Strange loop

A strange loop arises when, by moving only upwards or downwards through a hierarchical system, one finds oneself back to where one started.

Strange loops may involve self-reference and paradox. The concept of a strange loop was proposed and extensively discussed by Douglas Hofstadter in Gödel, Escher, Bach, and is further elaborated in Hofstadter's book I Am a Strange Loop, published in 2007.

A tangled hierarchy is a hierarchical consciousness system in which a strange loop appears.

Definitions

A strange loop is a hierarchy of levels, each of which is linked to at least one other by some type of relationship. A strange loop hierarchy, however, is "tangled" (Hofstadter refers to this as a "heterarchy"), in that there is no well defined highest or lowest level; moving through the levels, one eventually returns to the starting point, i.e., the original level. Examples of strange loops that Hofstadter offers include: many of the works of M. C. Escher, the information flow network between DNA and enzymes through protein synthesis and DNA replication, and self-referential Gödelian statements in formal systems.