Part I stopped at the failure of the linear model.
Visually, two observers with opposite temporal directions still seem able to meet at a single point. A moves from the past to the future, while B moves from the future to the past. If “meeting” only means occupying the same external coordinate, then the problem looks simple.
But that simplicity is deceptive.
Imagine a cup of coffee falling from a table. For A, the sequence is clear: intact cup, falling, broken. Entropy increases. But for B, the sequence is read in reverse: shards on the floor gather together, rise, and become an intact cup again.
At this point, my question is no longer “can they meet?”, but “if they interact, whose physical law applies?”
This is the part that makes the linear model feel fragile. Meeting does not only require the same location, but also causal agreement. Two beings may stand in the same room, but if one lives in the direction of increasing entropy while the other lives in the opposite direction of entropy, then they do not truly share the same physical world.
They are like two sentences written on the same sheet of paper, except one is read from left to right and the other from right to left.
The problem is not merely the direction of the clock. The problem is the direction of order, memory, and cause and effect. For A, cause precedes effect: the cup falls, then breaks. For B, the sequence appears otherwise: the shards gather, then the cup becomes whole again.
If both of them touch the same cup, which event should be considered “normal”?
From Arrow to Form
This is where I begin to suspect that the problem is not only the arrow of time, but the shape of time itself.
So far, the time we experience in everyday life appears linear:
This model fits human experience. We remember the past, not the future. We see eggs break, not broken eggs assembling themselves back into eggs. We see coffee cooling down, not the air in the room returning its heat back into the coffee.
In the language of thermodynamics, entropy tends to increase.
But in my imagination, another possibility appears: what if time is not only a line, but something curved, closed, or returning to itself?
Maybe time is not like an arrow shot once from beginning to end. Maybe it is more like the number 0, a circle, or a cycle. In such a form, what we call “beginning” and “end” are not completely separate. They may be two sides of the same structure.
Of course, this does not solve the cup of coffee problem yet. A circular time does not automatically allow broken shards and an intact cup to live peacefully in the same room. Local thermodynamic law remains stubborn. At the everyday scale, entropy does not suddenly become romantic and walk backward just because I draw time as a circle.
Still, a cyclic form gives another way to imagine the question. If a straight line makes two directions of time look like a collision, perhaps a cycle makes them look like different phases inside one larger pattern.
Closed Paths and the Cosmic Security Guard
In general relativity, the mathematics even permits certain possibilities called closed timelike curves, or CTCs: paths through spacetime that, in theory, can return to a point in the past.
But this possibility immediately brings the problem of paradox. If someone could return to the past, what would prevent them from changing the conditions that made their own existence possible?
The classic example is often called the grandfather paradox: someone returns to the past and prevents their grandfather from meeting their grandmother. If that succeeds, the person will never be born. But if they are never born, who returned to the past?
This is where ideas such as Stephen Hawking’s Chronology Protection Conjecture appear: the conjecture that the laws of physics may prevent the formation of situations that allow time paradoxes to occur. It is as if spacetime has its own security system, a kind of cosmic guard saying, “Sorry, this path is closed for the sake of narrative consistency.”
But there is also a more cosmological kind of cyclic form, not a local time machine.
One of them is Roger Penrose’s Conformal Cyclic Cosmology. In this model, the universe does not have only one Big Bang and one absolute ending, but a sequence of cosmic cycles. The extremely distant future of one universe can, through a conformal transformation, become something like the beginning of the next cycle.
In other words, this is not a story about someone entering a wormhole and appearing yesterday. It is more like cosmic history arranged into enormous chapters: one aeon ends, and then its geometry can be understood as the beginning of the next aeon.
I do not yet know whether such a model answers my question. Maybe it does not.
My question is too small and too troublesome: two observers, one cup of coffee, two directions of time reading the same event in reverse.
But at least I begin to see something. If time is only imagined as a line, this question immediately becomes a collision. If time is imagined as geometry, the question changes.
It is no longer “which one is forward and which one is backward?”, but “what kind of structure allows those directions to appear?”
Maybe time is not only something that flows.
Maybe time is a form.
And if it truly has a form, perhaps the strangest question is not “what happened before the beginning?” or “what happens after the end?”
Maybe the question is simpler, smaller, and more annoying:
If the cup breaks for me, is it healing for you?
This question will certainly not be solved by 500 leaked exam answers, because an education system that only distributes answers often forgets to teach how to treat a question.
And maybe that is precisely the problem: some questions do not ask for an answer key. They ask for room to stay alive.
There is no direct evidence that time is shaped like a circle. But mathematically, some forms of spacetime do allow possibilities stranger than a straight line.
You forbid it?
Fair enough.