In a digital image, resolution is measured in pixels. At a given ground scale, the less pixels are used to represent an object, say a building in a satellite image, the less detail can be perceived. A high resolution image will let you count the rivets on an aircraft wing. A low resolution image may be barely adequate to identify the feature as a plane.

If space can be measured in discrete units, then it stands to reason time can as well. We know that at extremely small pixels (or intervals) our perception changes, even our physics. We use Quantum theory for the small and short, General Relativity for the large and long, and Classical physics for everything in between, the world of ordinary human experience. It can be argued that in any particular resolution domain, the behavior of reality is an average of the reality at some higher resolution.

I read a science fiction story once (sorry, can’t remember name or author) that was based on the concept of the curvature of time. The idea was that time is curved either positively or negatively. Negative curvature implies that any small perturbation initiates changes that tend to propagate into the future with ever-increasing effect. In other words, a butterfly flapping its wings in the Jurassic sets in motion a cascade of events which results in a hurricane, or an ice age, millions of years later. Positive temporal curvature results in the opposite, a tendency to return to some mean. That is, any event, even the most catastrophic (like the Cretaceous asteroid strike) will eventually damp out and the world will return to its normal evolutionary path. In other words, if you wait long enough, history settles down into some long term average. Local events are eventually blurred or erased if enough time passes. A negative temporal curvature implies the universe is chaotic. A positive one implies it is predictable.

Think of the analogy (not necessarily the example) of the seat of a horse’s saddle: It is convex from side to side, and concave from front to back. It is simultaneously concave and convex. That’s just a metaphor of the temporal curvature I’m talking about, not the same thing at all, but perhaps it helps communicate what I’m trying to say; especially the idea that two contradictory curvatures can simultaneously exist in the same manifold.

Now, the question arises, is space-time positively or negatively curved? And is it plus or minus at all temporal resolutions? We know it is chaotic at small scales, (quantum), smoothly bent at large scales (relativistic) and flat in our own perceptual range. This temporal curvature, if it exists at all, may switch from positive to negative and back, depending on the resolution at which we are observing or experiencing it.

Everything I say here makes sense, it is in perfectly grammatical English and it is reasonable, logical, and I hope, understandable. But it may not have anything to do with reality, how the universe is actually put together. The linguistic (and perhaps even the mathematical) universe has its own standards of consistency and logic, its own Truth. The real world has another.

Keep that in mind. I might be on to something. Then again, I may have no clue what I’m talking about.

But I know that.