| February 22, 2010 5:49 pm

Charles Minard - Railroad Routes

No study of the history of scientific communication can be complete without mention of Joseph Charles Minard, a 19th Century French civil engineer and cartographer.

At the end of his life, Minard created two very famous examples of statistical charts, called flow maps, that every scientist, engineer and student should be familair with.  The first showed Hannibal’s crossing of the Alps (218 BC, Second Punic War), and the second describes Napoleon’s disastrous invasion of Russia (1812-1813).

Both examples are beautiful works of art and masterful examples of evidence.  But they are also more than that, they tell cohesive and interesting stories.  In this post, I thought it might be interesting to take a closer look at the history of Hannibal and Napoleon, and highlight the ways which Minard’s charts help us to explain their eventual outcome.

(Note: High resolution, PDF versions of the two maps are available for download.  These versions have been translated from the original French.  To download, either click on the images, or here for the Hannibal invasion of Northern Italy, and here for the French Invasion of Russia.)

Hannibal Invasion of Italy (218 BC, Second Punic War)

Hannibal was perhaps the single greatest threat to Roman power to ever live.  At the same time that Roman legions marched unopposed through most of the Mediterranean world, Hannibal lead a force of twenty-five thousand soldiers into the heart of Roman territory. He then spent the next fifteen years occupying portions of the Italian peninsula and generally wreaking havoc.  But even though he ravaged the Roman countryside, Hannibal was never successful in subduing Rome.  Ironically, this might be due to one of his greatest exploits: the overland crossing of the Alps.

Hannibal departed his home base in Spain with nearly 90,000 troops (one of the largest armies that had ever been fielded at that point in history) and had a number of early successes.  He marched north over the Pyrenee mountains and into Gaul (modern day France).  He subdued the Celtic tribes and crossed the Rhone River before the Romans could take measures to stop his advanced.  He forged important alliances and found unexpected friends in his fight against the Romans.

After crossing the Rhone, however, Hannibal’s luck began to change.  He received word that a large Roman force was marching from the Mediterranean coast to intercept and destroy him.  As the force outnumbered him by a significant margin, Hannibal was faced with a difficult choice.  Should he stay at his current location and engage the Roman army or retreat and prepare a defense?

Not content with either choice, Hannibal ultimately chose a third option; which, ironically, would have enormous consequences for his overall campaign.  To evade the Romans, Hannibal took the unprecedented action of turning inland and marching over the Alps.  (It is thought that he probably crossed over the valley of the Drome and south of the Col de Montgenevre or near the Col de Mont Cenis.)  This had never been done before – indeed many thought it impossible – and has long been praised as a brilliant tactical decision.

Minard’s reconstruction of Hannibal’s journey shows the journey from Spain, through Transalpine Gaul and eventual arrival in Italy, allows it to be seen a slightly different light, however.  Through use of a flow line, Minard shows how the strength of Hannibal’s army waned through the march, with a disastrous loss of twenty thousand men while passing over the Alps.  This steady loss of strength, subtly reinforced by Minard’s map, helps to explain why Hannibal failed to subdue Rome.

Hannibal’s brilliant tactical decision was also a strategical disaster.  It came at a dramatic loss of men, war elephants, and material with the most disastrous loss being the destruction of his siege engines.  Without the siege engines, Hannibal was never able to successfully attack Rome.  And eventually the Romans realized this and changed their tactics.  Instead of engaging Hannibal directly, they instead fought a long-pitched war of attrition and eventually destroyed the one resource he couldn’t replace: his men.  Thus, even though crossing the Alps helped Hannibal to win a few stunning victories, the decision eventually caused him to lose the war.

Hanibal's invasion of Italy over the Italian Alps.

Napoleon’s Invasion of Russia (1812-1813)

Like in the case of the Hannibal, Minard’s depiction of the 1812-1813 invasion of Russia also tells an extraordinary story.  It combines information about the size of the army, geography, sub-campaigns and temperature into a single narrative.  This time, though, it is anything but subtle.

Note: Because of  the elegant management of all this information – at any time showing the army’s direction, size, and loss relative to the start – some statisticians and data visualization experts (such as Edward Tufte, Etieene Jules Marey and Howard Wainer) have declared Minard’s depiction of Napoleon’s Invasion of Russia to be the greatest numerical graphic ever created.

From the very beginning, the army met with tremendous hardship.  The cold temperatures and lack of available resources took an enormous toll.  Napoleon had planned on scavenging for supplies to support his massive army, but the Russians had destroyed all of their crops and burned their villages so that Napoleon wouldn’t be able to make use of them.  As a result, the army was heavily reliant on slow supply trains from Europe that were unable to keep pace with its quick advance.  Hundreds of thousands died from starvation and exposure, greatly outnumbering those lost in combat.

Minard’s map shows this trend of devastating loss.  Napoleon’s Grand Army starts out as a wide, brown line to the left of the map.  As the army progresses across Russia, the number of men decreases dramatically.   A few ribbons of men are dispatched to other targets, but by far the majority succumb to the elements.

Eventually, a substantially reduced force (100,000 men, about 20% of those who began the campaign) arrived in Moscow.  What they found did little to improve their circumstances.  The city had been abandoned and burned to the ground.  No food was available.  The only available option was to return to France.

Demoralized and broken, the Grand Army began a slow retreat to the west.  Their progress is shown in the black.  As they crossed the vast Russian wilderness, the temperature turned bitter cold (shown in the bottom third of the map).  When the army arrived at the Niemen river, there were a scant 10,000 troops.  More than 400,000 had died.

Such a devastating loss of life crippled Napoleon’s young empire and left him open to invasion by his enemies.  He was defeated later in 1813 and exiled to the island of Elba.

Minard's map showing Napoleon's invasion of Russia and the catastrophic losses he suffered.


Minard’s graphics are successful because they demonstrate powerful trends and place evidence within its proper context.  In the case of Hannibal, it shows how he began in a position of strength and then undermined himself through a brilliant tactical innovation.  In the case of Napoleon, it shows how distance and temperature ravaged an army and destroyed an emperor.

The clear evidence and thoughtful presentation define the story, they show where things are headed and help to foreshadow the inevitable conclusion.  For this reason, they are powerful examples of clear communication.


Unrelated Thoughts: Re-Visioning Minard with Open Source Tools

Since first seeing these charts as part of an undergraduate statistics course, I’ve been obsessed with them.  I even have a poster sized copy of the Russian invasion (available from Graphics Press) hanging in my office.  Given this obsession, it should come as no surprise that I’ve wanted to include the maps in my book.

There is, however, just one problem; there is not anything new to say about them.  Edward Tufte has held up Minard as a “Da Vinci of Data” for the better part of thirty years.  Nearly every one of his books includes a copy of the maps (in the case of Beautiful Evidence, his most recent work, there is an entire chapter devoted to the graphics; including eight different reproductions).  Other than, “They’re beautiful, study them carefully, read Tufte’s analysis,” there just isn’t that much to say.

That is, until I started looking for examples of scientific illustration that could be reproduced using the vector illustration program, Inkscape. Any such example should have simple lines and clean integration of text and images.  I’m not sure that a better description of Minard’s work exists.

The two images above (and attendant PDFs) were my first pass at re-drawing the maps.  And I have to say, I’m rather happy with the result.  For the most part, I was able to get a very faithful reproduction (with the exception of the type face, which I deliberately changed because I hate script fonts), and only required a couple of hours worth of work.

I think that I may have found my book examples.  It allows me to include one of the best statistical charts of all time, talk about flow maps, and even include some interesting how-tos which show how the graphics can be built in an automated fashion.  Which, come to think of it, might just count as a new contribution after all.

Acknowledgements and Further Reading

More information on the book can be found at the publisher’s website.

The source images for the two maps included “Re-Visions of Minard” by Michael Friendly (1999) and the reproductions in “Beautiful Evidence” by Edward Tufte.  Translation for the Hannibal map was adapted from those available on Edward Tufte’s website (Dawn Finley) and sources available at Re-Visions of Minard.  Translation for the Russian campaign map were taken from the reproduction in Edward Tufte’s “Beautiful Evidence”, Wikimedia Commons and sources available from Re-Visions of Minard.

Additionally, the Re-Visions of Minard Website include a number of interesting adaptations of the Napoleon graphic that might be of interest, including both Matlab and GGPlot2 reconstructions.


One Response to “Hannibal, Napoleon, and Joseph Charles Minard”

Stephen wrote a comment on March 12, 2010

Seeing the railroad routes triggered a memory — once I had a discussion with a friend’s father about re-drawing maps (specifically rail maps) in terms of journey time rather than actual distances. We thought it might position some places in Sussex effectively in the middle of the Channel, when compared to the mainline routes such as Brighton. Perhaps one could add an average wait time for services too – these branch lines have fairly infrequent services, it would place them relatively further away. Of course all the relative distances/journey times I have assumed to be commutes from London.

Care to comment?