One serious possibility for understanding entropy and the arrow of time, given that all events in quantum field theory (QFT) seem to be reversible (equally workable forwards and backwards in time, with directly equivalent particles), is that time ordering is a property of minds, rather than the world. The nature of time is a major, maybe the major, source of tension between QFT & general relativity.
Causality, as considered in the -unresolved- Problem Of Induction, may not reside so much in the world, as in our making sense of it.
"Alice laughed: "There's no use trying," she said; "one can't believe impossible things." "I daresay you haven't had much practice," said the Queen. "When I was younger, I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast." - Alice In Wonderland
We can imagine a world which does not make sense, but even in doing so we seek ordering principles, like Alice. Dodgson was satirising the 'new mathematics' of his time, with apparently impossible things like imaginary numbers.
Jung suggested that causality is a way of grouping phenomena, of finding patterns. And posited synchronicity as an alternative principle, linked to ideas like the astrological 'as above so below'.
We like to imagine meaning, causality and so on, as external to us. An alternative view, is that meaning is like the turbulence a fishes fins make in water, that we makd in the substance of our impressions of the world. In this view, we cannot but help make meaning when we navigate. To not do so, would be to stay stationary in our thoughts. But this picture draws attention to our freedom, our choices, in how we make sense of the world.
Carlos Castenada talks about the realm of the https://en.m.wikipedia.org/wiki/Nagual The non-conceptual realm, between the islands of meaning in which our interactions occur. It is a realm of 'impossibilities', but also one in which action and intention are still possible, but without many of the assumptions which in every-day mind obscure the world as it is in some ways.
Mathematics is a language. 1+1=3 is just redefining words, and doing so will be subject to a judgement of how good the new system of definitions is. Defining the complex number line is much more subversive, and in some ways was more unsettling to people when it was proposed. Whatever languages we have, whatever systems and organising principles, the world exists out there beyond them. And unbound by them. We can, we must, be able to explore it without the concepts neccessary to understand it. Or we could create no new concepts. Our experiences form fixed points on a larger landscape of the unexperienced, like the proofs of maths do, or the experimental results of science, and the unproven and unevudenced beyond. Outside of those, we can find new places to stand, which reinterpret and simplify those, explain them with deeper and more universal insights, which we call knowledge. The creative space of hypothesis generation can include far more subversive ideas than 1+1=3. To reach new high points on the landscape of ideas, we may need to cross valleys of chaos and impossibility. And we do.