Narrative & Data

Authors note: This is a very rough draft and an attempt to treat this subject with some degree of formality. For a more cogent but less formal exposition, see my essay Narrative Engineering.

Models and Fictions

The philosopher of risk and probability Nassim Nicholas Taleb attributes many of the current problems of the popular imagination to what he calls The Narrative Fallacy: in our everyday discourse there is an inevitable and deeply human tendency to attribute cause and effect to phenomena whether or not we can justify it. Just like one can see a duck, or perhaps a rabbit, in a cloud, the newspaper might also tell you that the stock market crashed upon fears of a war between two countries but had the stock market gone up would just have quickly as told you that the stock market rallied because an impending war will stimulate the economy.

He's absolutely right, but the obvious fallacy of unnecessarily pretending to know why somethign happened is often carelessly generalized into a blanket condemnation of "narrative", where narrative is vaguely defined as some kind of summarization of what happened. This is a bit problematic, since narrative can mean many different things that don't fit this definition: it can mean a fictional story like what you would find in a novel, or an idea of one's purpose, or an underlying ideal that upon which a society bases its social contract. The kind of "narrative" that this fallacy refers to is none of those, what it is really talking about is a model.

A model is a system of cause and effect that explains, and by extension abridges, an observed phenomenon. Why abridges? This can be understood according to a field of applied mathematics known as information theory: imagine that I tell you to memorize the following string of bits: 010110101001011110101001011. All I can say is good luck. But now memorize this one: 00000000000000. This is easy: all you have to do is remember how many times you're supposed to repeat "zero". Or how about this one: 0000000000001111111. This one is a bit harder, now you have to remember how many times to say "zero" followed by how many times to say "one". But if it's 00000000001111111111, that's easier: once you realize they're repeated the same number of times, you only have to remember one number. The point should be clear: the simpler a pattern you can find to explain something, the less effort it takes to remember or utilize it.

More technically, the simpler a pattern, the less space it would take in a computer (or on a piece of paper) to store it. If the string is one billion zeroes, you don't need to store all billion zeroes; it in fact would take up no more space than repeating zero ten times (for more detail, refer to the appendix for notes on entropy and Kolmogorov complexity).

Models are what allow science to progress: if you can reduce things to simpler patterns and sets of rules, it becomes easier to apply them to discover new things, and by doing this one can steadily accumulate knowledge. The entire concept of Occam's Razor is built around this idea: it's not that something being simpler makes it correct, it's that if you have no criteria to tell you whether one theory is correct or another, you may as well save yourself effort by going with the simpler one; if it's later disproven, you can always use the other one assuming it's still working. Some thinkers claim that a true scientific theory is something different from a model, but for the time being it suffices to imagine that successful scientific theories such as Newton's laws of motion are just really really good models.

There's an old saying that all models are wrong but some are useful, and in the spirit of that one can think of models on a basic level as being useful fictions--that perhaps since, as Hume posited, we can't ultimately know for sure what we'll observe next and that we can only see the events that happen and not anything between them, that any "understanding" we claim is just a fiction that may or may not serve our needs. Whether one finds this idea satisfying or deeply unsatisfying, it begs the question of what this or that model "summarizes" in the first place. If I'm making a model of changes in temperature, the thing I'm technically summarizing is some kind of reading of an instrument: maybe of a single thermometers, maybe an average of several thermometers, or maybe some meteorological data from a ton of places that's calibrated with a ton of mathematical equations. I'm not saying that it's all fake, obviously I'll put on a coat if the weather channel tells me it's 20 degrees farenheit outside, I'm saying that in order for a model to be in any way usable it has to have clearly defined inputs and outputs and that requires that what you're summarizing is ultimately something "formal" and not just a bunch of "raw phenomena" (whatever that would mean.)

And if this is the case, then that means that in the final analysis, not only is the structure of the model going to be based on what ultimately works well enough, but so will the semantics of what you're trying to model. To put it another way, anything a model summarizes is itself something based on a model. Does this mean that knowledge is models all the way down, or at the very least fiction all the way down? This doesn't quite work out because there is still a real world in which people are acting: even if everything were mediated through some kind of model, it still remains the case that a giant tiger that wants to eat you for dinner does not in any way care how you choose to conceptualize him.

Narrative Is Material

A model is ultimately static: it might describe things that are dynamic, but the model itself is a fixed set of rules that tells you how something allegedly works and by extension what you'll get out of whatever you put into it. This clearly is not enough on its own to describe how one makes a decision: even if I were to assume for the sake of argument that one always uses some kind of model, one still has to make the decision of which model to use whether that decision is made by creating, modifying, or taking a model off of the proverbial shelf, and this decision would itself require some choice of model, leading to an infinite regress. More importantly, the reduction of every choice to a model completely omits the part where you actually do anything instead of just "deciding" what to do.

We may use models in all sorts of ways to aid us in our endeavors, but it's not models by which we traverse life but by doing things that either work or don't work. This is especially important because nothing is stopping anyone from choosing how to use a model: you don't have to treat it as gospel, you can always decide for yourself whether it doesn't apply somewhere or whether you're going to just take it as a suggestion. "But wait, that just means that implicitly you're using a different model!" says the pedant. He would have a point were it not for one issue: because of the fact that a model ultimately circumscribes the semantics of its inputs and outputs, one must necessarily decide for themselves how to translate their situation into an input for the model and translate the model's output into a real world decision. In words, there is no getting away from the work, however large or small, or interpreting the model. Also note that this means that how one uses a model is synonymous with how one interprets it.

And since the choice of how to use any such model is unavoidable, a model is itself ultimately nothing more than an affordance with which one takes action. But of course, can't one just make decisions without models anyway? Maybe I just choose to grasp a handle because something about it interests me, or maybe I temporarily startle myself because I thought I saw a snake but it was just a scarf. Are these themselves not models? Was not the misunderstanding about the scarf rooted in a simplification of what a snake looks like that is useful for survival, or the choice to grasp a handle based on some underlying idea of how things work? I leave that up to you, the question is not important because it's already been established that when people use models, they're used for some kind of practical reason, and so even if they differ from other kinds of affordances, the "meaning" of a model qua affordance is in no way necessarily about the model's "accuracy" in any usual sense of the word.

Affordances do not simply allow new actions, they are also necessary for cogently defining action in any way--just like a sentence in English requires a subject and also an object if the action is anything other than a pure movement of one's body, a subject requires affordances against which to define any action. Nor is this just about what one is able to do, affordances also define corresponding constraints: a doorknob turns to the side but does not go in and out, I can pull a lever but I can't swing it around, and so on *Zizek sniff*. Of course, within these degrees of freedom, there are potentially infinite ways to carry out the action, and in some cases one may have the potential to utilize it for some "unintended" purpose, and this partial ambiguity is something that will prove important later but for now I digress.

Taken together, an interconnected collection of affordances, be they models or anything else, comprises a text that serves as a guide to action by defining the import of any one affordance according to its relationship to other affordances. A text could be any number of things: it could be a family of mathematical models that guide scientists or policymakers in their hypotheses and prescriptions, or a script that actors read off of in a play, or the content of a novel that tells gives you an idea of what you're supposed to be imagining happening, an set of rituals one performs in religious or civic life, a philosophical manuscript by which people find common ground in debates by appealing to commonly understood concepts, a set of axioms for mathematicians to work with and prove theorems to one another, or other body of constraints that defines a set of possible enactments.

Since affordances can be physical, it follows that the text is not something inherently abstract or ephemeral. In addition, while it might be the case that the content of a novel is in the most naive sense independent of the paper it's printed on or the screen it's displayed on, one cannot simply take the text to just mean the content. What one imagines when reading a novel will, by simple neurological principles, may potentially be changed based on what they're simultaneously experiencing, which in turn may be affected by whether they're reading the book on a computer screen, a spanking new paperback, or an old hardcover edition found in the depths of a university library. Even if one identifies an affordance in some kind of content that can be conceived independently of the physical substrate, the traversal of the text in which any such affordance is situated is ultimately a physical process.

The physicality of utilizing an affordance means that it's not a question of how one acts on it but how one acts through it. When I turn a doorknob, I may turn it slowly or quickly, only half way or all the way--the final result is probably the same no matter what, but I could easily enough have used an example of choosing how hard I swing a bat at an object. The same can be said just as easily about a line of poetry: my emotional reaction is something that takes time and is itself some kind of enactment. I could even go as far as to say the same about mathematical propositions, but for the sake of clarity I will hold off on elaborating.

Does this mean that the content is trivial and intractable, that the "message" is nothing more than the medium? This debate, revolutionized by the great Marshall McLuhan, is only relevant when one mistakenly supposes that media is some vessel that "contains" content, when this is not how a text works at all. To say that the words or the story they tell is "in" the physical book is little different than the scene in Zoolander where Ben Stiller is told that the files are "in the computer." The "content" of a book is not something separate from its material instantiation, but that which remains invariant across all publications of the book. In other words, it is a kernel of the medium rather than anything fundamentally separate from it.

But what about word changes in different editions or the arguable irreconcilability of different translations? Does that mean the content is more narrow than the words? In many respects, yes. Even when a book is translated into many different languages, readers still find common ground in their ability to talk about that book. Nonetheless, "content" is still a relative term: one could argue that two translations of the same book have the same content or do not have the same content depending on whether they think the content is the words or some idea common to both phrasings. But since a text is ultimately a question of affordances and actions, to talk about underlying abstractions is little more than a sloppy approximation of what enables two readers to establish common ground.

Therefore, despite what I had said earlier, it's extremely iffy to attribute "content" to the text in any simple way. Instead, one must consider these kinds of commonalities on the level of narrative where narrative is defined as the actual traversal of a text. Words on a page do not a story make: without any actors, you do not have a play any more than a recipe can't make an apple pie without someone to actually bake it. This is true even of something like a novel: everybody pictures different things and fills in different inferential gaps when reading a novel, the words are, as I said earlier, the affordances that help you do that. In both cases, the traversal of the text manifests itself as a series of enactments, whether that be the actors playing out the scene or the actions of fictional characters manifesting through the movements of the neural substrate generously provided by the reader.

At this point, it's extremely important to note that a narrative is not necessarily something private, there's no rule that it be confined to one person. When a group of people put on a play, the narrative is shared between all of them in addition to the audience present. This even has interesting implications for something like cinema: David Lynch said in Catching The Big Fish that he believed every running of a movie in the theater was different, and he was absolutely correct: you are sharing that narrative with the audience, and while the same thing plays on the screen every time there will be a different atmosphere interfacing with it. This is important to understand for many reasons, but as of right now what's key about this is that it creates a clear difference between what Todorov called the discourse and the fabula of the story, where the discourse is the telling of the story and the fabula is the alleged underlying thing the story is describing.

Why does that make it possible to identify these two parts? Because in order for the show to go on, there are things that have to be agreed on. It's not just about everyone following the script, that's like saying that all you need to do to make something is put the parts together. You have to put the parts together the right way, and that requires a skill beyond just the parts themselves: similarly, actors in a play, or any other kind of narrative, have to tacitly see eye to eye about all sorts of things to smoothly execute the narrative. It's important to note that the fabula is not necessarily entirely, or even at all, a set of explicit statements about the world: there might be propositions we can all agree on like "Odysseus poked out the cyclops' eye", but the ability to make these universally accepted propositions is a byproduct of the way in which the actors successfully coordinate their traversal.

How would this work for something private like a novel? On the level of the individual, discourse and fabula still exist insofar that as one reads through the text, an increasing number of "underlying" things need to be immutably true in for a given runthrough of the novel to remain consistent. On the level of discussing a novel with others, there will inevitably have to be agreements about what "factually" happened in the novel, even if that could change with debate.

But for something like a play, does that mean that the fabula is simply the script? Far from it: there are lots of things that are "true" about the story's "world" that one knows through inference even if nobody said it outright in the script. And even regarding the script, there's no reason one can't allow some degree of improvisation during the runthrough--the script is not itself the fabula or the discourse, but like every text, the common set of affordances that allows these things to exist .

Conflict and Abduction

This still leaves the question of why people utilize affordances, why texts are traversd at all. There's really only one answer to any such question: because they want to. Yes, we do things we don't want to do, but that's just delayed gratification, which itself is not all that straightforward. Of course, this just begs the question of why people want something or what that even means.

To desire something means that that something is conceivable, that the idea of that "something" has to exist in some way. Since all "ideas" are ultimately co-extensive with enactments and their kernels, such an idea is ultimately defined with respect to our affordances: I can't want to push a specific button unless that specific button exists, and I can't want to sit down if I don't have a certain kind of body that makes sitting a conceivable (not necessarily possible, but conceivable) idea.

It's also the case, however, that we want what we don't yet have. Yes, this is trivial, but nonetheless important. It's also seen as a pretty reliable rule of thumb that people want what they can't have, and while this obviously isn't an iron law, it gives us a hint at what the driving force behind "desire" is: the quest for an increase in one's degrees of freedom. This is not a "psychological" truth but one that relates to whether or not a system survives: the more options you have, the higher your chances of survival (see Ashby's Law).

When something is conceivable but not trivially obtainable, that's conflict. Of course, not every endeavor is a conflict in any meaningful sense of the word: if I'm hungry and I have food in my fridge all I have to do is go to my fridge and make myself a sandwich, it's more or less just an algorithm. It's really only a conflict if there are real stakes, no guarantees; otherwise, one needs only a set of instructions with enough precision that they don't fuck it up, which is why I can say that making yourself a sandwich is an algorithm even if there might be an uncountable number of physical variations on how you do it that couldn't be captured by symbolic logic.

On the other hand, when some task cannot simply be reduced to a series of rote steps, one must perform abduction and think outside of a bare chain of logical propositions in order to figure out how to get from point A to point B. It nonetheless remains the case that our actions are always inscribed in our affordances, and that by extension affordances can therefore only be defined in terms of their relationships to other affordances, thus making them arguably equivalent to such a chain of propositions: with each affordance being a proposition that itself is made up of formal transitions to other affordances (propositions.)

How then, does one say that any of this is not an algorithm? This goes all the way to the heart of Godel's Incompleteness Theorems, which in essence tell us that in any sufficiently complex formal system made up of axioms, there exist conceivable questions with respect to those axioms that cannot themselves be answered by any chain of entailment from those same axioms. One must therefore create new axioms to allow that question to be answered, which effectively involves an act of abduction. Of course, if all affordances are defined according to how they formally relate to each other, how could we possibly look "outside" such a system?

The answer is that while the formal nature of affordances are a product of how they are composed with one another, that formal definition is not the same thing as the material nature of affordances. A doorknob opens a door if it's turned to a sufficient degree, but that formal relationship between the knob and the door does not account for all of the affordance's degrees of freedom: we can still turn it at varying speeds or to varying degrees or with varying amounts of force. Sometimes these physical differences are utterly immaterial, but other times doing things a certain way in a certain context creates an entirely new affordance through an act of co-evolution.

Therefore, while a trivial goal can be reached through an algoirthm, what is effectively the physical execution of a chain of propositions, a conflict is resolved through the enactment of a narrative: one must continuously generate new and unforeseen concepts through the unfolding of their own active interpretation of the text in order to reach that conceived goal. Of course, a narrative may end in many more ways than just simple sucess so it's not so much about "accomplishing a goal" as it is to answer a well-formed question that has no trivial answer.

The conflict is what defines the narrative and by extension the formal (though not necessarily material) nature of the text: all affordances are either directly related to the defined conflict or indirectly related by being related to some other affordance related to the conflict. What makes it possible to utilize these affordances in a non-trivial way such that the core undecidability is answered is that one's own utilization of a given affordance does so with an irreducible signature and opens up the possibility of composing with other such utilizations of other affordances such that a new affordance is born, and with such new affordances one may find a path that formally answers the question.

Of course it's not simply that one just does this at random: our own way of reading a text itself comes from how we see it through our own life experience, and so our own way of interpreting a text ultimately comes from the fact that, insofar that all of our actions are contextualized by some kind of narrative, we utilize affordances from other texts in order to more cogently interpret the affordances of the text in question; this concept is known as intertextuality. This is essential to understanding why we cannot simply "brute force" our way thorugh problems but instead must develop literacy before we expect anything to happen: without knowing how to effectively compose new forms within the bounds of a given text, there is a, not merely infinite, but uncountable number of ways we could traverse a text with no gurantee that any significant number of them will cogently create affordances that would bring us any closer to ending the conflict. Our ability to supplement the text with our own writing is ultimately our ability to read the text, and only the right kind of experience can give us this ability.

And so with each such act of authorship, more affordances may yet be unlocked with a resulting increase in the possible affordances to be utilized. This process may continue indefinitely, but when it reaches its nadir, a point of maximum entropy, this is known as the climax of the story, after which things fall into a state of denouement, a winding down of any remaining affordances as the conflict, however it may have been "resolved", or whether or not it's even been resolved, is now an increasingly dead horse. Desire is nothing more than the drive to bring the story to a satisfying conclusion, with afflictions like anomie and narcissism being respectively a lack of any such conflict and a conflict so mired in confused introspection that the actor imprisons themselves by means of a fourth wall.

The Fourth Wall

[In progress, will talk about the phylogeny/ontogeny of narrative from ritual to drama to fiction to media and what this tells us, as well as the narrative basis of science, politics, and biology]

Data Are Limits

The expansion of affordances that defines the progression of narrative makes it a divergent process--that is, there is no reliable way to ultimately bound how it ultimately plays out. Algorithms, by contrast, however they are enacted, stay within certain bounds: one can unambiguously define the steps to making a ham and cheese sandwich because even if there are lots of different ways one could do it, one can guarantee the same defined result as long as the stated steps are executed in a way that fulfills their conditions.

When one has an algorithm, one can feed it data: inputs that are completely unambiguous in their formal meaning due to the fact that all formal relationships between affordances are definitively set. For an algorithm defined with literal computer code, this is pretty trivial: anything that's entered as data automatically has a definite meaning with regards to the program's code. Outside of computer code, certain conditions have to be met for a process to be an algorithm: specifically, the input cannot act on affordances in a way that potentially diverges from some kind of immutable formal structure, i.e. it cannot alter the underlying text. Since one always acts on a text via enactments, this means that the series enactments that traverses such a text must converge on some kind of output that is definable according to the formal system as it currently is without the addition of any new formalisms. Data as such is a limit point of a series of enactments.