What’s in a Name?

What’s in a name? What does it mean for a map to be titled a comparative? It’s been a while since I discussed the fundamentals of comparatives; this post reviews those but is by no means exhaustive.

I have developed a few criteria for comparative views. Comparative views must be: continuous depictions of geographic features, arranged by size (with a few exceptions), to show variation in size with an accurate scale, and usually have a human scale benchmark.

Possibly the first comparative view of the early style, showing mountains of the old and new worlds.(Own work)
Hohen der Alten by Bertuch, c1810. Possibly the first comparative view of the early style, showing mountains of the old and new worlds. (Own work)

A Brief History
Comparative views were inspired by Humboldt’s 1805 chart. Although it wasn’t a comparative, it planted the seed for visual display of altitude related data visually. Bertuch was the first to widely publish a comparative, c1810, in the form of a fictionalized landscape. This style gave way to the stylized graph format seen in most comparatives, often found in atlases. By the late 19th century comparative views had fallen out of favor.

Principal Mountains by Carey and Lea, 1832. This miniature map of mountains shows pyramids as a human scale benchmark.
Principal Mountains by Carey and Lea, 1832. This miniature map of mountains shows pyramids as a human scale benchmark. (Photo: own work)

Comparatives must give the illusion of looking at a scene or “view” of geographic features. The first comparatives did this by taking the form of a landscape. Later comparatives, those of the graph style, achieved this through abstract means where the peripheral attributes of one feature blended into another; mountains slightly overlapped to form a range and rivers drained into a common body of water. Without this unity among the features, the comparison would hardly exist as it would be district images, not inviting the reader to compare them.

Five panel lithograph mountains and rivers comparative view.
Five panel comparative chart of mountains and rivers by Johnson. Note the graph like style, where mountains are simple cones. c1855. (Photo: Own work)

Arrangement and Scale 
A comparative view is a device to highlight the large (usually, although as always, there are exceptions) mountains, rivers, etc., of the world. As such, they must be laid out so that the reader can readily identify the largest of the objects. Employing (usually) a sorting methodology achieves this. Sorting so as to create a gradient, largest to smallest or vice versa, is common. Pyramid sorting is common with mountains, placing the largest mountain in the middle and the smaller ones to the sides, alternating. Scaling objects on a similar basis is essential to allow readers to evaluate their relative sizes.

The Great Pyramids and Paris as shown on Thomson & Lizars' A Comparative View.
The Great Pyramids and Paris as shown on Thomson & Lizars’ A Comparative View. The Great Pyramids serve as a human scale benchmark. (Photo: own work)

Human Scale Benchmark
Heights of very large objects like mountains are hardly meaningful without something of a translation. That translation is achieved through a benchmark that is an intermediary. Many comparatives use the Great Pyramids of Giza as such an intermediary; albeit large, pyramids are still on the human scale to the extent that they were built by hand, people can easily walk around them, and they can be scaled. Despite being on a familiar scale, their size is substantial enough to be compared to mountains.

Check out some of the great resources from David Rumsey, Geographicus, and Hautdidier.

© Peter Roehrich, 2016


The Long River

Most rivers comparatives look like stylized column graphs, where the rivers are scaled down and function as columns indicating length. Column graphs certainly lend themselves nicely to comparing lengths of rivers and at the time comparative views were popular, column graphs were still new, having been developed a few decades earlier by William Playfair. While just about any rivers comparative view resembles a column graph, the well executed among them are faithful, albeit smaller and straightened, facsimiles of the the rivers, providing more than just length, but also falls, lakes, deltas, tributaries, and adjacent cities.

Image of Carey and Lea's 1832 Chief Rivers.
Chief Rivers by Carey and Lea, 1832. This miniature map of ‘chief’ rivers clearly shows tributaries, lakes, deltas, and cities. (Photo: own work)

Carey and Lea’s 1832 Chief Rivers does an excellent job of showing both rivers, but also the figurative and literal landscape through which they flow.

Photograph of comparative map by Carey and Lea showing Amazon and Mississippi Rivers
Amazon and Mississippi River detail from Chief Rivers by Carey and Lea, 1832, clearly showing tributaries, lakes, mountains, and cities. (Photo: own work)

They show the Amazon (watch out for piranhas!) stretching from the Atlantic Ocean across the continent of South America, through the Andes, tracing the Beni River and showing Lake Titicica (the highest navigable body of water, by the way, at over 12,000 feet of elevation), and passing no fewer than five cities. From this image, we can tell that it supports a lot of people, with the cities serving as a proxy for population. Further, we can tell from the many tributaries that it drains a large basin, and from the mountains approximately 2/3 of the way inland from the ocean that it has alpine headwaters. Looking at the Mississippi, its delta and New Orleans–the Crescent City–are clear as day. The map shows two forts on the Mississippi, each indicated by a small cross, including Ft Mandan, where Louis and Clark spent the winter of 1804-1805. The presence of these forts and the several towns shown, with their histories in mind, tell us that this river was important in the European settlement of North America.

The detail Carey and Lea provided in the cases of the Mississippi and Amazon, as well as in the other rivers shown, makes clear that they are chief rivers in addition to simply being long rivers. Certainly being a long river is a compelling argument for it being important, however Carey and Lea show several very small rivers. The Thames and Forth rivers are tiny in the shadow of the Nile, Amazon, and Mississippi, but Carey and Lea provide context; showing London and Edinburgh provides the detail to understand that these are important rivers as they support capital cities despite being relatively short. After looking at the Mississippi and Amazon rivers, it is clear that their importance is not just in their length but also because of their ecology, the populations they support, and the commerce they facilitate. All of this insight would be lost if they were mere lines on a chart.

© Peter Roehrich, 2016.

Rivers of the Bible

The rivers of the bible may bring to mind Noah hidden among bulrushes, but that’s not where they end. The Countries of Exile with Mountains and Rivers of the Bible by Hardesty, 1883, shows 11 biblical rivers in a small panel below another comparative panel of biblical mountains. This is the companion panel to the mountains piece that shares the same page.

Comparative view of the mountains and rivers of the bible. Own work.
The Countries of Exile with Mountains and Rivers of the Bible by Hardesty, 1883. Note the inconsistent scales used. Own work.

As comparatives go, it’s unusual. Where comparatives typically (everywhere except perhaps this example) concern themselves with ‘principal’ features (I find that usually means largest, although that is up in the air with some comparatives), this comparative shows features described in the bible. Further making this view unique are the inconsistent scales used. A uniform scale is critical to a comparative in that without one, the ability to visually ascertain the relative size of a feature is lost.

To perform a scale analysis I measured lengths of the rivers as drawn and plotted that against their stated lengths, with each river shown as a dot. If the comparative had a uniform scale, the plotted points would fall on a line.

Plot of river lengths as drawn and stated to determine uniformity of scale.
Scale analysis of rivers from The Countries of Exile with Mountains and Rivers of the Bible by Hardesty, 1883. Note the non-linear arrangement of points. Own work.

The scale plot generated in the analysis is not a flat line. Instead, it’s more of a curve, climbing steeply on the left hand side of the plot, then becoming shallower.

Scale analysis of rivers from The Countries of Exile with Mountains and Rivers of the Bible by Hardesty, 1883. The rivers sorted into two groups. Own work.
Scale analysis of rivers from The Countries of Exile with Mountains and Rivers of the Bible by Hardesty, 1883. The rivers sorted into two groups. Own work.

I split the longer rivers (Nile, Tigris, and Euphrates) which fell on the right hand ‘spur’ of the graph into a separate group and replotted them so that I could fit lines to each group individually. The result: within groups, the rivers scale consistently.

This finding points to the possibility that the author intended for this piece to be a visual tool for showing the lengths of the rivers, but for practical reasons could not do so in a way that would adequately address all 11 rivers. Quite simply, to show a 3,700 mile and a 19 mile river on the same chart would require either a chart so large as to be unwieldy or a chart that condenses the smaller features so much that it lacks resolution. The author no doubt wanted for the reader to see the differences in river lengths, but lacked (or chose not to devote) page space to show it, instead hoping that the reader would figure it out.

 © Peter Roehrich, 2016

Scaling Rivers

In previous posts I have discussed the scaling of waterfalls and Johnson’s scaling of mountains in his 5 panel comparative. This post revisits that comparative to examine the scaling of the rivers.

Comparative Heights of Mountains and Lengths of Rivers (Johnson from David Rumsey).

This is an innovative comparative in that it follows the Mountains and Rivers approach pioneered earlier in the century, but splits the features out by continent. This allows the reader to see the range in heights of the peaks within each continent. The same is true of the rivers aspect; the rivers are first grouped by continent, then sorted by length. Breaking the view into panels allows him to show more features and begets ready comparison within the continental grouping.

This approach carries with it a major hazard, however: the increase in resolution and organizational capabilities of this display, because it doesn’t maintain a constant scale across the panels, comes at the cost of distorted heights and lengths between continents. Where mapping is a discipline of tradeoffs, the impact of this is dependant on the purpose of this comparative.

We can envision several candidate reasons Johnson included this comparative in his atlas. The first, and most simple is to document the sizes of mountains and rivers around the world visually. The second, which piggybacks on the first, is to display the size statistics but to animate them with drawings. We can compound both of these objectives by considering whether he wanted to show the diversity within continents or across them.

In the case of the second reason, to show otherwise dry statistics in a more intuitive display, the distortion between panels is less important because the image is merely a scaffold to support the numerical height or length description. Whether he hoped the reader would compare within or across continents we’ll examine further down.

As to the first proposed reason, to visually display the heights/lengths, with the statistics playing second fiddle, the distortion is much more important, and distorted they are!

River exaggeration between panels on Johnson's comparative (own work).

In Johnson’s comparative view the longest rivers of each continent (which I am terming “index” rivers) are all shown to be about the same length, within about 10% or so, while their stated lengths vary by as much as about 90%. When their differing scales are compared, the Volga, the smallest of the index rivers, is overstated by 70%.

If his motivation was to show variation within the rivers of each continent, this scale distortion is confusing but necessary as magnifying the shorter Volga makes it easier to perceive its size vis-a-vis the other European rivers. On the other hand, if his purpose was to show the differences in lengths across the continents, this is a disservice to his readers at best, if not downright dishonest.

But would he intend his readers to compare the rivers’ lengths across continents? Probably not. The first evidence for this is that each continent’s rivers are compartmentalized to distinct panels. The second piece of evidence to this end is the alternating sort direction: longest to shortest in the first panel, shortest to longest in the second, and so on. Because the rivers are stacked and alternating, the evaluation of the index rivers between panels is difficult, versus the side by side presentation of most mountains and rivers charts (which he’d previously published). Johnson without doubt knew this layout would make intercontinental comparison difficult and would not have chosen it had he wished for the reader to draw such comparisons. As for whether he sought to intentionally mislead the reader, it’s an intriguing proposition, and we may never know for sure, but we can easily dispute it as both not parsimonious and, as someone who relied on his reputation as a reliable authority on geography, playing with fire.

© Peter Roehrich, 2015

Comparatives with Balloons

Comparatives often feature objects that were well known to their readers to give a sense of scale. This is especially true of mountains comparatives. Showing a large man-made object on the comparative serves as an intermediary between the human scale and the geologic scale. Pyramids, monuments, and cathedrals often play this role.

The Great Pyramids and Paris as shown on Thomson & Lizars' A Comparative View.
The Great Pyramids and Paris as shown on Thomson & Lizars’ A Comparative View.

Where structures aid readers in understanding how large something is, they do not tell the reader what it’s like to be at that altitude. Cities of various elevations are also commonplace on mountains comparatives, giving the reader points of reference–understanding the climate, vegetation, animal husbandry, etc. at an altitude is achieved by studying one of the case cities.

That said, the natural features can reciprocally serve as points of reference for human accomplishments. Nowhere is this more apparent that in depictions of high altitude balloon flights.

Gay-Lussac's 1804 balloon flight as shown on Thomson and Lizars' A Comparative View.
Gay-Lussac’s 1804 balloon flight as shown on Thomson and Lizars’ A Comparative View. Own work.

In 1804, Frenchman Gay-Lussac flew a hydrogen balloon to 23,000 feet setting a record that would stand for nearly 50 years. This is no small accomplishment as the first balloon flight had been only 20 or so years before. To show humans aloft, above the birds, would drive home the capabilities of technology. In reviewing the comparatives in David Rumsey’s collection, 16 show balloon flights. While all are spectacular, a couple stand out.

Smith’s 1816 Comparative View of the Heights of the Principal Mountains of the World is the oldest comparative among the holdings and shows Gay-Lussac in his balloon about to break through the border of the image. Its appearance on such an early comparative tells us that the cartographer intended for the concept of the comparative to be reciprocal. The comparative writ large was both to inform the reader about nature’s massive scale, but also to emphasize that having entered the age of science, man could literally soar above it. If the first appearance of a balloon flight were on a later comparative, say of the mid 19th century, we would be forced rather to conclude that it had simply been added to distinguish one cartographer’s product, rather than being able to conclude something fundamental about comparatives.

We continue to see Gay-Lussac’s balloon on comparatives through the first half of the 1800s. By 1851 the Industrial Revolution was in full swing and it was time for the Great Exhibition in London, a World’s Fair to highlight, among other things, technology. For this, the publisher Tallis prepared a book of engravings, mostly maps, that included truly stunning comparatives for both hemispheres. Not wanting to fall short on depictions of achievements, Tallis included Green’s 1840 record setting flight, showing it centered over Dhawalagiri (now Dhaulagiri) in Nepal. It is noteworthy that while his comparative is up to date vis-a-vis Green’s balloon flight, he neglected to show Kangchenjunga, even taller, surveyed in 1838. Perhaps he didn’t have access to that information. Perhaps he elected not to show it so that Green in his balloon would appear on top of the world, sure to delight the exhibit goers.

Tallis' gorgeous 1851 comparative view of waterfalls, islands, lakes, mountains, and rivers of the Eastern Hemisphere. (Photo credit: Ruderman).
Tallis’ gorgeous 1851 comparative view of waterfalls, islands, lakes, mountains, and rivers of the Eastern Hemisphere. Note Green’s & Gay-Lussac’s balloon flights over the mountains. (Photo credit: Ruderman).

The last example I will mention is an enigma. While the examined comparatives so Gay-Lussac’s balloon reaching differing altitudes, most if they specify, either 22,900 feet or 23,100 feet which brackets the 23,018 feet computed from the French accounts of 7,016 m, Weiland’s comparative isn’t even close. He pegs the altitude attained at 21,386 ft. Adding to the mystery, where this comparative has grouped the peaks by continent, he chose to show the balloon over Quito, Ecuador, nowhere near Paris. What could this discrepancy be attributed to? It hardly seems likely that he made a conversion error from meters to feet; as a cartographer he would no doubt be adept at this. As other cartographers of the day accurately stated Gay-Lussac’s altitude, and 16 years had elapsed, it further is difficult to believe that the correct information was not available. We can turn attention to whether this is due to any differing definitions of foot; he stated other heights in feet that approximate modern measurements, but are not exact.

Weiland's comparative. Note Gay-Lussac's balloon on the far left of the upper panel (shown as though it was flown over South America).
Weiland’s comparative. Note Gay-Lussac’s balloon on the far left of the upper panel (shown as though it was flown over South America).

There may be some traction here, as the German states used differing definitions of the foot. This can be tested by plotting the heights reported on Weiland’s view against those used on another, and Thomson’s 1817 is an ideal benchmark. If the plotted points form a cloud, then the difference between the measurements shown on the charts cannot be attributed to some difference in the definition of foot. On the other hand, if the points form a line we can infer that there is a difference in factors is at work. A selection of points in common to both comparatives was plotted and the relationship qualified. They fell nicely on a line.

Plot of the Heights shown by Thomson & Weiland.
Plot of the Heights shown by Thomson & Weiland.

Hard to believe this could be the result of chance; the relationship has incredibly strong statistical significance at less than one in a trillion. (Statistical significance is a measure of how confident one can be that the finding isn’t due to chance; less than a 1 in 20 likelihood of a chance occurrence is the gold standard in scientific research.) Moreover, the slope of the line explains 99.9% of Weiland’s number. The slope of the line is 0.924, meaning that Weiland’s foot was slightly different than that used by the other cartographers. This equates roughly to the foot used in Geneva at the time, 325 mm. It is interesting and surprising, however, that he would use the Geneva for as Weimar, the place of publication, was using its own foot, 282 mm.

© Peter Roehrich, 2015

And So It Began

Previously I credited Humboldt with kicking off the discipline of the comparative. This is true, but the first cartographers to run with the idea were Thomson and Lizars.

Thomson and Lizars A Comparative View. Published in 1817, is among the first of the comparatives. A lovely mountainscape. Photo credit: Ruderman
Thomson and Lizars A Comparative View. Published in 1817, is the first of the comparatives. A lovely mountainscape. Photo credit: Ruderman.

Their A Comparative View of the Heights of the Principal Mountains and Other Elevations in the World is just that: a gorgeous view of a mountain landscape. I use view in this context to mean a picturesque scene (think Hudson River School) rather than the more ‘technical‘ presentation that emerged later.

That all the features to be compared are shown in a single panel is important. Whereas these were western cartographers, the European mountain ranges are diminutive compared to those of Asia. In subsequent comparatives the mountains of each of the eastern and western hemispheres are shown in separate panels, even separate pages, and in the technical presentation; some of the later comparatives even show them in distinct panels by continent. Grouping the peaks in a single view invites intercontinental comparison that separate panels or pages discourage. Moreover, a single view prevents the cartographer from using differing scales that might ‘puff up’ the appearance of the European or New World ranges. This is again treated here, as well. In this sense, while it is completely false to show the world’s major peaks (save those, like Everest, which hadn’t been measured) within thousands of feet of each other, use of a uniform scale allows Thomson and Lizars to stake a claim to one of the most accurate comparatives.

Thomson and Lizars also establish the standard among comparatives of including man’s accomplishments as points of reference in addition to those of the natural world. The first feat of man, in the chronological order in which they occurred, to be shown in this view are cities themselves. Uruk, one of the earliest cities, was formed about 4500 BCE. The capacity to build cities being one of the defining criteria of a civilization, that these are shown is both a statement that man is different from the rest of the natural world, and that we are able to conquer the extreme elements of life at altitude.

The Great Pyramids and Paris as shown on Thomson & Lizars' A Comparative View.
The Great Pyramids and Paris as shown on Thomson & Lizars’ A Comparative View. Own work.

The Great Pyramids follow as the next landmark, in both geographic and engineering senses. They show a mastery of tools and materials, written language, burial of the dead, and religion. All traits that separate humans from other animals (or are perceived to separate us, as evidence has emerged that other species use tools and bury their dead).

Humboldt’s South American expedition is the next accomplishment featured. In 1799 he set off from Spain on a 5 year exploration of Latin America. A scientist, his travels generated much knowledge, and his presentation of his geological and biological findings in Geography of Plants set the stage for this comparative, where he is shown climbing Chimborazo, the subject of the aforementioned. Humboldt’s ascent is evidence of the recent shift to a scientific mindset during the Enlightenment. In this way, man conquered his own naivety.

Humboldt's ascent of Chimborazo as shown on Thomson & Lizars' A Comparative View. Own work.
Humboldt’s ascent of Chimborazo as shown on Thomson & Lizars’ A Comparative View. Own work.

Gay-Lussac’s historic balloon flight of 1804 is recognized at the center of the view, and as higher than the flight of the condor. I won’t say more about this, other than it’s remarkable that he pulled it off, as I will cover it in a subsequent post.

Gay-Lussac's 1804 balloon flight as shown on Thomson and Lizars' A Comparative View.
Gay-Lussac’s 1804 balloon flight as shown on Thomson and Lizars’ A Comparative View. Own work.

Thomson and Lizars’ comparative is a masterpiece both for its beauty, accuracy, and the arguments about human accomplishments it presents.

©Peter Roehrich, 2015

Interpreting Mountains’ Scaling

In a previous post I examined the scale of waterfalls and in yet another post I discussed Johnson’s mountains and rivers comparative. This post draws on both.

The importance of scale is a matter of a map’s purpose. Scale is incredibly important in a plan (plat), where each line must be represented on equal scale so as to ensure accurate delineation of land ownership (think Mason-Dixon Line),

Plan of Mason-Dixon Line, 1768 (Library of Congress).
Plan of Mason-Dixon Line, 1768 (Library of Congress). In such a map, an inaccuracy in location of a line could have substantial legal and political consequences, even military in the case of the Civil War. (Library of Congress).

but less important on a subway (topological) map, where the rider is concerned with the order of the stops more so than the distance between stops (WMATA Map).In the context of a comparative, scale is critical–the whole point of the view is to demonstrate the relative size of geographic features.

With this in mind, Johnson’s choices in scaling are noteworthy.

Comparative Heights of Mountains and Lengths of Rivers
Comparative Heights of Mountains and Lengths of Rivers (Johnson from David Rumsey).

Johnson composed his comparative of 5 panels, one for each of Africa, Asia, Europe, North America, and South America. As an aside, while it’s obvious why Antarctic mountains were omitted, it’s curious that Australian mountains were excluded given that it is one of the 6 inhabited continents, and the largest of the British possessions. The compounding of 5 panels is a logical means of grouping the mountains, facilitating showing more mountains than would be manageable in a single panel. That he chose to use different scales for each panel grabs my attention; by modern data visualization standards it is a mistake at best, if not dishonest, giving the casual reader the impression that the highest peaks of each continent are of about the same altitudes.

Johnson comparative scale analysis.
Scale analysis of the heights of mountains in Johnson’s comparative. Note Everest, second from left, is the index at 1. Mt. Blanc is the most exaggerated at 1.7x, followed by St. Alias at 1.6x (values rounded to one decimal). (Own work).

At issue here is that this choice erodes the comparison between mountains of different continents. One has to wonder whether this was purely an oversight, intentional but innocent for purposes symmetry, or to mislead the reader. The first possibility is self explanatory, requiring no further treatment. On the other hand, the remaining possibilities have the same effect, to confuse the readers’ perceptions of mountain height, but have drastically different implications. An aesthetically motivated scaling decision is questionable–a visualization expert, Johnson no doubt knew that scaling the panels differently would cause readers (those who do not read the heights of mountains) to misperceive the height differences across continents. The plausibility of this explanation hinges on the purpose of the comparative. If it is to show that the heights of mountains vary within continents without regard to intercontinental variance, then perhaps the scaling decision is more likely (and more excusable), but if the purpose is to show the might of mountains across the continents, it is dubious. To that end, if showing the spread in heights across the continents, the map falls short, unless of course, Johnson’s intent was to bamboozle the reader into believing that the mountains of the industrialized world rivaled those of Asia. Whether this was his goal, we do not know.

© Peter Roehrich, 2015.