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Extra 2,000 men in Minard's drawing?

My wife and I were looking at the large print of Minard's depiction of Napoleon's march to Moscow (Tufte, Visual Display of Quantitative Information [second edition], p41), and noticed that on the return trip, near the end, the army's size apparrently swells from about 12,000 men to 14,000 before dropping once again to 8,000. However, we see no indication that a 2,000 person contingent has joined the army.

What's going on here? I'm fairly certain that I'm not the first to notice this oddity, but I'm at a loss to explain it based solely on the text.

-- Scott Zetlan (email)

The historical sources for Minard's graphic (listed in his paragraph at the top in the final version of Napoleon's March, as shown on page 176 of The Visual Display of Quantitative Information and on the poster) describe the enormous chaos during the entire disastrous invasion. On this, see Segur's book, Napoleon's Invasion of Russia, one of Minard's sources. It is clear that no one is taking a daily census of the Grand Army; the death numbers are surpassingly fuzzy.

By the way, Minard counts only the Grand Army. With Russian casualties, the total number of deaths is estimated at 700,000.

To reason about variation of death counts, it is informative to recall the difficulties in obtaining an accurate account of the numbers of deaths in the attack on the World Trade Center. During the two months following the attack, the death count went down from the initial estimate of 6,000 to the final confirmed total of 3,000.

Now contemplate how much greater measurement errors would be in 1812 in a chaotic disaster spread all over western Russia with some 250 times the total number of deaths compared with the WTC attack.

Wobbles in Minard's numbers are to be expected.

-- Edward Tufte

Very good observation!

-- Edward Tufte

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