EdwardTufte / The March to Moscow

The March to Moscow

March to Moscow
Click on the image to see a larger version.

According to Mr. Tufte, this “may well be the best statistical graph ever drawn.” Drawn by a French engineer, Charles Joseph Minard, in 1869, this graphic depicts the fate of Napoleon’s army in its ill-fated Russian campaign during the winter of 1812-1813. The tan-colored band represents the march toward Moscow (i.e., time moves from left to right, or in an easterly direction) and the black-colored band represents the retreat back toward France (i.e., time moves from right to left, or in a westerly direction). The bottom section of the chart is a graphic representing the temperature during the retreat phase of the campaign. The width of the band, as detailed by Minard in the text at the top of the graphic, represents the number of soldiers in the army at any geographical (or timeline) point along the campaign: 1mm (on the original graphic) representing 10,000 soldiers. Also depicted are the movements of auxilliary troops which protected the rear and flank of the advancing army. One can clearly see (on the larger version of the above image) the catastrophic result of the crossing of the frozen Berezina River during the retreat (the ice giving way drowning half the remaining troops).

Minard’s graphic tells a rich, coherent story with its multivariate data, far more enlightening than just a single number bouncing along over time. Six variables are plotted: the size of the army, its location on a two-dimensional surface, direction of the army’s movement, and temperature on various dates during the retreat from Moscow. Visual Display of Quantitative Information, p. 40

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A government is the most dangerous threat to man’s rights: it holds a legal monopoly on the use of physical force against legally disarmed victims.

Ayn Rand

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