A Generalised Heterogeneous Dynamical Network and a Spinfoam Model of Knowledge Emergence and Evolution

Accounts of how knowledge spreads ordinarily treat difficulty as loss in transit, and take the ideal case to be one in which what arrives is what was sent. On a relational account that ideal is incoherent: what a party holds is reconstructed from the representations available to it under the interpretation it holds, so what crosses between parties is a perturbation and heterogeneity is primitive. This paper provides two preliminary formal models of knowledge emerging from dynamics over heterogeneous structures. The first couples components whose state spaces differ in structure and in whether they carry a metric, whose laws differ in kind, and whose events are their own, by propagation operators that carry occurrences and presuppose no common space; a coupling is itself a component with a state of its own, and a coupled assembly is a component of the same class under stated conditions. The second takes the combinatorial structure of spin foam models and reassigns it: faces are the histories of primitive elements, edges are couplings persisting across intervals, vertices are events at which couplings rearrange, and a boundary is a state, so that a history is a two-complex whose one-dimensional shadow is a record of transitions between identified states. The justification for the physical borrowing is background independence, which this account requires twice, and the amplitudes that carry the physical content are declined with the reason given. Knowledge is located within a design: for a party it is the set of couplings surviving reconstruction under every perturbation that party can undergo, for a pair it is an invariant of the coupled system that belongs to neither component, and at an event it is the couplings present after it and absent from everything it received. The definitions yield tests. Deleting a coupling settles whether a capacity belongs to a party or to the coupling; a difference between two sets of couplings settles whether a causal attribution was made at an event or carried through it, which gives the construction of a social fact an operational form. The models also expose a commitment the account had carried unnoticed: a weight over histories presupposes recurrence, while an account holding interpretive conditions to be historically produced is committed to the singularity of a trajectory, so the position itself withholds the dynamics such a weight would require. A news-reporting case runs through both models and a simulation exhibits the design.