Editing Strange loop (section)

== 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 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 ''Canon 5. a 2'' from J.S. Bach's [[Musical Offering]], the information flow network between [[DNA]] and [[enzymes]] through [[protein synthesis]] and [[DNA replication]], and [[self-reference|self-referential]] [[Gödel's incompleteness theorems|Gödelian statements]] in [[formal system]]s.

In ''[[I Am a Strange Loop]]'', Hofstadter defines strange loops as follows:

<blockquote>And yet when I say "strange loop", I have something else in mind — a less concrete, more elusive notion. What I mean by "strange loop" is — here goes a first stab, anyway — not a physical circuit but an abstract loop in which, in the series of stages that constitute the cycling-around, there is a shift from one level of abstraction (or structure) to another, which feels like an upwards movement in an hierarchy, and yet somehow the successive "upward" shifts turn out to give rise to a closed cycle. That is, despite one's sense of departing ever further from one's origin, one winds up, to one's shock, exactly where one had started out. In short, a strange loop is a paradoxical level-crossing [[feedback loop]]. (pp.&nbsp;101–102)</blockquote>