The modern world … at least since the time of Descartes … has gotten confortable with the notion that things happen “in” time and space. Everything has its coordinate. Film is just a simulation of what is happening – but in some sense a good simulation: it has the same genus, as it were, as reality itself.
But from a data structure point of view — what a waste! Zillions of addresses, almost all of them empty! What’s it all for? What evidence could there be for all of that? When two things interact, they are coincident. If you have many things interacting, why not represent these interactions as a graph? Sure we can invent a metric space and embed this graph, but just as surely our choices on the lengths of lines, etc., if it is not arbitrary, should depend on the pattern of interactions: we should put groups of things that tend to interact a lot with each other near each other.
But this is the point (no pun intended): the coordinates are logically dependent on the interactions, not vice versa. Indeed, perhaps this point of view can be used to solve some of the conundrums thrown up by modern physics. If you are inducing coordinates from interactions, then large gobs of interactions cannot be arbitrarily placed: the law of large numbers kicks in, and things will be seen to have an “average” place and time with respect to the rest of the system. But presumably you have a lot more freedom in placing individual pieces.
Could this not contain the seeds of an explanation for quantum-mechanical “action at a distance”? When two particles interact, the are coincident. Where should either of them get the information that they are not coincident until one of them has another interaction not shared by the first? Our metric that statistics builds over many interactions might be a fiction when looking at just a few….
Or consider gravity: if you have a big mess of interactions, you will assign it more coordinates. Looking at this from the outside, we might say that as the probability of interacting grows larger, spacetime “bows outward” as modelled by the theory of general relativity…..