Now it is a computation because you are the computing entity that encoded a problem into the system and later decoded the answer. They paper essentially establi

Now it is a computation because you are the computing entity that encoded a problem into the system and later decoded the answer. They paper essentially establishes the distinction of a system just evolving under the laws of physics and using this evolution to compute something by assigning an interpretation to the state of the system. I could use the same stone to compute something different, for example the boring trajectory of a stone placed on a surface in a gravitational field, but without specifying what you are computing the stone is not computing anything.