Complex Means Interesting

There are many definitions of complexity. Entropy, Kolmogorov complexity, logical depth, statistical complexity. Some contradict each other. Yet intuitively we rarely struggle to recognize complexity when we encounter it.

My current intuition is simple. Complex means interesting. From an evolutionary perspective, interesting means something more precise: it signals that investing energy to understand a phenomenon may produce advantage. Order is not interesting because there's nothing to gain. Pure randomness is not interesting because there's nothing to exploit. What we call complex sits exactly in between — it is structure that rewards stronger observers.

There's also a small paradox hidden here. If complexity is a signal of whether investment will pay off, then we need to know whether to invest before investing. This makes complexity less like an explicit metric and more like an internal heuristic. Perhaps this explains why complexity is so hard to define formally yet so easy to feel.