Hierarchy

A strange loop arises when, by moving up or down through a hierarchical system, one finds oneself back where one started. It 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 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.

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

“ 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 a 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.

Hofstadter claims a similar “flipping around of causality” happens in minds possessing self-consciousness. The mind perceives itself as the cause of certain feelings, (“I” am the source of my desires), while scientifically, feelings and desires are strictly caused by the interactions of neurons, and ultimately, the probabilistic laws of quantum mechanics.

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