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.

And so it was nice to run across this map of every building footprint in Montgomery County (Dayton), Ohio while idly browsing the “Maps” folder on my computer. I cranked it out from GIS data some six years ago. Give it a click for a large version.

Granted this map is more interesting if you know the area, but nonetheless it’s fascinating how much something like this can indicate about the patterns of human settlement in a typical American city. It’s not too difficult to see where settlement has followed or been bounded by highways and rivers. Industrial areas are discernible from residential areas, and city from suburb from rural. (By the way, this map only shows a sliver of Greene County—including my hometown of Beavercreek—where a good chunk of additional suburbia is located.) Owing to its simplicity, I believe this map shows urban patterns much more clearly than a satellite image or a road map.

If you’re familiar with the Dayton area, check out the patterns that probably confirm what you already know. See how to the north, settlement extends in spokes between the Mad, Stillwater, and Miami Rivers. Notice how immediately south of west Dayton, there’s hardly anything on the west side of the river. And look at the difference in suburban density on the west and east sides of Far Hills Avenue through Oakwood and Kettering.

If you’re not familiar with the Dayton area, the wonderful thing is that despite being nothing more than polygons, this map can probably teach you a bit about it.

Remember, the sweetest sentiment today and forever is:

The same goes for Terra Australis, but it is customary to retain an “Antarctica” label as a joke.

Seen at Franklin Park Conservatory, Columbus, Ohio.

I’ve recently returned from Sacramento after attending the 2009 conference of the North American Cartographic Information Society (NACIS), and I wish to briefly plug the organization here in case either of my readers is not already familiar with it.

If you work with maps, you should join NACIS and go to its meetings. Consider these facts:

• NACIS represents all sorts of cartography, and you will see some amazing maps and learn about lots of work that’s going on in the field.
• NACIS comprises all sorts of cartographers, and you will meet some all-around fantastic people and make useful contacts.
• NACIS offers some incentives for students, including several map awards and I believe one or two travel awards.
• NACIS not only accepts, but embraces and encourages your drinking habit.
• NACIS is a darn good time.

Except that an outbreak of swine flu among my friends apparently occurred, I had a blast this year and greatly enjoyed shaking many hands and talking (with varying coherence) to many people whom I hope to call friends and whom I very much look forward to seeing again next year or sooner.

Some quick highlights:

• Stamen Design’s Michal Migurski was the keynote speaker. I was thrilled to meet and chat a bit with Mike, whom I admire to a point just shy of having posters of him on my walls. He’s posted his talk on his site, so check it out. It was very good to see someone like him and a topic like his invited to NACIS, as I think the organization has hitherto been lacking in representatives of some important new trends in cartography.
• Natural Earth Vector was unveiled here by Nathaniel Vaughn Kelso and Tom Patterson. This project is, quite simply, a godsend to cartographers. It’s a big collection of geographic reference vector data designed by cartographers for cartographers (i.e., designed to look good at various scales). Keep an eye out; it’s due to be released soon.
• Cartographic Perspectives, the NACIS journal, was introduced in a new digital, open-access format. You can download the special issue (PDF). Also see the CP page on the NACIS site, where you can access archived issues.
• Another face that was good to see at a NACIS conference: a representative from Google! Andy Szybalski, the designer of Street View, spoke about the powers and limitations of combining immersive views with maps, and gave us a look at the evolution of Street View’s design. All told he seemed to be a hit with everyone and was a pleasure to meet.
• Of course I’m going to promote my own work here. We gentlemen proprietors of Axis Maps showed off indiemapper for the first time, and are getting ever closer to being able to launch this awesomeness. I’ll let the website do the advertising, but if anyone who was present at NACIS should happen by here and didn’t already give us an earful (or, um, suspects that the Axis end of the conversation may not have recalled it the next morning), we welcome your feedback! Hit me or anybody else at Axis Maps.
• There was a bathtub full of beer.

And there were many other excellent people to meet and things to see and hear, too numerous to list. So get in on this! Next year, St. Petersburg, Florida!

A note on the post title: somebody (I don’t remember who) characterized the group this way in the past, so it’s not just me saying it, although we who came up through UW-Madison have tried to be the standard-bearers.

Apparently we’re allowed to just put warning labels on our maps instead of trying to make them, you know, accurate. Either that or this sphere has particularly sharp corners and is not safe for a classroom full of children.

Remember, bad maps kill! Cartographers, always protect yourselves with warning stickers! It’s not our fault if someone decides to use our maps!

There’s a lot of information on the internet, if you haven’t noticed. Far too much for any mere human to wade through. And that’s why we find simple beauty in Google. Instead of overwhelming us with links and content, its home page provides a single search field. “Remain calm,” it says in a soothing but vaguely sinister voice, “just tell us what you’re looking for and we’ll bring it to you.” But God help you if you don’t know what you’re looking for.

Okay, it’s not that bad. Research and debate about searching versus browsing behaviors have played out over centuries (assuming that measurement of time in this information age is something akin to dog years), and it seems safe to say that most of the time information can be accessed by either means. Back in the wild days of the 1990s, web usability guru Jakob Nielsen found that “half of all users are search-dominant, about a fifth of the users are link-dominant [browsing], and the rest exhibit mixed behavior” and argued that “[d]espite the primacy of search, webdesign still needs to grounded in a strong sense of structure and navigation support” for the sake of not only those link-dominant users but everyone else too (link). Most of the web seems to adhere to that principle, but it’s a search-based world out there.

And I kind of hate it.

Sure, it’s obviously crucial to be able to search for what I’m looking for, but I’m not always looking for anything in particular. I want to explore or, to frame it (perhaps more accurately) in terms of mental lethargy, to avoid having to think of something to look for. It’s like Christmas shopping for all my relatives: as torturous as it already is, if I weren’t able to browse store shelves and instead had to think of specific gifts to ask the shopkeeper for, I’d probably collapse and bust into tears. (I titled this post after Steve Krug’s wonderful “common sense” book on web usability Don’t Make Me Think, not that I’m quite what he was talking about.) It bugs the hell out of me whenever I go to check out the newest Coolest Web Tool or Visualization Ever, only to find that I must think of something to search for in order to see it in action.

So it goes especially with maps. Obviously I speak from the perspective of a hardcore map nerd, but for me a map is something to experience and explore, not simply a canvas on which facts are presented. In any cartography work I’ve been a part of, we have tried to ensure that information can be attained either directly by search or by browsing the map. Consider the University of Wisconsin-Madison campus map, for instance. The same information is visible via both the search box and clicking things on the map.

That’s great for single-purpose, limited-scope maps where all the data can pretty easily be organized within view. What about maps that contain massive amounts of data of every conceivable sort, such as Google Maps? These maps justifiably revolve around searching. But ideally they’d be able to answer not only the question “where is X?” but also “what is here?”.

The easy solution is of course to just list every data point within certain location bounds, either the current map view or a specific chosen area. I find Yelp to be a good example of a site that has a lot of data and offers a way to browse it all via map. I can click on my local neighborhood and thumb through all 1175 businesses therein, filtering as desired.

Google et al. offer some similar capabilities, suggesting some categories of data to explore within the extent of the map you’re looking at, particularly user-generated content. Google has its photo, video, and Wikipedia layers. Microsoft provides categories in its sidebar and lets you explore user “collections.”

Those options are useful, but they still don’t allow you to get at everything. They’re using the normal top-down browsing approach in which results are refined by category; in this case location is like another category. What I think would be an interesting addition is a bottom-up approach, where all available data are presented, but only within very short range of a specified point. Google has a start at this. After searching for an address, a list of businesses at that address is provided.

This kind of thing is a pretty useful way of exploring a place, I think. Say you were thinking of moving into an apartment and wanted to find out what’s on the same block. You could zoom in very close and tirelessly search for every category you can think of, but wouldn’t it be great to be able to just click once and be shown everything that’s on the block? I’d bet that in most cases the amount of information returned for such an extent would be manageable.

There are a couple of ways in which the Google Maps browsing approach would be improved in my eyes. First, don’t make me search! It would be helpful to be able to click the map and find out what I clicked on. In addition to Google’s current right-click menu (“Directions to here”? Where the F is “here”?)…

…simply do a reverse geocode on the click location and give me the street address if possible. (As one who often uses Google Maps just for reference, this would be immensely useful in general.) Clicking on that would be the same as having searched for the address, as in the screenshot before last.

Second, in addition to the “All businesses at this address” link that appears in the results for a specific address, a “Businesses near this address” link would allow the user to explore beyond the single point while limiting the volume of data to a reasonable level, assuming a small enough radius like one city block. Obviously the amount of data depends on the density of the place, but I’d guess that most of the time it wouldn’t be overwhelming if it were grouped by address.

In my master’s thesis work, one way of describing online map reading was a continuum from map as tool to map as answer, where on one end the user interacts with and explores the map to eventually arrive at some end goal, and on the other end the user asks the map a question and is given the answer. The major online map services lean toward map as answer. But me, well, as people are always telling me, I’m a total tool.

Lynch made use of many sketches and diagrams in the margins of the book. These are small, about an inch or less, and appear beside the section of text with which they are associated. They don’t break up the text, and the text doesn’t even include any references to them; they’re just right there next to the words you’re reading. Above, for example, are the paragraphs defining paths, edges, districts, and nodes, which along with landmarks (next page) are Lynch’s elements of the city image. Next to each paragraph is a little illustration of the concept described within. I really like this idea. Naturally, most interesting to me are the occasions where the margin diagrams are actually maps of real places.

Boston

Jersey City

Tiny, non-intrusive supplemental maps bring to mind the Tufte-championed sparklines, hence the post title. (I don’t care if “spark map” refers to something else; I make my own rules around here.) Most maps, unless they are linear and horizontal, are substantially more difficult to insert directly into text than is the archetypical sparkline, of course, but I think the spirit is at least similar. As a sparkline provides at a glance a reasonably clear picture of numerical data, so can a small map provide context and clarify otherwise confusing or vague text. For example, in the image below Lynch mentions Boston Common’s “peculiar shape, difficult to remember: a five-sided, right-angled figure.” Peculiar and difficult? What better way to give that sentence meaning than to include a little sketch map right beside the text, toward which your eyes will be moving anyway?

(By the way, he was talking about the shape being confusing to residents. If there is one American city whose description can be aided by small supplemental maps, it’s Boston. Then again, you’d think that in a city where a “square” bears no resemblance to that shape, the residents would have developed an understanding of irregular polygons with more than four sides.)

The interactive interweb equivalent, it would seem, might be some map—Google or what have you—embedded in a small pop-up revealed on mouse over of the text. I’m sure I’ve seen something like this, but handy examples escape me at the moment. This suggestion, however, can surely be much less effective than the old-fashioned marginalia approach, because any automated map is likely to contain too much detail for the purpose and because the effort of interaction can easily break the narrative just as well as a big image that breaks up the text. Other interactive suggestions and examples are welcome, but as far as I’m concerned these little maps in the margins are as good an idea on the web as they are in books.

We’ve once again arrived at that special time of (every fourth) year when the internet abounds with maps, charts, and other graphics attempting to depict and analyze every geographic and demographic angle of the US presidential election. I am happy for these, both in the perspectives they provide on the election and in the demonstration of interesting visualization methods.

But as a cartographer in the eternal quest for the Perfect Map, I find myself complaining about some map and graphics. In particular, I take exception to this:

For anyone who doesn’t know, the above is a cartogram (’bout time I wrote about that which my site is named after!) of the United States, in this case a map by Michael Gastner, Cosma Shalizi, and Mark Newman showing the results of the 2004 presidential election by county (we’ll soon be seeing one for 2008). A cartogram is a map that does not strive for geographic accuracy, but rather in which the area of units actually represents some value. In the election map, each county’s size represents its number of voters. The point of the map is to show that while a geographic red-blue election map would show an apparent vastness of Republican votes, those “red” areas actually account for about the same number of votes as the tiny “blue” areas. (The message is further conveyed by coloring counties along a red-blue continuum to show the actual balance of votes rather than simply coloring by the winner, something first seen in Robert Vanderbei’s election maps.)

I’ve written several drafts of many paragraphs to try to explain my opinion, but really, who has time to read all my ranting? Short version: apologies to Drs. Gastner and Newman, but as a cartographer interested in clear and effective design, I really believe that cartograms generated from their method are severely over-hyped and far more popular than they should be. Consider the election map (or any number of examples)…

• Ugly! All that puckering and bloating… I wouldn’t want to share an elevator with that America.
• Topology preservation at the expense of shape: even if I know what a county looks like on a normal map, I’m going to have a hard time identifying it here.
• On shape, still: curvy shape distortions are harder to recognize than simplified polygonal shapes.
• The overall distortions leave me gleaning only about five things from this map: east, west, Florida, Michigan, and that there is roughly the same amount of blue as red. Yes, I know that last one is the whole point, but if I can barely discern the geography, why bother to use a map? There are lots of cool visualization works that deserve attention too.
• Fast and easy cartograms (including this particular map) are not useless, and the work by Gastner and Newman is an important contribution, but there are under-appreciated careful designs out there. Consider the excellent cartograms from Mapping Worlds:

The bottom line is that many—perhaps even most—cartograms are essentially used for shock value, for the “holy crap, that’s a different perspective!” response, which is exactly what they get. Too frequently they can’t stand as maps on their own. I think the election cartogram is only of use when it’s next to an undistorted map. The best maps and graphics are those that tell their story clearly and elegantly, not those that simply evoke an emotional response. There are a million good reasons why I’m wrong to complain, but rather than going on and on in an attempt to counter them I will simply acknowledge that they exist and expound later if necessary.

“Put your money where your mouth is, jackass!”
Oh, actually that’s a pretty important reason I’m wrong to complain. Okay, I promise I will attempt to come up an alternative visualization of the same information as that election cartogram, as soon as I figure out where people find such detailed election data so quickly. (And, as I stressed “careful design,” it’s not going to be instant.) I’ll also keep an eye out in the coming days for maps and graphics that I think are more effective.

Having deleted most of what I previously wrote for this post, I wasn’t left with a good place to bring it up, but I must, as I seem to do in nearly every alternate post, refer to the work of my mortal enemy Zachary Johnson, who wrote his master’s thesis on cartogram designs in political maps. (He should be writing about this stuff. Maybe someday he’ll at least finally write about his findings. Eh, Joncy?) At the University of Wisconsin-Madison, specifically in room 412 Science Hall, we did not take cartographic research seriously if it could not be depicted by a cube. As such, Zach defined a cartogram typology (Cartogram³) by three characteristics: shape preservation, topology preservation (the preservation of boundaries and connectivity), and density equalization (essentially, how accurately area corresponds to value). No cartogram can be perfect in all three, and in fact most compromise all three to some degree. Zach tested several designs, each making different sacrifices, in political map-reading tasks. Note that I have bitched about shape preservation versus topology preservation. His research backs me up in some respects, but not in others. But I’m not in academia anymore; I don’t need “research” to know that I’m right!