Douglas Hofstadter (1979: 18) argues that a strange loop occurs whenever, by moving upwards or downwards through the levels of a hierarchical system, you unexpectedly find yourself right back where you started. He sometimes uses the expression tangled hierarchy to describe a system in which a strange loop occurs. They are thus paradoxical structures that nonetheless undeniably belong to the world in which we live (Hofstadter, 2007: 103).
He elaborates that a tangled hierarchy occurs when what are presumed to be clear hierarchical levels unexpectedly take a hierarchy-transgressing twisting- or folding-back. The surprise element is important and is the reason he calls such loops ‘strange’. He distinguishes them from simple tangles, such as feedback, which do not involve transgressions of presumed clear distinctions among levels (Hofstadter, 1979: 686; Hofstadter, 2007: 160). A loop’s strangeness comes solely from the way in which a system can seem to engulf itself through an unexpected twisting-around, violating what had been taken to be an inviolable hierarchical order (Hofstadter, 2007:159)
What he means by strange loop, he says, is 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 returning to the point of departure. That is, despite one’s sense of departing ever further from one’s origin, one winds up, to one’s great surprise, exactly where one had started out. In short, a strange loop is a paradoxical level-crossing feedback loop (Hofstadter, 2007: 101-102)
Such loops may take the form of one-step self-reference, such as the Epimenides paradox, in which Epimenides, a Cretan himself, made the statement: “All Cretans are liars”, a sharper version of which is simply “I am lying”, or, “This statement is false”. However, the loop can be made wider, by choosing to insert any number of intermediate levels, creating many-step strange loops,
Hofstadter (1979: 705) places strange loops at the crux of our understanding of ourselves, through which will come an understanding of the tangled hierarchy of levels inside our minds. His thesis in I am a Strange Loop (Hofstadter, 2007: 103) is that we ourselves, not as bodies but as selves, are strange loops.
Tangled hierarchies, Metalepsis and Narrative Environments
Hofstadter does not use the term metalepsis in his work, but his notions of strange loop and tangled hierarchy, as John Pier (2013) brings to attention, have great significance for narratology, a relevance which we extend here to the design of narrative environments. Pier notes that for narrative metalepsis, understood ontologically, paradox is central, as it involves the logically inconsistent passage between two separate domains through suspension of the excluded middle.
Of central concern is the problem of maintaining distinct levels while seeking to avoid self-reference, a problem elaborated initially in logic and mathematics. Avoidance of self-reference is achieved by elaborating meta-levels, requiring the addition of recursive meta-levels ad infinitum. The eventual, inevitable paradox is captured by Gödel’s theorem. This paradox has long been discussed in scientific thought using the example of the Epimenides paradox, mentioned above. It is also conveyed visually by the Möbius strip, Klein’s bottle and Escher’s drawings.
Brian McHale (1987) takes these paradoxes into account in his discussion of postmodernist fiction which, he argues, brings to the fore the ontological status of text in relation to that of world. McHale recasts Gerard Genette’s narrative or diegetic levels in terms of ontological levels by adopting an ontology borrowed from possible worlds theory. Thus, a metalepsis produced by transgression of narrative levels has ontological implications, which arise from recursive embedding. McHale explicitly identifies metalepsis with the strange loop.
McHale also draws attention to the metaleptic function of the second-person pronoun, following Genette, although he does not distinguish between rhetorical and ontological metalepsis, a distinction proposed by Marie-Laure Ryan, who argues that metalepsis breaks down into a rhetorical (Genette) and an ontological variety (McHale).
Metalepsis, as Pier (2013) comments, is not a media-specific phenomenon. Transgressions of levels and boundaries are not limited to narrative. This means, Pier suggests, that metalepsis has a significant role to play in transmedial narratology and in intermediality. While rhetorical metalepsis is of interest, it is ontological metalepsis which is of central concern for the design of narrative environments, given that its material and media elements stretch from the digital, through the printed, graphic textual, to the theatrical and the built and natural environments. The design of narrative environments takes advantage of the symbol-object dualism by means of which the fictional and the real and the actual and the possible are interwoven. Narrative discourse is taken into the world and the world is taken into narrative discourse, creating, through strange loops, possible worlds and imaginary worlds beyond narrative storyworlds.
The different ontological levels, traversing the fictional, the real, the actual and the possible, are linked by the deictic acts that specify, first, the ontological level from which the narrative environment as event begins and which serve as its deictic centre and grounding, second, the transgressions that are occurring through the strange loops that are being enacted and, third, the tangled hierarchy of worlds that ensues: the imaginary world of the narrative environment.
Allan Parsons, May 2021
Hofstadter, D. R. (1979) Godel, Escher, Bach: an eternal golden braid. New York: Basic Books.
Hofstadter, D. R. (2007) I am a strange loop. New York, NY: Basic Books.
McHale, B. (1987). Postmodernist Fiction. London: Methuen.
Pier, J. (2013) Metalepsis. The Living handbook of narratology. Available at: http://wikis.sub.uni-hamburg.de/lhn/index.php/Metalepsis (Accessed: 28 February 2016).