Process and Space

From the perspective of process, time may be viewed as that which marks the occurrence of change, as previously proposed by this author. In contrast, spatial distinctions may be viewed as enabling the individuation and counting of events generated by processes. Following a conceptual discussion of Whitehead's process theory, temporal distinctions, and spatial distinctions, a formal model of spacetime as history is presented based upon process actions as generators of spacetime, and a new geometric concept of 'thereness' is introduced. Each process action propagates information to the next generation (time) and to a particular 'there' (space). This generates a mixed multigraph where the directed subgraph represents the timelike component (causal propagation of information) and the undirected subgraph represents the spacelike component (informational correlations arising from common causes). A spatial position is an equivalence class of generated events; thus, it is emergent. Each spacetime is local to its generating process, consistent with the concept of local becoming proposed by Arthur. If the set of process actions forms a commutative monoid, then the resulting spacetime takes the form of a discrete lattice. It is speculated that the intransitivity and incompleteness of the spacelike subgraph may be linked to the presence of contextuality.