Even when we are not conscious of it, we actually assume the nature of the coordinate system in advance. Our descriptions of X or Y, then, must always fit within boundaries imposed by our definitions. Thus, by definition, we can't begin on a Cartesian graph and make a transformation to any and all conceivable sorts of coordinates. But with tensors in a Riemannian kind of universe, we're able to make any transformations we please. The answer, remember, is that with tensors the coordinate system doesn't come in advance.
Tensors reverse the conventional wisdom.
With tensors the definition follows rather than leads the description. We must calculate the universe. It's not ours by divine revelation. We need a description of intelligence before we can even attempt a definition. There's more to intelligence than dimension.