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This article was originally published at The Conversation. The publication contributed the article to Space.com's Expert Voices: Op-Ed & Insights.

The nature of time has plagued thinkers for as long as we've tried to understand the world we live in. Intuitively, we know what time is, but try to explain it, and we end up tying our minds in knots.

St. Augustine of Hippo, a theologian whose writings influenced western philosophy, captured a paradoxical challenge in trying to articulate time more than 1,600 years ago:

"What then is time? If no one asks me, I know; if I want to explain it to a questioner, I do not know."

Nearly a thousand years earlier, Heraclitus of Ephesus offered a penetrating insight. According to classical Greek philosopher Plato’s Cratylus:

"Heraclitus is supposed to say that all things are in motion and nothing at rest; he compares them to the stream of a river, and says that you cannot go into the same water twice."

Superficially, this can sound like another paradox — how can something be the same river and yet not the same? But Heraclitus adds clarity, not confusion: the river — a thing that exists — continuously changes. While it is the same river, different waters flow by moment to moment.

While the river's continuous flux makes this plain, the same is true of anything that exists — including the person stepping into the river. They remain the same person, but each moment they set foot in the river is distinct.

How can time feel so obvious, so woven into the fabric of our experience, and yet remain the bane of every thinker who has tried to explain it?

An issue of articulation

The key issue isn't one most physicists would even consider relevant. Nor is it a challenge that philosophers have managed to resolve.

Time itself isn't difficult to grasp: we all understand it, despite our persistent struggle to describe it. As Augustine sensed, the problem is one of articulation: a failure to precisely draw the right boundaries around the nature of time both conceptually and linguistically.

Specifically, physicists and philosophers tend to conflate what it means for something to exist and what it means for something to happen — treating occurrences as if they exist. Once that distinction is recognized, the fog clears and Augustine's paradox dissolves.

The source of the issue

In basic logic, there are no true paradoxes, only deductions that rest on subtly mishandled premises.

Not long after Heraclitus tried to clarify time, Parmenides of Elea did the opposite. His deduction begins with a seemingly valid premise — "what is, is; and what is not, is not" — and then quietly smuggles in a crucial assumption. He claims the past is part of reality because it has been experienced, and the future must also belong to reality because we anticipate it.

Therefore, Parmenides concluded, both past and future are part of "what is," and all of eternity must form a single continuous whole in which time is an illusion.

Parmenides' pupil, Zeno, devised several paradoxes to support this view. In modern terms, Zeno would argue that if you tried walking from one end of a block to the other, you'd never get there. To walk a block, you must first walk half, then half of what remains, and so on — always halving the remaining distance, never reaching the end.

But of course you can walk all the way to the end of the block and beyond — so Zeno's deduction is absurd. His fallacy lies in removing time from the picture and considering only successive spatial configurations. His shrinking distances are matched by shrinking time intervals, both becoming small in parallel.

Zeno implicitly fixes the overall time available for the motion — just as he fixes the distance — and the paradox appears only because time was removed. Restore time, and the contradiction disappears.

Parmenides makes a similar mistake when claiming that events in the past and future — things that have happened or that will happen — exist. That assumption is the problem: it is equivalent to the conclusion he wants to reach. His reasoning is circular, ending by restating his assumption — only in a way that sounds different and profound.

Space-time models

An event is something that happens at a precise location and time. In Albert Einstein's theories of relativity, space-time is a four-dimensional model describing all such occurrences: each point is a particular event, and the continuous sequence of events associated with an object forms its worldline — its path through space and time.

But events don't exist; they happen. When physicists and philosophers speak of space-time as something that exists, they're treating events as existent things — the same subtle fallacy at the root of 25 centuries of confusion.

Cosmology — the study of the whole universe — offers a clear resolution.

It describes a three-dimensional universe filled with stars, planets and galaxies that exist. And in the course of that existence, the locations of every particle at every instance are individual space-time events. As the universe exists, the events that happen moment by moment trace out worldlines in four-dimensional space-time — a geometric representation of everything that happens during that course of existence; a useful model, though not an existent thing.

The resolution

Resolving Augustine's paradox — that time is something we innately understand but cannot describe — is simple once the source of confusion is identified.

Events — things that happen or occur — are not things that exist. Each time you step into the river is a unique event. It happens in the course of your existence and the river's. You and the river exist; the moment you step into it happens.

Philosophers have agonized over time-travel paradoxes for more than a century, yet the basic concept rests on the same subtle error — something science fiction writer H.G. Wells introduced in the opening of The Time Machine.

In presenting his idea, the Time Traveller glides from describing three-dimensional objects, to objects that exist, to moments along a worldline — and finally to treating the worldline as something that exists.

That final step is precisely the moment the map is mistaken for the territory. Once the worldline, or indeed space-time, is imagined to exist, what’s to stop us from imagining that a traveller could move throughout it?

Occurrence and existence are two fundamentally distinct aspects of time: each essential to understanding it fully, but never to be conflated with the other.

Speaking and thinking of occurrences as things that exist has been the root of our confusion about time for millennia. Now consider time in light of this distinction. Think about the existing things around you, the familiar time-travel stories and the physics of space-time itself.

Once you recognize ours as an existing three-dimensional universe, full of existing things, and that events happen each moment in the course of that cosmic existence — mapping to space-time without being reality — everything aligns. Augustine's paradox dissolves: time is no longer mysterious once occurrence and existence are separated.