousness is the intrinsic nature of physical structure, with formal foundations in category theory.
Technical paper establishing the formal correspondence Θ: Con → MB with complete proofs of compositional properties.
The P·D·A kernel factorization of a conscious agent implies the Markov blanket property: internal states are conditionally independent of external states given the blanket.
For non-interacting agents: $\Theta(\alpha \otimes \beta) \cong \Theta(\alpha) \otimes_{\mathbf{MB}} \Theta(\beta)$. The functor preserves the monoidal structure.