Narrative Landscapes, Part I:
The emperor has no clothes that fit

The term “landscape” has something powerfully seductive about it. The imagery it evokes is so appealing, that further thought can be completely suspended. — Jones (1995)

Seductive indeed: use story-related data on a contour plot to identify clusters or loci of desirable and undesirable responses; look at plausible pathways across the “topography” between these loci; and then devise interventions or other environmental tweaks to yield stories that match, respectively, the “more like this, fewer like that” mantra. This post takes a step back to look at some of the foundational ideas and usages of such landscapes in the originating life-science disciplines and then examines how the particularities of story data fit into this construct.

In brief, the outcome will be that stories and story data are generally not well-suited to analysis with this approach. The simple topo-map metaphor should be abandoned. Instead, recent developments in other areas of biochemistry and genetics provide a more abstract alternative that is amenable to multiple visualizations, none of which, however, resemble the topo-contour model. We have tested a simple version of this more abstract approach with real story data and found it effective. That approach and the test-case results will be described in Part II.

Sewall Wright was trying to be helpful

The story begins with Sewall Wright, an American geneticist invited to speak at an international conference in 1932 at Cornell University. According to his biographer (Provine, 1986, p. 283), one of the conveners asked if he could make his presentation more accessible to the audience of biologists, most of whom were not as mathematically astute as the level of his material demanded. In response, Wright (1932) created the first “adaptive landscape” as a visual alternative.

Here are the first and fourth figures from Wright’s paper:

The first is a node-and-edge network diagram for all possible combinations of two, three, four, and five genetic components. This graph-theory representation, which was presumably the source of the problem for Wright’s audience, continues today as a standard way of dealing with genetic information. By contrast, the second (Wright’s Fig. 4) uses a topographic-map metaphor as the base for demonstrating how mutation, selection, and other evolutionary mechanisms might “move” a population across a “landscape.” Compared to the equivalent diagrams today, for example, the elegant simulations by Bjørn Østman and Randy Olson, Wright’s six-panel figure is cartoonish. [1]

Limitations on the landscape metaphor

The value of the metaphor as a metaphor

There has been extensive discussion about the value of the landscape metaphor qua metaphor. Not surprisingly, much of this has been in the philosophical literature, which provides some of the more accessible sources for the non-specialist (though rudimentary knowledge of relevant biological material is still necessary). There are four oft-cited papers, published together in a journal aptly titled Biology & Philosophy (Pigliucci, 2008; Plutynski, 2008; Kaplan, 2008; Calcott, 2008), that are a good starting point. These and others by philosophers (Pigliucci, 2012; Petkov, 2015), biologists (Welch and Waxman, 2005; McCandlish, 2011; Svensson and Calsbeek, 2012; du Plessis et al., 2016), and even a biologist-philosopher collaboration (Skipper and Dietrich, 2012) argue for a spectrum of options. These range from one extreme of abandonment to the opposite one of retention, whether as a generative prompt, a framework for evolutionary modelling, or a teaching tool. Claudia Bank — then at the Instituto Gulbenkian de Ciéncia in Lisbon, but since moved to the faculty of the University of Bern — has taken this last item to heart with a fitness landscape board game, rendered in LEGO blocks, which was used at a local music festival and an open house at the Instituto in Lisbon.

Here is a fairly middle-of-the-road quotation from philosopher Pigliucci (2008, p. 598-599), whose overall perspective is shaded toward abandonment, though he always writes with a clear sense of balance. This brief passage illustrates two of the on-going tensions (references to third-party sources are omitted for clarity in this and most subsequent quotations):

Given the serious conceptual issues surrounding Wright’s metaphor of adaptive landscapes, one could reasonably ask whether it is not time to simply drop the metaphor altogether…. At the very least, biologists ought to be very specific about what sort of ‘‘landscape’’ they are referring to…, as well as constantly be reminded that they simply cannot assume that the intuitive properties of low-dimensional landscapes are a reliable guide for the real thing.

We’ll come back to Pigliucci’s issue of landscape dimensionality in the next two sections. But first it is important to notice that there are multiple “sorts” of landscapes. In fact, over the slightly more than nine decades since Wright’s talk and paper, the lexicon has grown to include adaptive, fitness, evolutionary, epigenetic, holey, affinity, dynamic, and dancing landscapes; distinct genotype and phenotype landscapes; fitness and performance surfaces; morphospaces; and more (see discussion of selected distinctions in Arnold et al. (2001) and Pigliucci (2012); and tabulations in Arnold (2003), Klemm and Stadler (2014), and Erwin (2017)). Some of these are used interchangeably — for example, “adaptive” and “fitness” are both sometimes seen as sub-forms of “evolutionary” — but only by some authors. By contrast, “epigenetic” has no direct connection back to the others (Ferrell, 2012; Baedke, 2013), except through having been inspired by Wright’s work — a good example of a generative prompt attributable to the original metaphor. Finally, Mustonen and Lässig (2009), for example, have taken the plunge into the other two-thirds of the terrestrial metaphor with adaptive/fitness seascapes (Merrell, 1994).

Here are two evolutionary biologists (Carneiro and Hartl, 2010, p. 1751) who want to save the adaptive/fitness metaphor from itself, even as they acknowledge its spread to many other disciplines outside the life sciences (again, we’ll come back to this later):

If one may be permitted a metaphor for a metaphor, one could think of the adaptive landscape as a small pack burro that has been loaded with excessive baggage. The mistreated beast has been asked to carry central optimizing principles in population genetics, developmental biology, systems biology, gene regulation, neural dynamics, computer algorithms, protein folding, manufacturing strategy, technology policy, and who knows what else. Should the overloaded landscape metaphor, therefore, be abandoned? We think yes and no. The adaptive landscape is a metaphor, nothing more, and like all metaphors and analogies is misleading when pushed too far…. It should be taken in the spirit in which [Wright] intended. Fitness landscapes should not be abandoned, but rather studied in less picturesque but more quantitative ways.

Other disciplines notwithstanding, that final sentence could be replaced by a barely-disguised paraphrase of Marie Antoinette’s supposed quip: “Let the biologists eat math!” Which brings us to the underpinning domain of this entire subject.

What are the dimensions?

The most important thing we learn when looking at a “map” for the first time is that the x-y or Cartesian dimensions in the plane of the page represent locations. In a highway or topographic map, these are latitude-longitude, respectively, or some other spatial measure. These location parameters can be divided and sub-divided indefinitely — hours, minutes, seconds, hundredths of seconds… for lat-long; light-years, km/mi, m/ft, cm/in… for distance — limited in practice only by the resolution of an image or printing press. This smooth divisibility is the very definition of spatial/graphical “continuity” (not to be confused with the abrupt, discontinuous change in velocity you would experience in a single step that crossed a number of highly-compressed contour lines, otherwise known as falling off a cliff).

In an adaptive/fitness landscape, however, the identity of the x-y “location parameters” depends on the purpose(s) of the person creating the image. And this has been a problem from the very beginning, since Wright sometimes plotted variables that could change smoothly, such as measurable traits of individuals in a population (think “height”), but at other times used genetic information that could not even be sensibly arrayed side-by-side in a grid. His biographer Provine (1986, p. 310) famously took Wright to task:

His construction does not in fact produce a continuous surface at all. Each axis is simply a gene combination; there are no gradations along the axis. There is no indication of what the units along the axis might be or where along the axis the gene combination should be placed…Thus …the most popular of all graphic representations of evolutionary biology in the 20th century, are meaningless.

Notice that we haven’t even considered the third, vertical dimension — fitness or some other metric for adaptive value or speciation — the thing that ideally should convey some evolutionary insight. There is a large modern literature on this — originally theoretical or model-based, but now increasingly experimental — detailed discussion of which would take us even farther afield than we have already gone (but see Pigliucci, 2012, pp. 26-30, for a useful summary). Hopefully this brief excursion will have been enough to establish two conclusions. Firstly, the shaky foundations of the original landscape metaphor indicate that extension of it in a new direction, no matter how appealing as a heuristic, is not to be done casually, if at all. [2]

Secondly and more subtly, notice that Sewall Wright already had a well-developed mathematical model for genetic interactions and evolutionary change. He abstracted the visual metaphor out of the mathematics, replacing his Fig. 1 with his Fig. 4 (see my Fig. 1 and 2 above). But regardless of the graphical representation, he started from a set of equations with well-defined parameters. Contrast that with a typical plot of story-related data (my Fig. 4 immediately above), on which are superimposed the contours of a (non-parametric) probability density function (PDF). Regardless of the visual appeal and the conviction that we should be able to “read” the topography, to effect “more like this, fewer like that” (MLT/FLT), we have no prior basis for such reverse engineering. We have nothing like a set of parametric equations, no model toward which we can work. We’ll have to invent one… after further-but-necessary digression.

How many dimensions are there?

Here is a quotation from McCandlish (2011, p. 1552, emphasis added) that succinctly recapitulates the foregoing and brings the issue of dimensionality to the fore:

Much of the reasoning about fitness landscapes has involved a visual metaphor in which the fitness landscape is depicted as a low-dimensional continuous surface. However, such reasoning may not provide appropriate intuitions for evolutionary dynamics in high-dimensional discrete spaces, and furthermore, no procedure exists to construct these surfaces from actual data.

Wright recognized that the use of a two-dimensional (2-D) framework for his genetic landscape metaphor (3-D when a vertical “fitness” axis is added) was a substantial underrepresentation. He estimated that 9,000 dimensions would be necessary for dealing with the genetic field as then understood (Wright, 1932, p. 357). Modern ways of looking at this issue depend on the type of system being studied, but all are much larger than 3, or even 10^3. We need to look at why that matters, both for evolutionary considerations and, as it turns out, for narrative.

From the beginning, the landscape metaphor inevitably led to thinking about evolution — of either a “genotype,” the ensemble of inheritable information, or a “phenotype,” the physical expression of a genotype — as a process of migration across the (implicit) continuous surface. That, of course, meant negotiating peaks and intervening valleys (see Wright’s Fig. 4C-F, above). But why would an organism/population leave a local peak that it would see as optimal? More to the point, how could it know there was a higher global maximum elsewhere on the landscape? Or, assuming that it started moving, how could it survive crossing a “valley of death” between peaks? These questions arose in the aftermath of Wright’s presentation, including in his own writings, and they continue to be studied to this day. The beautiful thing is that, since evolution in the wild often (though not always!) operates on a geological time scale, possible answers can be hypothesized with mathematics and tested with simulations.

The most relevant of the latter is a series of models by Gavrilets (1997, 1999, 2004, 2010), using percolation theory from statistical physics. These results demonstrated that the long-standing worries over the loss of fitness when a population tried to move peak-to-peak across a valley in a fitness landscape were misplaced… because these features are non-existent in higher dimensions. Instead, there would be a “holey” landscape (above, Gavrilets, 2010) with paths along ridges of “viability” that avoid embedded holes of “lethality” (see Szendro et al., 2013, p. 6; also described as “plateaus of viable states and stretches of lethal states” by Franke et al., 2011, p. 4; see also Kaznatcheev (2019) for an argument from very general principles of computational complexity that a maze would be an even better metaphor). This high-dimensional perspective allows the stochastic (statistical) operation of evolutionary change without the need for extreme swings in fitness.

Story-related data, as we will see in Part II, occupy enough dimensions that Gavrilets’ general results likely apply. Hence, looking at peaks and valleys on a 2-D plot with probability density function contours and imagining interventions to get MLT/FLT stories is also misplaced. Visualizations with such features may be useful for presentations to clients, but they reveal nothing about relationships in the real story-data space. We need to start thinking about a high-dimensional Swiss cheese or sponge, instead of a simple 3-D topo map.

Optimization, or Know Your Fitness Function

Defining “fitness”… or not

The phrase “survival of the fittest” is arguably the most familiar concept in evolutionary theory, perhaps in all of biology, that has escaped from professional jargon into popular usage. The irony from a casual, colloquial perspective, however, is that “survival” (measured as duration or life span) is not what evolutionary biologists mean by “fitness” — it is not the tautological “survival of the survivor” (see Eigen et al., 1988, p. 6881-6882). Instead, it has to do with reproductive success by individuals or populations. Even in evolutionary theory, however, where I would have thought that the mathematical definitions had long since been worked out, there continues to be room for discussion and improvement (see Hansen, 2017). Rather than say more, I will follow the wise lead of physicist Richard Palmer (1991, p. 4), writing the introductory chapter in a volume on molecular evolution on rugged landscapes: “I entirely shy away from the tricky problem of trying to define ‘fitness’….”. If you insist on knowing more, however, the first few paragraphs of the Wikipedia entry on “Fitness (biology)” might be helpful.

Beginning in the 1960s and 1970s, the fitness landscape metaphor was discovered by other disciplines. The most widespread adoption and greatest impact has been in quantitative and mathematical disciplines — chemistry and physics; classical optimization, including operations research; and computer science. Adoption in most social sciences has been narrowly-focused and less impactful; in some fields, the most generous description might be “superficial.” If you want to know more, there are two excellent reviews (Gerrits and Marks, 2015; Rhodes and Dowling, 2018) and a few exemplary studies (Frenken, 2000; Beinhocker, 2007; Rhodes, 2008; Rhodes and Donnelly-Cox, 2008; Valente, 2014; Gerrits and Marks, 2017). [3]

The commonality among applications of “fitness landscapes” in the most impacted disciplines is optimization — there is a minimum or maximum metric of interest, like “fitness” in biology. In chemistry and physics, it might be lowest (most stable) energy state of a material or reaction; in computer science, fastest run time for an algorithm; in a business application, lowest cost or highest revenue. All of these can be cast as a “hill-climbing problem” (see my Fig. 6 immediately above from Reidys and Stadler, 2002), hence the resonance with the landscape metaphor (for example, Stadler and Stephens, 2003, p. 390-392). Except that it is not just a metaphor — the equivalent of the vertical, topographic metric in all of these fields has an a priori mathematical or algorithmic structure, just as Sewall Wright had before he was prompted to draw that first landscape.

Defining “fitness landscape”… which is not the same thing

The good news about fitness landscapes being adopted in these disciplines, especially chemistry, physics, and computer science, is that their denizens have the mathematical facility that Wright’s contemporaries in biology lacked. The bad news, at least for readers interested in how this might be extended to “narrative landscapes,” is that there’s no getting around the math. There is a little more good news. I’ll make it as un-impenetrable as I can, and there will be almost no equations. But also a little more bad news. We will need some concepts that are pretty abstract, which is where we will begin.

There is near-universal agreement that the mathematical definition of a fitness landscape needs three components (but see Jones, 1995, pp. 25-35, for a more expansive algorithmic model). The variety of jargon across the various disciplines and/or authors, however, can be a bit bewildering. In what follows, I’m drawing on papers from computer science and combinatorial optimization (Palmer, 1991; Moraglio and Poli, 2004; Whitley et al., 2008; Pitzer and Affenzeller, 2012; Richter, 2014; Morgan and Gallagher, 2017); polymer biochemistry (Perelson and Macken, 1995); and evolutionary theory (Weinreich et al., 2013). The review by Richter (2014, see pp. 12-15) has an excellent comparison of the differing perspectives of evolutionary biology and evolutionary computation. And then there is the prolific work of theoretical chemist Peter Stadler, Professor of Bioinformatics, University of Leipzig, herewith a sampling: Stadler, 1996; Stadler and Wagner, 1998; Stadler, 1999; Flamm et al., 1999; Stadler and Happel, 1999; B. Stadler, P. Stadler et al., 2001; Rockmore et al., 2002; Reidys and Stadler, 2002; Stadler, 2002; Stadler and Stephens, 2003; P. Stadler and B. Stadler, 2006; Klemm and Stadler, 2014; Klemm et al., 2014. As Whitley et al. (2008, p. 585) aptly said, Stadler has “energetically explored properties of… landscapes.”

We’ll now look briefly at the three components of the definition for the simple reason I’ve already stated: There is no existing theory for narrative landscape, the visual allure of those PDF topographies notwithstanding. So, if we are to adopt or modify or create a useful tool, we need to know what already exists that might guide us. Then we’ll conclude Part I with some examples that show how these definitional components work in practice. (For easier reading in what follows, I omit specific attributions for use of symbols and descriptive phrasing, all of which come from the 20+ sources in the preceding paragraph.)

1. Configuration

The configuration X (or S or V) is a set of all elements or types or things that are present in a particular state (configuration) of a system of interest. This abstract representation usually has many dimensions, often very many. Some general and disciplinary examples (that may share descriptors!):
– in generalized search, a string (S) of candidate or feasible solutions;
– in a graph-theoretic problem, the nodes or vertices (V) of a graph (as in Fig. 1 from Sewall Wright’s 1932 paper, above);
– in solid-state physics, spin-glass structures;
– in biophysics, the shapes (conformation) of some large molecules;
– in genetics, sequences of genomic/genotypic information (for RNA/DNA, viruses, living organisms, etc.);
– in biology, quantitative phenotypic traits for individuals in a population (e.g., weight, length of limb); and
– in classical optimization, the start-to-finish, non-repeating, city-to-city tours of the Travelling Salesman Problem (TSP, see below).

Note that, as expected for a set, the example elements are plural — solutions, nodes, structures, shapes, sequences, traits, tours.

2. Fitness function

The fitness function F(X) (or f: V → ℝ, U: S → ℝ, etc.) evaluates each member of configuration X, which means that it assigns a real (ℝ) numerical value (scalar) to each based on the mathematical properties of F. If there is an appropriate 2-dimensional visualization for X in a Cartesian (x-y) plot, then F defines a 3rd-dimensional surface lying above X, which may include peaks or basins as dictated by the positive or negative sign, respectively, of the scalar values at each point in X. In general, these scalar values can be calculated (searched for) if the form of F is known; or they can be measured in the lab or other empirical contexts. Some examples:
– in generalized search, an objective or utility (U) function optimizes (minimizes, maximizes) the returned value;
– in physics and chemistry, some energy measure (e.g., Gibbs Free Energy) or other potential function is minimized;
– in typical algorithmic problems, computational run-time or other cost function is minimized;
– in evolutionary biology and genetics, survival or reproductive success (whatever — see above) is maximized; and
– in the TSP, travel distance is minimized.

Note that these functions were chosen to help locate the largest/smallest numerical value among all the elements in the configuration being searched.

3. Neighborhood structure

The neighborhood structure Τ is essentially a rule or operator that describes how configuration X can be traversed or searched. It defines a notion of nearness, distance, separatedness, connectivity, accessibility, reachability, or similarity — colloquially, what is connected to what. Taken together, T acts on or augments X to create a configuration space or search space. (A set X whose elements have been interrelated by an operator T is a formal space, G(X,T). Except for a couple of passing mentions, we will ignore the structural “hierarchy” of different kinds of spaces — vector, metric, topological, etc. — though the paper by B. Stadler, P. Stadler et al., 2001, especially pp. 241-245 and 250-251, has a very lucid and relatively accessible discussion of this topic.) Some examples of these rules or operators:
– in generalized search, distance between two strings is measured by the number of positions in which they differ;
– in genetics, two sequences are separated by the number of mutations that would need to occur to make them identical;
– in solid-state physics, two disordered glasses differ by how many spin flips would be needed to make them indistinguishable (“near” or “close”);
– in combinatorial algorithms, “genetic operators” search for optima by exchange, reversal, displacement, etc., of adjacent elements in the search set; and
– in the TSP, a “move operator” or “move set” can transpose or otherwise change the order in which cities are visited.

Note that all of these rules or operations have in common an (implicit) assumption or expectation that any changes are done in small steps, whether in a natural or designed setting. This is a particularly important design principle for practical optimization algorithms (Palmer, 1991).

Real fitness landscapes

If you do an image search on Google for “fitness landscape,” the first rows of returned results will likely be familiar-looking “topo maps,” similar to almost all of the figures in this post so far and variously arrayed across one, two, or three dimensions. Most of them are schematic, conceptual, or model-derived (simulations), but here is an example of one — a potential energy surface (PES) — that is physically grounded:

Potential energy surfaces are used extensively by chemists and physicists to portray and compare the *stability* of various materials, including complex organic chemicals, large biopolymers, metal alloys, and some glasses. Although a PES is calculated theoretically (Wales et al., 2000), it can virtually always be compared to experimental or laboratory data that serve as calibration points. In this example, notice that the coordinate axes are two angles measured in the geometry of the molecule; in other applications they might be interatomic distances or another physical property of a material. More generally, the configuration space (see neighborhood structure, above) is a high-dimensional Euclidean space defined by the coordinate locations of the constituent atoms, and the resulting PES is continuous and smooth (a “manifold” in math-speak).

Now, if you go back to that page of Google image results and scroll farther down, you will see the occasional plot that does not look like a topo map. Here are three examples, becoming progressively less familiar and more complicated:

Szendro et al. (2014, Fig. 1a) describe this figure as an “empirical fitness landscape.” It is based on observations of four beneficial mutations for a bacterium, with the red arrows indicating directions of increasing growth rates (a proxy for fitness); the underlined node (1111) is the global fitness optimum. Notice that this figure would be very familiar to Sewall Wright.

Bank et al. (2016, Fig. 2A) also describe this figure as an “empirical fitness landscape.” It is based on growth rates (vertical axis) of a much larger pool of 640 mutants in a yeast strain, with data displayed for mutations in 13 amino acids at 6 sites. Each vertical line represents a horizontal “step” away from the parent (at 0), with the colored zig-zag lines tracing successive single-step mutations. Notice that in this example it is much more difficult to follow individual paths (than in the preceding network diagram); and yet it is also clear that many of the combinations become strongly deleterious after only a few mutational steps, for example, the purple, green, and many of the gray paths have downward slopes and growth rates less than 1.0 after three or fewer mutations.

Steinberg and Ostermeier (2016, Fig. 4D) offer several variants of my Fig. 10 (above) to present data on possible evolutionary pathways between two forms (alleles, located at the two large color-filled circles) of an antibiotic-resistant gene. The lines represent single mutations in the experimental pathways among 512 possible intermediate genetic sequences; the vertical dimension is “protein fitness” (W). This figure (and its variants) already represent a substantial reduction from the high-dimensional space of the full fitness landscape. Taking the dimensional reduction one step further, notice that the downward projection (parallel to the W axis) onto the x-y plane would yield a nearly-uninterpretable “mesh” of pathways, hinted at by the lowest grayish lines.

Just to make sure that readers interested in narrative landscapes don’t miss the point: this kind of projection is exactly what we do with story data every time we plot them on a plane defined by two signifiers (see my Fig. 4 above). The difference is that we have lost all the overlying detail. If you still imagine that we should be able to recognize pathways in that plane to reach some MLT/FLT nirvana, well, good luck with that! (We return to this topic in detail in Part II.)

Unlike most topo-map landscapes, the three preceding genetic examples are empirical, based on laboratory data. Their underlying configuration space is discrete, rather than continuous. Whatever else they may be, they are not smooth surfaces (manifolds) as in the PES example (Fig. 7 above). The following simple version of the Travelling Salesman Problem (Reidys and Stadler, 2002, Fig. 1.3) is particularly useful in emphasizing the difference:

We’re predisposed to think of this as a continuous problem, because the geographic map on which the ten locations are displayed on the left evokes a view of the surface of the earth that is familiar and “smooth.” But notice that there is no third dimension, no implied topography (though it is certainly there and quite beautiful, if you like austere desert settings). So this “landscape” and the shortest tour of the ten locations in the right-hand panel is solely an artifact for our visual convenience. Keep in mind that there are far more roads interconnecting the locations than the 10 segments shown in red, and it is that much larger collection of discrete, swappable segments (see Klemm and Stadler, 2014, Fig. 3.1) that would be explored to find the shortest path. The real fitness landscape would thus be one of those messy network diagrams (like the three genetic examples above) with many crossing lines that connect all possible combinations of locations, making it visually uninterpretable. Instead an optimization algorithm used an objective or utility function to calculate the length of all possible “mutational pathways” (tours) that satisfy the rules of the TSP neighborhood structure. The optimal (minimized) result is the red tour.

So what (do we do next)?

Despite the spoiler alert at the outset of this post, it probably comes as a surprise to most readers to realize that the topo-map metaphor isn’t likely to be useful as an analytical tool for narrative projects. (Heaven knows, I wasn’t prepared for that conclusion when I embarked on this research!) To learn further that biologists, chemists, physicists, and computer scientists don’t make use of the map version of a fitness landscape other than metaphorically (with the exception of the potential energy surface) pretty much turned this post into a long downhill slide. So, for the reader who has stuck with it this far, you are entitled to a sense of disappointment, frustration, and impatience, all blended into a simple, “What now? Where is the fairytale ending?”

In Part II, we will look first at a startling-yet-simple example from biochemistry that pulls most of the loose ends and threads from Part I into a coherent whole. From that example, I will suggest a new metaphor for looking at stories and story data; and from this, in turn, we can get a precise sense of a story-data space (SDS). Instead of being determined at the very end of the landscape-definition process, we can thus begin with the SDS already in hand. And, in combination with a global optimum (MLT) and nadir (FLT) custom-specified by the client for a project, we can invert the process: rather than define the neighborhood structure, we effectively derive it. Thus, in Richard Palmer’s (1991, p. 6) wonderful phrase, we will know “what is connected to what” without any of the algebraic and topological heavy lifting that Peter Stadler’s papers would have led us to expect. Finally, once we know what the neighborhood looks like, we can help clients better identify actions that have the best chance of achieving desired results, even if it means moving the storytellers and their stories across a landscape that we can’t visualize directly. But first….

A fairytale ending

As this post has documented, the “fitness landscape” is a metaphorical suit of clothes, available in many shops and styles, catering to many buyers — geneticists, evolutionary and developmental biologists, chemists, physicists, computer scientists, operations researchers, economists, policy makers, even philosophers. Anyone, really, who is interested in maximizing or minimizing things.

Unlike the eponymous title character in Hans Christian Andersen’s re-telling of the 14th-century Spanish fairy tale, however, each emperor, from each of those disciplines, actually has a suit of clothes — a “fitness landscape.” It is visible to all citizens of the discipline, in paper after book after dissertation after blog post after slide deck. Even a LEGO game! So the problem is not nakedness, but rather that the suit simply does not fit, either the person or the occasion. It is as though the emperor was invited to a dress ball, expected to appear in a tuxedo, but instead arrived in shorts, a tattered hoodie, and flip-flops. A get-up and appearance totally mismatched to the situation. There are no con men, no need for pretense by the other revelers, merely recognition that the time has come to move on, to voice a collective “OK then.”

The aforementioned disciplines have indeed moved on from the topographic metaphor (even if they still use the sartorial phrase, updated with the prefix “empirical”). Now it’s our turn in sensemaking and narrative, and the place to which we all must move is the tailor shop just down the street. If you’re wondering which street, that will be covered in Part II with the introduction of a new, non-landscape metaphor alluded to above. For now, we just need to know that the solution to the problem — for all of us interested in narrative, not just an emperor or two — is a new bespoke suit. One crafted for each of us. More precisely, one made-to-order for the needs of each individual narrative project. The party will be wonderful when we all arrive suitably attired.

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Footnotes

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References

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