Read an Excerpt
sum of the parts
the mathematics and politics of region, place, and writing
By kent c. ryden
university of iowa press
Copyright © 2011 University of Iowa Press
All right reserved.
ISBN: 978-1-58729-987-2
Chapter One
lets = meaningful space
the mathematics of region and place
One of my favorite types of recreational reading is popular discussions and histories of mathematics and mathematicians. There are a few reasons for this, I suppose. First, I like to believe that learning and thinking about functions, algorithms, Fermat's Last Theorem, and the like exercise different parts of my brain than does thinking about my usual environmental humanities, ecocriticism, and regionalism. Also, in school I was always very good at math, but I never had a teacher who gave me any idea that mathematics could be interesting and creative, that it could be more than a matter of mechanically following certain steps and grinding out the right answer. I had to find out otherwise for myself later. (Nothing personal, math teachers. I'm sure you were all doing your best.) Perhaps in an alternative universe somewhere, I'm working as a mathematician. Although I might not be up to it: a mathematician friend of mine once told me a joke about two math professors who were reminiscing about former students. At one point, one of the professors asked, "What ever happened to so-and-so?" The other replied, "Oh, he decided he didn't have enough imagination to become a mathematician. So he became a poet instead."
Also, though, I'm intrigued by suggestions that, far from being diametrically opposed, my interests in mathematics on the one hand and nature and landscape on the other may in fact have points of connection. Different mathematicians have always had different answers when asked whether their work is to invent new objects of thought or to unmask new concepts and ideas that already existed in the world, just waiting for someone to uncover them? Or, as science writer Karl Sabbagh puts it, "There is some argument over whether the stuff of mathematics is out there—facts and relationships waiting to be discovered—or in here—creations of the human mind that are akin to inventions, paintings, or poems." Yes, many branches of applied mathematics have multiple real-world implications and degrees of usefulness, but do even the most abstruse branches of pure mathematics, those seemingly furthest removed from tangibility, give body to aspects of the physical world that surrounds us, touch centrally on concepts that have the same immutability of other laws of nature? (This stance is described by philosopher Rebecca Goldstein as that of the "mathematical realist," for whom "the properties of the numbers 4 and 25—that, for example, one is even, the other is odd and both are perfect squares—are as objective as are, according to the physical realist, the physical properties of light and gravity.") Was noted Cambridge University number theorist G. H. Hardy correct when he claimed of the prime numbers (those numbers divisible only by themselves and 1 without leaving a remainder): "I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our 'creations,' are simply our notes of our observations.... Pure mathematics ... seems to me a rock on which all idealism founders: 317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way." When I look out my front window right now at a group of three maple trees, in addition to their individual physical presence do they give form to what might be thought of as a natural property of "three-ness," just as their falling leaves give evidence of a natural property of gravity?
My group of three maples puts me in mind of the mathematical concept of sets and set theory, a concept that I find useful for thinking about, of all things, the nature and meaning of cultural regions. Not that sets are not interesting in their own right, of course. They give rise to some interesting paradoxes, such as Bertrand Russell's famous set of all sets that are not members of themselves. (Think about it: if it is a member of itself, it is not a member of itself, and if it is not a member of itself then it is a member of itself. It's a version of the Liar's Paradox: Everything that I say is a lie. Think about that one too.) They also bring up counterintuitive ideas such as the fact that infinity comes in different sizes. On the surface, it would seem that there are many more natural numbers (1, 2, 3, 4, 5, 6 ...) than there are prime numbers (2, 3, 5, 7, 11, 13 ...). And yet, every prime number can be matched with a natural number in a one-to-one correspondence: 1 to 2, 2 to 3, 3 to 5, 4 to 7, 5 to 11, 6 to 13, and on and on over the horizon, both natural numbers and prime numbers being infinite in amount. So, according to the axioms of set theory, the sets of natural numbers and prime numbers are the same size—infinite—even though one intuitively "seems smaller" than the other.
Heady stuff, and I like the way it makes my brain hurt. But paradoxes aside, I think that the very nature of sets and their contents provides some useful insights for thinking about region and place. (As such, perhaps I'm exploring one of those instances where mathematical reality is made manifest "out there," and, like Hardy, I'm simply recording my observations.) According to German mathematician Georg Cantor (1845–1918), a set can be "any collection of definite, distinguishable objects of our intuition or of our intellect." (More breezily, mathematical writer David Berlinski, from whom I cribbed the Cantor quotation, notes that "a set is a collection, a class, an ensemble, a batch, a bunch, a lot, a troop, a tribe.") Now, think of a cultural region—say, New England, a region I know well. In order for a more-or-less clearly bounded physical space to be seen to have enough internal consistency to justify being called by a single place name, it must contain a collection of like objects, physical or ideational, that are spread widely enough over its surface so that we feel justified in saying that Maine and Connecticut belong together spatially.
In other words, a region is a set—not merely of states, but of things that link many disparate places in common. And, I would argue, regions can usefully be seen as sets of narratives, or of objects that invoke narratives. Certain historical personages and the narratives associated with them—the Pilgrims, the Revolution, the Yankee farmer, that nebulous place we think of as "the colonial"—have been concretized in books, magazines, architecture, public monuments, schoolrooms, and elsewhere and made to stand for what has made New England a distinctive region over time. At least within American popular culture, then, one prominent way that New England has been defined is as the set that contains those narratives, those "objects of our intellect," as Cantor might put it.
There are two more important points to make before we go on, though. First, sets are ultimately arbitrary in content. The mathematician says, "Let S be the set containing the prime numbers, or the numbers 1 to 10, or the even numbers," or what have you, and that's what S is, because the mathematician says so. It's not that the things within the set do not exist (insofar as numbers actually "exist," in this case, but I can sense those worms trying to wriggle out of the metaphysical can again), it's that the arrangement consists of whatever the mathematician wants it to for her or his own purposes. As David Foster Wallace describes the relevant axiom of set theory, "For a set S and a 'definite predicate' P, there exists the set SP that contains only those members of S that have the property designated by P," with a definite predicate being "something you can verify as definitively T v. F [true versus false, in Wallace-speak] for any set-member, like 'is blue' or 'weighs more than 28.7 grams' as opposed to 'is lovely' or 'tastes like chicken.'"
The second point follows from the first. Once a set has been constructed around a definite predicate, it takes on a reality and solidity of its own: Berlinski notes Cantor's "philosophical axiom that sets, no matter their size, are as real as their members." What this means in mathematical terms is that a set can be considered as a single thing, in the same manner that an individual number is a single thing, for purposes of performing functions and other mathematical operations. But I think that Cantor's axiom has at least metaphorical implications for those sets that we call regions as well. It's when we start treating arbitrary collections as real and individual objects that we get into trouble.
I want to discuss this point by talking about the Maine town I have recently moved to, Yarmouth, as a region: that is, a bounded geographical space given internal meaning and coherence by the set of historical narratives that it comprises. Remember, this selection is performed by human actors according to certain "definite predicates" in order to meet certain purposes, just as is the case with a mathematician's positing of a set. As a relative newcomer, I've been noticing ways and places in which local history has been marked in the landscape. It has become clear that, rather than there being a single unitary Yarmouth, the town contains a variety of sets selected by different actors, or sees itself as a subset of a larger national set—and not all of these sets talk to each other. To bring to mind the Venn diagrams that we learned about in school: the circles that represent the sets don't always overlap and create shared common subsets.
Scene One. At the side of Route 88, just inside Yarmouth's border with neighboring Cumberland, there stands an upright slate stone with the number 37 inscribed on it and a small sign posted next to it (fig. 1). It's nearly impossible to see while driving by; I only discovered it because I stopped once and looked around, knowing that sometimes you find interesting things on the roadsides of old New England highways when they cross town and state boundaries. Still, it makes an interesting historical statement. The sign reads, "Milestone on King's Highway, Boston to Machias. Set in 1761 by Order of Benjamin Franklin, Postmaster General. One of Six Known in Cumberland County. This Plaque Erected by Cumberland County." The inclusion of Benjamin Franklin seems rather extraneous: isn't it enough to say that this milestone is a rare artifact of a historic regional highway? That seems important enough. And yet, the words "Benjamin Franklin" are the largest words on the plaque. It seems to me that "Cumberland County," or whoever its representatives were in this case, wanted to establish at least a tenuous connection to one of the nation's most famous founding fathers. What makes this stone important is largely the fact that Franklin, sitting in an office far away, ordered its erection. In terms of Yarmouth as a set, what this monument seems to say is "Let Y be a subset of the set S that contains places connected in some way to Benjamin Franklin," or "connected in some way to the Founding Fathers." It is a way of defining a set that seems to have little to do with life in Yarmouth itself.
Scene Two. Continue up Route 88 until you come to the spot where Gilman Road veers off to Cousins Island, and you come across a cemetery with a sign standing next to its fence (fig. 2). The sign, erected by the Village Improvement Society in 1969, purports to explain "Historic Yarmouth" and includes historic information and a map indicating the sites of important past buildings (fig. 3). The Village Improvement Society in essence said, "Let Y be the set that includes the narratives defining Historic Yarmouth," and their selection thus delimits what qualifies as "historic" (and, implicitly through exclusion, what does not). We find that Yarmouth is "Part of the Plantation of 'Old North Yarmouth.' Originally settled in 1680 and Twice Destroyed by Indians. The Third and Permanent Settlement of 103 10 Acre Home Lots Was Laid Out on 'The Neck' in 1727, and the First Town Meeting Was Held in 1733." The sign's map indicates the location of certain historic sites—a meetinghouse, a minister's house, a school, some cemeteries—all of which were built or laid out between 1729 and 1770. Below, in small print, the sign politely notes, "Later, in More Peaceful Times, the Town Developed around the Falls and Inland," but in the sign's terms that part of Yarmouth is not "Historic." The set that the Village Improvement Society defined takes in only a small portion of the town's acreage, and its life began in 1680 and ended in 1770. After that, "nonhistoric" Yarmouth became the vital part of town.
Scene Three. If you live in Yarmouth and your house predates the twentieth century, you can apply to the Yarmouth Historical Society for a wooden plaque that lists the name of the original owner and the approximate date of the house's construction, insofar as the historical society can determine that information (fig. 4). Such signs appear all over town, but there is a particularly high concentration of them in the neighborhood I live in. (And I must admit that I am not immune to their charms. My partner, Brenda, and I applied for a plaque for our circa-1840 home and were disappointed to find it designated the ordinary-sounding John White House. We were hoping for a more regionally colorful name, like the Ebenezer Jedediah Frothingham House or something.) For any cartographically inclined readers who would like to look up the area I'm talking about, it is bordered by Hillside Street, Cumberland Street, South Street, and Main Street. This area contains eighty-nine residences or former Main Street residences that have been converted into businesses. Thirty-six of these houses have plaques, or just over 40 percent. Their dates range from 1793 to 1899, with the bulk of them having been built in the decades of the mid-nineteenth century. Many other houses could qualify based on their evident age, and in their architectural style and paint colors (white, light greens and yellows and grays) they closely resemble their plaque-bearing neighbors. While this neighborhood is not officially designated as a historic district, it has become one de facto by virtue of so many of its residents' having publicly linked their houses to a certain time and cast of characters (and the presumably old-fashioned ways of life that those characters followed) in Yarmouth's past. In a way, this neighborhood acts as a response to the "Historic Yarmouth" sign, with the area "around the Falls and Inland" seizing and proclaiming its own historic importance—but not, again, taking in the entire physical extent of the town nor all periods of its past. The set-makers in the historical society and the neighborhood itself are saying, "Let Y be the set of houses, occupants of those houses (particularly the patriarchs), and activities of the occupants of those houses that were built in town before 1900."
Scene Four. Meet Herbie (fig. 5). As a sign that was once affixed to him told you, he was the biggest elm tree in New England. As of 1997, he was about 225 years old, with a girth of 20 feet, a height of 110 feet, and a spread of 120 feet. Herbie was an impressive specimen. He was also doomed, and he is no longer around. Herbie had been able to stave off the death sentence of Dutch elm disease through years of careful doctoring and the occasional amputation, but the patient became terminal, and he was cut down in January of 2010. But trees, too, imply stories, narratives that can be bundled into sets. Writing of the American chestnut tree, itself a victim of disease, in the Appalachians of Virginia and of the uses to which residents had historically put the tree's wood and nuts, Susan Frienkel speaks "not only to the abundance of the trees in the region [in the past], but also to the role that they played in the community and culture. Just as chestnut wood once served as the unseen solid backing for the veneered furniture that used to be manufactured here, so the tree once provided the unsung foundation of the lives of the county's poorest residents. Its story is also their story."
And just as the chestnut was the iconic tree of the Appalachian countryside, the elm has figured centrally in the way that New England has pictured and imagined itself over time. Indeed, historian Thomas J. Campanella notes that "the tree was one of the quintessential symbols of the region. Other species may have been more commercially valuable or more useful, but the elm was rooted in the Yankee soul," and arborist Sheila Connor claims that "perhaps no other American tree inspired as much reverence." In colonial New England, large elms were valued for their presumed antiquity, for having stood witness to the growth and development of the region since the time of first English settlement. In the Revolutionary period, elms were often associated in the public mind with important events and personages, the most famous of these being the Washington Elm in Cambridge, Massachusetts, and the Lafayette Elm in Kennebunk, Maine. In the nineteenth century, countless village improvement societies planted equally countless numbers of elm trees along roadways and in parks. As New England cities began to industrialize more and more heavily, individuals and city governments launched elm-planting programs along city streets, believing that "elms evoked the pastoral New England countryside, and promised to transpose its grace and charms to the heart of the city." (Not for nothing is New Haven nicknamed, now anachronistically, the City of Elms—nor, for that matter, did Portland, Maine, receive the moniker Forest City; both cities were known for their plethora of elm-lined thoroughfares.) With the advent of Dutch elm disease, though, New England cities and towns lost their trees at an alarming rate, and with scarcity came an increased recognition of the elm's status as a symbol of the New England town of the past, and by extension a reminder of small-town ways of life, the innumerable narratives of past everyday existence. To have had the biggest surviving elm in New England, then, let alone an elm that may have been alive before 1776, is quite a claim to fame within the region. Herbie connected Yarmouth to its deep past, and thus could tell many stories; he witnessed countless comings and goings from his post on East Main Street. He seemed to belong to the set, "Let S be the set of all New England towns with surviving elms," but also, "Let S be the set of all threatened and vanishing icons of the New England past and the stories and ways of life that they represent." And within that set, Herbie was a prominent member indeed.
Scene Five. Route One, the main drag through town (fig. 6). This is where people go to buy groceries, get their cars worked on, eat fast food, and engage in all the rituals of franchised consumer culture. Nothing interesting or historic here. Move along. This isn't true, of course: every place has a history, no matter how banal or unromantic it may seem. People have even written books about U.S. Highway One. And yet, the sets that I have described above do not, indeed cannot include this scene. It falls outside their definitions.
(Continues...)
Excerpted from sum of the parts by kent c. ryden Copyright © 2011 by University of Iowa Press. Excerpted by permission of university of iowa press. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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