Complexity not as a mathematical concept, but as an almost intuitive sense of both complication and interconnectedness. Both are necessary components of a truly complex system or situation.

1. Complicated systems have many parts, or take many steps, or have many rules; complex systems are complicated systems connected to and interdependent with other systems (likely also complex).
2. There are rarely simple resolutions to complex (complicated+interconnected) problems; because a resolution must take into account the effects of changing a complex situation on the connected systems, the resolution will of necessity be at least as complex as the problem.
3. The associated complexity of a seemingly simple resolution generally shows up in unintended or unexpected consequences; complicated interconnections cannot be cut without repercussions.
4. For this reason, over time, simple solutions tend to increase complexity.
5. Complication can be the perverse result of simple interactions, but complexity is rarely so; because complex situations are also complicated, the two can be easily confused.
6. In situations where "complexity itself" is asserted to be the problem, the actual crisis is often around complication; the trick is to devise ways to reduce the complication without damaging the interconnections.
7. Unfortunately, that's not simple; in many cases, it may not be possible.
8. The only way to reduce and resolve the complexity of a given situation is to reduce its level of interconnection with other systems; doing so, however, can undermine the value or power of the given system, and will alter the systems to which it was once connected.
9. In other words, the opposite of "complex" is not "simple," the opposite of "complex" is "isolated."

[Just thinking about how the world works as I prepare for another intercontinental journey.]