The Fundamental Principles ofAnalytical Design Categories such as time, space, cause, and number represent the most general relations which exist between things; surpassing all our other ideas in extension, they dominate all the details of our intellectual life. If humankind did not agree upon these essential ideas at every moment, if they did not have the same conception of time, space, cause, and number, all contact between their minds would be impossible . Emile Durk.heim, Les formes e/ementaires de Ia vie religieuse (Paris, 1912), 22-23. I do not paint things, I paint only the differences between things. Henri Matisse, Henri Matisse Dessins : themes et variations (Paris, 1943), 37· ExcELLENT graphics exemplify the deep fundamental principles of analytical design in action. If this were not the case, then something might well be wrong with the principles. Charles Joseph Minard's data-map describes the successive losses in men of the French army during the French invasion of Russia in 1812. Vivid historical content and brilliant design combine to make this one of the best statistical graphics ever. Carefully study Minard's graphic, At right, English translation of item 28 in shown in our English translation at right. A title announces the design Charles Joseph Minard, Tableaux Graphiques method (figurative map) and subject (what befell the French army in et Cartes Figuratives de M. Minard, 1845-186g, a portfolio of Minard's statistical maps at the Russia). Minard identifies himself and provides a credential. A paragraph Bibliotheque de !'Ecole Nationale des Pants of text explains the color code, the 3 scales of measurement, and the et Chaussees, Paris, 62 x 30 em, or 25 x 12 in. This 1869 map is the last sheet in Minard's methods. Five data sources are acknowledged. lifetime portfolio. English translation by Then the Russian campaign of 1812-1813 begins. Dawn Finley, redrawing by Elaine Morse. 126 BEAU T I F UL E V IDEN C E 0 arte :Ji.9uralive c"'1''"""'-"""""'"'"·""&. .•..,., a....e·~;..~ .... ~"'"'A"'"'!'~""- ,._ ..J{LWO~ ./1 812-,-181 3. 6)~ ..J JL OtliMaxa, :'l.'f""' .... ~·~ ... 'l..·• .~er, .... k.<- "'-""~:<.'"-"" . , , , ~."-<- 2oJLwE«"""' 18 6:9· f,.,,,_.e,.u a~ rW~ .4D o -_..c..yU.leui~fa.f,.Ju~UY au ~u '~ .i.-taioi!otv..l:-.... mJt... ;t«..- 1 ""K.-a~"..;.re:_J.,_.~; ;f., .d .. - Cl~ IJi.u ~ta c.tt. lC.Wu.t \Moscou 3e.! .. J&t-4wj, 4 ilrdo«.-1.,._ rade..fl#t-di_f"id;L.- ~e.!. L....<Dur-<lU ~ ML-Je.,to>MKt(ll4 u V61 t i.WuJt.w,.-.){uoii LfL_.._,K.- cc ua:.- 1t Wt.tV_,dorti.t<t-. " _ ~~~ , ~ \ 3«M6 ~ otw<a~ a... Jtt.~ Chier.J1 J;,Jt/gur; d<.-cfeUJruJaL; tk-Cbamlm!!J n-~"""'"J.;.Jo~il--'.!c....1a co~ yf. -."...w...v~ L l'awc;v.alf "''d<-28 &Gt"tu.-. q.. ...c ...4.l-=-f.wu..jiJIJC..'.i..l'.,d.)..._..a~-".#c.)'.vr~1J'.W.-h • fr"JL 1 .wk t4tf' aM_.I?lc~0«; .. ~3"- Jfk«J,,.t O)""'D""';-'1"" a"' n.ic.ou-~ r; ~~ t <:tJ.& .:t , "-Jili~i<iiV' d---'JiL&J..w ~J~ ·••w tluJ."'c.t-- 'WU~K.,.,.,...~~.'j"lld"'"'"""~'"'~)'- ·•uv. \, \ "--J.F..-(,.. ... L.JJ.~} : ' ••• h Above, the original French version. This statistical map portrays the successive losses of the French Army in Napoleon's Russian campaign of 1812. The overall toll, French and Russian, was approximately 700,000 to 1,ooo,ooo. Described by E. J. Marey as seeming to defy the pen of the historian by its brutal eloquence,1 Minard's map exemplifies many 1 E.]. Marey, La methode graphique dans of the fundamental principles of analytical design. les sciences experimentales (Paris, 1878), 73: "Toujours il arrive a des effets saisissants, mais nulle part la representation graphique de la marche des armees n'atteint ce degre Principle 1: Comparisons de brutale eloquence qui semble defier la plume de l'historien." Beginning at the left, on the Polish-Russian border near the Niemen River, the thick tan line shows the size of the Grand Army (422,000 men, drawn from all Europe) as it invaded Russia in June 1812, as well as the army's path. As the soldiers die, the line narrows; the flow-line indicates the number of remaining soldiers at each position on the map. Also shown are movements of auxiliary troops, who sought to protect the rear and flank of the advancing army. In September, the 100,000 surviving troops reached Moscow, which was by then sacked, deserted, on fire. The departure from Moscow is depicted by the dark lower line, in turn linked to a temperature scale and dates in the statistical graphic at the bottom of the chart. During the retreat, it was bitterly cold and many soldiers froze and starved. Crossing back over the Niemen River with 10,000 survivors, the army struggled out of Russia. At the end, the map notes: "The Cossacks .£es LO.iat;u..eJ pa.Y.feflC iUb yalop [Russian horsemen] pass the frozen Niemen at a gallop," driving out f.e, .Ni6nuv Jdi . the scattered remnants of Napoleon's Grand Army. PRINCIPLES OF ANALYTICAL DESIGN 127 And it is at the Niemen River, where the invasion began and ended, that we see a small but poignant illustration of the First Principle for the analysis and presentation of data : Show comparisons, contrasts, differences. The fundamental analytical act in statistical reasoning is to answer the I question "Compared with what?" Whether we are evaluating changes over space or time, searching big data bases, adjusting and controlling for variables, designing experiments, specifying multiple regressions, or doing just about any kind of evidence-based reasoning, the essential point is to make intelligent and appropriate comparisons. Thus visual displays, if they are to assist thinking, should show comparisons. Minard makes several vivid comparisons, some over many months, others during the course of a few days. At the war's beginning, the army crossed the Niemen River with 422,000 soldiers, shown by the number itself and represented by the width of the tan line. At the end, 1o,ooo soldiers returned back across the Niemen, as indicated by the number itself and the thin black line concluding the retreat. Only 1 soldier in 42 survived this futile campaign (the widths of the black I tan lines at the Niemen River were inaccurately constructed in a ratio of 1 to 28). This graphic comparison at the Niemen summarizes the slaughter, 6 months from start to finish. At the Berezina River, another comparison. During the retreat (west­ ward, to the left), the black line crossing the river abruptly diminishes­ from so,ooo to 28,ooo soldiers, as 22,ooo died in 2 days. This change in line weight represents, in a blunt and incomplete way, the terrible events at the Berezina, described by Philippe-Paul de Segur (aide de camp to Napoleon, and a source cited by Minard): It was the twenty-eighth of November. The Grand Army had had two whole days and nights in which to effect the crossing, and it should have been too late for the Russians to do any harm. But chaos reigned in our midst. ... an immense confused mass of men, horses, and vehicles besieged the narrow entrances to the bridges and began to flow over them. Those in front, pushed by the weight of those behind or halted by the river, were crushed, trampled on, or forced into the ice-filled water of the Berezina. From the horrible, formless mob there arose a sort of dull murmur which swelled at times to a wild clamor mingled with groans and awful imprecations .... The confusion was so great that when Napoleon himself wished to cross at two o'clock, it was necessary to use force to clear a passage for him.... Then, as in all extreme situations, hearts were laid bare, and both infamous and sublime actions were witnessed. Some there were who, determined to pass at all costs, cut a horrible way for themselves with their swords. Others opened an even crueler road for their carriages, driving them pitilessly through the helpless crowd, crushing 2 Count Philippe-Paul de Segur, Napoleon's men and women, in their odious greed sacrificing their companions in misery Russian Campaign (New York, 1958), 246, 2 249; translated by]. 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