On the Geometry of Metafiction

We geometrically visualize the problem of embedding disparate storylines into a single unifying narrative. A Narrative Puzzle and its Geometric Visualization My three novels, The Death of Vishnu (2001), The Age of Shiva (2008) and The City of Devi (to appear, 2013) are disparate in setting, time period, characters and plotlines. The question I consider here is how to write a fourth novel that links them together to create a single connected work of fiction. The traditional strategy would be a new storyline that passes through the three separate narrative arcs. However, with all my previous three stories already written, trying to fit them into a new narrative (dashed curve) might make the result look particularly contrived, awkward or convoluted (see Figure 1(a)). Figure 1 : (a) Connecting story arcs (b) Closed curves cannot be connected In a purely mathematical sense, given n smooth (C or C) arc segments, it is of course possible to join them by a single smooth (C or C) curve. However, constraining the length of this connecting curve may result in large derivatives in the vicinity of concatenations (corresponding to the drastic contrivances needed to fit together far-flung narratives and characters without resorting to long-winded exposition). This solution method breaks down completely if rather than open arcs, one considers closed curves (which, translated to fiction, would correspond to the previous stories being essentially self-complete). See Figure 1(b). Of course, this mathematical problem is easily solved if one increases the dimension of the solution space by one, and allows a surface, rather than a curve, to be the connecting entity. As Figure 2 shows, one can always find a 3-d surface which intersects the plane of the paper precisely at the closed curves one would like to incorporate. (Essentially, the closed curves form the level set of this surface corresponding to z = 0, where z measures distance perpendicular to the paper). In fact, an infinite number of such surfaces can be found, with smoothness only limited by the smoothness of the original closed curves. To interpret this in narrative space, we note first that in Figure 1, the observer (i.e. reader) must be external to this space, with a vantage point that enables the simultaneous viewing of the different stories. If the narrative space is modeled by the x-y plane of the paper, a natural position for the observer would be looking down from an elevated position outside this space, i.e. from a spot with z > 0, where the z axis is perpendicular to the paper. Bridges 2012: Mathematics, Music, Art, Architecture, Culture