I didn't say linear, but devil's advocate, isn't that roughly how humans learn? We start out as "pre-intelligent" little creatures who, slowly, methodically, with help of others, develop aptitudes and learn about the world. Learning in fact continues in this manner your entire life should you continue... slow, incremental progress requiring teachers, peers, trials/ errors, crises, 1/3 of your life being unconscious in sleep, etc., in the absence of which no learning at all may happen ... and the bot may potentially have greater computation constraints than humans under current technologies, as the brain is far more efficient than any computer today.

I'm not convinced that each of the arcs, elementary intelligence --> average intelligence --> super intelligence, wouldn't be painstaking and roughly linear.