Making Numbers Legible

What do you do with numbers? I mean this in the context of writing, not research. How do you incorporate quantitative evidence into your writing in a way that makes it legible for your readers? I’ve been thinking more and more about this as I write my dissertation, which examines the role of the nineteenth-century Post in the American West. Much like today, the Post was massive. Its sheer size was part of what made it so important. And I find myself using the size of the Post to help answer the curmudgeonly “so what?” question that stalks the mental corridors of graduate students. On a very basic level, the Post mattered because so many Americans sent so many letters through such a large network operated by so many people. Answering the “so what?” question means that I have to incorporate numbers into my writing. But numbers are tricky.

Let’s begin with the amount of mail that moved through the U.S. Post. In 1880 Americans sent 1,053,252,876 letters. That number is barely legible for most readers. I mean this in two ways. In a mechanical sense we HATE having to actually read so many digits. A more conceptual problem is that this big of a number doesn’t mean all that much. If I change 1,053,252,876 to 1,253,252,876, would it lead you, the reader, to a fundamentally different conclusion about the size of the U.S. Post? I doubt it, even though the difference of 200 million letters is a pretty substantial one. And if instead of adding 200 million letters I subtract 200 million letters – 1,053,252,876 down to 853,252,876 – the reader’s perception is more likely to change. But this is only because the number shed one of its digits and crossed the magic cognitive threshold from “billion” to “million.” It’s not because of an inherent understanding of what those huge numbers actually mean.

Actual and perceived differences between 853,252,876 vs. 1,053,252,876 vs. 1,253,252,876

One strategy to make a number like 1,053,252,876 legible is by reduction: to turn large numbers into much smaller ones. If we spread out those billion letters across the population over the age of ten, the average American sent roughly twenty-eight letters over the course of 1880, or one every thirteen days. A ten-digit monstrosity turns into something the reader can relate to. After all, it’s easier to picture writing a letter every two weeks than it is to picture a mountain of one billion letters. Numbers, especially big ones, are easier to digest when they’re reduced to a more personal scale.

1,053,252,876 letters / 36,761,607 Americans over the age of ten = 28.65 letters / person

A second way to make numbers legible is by comparison. The most direct corollary to the U.S. Post was the telegraph industry. Put simply, the telegraph is a lot sexier than the Post and both nineteenth-century Americans and modern historians alike lionized the technology. A typical account goes something like this: “News no longer traveled at the excruciatingly slow pace of ships, horses, feet, or trains. It now moved at 670 million miles per hour.” In essence, “the telegraph liberated information.” But the telegraph only liberated information if you could afford to pay for it. In 1880 the cost of sending a telegram through Western Union from San Francisco to New York was $2.50, or 125 times the price to mail a two-cent letter. Not surprisingly, Americans sent roughly 35 times the number of letters than telegrams. The enormous size of the Post was in part a product of how cheap it was to use.

Cost of Telegram vs. Letter, San Francisco to New York (1880)

This points to a third strategy to make numbers legible: visualization. In the above case the chart acts as a rhetorical device. I’m less concerned with the reader being able to precisely measure the difference between $2.50 and $0.02 than I am with driving home the point that the telegraph was really, really expensive and the U.S. Post was really, really cheap. A more substantive comparison can be made by looking at the size of the Post Office Department’s workforce. In 1880 it employed an army of 56,421 postmasters, clerks, and contractors to process and transport the mail. Just how large was this workforce? In fact, the “postal army” was more than twice the size of the actual U.S. Army. Fifteen years removed from the Civil War there were now more postmasters than soldiers in American society. Readers are a lot better at visually comparing different bars than they are at doing mental arithmetic with large, unwieldy numbers.


Almost as important as the sheer size of the U.S. Post was its geographic reach. Most postal employees worked in one of 43,012 post offices scattered across the United States. A liberal postal policy meant that almost any community could successfully petition the department for a new post office. Wherever people moved, a post office followed close on their heels. This resulted in a sprawling network that stretched from one corner of the country to the other. But what did the nation’s largest spatial network actually look like?


Mapping 43,012 post offices gives the reader an instant sense for both the size and scope of the U.S. Post. The map serves an illustrative purpose rather than an argumentative one. I’m not offering interpretations of the network or even pointing out particular patterns. It’s simply a way for the reader to wrap their minds around the basic geography of such a vast spatial system. But the map is also a useful cautionary tale about visualizing numbers. If anything, the map undersells the size and extent of the Post. It may seem like a whole lot of data, but it’s actually missing around ten thousand post offices, or 22% of the total number that existed in 1880. Some of those offices were so obscure or had such a short existence that I wasn’t able to automatically find their locations. And these missing post offices aren’t evenly distributed: about 99% of Oregon’s post offices appear on the map compared to only 47% of Alabama’s.

Disclaimers aside, compare the map to a sentence I wrote earlier: “Most postal employees worked in one of 43,012 post offices scattered across the United States.” In that context the specific number 43,012 doesn’t make much of a difference – it could just as well be 38,519 or 51,933 – and therefore doesn’t contribute all that much weight to my broader point that the Post was ubiquitous in the nineteenth-century United States. A map of 43,012 post offices is much more effective at demonstrating my point. The map also has one additional advantage: it beckons the reader to not only appreciate the size and extent of the network, but to ask questions about its clusters and lines and blank spaces.* A map can spark curiosity and act as an invitation to keep reading. This kind of active engagement is a hallmark of good writing and one that’s hard to achieve using numbers alone. The first step is to make numbers legible. The second is to make them interesting.

* Most obviously: what’s going on with Oklahoma? Two things. Mostly it’s a data artifact – the geolocating program I wrote doesn’t handle Oklahoma locations very well, so I was only able to locate 19 out of 95 post offices. I’m planning to fix this problem at some point. But even if every post office appeared on the map, Oklahoma would still look barren compared to its neighbors. This is because Oklahoma was still Indian Territory in 1880. Mail service didn’t necessarily stop at its borders but postal coverage effectively fell off a cliff; in 1880 Indian Territory had fewer post offices than any other state/territory besides Wyoming. The dearth of post offices is especially telling given the ubiquity of the U.S. Post in the rest of the country, showing how the administrative status of the territory and decades of federal Indian policy directly shaped communications geography.

Revisiting Charles Tilly: “How (and What) are Historians Doing?”

In April of 2008, noted historian and sociologist Charles Tilly died of lymphoma. In addition to the 51 books or monographs and over 600 articles, he left behind a legion of friends and admirers. By all accounts, Tilly was a prolific and highly influential scholar whose work encompassed a staggering breadth of subjects. Back in April I decided I should at least acquaint myself with some of his writing, and filed away a recommended article for later reading: “How (and What) Are Historians Doing?”

The article covers several different topics, but begins by addressing the question: what distinguishes history from other disciplines in the humanities and social sciences? Tilly lists a six-part answer:

1. Time and place are fundamental characteristics
2. Historians specialize in specific times and places
3. The most dominant historical questions are rooted in national politics
4. The blurry line between amateurs and professionals
5. A strong focus on written documents and sources
6. A narrative style that focuses on the motivations of characters as supported by textual evidence

I think some of these characteristics already feel dated, eighteen years after he wrote them. For instance, the popularity of transnational history weakens the case for Numbers 2 and 3. Historians are increasingly straying outside the traditional specialties bound by time period and geographic location, and into more thematic realms such as diaspora and women’s studies. In many ways, this is a good thing. Without the constraints of specific time and place, scholars are able to tackle problems and questions from a radically different perspective.

On the other hand, I would contend that number 4 remains stronger than ever – historical writing consistently maintains a level of common popularity that is largely out of reach for many other disciplines (although a similar case could be made for sociology and, especially today, economics). Journalists, genealogists, librarians, curators, reenactors, armchair enthusiasts – all are contributing to the field of history as much as those within the academy. Finally, even though digitization projects are making sources such as print media, maps, video footage, and material culture more accessible, I would agree with Tilly that the solid majority of historical research is conducted using written documents and sources.

Later in the article, Tilly starts to systematically analyze common approaches to historical study. To do so, he uses a simple chart outlining these different approaches:


On the vertical access is the scope, or the size of the lens being used by the historian. On the horizontal access is a continuum of methodological/philosophical approaches. Like any good educator, Tilly then uses specific examples of historical monographs to illustrate the “Four Corners” of historical approach. For his sample, he selects Carlo Ginzburg’s (1980) The Cheese and the Worms, E.P. Thompson’s (1963) The Making of the English Working Class, E.A. Wrigley and R.S. Schofield’s (1981) The Population History of England, 1541-1871, and Olivier Zunz’s (1982) Changing Face of Inequality: Urbanization, Industrial Development, and Immigrants in Detroit, 1880-1920. After discussing each one individually, he charted them visually:


Although I have not read any of the works, Tilly did a great job of explaining them in terms of four different approaches to historical analysis. I was left with the urge to create my own charts using works I had actually read in the past year or two:

republic-of-suffering2Drew Gilpin Faust, This Republic of Suffering: Death and the American Civil War

The graph for Drew Faust’s This Republic of Suffering is largely concentrated in the large-scale, humanistic quadrant, as the book delves into the traumatic effects on the American psyche caused by the Civil War’s unprecedented slaughter. Its line extends down to the small-scale, humanistic corner in order to represent Faust’s use of individual experiences (such as those of Walt Whitman and Ambrose Bierce) to illustrate her broader points.

polio1David Oshinksy, Polio: An American Story

David Oshinsky’s Polio covers a wide area of scope and approach, but it leans towards a large-scale, social-scientific book, given his detailed narrative covering America’s medical struggle against polio in the twentieth century.


David Blight, A Slave No More: Two Men Who Escaped to Freedom

David Blight’s A Slave No More maintains a relatively tight focus on the small-scale and humanistic approach. Blight uses the narratives of two escaped slaves to explore their decisions, motivations, and actions – all within the larger context of slavery’s death throes and national emancipation.


Erskine Clarke, Dwelling Place: A Plantation Epic

Erskine Clarke’s Dwelling Place takes a small-scale, more social-scientific approach to chronicling several generations of a slave family and a slaveholding family on a Georgia plantation. The scope is kept relatively small, with a huge amount of detail that draws upon a range of quantitative and qualitative sources.

I enjoyed the process of creating these graphs. Information visualization is a growing field, and one that I believe will become ever more important to historians. Although the above graphs are imprecise and subjective, they forced me to really consider the content of the books in a new perspective. Most of these books probably touched every corner of the graph at some point during the course of the monograph, but visually plotting their content necessitates a careful aggregation of the author’s central themes and points. Where do the books cross the two axes of scope and approach? Where is their “centroid” on the graph? Just how far along each axis do they go? It’s a refreshing exercise, and one that I think could work in the classroom as a visual and quantitative supplement to a traditional book review.

I’d recommend anyone reading this to sit down with a pencil and paper, channel your inner Charles Tilly, and try to sketch out a graph for a favorite historical monograph. For those of you who have read the above books, I’d welcome any and all criticisms and disagreements regarding their graphs.

Scattered Links – 9/6/2008 (Map Edition)

The Washington Post ran an article on the separate efforts of Dan Alexander Hawkins and Dan Bailey to map historical Washington. In the words of the article’s author, “The two men came to their fascination with Washington’s history by very different paths — pencils vs. pixels — yet sometimes their goals appear nearly identical.” The article is well-written, and offers a real glimpse into the rewards and challenges of historical mapping, whether digital or analog. Also, I really need to get a tour of UMBC’s Imaging Research Center.

Meanwhile, the University of Richmond’s Voting America project has been getting some play in the blogosphere. I have not had the chance to fully play around with it, but Sterling Fluharty at PhDinhistory has reported problems when testing the site for accuracy compared to separately compiled statistics. I’d be interested to see if this issue gets resolved.

Finally, on a non-history note, if anyone likes beautiful infographics and maps, take a look at Aaron Koblin’s Flight Patterns. Koblin’s graphics of North American air traffic patterns appeared in Wired magazine and are very well-done. Be sure to not only look at the images, but watch the accompanying animations as well (my favorite is the 3-D blobular).

Scattered Links – 8/21/2008

Lisa Spiro has posted a great recap of her presentation “Doing Digital Scholarship” at the Digital Humanities 2008 conference. The presentation “focuses on a project to practice digital scholarship by relying on electronic resources, experimenting with tools for analyzing and organizing digital information, and representing ideas through multimedia.” All in all, I think the blog post is a wonderful introduction to digital scholarship, both as an overview and a jumping off point for further ideas. Spiro really displays that crucial trait necessary for a digital humanist: a seemingly unlimited willingness to try new approaches.

Errol Morris has yet another interesting post about interpreting photography and identifying fakes, inspired by the faked photographs of Iran’s missile launch several weeks ago. Also, if you haven’t read it, I’d highly recommend his three-part series “Which Came First,” which details his attempt to uncover the truth behind Robert Fenton’s famous “Valley of the Shadow of Death” photograph of the infamous Light Brigade skirmish. What I liked most about it was his microscopic attention to detail and an open willingness to crowdsource, as over a thousand people responded and lent advice, tips, and clues. He even did a recap of these comments, which shows a real embrace of the power of collective intelligence and digital media.

GOOD Magazine has put up an extremely sleek and user-friendly interactive graphic titled “Wanderlust: GOOD traces the most famous trips in history.” Included among these are not only the standard fare of Lewis and Clark, Charles Lindbergh, and Marco Polo, but also fictional accounts such as Pequod from Moby Dick, along with Journey to the Center of the Earth. Although I will point out that it’s phenomenally Euro/American-centric, I do applaud its interface and design. This rivals some of the NYTimes’ recent gold standard information graphics as far as usability, style, and depth.

Finally, if you’d like to get worked up and indignant, read Edward Luttwak’s “A Truman for our times.” His thesis is almost comical: “While anti-terrorist operations have been successful here and there in a patchy way, and the fate of Afghanistan remains in doubt, the far more important ideological war has ended with a spectacular global victory for President Bush.” But what makes me downright irate is his complete hijacking of history. In a characterization that smacks of imperialism, ignorance, and borderline racism, he breezily describes eight hundred years of Chinese history in this pithy statement:

“That describes everything that the Chinese are not, and have never been. The Chinese empire was aggressive and expansionist under the Yuan dynasty and again under the Qing. But one dynasty was established by horseriding Mongols, the other by horseriding Manchus, both the products of foreign warrior cultures. The Han Chinese prefer other pursuits. Perhaps they will change, as cultures sometimes do.

Historical determinism and unprofessionalism at its worst. I wouldn’t have been at all surprised if he then pulled a Lawrence of Arabia and ended with “A little people, a silly people – greedy, barbarous, and cruel.”

Review: Placing History (III)

(This is the third installment of my review of Placing History. See the first and the second parts.)

I’ve finally finished Placing History: How Maps, Spatial Data, and GIS are Changing Historical Scholarship. As my previous posts have made clear, I’m quite impressed with the breadth and depth of the compilation. As before, I’ll briefly recount the remaining chapters, and wrap up my thoughts at the end.

“Mapping Husbandry in Concord: GIS as a Tool for Environmental History,” by Brian Donahue. I liked this chapters for a multitude of reasons. On a personal note, his research is quite similar (though wider in scale) to the work I did in mapping property holdings and transactions of Venture Smith. So in a self-congratulatory mood, I found myself nodding with satisfied agreement at his various points about the benefits and drawbacks to mapping land deeds and parcels. On a less personal level, I liked the various angles he took in pursuing his study of Concord – especially examining seemingly disparate holdings of a variety of original families and noting patterns of land use.

“Combining Space and Time: New Potential for Temporal GIS,” by Michael Goodchild. For starters, the cover illustration for this chapter was a piece of Charles Minard’s famous “Carte Figurative,” which depicts a staggering array of geographic, temporal, and statistical information regarding Napoleon’s ill-fated Russian campaign:

Charles Minard
Charles Minard's "Carte Figurative"

Information graphic guru Edward Tufte described it as “the best statistical graphic ever drawn,” which effectively canonized it for any map and information graphic nerd such as myself. This is a roundabout way of saying I was excited to start reading Goodchild’s chapter. Goodchild doesn’t dissapoint, as he uses decades of geography experience to explore ways in which the field is gradually shifting to incorporate temporal data. Although its heavy on technical geography, it’s a rewarding chapter that covers one of the fundamental challenges of historical GIS: how do you visually display the relationship between space and time? Goodchild predicts that this challenge will rapidly diminish, as tools and systems to display things such as dynamic data, or even a history-specific model, will become more and more accessible and widespread.

“New Windows on the Peutinger Map of the Roman World,” by Richard J.A. Talbert and Tom Elliot. Talbert and Elliott present an analysis of the Peutinger Map, a nearly 7 meter long Roman map depicting the Mediterranean world and beyond, constructed around 300 CE:

Detail of Peutinger's Map
Detail of Peutinger's Map

I liked this chapter a lot, despite my complete unfamiliarity with the subject matter. The authors make compelling arguments backed by GIS analysis, such as: “the basis of the map’s design was not its network of land routes (as has always been assumed) but rather the shorelines and principal rivers and mountain ranges, together with the major settlements marked by pictorial symbols.” They present a quantitative analysis of routes, and utilize a histogram to further examine the segments and their distances.

“History and GIS: Implications for the Discipline,” by David J. Bodenhamer. This chapter, along with the first chapter and conclusion, gives the best “big-picture” perspective on historical GIS. Bodenhamer describes the field of history as a whole, in particular elements of it that relate to spatial analysis. He believes that in order for GIS to become a valuable historical tool, “it must do so within the norms embraced by historians…” GIS is well-situated to do so, because it uses a format of presenting information (the map) that historians are already familiar with, and its visualization and integration of information makes it easier to display the complexity of historical interpretation. He also discusses the challenges to historical GIS. One point I really liked was that technology as a whole, and GIS in particular, often requires a level of precision that historical documents cannot display within “a technology that requires polygons to be closed and points to be fixed by geographical coordinates.” Other challenges range from the theoretical (ex. temporal analysis) to the practical (ex. learning a completely new discipline). Finally, he succinctly sums up one of the greatest challenges: “GIS does not strike many historians as a useful technology because we are not asking questions that allow us to use it profitably.” I could not have said it better myself – until historians begin to ask the type of questions that can be addressed through spatial analysis, GIS will likely remain a technological oddity within the discipline.

“What Could Lee See At Gettysburg?” Anne Kelly Knowles. This is probably one of the most accessible chapters in the book for a layperson. It combines an engaging narrative prose with rich, stylistic maps, and a “popular” subject matter (the Battle of Gettysburg). But more importantly, it clearly presents an answer to a historical question, while contextualizing the issue and presenting possible ideas for future studies. Viewshed (line-of-sight) analysis is of obvious and particular interest to military historians, but it has other implications as well. In particular, this chapter illustrates the phenomenal power of GIS to transport the reader to the past, and get a micro sense of “being” there.

Beyond thoroughly enjoying Placing History, I believe it’s an important contribution to the field of historical methodology in general, and (of course) historical GIS in particular. The compilation gives a wonderful balance while thoroughly exploring the topic: its current state and background, case studies ranging from micro to macro and “hard” to “soft”, discussions on theory and approach, and an outline for the future. I recommend the book to educators, historians, digital humanists, or anyone with even a passing interest in a growing and valuable area of scholarship.