Nothing But Time

[Captain Jack Sparrow]

[Captain Jack Sparrow]

What is a moment?

A specific point in time? A brief period in time?

“Wait a moment” means give me a little time. This is a brief period in time. But then there are also those significant instances in time that we sometimes call “special moments” — these are memorable points in time: the first kiss, the wedding vow, the glance that alters a life's course. 

A “moment” is a slippery concept — because time is relative, what feels like “a moment” to one observer might not match another’s. It’s less a technical term and more about perception.

If we set physics aside and talk about a moment as a slice of experience, it becomes clear that a "moment" is indeed contextual, tied to subjective experience or perception — like a fleeting event, emotion, or significant instance that stands out to someone. It’s not a fixed, measurable thing like time in physics (e.g., seconds). There’s no "objective moment" in this sense; it’s relative to the person or situation describing it. For example, "a moment of silence" will weigh differently upon each heart, and no hourglass could ever pin it down.

What is a moment?

The word gestures toward something notable — a snapshot of experience that stands out — but it doesn’t require objective boundaries or a fixed duration. It’s more like a mental bookmark for something meaningful, vague in length but vivid in context. It’s not strictly a "period" with objective edges; it’s more fluid, defined by what makes it stand out to the observer or in the context.

If a "moment" is a contextual snapshot — a subjective, notable instance tied to an event, emotion, or experience — then what exists "outside" of a moment? What lies beyond it?

[Captain Jack Sparrow]

It's seems impossible to see what lies beyond a moment. The instant you try to see, you've already created a new moment — or stepped into it.

The “beyond” is always just out of reach, like trying to see the horizon while walking toward it — it always moves with you. The act of noticing, the act of paying attention, draws a boundary around experience. You can't stand outside the frame and still be inside the picture. 

We've been led to believe that what lies beyond a moment is pure continuity — unmarked, unframed — but we only ever encounter it by stepping into it and, in doing so, marking it, binding it, turning it into a moment itself.

It's a paradox, you see, because the moment you attempt to grasp what's beyond a moment, you inevitably collapse it into a moment. 

A moment is defined by attention. The instant you notice something, you've framed it — given it edges in time. 

Contrary to a moment, the “beyond” is unframed, continuous rather than momentary, undifferentiated in occurrence.

To perceive the beyond, you must stop making moments. But the very act of realising, “Ah, I'm seeing it.” turns it into a moment. It's like trying to photograph “what happens between photographs”. The act of pointing the camera erases the very thing you wanted to capture.

This begs the question: How do we even know that what lies beyond a moment is continuity? 

[Captain Jack Sparrow]

What is continuity ?

When we look at the definitions, mathematics gives the most rigorous meaning of continuity: It describes a function that has no sudden leaps , no curious gaps or holes. Drawing a line without once lifting your quill is the idea. 

Mathematics, in its very prim and proper ways, keeps this concept tidy, especially in calculus and all that… analysis. But the notion turns up everywhere — physics, stories, life itself.

In physics, continuity is described as smooth changes in quantities. For example, a continuous motion without sudden velocity jumps, or the continuity equation in fluid dynamics which expresses the conservation of mass. 

In everyday language, we say a story has continuity is when the events follow on in some reasonable fashion: no contradictions, or what we call continuity error — when something suddenly changes from one shot to the next. 

However, and most interestingly, in philosophy, the concept has been used for centuries when discussing the nature of reality — whether time, space, or change is truly continuous or made of discrete parts. 

Time is described as a continuum — a continuous nonspatial whole or extent or succession in which no part or portion is distinct or distinguishable from adjacent parts. This is a concept that's deeply related to continuity — the core idea being smooth , unbroken progression.

When we say “time is a continuum”, we're saying:

1. No gaps — you can always find a moment in between any two moments.
2. Infinite divisibility — you can zoom in forever, there are no sudden jumps between any two moments.

Historically, the idea comes from philosophy first — thinkers like Aristotle debated whether time was made of indivisible “atoms” or was continuous. Mathematics later formalized the continuum idea using the real numbers, and physics adopted that model for time in classical mechanics.

But here's the big twist: In modern physics (especially quantum gravity theories), it’s still an open question whether time is truly continuous or actually quantized at incredibly tiny scales. Why? The mathematical continuum model of time is a model built from real numbers, but that's not the only possible way to think about time.

[Captain Jack Sparrow]

Mathematically, the real number line is our prototype for a continuum. Why? It has three key properties:

1. Order: Any two numbers can be compared.
2. Density: Between any two numbers, there exists another number with.
3. Completeness: There are no “holes” — limits of converging sequences are themselves real numbers.

These properties make a continuous set — no gaps, no smallest “steps.” And in classical physics, time is treated the same way — a one-dimensional number line. An instant of time corresponds to a single real number.

Motion, here, is then described by a function, which can be continuous (smooth change) or discontinuous (sudden jumps). This gives us infinite divisibility. Between 1.000000 seconds and 1.000001 seconds, there’s always a ‘time’ in between — and between those, another, and so on forever.

Why this feels “continuous”?

This model fits our everyday perception: clocks tick smoothly, events flow without gaps, and we can always talk about “half a second later” or “a thousandth of a second earlier.”

But here's the thing — it’s not the only possible model. While this is the assumed backdrop in classical physics, there are always alternative ideas:

• Discrete time: Time is a sequence of equally spaced instants (like integers or a lattice). No values “in between.”
• Rational time: Only ratios of integers exist — dense but not complete. (Strange things happen here: limits of sequences might not exist in your system.)
• Planck time hypothesis: In some quantum gravity theories, the smallest possible meaningful time interval is about 5.39 \times 10^{-44} seconds. Below this, “time” might lose its continuity.

So, why does science stick to the continuum model?

The real-number model of time makes calculus work perfectly, and calculus underlies most physics equations. And, so far, experiments show no sign of discrete jumps in time. Although, at very tiny scales, our measuring tools do hit fundamental limits, see?

In short, this is an assumption that works very well for now, but might break down at the smallest scales.