What is Intelligence? A Cycle Closure Perspective

What is intelligence? We argue for a structural-dynamical account rooted in a topological closure law: \emph{the boundary of a boundary vanishes} (${\mathrm{\partial }}^2=0$). This principle forces transient fragments to cancel while closed cycles persist as invariants, yielding the cascade ${\mathrm{\partial }}^2\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}0\Rightarrow \text{cycles (invariants)}\Rightarrow \text{memory}\Rightarrow \text{prediction (intelligence)}$. Prediction requires invariance: only order-invariant cycles can stabilize the predictive substrate. This motivates the $\mathbf{\text{Structure-before-Specificity}}\mathbf{\text{(SbS)}}$ principle, where persistent structures ($\mathrm{\Phi }$) must stabilize before contextual specificities ($\mathrm{\Psi }$) can be meaningfully interpreted, and is formalized by the $\mathbf{\text{Context-Content}}\mathbf{\text{Uncertainty}}\mathbf{\text{Principle}}\mathbf{\text{(CCUP)}}$, which casts cognition as dynamic alignment that minimizes the joint uncertainty $H(\mathrm{\Phi },\mathrm{\Psi })$. We show that $\mathbf{\text{Memory-Amortized}}\mathbf{\text{Inference}}\mathbf{\text{(MAI)}}$ is the computational mechanism that implements SbS,$\to$,CCUP through dual bootstrapping: \emph{temporal} bootstrapping consolidates episodic specifics into reusable latent trajectories, while \emph{spatial} bootstrapping reuses these invariants across latent manifolds. This framework explains why \emph{semantics precedes syntax}: stable cycles anchor meaning, and symbolic syntax emerges only after semantic invariants are in place. In an evolutionary perspective, the same closure law unifies the trajectory of natural intelligence: from primitive memory traces in microbes, to cyclic sensorimotor patterns in bilaterians, to semantic generalization in mammals, culminating in human symbolic abstraction by natural language. In sum, intelligence arises from the progressive collapse of specificity into structure, grounded in the closure-induced emergence of invariants.