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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:

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. 101-102)

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