@nntaleb argues that payoffs from progress are related to gain over pain, rather than teleology (i.e. pursuit of goals) and formal science (i.e. analysis of data).  Convexity bias favours uncertainty when gains and harm are assymnetric.

… we have vastly more evidence for results linked to luck than to those coming from the teleological, outside physics—even after discounting for the sensationalism. In some opaque and nonlinear fields, like medicine or engineering, the teleological exceptions are in the minority, such as a small number of designer drugs. This makes us live in the contradiction that we largely got here to where we are thanks to undirected chance, but we build research programs going forward based on direction and narratives. And, what is worse, we are fully conscious of the inconsistency. […]

… logically, neither trial and error nor “chance” and serendipity can be behind the gains in technology and empirical science attributed to them. By definition chance cannot lead to long term gains (it would no longer be chance); trial and error cannot be unconditionally effective: errors cause planes to crash, buildings to collapse, and knowledge to regress.

The beneficial properties have to reside in the type of exposure, that is, the payoff function and not in the “luck” part: there needs to be a significant asymmetry between the gains (as they need to be large) and the errors (small or harmless), and it is from such asymmetry that luck and trial and error can produce results. The general mathematical property of this asymmetry is convexity (which is explained in Figure 1); functions with larger gains than losses are nonlinear-convex and resemble financial options. Critically, convex payoffs benefit from uncertainty and disorder. The nonlinear properties of the payoff function, that is, convexity, allow us to formulate rational and rigorous research policies, and ones that allow the harvesting of randomness.

Figure 1- More Gain than Pain from a Random Event. The performance curves outward, hence looks
Figure 1- More Gain than Pain from a Random Event. The performance curves outward, hence looks “convex”. Anywhere where such asymmetry prevails, we can call it convex, otherwise we are in a concave position. The implication is that you are harmed much less by an error (or a variation) than you can benefit from it, you would welcome uncertainty in the long run.


Let us call the “convexity bias” the difference between the results of trial and error in which gains and harm are equal (linear), and one in which gains and harm are asymmetric ( to repeat, a convex payoff function). The central and useful properties are that a) The more convex the payoff function, expressed in difference between potential benefits and harm, the larger the bias. b) The more volatile the environment, the larger the bias. This last property is missed as humans have a propensity to hate uncertainty.

Antifragile is the name this author gave (for lack of a better one) to the broad class of phenomena endowed with such a convexity bias, as they gain from the “disorder cluster”, namely volatility, uncertainty, disturbances, randomness, and stressors. The antifragile is the exact opposite of the fragile which can be defined as hating disorder.

In the full article, Taleb lists “Seven rules for antifragility (convexity) in research”.

See “Understanding Is A Poor Substitute For Convexity (antifragility)” | Nassim Nicholas Taleb | Dec. 12, 2012 | edge.org at http://edge.org/conversation/understanding-is-a-poor-substitute-for-convexity-antifragility.

Understanding Is A Poor Substitute For Convexity (antifragility) | Conversation | Edge