The Perpendicular Present

1700 words, 8 minute read

At first glance, life seems to be a string 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. Events have durations, and in a Euclidean cosmos, durations may overlap. But do they IRL? Is the cosmos Euclidean? 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 and our cognitive apparatus, like a radio, is tunable only within a very narrow range.

Potentially, an event could have a wave length as long as 10^25 meters or as short as 10^-35 meters; we can only experience events with wave lengths close to 10^0 m. Just as we can only ‘see’ a narrow range of the EM spectrum, so we can only experience a narrow range of the ‘event spectrum’.

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 be totally unaware of it.

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 reason to doubt that the universe is ‘eventing’ across all of its 60 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 up! Why should a single order of magnitude, the Universe’s ‘25^throot’, be so important?

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 seems to be the only way to make sense of the tidal wave of sensations pouring over us every moment of our lives.

We need to ask, what are the ways in which events seem to relate to one another? What are the ways in which such events do in fact relate? As soon as we contrast ‘do in fact’ with ‘seems’, we find ourselves back in the 5^th century BCE hanging out with Parmenides, the father of Western philosophy. 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 at least four different ways:

(1)     They may not relate: They may be disjoint with neither existing in the other’s universe.

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

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

(4)     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 all these modes of relationship. 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°. Would you believe 540° (Spherical Geometry)?

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 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) that include infinite and infinitesimal quantities.

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 tangent or overlapping. B is embedded in A (or A in B) or they are disjoint. Now add a third event, C, also embedded in A.

Unless C is embedded in B (or B in C), B and C are disjoint. However, B and C, though disjoint, nevertheless share a common host (A) which can serve as a medium enabling indirect communication between B and C. As we say in Boston, ‘Lowells (B) speak only with Cabots (A) and Cabots (A) speak only with God (C)’.

How does our cherished ‘past-present-future’ model of time make out in such a non-Archimedean universe? It doesn’t. No way! No how! We need a fresh start:

First, every event has its own ‘metric’, its own duration. To be an event is to endure, i.e. to constitute an extensive Presence. The duration of an event is its present.

Sidebar: Duration is not a species of time, as ordinarily supposed; duration is the negation of time. Time measures the exterior relationship between events; duration is an internal characteristic of an event. When we quantify the duration of an event, we are not measuring the event itself; we are triangulating. We measure the event’s external relationships with other events and infer a virtual internal value where none exists IRL.

The virtual measure of an event’s 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 along a perpendicular axis.

So the Present is not an extensive region on the timeline. Each event originates from a Planck-size point (10^-35 meters) on the timeline. Each event is present to itself. Each event establishes its own Present with a virtual duration on the timeline. In fact, Presence is a defining characteristic of Event.

It is better to understand Presence as perpendicular to linear (past-future) time. From any point on the timeline, we can use a virtual compass to draw a series of concentric semi-circles, each including ever broadening segments of that timeline, each potentially corresponding to the Present of some event at some order of magnitude.

Each Planck length (10^-42 seconds) ‘point’ on the timeline is the origin of its own perpendicular axis which generates its own hierarchy of embedded Presents with the Cosmos as its final term. In this geometry, all perpendicular lines intersect at a common horizon. Therefore the Cosmos is ‘present’ at every point on the timeline. Another pre-Socratic Greek philosopher, Anaxagoras, nailed it: The cosmos is pan in panti(everything in everything).

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:

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

Ø  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 universe).

Ø  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. According to Nicholas of Cusa (c. 1450), this cosmic event horizon templates God. The interior surface is what we call Universe; the exterior surface is what we call God.

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. All events are internally atemporal and, ultimately, it is the uber-Present, aka Eternity, that holds Universe together, enfolds all, and constitutes the unity of all.