Chapter 1: Spacetime

Ex Nihilo

The tension between infinite and Euclidean geometries is a conceptual subtlety. Logic dictates that the apparent presence of a paradox is evidence of an error in reasoning. It is most definitely not evidence that reality itself is paradoxical. And yet the void is infinite, while the four dimensions of space and time are decidedly Euclidean. Theoretical or not, this tension is real. The entities to which this tension applies are dimensionless, infinitesi- mal points—the fundamental elements of any geometry. Being infinitesimal, a point has no mass, no size, no extent of any kind. It is, at least from a Euclidean perspective, non-existent, a mere abstraction. And so, whether or not it makes any sense to say so, it would require no effort to move such an entity. Having no mass, no force is required to push a point around. Or again, having zero mass, a zero force would suffice to move a point, particularly if we had an eternity over which to apply such a force. And, as luck would have it, we have exactly the right force for the job—the theoretical tendency of points to merge in order to reconcile the contradiction between infinite and Euclidean geometries.

The tension between points in the void is purely conceptual, a zero force. However, given that the entities to which this force applies are also purely conceptual and have zero mass, and that an infinite temporal span is available over which to apply this force, it is not only possible, but absolutely certain, that points will gradually coalesce. Though this tension is apparently non-existent, so too are the points to which it applies. In essence, eternity transforms nothing into something, just as it turns something into nothing. Infinite time and infinite space come together and give rise to spacetime, the fundamental substance of reality.

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