A Narrative Morphology (Abstract)

Gödel, Escher, Bach and Borges A Narra�ve Morphology

Content: Abstract Chapter One -The Strange Loop -The three models of the strange loop Chapter Two -Escher: Ascending and descending/ Rela�vity -Bach; Cannon/Fugue -Gödel’s Epimenides (theorems) Chapter Three Narra�ve and architecture in Borges’s fic�on Bibliography

AbstractThis paper attempts to establish the extraordinary prevalence of the strange loop in the short fictionstories by Jorge Luis Borges. The opening chapters will unpack and explain the contributory branchesof paradoxical construction that Douglas Hofstadter develops In ‘Gödel, Escher, and Bach: An EternalGolden Braid (1979)’. The interim chapters draw upon parallels between Borges’s literature and thephilosophies entertained by Hofstadter; exploring the potential of allegory and fable to create‘spatiotemporal paradoxes’ to ‘unify ideas, media and disciplines that in architectural discourse andarchitecture application remain separate and distinct’ (Psarra 2009). Borges’ prose are grounded onordering system. The experience for the reader is sequential, unfolded piece by piece. This sequencecontains the strange loop. Can architecture be represented through the ordering system of Borges’fiction?

IntroductionAccording to Hofstadter, the work of mathematician Kurt Gödel, artist Maurits Cornelis Escher andmusician Johann Sebastian Bach, can be defined by an ordering mechanism; “a shift from one level ofabstraction to another, which feels like an upwards movement in a hierarchy, and yet somehow thesuccessive upward shifts turn out to give rise to a closed cycle. That is, despite one’s sense of departingever further from one’s origin, one winds up, to one’s shock, exactly where one had started out. Inshort, a strange loop is a paradoxical level-crossing feedback loop”. (Hofstadter 2008, 102).Similar to ascending an endless staircase, a Strange Loop moves further and further away from astarting point, yet ultimately ends up exactly where it began due to an impossible, tangled hierarchyof levels that stage from finite to infinite realities and non-realities (Hofstadter 1979). I argue thatBorges’ short fictions contain the strange loop in much the same way as does Escher ‘ascending anddescending lithograph, as Bach’s cannon and fugues and Godel’s mathematical theorem. Borges’strategy combines the term ‘seduction’ and Deleuzian term ‘fold’. There are two step process inBorges’ fiction-creating strategy:The first step in his strategy is to transform a continuity into a succession of points, and to suggestthat these points form a sequence; there follows the insinuation that the sequence progresses beyondthe expected terminus to stretch into infinity; then the sequence is folded back on itself, so thatclosure becomes impossible because of the endless, paradoxical circling of a self-referential system.This complex strategy (which may not appear in its entirety in any given story) has the effect ofdissolving the relation of the story to reality, so that the story becomes an autonomous object existingindependently of any reality. The final step is to suggest that our world, like the fiction, is a self-contained entity whose connection with reality is problematic or non-existent (Halyes 1984, 143)Halyes reinforces the prevalence of the strange loop in Borges’s fictions by laying out the hypothesisthat the ordering mechanism is parallel to that of a strange loop. The sequence of suggestedmovement is also similar to the ‘ascending and descending’ phenomenon.The above hypothesis will be explored by examining the morphological structure of Borges’ shortfiction from the Aleph; The immortal and The library of Babel. Furthermore, the reinforcementmethod of instilling the philosophical content, as demonstrated by Gödel, Escher and Bach in thestrange loop phenomenon. This exploration will first be conducted descriptively and theninterpretively through the analysis of parallel themes of the strange loop and Borges’ Short Fictions.

The final chapter will conclude with the premise that if there are any tangencies between narrative-labyrinth and the strange loop, they exist in the way they are created. Can unpacking the conceptualsymmetries, the linear sequences, the structuring of experience, illuminate a new way of thinkingArchitecture.

Chapter OneThe strange loopThe strange loop is a phenomenon that Douglas Hofstadter defines as an event of “movementupwards (or downwards) through the levels of hierarchical system, we unexpectedly find ourselvesright back where we started” (Hofstadter 1979). The strange loop in Hofstadter’s explorationsfunctions as the intellectual edifice where channels of thought in mathematics, cosmology, music, art,philosophy and literature, intersect and vehemently unite. The strange loop exists within a spectrumof finite and infinite boundaries. Shifting back and forth, potentially creating perceptual perplexities.After observing a strange loop paradox, one may seek to find facsimiles in the ordinary world that theythemselves occupy. Though one would not come away from the paradox with the intent of examiningtheir surroundings by applying the same logic; in that one would not see Escher’s lithographs ofascending and descending staircase and try to apply the same vision to their own staircase, but Borgesdraw the viewer as a another dimension of fiction within his stories.The library of BabelIn the story ‘The Library of Babel’ Borges demonstrates the application of the strange loop but alsohow it differs from the scientific model that Hofstadter analysis in Gödel, Escher, and Bach: An EternalGolden Braid (1979). In ‘The library of Babel’ Borges suggests that everything including even the realsubject is a fiction in his story. The story unfolds with the reader himself. As it unfold the reader findsthemselves in the strange loop. There is a narrator, who calls himself the librarian. The librarian issuspicious of the extreme symmetrical order of the library and convinces himself that there must behidden meaning behind the symmetrical order of the library. However he (and the audience) come tounderstand that the order is not the same as meaning. The narrator is then faced with the dilemmaof what he states as the major fact of the history. The library has to be infinite, but the capacity ofbooks attainable from the library, regardless of its immense size is still finite-argues the narrator. Thenarrator convinces himself that the answer lies in the speculation that the finite collection can becomean infinite series once they are continued indefinitely. The narrator then further speculates that theperiodic repletion then becomes and order possessing a precious sequence.It is not the narrators rational that renders his speculation good worth, but it is the inevitability of theevents in his speculation. It demonstrates the human nature to find meaning, even if it is inmeaningless order of sequences. Borges demonstrates the use of the strange loop with the sameelement of inevitability in its appearance; it encompasses the reader itself in the circle of the narrative.

Borges himself stated that “if the characters in a story can be readers or spectators; then we, theirreaders and spectators, can be fictitious” (Stabb 1991, 46).Canon and fuguesHofstadter introduces the strange loop phenomenon through the engagement of the types ofintellectual musical “playing”. A canon is a repetition of a piece of music that is ‘played against itself.It contains single theme. The complexity is achieved through interplaying layers of the same theme inthe following ways;Copy of the theme is played a fixed time laterThe theme is staggered in time and pitch,The theme is played at different times and pitchThe theme is played at different speeds, the theme is inverted,The theme is played backwards, noted as crab canon (Hans T. David 1972).The step of inversion is one that Bach play with throughout his work, for therein lies the strangeness.An inverted melody is rather weird at first instance of hearing. However, as the repletion of it isimpressed on the hearing senses, it begins to sound exceedingly natural.A fugue is also a form of musical offering that resembles the composition capabilities of the cannon.However, whilst the cannon is inflexible and rigid, the fugue permits opportunities to extend the‘emotional and artistic expression’.The staggering ‘copies’ of the theme in both the cannon and the fugue endows its possibility to thefundamental principle of preservation. Every type of copy entirely preserves the information in theoriginal theme, in the sense that the theme is fully recoverable from any of the copies. “Such aninformation-preserving transformation is often called an isomorphism” (Hofstadter 1979).Endlessly rising cannonEndlessly rising cannon of the musical offering piece which openly demonstrates the notion of strangeloop. The fundamental principle lays in the tangency between the upward and downward levelhierarchies. The musical notes are so constructed that the ending joins smoothly to the beginning.One finds themselves right back to where they started. Bach somehow contrives to ‘modulate’ thekeys right under the listener’s nose (Hofstadter 1979).

Sequences play a significant role in Borges’s development of narratives, but more importantly theyare a key to developing the dual concept of word and world. Sequence allow Borges to develop ideaswhich demonstrate that fiction and world are ‘self-referential systems’. The sequences also providethe structure for his narratives. It’s upon these sequences that he builds his plots, puzzled, conceptualsymmetries (Psarra 2003). The correlation can be further defined by the paradox, parable of thetortoise and the hare. The tortoise who has a head start and goes one length before the hare begins.However, after the hare has gone one length, the tortoise would have travelled one plus one-tenthlengths. Therefore the tortoise will still be ahead.This means that the points of infinity can be achieved between any two points simply by convertingthe distance from a ‘continuum’ to an infinite series of decreasing magnitude/notes.The geometric construction of Borges’s fictions also use the same method to construct the paradoxes.The principle of continuousness of space time is of similar importance to that in Bach’s musicaloffering. The continuity of space and time implies a journey from point A to point B which of courserequires the crossing the transitional distance. However, Borges’s narrative structure breaks thiscontinuity into firstly intermediate term. For the reason that the transition between terms isdiscontinuous, it also allows the space to intervene between terms. This further allows the space tobe occupied by sub-series of infinite length. In this way of sequencing the narrative, Borges gains theability to influence immediate transitions between continues terms. For example, ‘by placingopposites as the terms of the same sequence so that the progression along the sequence suddenlytransforms one thing into its opposite. This method is parallel to the notion of the endless cannon inthe musical offering piece, in that Bach is also implicitly introducing a new musical note in creating astrange loop. This note becomes the continuum between the series on infinite melodies already atplay.The potentially never ending nature of the formation is what situates it in-level with the idea of aMobius strip; an infinitum- of thought and existence.This concept of infinitum- of thought and existence is ever prevalent in the images of the Dutch graphicartist M.C, Escher.

Chapter TwoImplicit in the concept of Strange Loops is the concept of infinity, since what else is a loop but a wayof representing an endless process in a finite way?...In some of his drawings, one single theme canappear on different levels of reality...But the mere presence of these two levels invites the viewer tolook upon himself as part of yet another level, and by taking that step, the viewer cannot help gettingcaught up in Escher’s implied chain of levels, in which, for any one level, there is always another levelabove it of greater “reality” and likewise, there is always a level below, “more imaginary” than it is.This can be mind-boggling in itself. However, what happens if the chain of levels is not linear, butforms a loop? What is real, then, and what is fantasy? The genius of Escher was that he could not onlyconcoct, but actually portray, dozens of half-real, half-mythical worlds, worlds filled with StrangeLoops, which he seems to be inviting his viewers to enter (Hofstadter 2007).The lithograph; Ascending and Descending by Escher (1960) Fig1, represents this notion of paradoxicallevels of realities and creative imagination. One level is established upon the preconceived speciallogic of upwards and downwards that one enters with complete submission. The second level isdiscovered via what initially seems like a linear progression, but as one moves away from any givenpoint, their expectations are overturned and an interchange takes place. Not only between the twolevels, but also the third; the viewer. The viewer represents another reality, creating potentiallyinfinite chain of paradoxical hierarchies; resultantly a strange loop of realities-non-realities.The Immortal is a story by Borges which comprehensively demonstrates the previously studiesconcepts relating to the strange loop phenomenon. Borges creates a setting which portrays manysimilarities to the graphical nature of Escher’s lithographs. The story from the offset frames the maincharacter; Marcus Flaminius Rufus, as he is on the journey into the “City of The Immortals” (Borges1998, 4). As Rufus travels afar from a given origin into the city, he finds himself back at the point oforigin.The centre of the narrative lays in the task that Rufus is awarded, together with an army of soldiers;the task of finding the ‘the city of the immortal’. In the quest for the city and its river, the soldiers getlost in the desert, without water for several days, then in captivity. The vision of the “patent city ofthe immortal shone dazzlingly in the rays of the sun” (Borges 1998, 6) encouraged Rufus to escapefrom the capture and descend once again on his conquest. He crosses the stream trailed by thetroglodyte tribe.

The city was built on a “stone plateau” (Borges 1998, 8). Rufus was received by a series of cavern toseek refuge. Under the earth “nine doors opened to the cellar-like place; eight led to a maze thatreturned deceitfully, to the same chamber; the ninth lead through another maze to a circular chamberidentical to the first ” (Borges 1998, 8).There was a hostile silence. The architecture consisted of triangular pediments, columns and confusedglories carved in granite. Rufus is horrified by what he witnesses. He sense more intellectual horrorthan sensory fear, sensation of oppressiveness and complex irrationality. He describes the maze ashouse built just for the purpose of confusing men (Borges 1998, 9). There were corridors that did notlead to anywhere. Rufus ends the story with the statement that “I cannot say whether these are literalexamples I have given; I do know that for many years they have plagued my troubled dreams..I cannotrecall the stages by which I returned” (Borges 1998, 10).The description of under earth chambers in ‘city of the immortals’ is worthy of comparison with thestrange loop. The nine cellar doors, out which eight led to a maze that returned deceitfully, to thesame chamber and the ninth lead through another maze to a circular chamber identical to the first.The function of a door is either in direction of entrance or exit, it provides a concurrent function forgetting from one space to another. However, the description of the mazes with 8 out of 9 doors is aperfidiously constructed strange loop.Borges allow the narrator 1 in 9 chance of escaping the bounds of the strange loop. However he is leftto wonder through ‘city of the immortals’. Also, strangeness lies in the narrator’s recollection theevents that took place after the maze, how did he escape the city? The distortions and the dramaticperplexing experience. Rufus’s encounter with the strange realities-non-realities conforms to thesame decorum as the strange loop. The story its self as a structure does not follow continuessequence. The narrator’s experience of the strange loop causes him to narrate bot the event of pastand also the how they lead to the present.Furthermore, the narrator declares that he does not want to describe his experience. This reluctanceof the character is a symbol of vulnerability which indicates to the reader the significantly horrendousexperience he must have had. It prepares the reader for the description that the narrator then usesto further expose the city and the extraordinary effect it has had. The description of ‘city of theimmortal’ create architectural images that are although approximate (the construct of maze), butcreate a correspondence to reality. The architecture renders the ideas and actions that take place in‘city of the immortal’ Psarra (2003).

Analysis of the ‘The immortal’ demonstrates that not only does architecture has the capacity to feedpopular imagination but fiction narratives, such as those by Borges provide an infinite list of creativeideas that one can engage with to exceed in creating an experience that is extraordinary.Contributing to this function of hierarchies is the fundamental notion of paradoxical return-movementto the point of origin. In a strange loop, at any level this movement is undisturbed. Hofstadter impliesthe term ‘violation’ that does not occur at hieratical level. It is rather a violation of ourpredeterminations of the motif such as that “I climb this staircase upwards from the first floor andthen I reach the second floor.” The violation occurs when the determination changes to “I climb thisstaircase upwards from the first floor and arrive at the first floor.”Gödel’s Self-reference philosophy further expresses the infinite process of ascending and descendingundertaking of a strange loop in a finite statements of self-referential proof. Continuing with theanalysis that we made of Borges’s fiction the library of Babel, the following statements structureGödel’s logic;The library contains meaningless volumes (statement 1)The library of Babel is a story contained in the library (statement 2)The library of Babel is nonsense (statement 3)If statement 3 is true, then statement 1 is false, if statement 3 is false, then statement 3 is false.Statement 3 has paradoxical nature of being both true and false. As previously established in the visuallanguage Escher graphics, strange loops also “contradict our habitual understanding of sentences asbeing exclusively one or the other” (Psarra 2009). The ‘incompleteness theorem’, as proposed byGödel 1931, demonstrated that there are propositions that cannot be proven within a mathematicalsystem or are inherently insolvable (Gödel 1962).This brings us back to Borges strategy in creating fiction. The self-referencing philosophy consists of asingle term that repeats itself endlessly. This could be in form of circle of linear sequences. In this, thesequence turn back on themselves in undecidable propositions.Gödel’s proposition of proof is comparable to that of ‘The Liar Paradox’. This paradox has a Cretanasserting, “Cretans always lies” (N. Shankar 1997). If the Cretans always lie, then the above statementis true. Then, however, since the statement is true and spoken by the Cretan, it cannot be the case

that Cretans always lie. Therefore, if the statement is true, then it is also false. Conversely, if thestatement is made by a single Cretan, then if the stamen is false it is also true. Since The Liar Paradoxemploys the notion of meaning, truth and falsity, it is a semantical paradox. It suggest that the notionare not properly definable for a language within a language within the language itself.The work of Jorge Luis Borges and other contemporary writers such as Beckett, John Barth andPirandello consist of ‘Gödelian’ qualities: their narrative, in the manner of the liar paradox, isrepeatedly self-negating, it refers self-referentially to that of which it is composed and it often impliesvicious circularity of infinite regress. Like Escher’s print of a hand drawing another hand which in turnis drawing the first hand. Like Bach’s endlessly rising cannon, Borges recursive labyrinths are set intexts, that are predominantly at war within themselves: they oscillate between the either and or avacillating, flickering, scintillating Moiré effect of constant movement in the midst of stasis-theypromise symmetry, but somewhere the harmony is inevitably tainted, though ever so slightly (Merrell1988).Merrell refers to Borges’s fictions, as stated in above statement, as recursive labyrinths. This relatesto the structure of the narratives. The discontinuations structure of the terms within the stories allowsthe opportunity to transcend between points, creating the ‘recursive’ labyrinths of transcending backand forth from point A- B.Parallel to the proposition of Gödel’s incompleteness theorems, Borges’s fiction making entails manyinteroperations of the language of hierarchies which signify something other than what they wouldordinarily signify. As a way of examination let’s make the statement that “This sentence is false”. Itdenies of itself the very reason for a propositions existence; for it cannot justify its beingness. It is nomore effective than its equivalent: “This sentence is a Fiction”. Which if fictive, then it is unreal, henceoutside the realm of true proposition. But if so, then it is “false”, and if “false”, then real, so on and soforth. Now, the proposition that fiction making entails systems familiar with those entertained inGödel’s strange loop conjunctions is entirely worthy of acceptance. In Borges’s short fiction narratives,the strange loop exists in a labyrinth of two interchanging levels of motif and structure. This is furtherevident in the theories that have been explored in previous pages. Mainly it is evident in the structureof the narratives, the way they are created. The structure of the narratives is created so to carry themotif. It is particularly the sequence structure that contains the potential to succeed the narrative.

This point is reinforced by Hayles analysis of Borges’s application of the Georg Cantor’s set theory.Hayles states that Borges himself confessed that he had resolved the “spells of mathematics”. In thatthe strange loops are the essence of these spells.ConclusionThe study of Gödel, Escher, and Bach: An Eternal Golden Braid (1979) as a means of exploring thestrange loop phenomenon exquisitely instilled in Borges short fictions. Having unpacked and analysedthe various branches of the paradoxical construction Douglas Hofstadter develops In ‘Gödel, Escher,and Bach: An Eternal Golden Braid (1979), it has provided an insight into the multidisciplinaryphilosophies that Borges evidently entertains in his fiction stories; the immortal and the library babel.The extraordinary prevalence of the strange loop in Borges fictions proves that fictional and narrativescontain multi-disciplinary ideas and imaginations. The structure of Borges narratives, the sequentialorder to contain labyrinth, the conceptual symmetries all contribute to an extraordinary experiencewithin Borges fictions. Adopting these systems of thinking with in the architecture and designdiscipline could liberate the fixed mind-sets of the professionals within the field.The strange loop phenomenon is contained with unlimited resource and when introduced intangencies with narratives and fiction in the scope of architecture, as demonstrated in this paperthrough the studies of Borges stores, it could provide a revolutionary discourse amongst the manydesign disciplines that are now more and more integrated.The concept of time and space as a scientific model is explored in different degrees in Gödel, Escher,and Bach: An Eternal Golden Braid (1979). Hofstadter’s strange loop contain horrific qualities forhuman experience. In Borges’s paradoxes, the concentration is intensely on the dimension of time, astime is the more venerable capacity of a paradox. The combination of finite and infinite the Borges’capability of stretching the motif to both extremes of the spectrum.

Ascending and Descending by M.C. Escher lithograph 1960

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