While that is a world without rationality, it seems a fairly extreme case.

Another example of a world without rationality is a world in which, the more you work towards achieving a goal, the longer it takes to reach that goal; so an elderly man might wander distractedly up Mount Everest to look for his false teeth with no trouble, but a team of experienced mountaineers won't be able to climb a small hill. Even if they try to follow the old man looking for his teeth, the universe notices their intent and conspires against them. And anyone who notices this tendency and tries to take advantage of it gets struck by lightning (even if they're in a submarine at the time) and killed instantly.