Convexity

In mathematical terms, a function is convex if a line segment connecting any two points on its graph lies above the graph. This property creates asymmetric payoffs—limited downside but potentially unlimited upside. Convex systems benefit from volatility and uncertainty, as exemplified in options trading where small investments can yield massive returns. The concept extends beyond mathematics to decision-making strategies, where 'convex tinkering' involves making many small, low-risk experiments with potential for outsized rewards. Understanding convexity helps identify opportunities for asymmetric advantages and explains why some systems become more robust under stress while others collapse.