This article is the second of a 5-part series covering the Real World Risk Institute’s 1-week mini-course on Real World Risk, held in NYC. There’s statistics, complex systems theory, and strong opinions ahead. I’ve learned far more than I can adequately represent here, so these will more or less be my raw notes. You can find Part 1 and a Table of Contents here.
What you expect to get out of a system doesn’t matter if you can’t get to that point. In order to achieve your goals in a system, that system must first survive. So must you. Systems don’t have “infinite capital”. There are points at which they can “no longer play”, so to speak. That’s risk.
Concavity vs Convexity
A concave function looks like this:
Many systems are concave in their behavior, particularly with regards to stressors, changes, volatility, or the march of time. They have a sweet spot, like Goldilocks, in which they perform highly, but that performance degrades significantly if things are too hot or too cold.
A convex function looks like this:
Systems that are convex benefit from volatility, from changes and variety and from the march of time. If the X axis in the above chart is “some good thing”, then spending time at x1 and at x2 will give you an average that is on the red line, not the black one. (I’m avoiding financial terms here — bear with me). The overall value is higher because you moved about a bit, even though you spent some time at x1.
At a higher level, the idea is to try to set up your systems so that surprises, stressors, changes, and the march of time (etc!) make your system better, not worse. If you need a sweet spot, you are fragile, and the narrower your sweet spot the more fragile you are.