The Dynamical Topology of Mind: An Ontology of Attractor Basins, Agency, Desire, and Navigation

Abstract

This paper develops a unified geometric ontology in which mind, culture, biological form, and large-scale cosmic structure are treated as dynamical landscapes populated by attractor basins. Attractors are understood as real features of high-dimensional state spaces. Agency is the capacity to read topology and modulate desire; desire is the felt gradient toward compatible basins; much psychological friction is re-interpreted as navigational cost arising from low - affinity engagement or opaque topology. Cultural and technological interfaces are shown to alter accessible topology rather than merely transport agents across a fixed map. A provisional mathematical characterization of affinity is offered in terms of subspace alignment between an agent’s local Jacobian and the stable eigenspace of a target attractor, with persistent homology supplying the multi-scale skeleton of the landscape. Concrete engineering implications and testable hypotheses for representation engineering and human–AI systems are stated. The framework diverges from renunciate treatments of desire and from pure engagement optimization, proposing instead a craft of navigation.