Back in December 22nd, I published the post "The endless desert at the afterlife" (I'm not sure how to link, but you can see it at the "Latest posts").
Perhaps a bit of thought experiment, applied math and science are interesting to complement philosophy.
Suppose a scenario similar to Conway's Angel Problem: two figures are roaming through an infinite plane.
However, there are plenty of differences from the original thought experiment.
First of all, no figure is trying to block the other's path, nor is trying to evade the other.
They start at very different coordinates within the infinite plane and they both have a common goal: to meet each other.
They have a limited sight range: the farthest each one of them can see is 1 km to all 180° directions ahead of their current walking direction (like a 180° "cone" branching from the center of their stereoscopic pair of eyes, all the way to 1 km, where they gradually become "fogged" due to the distance).
They can't communicate, ever. They can't scream, as there's no air to propagate sound. They can't coordinate their routes, they can't even remember their past paths, as the plane is featureless. They have to rely solely on both their own movement (proprioception) and their own sight.
They must NOT stop: each one of them can either walk or momentarily run until fatigue requires to resort to walking again, which will replenish the stamina in order to allow for another running. The only exception is when one of them see the other, otherwise they must continue walking or running. If one stop, it doesn't mean that the other will stop, because stopping depends on actually seeing the other.
They can change their courses at will, so they can curve or walk straight or even turn and go backwards, at any moment.
Given infinite time, can they ever meet each other?
It's funny. They can spend their eternities trying to find the other, and never getting to actually meet, even when "gifted" with infinite time. They can even get closer without actually meeting: let's say the first is right behind the second, and while the first finally stopped as they saw the second, the second didn't see the first so the second continues to walk indefinitely... Perhaps the first figure can start to follow the second at a very close distance ("I'm right behind you"), but the second won't even know they're being followed, and the pursue will last for eternity.
They seem to possess free will, as they can change courses at any moment and they can choose to walk or run, but the grand scheme frustrates it all.
Does it sound like just a thought experiment? Or does it actually resemble the mechanisms of life and existence themselves, from macro to micro?
See, mass is always trying to meet (i.e. gravitational force) but they seem to be fated to miss and break apart (i.e. cosmic expansion, dark matter). Individual living beings can spend their whole lives trying to find THE partner, but they can miss and die without getting to find. Photons could be linked with another photon through quantum entanglement, but they can roam indefinitely through the fabric of spacetime without actually getting to converge and meet their entangled pair.
It sounds like a paradox, a bleak paradox, revolving around the harsh nature of the reality and existence. It's an unsolvable problem. The existence. The possibility of ethereal connection. Stuff is fated to seek but always miss.
Existence is fated to try to reach the unreachable. It's purposeless to even try, however, just like Sisyphus, there's the fate to never stop trying to push this non-existent boulder made of baryonic stuff, just to face it rolling down the slippery slope of the cosmic existence. It doesn't imply "resilience" and "determinism to continue", because stopping is definitely not a choice, it's the cosmic rule of existence. It's a goal, frustrated from the very beginning, just like trying to make a closed 2D polygon out of one straight short line. On the infinite plane.
I'm fated to the grand scheme of bleak logical and mathematical indifference composing the cosmos, and so is every stuff ever existent, every living being, every human, everything and nothing.
Perhaps I can turn back? Not exactly: I'm walking as I'm turning... So, never mind walking in circles again, huh?
In essence, She can be right behind me, haunting my back, but I can't even see Her and I must continue to seek. For eternity.