Gullibility is the principal cause of bubbles. Investors and the general public get snared by a "beautiful illusion" and throw caution to the wind. Attempts to identify and control bubbles are complicated by the fact that the authorities who might naturally be expected to take action have often (especially in recent years) been among the most gullible, and were cheerleaders for the exuberant behavior. Hence what is needed is an objective measure of gullibility. This paper argues that it should be possible to develop such a measure. Examples demonstrate, contrary to the efficient market dogma, that in some manias, even top business and technology leaders fall prey to collective hallucinations and become irrational in objective terms. During the Internet bubble, for example, large classes of them first became unable to comprehend compound interest, and then lost even the ability to do simple arithmetic, to the point of not being able to distinguish 2 from 10. This phenomenon, together with advances in analysis of social networks and related areas, points to possible ways to develop objective and quantitative tools for measuring gullibility and other aspects of human behavior implicated in bubbles. It cannot be expected to infallibly detect all destructive bubbles, and may trigger false alarms, but it ought to alert observers to periods where collective investment behavior is becoming irrational. The proposed gullibility index might help in developing realistic economic models. It should also assist in illuminating and guiding decision-making.