Have we “given it” the goal of solving maths problems by any means possible, or the goal of solving maths problems by thinking about them?
The distinction that you’re pointing at is useful. But I would have filed it under “difference in the degree of agency”, not under “difference in goals”. When reading the main text, I thought this to be the reason why you introduced the six criteria of agency.
E.g., System A tries to prove the Riemann hypothesis by thinking about the proof. System B first seizes power and converts the galaxy into a supercomputer, to then prove the Riemann hypothesis. Both systems maybe have the goal of “proving the Riemann hypothesis”, but System B has “more agency”: it certainly has self-awareness, considers more sophisticated and diverse plans of larger scale, and so on.
The distinction that you’re pointing at is useful. But I would have filed it under “difference in the degree of agency”, not under “difference in goals”. When reading the main text, I thought this to be the reason why you introduced the six criteria of agency.
E.g., System A tries to prove the Riemann hypothesis by thinking about the proof. System B first seizes power and converts the galaxy into a supercomputer, to then prove the Riemann hypothesis. Both systems maybe have the goal of “proving the Riemann hypothesis”, but System B has “more agency”: it certainly has self-awareness, considers more sophisticated and diverse plans of larger scale, and so on.