One common understanding of transcendence is an encounter with a world beyond ourselves, beyond full comprehension. But why must this be interpreted as supernatural?
But why preclude such an interpretation? The reasoning seems to be, "Oh, I've had an experience that thousands of years of tradition has regarded as "supernatural," but I don't believe in the "supernatural," so I'll have to find some other way of explaining it. I know: I'll expand the comprehension of the term "natural" to include experiences usually thought to be "supernatural."