I think of uniformitarianism as constancy in the array of physical laws at work in the universe. They're the same everywhere throughout the universe and throughout all time.
The trick is determining what are the physical laws. Matter and energy always produce gravity, and the Nile always floods every year (pre-Aswan Dam everywhere along its course, now only in Sudan), but gravity is a physical law and the annual Nile flood is not (and anyway, the Nile doesn't always flood).
We know that food doesn't explode, and farmers store their grain in elevators year after year under the assumption that grain doesn't explode, but sometimes it does. But an exploding grain elevator is neither a miracle nor a physical law.
What we do know is that when the Nile floods or when a grain elevator explodes that both are following the physical laws of the universe. Which, from all the evidence we have, are the same everywhere across all time.
--Percy