By Horus Alas

We typically think of motion as the physical displacement of an object taking place over a given amount of time. And time can be thought of as a unit of measure allowing us to track that same motion.

Our day-to-day experience tends to make us perceive time in a linear way. Each of us human beings undergoes the same processes of birth, growth, maturation, aging and eventually, death. Because the trajectory and sequence of these processes never changes, we’re prone to think of time as a linear conduit guiding us all in the same direction.

But what if—insofar as we’ve assigned units to time to help us track motion—the nature of motion lends itself to a more cyclical view of time, as opposed to a linear one?

Around the late fifth century BCE, the Greek philosopher Zeno of Elea put forth a number of paradoxes arguing against the logical possibility of motion. His teacher, Parmenides, had famously claimed reality to be a single, static, unchanging unit of being; Zeno aimed to demonstrate logically that this was the case.

The original texts are now lost to us, but Aristotle gives us an account of what we now refer to as Zeno’s dichotomy argument:

“The first [of these paradoxes] asserts the non-existence of motion on the ground that that which is in locomotion must arrive at the half-way stage before it arrives at the goal.” (Physics, 239b11)

Imagine you’re walking up the hill from Regents Drive to the Adele H. Stamp Student Union Building. Before you arrive at Stamp, you must reach a point halfway up the hill. But before that still, you’d need to arrive at a point halfway between your starting point at Regents and the overall halfway point to Stamp, or one quarter of the way up the hill.

Before you reach a point ¼ of the way up the hill, it follows that you’d need to reach a point 1/8 and 1/16 of the total distance up the hill, and so on. The number of half-distances to be traversed can be divided infinitely.

Zeno’s argument alleges our standard view of motion requires an object to move an infinite number of distances within a finite amount of time. And on purely logical grounds, that’s impossible.

Logical powerhouse that he was, Aristotle had an answer.

If we’re dividing distances, it also makes sense that we’d divide the total units of time required to traverse them.

So if it normally takes you 10 minutes to walk up the hill to Stamp, it should take you five minutes to reach halfway up the hill; two and a half  minutes to be a quarter of the way up the hill, one and two eighths of a minute to be an eighth of the way up, and so on. Although potentially divided an infinite number of times, we’re still dealing with a finite total unit of time in Aristotle’s schema.

Even as far back as 2,400-plus year-old motion riddles, we find the ancients relying on essentially the same formula underpinning much of Newtonian mechanics — v=dt , where v is velocity, d is distance and t refers to time.

Each of these terms is worth exploring in its own right in order to hone in on a more acute understanding of what time is.

Distance seems straightforward enough. If I’m standing five meters away from a tree, we can say that all observable space between myself and the tree comprises a linear segment of five meters.

It should be noted that here, too, humans have invented units of measurement to help explain where things are with respect to our reference points. Without the development of the metric system, I would be standing an indeterminate distance from the tree, without any idea how to quantify it.

If I decide to walk up to the tree, my motion can be described in terms of physical displacement over time.

Supposing it takes me 10 seconds to walk up to the tree, which was five meters away, my velocity vector in traversing that distance can be given as .5 m/s, where m denotes meters and s indicates seconds.

As a unit of measure, seconds aren’t just coincidentally the most readily observable marker of temporal displacement for human beings.

According to the National Institute of Standards and Technology, “The unit of time, the second, was defined originally as the fraction 1/86 400 of the mean solar day. The exact definition of ‘mean solar day’ was left to astronomical theories.”

A solar day refers to the amount of time it takes a planet to undergo a full rotation along its axis. We’ll say that a full day has elapsed here on Earth, for example, between 12:00 noon Eastern Standard Time today, March 29, and 12:00 noon EST tomorrow, March 30.

The Earth’s full rotation gives us an easily-perceptible motion to track and hence ascribe units of measurement to the perceived duration of that motion cycle. From the day, we derive hours, minutes, seconds; months, years, centuries.

Ultimately, because the motion we choose to track on a macrocosmic scale (i.e. the Earth’s rotation and revolution) are circular, time as an independent ontological entity must likewise be cyclical and circular as opposed to linear.

It always follows that hours turn into days, days into weeks, weeks into months, etc. The hours of each day repeat themselves in a cycle, as do our Sunday to Saturday weeks, January to December months, Spring to Winter seasons, and so on.

In theory, we’ve come a long way in our understanding of time and our place in the universe since Zeno put forth his paradoxes nearly 2,500 years ago. In all that time, the Earth has kept spinning and revolving around an enormous ball of flame and gas at the center of our Solar System.

People, ideas and entire civilizations have faded in and out of time as the Earth continued its inexorable motions through the heavens. These have taken us centuries to grasp as the planet we call home has steadfastly undergone the same cycles which generate the basis for what we understand as time.

On the third planet from the Sun, we tend to think of time as linear because our lives are structured that way. In much the same way that if we were far enough from the ground, we could see the curvature of the Earth, if we lived long enough, perhaps, we could grasp the curvature and ebbs and flows of time.

Featured Photo Credit: Courtesy of frankieleon’s Flickr page.

Horus Alas is a freelance writer and can be reached at heliocentricnonchalance@gmail.com.