For what it's worth, if anyone is interested, "paradox" has been the thing for me since.
For me, it was neurotic as fuck. I started to question how predictable I was, and whether or not I could prove that the world around we wasn't just a tiny fake spec generated in real time based off predictions of what I would do next. The notion that my entire world could actually be very, very tiny as long as I was predictable enough kind of got to me. I started trying to do things I wouldn't do, and that was sort of a paradox. Eventually I began to use randomization to try to throw off the feeling. Nothing really worked, there's no way to prove that this isn't the tiniest matrix using advanced predictions to generate just a little more than what I sense. Also can't prove it's not a giant amazing universe. What-if-ism means: if it doesn't hurt to believe something, and you're willing to cede it's probably not reality, go for it. I like to believe in the universe as it's normally described.
Anyways, I find that the more I think about something, the closer I get to a paradox. What's the point of philosophy? To prove there is no point. What's the meaning of life? To understand there is no meaning. How do I achieve x goal? Stop caring about achieving it.
In a few words, rather than things existing as opposites, they exist as a paradox. They really shouldn't exist together.
As a WIP tangential thought (take it with a grain of salt, it's just for fun right now): as much as we take it for granted, I think there's something fucked up about a universe with both Cartesian and radial coordinates. Like, they shouldn't be together. And why just those two? Why not more? Why not just one? Seemingly things should be either universally relative, or personally relative, but not both simultaneously. It's like we're trying to survive in a universe with two disparate rule sets that by all accounts shouldn't be able to happen at the same time, and yet they are. It's a fucking paradox.
As a relevant example, consider the yin/yang symbol. It is composed of a duality which at first glance seems mutually exclusive, but what is most interesting about the two is actually where they interact. The paradox is that one cannot exist at the same (space-)time as the other, but each requires the other's existence to fully specify itself in terms of a cohesive concept. The light and dark sides are descriptors of two sides of the same coin. Finding the way to conceptualize that coin, rather than its sides, leads you to paradox that paradoxically makes sense! Just goes to show how "rationality" in the Greco-Roman sense is just one way to conceptualize our understanding, and that there are more ways than that.
We understand reality through language primarily built on identifying by what things are and what things are not. But maybe this form of understanding is limiting because it pre-supposes those dualities that make the language work.
To your point about coordinate systems -- there's something to be said about the ability to rationalize our sensory experiences into a formal logical system of description. However the paradox is actually that neither of those coordinate systems are "canonical" in the universal (literally and metaphorically) sense. They are first-order approximations to make our methods of reasoning (i.e., math) easier. But they do not reflect reality because, if you take the dominant theories of physics as true, the idea of space with curvature 0 or curvature +1 is a platonic ideal that cannot exist because matter and energy are distributed inhomogenously throughout space and time.