Considering vector spaces..
1. Temporal Flows as Vectors: Each temporal flow F_i(t) can be thought of as a vector in a multidimensional temporal space, with the vector's magnitude and direction capturing the intensity and "movement" of that particular flow. 2. Temporal Rates as Vector Sums: The overall temporal rate R(t) can be expressed as the sum of the weighted temporal flow vectors: R(t) = Σ w_i * F_i(t). This vector sum represents the combined influence of the various temporal flows, with the weights w_i determining their relative contributions. 3. Emergence of Dimensions as Vector Spaces: The spatial dimensions D(t) that emerge from the temporal flows can be viewed as vector subspaces within the broader temporal vector space. The equation D(t) = Σ (w_i * F_i(t)) suggests that each dimension arises as a projection or linear combination of the temporal flow vectors, with the weights w_i determining the "directions" of these dimensional subspaces. 4. Gravitational Field Tensor as a Vect...