> With the advent of modern computing, we (as a species) have finally created a tool that can "think" recursively, to arbitrary levels of depth.

I don't know what this means; when a computer "thinks" recursively, does it actually?

The recursion is specified by the operator (i.e. programmer), so the program that is "thinking" recursively is not, because the both the "thinking" and the recursion is provided by the tool user (the programmer), not by the tool.

> If we ever do create a superintelligent AGI, I'd wager that its brilliance will be attributable to its ability to loop much deeper than humans can.

Agreed.