From a computer science perspective, isn't the index card functioning like an external memory, albeit one with somewhat pre-arranged linked paths? It's the movement through the machine's various paths that is doing the "thinking". Or the user's (active) choices that create the paths creates the impression of thinking.
Perhaps it's the pre-arranged links where the thinking has already happened (based on "work" put into the system) and then traversing the paths gives the appearance of "new" thinking?
How does this relate to other systems which can be thought of as thinking from a complexity perspective? Bacteria perhaps? Groups of cells acting in concert? Groups of people acting in concert? Cells seeing out food using random walks? etc?
From this perspective, how can we break out the constituent parts of thought and thinking? Consciousness? With enough nodes and edges and choices of paths between them (or a "correct" subset of paths) could anything look like thinking or computing?