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 model is too restrictive. Events seem to overlap. I am all at once aware of many sensations, thoughts, feelings, and acts; it is often unclear when one stops and another begins.  Events are not points…or beads. Events have durations, and in a Euclidean cosmos, durations may overlap. But do they really? (Stay tuned!)

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

If an event has duration of less than one-tenth of a second, we don’t consciously register it though it may still impact our behavior because of an unconscious, subliminal effect. If an event has duration of more than a second, we must either break it up into multiple events, sequentially ordered…or remain entirely unaware of it.

Our naïve sense of event duration has everything to do with our cognitive apparatus and absolutely nothing to do with the nature of events themselves. There is no reason to doubt that the universe is ‘eventing’ across all 60 known orders of magnitude – from Planck scale to the Cosmic Event Horizon. To bastardize Stephen Hawking’s quip, “It’s events all the way down,” or in our case, all the way up!

We can only directly perceive events within a single order of magnitude. Accordingly, we shoehorn the Heraclitean flow into relatively tiny packets of perception. This is the origin of our sense that events occur as beads strung along a timeline and it explains our felt need to categorize events as past, present or future. It’s seems to be our only way to make sense of the tidal wave of sensations pouring over us every moment of our lives.

We need to ask two different questions: First, what are the ways in which events seem to relate to one another? Then, what are the ways in which events do in fact relate to one another? As soon as we contrast ‘do in fact’ with ‘seems’, we find ourselves hanging out with Parmenides in the 5th century BCE. His distinction between being (Aletheia) and seeming (Doxa) has informed philosophers from Plato to Kant to Whitehead.

It seems that events can relate to each other in a number of different ways:

First, obviously, they may not relate at all; they may be disjoint, in which case neither exists in the other’s universe.

They may be tangent: 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.

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

Or one may be embedded in the other: While washing my car, I’m also listening to some Bach on the radio and day dreaming about the time I threw a no-hitter for the Red Sox in a World Series, or not.

Euclidean Geometry allows any two events to be related in any of these four ways. 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°, etc. 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 Archimedean geometries that includes Hyperbolic, Spherical, and Projective Geometries plus geometries named after their founders, such as Riemannian and Minkowski Geometries. Suffice to say, the angles of a triangle do not always add up to 180°. How about 540°?

Strange as that may seem, reality might be even weirder. All of these geometries (above) are ‘Archimedean’, meaning roughly that you can measure any distance using just Real (plus Complex) Numbers. But Archimedean Geometry is not the end of the story. Still other geometries are modeled on systems involving ‘Unreal’ Numbers (e.g. hyperreal or p-adic numbers).

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? It doesn’t!

Every event has its own duration. To be an event is to endure, i.e. to constitute an extensive Presence. That duration can be dozens of orders of magnitude less than a second…or it can span 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. Each event establishes its own Present. In fact, Presence is a defining characteristic of Event. Every event must be embedded in at least one other event, or it must be disjoint from all other events and therefore not part of our Universe at all. To be is to embed or be embedded.

The naïve notion that the 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.

A, B, and C are three events in a single universe. A and B can be disjoint with respect to each other but embedded with respect to C. Or A may be embedded in B which is in turn embedded in C. There are even systems that permit circularity:

A is embedded in B, B is embedded in C, and C is embedded in A.

The perpendicular axis appropriate to the hierarchy of embedded events (the ultra-metric) measures the duration of each event relative to the events it embeds and the events in which it is embedded:

The ultra-metric does not measure an event’s sequential position relative to other events (because there is no sequence in Presence).

Nor does it measure the duration of any event relative to the durations of events disjoint from it (because they are not part of its present universe).

Nor does it measure gaps between such disjoint events because the concept of ‘gap’ implies a species of metric continuity that is not permitted in non-Archimedean systems.

As we measure magnitude along the hierarchical axis, we subsume ever longer segments of what was once considered serial time into single events each with their own unique presents. Ultimately, the timeline itself, time itself, is embedded in an 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 not to be, never not to have been. Therefore, all events, including Universe, are eternal, because presence is atemporal. Ultimately, it is the single, common uber-Present, aka Eternity, that holds universe together and constitutes the unity of all that is.

The concept of the uber-Present closely resembles the concept of logos in pre-Socratic philosophy (esp. Heraclitus) and early Christian theology (esp. the Gospel of John and the Letter to Colossians). It refers to the fundamental ordering principle of the cosmos.

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.