The modern description of monads is very "data centric" -- i.e., that somehow the T is an encapsulator of vital information. To me, I think this view causes more confusion than necessary. In the original conception, however, it represents the computation, and any information in the type other than the value is only necessary for the computation. In this view, you almost don't care about what is inside the type. Then T is a primary indicator of computation and what it contains is only incidental and hence secondary.