We seek to develop a deep mathematical understanding of the point potential model. The model is simple to specify — point objects following continuous paths (q, t, s, ds/dt) in linear time and Euclidean 3D space, and the point objects continuously influence each other after a transmission delay. Yet, like Conway’s Game of Life, sometimes semi-stable assemblies form and may move and interact with each other. The emergent assemblies have both common and unique attributes, and we can study ideal isolated assemblies and understand their mathematical dynamics as well. In the unperturbed assembly cases, there may be closed form analytic solutions or useful mathematical techniques. The general chaos case may not lend itself closed form solutions. Our goals must also include pushing the envelope of scale in number of point objects, orders of magnitude in time scale, and orders of magnitude in space scale. I asked Ai for advice on which subjects might address these needs and it named three key areas of interest: Dynamical Systems Theory, Delay Differential Equations, and Control Theory.
Other than leveraging the mathematical areas above, I also want to understand how a simulation could work with precise paths (q, t, s, ds/dt), efficiently, over large scales. By efficiency I mean compute efficiency, storage efficiency, footprint on the channels to memory and parallel processing units. These are important areas. Clearly the techniques will need to be cognizant of the scale of the output and pursue efficiencies for point objects that are slow movers in that scale.
As I noted, there may be many mathematical techniques that apply to various aspects of the point potential universe. These are exciting times.
J Mark Morris : Lynn : Massachusetts
Neoclassical 