Behavioral Despair in the Talmud: New Solutions to Unsolved Millenium-Old Legal Problems

Abstract

We solve two "unsolvable" (teyku) problems from the Talmud that had remained unsolved for about one and a half thousand years. The Talmudic problems concern the implied decision-making of farmers who have left some scattered fruit behind, and the alleged impossibility of knowing whether they would return for given amounts of fruit over given amounts of land area if we aware of their behavior at exactly one point. We solve the problems by formalizing the Talmudic discussion and expressing five natural economic and mathematical assumptions that are also eminently reasonable in the original domain. If we also allow a sixth assumption regarding the farmer's minimum wage, we can solve two other related unsolvable problems.