Abstract
Judging by what Douglas Hofstadter 1 has to say about Escher's 'Print Gallery' (1956), it is clear that it was a liminocentric structure that the painter intended
to depict. Liminocentric structures are organized like a series of nested boxes in which the innermost box is, paradoxically, identical to (and indistinguishable from) the outermost box. In an earlier paper, The Structure of Consciousness: Liminocentricity, Enantiodromia, and Personality, we explained why it is that we believe that consciousness itself may in fact be liminocentrically structured. In the same paper we explore the idea that it is the enantiodromic relationship between the four Jungian 'mental functions' that permits us to conceive of personality as having a complex and essentially paradoxical structure.
Since we have considered the concept of liminocentricity in depth elsehwere 2 we will not do so here. Having
previously explored the presence of liminocentric structurings in religion,
myth, storytelling, music, dance and movement, drama, theatre, and science, in this issue of our Journal we focus primarily on the visual arts. So in the present paper, which is very brief, all we really intend to do is present the one painting by Escher, along with what Hofstadter has to say about it. For more on the subject of art and liminocentric structures, and Escher, please see
About Face Again.
Escher mastered the fine art of incorporating what Hofstadter calls
'Strange Loops' into his paintings. These loops are heirarchies that are non-linear (i.e., circular, or 'tangled' - to use Hofstadter's terminology). They thus wrap back around on themselves - and are what we would call liminocentric structures. Below is a reproduction of Escher's (1956) 'Print Gallery'.
'The tightest of all strange loops,' says Hofstadter, 'is
realized in Print Gallery: a picture of a picture which contains itself.
Or is it a picture of a gallery which contains itself? Or of a town which contains
itself? Or a young man who contains himself?' 3
Some of the features of this painting that are crucial to understanding it are unfortunately difficult to discern in this particular reproduction. [For a pop-up window with a larger (240k) version, from an external site, double-click here]. Perhaps the following passage, by Hofstadter, will help the reader to pick out some of the necessary details - A strikingly beautiful, and yet at the same time disturbingly grotesque, illustration of the cyclonic 'eye' of a Tangled Hierarchy is given to us by Escher in his Print Gallery. What we see is a picture gallery where a young man is standing, looking at a picture of a ship in the harbor of a small town, perhaps a Maltese town, to guess from the architecture, with its little turrets, occasional cupolas, and flat stone roofs, upon one of which sits a boy, relaxing in the heat, while two floors below him a woman - perhaps his mother - gazes out of the window from her apartment which sits directly above a picture gallery where a young man is standing, looking at a picture of a ship in the harbor of a small town, perhaps a Maltese town - What!? We are back on the same level as we began, though all logic dictates that we cannot be. (Hofstadter, page 715) That 'blemish' about which Hofstadter speaks reminds us of the anomalous center of the Shri Yantra (see the analysis of the Shri Yantra presented in The Enneagram as Classic 'Double Mandala' - Part II -Shri Yantra, Kabbalah, and Inner Alchemy, which is based on John's 1976 analysis of it, presented in Consciousness). It is the experience of 'the anomaly at the center' that we were trying to capture by using the prefix 'limino' in the word that we coined for such structures - the term 'liminocentric'. This word implies that it is possible to bring what is liminal or marginal - i.e., beyond the 'limen' (the 'threshold' or 'limit' which distinguishes what is in the center from what is in the margin) - into the CENTER. When used as an adjective modifying the noun 'structure', it conjured up - for us - the image of a structure turned paradoxically outside in (and inside out), rendering central the 'mystery' that is characteristically relegated in our culture to the fringe. 4 Unlike Escher's painting, it IS the intent of the Shri Yantra to suck us into the experience that is the result of its central anomaly. This is what makes the Escher painting, although instructive, somewhat less satisfying - for it is an attempt to REPRESENT liminocentric structure, whereas the Shri Yantra is (as Evans and Fudjack pointed out in Consciousness) best understood as an attempt to INDUCE such an experience in the subject/viewer. Such diagrams (of a meditational, magical, or medical nature) were a very common source for painting in the later 19th and early twentieth centuries, and played a role in the advent of 'abstract' art. 5 In comparing these two works in particular - Escher's Print Gallery and the Shri Yantra - we see that the association between the two fields of endeavor may be less of a coincidence than one might at first suspect. Another example of the deeply rooted similarity between the endeavor that we call 'modern art' and the one that is sometimes described as the 'spiritual path' is the mandala that came to Yeats and his wife in a vision they induced by 'automatic writing'. He called his diagram, which has as its underlying structural principle two 'gyres' (or vortices), 'the Great Wheel'. On it he mapped a complex personality system. For more on Yeats's project, see About Face. But Yeats's diagram, like Escher's painting, does not try to induce the experience, it merely represents it. For a discussion of a modern painter whose work WAS an attempt to induce the experience of a liminocentrically structured experience, see our current paper on Picasso, About Face Again. Footnotes and References
1. Douglas R. Hofstadter, Godel, Escher, Bach: an Eternal Golden Braid, 1979, (New York: Vintage Books). Our thanks to C.O. Evans for reminding us of the existence of Hofstadter's book and pointing out that some of the things that he had to say parallel what we've said about liminocentricity. Hofstadter's book came out a few years after it occured to John, in 1976, that consciousness might have a liminocentric structure. Although Hofstadter wants 6, like we do, to say that 'strange loops' will eventually turn out to be the focus for understanding how the human 'mind' works, he does not explicitly characterize consciousness itself as looped or liminocentric. There are probably two reasons for this. 1) Although Hofstadter focused squarely on how a process could loop back on itself,
he did not seem to think primarily in terms of STRUCTURE, and did not tend to
characterize such loops as constituting structures per se; and 2) More importantly, perhaps, is the fact that at the time that Hofstadter was writing his book he apparently did not have the benefit of a theory of consciousness such as the one
proposed by C.O. Evans - which conceives of consciousness itself as structured. Once consciousness is conceived as structured, as we point out in The Structure of Consciousness: Liminocentricity, Enantiodromia, and Personality, not only does it become theoretically possible to think of it as a heirarchy of nested contexts, but also to view it as a heirarchical structure that loops back on itself.
2. For more on the concept of liminocentricity see -
3. Douglas R. Hofstadter, Godel, Escher, Bach: an Eternal Golden Braid, 1979, (New York: Vintage Books), page 15. In previous articles (see, for example, The Structure of Consciousness: Liminocentricity, Enantiodromia, and Personality) we characterized 'liminocentric' structure in two general ways that may at first glance seem to be unrelated: 1) as a structure comprised of a series of nested frames in which the innermost frame is identical to the outermost; and 2) as a structure exhibiting 'paradoxical containment' - in which a particular object 'X', in a context 'Y', might equally well be alternately described as an object 'Y' in a context 'X'. Hofstadter recognizes that each of these characterizations entails
the other and thus both equally well characterize non-linear nested hierarchies
or 'strange loops'(which Hofstadter also calls 'heterarchies' - as opposed
to 'heirarchies').
4. Our search for a word that would imply that consciousness could be inverted in such a way was undertaken in the same spirit, apparently, that moved surrealist Paul Reverdy to write the following - We no longer believe in miracles - nothing is more obvious. But the miracles in which we no longer believe are as nothing in comparison with those that each man carries in reserve in his innermost self and which his imagination offers him at all time. - Reverdy, circa 1932 (page 76, in Balakian, 1959) 5. In her book, Surrealism & the Occult: Shamanism, Magic, Alchemy, and the Birth of an Artistic Movement, art historian Nadia Choucha writes about Kupka - a painter who, in the 1880s, had studied oriental philosophy and became a vegetarian and spiritual medium. Kupka produced paintings in 'a purely abstract style' circa 1911, around the same time as Composition 5 the painting by Kandinsky reputed to have been the first 'abstract' painting. She says - His development to abstraction was a result of introducing Theosophical imagery and theory into his art. ... Kupka must have been aware of Theosophical diagrams such as The Planetary Chain from Sinnett's Esoteric Buddhism, which appeared in the 1890 issue of the Paris Theosophical Review. The diagram represents the reciprocal interaction between the descent of spirit into matter (involution) and the ascent of spirit beyond matter (evolution). (Tuchman et al., 80)
For more on the notion of the 'reciprocal interaction' between 'incommensurable
orders' see the material on Bergson and Yeats in About Face.
The important idea is that this 'vortex' of self is responsible for the tangledness, for the Godelian-ness, of the mental processes. People have said to me on occasion, 'This stuff with self-reference and so on is very amusing and enjoyable, but do you really think there is anything SERIOUS 7 to it?', I certainly do. I think it will eventually turn out to be at the core of AI [artificial intelligence studies] and the focus of all attempts to understand how human minds work. And that is why Godel is so deeply woven into the fabric of my book. - Hofstadter, Godel, Escher, Bach: an Eternal Golden Braid, 1979, page 714.
7. If you arrived here by clicking on footnote 1, in the main body of the text,
and then clicking the 'internal' footnote within footnote 1, and so on, you will soon discover that if you click the footnote within this paragraph, you'll arrive back where you started. This not only demonstrates what a liminocentrically organized paper -
made possible by hypertexting - might look like, it shows how such a thing invariably involves a 'self-reference' (this footnote - footnote 7) that crosses contextual levels. In a valiant attempt to save logic from paradox, Bertrand Russell tried to outlaw these. But Hofstadter, for one, didn't buy his argument, and delighted in examples of cross-contextual loops such as the one provided by Escher in his painting, 'Print Gallery' 8
9. This footnote is absolutely superfluous. No link in the text brings you here,
and from here you can't get anywhere by clicking. So what are you doing here?
By the way, what happened to footnote 8? It was here a minute ago; I swear!
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