are based on empirical data and that fail to consider events that have not taken place, but could have taken place. Discussing the ludic fallacy in The Black Swan, he writes, "The dark side of the moon is harder to see; beaming light on it costs energy. In the same way, beaming light on the unseen is costly, in both computational and mental effort." In the second edition of The Black Swan, he posited that the foundations of quantitative economics are faulty and highly self-referential. He states that statistics is fundamentally incomplete as a field, as it cannot predict the risk of rare events, a problem that is acute in proportion to the rarity of these events. With the mathematician Raphael Douady, he called the problem statistical undecidability (Douady and Taleb, 2010). Taleb has described his main challenge as mapping his ideas of "robustification" and "antifragility", that is, how to live and act in a world we do not understand and build robustness to black swan events. Taleb introduced the idea of the "fourth quadrant" in the exposure domain. One of its applications is in his definition of the most effective (that is, least fragile) risk management approach: what he calls the "barbell strategy" which is based on avoiding the middle in favor of linear combination of extremes, across all domains from politics to economics to one's personal life. These are deemed by Taleb to be more robust to estimation errors. For instance, he suggests that investing money in 'medium risk' investments is pointless, because risk is difficult, if not impossible to compute. His preferred strategy is to be both hyper-conservative and hyper-aggressive at the same time. For example, an investor might put 80 to 90% of their money in extremely safe instruments, such as treasury bills, with the remainder going into highly risky and diversified speculative bets. An alternative suggestion is to engage in highly speculative bets with a limited downside. Taleb asserts that by adopting these strategies a portfolio can be "robust", that is, gain a positive exposure to black swan events while limiting losses suffered by such random events. Together with Donald Geman and Hélyette Geman, he modeled the "maximum entropy barbell" which consists in "to constrain only what can be constrained (in a robust manner) and to maximize entropy elsewhere", based on an insight by E. T. Jaynes that economic life increases in entropy under regulatory