If we view nature as our "programer", we could even be called self recursive, as with each passing generation our knowledge as a species increases.

Kind of, but kind of not. I think self-recursing human intelligence would be parents modifying their babies to make them smarter.

The really interesting part of FOOM is when the intelligence being produced is the optimization process, and I think we really have no prior analogy for this.

Humans rapidly got smarter, but we were optimized by evolution. Computers got faster, but were optimized by humans.

When an optimization process improves itself, it makes itself even better at optimizing.

I think that's a pretty decent definition of FOOM: "When an optimization process optimizes itself, and rapidly becomes more powerful than anything else seen before it."