Visions and Re-Visions of Charles Joseph Minard

Journal of Educationaland Behavioral Statistics Spring 2002, Vol. 27, No. 1, pp. 31-51

CharlesJoseph Minard is mostwidely known for a single work-his poignantflow- map depictionofthe fate ofNapoleon's GrandArmyin the disastrousRussian campaign of 1812. In fact, Minard was a true pioneer in thematiccartography and in statistical graphics; he developed many novel graphicforms to depict data, always with the goal to let the data "speak to the eyes." This article reviews Minard's contributionsto statistical graphics, the time course of his work, and some backgroundbehind the famous March on Moscow graphic. Thisarticle also looks at some modern re-visions of this graphfrom an informationvisualization perspectiveand examinessome lessons this graphicprovides as a test case for the power and expressiveness of computersystems or languagesfor graphic information display and visualization.

Keywords: data visualization,dynamic graphics, history,Mathematica, Napoleonic wars, statistical graphics, thematiccartography

RE-VISIONn. ri-'vizh-en (ca. 1611) 1. To see again, possibly from a new perspective; syn: review, reconsideration, reexamination, retrospection. 2. An act of revising; syn: rewrite, alteration, transformation.(Merriam- Webster, 2002) Readersof Tufte (1983) and Wainer(2000) have become acquaintedwith some early developments in the history of statistical graphics by Playfair, Florence Nightingale,and others. The "others"include Charles Joseph Minard, whose Carte figurative des pertes successives en hommes de l'Armee Frangais dans la cam- pagne de Russe 1812-1813 (hereafter, the "Napoleon's March on Moscow" graphic)is, some have claimed, "thebest graphicever produced"(Tufte, 1983). This graph(see Figure 1, Figures 1-8 on pages 37-44) shows the catastrophic loss of life in Napoleon's GrandArmy. The diminishingsize of the army,initially 422,000 strong (includingconscripts from his empire),is shown by the width of a steadily diminishing line, overlaid on the map of Russia, ending with 10,000 returningat the end of the campaign.A subscriptedgraph of declining temperature over the Russian winter shows the brutalconditions which accompaniedthe sol-

The authoris indebted to ArthurH. Robinson, Gilles Palsky, and Antony Unwin for helpful background information and comments on earlier drafts, and to Guillaume Saquet, Carine La Tela, and LauretSaye of the ENPC for generousassistance and access to archivematerials. The authoralso thanks Les Chevaliersdes Albumfor joining his quest for copies of l'Album.This work is supportedby Grant 8150 from the National Sciences and EngineeringResearch Council of Canada.

This content downloaded from 130.63.134.82 on Thu, 6 Jun 2013 16:02:04 PM All use subject to JSTOR Terms and Conditions Friendly diers on theirterrible retreat. This graphic,as Marey (1878) put it, seemed to defy the pen of the historianby its brutaleloquence. Later, Funkhouser(1937), in the first modem overview of graphicalmethods, devoted severalpages to Minard'swork and called him "thePlayfair of France,"to suggestthe scope of his contributions.Tufte (1983) broughtthis image to wide attention, describing it as showing "multivariatecomplexity integratedso gently that viewers are hardlyaware that they are looking into a world of six dimensions.... It may well be the best statisticalgraphic ever produced"(Tufte, 1983, p. 40). It is thereforeironic that this Marchon Moscow graphicis often seen as an isolatedwork. Apartfrom this, Minard'swider contributions to statisticalgraphics are little known, especially outsideFrance. My introductionto the largercontext of Minard's work and the motivationfor the present study arose from a copy of an 1883 volume of l'Albumde Statistique Graphique,published annuallyby the Bureau de la StatistiqueGraphique of the Ministryof PublicWorks from 1879 to 1899.A large-formatbook (about12 x 15 in.), each of its figures folds out to either three or four times that size, and contains exquisite detail and beautiful color tones. Most important,the figures display an astonishingrange and depth of visual information,using all known graphicforms (map-basedpie and starcharts, mosaic plots, line graphs,bar charts, and, of course, numerousflow maps). Collectively, these works may be consideredthe epitome of the "goldenage of statisticalgraphics" (Palsky, 1996; Friendly& Denis, 2001). Some copies of these images may be seen on my Gallery of Data Visualization (GDV) (http://www. math.yorku.ca/SCS/Gallery/). That lovely volume was the springboard for this re-vision of Minard, presented in two parts correspondingto the Merriam- Webster definitions of "re-vision."

Re-Visions of Minard's Other Graphics Minarddied in 1870, and the well-known Marchon Moscow graphic(Novem- ber 20, 1869) was, along with a similar graphic of Hannibal's army in Italy, among his last published works, yet all of the volumes of l'Album (carriedout under the direction of Emile Cheysson) show the unmistakablesignature of the graphic inventions of Charles Minard, whose role and inspirationare acknowl- edged in the preface. Re-examining some of Minard's works is the first sense of my title phrase"Re-visions of Minard." Minardwas a truepioneer in what geographerscall "thematiccartography" and also in statistical graphics. The authoritativearticle by Robinson (1967) listed 51 cartesfiguratives among his known works, but only four redrawings,pale imi- tations of the originals, are shown in that article. Several color reproductions appear in Robinson's Early Thematic Mapping in the History of Cartography (Robinson, 1982), and 15 appearin Palsky (1996), who lists 58 graphicworks by Minard.A comprehensive,indexed bibliographyof all of Minard's graphicworks appearson the GDV website.

This content downloaded from 130.63.134.82 on Thu, 6 Jun 2013 16:02:04 PM All use subject to JSTOR Terms and Conditions Visions and Re-Visionsof Charles Joseph Minard Thematiccartography always involves a tensionand trade-offsbetween the con- fines of the map and the representationof data. Minardalmost invariablychose accuracy of the representationof data over the "tyrannyof precise geographical position" whenever conflict arose. "Accordingly,he revised coastlines, paid little attention to projections, and forced the scales of the geographic features on his maps to fit the data being portrayed,rather than vice versa, as is usually done today" (Robinson, 1967, p. 95). It is for this reason that he carefully labeled his maps cartesfiguratives et approximatives.As one may see in the fine detail of the March on Moscow graphic,he also took considerablecare to representthe quan- titative informationin both numericaland visual forms. Minardwas first a civil engineer, then an instructorat the Ecole Nationaledes Ponts et Chauss6es(ENPC), the premiertraining school for engineersresponsible for building the roads, canals, and railroadsof France.Later, he was an Inspector Generalof the Councildes Ponts et Chauss6es.As a result,a greatdeal of Minard's graphicwork is concernedwith the visual representationof the movementof goods and people. He made dozens of "flow maps,"depicting passenger traffic on Euro- pean railways(see Figure2), the transportof meat and produceto feed the growing populationof Paris(Figure 4), the internationaldistribution of Frenchwines, cotton, coal, and so forth.As in Figure2, Minardtypically included the numericalinforma- tion on the mapas well, eitherannotated or in tabularform, and included lengthy leg- ends describing exactly what was being portrayed, the nature of the visual representation,and conclusionswhich could be drawnfrom these. Minarddid not invent the idea of using flow lines on a map. Thathonor belongs to Henry DruryHarness (1837), showing passenger traffic and the flow of goods in Ireland (Robinson, 1955, 1982). WhetherMinard knew of Harness's work or developed the flow map independentlyis unknown.However, it is fair to say that Minarddeveloped this graphictechnique to an artform, and the Marchon Moscow graphic,his last such effort, representshis finest achievement,for reasonswe shall see later. These mapsand charts were all madewith the expresspurpose of informingdeci- sion makersresponsible for planningin an era of rapidgrowth and development- what we might now call the "dawn of the age of globalization."In these works, Minardhad moved from work as a civil engineer (designing canals and railways) to work as a visual engineer (designing informative visual data displays). For example, in 1865 the location for a new central post office was to be chosen in Paris. Minard's ingenious map (Figure 3) showed the population distributionin Paris as population-sized squares for each arrondisement,and located the post office at their visual center of gravity. Minard's influence and contributionto visually based planning was such that, from about 1850-1860, all Ministersof Public Works in Francehad theirportraits paintedwith one of Minard's creationsin the background(Chevallier, 1871, p. 17). In 1861, some of Minard's works were presentedto Napoleon III (a singularhonor for an engineerof middle-classbackground), who received them with enthusiasm.

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Robinson(1967) providedfurther insights into Minard'srole in the developmentof thematiccartography in the latterhalf of the 19th centuryand his personalhistory.

Minard's GraphicInventions Minard'smaps and chartsused and extended a numberof other graphicforms to display data:pie charts,the Coxcomb (or "rosediagram") attributed to Florence Nightingale,a shadingscheme with two colors of varyinglightness to show a bipo- lar dimension, and so forth, but always with the goal "to make the proportionsof numericalrelations apparent to the eye immediately".(Minard, 1862, p. 2 quoted in translationin Palsky, 1991, p. 114). Like Playfair's charts, Minard's graphic inventionswere designed "to speakto the eyes" (Minard,1862, p. 4 quotedin trans- lation in Palsky, 1991, p. 114). For example, Playfair(1801) inventedthe pie chart,but Minardwas the firstto use a divided circle in cartography(Wallis & Robinson, 1987), and he used it in a novel way-to show both amounts and relative proportionson a map. Figure 4 shows the quantitiesof butcher'smeats suppliedto the Parismarket by each depart- ment. The total quantity of all meat from each departmentis shown by a circle whose areais directlyproportional to this total by weight. Each circle is subdivided to show the relative proportionof beef (black), veal (red), and mutton(green). In the color originalit is immediatelyapparent that regions close to Parissupplied large proportionsof veal or mutton,while those far from Parissupplied mostly beef. The backgroundshading also distinguishesthose departments with no contribution(beige) fromthose with any nonzerocontribution (yellow). The mapwas producedby litho- graphand handcolored. This idea of scaling an icon to a size that representsa regional total, while the internal subdivisions representthe relative proportionswithin the geographical region, is anothersignificant contribution of Minard.Also noteworthyare a series of tableauxgraphiques, using variable-widthdivided bars, shadedin differentcol- ors to displaythe numbersin a two-way table as proportionsin relationto theirrow or column totals, an early precursorof the mosaic display (Friendly, 1994, 2001). Minardhimself never used this graphicform on a map, but figuresfrom l'Albumin 1883 and 1884 depict the transportationof goods and passengersin France,where the datafor each city is portrayedas a mosaic, with an overall size proportionalto the total for thatcity, just as in the pie-mapfor meat. These figuresare also remark- able in theiruse of spatialrecursion-the transportout of each city is connectedto its destination,where a smallermosaic recordsthe distributionfrom there.

The Ebb and Flow of Minard's Graphic Output Some additional observations on Minard's career came from a visit to the Archives of the ENPC to view Minard'soriginal and subsequentattempts to doc- ument his contributions.As Robinson (1967) pointed out, there were two, largely distinct,phases to Minard'sremarkable career. The first,from 1810 (age 29), was as an engineerand later instructorand administratorfor the ENPC, until his (manda- tory) retirementat age 70 in 1851. 34

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His second careeras cartographerand graphicalinnovator-a visual engineer- datedfrom the 1844 publicationof his tableauxgraphiques and lasteduntil his death in 1870. The significantevents and accomplishmentsin Minard'stwo careersare listed as .pdftimelines on the GDV website,which drawson the obituaryby Cheval- lier (1871), and the accountsof Robinson(1967) and Palsky (1996). Events in his careeras a thematiccartographer are shown here in Table 1. As a practicalengineer, Minardhad no ciriculum vitae, but the catalog of his works held by the ENPC is impressive.Among 105 items, it lists eight shortbooks (including La Statistique, 1869), 10 sets of course or lecture notes, 30 published brochures,and 17 articles in the Annales des Ponts et Chaussees, in addition to nearly60 maps, tables, andother graphic work. Threegraphic construction designs for bridges and archesexecuted while he was a student(circa 1812) show the early hand of a master draftsman;a later example of this work may be seen in Tufte (1983, p. 39). Minard(1862, p. 4) dates his firststatistical graphicto 1826, but says he had just followed a form of graphic tables used earlier by Layton Cooke in England. TABLE1 MinardsTimeline: Later Years.

Lateryears (1843-1870): Thematic Cartographer, Visual Engineer for France

Concern with passenger travel:parcours partial 1843 * Tableauxgraphique: travel vs. distance, area - income 1844 * 1" flow map: travellersfrom Dijon to Mulhouse Mar. 1845 * Appointed InspectorGeneral of ENPC (age 65) 1846 *

Retires from ENPC (age 70) Mar. 27, 1851 * * 1851 Map of transportof combustible minerals, presented to Ministers of Finance, Public Works

* 3" Intl. Statist. Cong. (Vienna) 1857 * 1857 Forms of graphics includes flow maps I"use of proportionalpie charts on map (butcher's 1858 * meats in Paris)

Minard'smaps presented to Napoleon III 1861 * Des tableaux graphiqueet des cartes figurative: 4 plates 1862 * First use of comparativeflow maps 1863 *

Center-of-gravitymap (Paris) 1865 * * 1865 Flow map of movement of passengers on principal of Population density of Spain, shading - pop. density 1866 * railways Europe Movement of ancient languages graphic 1867 *

Marchon Moscow and Hannibalgraphic 1869 * * 1869 La Statistique:the applications of statistics Leaves Paris to escape feared Prussian siege Sep., 1870 *a Oct. 24, 1870 Dies in Bordeaux (age 89)

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In this review, it seemed appropriateto attempta graphic view of Minard's later career from the catalog and bibliographicmaterials. A smoothed time plot of his graphicoutput (see Figure5) proved quite revealing, in both numbersand content. First, we see that Minardpublished about two graphic works per year over the 27-year period, but the rate varied systematicallywith events in his life. The rate dropsprecipitously after his promotionto InspectorGeneral of the ENPC in 1846. After his retirement,it rises steadily over the next 10 years to a peak of twice his average rate in the early 1860s at age 80. Minardsuffered increasingly from arthritisand rheumatismin his later years, requiringcrutches, which may account for the decline over the last nine years- but only down to his averagerate. In September1870, as the Prussianarmy moved steadily towardParis, the 90-year-oldMinard became increasinglyfearful and fled with his family to Bordeaux,regretfully leaving behind the books and papers he had workedon for the last 25 years. Six weeks later,he took ill with a terriblefever and died threedays later,on October24 (Robinson,1967, p. 99). He had takenwith him several works in progress (Chevallier, 1871, p. 21), but these evidently have been lost. As much as this quantitativeportrayal tells a part of Minard's story, Minard's choice of subjectmatter and graphicformat tells anotherpart (Figure 5). After several initial tableauxgraphiques depicting the movementof passengerson railways (designedto informthe choiceof ratestructure for shortversus long journeys), Minard developedthe flow map in 1846, andused this graphicform almost exclusively until 1864 to portrayhis breadand butter topics-the transportationof goods by wateror by land. He wrote, "I realized,by substitutingmerchandise for voyagers,my maps andgraphic tables acquired numerous commercial applications" (Minard, 1869, p. 8). In 1862, he publisheda flow map showing patternsof emigrationfrom Europe throughoutthe world (colored by origin of departure),and in 1863, a pairof beautiful flow maps comparingthe importationof cotton to Europein 1858 and 1862, showing dramaticallythe effects of the AmericanCivil Waron trade(Palsky, 1996, Fig. 46-47). His spurtof five graphsin 1865 includes threecomparative maps, one relatingthe strategicdisposition of the forces of Charlemagneagainst the Huns in 791 to those of Napoleon against the Austrians in 1805. These also include the center-of-gravitymap for the Parispost office. In addition,a map showing the population density of provinces of Spain by cross-hatching, uses a visual scheme (1/spacing ~ population)in which the numericalvalue can be read directly (rather than using class intervals), one of the first such uses. In 1867, he produced an entirely different form of map, showing the movement of ancient languages throughoutEurope. The "Napoleon'sMarch on Moscow" graphicof 1869 was followed only by two tableaux graphiques, one showing the decline in the study of Latinfrom 1818 to 1864 and the other showing an increasein the mean age of stu- dents at each level of promotionat the Ecole Polytechnique. Thus, we see thatthe fluctuationsin Minard'squantitative output were accompa- nied by a qualitativeshift in emphasis.They also includedwide experimentationwith new graphicforms, an intellectualconcern for the uses of historicaldata and social statistics,and the continuingdesire to portraythese graphically. 36

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FIGURE3 Minard'scenter-of-gravity map of Paris. Note. The visual center of gravity of population density was used to choose location for a new post office. (Col. et clich6 ENPC, 10970/C589; used by permission.)

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FIGURE4 Minard's 1858 divided-circle map, showing the amountsandproportions of butcher's meats supplied to the Paris market. Note. This is the first known use of pie charts in cartography. (Col. et clich6 ENPC, 10969/C590; used by permission.)

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Minard's graphic output

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0 ODD *S * * Goods j 1840 1845 1850 1855 1860 1865 1870 Year

FIGURE 5 The ebb and flow of Minard's graphic output. The dotted horizontal line shows the mean numberof graphics produced each year from 1844-1870. The smoothed curve is a nonparametricquadratic lowess smoother. Vertical lines at the top and bottom show individual graphics, classified by content: Goods vs. Other.

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S•,o, Napoleon's1812 RussianCampaign ?

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,u Temperature in Celcius

S3*Reference renc -33+ .38. *PeP 'e FIGURE6 Re-visionof Minard'sgraphic as a clickableweb imagemap.

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FIGURE 7 SAGE graphic, re-visioned to link temperatureinformation directly to the path and strength of Napoleon's army.

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FIGURE8 SAGEgraphic, re-visionedto show the relations between longitude, time and temperatureexplicitly.

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Napoleon's March Re-visited A final historicalunderstanding came as I viewed Minard'soriginal of the "the best graphicever produced."The Napoleon's Marchon Moscow graphicand the flow map of Hannibal's army were in fact printedtogether, and it is certain that Minardmeant for them to be compared,as in his earliercomparison maps. Hanni- bal's campaign begins in southern Spain with 96,000 troops, crosses southern France,and ends in Italy with 26,000 troops.The loss of life was not nearlyas dra- matic as that suffered by Napoleon's troops, but the map does draw visual attention to the relatively large loss as Hannibalcrossed the Alps. Together, the maps of these two campaignsprovide a visual lesson to historiansand generals, which might have been subtitled,"Some things to avoid in planninga militarycampaign." In fact, thereis a more personaland more emotive meaning to this graphic-as an antiwarstatement by an engineer who had witnessed the horrorsof war in his youth and who, in his final year, was forced to flee his home as the Prussianarmy approachedParis in September1870. Chevalliersays, "Finally,.. . as if he could sense the terribledisaster that was about to disruptthe country,he illustratedthe loss of lives that had been caused by ... Hannibaland Napoleon. ... The graphical representationis gripping;... it inspiresbitter reflections on the humancost of the thirstfor militaryglory" (Chevallier, 1871, p. 18). It may well be for this reason that Minard'smost famous graphicdefied the pen of the historian. Nevertheless,Marey (1878, p. 72) printedonly an initial draftof the Napoleon portionin his book on graphicalmethods (one of the firstgeneral books on this subject); althoughhe refersto the map of Hannibal'scampaign, he does not make the thematiclink between them. Funkhouser(1937) apparentlyrelied on Marey, and, with Marey'seffusive praise, it appearsthat he treatedthe Napoleon'sMarch graphic as a separate,isolated work. Robinson(1967) describedboth togetherand, having studiedChevallier's necrology, appreciated their significance. Tufte (1983, p. 176), who reintroducedMinard to modern statistical graphics, printed the combined Napoleon-Hannibalgraphic, but he used it to illustrategraphical aesthetics, rather thaninterpreting its meaning,either regarding Minard or the historyof graphics.

Modern Re-Visions My second sense of "Re-visionsof Minard"stems from the thoughtthat it would be a wonderful (if somewhat irreverent)challenge to take "the best graphicever produced"and to try to improveit-or even, to reproduceit. As it has turnedout, there are alreadya numberof entries in this contest, and they prove instructive- both for appreciationof the past, and as sign-posts for the future. These may be seen in color in the GDV web site mentionedearlier; a few are worthreproducing and describinghere.

Have YouEver Seen Voice-Mail? In fact, I do see voice-mail,now thatmy telephonehas call-display,but this question, from The Hacker's Test (Lee, Hayes, & Thomas, 1989), is meant to suggest 45

This content downloaded from 130.63.134.82 on Thu, 6 Jun 2013 16:02:04 PM All use subject to JSTOR Terms and Conditions Friendly the wealth of new possibilities for statisticalgraphics now being createdby new technology.The WorldWide Web, Java,CD ROMs, and DVDs providea glimpse of futuresystems which will allow the easy integrationof text, graphics,sound, and othermedia. As one illustration,an InformationDesign course at the University of Texas at Austin taughtby AndrewDonoho, asked studentsto design a web presentation based on Minard'sgraphic. Sunny McClendon'spage (http://www.ddg.com/LIS/ InfoDesignF96/Sunny/Napoleon/welcome.html)is one example of the graphic linked (as a clickable image map, or graphicmenu) to pages of text describingthe major battles of the campaign. The graphic itself, Figure 6, is quite similar to Minard'soriginal, but the text labels for dates,troop strength, temperature, and bat- tle sites have been made more visible. The design work of other studentsmay be seen at http://www.ddg.com/LIS/. It is not too large a jump from these studentprojects to imaginean authoritative, historicalaccount (e.g., Chandler,1996) of Napoleon's 1812 campaignlinked dyna- mically to Minard'sgraphic. Re-Visioningthe RelationsAmong Time,Space, and Temperature Tufte (1983) cited Minard's graphic as a narrativegraphic of time and space which illustrates"how multivariatecomplexity can be subtly integrated"(p. 40). It is instructiveto ask how this multivariatecomplexity can be re-visioned. Steven Roth and others(Roth, Chuah, Kerpedjiev, Kolojejchick, & Lucas, 1997) in the Visualizationand IntelligentInterfaces Group at CarnegieMellon University have developed, a System for Automated Graphics and Explanation (SAGE) (http://www.cs.cmu.edu/groups/sage/).Several illustrationsof the use of SAGE redesign the relations among the graphic elements portraying space, time, and temperature,in relation to the diminishingstrength of Napoleon's army.(Exactly how much of the redesign was done automaticallyand what criteriawere used are not described.) Figure 7 attemptsto link the informationabout temperaturedirectly to the path andstrength of Napoleon'sarmy, emphasizing their interrelations more directly. The (x, y) coordinatesare still map-based(latitude and longitude), but temperatureis shown by the color of the bandsin continuoustones, from full red (hot) to full blue (cold); the width still portraystroop strength.The SAGE group says, "Theuse of color clearly shows the heat wave duringthe advanceand the steadydecline in tem- peraturethrough the retreat.The exception, a spell of temperaturesabove freezing, is clearlyvisible when the retreatingarmy is betweenthe cities of Krasnyjand Bobr." A second redesign (Figure 8) makes the temporalcharacteristics of the march explicit, by replacingthe map coordinateswith a graphof longitude (because the campaign was essentially East-West-East)versus date. Now, the peculiar side- marchto Polotsk (designedto cut the Russians'communication with St. Petersburg on the outboundleg, and returnthere at the end) stands out more clearly than in Minard'soriginal. The Bavariantroops, commandedby St. Cyr, capturedPolotsk in August, and remained there until October, when they rejoined the main campaign. The horizontalgaps betweenrectangles also serve to distinguishthe lengthy 46

This content downloaded from 130.63.134.82 on Thu, 6 Jun 2013 16:02:04 PM All use subject to JSTOR Terms and Conditions Visions and Re-Visionsof CharlesJoseph Minard stays at certainlocations, the siege of Moscow being the longest, from the periods of steady marchon the disastrousretreat.

Dynamic Graphics:Interactivity and Linking Partof the wonderof Minard'sgraphic is how seamlesslyhe linkedthe multiple dimensionsof maplocations, troop strength, advance and retreat, and temperature into a coherentand poignantdisplay. A modernapproach to high-dimensional,complex datais to use dynamic,interactive graphics, with multiple,linked views to provide: selection (brushing),subdivision (drill-down), aggregation (roll-up), and so forth. These capabilitiesare illustratedas well by SAGE, as describedby Roth et al. (1997). The two graphsin Figures7 and 8 (and others)can in fact be linked, so that selection in one graphhighlights or paints correspondingdata in all graphs.More- over, one can dragand drop various tools, includinga slider,onto the SAGE frames. Embedding a slider linked to date allows the viewer to see the changes in troop strength,for example, dynamicallyover the course of Napoleon's campaign.Roth et al. (1997) pointedout thatthis technique(using anotherlinked bar graph of troop strengthover time) reveals (a) differencesin casualtiesamong the majorbattles at Smolensk, Borodino andTrautino, and (b) the fact thatmost of the losses in troops were unrelatedto battles, and occurredearly in time. Chandler(1966) and others pointed to desertionand disease as majorcontributors.

Lessonsfor Data Visualization Minard's graphichas as least one more lesson as a test case for the power and expressiveness of computersystems or languages for graphicinformation display and visualization.Computer languages and systems, unlike naturallanguages, dif- fer widely in "elegancefactors" of power and expressiveness. A languagefor data graphicsis elegant, in the sense used here, to the extent that it provides represen- tations of dataand processes which areboth simple andtransparent, so thatthe link between specificationand display-between the programstatements and the visible result-is readily apparent.What can we learn from the structureand process of programmingto duplicateMinard's March on Moscow graphic?Two examples provide some answers to this question. Mathematica(Wolfraam, 1991) was designed as a computersystem for doing symbolic mathematics, and also provides powerful facilities for visualization. It is similar to Lisp in certain respects, particularlyin its emphasis on list processing, recursion, modularity, function mapping, and the syntactic identity between user-defined and built-in procedures.Shaw and Tigg (1994) describe a function, NapoleonicMarchOnMoscowAndBackAgainPlot [ ], as a tour-de-force of Mathematica graphics. Their figure and the complete code (Minard.m)may be found on the GDV website. They use nested lists containing map (x, y) coordinates plus additional information to represent the strength of Napoleon's army, temperature,rivers, labeled points, and so forth. For example, the temperaturescale at the bottom of the graphicis representedas the list: 47

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TempData= { {0.955, 0.306, 0), {0.885, 0.304, 0), {0.700, 0.259, -9 }, {0.612, 0.228,-21 }, (0.433, 0.177,-11), {0.372, 0.170,-20), {0.316, 0.201,-24}, {0.279, 0.181,-30}, {0.158, 0.195,-26} ; where the final element in each sub list is the temperaturein degrees Reaumuras used by Minard.Using these lists, the program(in slightly simplifiedform) is just: NapoleonicMarchOnMoscowAndBackAgainPlot [ ] : Show [Graphics[ {ProcessStrength[StrengthData], ProcessTemp [TempData] , ProcessRivers[RiverData], ProcessBoxes [BoxData] , ProcessTitle[TitleData], ProcessPoints[PointData], ProcessText [TextData] } i ] Some of the Process functionsare complex, but most are simple uses of the idea of mappinga functionover a list. For example,all the riversare drawn simply by mapping the Line [ ] functionover the list of coordinatesrepresenting the rivers: ProcessRivers[riverdata_] := Map[({RGBColor[0, 0, 1], Thickness [0.001], Line [#] }&), riverdata] Each Process functionreturns a list of graphicsprimitives to the Graphics [ I function,which are renderedon the displaydevice by Show [ ] . Such simplicity,I believe, tells us somethingabout both the structureof Minard'sthematic map, and aboutthe capabilityof list processing and functionalprogramming to recreateit. A quitedifferent form of specificationis used by Wilkinson(1999), who describes a grammarfor representingthe data(variables, their attributes, transformations) and graphelements (coordinates,frames, scales, andguides) which compose a graphic, along with hints for how these may be implementedin an object-orientedgraphic display system. Wilkinsonrepresents the dataas seven variableswhich derivefrom a raggeddata table giving the maplocations (latitude,longitude) and name of cities, locations, dates, and temperaturesfor the temperaturescale, and the locations, direction (advance/retreat),and troop strengthfor the main display of successive losses over the campaign. A particularfeature of his analysis is to add a three- category "group"variable correspondingto (a) the main army, (b) the left-flank group going to and from Vilnius, and (c) the side-marchgroup to Polotsk. (In the Mathematicadata, this structureis representedimplicitly in the StrengthData using six sublists--one for each group,and for advance/retreat.)The particularfea- tures of the data structuremay or may not matter, but it is clear that parsing Minard's graphicinto these three groups is essential. Wilkinson notes that the graphic consists of two sub-graphics,the march and temperature,linked by the common horizontalscale of longitude. His analysis of the marchportion represents the graphicby the grammaticalspecifications, 48

This content downloaded from 130.63.134.82 on Thu, 6 Jun 2013 16:02:04 PM All use subject to JSTOR Terms and Conditions Visionsand Re-Visionsof Charles Joseph Minard FRAME: lonc*latc GRAPH: point(label(city), size (0)) GRAPH: path(position(lonp*latp), size(survivors), color(direction), split(group)) GUIDE: legend(color(direction)) where lonc and latc give the city locations,lonp and latp give locationsalong the paths in each direction, and survivors gives troop strength.Wilkinson says, "Theplot frameis determinedby longitudeand latitude;plot the names of the cities at theirlocations, and plot one pathfor each group,whose widthreflects troop strength,and is colored accordingto the directionof the march."The economy of this descriptionis againnoteworthy. (Wilkinson's re-vision also highlightedseveral anomaliesin Minard'sgraphic or thehistorical data; the most strikingis the largegap betweenthe locationslabeled "Dec. 6" and "Dec. 7" on the temperaturegraph, sug- gesting the improbablemovement of morethan 50 miles in one day at the end of the retreat.) There are certainlyfurther programming details necessary to display the complete graphicfrom these specifications,just as thereare with the Mathematicaver- sion, but these attempts have something useful and importantto say about the connection between specificationand display (and data) requiredin each. As we develop datavisualization systems in the future,it is well to rememberthat a computer language can be a tool for learning and thinking, as well as for doing. The kind of comparativeanalysis I have sketchedhere may prove helpful in the analysis and design of computersystems for graphics and visualization,and Minard's Marchgraphic may be a diamondstandard against which all should be scratched. Conclusions CharlesJoseph Minard was most definitelynot a "one-hitwonder." His graphic inventionswere numerous,his thematicmaps meticulouslydesigned to aid graphic communication,"to convey promptlyto the eye the relationnot given quickly by numbers"(Minard, 1862). This workinfluenced several generations of statisticians and cartographersand still has deep lessons from which we may learn,but regret- tably it is little known today. It is hoped that this re-visioning of Minardwill cor- rect thatto some degree andperhaps help rekindlea wider interestin the history of statisticalgraphics (Friendly & Denis, 2001). Some say, "Thosewho do not know theirhistory are doomed to repeatit", but, in the case of Minard,my only reply is, "If only we could!" Note Reproductionsof Minard'sgraphic works may be obtainedfrom the Multime- dia Library(M6diatheque) at the Ecole Nationaledes Ponts et Chauss6es(ENPC): 6 et 8, avenue Blaise Pascal, Cite Descartes, Champs-sur-Marne,77455 Marne- la ValldeCEDEX 2, France.Tel: +33 1.64.15.34.68.Fax: +33 1.64.15.34.79.Isaye@ enpc.fr;www.enpc.fr/docparis/media.htm. 49

This content downloaded from 130.63.134.82 on Thu, 6 Jun 2013 16:02:04 PM All use subject to JSTOR Terms and Conditions Friendly References Chandler,D. G. (1966). The campaigns of Napoleon. New York: Macmillan. Chevallier,V. (1871). Notice n6crologiquesur M. Minard,inspecteur gdndral des ponts et chausdes,en retraite.Annales de Ponts et Chausdes,2(Ser. 5, No. 15), 1-22. Friendly, M. (1994). Mosaic displays for multi-way contingency tables. Journal of the AmericanStatistical Association, 89, 190-200. Friendly,M. (2002). A brief history of the mosaic display. Journal of Computationaland GraphicalStatistics, 11(1), 89-107. Friendly,M., & Denis, D. J. (2001). Milestonesin the historyof thematiccartography, statistical graphics, and data visualization.Retrieved April 16, 2002 from http://www.math. yorku.ca/SCS/Gallery/milestone/. Funkhouser,H. G. (1937). Historicaldevelopment of the graphicalrepresentation of statistical data. Osiris, 3, 269-404. Harness,H. D. (1837). Atlas to accompanythe second reportof the railwaycommissioners, Ireland. Dublin: Irish Railway Commission. Lee, F., Hayes, J., & Thomas, A. (1989). The Hackers Test. LysatorUniversity. Retrieved April 16, 2002 from http://www.lysator.liu.se/-cordeci/hacktest.html. Marey, E. J. (1878). La methode graphique dans les sciences experimentales. Paris: G. Masson. MerriamWebster (2002). Merriam-Webster'sCollegiate Dictionary: Retrieved April 30, 2002 from http://www.m-w.com. Minard,C. J. (1862). Des tableaux graphiques et des cartesfiguratives. Paris: E. Thunot et Cie. ENPC: 3386/C 161. Minard,C. J. (1869). La Statistique.Paris: Cusset. ENPC: 3474/C171. Palsky, G. (1991). La cartographiestatistique de la populationau XIXe siecle. Espace, Pop- ulations, Societes, 3, 451-458. Palsky, G. (1996). Des chiffres et des cartes: Naissance et ddveloppementde la cartogra- phie quantitativefrancais au XIXe siecle. Paris:Editions de CTHS. Playfair,W. (1801). Statisticalbreviary: Shewing, on a principle entirelynew, the resources of every state and kingdomin Europe. London:Wallis. Robinson, A. H. (1955). The 1837 maps of Henry Drury Harness. GeographicalJournal, 121, 440-450. Robinson, A. H. (1967). The thematicmaps of CharlesJoseph Minard.Imago Mundi, 21, 95-108. Robinson, A. H. (1982). Early thematicmapping in the history of cartography.Chicago: University of Chicago Press. Roth, S. F., Chuah,M. C., Kerpedjiev,S., Kolojejchick,J. A., & Lucas, P. (1997). Toward an information visualization workspace: Combining multiple means of expression. Human-ComputerInteraction, 12(1/2), 131-185. Shaw, W. T., & Tigg, J. (1994). AppliedMathematica: getting started,getting it done. Read- ing, MA: Addison-Wesley. Tufte, E. R. (1983). The visual display of quantitativeinformation. Cheshire, CT: Graphics Press. Wainer,H. (2000). Visualrevelations: Graphical tales offate and deceptionfrom Napoleon Bonaparte to Ross Perot. Hillsdale, NJ: LawrenceErlbaum and Associates. Wallis, H. M., & Robinson, A. H. (1987). Cartographicalinnovations: An international handbookof mappingterms to 1900. Tring, Herts:Map CollectorPublications. Wilkinson, L. (1999). The grammarof graphics. New York: Springer.

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Wolfraam,S. (1991). Mathematica:A systemfor doing mathematicsby computer[computer program].Redwood City, CA: Addison-Wesley. Author MICHAELFRIENDLY is Professorof Psychology and the Coordinatorof the Statistical ConsultingService at York University,4700 Keele St., Toronto,ONT CanadaM3J 1P3; [email protected] specializes in psychometrics,statistical graphics, and the history of data visualization.

Received January2002 Revision Received January2002 Accepted January2002

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