Stat & Astonished

As a fiction writer — primarily — I think a lot about imaginative literature and how it fits, nowadays, in a tightly-wired yet tatterdemalion world.  Yet over the weekend the most provocation considerations on the issue turned up in the papers, the New York Times.

On the Times “Opinion” pages, recently, they’ve invited contributions from philosophers.  The series is called “The Stone,” and the Oct. 24th take “on issues both timely and timeless” (as the subtitle has it) was by John Allen Paulos, a mathematician as well as philosopher.  Paulos went to one of his specialties, statistics, to try and explain the human impulse to storytelling.  He says:

[T]he notions of probability and statistics are not alien to storytelling. From the earliest of recorded histories there were glimmerings of these concepts…. Consider the notions of central tendency — average, median, mode, to name a few. They most certainly grew out of workaday activities and led to words such as (in English) “usual,” “typical,” …and so on. The same is true about the notions of statistical variation — standard deviation, variance, and the like. Words such as “unusual,” “peculiar,” “strange,” “…come to mind. It is hard to imagine even prehistoric humans not possessing some sort of rudimentary idea of the typical or of the unusual. …These and other fundamentally scientific concepts have in one way or another been embedded in the very idea of what a story is — an event distinctive enough to merit retelling….

Paulos continues for a few hundred words, his argument always intelligent if a bit, hmm, unexceptional.

The entire piece can be found here:  http://opinionator.blogs.nytimes.com/2010/10/24/stories-vs-statistics/?ref=global-home
, and a typical argument for the mathematician addresses what he called the “conjunction fallacy.”  That fallacy underlies the way a creator, constructing a story in which psychological consistency matters, will layer on details in keeping with his conception of a character.

For example, imagine the tale of Fabio, a talented Italian soccer player who also happens to be gay.  He feels compelled by the standards of his profession to stay in the closet, and so the poor giovannoto‘s hidden sexual orientation will find much-needed expression in many  elements common to Italian masculinity.  Fabio will revel in fine, tight clothes, in his exceptional skill around the kitchen, and in both welcoming his teammates and saying goodbye by kissing them on both cheeks (on the face, the face).  The compiling of linked detail, in this way, certainly contributes to the creation of just about any fiction one can think of.  But it’s a fallacy, Paulos reminds us.  Such conjunctions aren’t the norm, statistically.  He expresses the “cognitive foible” this way:

For any statements, A, B, and C, the probability of A is always greater than the probability of A, B, and C together since whenever A, B, and C all occur, A occurs, but not vice versa.

So Paulos turns up, one after another, the logical breakdowns on which storytelling depends.  He concludes, indeed, with”the most fundamental tension between stories and statistics,” namely, fiction’s “focus… on individual people rather than averages.”

The upshot?  Hmm, intelligent, even witty now and again, but… unexceptional.

Paulos, for all that he seems to enjoy imaginative literature, referencing Moliere and Gilgamesh and more, continually neglects how much storytelling relies on the exceptional: the marvelous, the fabulous.  “Statistical improbability” seems far too mild a description for, say, Odysseus slipping past monsters and seducers to return home in late middle age — at which point, in a single busy day, he slaughters his wife’s many virile young suitors and, more’s the challenge, wins back her trust.

Such an outlandish gallimaufry (evinced also by a carnival word like “gallimaufry’) characterizes narrative and its hold on the human animal, much more than do pallid compilations of A, B, and C.  Conjunctions certainly matter to storytelling, and especially in a story like the closeted Fabio’s.  His would be another novel of society and its discontents, essentially realistic, bounded by a certain era and its expectations. Yet even a great social realist seeks to astonish, first.  The Tolstoy of War and Peace, for instance, seeks to expose timeless mysteries of armed conflict and what, if anything, it might accomplish for a person, a family, and a culture.  He’s about the serendipitous and terrifying reach of the animus, far more than about social and economic hegemonies.

Science tends to close down modes of astonishment.  Indeed, that’s its job, rendering the Unknowable knowable, and it’s performed this job especially well over the last century or so.  The human brain has heldthe concepts of “average” and “peculiar” for millennia, just as Paulos argues, but only recently has the species developed the kind of statistical machinery he operates so efficiently.  Nor would any reasonable person object to such efficiency, in a wide range of cases, from when need an appropriate antibiotic to when we need the quickest way out of a hurricane’s path.

Yet when applied to an art dependent on the imagination, that machinery functions dangerously like a compactor.  It turns out boxes of conjunction fallacies, when the true storyteller finds his or her vocation in those very fallacies and mashups.  A story-minded man or woman will call for madder music and stronger wine, and louder call as the chatter of science and its applications rises around them.  I mean that the canniest fiction-makers of our ever-more technologized era have seen the need for new-style freak shows, and they’ve delivered accordingly: with Kafka’s harried and underpaid bug, Borges’ world-smashing encyclopedia, or Barth’s infinite funhouse.  Imaginative leaps like these don’t merely confound probability; they enlarge the spirit, and ennoble it by their very strangeness, their cosmicomics.

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15 thoughts on “Stat & Astonished

  1. When I was a math major in Pennsylvania, John Allen Paulos was one of my heroes. And I still appreciate his ongoing struggles against innumeracy, but… He has, as you note in this post, John, a way of reducing wondrous and mysterious concepts to a point just past mundanity. I remember reading his book Once Upon a Number and marveling at how uninteresting he was able to make fiction.

    But what I find odious in this particular article, however, is an unvoiced assumption omnipresent in Paulos’s writing: the Platonic faith in the eternalness of math and science, which appear as higher forms of human knowledge—or even super-human knowledge—that mere mortals have spent history gradually inching up closer and closer to. And in all fairness to Paulos, this is one of the mass-ideologies of the sciences, an assumption as invisible to its converts as water is to a fish. In Paulos’s reckoning, scientific principles are “fundamental,” nascent in storytelling and language, just waiting to be evolved toward—rather than be created by people as, you know, occasionally useful tools. Why, it’s as though humans evolved ten fingers in order to better use the decimal system! How fortuitous! Guess we must be on the right evolutionary path! How much longer until we shed our embarrassing meat-forms and become light beings? (Think of the rapid calculations we’ll be able to perform then!)

    What so many on the science side of Snow’s “Two Cultures” divide failed to understand then, and still fail to understand now, is that math and science are human creations, and as such aren’t necessarily any more objective or truthful than those other human creations, poetry or the narrative arts. Rather, they just tell a different set of truths, according to a different methodology—all of which is, to be sure, at times extremely true and useful. (You can’t put a man on the moon using a poem.) But they only operate within their own artificial contexts, their own logical systems, which can be just as riddled with foibles and shoddy assumptions—their own false grand narratives—as anything on the lit side. (For instance, whence the assumption that putting a man on the moon is indeed a good thing to do? Because we have the math to do it? Well, then let’s fucking do it!) Statistics and its inexorable accompanying logic (objectivity!) have brought us the brave new world of bureaucracy, technocracy, positivism, “administered” nature, eugenics, radically awesome military toys like automated Predator drones, and the modern insurance industry. Thanks, statistics!

    To which Kafka’s irrationality is the only sane response. His writing tells a greater truth about bureaucracy and the military-industrial complex than any statistician ever will, or could—which is precisely why it’s so valuable…even though you can’t, you know, graph it.

    (Though lord knows Paulos will try.)

  2. Hi John,

    Interesting post… I agree that literature “relies on the exceptional: the marvelous, the fabulous.”

    And it’s true that some sciences “close down modes of astonishment” though I find some scientific concepts to be extremely invigorating in terms of literature. This is Andrew Joron talking about complexity theory vis-à-vis surrealism:

    “Recent studies of complex systems (from which the concept of emergence is derived) appear to confirm the surrealist insight into the poetic-revolutionary nature of reality. Investigations have shown that systems comprised of a large number of elements far from equilibrium are prone to beautiful convulsions called “phase transitions.” In this process, chance associations within the system, after reaching a critical point, undergo spontaneous self-organization. At this point, the Novum—an unexpected, unprecedented superaddition to reality—emerges…The origins of order are vertiginous: by ‘riding’ its own chaotic tendencies, the system propels itself to a higher level of organization.”

    In this account, it seems like Breton’s ideas were in advance of science — and science allows us to appreciate his discoveries.

  3. A.D., Michael, thanks for such thoughtful responses. It appears that, first time out, I strayed right into your cross-hairs — though in this case, that’s a sweet spot. A.D., your anger over statistics feels (dismayingly) well-placed. Michael, the Jeron passage is itself quite an astonishment. I’ve really got to go dig it out.

    • Hey, John,

      To clarify, I don’t think of it as an anger over statistics, so much as anger over a certain…myopia I often see in the sciences (or at least believe that I see in the sciences). I actually love the sciences, and math, and use statistics all the time. They’re all useful tools! And rather beautiful, in their own ways.

      But when scientists and math types start going all gooey-eyed and fantasizing about the eternal purity of numbers, and how they predate us, are external to the human mind, and are therefore beautiful and true, and crap like that, I reach for my revolver. I can’t believe they can’t see how it’s a form of mysticism—although it’s very rational mysticism, to be sure—that they’ve convinced themselves is objective rationality (and therefore a form of superiority). Me, I’m all for mysticism, but not when it comes disguised as objective truth. And, meanwhile, it’s good to be critical of the sciences: a simple survey of its history shows it’s a rather flawed human endeavor…as are all human endeavors… A lot of what we believe about math and science to be true simply isn’t true; it’s an approximation of truth, as far as we can tell. And it’s usually good enough that we can use it for useful things. (Newtonian physics aren’t “true”—Einstein demonstrated the flaws in that system of belief—but you can still use Newtonian physics to go to the moon and back. Because Newton was right “enough.”)

      And I love Paulos, really I do, but he’s also a bit of a loon sometimes. And I think he’s being pretty loony in that article, honestly:

      I’ll begin by noting that the notions of probability and statistics are not alien to storytelling. From the earliest of recorded histories there were glimmerings of these concepts, which were reflected in everyday words and stories. Consider the notions of central tendency — average, median, mode, to name a few. They most certainly grew out of workaday activities and led to words such as (in English) “usual,” “typical.” “customary,” “most,” “standard,” “expected,” “normal,” “ordinary,” “medium,” “commonplace,” “so-so,” and so on. The same is true about the notions of statistical variation — standard deviation, variance, and the like. Words such as “unusual,” “peculiar,” “strange,” “original,” “extreme,” “special,” “unlike,” “deviant,” “dissimilar” and “different” come to mind. It is hard to imagine even prehistoric humans not possessing some sort of rudimentary idea of the typical or of the unusual. Any situation or entity — storms, animals, rocks — that recurred again and again would, it seems, lead naturally to these notions. These and other fundamentally scientific concepts have in one way or another been embedded in the very idea of what a story is — an event distinctive enough to merit retelling — from cave paintings to “Gilgamesh” to “The Canterbury Tales,” onward.

      Maybe it’s just me, but I can’t help but see Paulos arguing here that The Eternal Statistics predated human understanding of it, and waited patiently while humans clumsily evolved toward it. Maybe I’m just being crazy/oversensitive, but I see—sense?—traces of that belief in there.

      Statistics is just a way humans have devised for analyzing certain phenomena. It’s more precise in some ways than words like “normal” and “atypical,” etc., but it’s still just a human creation, that in other ways is less precise, less powerful. Being its own system, it has its own inherent flaws, and it can tell its own unique lies.

      I mean, even the idea of numbers is an artificial construct. It may seem external and objective, but that’s just because we’ve convinced ourselves that it is. Anyone who doesn’t believe me is encouraged to go outside and start counting all the dirt that’s on the ground. (Before you can count something, you have to determine a prototype that you’ll count, then insist upon that prototype. That’s easy to do when you’re counting countable things, like say sheep (although even then you run into fuzzy areas, things that are more and less like sheep; we just usually ignore those cases). But it really breaks down when you can’t define the prototype accurately: noncount nouns are non-countable precisely because they make it hard, if not impossible, to do that.)

      Cheers, Adam

        • This post and discussion, which I love, has put me in mind of a Borges essay, “Kafka and His Precursors,” which begins like this:

          “I once premeditated making a study of Kafka’s precursors. At first I had considered him to be as singular as the phoenix of rhetorical praise; after frequenting his pages a bit, I came to think I could recognize his voice, or his practices, in texts from diverse literatures and periods. I shall record a few of these here, in chronological order.

          The first is Zeno’s paradox against movement. A moving object at A (declares Aristotle) cannot reach point B, because it must first cover half the distance between the two points, and before that, half of the half, and before that, half of the half of the half, and so on to infinity; the form of this illustrious problem is, exactly, that of The Castle, and the moving object and the arrow and Achilles are the first Kafkian characters in literature.”

  4. Provocative post here. I just read the Paulos article and thought it started fairly strong, then tapered off when he got into intensional versus extensional properties, maybe because he was a few miles too far into logic territory there for my personal attention-span this morning. When it comes to this two cultures business I’m myself of two minds. I think, for instance, the contributions of evolutionary theory to talking about literature are among the most fascinating going right now–Brian Boyd’s On the Origin of Stories I take to be a touchstone book in many ways. On the other hand, when it comes to the Literary Darwinists who are trying to do more statistic studies–and there are many, studying archetypes cross-culturally, studying how appealing undergraduates find characters in Victorian novels–I find myself in a full-body grimace.

    But I will say in response to Adam’s point that I don’t find in Paulos’s characterization of primordial statistics, with its notion of recurring patterns of observed nature and even supernatural ideas about fate, as presupposing, implicitly or explicitly, any kind of ideal, Platonic stats or number-forms out there. On the contrary, the types of regularities and irregularities that he’s talking about don’t make sense except given human beings to notice them and make, if you’ll pardon the pun, heads or tails of them. They fit right into Boyd’s theory, for instance, which starts out with what patterns we attend to, how we experience events.

    I also think scientists can and do feel as much astonishment as any of us. In many ways I think becoming a scientist is a way of institutionalizing your astonishment, bankrolling it, giving it a legitimate societal status. Of course there are exceptions. And one indispensable piece left out of Paulos’s story of stories is what John points out, the way a work like War and Peace resonates on so many different levels in ways that have little to do with probability. There’s plenty of astonishment to go around.

    One thing that would’ve been cool for Paulos to discuss is the way statistics can tell a story in and of themselves. That’s what I love about the Harper’s Index. Stories about human folly, warped priorities, hypocrisy, etc.– tragedies and comedies and histories, all in two/three line bursts whose epiphanies are little numbers.

    • I might be reading too much into the Paulos, that primordial characterization (good description!) being something I’ve been seeing in him—or think I’ve been seeing in him—for fifteen years now. I did note his use of the word “notion” here in regard to statistics, so perhaps I should be more charitable.

      I also think scientists can and do feel as much astonishment as any of us.

      Total agreement there. Scientists are just people trained in a certain methodology. (Which they often mis-employ. Just like anyone else.)

  5. Thanks again, Adam, & yes, good to be here. The clarificaton you make is useful’s not statistics per se that irk you, but the smugness of the numbers man that he’s in possession of the whole truth. You might look into the latest novel by Richard Powers, GENEROSITY, for a moving investigation into the attraction & the dangers of reducing a human essence to numbered quantities.

    Edward, that Borges piece is one of the essays of his that’s lingered w/ me — in part, no doubt, because Borges is one of those who suffered an inveterate fascination with attempts to number, prioritize, & otherwise scientifically arrange the unruly universe.

  6. Tim, sorry, I was late seeing yours. Your points seem on the money. I guess I need a look a that Boyd book, & I too am dismayed at a numbing contemporary fashion for the the “historicity” of a literary work (like say, what sort of vodka was Pierre B. was drinking, the night he met Natasha?).

    None of which is to suggest that great stories & their tellers don’t turn to science. I mean, who’s a greater geek, a stickler for mathemetical rigor, than Dante? Doesn’t he impose strict numerical formula on all three realms? The very direction of Virgil’s & the Pilgrim’s movement, clockwise or counterclockwise, matter enormously.

    • No worries, John. And welcome. You know a lot more about Dante than me… future post, maybe? Also there’s Calvino and the Oulipeans when it comes to the math/literary crossover, with bridges of combinatorics. And in another medium, “Pi,” still one of my favorites.

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