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From Fluid to Braid: A Relational-Ontological Model of Value and Power, and Its Computational Horizon

Year: 2026
Type: article
Abstract: We develop a formal model of how value and power circulate in relational systems, and use the model's internal failure to motivate a stronger one. Beginning from a fluid-dynamical description in which value is a non-conserved flow and power is a gradient driven by the history of that flow, we prove a structural result: the appropriative component of value transport—the part driven by a scalar potential—contributes nothing to circulation, so that the holonomy of the value field (its net generation around a closed relational loop) can arise only from non-appropriative sources. This vindicates, in exact form, the thesis that genuine relational value is non-possessive. We then argue that the fluid model is ontologically self-undermining. Fluid dynamics presupposes a fixed background space and a conservation law; a relational ontology—one on which relations are prior to the entities they relate—requires neither, and the non-conservation of value (its genuine emergence and extinction) forbids the conservation law outright. We diagnose the underlying split: entity-first formalisms (graphs, neural dynamics) get the dynamics right (emergence, causal asymmetry, plasticity) but the ontology wrong; fluid formalisms get the ontology right (form as the secondary condensation of a prior flow) but the dynamics wrong (conservation, no causal attribution). We resolve the split by relocating the formalism onto the braid group and its unitary representations. Subjects become topological excitations of a relational field; their identity is topological rather than substantial; power becomes the non-commutativity of braiding; resonance-without-fusion becomes a non-trivial fusion space; and generativity becomes multi-channel fusion. We prove that the normative discriminating power of the model requires the chosen representation to be non-abelian yet non-universal: universality (the capacity to compute anything) destroys the capacity to discriminate good from bad circulation. Finally we locate the model's computational horizon. Reservoir computing and morphological computing retain an entity-first residue (an external readout); a fully relational model of computation identifies computation with the holonomy of braiding itself. We close by noting that topological protection captures only the relational skeleton of value; its local, incommensurable flesh is the protected remainder, and we conjecture that the good is the appropriate proportion of the two.
DOI: 10.17613/j9kjd-vce60
Language: English
Subfield: Philosophy
Open Access status: gold
OpenAlex ID: W7166350119
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