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.

ActualPerceived
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.

telegraphvspost
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.

PostOffice_Military

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?

1880_PostOffices

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.

The County Problem in the West

Happy GIS Day! Below is a version of a lightning talk I’m giving today at Stanford’s GIS Day.

Historians of the American West have a county problem. It’s primarily one of geographic size: counties in the West are really, really big. A “List of the Largest Counties in the United States” might as well be titled “Counties in the Western United States (and a few others)” – you have to go all the way to #30 before you find one that falls east of the 100th meridian. The problem this poses to historians is that a lot of historical data was captured at a county level, including the U.S. Census.

521px-Map_of_California_highlighting_San_Bernardino_County.svg
San Bernardino County

San Bernardino County is famous for this – the nation’s largest county by geographic area, it includes the densely populated urban sprawl of the greater Los Angeles metropolis along with vast swathes of the uninhabited Mojave Desert. Assigning a single count of anything to San Bernardino county to is to teeter on geographic absurdity. But, for nineteenth-century population counts in the national census, that’s all we’ve got.

TheWest_1871_Population-01-01

Here’s a basic map of population figures from the 1870 census. You can see some general patterns: central California is by far the most heavily populated area, with some moderate settlement around Los Angeles, Portland, Salt Lake City, and Santa Fe. But for anything more detailed, it’s not terribly useful. What if there was a way to get a more fine-grained look at settlement patterns in these gigantic western counties? This is where my work on the postal system comes in. There was a post office in (almost) every nineteenth-century American town. And because the department kept records for all of these offices – the name of the office, its county and state, and the date it was established or discontinued – a post office becomes a useful proxy to study patterns over time and space. I assembled this data for a single year (1871) and then wrote a program to geocode each office, or to identify its location by looking it up in a large database of known place-names. I then supplemented it with the the salaries of postmasters at each office for 1871. From there, I could finally put it all onto a map:

TheWest_1871_PostOffices

The result is a much more detailed regional geography than that of the U.S. Census. Look at Wyoming in both maps. In 1870, the territory was divided into five giant rectangular counties, all of them containing less than 5,000 people. But its distribution of post offices paints a different picture: rather than vertical units, it consisted largely of a single horizontal stripe along its southern border.

Wyoming_census-02   Wyoming_postoffices-02

Similarly, our view of Utah changes from a population core of Salt Lake City to a line of settlement running down the center of the territory, with a cluster in the southwestern corner completely obscured in the census map.

Utah_census-01   Utah_postoffices-01

Post offices can also reveal transportation patterns: witness the clear skeletal arc of a stage-line that ran from the Oregon/Washington border southeast to Boise, Idaho.

Dalles_Boise

Connections that didn’t mirror the geographic unit of a state or county tended to get lost in the census. One instance of this was the major cross-border corridor running from central Colorado into New Mexico. A map of post offices illustrate its size and shape; the 1870 census map can only gesture vaguely at both.

ColoradoNewMexico_census-02   ColoradoNewMexico_postoffices-02

The following question, of course, should be asked of my (and any) map: what’s missing? Well, for one, a few dozen post offices. This speaks to the challenges of geocoding more than 1,300 historical post offices, many of which might have only been in existence for a single year or two. I used a database of more than 2 million U.S. place-names and wrote a program that tried to account for messy data (spelling variations, altered state or county boundaries, etc.). The program found locations for about 90% of post offices, while the remaining offices I had to locate by hand. Not surprisingly, they were missing from the database for a reason: these post offices were extremely obscure. Finding them entailed searching through county histories, genealogy message boards, and ghost town websites – a process that is simply not scalable beyond a single year. By 1880, the number of post offices in the West had doubled. By 1890, and it doubled again. I could conceivably spend years trying to locate all of these offices. So, what are the implications of incomplete data? Is automated, 90% accuracy “good enough”?

What else is missing? Differentiation. The salary of a postmaster partially addresses this problem, as the department used a formula to determine compensation based partially on the amount of business an office conducted. But it was not perfectly proportional. If it was, the map would be one giant circle covering everything: San Francisco conducted more business than any other office by several orders of magnitude. As it is, the map downplays urban centers while highlighting tiny rural offices. A post office operates in a kind of binary schema: no office, no people (well, at least very few). If there was an office, there were people there. We just don’t know how many. The map isn’t perfect, but it does start to tackle the county problem in the West.

*Note: You can download a CSV file containing post offices, postmaster salaries, and latitude/longitude coordinates here.*