Smilla's Sense of Snow/paper

From Mindspillage

The Elements of Style: Interpreting Smilla's Sense of Snow through mathematical and mythical metaphor

“It turned out to be Euclid's Elements, after all.”

Almost immediately upon picking up Smilla's Sense of Snow, the reader is confronted with the idea of a life seen through the framework of mathematics. The protagonist, Smilla Jaspersen, is a scientist and mathematician with a reverence for Euclid's Elements—one of the few things she has reverence for at all—and we see her character presented as nearly cold and untouchable as the mathematics and the ice that she loves. She cares about little else: not her neighbors, not her father, not men, not political maneuvering nor social propriety. Her life is shaped by the ideas of mathematics, the integers as limitless as the expanses of ice and snow that she needs for her sanity, the axioms providing a grounding. “The foundation of mathematics is numbers. If anyone asked me what makes me truly happy, I would say: numbers. Snow and ice and numbers.”

It is possible to read the novel and see a straight detective story: woman, upset over the death of a friend, uses her unique skills to pick up where the police left off. After tracing a complicated string of motives and events, making friends (or at least alliances) with a few interested characters and occasionally wandering into danger, she discovers the identity of the murderer, and the incredible reason behind the boy's death and the coverup. But this plot-level reading of the novel leaves the reader without a sense of resolution, particularly the events in the last third: at first bewildered at the crowd of new characters and the complication of the various plot twists and turns, then unsatisfied with an abrupt ending that doesn't begin to address the proliferation of loose ends. Sherlock Holmes doesn't simply disappear into the ice. Why, then, is it the most natural place for Smilla to go?

Høeg throws out mathematical metaphors throughout the novel as a way of analogizing: Fermat's marginalia as compared to Elsa's; Cantor's infinite hotel as a testament to the value of solitude. Considering this, Høeg almost asks us to step outside ourselves and consider the novel the way Smilla might—through the lens of mathematics, taking analogies and ideas to determine how to interpret the book, how to see what it is really about. The novel is fractal in the ways its elements echo themselves at each level of magnification: consistency, internal conflict, oxymoron, and the validity of different points of view. Even at the meta-level: the fact that it is both so neatly constructed and leaves so many loose ends, forming the big picture we zoom in upon.

The elements of a consistent universe

The clearest jumping-off point is Euclid's Elements itself. The starting point for the novel and the starting point for geometry, the Elements provide the foundations of Western mathematics; its axioms provide the basis for Euclidean geometry. Only those who have dug deeply into the subject have seen the other ways of understanding the geometry of the physical world, mathematically. Most accept the ideas that seem so obvious on a first reading: that straight lines extend indefinitely, that parallel lines never meet. Give us a few points of guidance, a compass and a straightedge – a way to find direction and a way to know we can continue going in the way we set out to go—and everything else follows.

Smilla reads the Elements to the young Isaiah, whose death sets the story in motion. It's a strange choice for a children's story (having, as one may guess, little in the way of plot or narrative, and pictures only at their most abstract). She expects it to bore him so thoroughly that he leaves her alone: Smilla has no maternal leanings, no desire to spend time reading children's tales to a creature who will demand the kind of solicitous attentions she's not equipped to give, and she reads only reference books and scientific papers. “I have no books that would interest a child,” she says; “he and I cannot meet over a book.” But Isaiah surprises her by staying to listen.

It would not have made a difference what the book was, she claims, but just that she read; he continued to listen no matter what she chose for reading material. Isaiah, like Smilla, is a transplant from Greenland. His father is dead, his mother a neglectful alcoholic. Smilla herself is as unwelcoming a presence as the snow and ice she studies. But the boy is not put off by her coldness—instead, they grow close, recognizing a certain kinship in their unusual ways of socializing and thinking. Isaiah, too, does not fit in to the society of Copenhagen. He speaks poor Danish, and has not been socialized well by his mother, but even under the best of conditions would be on the fringes: a loner, quiet, withdrawn, skilled at mechanical tasks and desiring intense concentration on them to the exclusion of social play. Smilla is a gifted scientist, but her history is marked by a failure to integrate into Danish society and submit to its rules; she is invaluable on expeditions to sensitive territory, but has been kicked out of every institution she's ever belonged to and lives alone, unemployed, dependent on her father's money. And though she adds a story or two to her repertoire, cracks in the ice, it is the Elements that she keeps returning to, over which the two bond.

The Elements begin with a series of postulates: axioms that must simply be accepted, upon which the rest of the work depends.

A straight line segment can be drawn by joining any two points.
A straight line segment can be extended indefinitely in a straight line.
Given a straight line segment, a circle can be drawn using the segment as radius and one endpoint as center.
All right angles are equal.
If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.

Common notions:

Things which equal the same thing are equal to one another.
If equals are added to equals, then the sums are equal.
If equals are subtracted from equals, then the remainders are equal.
Things which coincide with one another are equal to one another.
The whole is greater than the part.

The book can be read as borrowing the axioms of the Elements. A straight line segment can be drawn between any two points. In the universe of the novel, everything is connected. Any two points Smilla picks, no matter how seemingly remote or implausible, have a story-thread running directly through them. No avenues of inquiry are fruitless. Every possible line can be extended indefinitely, leading into further and further ways that points line up. Things which coincide with each other are equal to one another. And how many strange coincidences there are: things which line up almost too perfectly.

“It seems to me that I've seen him before. It's a feeling that I get from faces and places more and more often. I don't know whether it's because I've seen so much that the world is starting to repeat itself, or whether it's due to wear and tear on the mental apparatus.”

Smilla's encounter with Dr. Licht in the floating museum is an early clue that the novel may have more structure than a linear reading of the plot. How strange and how convenient, that he should appear there, after presiding over Isaiah's funeral, and in the roster of the mysterious expeditions to Gela Alta—a fine set of transformations. A recurring theme is how characters seem to show up where they are least expected, woven even more tightly into the plot that previously imagined.

If we borrow more metaphors, a system setting out the rules with n unknowns and n equations is perfectly solvable: there must be a consistent solution. More unknowns than equations and it is underdetermined; too many competing interpretations can be found and we cannot be sure which is true. More equations than unknowns and it is overdetermined. The only way an overdetermined system has a solution is where the equations are linearly dependent: where they can be described in terms of each other, where they line up.

(The History of Danish Dreams has a short aside on consistency as the apotheosis of polite society: "The way in which her guests and [Amalie] herself are polite [...] is just that: consistent. ... [T]his is a social convention, a way of life, that requires a great deal of energy, since one is constantly having to combat any tendency toward inconsistency—and life is full of such tendencies." And on a novel, as in social protocol, consistency requires much energy input, and it is difficult to be consistent by mistake; it usually represents a great deal of structure and planning.)

In a straight reading of the text, we accept the story presented as true within the world of the novel. The story presented by Smilla happened as described. Parallel lines of narrative never meet. The universe is centered on the character of Smilla Jaspersen; events appear smaller the further from her consciousness we travel, but a straight line of reasoning can connect one event to the other. But this reading, the most neat and obvious, presents a universe that gets more troublesome on close examination. The sequence of events is confusing, transitions happen abruptly, holes exist where there are several competing interpretations.

But the straight reading is not the only possible one. Discarding the parallel postulate, allowing another consistent reading, Smilla's confinement drives her to madness. The events after the authorities are called to apprehend Smilla at her father's house take place not in a tiny cabin on a Greenland-bound vessel but in the confines of a cell, and in the confines of Smilla's mind. Details that appear inconsistent or impossible (the way everyone has turned against her and yet she continues associating with them, the physical confrontations, the child's having accompanied his father on a dangerous expedition, the unusual parasite) suggest by their inconsistency with the universe as we know it that they exist only within Smilla's mind, or at least in something other than the universe as we generally see it.

There is more than one non-Euclidean geometry; other possibilities exist. Like the characters in The History of Danish Dreams, it is possible that Smilla continues living normally (if mundanely), but builds up a narrative around herself so densely that she believes it. Events don't happen as depicted but are transformations of the events we would see from an external point of view. Perhaps she gives up on the mystery but manages to secure a spot on another scientific expedition; unwilling to face the possibility that she has failed Isaiah, she constructs a view of reality where she is still the hero of the story; able to find no analogue to returning victorious after bringing the wrongdoers to justice, the narrative trails off into nothing as she disappears onto the ice.

Minds, maps, and territories

There is a way of looking at the world that wants to see everything in terms of mathematics. Someone outside that sort of worldview might say “reduced to mathematics”, but it would be a mistake—for from that point of view it is not a reduction at all, but just the way things are. Instead, the things that appear not to be mathematical are indeed instances of abstract theories and concepts, though perhaps infinitely complicated ones, expressible and describable. Everything fits into a pattern. And to ascribe too much mystery to them, to claim they only exist on some more ineffable level untouched by reason, is to deliberately fail to understand. One part of Smilla understands the world through that lens. She translates human emotion into their analogues: negative numbers as the sense of longing, something missing, irrational numbers toward madness, and the incomprehensible vastness of the complex number system as the incomprehensible complexity of the horizon filled with ice.

But it would be a mistake to think of the mind that can hold that view as cold and emotionless. A bearer of the same sort of mind may also see herself as the center of a grand romantic narrative, though she might deny it if pointed out. They see themselves as special in some way, seeing things that others don't see. (This is a theme that appears in Høeg's History of Danish Dreams, in more obvious fashion: we see not only the narratives that the characters have constructed around themselves, but we see the outside view, as well as what happens when they burst.)

Smilla has a dual heritage: her Danish father embodies the cold and logical. A wealthy doctor whose life is the very picture of success, almost too perfect. Her Greenlandic mother was no softer, in her way, but her life did not fit neatly into the Danish picture of success; she hunted as skillfully as a man and raised her child as skillfully as any woman. Moritz wishes for comfort and luxury, a well-appointed mansion; Ane could not bear to be cooped up away from the expanses of North Greenland. It is implausible that these two would come together, complements as they are. Smilla is not able to say how they met.

When someone with such a combination of traits comes up with a model for how the world works it is a convincing one: they are both sure they have come up with a fitting theoretical way for seeing and thrilled to be at the center of the fantasy where they have figured everything out. That sort of mind may be most susceptible to falling into a self-created narrative. Smilla is one of these people, holding this conflict within her. And both aspects factor into her intense desire to be in control of her life, not cooped up by forces and structures outside herself. (When that control begins to get away from her she breaks into violence: when her father is going to stop her, when she is going to be discovered accessing the secret records and her plans foiled, when she is facing an impossible situation on the ship.)

Euclid's Elements is a foundational text: the starting points from which modern geometry is derived. Follow a logical path from its axioms and the result is a mathematical truth: not necessarily the only truth, but necessarily a truth, consistent with everything else in the system. But the Euclidean universe only has room for straight lines that never meet. Though Smilla is a scientist, she places a dubious value on the scientific method as a path to truth—or at least as the only path to truth, characterizing the European obsession with scientific measurement and analysis as distancing it from some of the truth they supposedly seek. This narrowmindedness is part of what leads to the uneasy relationship between the “enlightened” Danes and the “primitive” Greenlanders. “Technological culture is superior in the very reality it defines... Any race of people that allows itself to be graded on a scale designed by European science will appear to be a culture of higher primates.” Smilla reveres the Elements, a foundational text of Western science and logic, as well as the understanding of the world of the Inuit who live out in it, who depend on it and interact with it directly in the way the Danes do not, try to shelter themselves from. Smilla cannot stand to hunt; she is nauseated at the thought. But she recognizes this not as an enlightened sensitivity but as weakness, alienation. She speculates that this is why she wants to understand the ice: to regain something she has lost.

And of course it is ice that she studies: having a highly self-similar crystal structure, yet requiring deep and complex mathematics to fully understand how it moves and transforms. A glaciologist, when ice structures are the clichéd analogy to something where only the minor part is visible from the surface.

Smilla's talents are not limited to snow and ice: she is also a navigator and a mapmaker, with a keen sense of place. Rather than relying on external sources, she uses her own internal map to navigate, the idea that others don't have one so keen being foreign. In the Mercator projection used by most of the Western world for its hanging maps— including the “enlightened” Denmark—Greenland may get the worst of the distortion, often being cited as an example of the failings of the projection. More echoes of themes: Denmark's distorted view of Greenland goes even this far, but Smilla is intimately connected to both ways of seeing.

But every projection of one space onto another faces some losses and tradeoffs. A map focused on a particular point becomes less accurate toward its borders; we get a clear picture of what the cartographer deems important but the further beyond the focus we go, the more distorted the picture grows. Any projection of the earth onto a map that seeks great accuracy in one aspect will fail us somehow in others. A map that attempts to treat all points with equal focus only manages to distort all points; the whole is more true even though no part is true.

A story told in first person tells us in great detail how the narrator sees herself, from her own perspective. But the further we get from the narrator's view of herself, the more distorted the picture becomes. The storyteller's choice is which sort of distortion makes the story most true to the vision he wishes to present. The choice of first person is deliberate; Smilla is at the center of this world, and accuracy about the single point of her character most important to understand the world he creates. A third-person omniscient may give a more truthful picture of the whole even while being less faithful to any individual part. Why choose Smilla, then? Her duality and internal conflict, her ways of seeing and thinking, her fields of study most closely mirror the intended way of understanding the book; it is most important to have the view around her to navigate the story properly.

(Even if we accept the interpretation that Smilla is slightly mad, no choice of character would provide an accurate telling even under the best circumstances. And in this novel, everyone has some quirk—some characteristic of the function mapping reality onto their own mind—that would make them noticeably distorted. The most obvious distortions would be Juliane's drink, Licht's blindness, Jakkelsen's drugs, but also Elsa's faith, or Hviid's lust for success. The analogy of Elsa to Fermat may be particularly deliberate as well: though Fermat's Last Theorem was eventually proven, it took years to crack, using analytic techniques first recorded in the mid-to-late twentieth century. It is beyond belief that Fermat would have approached the problem in the same way as mathematician Andrew Wiles, whose near-obsession with the problem over a span of several years, as well as perhaps a touch of madness, eventually cracked it. Fermat's scribbled note in the margin may then have been either a mistake—a proof of the theorem that seemed sound but would not have held up under rigorous examination—or a deliberate falsehood, meant to leave a vexing mystery, to leave a lasting reputation, or to spur others on to finding the truth he could not grasp for himself.)

Smilla's Sense of Snow is sometimes classified as magical realism (The History of Danish Dreams fits the label even better): a genre characterized by resembling the normal world, but with a few elements that would be impossible—magical—in reality. The world built by the author simply takes these magical elements as given, nothing unusual. We can think of a world built in a magical realist novel as having a different set of axioms which we are simply given to accept, and from there the rest flows logically.

If the given set of axioms lead to contradiction, as is likely, the author will never probe far enough along the line of reasoning that would discover it—or may simply gloss over it in a prose analogue to the sort of sleight-of-hand proof that shows 1=2, or that all triangles are isosceles. But the author cannot reject or discredit whatever leads to the fantastic element, for then the world he's created comes crashing down. (And here it differs from science fiction: science fiction attempts to be plausible, and where its scientific premises fail, the novel doesn't work: though seemingly impossible elements may be explained away as being some incredibly advanced technology about which no substantial detail is given, they are not simply taken as part of the existing natural universe.)

Magical realism is a conflicted genre; Smilla herself represents that conflict. It assumes a modern world with modern, logical ways of thinking and forces you to accept the mysterious, illogical, mystical, and tells you this is real too. Smilla is half-Danish and half-Greenlandic, half-logical and half-romantic. She lives in Copenhagen, one of the places where "civilization" has most thoroughly taken over, but cannot escape her home and heritage of Greenland.

In the novel the most obvious fantastic element is the mysterious meteor, teeming with some sort of adapted parasite that leads to the death of the scientists who encounter it. The encounter is jarring: in a novel that takes pains to speak about the science of snow and ice, of Danish-Greenlandic relations, and of mathematics, to throw in a major plot device straight from a sci-fi B-movie seems out of place. Were it just this element, it might possible to simply shake your head at the author's failure to invent something credible and move on. But even the characters all have mythic qualities about them, characteristics tempered to exist in a world that doesn't recognize the mystical point of view as valid.

Smilla, with a dual heritage, a gifted rogue, nearly androgyne, internally conflicted, on a quest of honor. Isaiah, the young child mature for his age, abandoned by his parents, having unusual abilities. Smilla's feeling for the young Isaiah is almost a romantic love, despite his youth. Everyone has their magical power: Licht with his nearly supernatural abilities, his blindness, his popping up in many different roles, like an ancient god. The Mechanic, known by his role and not by name. Smilla's father is godlike—fabulously wealthy, with the power to make anything he wants appear simply by wishing it; his trade is manipulating life and death, and thought distant as a god he comes down as a deus ex machina to give Smilla the money to start her adventure. He meets his complement, Ane, whom he is drawn to without explanation; together they form the daughter that holds both parts of them.

The baby-faced Lander, also fabulously wealthy and appearing from nowhere to set off the final part of the novel and then disappearing again. The ship's crew, each with their compromised pasts leading them to set off on a journey to nowhere. Dark and powerful forces, controlling natural resources, come together to act as the villains and cover up their misdeeds. Elsa, the inverse function of Smilla, light and to Smilla's dark. Smilla has made her whole life subverting the rules; Elsa has made her whole life administering them, but they can both be redeemed through the same act, needing each other's assistance to complete it. Mythical archetypes, duality and conflict, linear transformations, equations turning from overdetermined to solvable as things are found equal to each other.

The map is not the territory

“At some point I stop. And we simply sit there, gazing straight ahead... Some time later he gets up very quietly and leaves. I watch the sunset, which lasts three hours at this time of year. As if the sun, on the verge of leaving, had discovered qualities in the world that are now making its departure a reluctant one.”

The book ends without resolution. Smilla has walked out onto the ice, into an uncertain future; the book, like the sunset, has been winding down for something on the order of hours (even for a slow reader, an incredible contraction, mapping author-time to reader-time), and at this point it simply stops, leaving us as the readers to wonder what happened. Høeg has been so careful to make everything connect elsewhere in the novel: why would he leave us hanging? In a less carefully crafted and researched book we might want to put it down to a sloppy author, one who was driven by a publisher's deadline rather than the natural conclusion of the work.

Achilles: ...[I]t never takes an infinite number of reasons to account for some arithmetical truth. If there WERE some arithmetical fact which were caused by an infinite collection of unrelated coincidences, then you could never give a finite proof for that truth. [...] Are there actually those who disagree with this view? Such people would have to believe that there are 'infinite coincidences', that there is chaos is the midst of the most perfect, harmonious, and beautiful of all creations: the system of natural numbers.

Tortoise: Perhaps they do; but have you ever considered that such chaos might be an integral part of the beauty and harmony?

Achilles: Chaos, part of perfection? Order and chaos make a pleasing unity? Heresy!

Gödel, Escher, Bach, p. 398

Douglas Hofstadter, in Gödel, Escher, Bach, describes the unintentional leaking of information by the form of a book, its plain physical format. A reader has some sense of how far along the story is, how far from resolution, by the number of pages remaining – information that the author has not intended to reveal. But how to avoid it? (That is, without reading on the Kindle!) One could simply leave more blank pages at the end of the book. But the reader is then easily able to cheat, peeking to see when the block of blank pages begins. Printing plain gibberish or nonsense has the same problem. Instead, he proposes, the author should continue the story after the true ending, leaving small stylistic clues that the true ending has already happened, just enough that a careful reader catches on: some "small but telltale feature in the text... And he must be ingenious enough to think up, and hunt for, many such features until he finds the right one."

Numerous book reviewers have marked the point where Smilla boards the ship as where the story begins to go off the rails. There is no agreement as to just how it has gone off and why, but readers notice a change. Perhaps Høeg has taken a few pages from Hofstadter. (Infinite coincidences indeed: these few pages I quote, which are a very minor and almost offhand part of a long, sprawling book, were mentioned in the surprisingly short Wikipedia article when I wished to recall the passage.) The first part tells the substance of the story, and the true end comes after Benja has called the authorities to apprehend Smilla; we are left to infer that they succeed and her quest ends.

What is Part Two, then? Hofstadter goes on: "The padding is, in a way, a 'post-ending ending'. It may contain extraneous literary ideas, having little to do with the original theme." Hofstadter's dialogue continues after its "true end", but its self-description doesn't accurately describe its nature. The whole thing has to do with the original theme, but the "post-ending ending" simply does not continue the same narrative.

In Smilla, the dialogues between structure and form form the structure almost of a Gödel paradox: it is trying to describe itself. It can't, of course; you would have to jump outside the system of the novel to take it all in. To be perfectly descriptive it would lose consistency; no consistent system can describe itself. Something has to give. A description that holds to the Danish virtues of consistency and reason can never be able to capture everything about itself: there will always be a level it cannot describe.

The mathematical suggestions and analogies run deeply through Smilla's Sense of Snow. That Smilla herself is chosen as our vantage point, she who wishes to express life in terms of number, she who is drawn to studying self-similar structures mainly hidden from the the surface, and who herself is internally conflicted, showing signs of being fundamentally unreliable, is as informative as the actual elements of the plot.

And so we can't pin down a definitive interpretation of what has really happened to Smilla; not only is she fundamentally unreliable, but so is everyone in her universe, whether viewed through her projection or not. But then so am I; I too have the kind of worldview that wants to fit everything into patterns, wants to map everything to a universe that seems more clearly understandable. Things which equal one thing are equal to one another; longing can be represented by the negative numbers, madness by the never-terminating irrationals. And I too enjoy the notion of myself as the protagonist of a story, so thoroughly creating a world around me that it crowds out the third-person view. I have just enough self-awareness to notice it and correct for it, but can never jump outside myself to see. It is with this mind, that wants also to map everything onto itself, that I read the novel; even attempts to choose another are only filtered through the same function.

“The loneliest thought in the world is that what we have glimpsed is nothing other than ourselves.” —The History of Danish Dreams