Thursday, November 8, 2012

Numbers, Novels, and Other Objects of Towering Significance: A Series of Tangents

Today we will not discuss politics. Why don't we talk about math and books instead?

A few days ago I advanced from Chapter 3 to Chapter 4 in my secondhand calculus textbook. When given problems involving related rates and implicit differentation, I can now produce the correct answers, which is incredible to me. Only a year ago it would have been unthinkable. (Have I mentioned before that I only passed precalc with a D- and graduated high school because the teacher felt sorry for me? I think I probably have.)

So the mathematics kick continues. When I'm not cobbling together a working knowledge of all the algebra I deliberately ignored throughout high school, I'm often reading about mathematics instead. These are unusual times indeed.

Over the weekend a piece by Eugene Wigner ("The Unreasonable Effectiveness of Mathematics in the Natural Sciences") pointed me towards a Bertrand Russel essay ("The Study of Mathematics," which I heartily recommend to educators and closeted mathphile kindreds alike) that sent flames running along a pair of fuses in my cortex.

First of all, Russel begins with:

In regard to every form of human activity it is necessary that the question should be asked from time to time, What is its purpose and ideal? In what way does it contribute to the beauty of human existence?

Sound advice, even (or especially?) on the personal scale. "Do I maintain my habits and beliefs out of reasoned conviction or behavioral inertia?"

So my first impulse was to put Russel's question to a some folks on a gaming forum, replacing "it" with "video games." Some responses were genuinely compelling -- but I realized after the fact that there are only a few ways of putting such a question to gamers without coming across as though you're trying to start an argument, and I chose none of them.

Then I looked away from my special six-button Chun-Li joypad and noticed the rough draft of a new short novel lying on my desk, still unedited. My asking myself the next question was inevitable.

What is the novel's purpose and ideal? In what way does it contribute to the beauty of human existence?

And: what, if anything, makes it indispensable to us?

First: I don't accept "entertainment" as an answer, although a good book must necessarily be engaging. There must be some kind of utility value to fiction. It must be able to make an argument for its worth on its own behalf, and one with more weight than "well, I'm amusing" or "because I'm beautiful/because I'm art." (The first statement is pablum, the second means nothing.)

On this planet we have millions of books consisting entirely of information about things that didn't actually happen, and words that were never said by people who never existed. Many such books form a mandatory constituent of a student's education, from primary school to university. I certainly hope there's a reason for this, and that we remember what it is.

(Mr. Russell grumbles about pedantic math teachers dissuading students from discovering the beauty of pure mathematics for themselves. I'm just as concerned when I hear students or former students complaining about being unable to enjoy The Great Gatsby -- a valuable novel that should be virtually impossible not to enjoy -- because of the way the instructor presented it.)

(I hope to god we know there are better reasons for teaching literature than to improve vocabulary and reading comprehension.)

The library that's the setting and focus of my day job hosts a modest a fiction section. The contents of these shelves don't get much love from the collection stewards, least of all me. I've been assigned the task of culling expendable books to make room for an influx of about 250 linear feet of material (blah blah blah job) and so far the majority of Goodwill fodder has come from the fiction shelves.

The consensus among the library's decision-makers is that a fiction section is a fine thing for our library to have, provided it is small and assigned less priority than anything else on the shelves, including the decorative little plants. Meanwhile, we'll put just about any book on spirituality or theology on the shelves (remember that I am employed at a facility associated with the Religious Society of Friends), provided its author isn't some self-published whackjob. For a novel to be absolutely safe from deaccessioning, it needs to have been written by an author found in college-required texts or a Pulitzer/Nobel prize winner.

But this is a value judgement informed by the policies of an institutional collection. After all, we have limited shelf space and the material on display should reflect the establishment and its values. Still -- I was initially taken aback by the committee's willingness to part with the novels in the collection before anything else. (This was, however, before I noticed that most of the stuff in the fiction section isn't exactly high-caliber. On a related note, I occasionally wonder if the contempt I feel for books counted in the "popular women's fiction" set is actually warranted. Maybe I'd find a specimen I liked if I could just check the urge to fling the book across the room after reading two pages.)

Meanwhile, I've been starting to notice that the majority of my friends who habitually read for pleasure are usually sitting down with nonfiction rather than novels. Hell, I've been mostly reading nonfiction for the last year or so.

A member of the library committee once offhandedly told me he never reads fiction. Not in decades.

And that chat brought to mind something I'd read some months before: a person explaining why he'd stopped reading novels and exclusively reads philosophy texts. Fiction doesn't go far enough, he says. Philosophy isn't just pithy; it is pure. In literature, the royal perfection of raw philosophic principle is diluted and muddled by the mundane exigencies of narrative.

And that's the second fuse. Russel again:

Real life is, to most men, a long second-best, a perpetual compromise between the ideal and the possible; but the world of pure reason knows no compromise, no practical limitations, no barrier to the creative activity embodying in splendid edifices the passionate aspiration after the perfect from which all great work springs. Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos, where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world.

And that's just it. Brilliantly and probably unintentionally, Russel implies the value of art even as he asserts the value of mathematics.

Mathematics and human experience don't occur in the same world. The study of mathematics, logic, philosophy, etc. might temporarily vault the human practitioner into a loftier realm (metaphorically speaking), but he's still stuck on planet Earth.

Mathematics, our conduit to Russel's world of pure reason, is damn near absolutely consistent and infallible. That's the beauty of it. I wouldn't be the first person to point out that 1 + 1 = 2 is practically a creed attesting to the existence of order in this world.

"One," "two," and the relationship between them only exists in the perfect, imaginary realm of pure mathematics. They don't live here with us.

Objects and quantities in the physical universe we inhabit aren't as simple. They're harder to parse. They're more elusive. A human being's sensory perception of reality doesn't always reflect the physical fact of reality. The individual's subjective experience of reality leads to disagreement and confusion regarding the contents of reality. To the physcial contents of the world we've added abstractions like "freedom," "love," "justice," "hope," "beauty," "meaning," etc., and assigned them tremendous importance without really taking the time reach a consensus what they are and what they mean. We can hardly concur on what apparently blitheringly obvious concepts like "good" and "bad" really mean, much less decide how these labels should be apportioned.

(Related, from Constance Reid:

Actually modern mathematicians have a considerable respect for the obvious. They have found that quite often what appears obvious is not at all; in fact, quite often it is not even true. They have also found that even when it is true, it is often almost impossible to prove that it is true. )

Mathematics and logic operate -- and they operate unreasonably well -- because they work in a system with clearly defined objects and rules. No such rules exist for subjective human experience.

Philosophy, logic, and mathematics have yet to conclusively solve humanity and the world. The qualitative experience of human existence has, of yet, resisted quantification.

In this life there is always ambiguity and uncertainty. And on the basis of this fact rests the continent where a search for the real value of art and of the novel should begin.

Literature is, like economics, a dismal science. We can create and read it as study of something about which we can guess and learn, but staunchly resists systematization: subjective human experience. If the principles along which human life acts are the stuff of philosophy, the novel makes an excellent petri dish in which we can observe what happens, how well they work, and what changes when our Ideas (in the Platonic sense) descend from the ethereal to the material.

We teach The Great Gatsby to instruct students on the meaning of America -- a thing that can't be quantified, that doesn't exist in any material sense. We teach Catcher in the Rye as a lesson about adolescence -- a biological/psychological/social state that can be characterized in a litany of quantitative terms that somehow seem to exclude important information in spite of their thoroughness. We teach Lord of the Flies to instruct students about human nature and society without compelling neophytes to wade through millennia of unresolved academic squabbling. We teach Emily Dickinson and Walt Whitman because there are things in the dirty obscurity of subjective human experience that affect us profoundly, though most of us are as powerless to identify them as to articulate why and how they stir us.

The products of mankind's excursions into the world of pure reason -- math, logic, philosophy -- are our best hope for creating a better world for ourselves. But art is what can best teach us about who we are now and the world we're stuck for the time being.

And it is my partisan opinion that the novel, more than any other art, has addressed these things the most thoroughly and with the most maturity. (But this is a line of thought whose full pursuit would carry us much farther than the confines of a half-baked blog post.)

This fact that may well change as technology transforms the way information is created, transferred, and consumed. But I do believe the novel has value and potential that's far from being totally tapped -- despite what the existence of books like 50 Shades of Grey and Loving the Band might suggest to the contrary.

(Regarding my habit of writing novels, I suppose all this implies that I have a lot to which I must live up if I hope to assert the worth of what I do.)


  1. "I'm just as concerned when I hear students or former students complaining about being unable to enjoy The Great Gatsby...because of the way the instructor presented it."

    This is one of the most aggravating issues I have with education today. In elementary grades, so much focus is on learning through groups, reading/discussing literature as a class, and choosing differentiated activities based on ability. Then, on standardized tests that determine my abilities as a teacher, it's done in silent rows. The same applies as students progress into high school and college: goodbye group learning, hello hour-long lectures. Granted, some students just hate math and will never enjoy it, no matter how it is presented. However, there must be something wrong with the system when a C math student (myself) writes basic freshman-year equations with multiple variables to solve everyday problems, and everyone else needs an EZ Tip calculator on their smartphones.

    There is a push for a new way of teaching an discussing mathematics meant to build a stronger number sense. There's a big focus on using ten and its multiples to solve basically everything. I'll explain it to you next time I see you. It's actually kind of cool.

    1. Using ten and its multiples? Do you mean scientific notation?

    2. Oh right. More or less. We just don't call it that with ten year olds (although we SHOULD). It is interesting teaching exponents to children, though. Who knows? Maybe after learning math this way, these kids will finally agree to switch over to the metric system.

    3. Awesome. I find that very heartening. I automatically reckon weights and measures in in feet and pounds, but I really hope my generation will be one of the last to do so. THE METRIC SYSTEM IS SO MUCH BETTER.

  2. I read literature because I am drunk on words, and to myself at least, nonfiction hasn't succeeded in the same sort of seduction of the written word (except for history, which I indulge in sometimes as well). I don't know if this fact makes me some kind of Sophist caveman or not, but it is what it is.

    As for math...I'm awful at but, but still have quite a bit of respect for it, and wish I could understand it better. I remember reading David Foster Wallace's meditation on infinity 5 or 6 years ago and being wowed by it, but then again it read more like a history than a mathematics book, so there you go.

    1. Nothin' wrong with aestheticism, but I'm one of those people who can't leave well enough alone and needs to put the microscope to the things striking me as beautiful.

      When I wrote part of this thing I was thinking of something Tolstoy wrote in "What Is Art?" I don't have it on hand, but he basically calls the "beauty/art" statement a circular argument: "it's art because it's beautiful. And it's beautiful because it was created as art."

      (I've hard a hard time finding a full etext for some reason. Probably because it's a hard essay to like, especially if you happen to enjoy art or be an artist.)

    2. To me, art and beauty seem to have something indescribable that speaks to me on a deeper level, though I guess instead of examining it with a microscope I allow myself to float in it. To me there is nothing as wondrous as laying on the couch with my eyes closed and allowing that formless beauty to envelop me. Easier to do with, say, music of course, or at least something that doesn't require sight, though it can be just as impressive when it's an idea that hits you with that nameless something. Of course, saying things like "I like beauty because it swallows me" makes me a bad critic, I suppose.

    3. Remember that Whitman poem about the learn'd astronomer...?

  3. "The products of mankind's excursions into the world of pure reason -- math, logic, philosophy -- are our best hope for creating a better world for ourselves. But art is what can best teach us about who we are now and the world we're stuck for the time being."

    This is the best defence of fiction that is raised time after time: Fiction is a mirror to reality. As with a mirror, looking upon it is not a productive activity on itself; in fact, it can easily be misconstrued as vanity (and with books as 50 SoG existing, it's not an unfair accusation.) However, gazing upon a looking glass is an /informative/ action that brings to our attention things that we're physically incapable of seeing by looking directly at ourselves: the blind spots of personal bias and self-entitlement will never allow us to figure a complete picture of ourselves.

    More importantly, fiction constitutes an skewed mirror: by portraying human nature in completely improbable settings or circumstances exercises our comprehension of day-to-day behaviour and our understanding on the reasons we act like we do. By being spectators to the struggles and reactions of imaginary people in a non-existent setting we relax our defensive psychological barriers and may be "trapped" into questioning our own choices and actions before we notice.

    1. I really need to reread Milan Kundera's The Curtain. It's basically a series of essays about the novel. What it is, what it does, what it SHOULD do, etc. I read it a couple of years before successfully finishing a novel, but now I feel like I owe it to myself to revisit it.

      (Oof. Talking to myself. But perhaps The Curtain is a book you'd be interesting in reading sometime!)

  4. Very well put, though I would add that much of the appeal of fiction lies in its usefulness as a device for escapism. It seems like a too-simple answer, almost to the point of being an excuse rather than a legitimate response, but I believe the fact remains that the world is home to a great many people who would rather think about damn near anything except reality. Mathematics and philosophy may be pure, but their study often forces students to take a ruthlessly uncompromising look at the world around them. Fiction, on the other hand, allows the reader to tour worlds besides this own--worlds that may behave so drastically unlike what he finds familiar that the grip of reality of his mind relaxes itself for a time, and he becomes free to explore new ideas and concepts without the cumbersome burden of everything that weighs him down in whatever reality in which he finds himself trapped the majority of the time. This distraction is the fundamental appeal of all entertainment.

    The difference between The Great Gatsby and Fifty Shades of Grey doesn't lie in how closely the prose adheres to academic standards of their time, or how well each book encapsulates the complexities of human existence, or which one best challenges its audience to reflect upon ideas that transcend the limits of its narrative. The only real difference between the two stories is how far each is able to remove its reader from reality. Fifty Shades of Grey is not a mirror into our lives, because a mirror is the last thing some people want; the thing they desire most is an escape hatch.

    1. I can think of a few more differences than that. Hrm.

      I'm thinking that, on the face of it, saying that people read for pleasure rather than distraction reduces the matter to its lowest terms. And I think different sorts of people obtain different sorts of pleasure from different sorts of things.