Napoleon, Trump, and the Best Statistical Graphic Ever Drawn

Now that I have your attention, let me ask you three simple yes-or-no questions. 

• Do you believe that we gain a better understanding of the world by looking at statistical graphics? 
• Have you seen Minard’s diagram of Napoleon’s invasion of Russia?
• Do you know what the designer was trying to communicate?

Why you have seen Minard’s diagram of Napoleon’s invasion of Russia

When Charles Joseph Minard died in 1870, his diagram of Napoleon’s invasion of Russia had not appeared in any publication.

Its first appearance in book form was in 1878. It was redrawn and reproduced in black and white as Figure 37 in La méthode graphique by Etienne-Jules Marey. That book pushed the radical idea that the future of experimental science was the use of graphics rather than tables of numbers. Marey made his case with representations of quantities, time, and other variables from drawings taken from the distant and recent past. He introduced Minard’s diagram as a “graphic representation of an itinerary route”. He pointed out that it included the variables of quantity, geography, time, and temperature. He also noted that the diagram shows Hannibal’s invasion of Italy. His description ended with language that was to be paraphrased over many decades:

Always a striking effect, but nowhere does the graphic representation of the march of the armies reach that degree of brutal eloquence which, in figure 37, seems to defy the historian’s pen.

The first English translation of the book, Etienne-Jules Marey, The Graphic Method, was published in 2022 by RJ Andrews’ Visionary Press. Marey’s book was cutting edge science in 1878, but it was quickly overshadowed by his own pioneering experiments with photography. Marey is remembered today not for starting the history of data visualization but because he went on to invent and apply a series of photographic innovations to document human and animal motion, brilliantly chronicled in Picturing Time by Marta Braun (1992).

But I am getting ahead of the story. There is no evidence that this first reprint of Minard’s diagram made it famous. The diagram languished in obscurity for more than fifty years until 1937 when H. Gray Funkhouser, an American mathematician and historian, reproduced the graphic in “Historical Development of the Graphical Representation of Statistical Data”. This book-length essay in the history of science journal Osiris introduced Minard to the English academic record. Funkhouser translated and paraphrased Marey’s statement that the graphic “seems to defy the pen of the historian by its brutal eloquence”, and cites Minard’s own essay “Graphic Tables and Figurative Maps” (1862) to emphasize the impact of the work. Funkhouser wrote:

Minard says that the dominating principle which had characterized his graphic tables and figurative maps was the immediate appreciation by the eyes of the proportions of the numerical results. He also speaks of the cordial reception given to his work by the Emperor Napoleon III. 

Looking closely at the sentence in Minard’s essay where he claims the Emperor viewed his graphics, there is a footnote.

Very recently the cotton import map having been placed under the eyes of the Emperor, “His Majesty examined it with keen interest, expressing the intention of consulting it if necessary.”

Apparently it was one of Minard’s “European Cotton Import” graphics that passed before the Emperor’s eyes. That series, reproduced in Sandra Rengen’s The Minard System, visualized how England and France replaced American raw cotton imports during the American Civil War by turning to sources in Egypt and India. The appearance of that book in 2018 was the first complete collection of Minard’s diagrams in book form. The French translation of Rendgen’s book, Le Système Minard, is the only complete collection of Minard’s diagrams to be published in France.

Whether the Emperor saw lines representing cotton or invading armies, Funkhauser was talking about the same designer. Thirty years later, the American geographer and cartographer Arthur H. Robinson restated the same quotation. “The Thematic Maps of Charles Joseph Minard” was published in the cartography journal, Imago Mundi, in 1967. He wrote:

The last thematic maps made by Minard deserve special mention here. In a pair of maps published in 1869 he showed, by the flow technique, the reductions in the sizes of the armies of Hannibal in his campaign into Italy and of Napoleon in the Russian campaign of 1812–1813. Especially striking is the map dealing with the Russian campaign, since the loss of life was so catastrophic in that futile exercise in military aggrandisement. The reduction of an army of 422,000 to only 10,000 is portrayed in startling fashion by the steadily diminishing line. This map apparently became very well known and, as Marey put it, seemed to defy the pen of the historian by its brutal eloquence.

Still, it wasn’t this essay in an academic cartography journal that brought the diagram of Napoleon’s invasion of Russia to the attention of a large public. 

That happened when Edward Tufte, a professor of Political Science, Statistics, and Computer Science, reproduced a color version of half the diagram in The Visualization of Quantitative Information. Tufte’s book first appeared in 1983 and grew in popularity as he wrote and published more books on the subject of data visualization. He introduced the diagram as “the classic of Charles Joseph Minard (1781–1870), the French engineer, which shows the terrible fate of Napoleon’s army in Russia.” Tufte writes a long and detailed description of the diagram, beginning with Robinson’s version of Marey’s brutal eloquence quotation. On the opposite page he reproduces “Minard’s French original, which was printed as a two-color lithograph in the form of a small poster” above a second reproduction with the text translated into English. To which he added:

It may well be the best statistical graphic ever drawn.

Bingo. In 21st century language, the diagram became The Greatest.

Tufte was the author, the promoter, the judge, and the publisher in this case. In combination with his books and public lectures, he prints and sells a version of the graphic as a poster. This combination has made it one of the best known information graphics in the world today. 

What the designer was trying to communicate

Let’s start with the original diagram.

The lithograph, dated November 20, 1869, contains two diagrams, one above the other, printed on a single sheet. On the top is Figurative map of the successive losses of Hannibal’s army during the march from Spain to Italy through Gallia (according to Polybius). Hannibal, for those not familiar with Ancient History, was a Carthaginian military leader who led an army across two major European mountain ranges, from Spain to Italy, in 218 B.C. The diagram illustrates how the distance travelled and mountains and rivers crossed reduced the size of the army. The reduction is most dramatic when crossing the Alps. Minard has numbers printed in his flowing lines indicating the number of soldiers before various crossings. An army of 96,000 leaves Spain. That number is reduced at each river and mountain crossing. After crossing the Alps, Hannibal enters the Po River Valley with only 26,000 troops. The invasion, which included several battles where Hannibal was victorious, eventually led to stalemate and his failure to conquer Rome.

Minard chose to print this directly above the second diagram titled Figurative map of the successive losses of the French army during the Russian campaign, 1812–1813. The position, title, technique, and color of the two diagrams suggest they illustrate a parallel relationship between the two events, one from Ancient and the other from Contemporary History. Without looking at the details, the common visual message is “Army size diminishes over distance”. The sheer size of the contemporary army contrasts with the ancient one. Two thousand years ago, the band representing a large army was 96,000. The band of Napoleon’s army represents 422,000. The ancient example illustrates the reduction  of the invading force which ultimately led to defeat. The modern example shows the more dramatic devastation of invasion, stalemate, and adds the black band of retreat.

“The Napoleon graphic manages to integrate six data variables in a condensed representation devoid of visual clutter, “ to quote Rendgen’s concise summary. Why was Charles Joseph Minard, Inspector General of Bridges and Roads in Retirement, transforming multiple data variables into a single coherent image? Who was he trying to communicate with in November of 1869 and what was he trying to say?

Minard was born in Dijon in 1781. He attended high school during the first French Revolution and completed his training as a civil engineer in 1803 during the First Empire of Napoleon 1st. He served as a senior government engineer in charge of national infrastructure, supervising canals and planning railroads, through periods of shifting monarchy, republics, and empires. In 1831 he became a professor at the School of Roads and Bridges in Paris where he was trained. He continued to fulfill multiple roles as a senior engineer and educator for another twenty years. He was required to retire at the age of seventy in 1851. During the decades of his service, the French government went through dramatic upheavals, moving from monarchy to republic to the election of Louis Napoleon, a nephew of Napoleon 1st, as president in 1848. Through a series of political maneuvers, this politician went from President of the Second Republic to King of France. Finally he declared himself Emperor Napoleon III. This is why Minard’s footnote mentions his diagrams being placed “before the Emperor”.

Minard produced more than fifty diagrams during his retirement. As a member of the elite government meritocracy, Minard had access to data sets from publications and government agencies. He spent nearly two decades producing several visualizations each year, each diagram based on statistical data having to do with the national and international flow of goods and people. Each diagram was printed at a local lithography company and sent to a list of people in the French government. The only evidence we have of their reception is an oil portrait of a government minister, Eugène Rouher, in which one of Minard’s diagrams appears draped across a chair.

Minard produced two exceptions to this pattern of data sets. In 1865, in addition to maps of the postal districts of Paris and the quantity and routes of international rail travel, he created a map on an historical military theme. The print titled Similarities of the strategic dispositions of Charlemagne and Napoleon Ist is a single sheet with two maps, arranged side by side. The maps show the similarity of military position used by Charlemagne against the Huns in 791 and by Napoleon Ist against the Austrian and Russian army in 1805. Both maps show the same region around Vienna. The theme here was visual similarity separated by a thousand years.

The second exception was the diagram we all know and admire. I can only speculate as to what motivated Minard that year to produce this comparison of two devastating military failures. By its second decade, the imperial ambitions of Emperor Napoleon III had produced many international interventions intended to expand French influence and territorial ambitions. He sent troops to Mexico in an attempt to establish a monarchy there, which failed. He supported military interventions in Algeria, Senegal, Southeast Asia, China, and Korea, which led to the establishment of the French colonies in Africa and Indochina. He established competing alliances against Prussia by projecting his power in Europe. 

Minard was in his 88th year when he printed this diagram in November of 1869. Political conflict with the Prussians was growing. The elite of Paris knew their Emperor was in very poor health. 

The octogenarian Minard chose to design a diagram that documented two dramatic military failures. He compared Hannibal’s decision to march his army against Rome, which ultimately resulted in the destruction of his own homeland, to the decision by the Emperor of the First Empire to project his power by invading Russia, which led to the destruction of his army and the end of his regime. Then he had this diagram of the classical Folly of the Past and the contemporary Folly of the Present printed. Both ideas were supported by data. For the Folly of the Present, he made sure to include very specific details: the specific locations where troop numbers declined, the names of towns and rivers, the time and temperature during the retreat. He had this finely-printed visualization delivered to the elite of the Second Empire.

Despite all that effort, the best statistical graphic ever drawn did not prevent the next Folly of the Present. 

Six months later, the Emperor’s projection of political power in Spain triggered the Franco-Prussian War. The French army was defeated by the Prussians, the Emperor was captured, and the Empire collapsed. As news of the defeat and the German army approaching Paris arrived in the Minard household, the designer of the best statistical graphic ever drawn made the decision to join the flood of escaping refugees. This description of the events that followed is from Minard’s obituary, written by his son-in-law (Dawn Finley’s translation)

In his later years, the bodily infirmities grew; he moved with more and more difficulty, but he worked always with the same ardor. He received freely those who came to see him, and he held them by the delight of his conversation. His surprising memory, his intelligence as alive as always, his regular habits, his sober life, the care with which his family surrounded him, all put at a distance the idea of a coming end. But faced with the progress of the Prussian army his imagination carried him away; and after some hesitation he decided all of a sudden, Sunday September 11, 1870, to leave Paris, his books, his papers, his intellectual riches and the office which he occupied for twenty-five years. Leaning on crutches, in the middle of this throng of women, of children and of old people who fled as he did, he left for Bordeaux with one part of his family, carrying only one light bag and some studies already begun. He endured very well the fatigues of a night journey, and barely installed at Bordeaux, without other resources than his memory, he reapplied himself to work; but six weeks after his arrival, as strongly frightened of the present as of the future, he was taken for three days by an irresistible fever, and on October 24 he returned [his] soul, full with gratitude towards God, according to his expressions, for the portion of happiness which had been given to him on this earth.

What history teaches

Gertrude Stein, the American-French immigrant LGBTQ+ writer, wrote “If I Told Him, A Completed Portrait of Picasso” about her friend Pablo Picasso, the Spanish-French immigrant painter, a man who can be described as an abusive male partner to the many women in his life. 

Her text will not fit in a social media post. It is short, not a simple text, and not an easy thing to read. But it is fun to read it out loud.

It begins:

If I told him would he like it.

Would he like it if I told him. Would he like it would Napoleon would Napoleon would would he like it.

and ends:

Let me recite what history teaches. History teaches.

This history demonstrates that statistical graphics devoid of visual clutter do not disarm despots. 

Do you believe that we gain a better understanding of the world by looking at statistical graphics?

If your answer is “yes” then apply your talents to improving the current situation.

Second Trump Administration, Day 27