Paradoxes of the Anomalous

What is "anomalous"? Different from the norm. And what is an "anomalous phenomenon"? It turns out to be something abnormal. But what is the norm at all? We don't know how to study rare and amazing phenomena, yet we are eager to label them conveniently, to fantasize wildly or, on the contrary, to debunk them at any cost. And how is it to observe the unusual while maintaining criticality, to believe the witnesses and double-check each of their words… Is such a thing even possible in principle?