I’ve recently returned from the annual meeting of the North American Cartographic Information Society in my old stomping grounds of Madison, Wisconsin. I’ve mentioned NACIS here in the past. It’s a wonderful organization and it holds the best conference ever.

While I will recap some of the conference (which was very good this year), this time I’ve been thinking about it as a good representation of the state of American cartography. Even if you don’t care about the conference, bear with me as I hit on a few of its points and contemplate their significance to the field.

How does design make a difference?
This was the tagline of the conference, and I’m not sure there was much of an answer. It’s not an easy question, really. We all agree that good design can make a difference over bad design, but what is design? Can we make maps with an absence of design, and if so what difference does design make over non-design?

Let’s assume there is some agreed-upon definition of “design” and think about what it means that this was the theme of the conference. In an era when it’s not always clear what a “cartographer” is, here is a core group self-identified cartographers identifying themselves as designers. I’m among them and have encountered surprise when describing cartography to the uninitiated as by and large a design practice. Maybe now that anyone is a mapmaker, this attitude is what defines cartography. Maybe that’s how design makes a difference. Cartography isn’t making a map; it’s designing a map.

Art in cartography
Or maybe a cartographer is an artist. Tim Wallace organized a session on art in modern cartography, a topic that has come up many times over the years but this time stemmed from a series of blog posts that Tim instigated this past spring.

It continues to be an interesting debate because of its technological facets. Daniel Huffman argued for the art in “human cartography,” lamenting computer automation, which to be honest I see as a bit of a straw man. Aaron Straup Cope, if I am not misinterpreting his points, noted that newfangled ubiquitous, easy mapping creates more room for artistic cartography now that we don’t need to put all our efforts toward painstakingly accurate maps for navigation and the like.

Practical Cartography Day
The main NACIS conference is preceded by a day of more workshoppy talks, which this time I think comprised a representative slice of modern cartography. There was some of the usual fare, tips for traditional print or desktop cartography such as Alex Tait’s top ten reference cheat sheets. But nearly half the talks dealt with web cartography, with several hot shots covering hot topics. They included Nathaniel Vaughn Kelso of Stamen, AJ Ashton of Development Seed (I mean, have you read anything about web cartography lately that doesn’t mention TileMill?), Adam DuVander of the Map Scripting book, and my good pals Jeremy White of the New York Times and (with a presentation that alone was worth the price of admission) Zachary Forest Johnson of GeoIQ and other fame.

Thanks to cool guys Tim Wallace and Sam Pepple for crafting this session so well!

The new crowd
Speaking of those guys, in the six years that I’ve known NACIS I’ve been pleased to see how the membership has evolved to better reflect the reality of modern cartography. At the 2006 NACIS meeting, which was also in Madison and was the first one I attended, Schuyler Erle was invited to give a keynote address. He spoke, as was his wont, about the democratized cartography afforded by things like the still young Google Maps. Listening to the murmurs around the room, one could hear that many of the old school cartographers—the core constituency of NACIS—were appalled by the idea of amateur non-cartographers making maps. But now we seem to welcome these types, as it’s been proven that some of the best cartography is coming from people without cartography backgrounds but rather, often, web backgrounds. It is excellent to see, for instance, Messrs. Cope (who is “from the Internet”) and Migurski (who gave the keynote two years ago) from Stamen showing up among the “mainstream” cartographers, if that’s the right word. Even almighty Google now has a presence.

Meanwhile, I’m looking forward to seeing how my generation of bona fide cartographers helps shape the community. We’re the ones who are trained in cartography but during this explosive period of web mapping, which perhaps gives us a different perspective on the field from that of the more established cartographers. NACIS meetings are attended by a fair number of students as well as people like me who are only a few years out of school, and some of them already have pretty strong and active voices.

Teaching cartography
So far in this post I’ve mostly ignored the academic side of cartography, and I should mention that NACIS comprises a mix of professionals and academics. For me the most fascinating session at this year’s conference was one that brought together both types: a panel discussion on teaching cartography. It sounds ridiculous, but I’ve never had such an easy time staying awake at a conference session. Many topics and challenges were discussed, like teaching software versus teaching concepts and thematic versus reference mapping. (Also, glad that panelist, Harvard scholar, and new local carto/drinking buddy Kirk Goldsberry was dragged to the conference for this.) But at a week’s removal, what’s really fascinating is my fascination itself. I sat there, engrossed in the discussions, kind of wondering why I, not being a cartography teacher, was so interested. Perhaps it’s just reflection on my own roots and where my education was good and where it was lacking. But more likely it’s that cartography is—and I don’t care if this sounds pathetic—my essence, and I care a lot about how it is taught or otherwise instilled in others. It matters to all of us who make maps in this time when, as I noted before, we’re not even sure what a cartographer is. However we arrived at map-making, let’s think about what people need to learn to practice the craft and how it can be taught.

Best week of the year
One of my happiest days a couple of years ago was when the top search term directing people to my website was “drinking in a bathtub,” which brought visitors to a post about a previous NACIS conference. I have certainly been much more serious this time, but don’t let that distract from the fact hat NACIS is simply the best time you will ever have at a conference, especially if it’s in Madison. NACIS truly is a community, where the people you meet are more like friends than professional contacts. The conference organizers do an amazing job of establishing a productive but fun environment. (I want to thank them profusely but don’t want to list names for fear of leaving someone out. If you’re a current or future NACIS attendee you’ll know them.) The schmoozing is easy, and there is a healthy drinking culture among cartographers (I’d like to think that we at UW-Madison were pioneers in that area).

Consider it plugged. NACIS is awesome. Cartography is awesome.

Are you doing mapping work with marvelous newfangled technology? Cartographic Perspectives (CP), the journal of NACIS, wants you! I am seeking how-to articles for a new regular section called On the Horizon, wherein cartographers can learn from one another about a variety innovative, new, or just plain useful implementations of current mapping technologies.

You’ve probably noticed that it’s hard to keep up with latest and greatest ways to do things like web and mobile mapping, even if that’s your line of work. Self-contained tutorials and examples of solid cartography with new technologies can be scattered and hard to track down, and everything looks intimidating to a non-developer. Let’s help CP establish a reliable, cartography-oriented repository of useful and accessible tutorial articles.

The scope is fairly wide here. It needn’t be something on the bleeding edge. Recent issues have contained tutorials on choropleth mapping with Google Maps, event animation with Google Maps, programming panning and zooming in ActionScript, and building mapping apps for the iPhone (if these links don’t work, try copying and pasting the URLs). There’s a big world out there of code libraries, techniques, and so on; if you can contribute your expertise in any of this to the cartography community, please do!

Any students out there? This is a good way to help get your name out there among a great community of cartography people. CP and NACIS represent a good mix of academic and practicing map people—a group that any cartography student will enjoy and benefit from knowing. Non-students, get in on this too! You can learn from CP, and we can all learn from you.

If you have something to submit or are interested in writing something, or if you have questions, I’d love to hear from you. Find me at andy@axismaps.com, in a comment here, by beating down my door, or however you wish. Let’s keep this digital cartography party going.

Remember red dot fever? That epidemic was back in the early days of web mapping APIs, when most of what was possible (and what was popular) was to throw a bunch of points on top of Google Maps and the like. Now the web still has plenty of pushpin-clogged maps, but web mapping has come a long way since those early days only a few years ago. Full-fledged thematic mapping, customized base maps, complex interactivity, and more are now possible.

Still, the essence of common web cartography has remained this: stuff on top of other stuff. Specifically, it boils down to base map plus thematic or location data. It’s just better now that we have so much more control over each level of stuff. That’s not necessarily a terrible thing; modern cartography always amounts to the combination of different data sources, albeit with better integration than the separate layers of web mashups.

It seems, though, that the control over each level of the map has now reached the point where there needn’t be a distinction between base map and thematic data. Will the web map of the 2000s go the way of the Royal Society for Putting Things on Top of Other Things?

I cracked a beer and started to outline some points in response to Tim’s post but decided it wasn’t worthwhile to attempt to talk about the finer points. Everything hinges on people’s differing definitions of “art.” I ended up progressing through three stages of thought on art and science in web cartography, presented here with sweeping generalizations, ridiculous exaggerations, offensive assertions, and my dumb versions of Tim’s original diagram. (Do read his post first.)

There is plenty of art and science in web cartography.
They’re just not in the process of cartography where Tim was mostly looking. In terms of aesthetics, web cartography is just as capable of being an art as anything; it just, as always in history, is accomplished with the latest tools. But if art were only a matter of aesthetics, the “my five year old could paint that” genre wouldn’t exist. Art is not necessarily in the map itself, nor its execution, and neither is science. During a moment’s break from his one million word dissertation, Robert Roth suggested to me these definitions of art, science, and cartography (in terms of ontology and epistemology, as academics are required to do):

Cartography is the art and science of mapmaking and map use.

Under this definition, mapmaking and map use are the ontologies; they are the bodies of knowledge to which academicians contribute and from which mapmakers and map users draw. These corpora clearly overlap, particularly in the case when map user is mapmaker. Art and science are the epistemologies; they are the ways of knowing or the methods of constructing new knowledge about how maps can/should be made or used.

I can get on board with that (although that language implies to me that pretty much anything is an art and science) if we want to get too philosophical to bother arguing over anything, the eventual point being that all this is at a different level from the actual act of designing and making a map, and that in this there is probably no difference between web cartography and any other cartography. To be a litte more down-to-earth, though, I won’t hold such a fundamental view of art and science, and would generally consider them to include the knowledge itself. The science is, say, How Maps Work, and it, along with whatever art is, informs and guides map design, on the web or anywhere else. But this assumes that “web cartography” really is like cartography as we usually know it. Maybe it’s not.

There is neither art nor science in web cartography.
This is the first of two rude things I will say: web cartography is unartistic and unscientific. The common “cartographer” on the web is either a machine or simply the final human element of everything that goes into a map—the mapmaker. The word itself doesn’t seem as common as it used to be, but the mash-up is still the heart of web cartography. The web map, in my mind, is all about combining your data with someone else’s base map, or your design with someone else’s data, and so on. When I make a map by coloring a bunch of polygons on top of Google Maps, have I done anything artistic or scientific? Art and science entered into the equation somewhere along the line (say, when Google designed their map tiles), but it probably wasn’t at my stage, and I’m probably (definitely) going against some good judgments that would follow from them. Despite all the good, artistically brillant and scientifically sound design out there, “web cartography,” if you ask me, is about the retrieval, mingling, and dissemination of data, at times almost willfully at the expense of cartography’s artistic and scientific roots. Web cartography is not about maps; it’s about hacks for moving data around. But hey, most of the time that’s just fine.

Who cares?
Having stated the above two perspectives, rude statement number two: so what? To even fret the “displacement of art” in web cartography (to quote Tim) is to be a traditionally trained cartographer grasping at relevance in the modern world. I like to take this cynical view often (recognizing that I too am just such a cartographer, but at least being real about it) when I see some of my ilk talking about the current wave of amatuer, so-called neocartography, typically to explain why it’s all badly designed or simply wrong. Web cartography, I generally hold, is what it is, gets the job done, and will evolve into something that incorporates the best of art and science. But I admit that it’s hard not to be bothered by moves in the wrong direction. “Art” being nigh impossible to definitively identify, I’d more point to science as the thing being marginalized in web cartography. Take, for example, the bit of excitement seen on Twitter the other day over a Where 2.0 workshop on Google Fusion Tables, which make it easy to load data into what is apparently being called an intensity map. Here is a deliberate advancement in the creation of what cartographic science would deem, well, bad maps. (Inappropriate map projection, a confusion of semi-transparent colors and basemap details, &c.) We do what we can with the technology available and that’s fine, but at some point we’ll have to make the transition from developing technology that makes what we are doing easier to developing technology that makes what we should be doing easier. Perhaps I’ll choose to care this time.

- – - -

Other writing in this inter-blog series: Tim Wallace, Daniel Huffman, and hopefully more to come.

Let’s cut to the chase. I traveled a path around town in the shape of a heart as best I could. It was 10.44 miles (that’s 9,872 smoots in the local system of measurement), and the reason it’s awesome is that part of it was on a boat. The GPS track became this sickly shape—not exactly an ideal heart but vaguely recognizable as one. Or at least some kind of pointy muffin. [Google Maps link]

This is my first foray into GPS drawing, and I certainly don’t expect to reach, say, Jeremy Wood‘s level of mastery of the art. But it’s not so much about the art; while this is indeed an attempt at a silly Valentine’s Day map, it is also an exercise in what has been my Cartographic Purpose lately. More and more what interests me is the idea of maps as drivers of activity in physical spaces, particularly as it relates to exploration and discovery in cities as well as personal construction of place and mental maps. My zombie and personal mapping posts touch on this—the map represents in its ordinary capacity the real world but in another capacity a fairly abstract, meaningless space that is acted upon in the real world. So I am driven toward or away from a place not because of what is actually there, but because in some virtual space it contains a zombie or because it is a blank spot on a map of lines or because it happens to be within a heart shape on a street map; and then I discover what is there. Some day when I collect my thoughts and do some more background research I’ll write more about this practice. For now suffice it to say that I am fascinated by this method of discovering and creating place.

For the actual report on this heart excursion you can check out my Bostonography blog post, as they are probably too Boston-specific to address in any detail here. Except this one. Yes sir, mister billboard!

(As long as I’m tying all this into older posts, remember that city boundaries are stupid. This liquor store is in a border zone and I am really not sure which city it’s in. Could easily find out, but now I refuse to.)

Light brown dot and badly drawn perspective aside, we were clearly going for a National Park Service look. So of course instead of anything like that we ended up with something else entirely.

Why this happened is beyond memory, but I kind of recall having something to do with benches and will take the blame. Believe, though, that we spent as much time on each of the zillion other features on the map, sometimes with better results. And this is how map design goes: endless scrutiny of every tiny detail.

Check out the map to enjoy some fine 2006 Flash cartography. The project was completed in the University of Wisconsin Cartography Lab that summer. A paper (PDF from the Cartographic Perspectives archives)by Robert Roth and Mark Harrower contains a couple more fun design materials from the process, as well as (primarily) some usability lessons learned.

You know when you’re two thousand miles from home and somebody asks where you’re from and you just name the nearby major city even though you actually live in an adjacent suburb, because who the hell would know where that suburb is? I wish we’d think of cities that way for real, not just occasionally out of convenience.

Let’s divorce the geographical notions of “city” and “place” from the legal definitions. I’m tired of people being so hung up on municipal boundaries when they think of their cities. Tired of imaginary lines on maps, having little or nothing to do with patterns of intraurban human settlement, separating “here” from “there.” Tired of people in my city thinking it functions in isolation from the larger city next door, and of people in that city thinking my city is just some other place, hardly different from a town 80 miles away. In your typical American urban area, instead of a great, proud city I see a bunch of heres and a bunch of theres, each one thinking it’s better than the others. Look at it from afar, or even from a hot air balloon. It’s one centralized urban place. One city. In my hippie dream America we’d know where the lines on the map are (let’s face it, they are of civic consequence) but wouldn’t live by them.

Interesting, then, is that these lines aren’t found in many of the maps we all frequently use now. Google Maps will show city names but not their extents. The new Stamen design of Bing Maps is even more wonderfully ambiguous. Here’s the map I see upon entry, showing where it thinks I am.

I see four levels of place labels, and not all of them correspond to municipal entities. One of the labels is even a place that contains parts of three different cities in three different counties. Most notable, though, is the large, semi-transparent “Boston” label, and I really like the overall impression it gives of the city. I live in Cambridge, which is labeled on the map and clearly is a real place, but its precise definition is unknown, and by the labels it seems to be a part of this greater city called Boston. And that’s just how one should think of the city from this distance.

Zoom in a couple of steps and you get a view that is almost officially ambiguous—the ghosted labels name neighborhoods that in my experience don’t have boundaries that any two people would agree upon. (Other cities have more certain neighborhood boundaries, but real neighborhoods are still hard to pin down.) Again the labels do more than allow for display of a hierarchy; they nicely depict the reality of fuzzy, uncertain extents of urban places. In a way, this map is more accurate than one with precise lines. (Bing does show county boundaries, though. Counties are stupid too.)

So here’s to Bing and others reshaping our urban geographical notions. Even if the vagueness is annoying when we wear our Practicing Cartographer hats and are looking for good reference maps.

On a closing note, an excellent attempt to move beyond political boundaries as geographical definitions is the CommonCensus project, which aims to map the spheres of influence of American cities (also sports teams). Have a look at the maps, and please do contribute your response to the survey questions!

I’m very weary of the hipster obsession with zombies by now. Cut it out, hipsters. So I felt shame the other night as my friend and I sprinted through the dark along treacherously uneven brick sidewalks, running from zombies and loving it.

Not real zombies, or even hipsters—we were responding to an awesome app for Android phones called Zombie, Run! It’s a location-based game of sorts that places a bunch of zombies between you and your destination on the map. When you’re near enough to a zombie, it begins to give chase. You must reach your destination without a zombie catching you and eating your brains. It’s lots of fun and can make mundane trips much more interesting, especially if you enjoy running around like a maniac in public.

But a game like this is also fascinating when you set down your can of High Life and put on your Geographer hat. It directs a kind of spatial behavior that technology more often stamps out in one way or another—wandering. While our gizmos usually tell us exactly where something is and how to get there, here is something that forces a person to stray from the direct path. Assuming the player keeps his eyes open and actually notices the world around him, the game provides an interesting way of experiencing and understanding urban spaces. By acting upon virtual landscape in the physical landscape, the player travels unpredicted paths and enters areas that might otherwise never have been seen.

It’s a little like an exercise in psychogeography, a field I can’t really claim to understand but a central activity of which seems to be the dérive, in essence a sense-driven wandering. But here instead of reacting to the sights and sounds and smells of the real urban landscape, a person is influenced by a random set of obstacles beyond anyone’s control. Such randomness may not lead to an especially deep understanding of the city, but its advantage is in ensuring wandering much more free of human biases—perhaps a better sampling of the landscape.

I have a hobby of going on long walks about town in order to check out areas I don’t know well (or at all) and often to capture a photo or three. Most of the time I end up plotting a general route beforehand to ensure that I hit a few key spots and maximize travel on routes I haven’t taken before. Invariably I second-guess myself after the fact. What did I miss by adhering to this route? What made me choose this route? What made me avoid other routes? So recently on what was only my second visit to South Boston, I let the zombies decide much of where I would walk, leaving me with perhaps not a representative impression of the place but certainly the feeling that I got a moderately more real, unbiased look at the neighborhood. Naturally it was an amusing mapping exercise too.

Here is my great Southie zombie adventure. From the point where I switched on the game (A) I had three destinations in sequence (B,C,D). Blue shows the direct route, and red is the GPS track of my actual route.

Apologies to any of you fine Southie people I hurriedly brushed past to escape a close call with zombies. Good thing none of you were angry Irish mobsters like in the movies.

Praise be to mobile technologies that promote discoveries of space and place instead of conveniently simplifying them.

Value-by-alpha maps (hereafter shortened to VBA), like everything noble and good, have their roots in somebody complaining about something on the internet—me, about election cartograms. Seeking an alternative to what I think are ugly and unreadable election results cartograms, I worked with my Axis Maps dudes to create a 2008 U.S. election map that used transparency rather than size to vary the visual impact of map units, thinking that avoiding the distortion of these units into unrecognizable sizes and shapes would make the map easier to read.

Rob Roth, a stellar Ph.D. candidate and shameless county collector at Penn State (studying under The Beard himself, the illustrious Alan MacEachren) became interested in further developing the idea academically and enlisted my Axis Maps partner and radical raw milk zealot Zach Johnson (who wrote his master’s thesis on cartograms) and I to collaborate on the now-published Cartographic Journal article. We were all graduate students at Madison together once upon a time, and we make a good team—striking a perfect balance between study, practice, and chili-eating.

Enough backstory. I’ll summarize at moderate length the idea and what we wrote.

WTF is a value-by-alpha map?

First things first: value-by-alpha is essentially a bivariate choropleth technique that “equalizes” a base map so that the visual weight of a map unit corresponds to some data value. Whereas cartograms accomplish this by varying size, VBA modifies the alpha channel (transparency, basically) of map units overlain on a neutral color background. Thus shapes and sizes are not distorted (except necessarily by the map projection, of course), but the lower-impact units with lower alpha values fade into the background and make for a map that is visually equalized by the data.

Solving Johnny’s Cube

To make a case for the limitations of cartograms, we point to Zach’s graduate work that compares several different types of cartogram designs. Zach developed a typology that describes cartograms in terms of three characteristics: shape preservation, topology preservation, and density equalization (basically a measure of how accurately the area corresponds to the data value; we’ve modified this to visual equalization to include more than just size variation). Depicted as a stylish and highly respectable cube, his typology reveals a back corner that is unattainable for cartograms, as none can be perfect in all three regards. Value-by-alpha, by leaving size and topology alone, allows us to nearly “solve” Johnson’s cube.

VBA works by wordplay

We must note that although creating VBA maps involves modification of transparency, the maps do not in the end symbolize via MacEachren’s visual variable transparency, which is more like a masking of one layer by another that is not aligned to it. Rather it’s two color variables, one of the late Jacques Bertin’s original graphic variables and a later addition—color value and saturation. In the end it is as though each map unit’s color was adjusted in value and saturation. “Value-by-alpha,” then, is an infinitely clever name (chosen by Rob) that refers to both numeric value (as in “value by area,” a term for cartograms) and color value.

Design considerations

On to the practical advice. There are basically three components to consider in the design of VBA maps: the modifying color, the equalizing variable, and the variable of interest.

The modifying color is the color that modifies the original unit color as its alpha value changes, i.e., basically the map’s background color. White or black are the only colors that make much sense here, as anything else will confuse hues and muddle the value and saturation too much. There is some difference in the way white and black affect value and saturation, but they both essentially map an overall “lightness” to the data (just in opposite directions). Black tends to make for a more striking map, I think.

The equalizing variable is the one that is symbolized by alpha and thus visually equalizes the map. First of all, this variable needs to be one of consequence to the variable of interest in order for the visual weighting and VBA altogether to make sense (e.g., counties with more voters are of more consequence to election results). With that out of the way, we recommend classifying the variable into five to seven classes. That number is pushing the limits of what can be visually distinguished, but we are suggesting some compromise for an improvement in aesthetics. To avoid units that are completely invisible, the lowest class shouldn’t have an alpha value of zero, but rather something in the 10–15% vicinity, from there stepping up to 100%. To assist with geographic context, we also suggest adding an outer boundary to the map units taken together.

The variable of interest is the variable being mapped with color and weighted by the equalizing variable. Because the alpha modifications introduce a lot of subtle variations in color, we advise a fairly limited number of data classes (unmodified colors) in this variable, specifically only two or three variants of each hue. For a sequential scheme that generally means two or three classes, and for a diverging scheme it means four to six. As always, ColorBrewer is the place to look for color schemes, a few of which are ideal for avoiding inherent lightness differences in hues that could upset the map’s intended visual hierarchy.

Below are some example color and alpha schemes, taken from ColorBrewer specs. Each is labeled with numbers that correspond to the intended visual hierarchy, where 1 should stand out the most, 2 the next highest in the hierarchy, and so on. Note that several colors may be meant to exist at the same level.

For the faint of heart

Cartograms are good for shock value. They’re an in-your-face radical perspective on a world you thought you knew, and they can really make a point. As a carto-curmudgeon, I remain meta-amazed by the amazement with which cartograms are received. We think that VBA can be a good choice when you want to show similar information but also want to be able to recognize what the hell you’re looking at. So when no shock is required, or it would hinder the intended map-use tasks, perhaps value-by-alpha can be your friend.

Limitations

Let’s be real—even I’m not convinced that VBA is broadly useful. We are proposing it and providing some theoretical support, but it is untested and carries important known limitations. It cannot be a universal replacement for cartograms, and we don’t want to imply that it is.

First, color value and saturation are not the most effective visual variables for encoding numerical data, certainly less so than size, which is what cartograms use. Furthermore they can’t as easily be tied to direct mathematical scaling as cartograms might. What all that means is that we can’t expect users of VBA maps to extract numerical estimations with much success, so the technique is best reserved for big-picture purposes, not precise comparisons.

Second, VBA is incapable of an important use of cartograms, which is to emphasize units that are small in area but thematically important, for example some of the European countries in the population cartogram below. VBA can only reduce the visual presence of a map unit, emphasizing the important ones only by diminishing the surroundings. Small geographic units may remain difficult to interpret.

Third, we can’t ignore varied unit sizes in a VBA map, just as in any choropleth map. Larger areal units carry a higher visual impact even if they are thematically less important, which is why some sort of standardization is generally encouraged on choropleth maps (e.g., mapping population per square mile instead of total population). Cartograms don’t have this problem, of course, because unit size represents thematic data, not geographic area. We didn’t really explore standardizing by area in VBA maps, but it may result in a more appropriately equalized map. However, standardization of the equalizing variable further hinders user estimation of data values in the map. For example in the election map equalized by population density below, it’s correctly visually equalized, but it’s not easy to compare one county’s impact to another’s because it requires calculating some combination of color and size.

Finally, there are display media issues that don’t exist with size variation in cartograms. The subtle variations in brightness and saturation in VBA are very difficult or impossible to hold constant in digital media. A map can look perfect on one screen and completely black on another. We got some feedback along those lines on the original election map. When you can’t control the display medium, a cartogram might be a better bet.

In action

Here I am obliged to point out that we’ve built value-by-alpha functionality into indiemapper, the Axis Maps web-based cartography application. Zach programmed most of that feature about an hour before my NACIS talk last fall. Otherwise, making a VBA map is simple: either programatically adjust alpha values of enumeration units or in a more graphical approach create layers for both the variable of interest and the equalizing variable, and use the latter to mask the former.

To close, it is worth providing an example of the value-by-alpha technique besides the election theme of everything posted so far. Below is a version of a map made by Rob Roth and Jin Chen at Penn State for some research they’re involved with. With a diverging color scheme it shows cervical cancer mortality rates by US county, above and below the national rate. Instead of using a VBA map to equalize by some variable of magnitude, this map uses it to display a measure of statistical reliability. A county’s alpha value corresponds to a score that indicates how reliably it lies in a cluster of elevated cervical cancer mortality, resulting in the spotlight effect on those important regions. Before I do more injustice to this work, check out the fully detailed poster (PDF) available on Rob’s ludicrously thorough online CV.

Paper citation

Roth RE, AW Woodruff, and ZF Johnson. 2010. Value-by-alpha Maps: An alternative technique to the cartogram. The Cartographic Journal. 47(2).

It is probably not permissible for me to post the paper online, but anybody who has read this far is probably an academic with access to the journal.

While preparing data for another spare time local interest map (forthcoming), I ran across a tiny bit of information (“Horsford’s Norse exploration theory”) that ended up captivating me for the weekend. It is the story of Norumbega, at various points a regional name applied to New England, a legendary city of riches, and thanks to a baking powder magnate, an 11th-century Viking city established by Leif Erikson in the modern-day Boston area.

Now, having been aware of this for no more than two days, and knowing little about historical cartography, I won’t claim any expertise or even to have all my facts straight, but let me summarize as best as I can.

In the 16th Century, not long after the European “discovery” of the Americas, Norumbega (with varied spellings and an uncertain etymology) began to appear on maps as the name for roughly what is now New England. It would come to refer to a region, a river, and a city, variously. As a city, it was apparently from the beginning legend—a place that was said to exist (no doubt along with other cities) but which had not been located. More than that, it came to be a downright mythical place, a city of endless riches—something like a northern El Dorado. The story of David Ingram, a shipwrecked English sailor who trekked all the way from the Gulf of Mexico to New England, made the rounds:

He saw kings decorated with rubies six inches long; and they were borne on chairs of silver and crystal, adorned with precious stones. He saw pearls as common as pebbles, and the natives were laden down by their ornaments of gold and silver. The city of Bega was three-quarters of a mile long and had many streets wider than those of London. Some houses had massive pillars of crystal and silver

Somehow Norumbega became associated more specifically with the Penobscot River in present-day Maine, with the city being around where Bangor is now. Samuel de Champlain explored the area in 1605, apparently looking for the city, but found no evidence of civilization. It seems that this quieted the myths of Norumbega’s fabulous wealth. But the name didn’t disappear and will still be encountered today in that area.

Many maps show the Norumbega region, and I can’t hope to do justice to that cartographic history, but Cornelius Wytfliet’s 1597 map, shown in detail at the top of this post and in full below (see a zoomable high-res version here) is a good example, and its Norumbega does bear some resemblance to the Penobscot River and Bangor.

Let’s fast-forward about 270 years to the dealings of high society in Boston, for the twist that makes Norumbega different from typical cartographic legend. In the 1870s a committee formed to back the erection of a statue of Leif Erikson, the famous Norse explorer. Proposing this was the renowned Norwegian violinist Ole Bull, with support from some others like the prominent American poet Henry Wadsworth Longfellow. Although proof would not be uncovered for another ninety years in Newfoundland, by this time the theory of Viking discovery of North America was somewhat popular. Furthermore some people had a notion that this Viking settlement had occurred in New England, i.e., that Vinland was or included New England. Gloria Polizzotti Greis of the Needham (Massachusetts) Historical Society explains why the idea of Norse discovery had traction with the Protestant elite of Boston:

So, Boston’s elite in their well-heeled gathering places, began to identify themselves with, of all people, Leif Eriksson. Why? Because of Christopher Columbus.

Columbus personified the growing political and social power of Boston’s Catholic immigrants. Even though the Irish and Italians maintained distinct communities themselves, to the old-line Protestant establishment they represented a significant threat to the status quo.

[...]

For the Protestant elite of Boston then, Leif Eriksson was the anti-Columbus. They saw him as fair and Nordic, where Columbus was Italian; Columbus brought (as they thought) superstition and slavery to the New World, Leif brought progress and commerce; if the possibility had existed in his day, Leif was the kind of man who would certainly have been, well – Protestant, like them.

Anyway, as time wore on, and as backers like Longfellow died, there emerged a Leif Erikson champion in Eben Horsford, a chemist and Science professor at Harvard. Horsford was best known for his formulation of baking powder but was also a strong proponent of the New England-as-Vinland theory in his spare time. Beyond that, he was convinced that the legendary Norumbega was actually Vinland. Using his baking powder fortune, he devoted much effort to uncovering evidence.

By 1890 or so, after a bit of digging near his home in Cambridge, Massachusetts, Horsford claimed to have found the site of Leif Erikson’s house at Gerry’s Landing on the Charles River near what is now Mt. Auburn Hospital (which is the last known site of my appendix, by the way). There he placed a plaque that remains today. Then he proclaimed that he had discovered a Viking settlement and the famous Norumbega itself farther west on the Charles River. He had a stone tower built to commemorate his first discoveries at the confluence of the Charles and Stony Brook in Weston, across from the soon-to-be-established Norumbega Park in Newton; the city of Norumbega was, as my opening quotation says, downstream at modern Watertown.

Leif, it seems, had hit Cape Cod and then entered Massachusetts Bay, sailing into Boston Harbor and up the Charles. The disastrously difficult-to-read map below (some shading to distinguish land from water, please!), from A guide-book to Norumbega, shows Leif’s route as the dashed line. In the upper left are indicated some of Horsford’s Norumbega sites. This book, written in 1893 by Elizabeth Shepard, directs visitors to Horsford’s supposed archaeological sites (even providing some directions via streetcar) while placing them within the context of the Icelandic sagas that tell of Vinland.

Another map shows the landing site of the Norsemen in present-day Cambridge. See also its location on a modern map.

Professor Horsford himself had of course published his discoveries, first briefly in The Discovery of the Ancient City of Norumbega and then with more detail in The Defences of Norumbega (among a number of works on the subject). Both of them include the Charles-as-Norumbega map below. I’m not entirely certain what the coastal shading indicates, but it seems to show the coastal area in Leif’s time. (Click the image to enlarge.)

Here’s a detail showing the sites—trenches, dams, etc.—along the Charles. Clicky for an expanded view. Three streets in western Cambridge—Norman, Norumbega, and Thingvalla Streets—commemorate Horsford’s theory and were laid out around the turn of the century at the Amphitheatre (one of the Norse sites) marked on this map just above the second W in Watertown.

The Leif Erikson statue was erected in 1887 and now stands (with a decidedly classical, non-barbaric appearance) as the westernmost of many statues lining Commonwealth Avenue in Boston. Although the Vinland theory that Horsford advocated enjoyed some popular support at the time, his claims have been dismissed for the lack of convincing evidence, not that he didn’t try to provide any. Nevertheless, in some local names and landmarks is preserved the idea that not only was legendary Norumbega a real place, it was a inhabited by people who sailed across the Atlantic some one thousand years ago.

Sources and further reading

• My two block quotes and much of the overview here comes from Gloria Greis’s fascinating article on the subject. It is probably the best source for learning this whole story.
• Professor Horsford’s report, available on Google Books, provides the opening quotation in this post and some additional information, but I only skimmed it and the subsequent Defences of Norumbega, instead trusting secondary sources like the one above.
• Elizabeth Shepard’s A guide-book to Norumbega and Vineland: or, The archæological treasures along Charles River is a nice summary and interesting approach to Horsford’s sites, and is also a fairly concise recap of how these mesh with the Icelandic sagas.
• The maps from Shepard’s and Horsford’s books are presented here as photographs, as you can tell. Those from the latter are poorly reproduced (if at all) in the digitized version on Goolge Books, so in both cases I consulted local libraries and brought a camera. Very few of the pages in Shepard’s book remain bound in the copy at the Boston Public Library, but at least they were all still present!
• Horsford’s address at the statue’s unveiling is also on Google Books. I’m not sure if it mentions his “discoveries” on the Charles, as it predates the other works, but I didn’t easily find references to it. It’s also dreadfully long, and I’m glad I wasn’t there to hear him.
• A second-hand account of Horsford’s work, and some cartographic history of Norumbega (though sans images), is provided by Rasmus B. Anderson in a chapter the 1906 book The Norsemen in America.
• I did little more than fan the pages of an edited volume called American Beginnings: Exploration, Culture, and Cartography in the Land of Norumbega, but it contains much more detailed history (cartographic and otherwise) of the region.
• Norumbega Reconsidered (PDF) is yet another work I didn’t really take time to read, but there is a section called “The Myths of Norumbega” that nicely summarizes the various things that Norumbega has meant.