On the paradox of infinite divisibility:

Required Reading: Asymptotes, Zeno's Paradoxes, Infinite Divisibility, On the Present


Preface: Last week, I went on about how there was no way of pinpointing any moment in time accurately, because accurate measurements require infinitely smaller increments. It is a dynamic relationship which means that truly accurate measurement of anything at all is impossible.


While it seems obvious that events do happen, and must have begun to happen at some point; any attempt to figure out at which point an event actually occurs only tells us the times when the event was or wasn't happening.

The starting point for an event is always a moment that we get close to, but never meet; a sort of asymptote (remember calculus, kids?). For convenience sake, I'm applying the concept of asymptotes to any thing that gets close to, but never reaches a given measure (anything that approaches zero or infinity). Asymptotes imply infinity in that no matter how close a curve gets to an axis, it will never intersect with it because of the infinite divisibility of the space between them.

The fact that accurate measurements for beginning and end points are asymptotic (see what I did there?) suggests that each event has either always been occurring, never occurred, or is actually one event that has no beginning or end; an infinite event. The best guess of anyone as to the starting point of an event is defined by when it did not commence, as opposed to the moment that it did - because we'll never figure out what that moment is.

It’s important to note that here, as in Zeno’s original Arrow and Dichotomy paradoxes (remember the required reading?); the infinite divisibility of both space and time seems to preclude movement (or in this case, commencement of events). However, as in all of Zeno’s paradoxes, we know from experience that despite the fact that from one moment to the next, there is no way of knowing exactly when something started moving and where it moved to, the fact is that it does start moving, and does move somewhere.

Here is a possible explanation for this problem: Just as objects in space do not displace space by existing in it (they are the space they occupy - more on this in a few weeks), objects and events in time do not displace time. Basically, what I'm saying is that space and time are absolute - not relational (these are fancy philosophy terms). We estimate when the beginning and end of events happen, in terms of time. The unity and identity of each event is maintained no matter how many divisions are made in the duration between those beginning and end points - just as objects maintain their form from one point in space to another. No matter how many arbitrary divisions we make in time, an event maintains its duration, just as an object maintains its size no matter how small the increments that we measure it with are.

So, the interpretation of the present as being a relative estimate rather than an exact point is a useful fiction, which allows us to distinguish between relative (and inaccurate) starting points and relative end points in time or space.

Are relative time and space a valid substitute for knowing exact values? My position is that, technically, we can't tell the difference in our every day life, and the problem doesn't really have any noticeable effect on us as it is.

On the other hand, the indeterminacy of one of the fundamental elements of human perception is at once puzzling and intriguing. What does it mean, on a subconscious level, that events never actually start happening?


Next Week: On Simultaneity in which I dance around the idea of whether or not two things can happen at the same time, when one thing can barely seem to happen in the first place.