is metamorphic code. Efron's dice are four dice that are intransitive under gambler's preference. I.e., the dice are ordered , where means "a gambler prefers x to y". Individual preferences are always transitive, excluding preferences when given explicit rules such as in Efron's dice or rock-paper-scissors; however, aggregate preferences of a group may be intransitive. This can result in a Condorcet paradox wherein following a path from one candidate across a series of majority preferences may return back to the original candidate, leaving no clear preference by the group. In this case, some candidate beats an opponent, who in turn beats another opponent, and so forth, until a candidate is reached who beats the original candidate. The liar paradox and Russell's paradox also involve strange loops, as does René Magritte's painting The Treachery of Images. The mathematical phenomenon of polysemy has been observed to be a strange loop. At the denotational level, the term refers to situations where a single entity can be seen to mean more than one mathematical object. See Tanenbaum (1999). The Stonecutter is an old Japanese fairy tale with a story that explains social and natural hierarchies as a strange loop. See also – Going back in time to kill one's own grandfather generates a circular contradiction - Paradox: One must already possess any given piece of knowledge, otherwise it could not be recognized when supposedly "discovered" References Citations Sources Hierarchy Paradoxes Philosophical analogies Self-reference