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

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