On the problem of local maxima

Finding a maximum is a natural tendency. We eat until we have had enough, then no more. We exercise until we are properly tired, then stop. It is always possible to have too much of something, so there is a finite optimal amount to anything.

I can only speak to personal experience here, but I'd say there is a natural pull towards a maximum. For example, I feel hungry until I am full, and if I continue eating I feel uncomfortable.

This natural tendency is confused when a local maxima exists, as in the graph. It's harder to find a single-variable example of this, generally they appear when considering multiple variables at once (more on that when I learn how to draw in 3D). But sleep is a close enough one. I know that I wake up feeling best when I wake up at the end of a sleep cycle. In increments of 1.5 hours, optimal times to wake up are after 1.5 hrs, 3 hrs, 6 hrs, 7.5 hrs, and 9 hrs. Practically, this means that if I am going to bed at midnight, I'd rather wake up at 6 than 6:30, but would definitely rather wake up at 7:30 over both of those.

With something like sleep it's easy to see that I would rather get 7.5 hrs a night over 6, I've had experience with both. But if this was with respect to something like learning to play guitar for the first time- it feels great to play an easy tune in 30 minutes, after that my fingers start to hurt. If I didn't push through, suffer, develop callouses on my fingers, I never would have found the greater joy that comes with learning for an hour a day.

Exploring different states will mean consciously inflicting suffering on yourself in order to find out if where you were at was a local maximum or global one. Philosophically, I don't think there is a static global maximum, and it is always rewarding to explore.

It's important to remember though, that while exploring means suffering, suffering does not mean exploring.