Higher-Order Morphologies: A Measure for Recurrent Computing

Recurrent computing extends computation through repeated transformation, allowing the outcome of one computational passage to condition those that follow. Yet recurrence raises a corresponding question: how can progression through successive recurrences be characterized without reducing the evolving process to isolated states or scalar measures? This note proposes Morphology Computing (MoCo) as a passage-sensitive perspective in which the relational organization of a system, rather than state alone, is treated as computationally consequential. When morphology at one recurrence participates in conditioning the morphology that follows, successive transformations generate not only changing morphologies but potentially higher-order morphologies: relational organization in the way relational organization itself changes through time. We hypothesize that such higher-order structure may preserve information about direction, coherence, strain, bifurcation, and reorganization that is unavailable from any individual state considered in isolation. On this view, higher-order morphology may provide a basis for assessing recurrent progression without requiring its premature compression into a single scalar metric. The proposal is presented as a testable conceptual framework rather than an established computational measure, with particular attention to the conditions under which morphological trajectories can be distinguished, compared, and falsified.Gemini Notebook podcast here.