The Eternal Present

At first glance, our lives seem to be strings of bead-like events. No sooner have we experienced one sensation, one thought, one feeling, one action than another takes its place. We have a vague, naive sense that we can string these events along a timeline labeled, “Past, Present, Future”.

But on further reflection, it is clear that this is absurd. Events overlap. I am all at once aware of many sensations, thoughts, feelings, and acts; it is hardly ever clear when one stops and another begins.  Events are not points…or beads. Events have duration and in a Euclidean cosmos, different events may not only follow one another sequentially but they may also overlap. One event may even be embedded in another.

We do not directly perceive this richness because the human nervous system is attuned only to ‘events’ whose durations fall within a very narrow band, from one second to one-tenth of one second. One may think of such duration as the ‘wave lengths’ of respective events.

If an event has duration of less than one-tenth of a second, we don’t consciously register it; if it has duration of more than a second, we break up the experience into multiple events, sequentially ordered.

Of course, there are exceptions. Mystics report periods of focus lasting minutes, even hours; but the more important point is that our naïve sense of event duration has everything to do with our cognitive apparatus and nothing to do with the nature of events themselves.

There is no theoretical reason why event duration should be confined within a single order of magnitude. On the contrary, we know that there are events with a duration dozens of orders of magnitude shorter than a second (e.g. radioactive decay); there is no good reason not to suppose that there are other events with durations dozens of orders of magnitude longer than a second. Absent theoretical argument or empirical evidence to the contrary, we should assume that events occur at all orders of magnitude. 

We can infer the existence of events outside our neurological bandwidth, but we only directly experience as ‘events’ those happenings that have a wavelength sync’d to our cognitive apparatus. Universe spans at least 60 orders of magnitude; we can only directly perceive events within one such order. 

Accordingly, we shoehorn the Heraclitean flow of experience into relatively tiny packets of perception. This is the origin of our sense that events occur as beads strung along a single timeline. It explains our felt need to categorize events as past, present or future. 

We need to ask a different question: What are the ways in which events relate to one another? It turns out…a number of different ways:

1. They may be tangent (as above): A billiard ball rolls across the felt with a certain momentum; it impacts a second ball and imparts momentum to that ball. This is the paradigm of what we call causality. 

2. They may overlap: While listening to a particular melody, a memory occurs which lingers long after the melody has played out.

3. One may be embedded in the other: While composing a thought, I suddenly hear a bird chirp. I am aware of the chirp, but it does not interrupt my thought process; in fact it may be incorporated into that thought process. 

4. Or they may be disjoint, neither embedded, nor overlapping nor tangent.

Euclidean Geometry allows any two events to be related in any of these four modes. For those of us with only a high school education in geometry, Euclid may seem to be the only game in town. I mean, what else could there be? a² + b² = c², right? The angles of a triangle always add up to 180°. Obviously!

Obviously…but not actually. It turns out that Euclidean Geometry is just one way to organize space. It is one of a family of geometries that includes Hyperbolic, Spherical, and Projective Geometries plus geometries named after their founders (like Euclid) such as Riemannian and Minkowski Geometries. Suffice to say, the angles of a triangle do not always add up to 180°. 

All of these geometries, including Euclid’s, are examples of Archimedean Geometry, i.e. they exhibit the properties of Real Numbers. But Archimedean Geometry is not the end of the story. Still other geometries are modeled on ‘Unreal’ Number systems (e.g. hyperreal numbers or p-adic numbers). These Non-Archimedean geometries share a common feature: if two events intersect in any way, one event must be entirely embedded in the other. No two events (A, B) can be merely tangent or overlapping. Either A is embedded in B, or B is embedded in A, or A and B are disjoint.

How does our cherished ‘past-present-future’ model of time fare in a non-Archimedean universe? In a word, it doesn’t!

Every event has its own duration. That duration can be dozens of orders of magnitude less than a second…or it can span the entirety of cosmic history. The duration of each event is that event’s own unique Present. These presents are not arranged sequentially on a timeline but are embedded in one another hierarchically.

So the Present is not a fixed region of time. Each event is present to itself. In fact, Presence is a defining characteristic of Event. Every event must be embedded in at least one other event, or be disjoint from all other events, and therefore not part of our Universe at all. To be is to be embedded and/or to embed. 

The naïve notion that Present is a point or region of time located somewhere between Past and Future on a linear continuum turns out to be a fairy tale. It is better to understand Presence as perpendicular to linear spacetime. From any point on the past-future timeline, we can use a virtual compass to draw a series of concentric semi-circles, each including broader and broader segments of that timeline, each potentially corresponding to the Present of some event at some order of magnitude.

The perpendicular axis appropriate to the hierarchy of embedded events measures the duration of each event relative to other events, not its serial position relative to those events. As we measure magnitude along the hierarchical axis, we subsume larger and larger segments of serial time into single events, single Presents. Ultimately, the timeline itself, time itself, is embedded in the uber-Present, and this uber-Present is the event we know as Universe. 

What holds the universe of events together is not the weak bond of temporal succession but the ironclad bond of embeddedness. The result is an ever broadening Present. All events are present to themselves; Universe is an event; therefore, Universe is present to itself. To be present to oneself in a universe present to itself, is never to not be (or not have been). Therefore, all events, including Universe, are eternal. Ultimately, it is a single, common uber-Present, aka Eternity, that constitutes the unity of all that is.

Even before Einstein, we were trying to treat space and time with a common metric. It’s challenging because one second in time is equivalent to 300,000,000 meters in space. Still, it’s not impossible. Hawking showed that we could treat time spatially but only by adding an ‘unreal’ factor equal to the square root of -1. Doing so effectively rotates time so that it is perpendicular to space. 

But now we know that our project was doomed for a much more fundamental reason: space and time have different, incompatible geometries. The geometry of space is Archimedean and follows the laws of Real Numbers while the geometry of time is non-Archimedean and doesn’t (the square root of -1 is not a Real Number).

The Present is not a region, or even a point, on a past-future timeline (time treated as space). Presence is a series of concentric circles, with its axis perpendicular to linear spacetime, originating at any (and therefore at every) point in spacetime.  

So Universe consists entirely of events; events are always present to themselves (presence to oneself is what an event is); therefore, to be is to be in the Present (past and future are Archimedean fictions) and Presence is another name for Eternity. 

Image: Dalí, Salvador. The Persistence of Memory. 1931. Oil on canvas, 24 cm × 33 cm. Museum of Modern Art, New York City. Accession No. 162.1934.

David Cowles is the founder and editor-in-chief of Aletheia Today Magazine. He lives with his family in Massachusetts where he studies and writes about philosophy, science, theology, and scripture. He can be reached at david@aletheiatoday.com.