Statistics by Mr. Minard, Inspector General of Bridges and Roads in Retirement.

Charles Joseph Minard, La Statistique (Paris, 1869), translated by Dawn Finley, August 2003



Statistics is the recording of similar facts in a systematic, numeric or chronological order.

Memory is the intuitive recording in the mind of ideas or of sensations, which have more or less made an impression on us.

Statistics is a knowledge acquired by experience and from which we deduce the consequences by reasoning.

Memory is an involuntary and primordial faculty of the soul, indispensable to all reasoning. 

By pointing out at the beginning the analogy between Statistics and one of the elements necessary to our understanding, I wished to liberate it from the inferiority where it has been placed by the learned; because if memory is indispensable for the acquisition of our intellectual knowledge, Statistics is the basis of several sciences at which we would not have arrived without it.  I am going to attempt to show this and in that way I will free Statistics from the kind of scorn where it remained for a long time.

Today opinion is modified; we have been enlightened on the real merit of Statistics since we are more occupied with the sciences; we have recognized the necessity of Statistics for some of them and its usefulness for others.  If there are some purely intellectual sciences, like [1] geometry, there are others for which Statistics is the origin and the foundation.

There is moreover a new genre of Statistics which is becoming more widespread these days and which distinguishes itself by the intervention of form; it is a Statistics at once figurative and numeric.  The applications, rare in other times, are numerous today.

An infinity of facts, of ideas, of principles, only have strength by the number of those who agree to them, so that they only acquire the title of truths by the comparison of numbers for or against, that is to say by the results of statistical research.

We could even establish three categories, one of those who advance a fact prone to controversy, the other of those who deny it, and the third of those who do not find any reason to have an opinion.

To give some examples:

Is there in the human heart some principle of justice, concerning good or evil, which we can apply to others?  In a word, is man born good or evil or neither one nor the other?

Consult the philosophers.  Some say yes, others say no, and there are even those who have said yes in one passage of their writings and no in others, so that to tell the truth, one does not know absolutely what they think.  Would it not be necessary, if one wanted to know how to leave it, for those who find in their heart no determining feeling, to do the Statistics which I indicate?

After it was found that electromagnetism has an effect on animal husbandry….. a German (I believe) thought that there was a great electrical current always flowing from the East to the West[1] at the surface of the earth, and that the recumbent position of a sleeping man being ordinarily the straight line from the feet to the head, he who has passed a great part of his life in the same bed has been pervaded by this current, whenever the length of the bed was in this direction; that accordingly the electromagnetic action producing always the same result during a third of his life, should result in physiological effect, to which this German thinks that we can attribute the different degrees of longevity.

What index did he have of this effect?  What proof of it did he give?  [2]  I am not aware of any; but it seems to me that the method to ascertain it would be to compare, all things being equal otherwise, as much as possible, the longevity of persons who have slept for a long time in beds having the same orientation; it is then statistical research alone which would be able to illuminate the question.

In 1863, in a crowded scientific meeting at Newcastle, a competent man declared that England would not have more coal at a reasonable price in two hundred sixteen years.  Great was the emotion of the assembly.  Little by little the alarm spread abroad and the question came to Parliament in May 1866.   The most contradictory opinions on the duration of saleable coal in England were found there.  The government acknowledged that it did not have sufficient information to respond.  In that case everyone, government, Parliament, manufacturers, tradesmen, scientists felt the necessity of complete Statistics for the coal banks of the United Kingdom, for their layers, for their depth, etc.  Accordingly, 28 June 1866, the Queen named, to do research and to draw up these Statistics, a commission composed of twelve members of the most illustrious competence.

Such is the homage paid to Statistics by one of the most enlightened people of the world.  Unfortunately Statistics alone cannot reassure England, because if it can say what quantity of coal is hidden in the depths of the earth, the figure of the future waste remains unknown in the depths of human ignorance; only providential foresight can tell.



The science of legislation begins as it were with Statistics.  In the Spirit of the Laws how did Montesquieu proceed?  He did not take men in the state of nature and search metaphysically for the laws to which they had to be subjected in order for them to live in society, nor what kind of government to ascribe to them.  He takes the societies such as he finds them with diverse governments; he considers, as d’Alembert says[2], the habitants of the universe in the real state where they are and in all the contacts they can have among themselves; he [3] occupies himself more with the laws that we have made than with those that we should have made.  His work, so highly esteemed, was hence conceived at the start in a spirit of analytic, descriptive, sometimes chronological Statistics.



What is physiology?  The explanation of the functions of the organs of the human body; but in order to better understand the interplay, words are not sufficient; it is necessary to see the configuration of the organs, and [the way] this varies with the sexes and age; from it one derives the demonstration of an anatomy, that is to say a description of the organs, at once figurative and chronological.  Thus treatises on physiology do not contain less than thirty illustrations for the embryo and the fetus, with various enlargements.

This is not yet all.  Functions having the same aim take place in organs of varied forms in the different animals; we soon recognized that the explication of the functions of human organs could be better remembered and more perfectly comprehended by  examination of the forms and similar organs of the animals, where there are very remarkable functions among some and almost none among others.  Also one finds today in the dissertations on human physiology several examples of comparative physiology.  Consequently, one sees what extension anatomical statistics takes.  Finally, the study of human physiology is accompanied by an anatomy of which figurative and chronological statistics becomes each day more extensive and more useful.



A lot of natural sciences have had as a base Statistics which are unique to them.

Tournefort had founded his botany on a figurative statistics of the flowers of the vegetables that he classed in diverse families, of which the names indicated the shapes of the corollas.

Thus, he had the family of the Papilionaceous, that of the Labiates, that of the Cruciferous, etc.

The eminent Linnaeus reversed these Statistics, and substituted for them his own founded on the number of the stamens.  Thus, he has the genres [4] Monandrious (one stamen), Diandrous (two stamens), Tetrandous (four stamens), etc.



A curious example of figurative Statistics is given by Mr. Baudoin in his handsome report on primary education and special teaching in Germany.  This inspector general of public instruction has added to the text and to the figures more than thirty colored figurative tables, which represent at once the nature, the succession and the time of studies, and make understood consecutively the course and the progress of the teaching.  One of the most remarkable[3] is that of Realschulen du Wurtemberg, where one follows with the eye the greater and greater curtailments of Latin from 1818 until 1864, the year when it was completely abolished[4]. 



What would paleontology be, that is to say the description of animal and vegetable fossils, if we did not add to it the order in which we suppose that they followed one another, that is to say chronological and figurative Statistics of these primitive beings?

Thus Mr. Bayle, the knowledgeable professor of paleontology at the school of Mines, has given an ingenious application of figurative statistics, in order to show the appearance on earth of animal fossils.

Here is the table that he drew for his course (1854) to show the appearance of Trilobites.

On a horizontal line were written the formations; on a vertical column were written the kinds of Trilobites.

Then drawing the horizontal zones from the nominal columns of types and interrupting them under the titles of formations in which one has not yet found the designated types, one has figurative statistics indicating the chronological appearances of Trilobites contemporary to the formations (See the diagram hereafter).  [5]




The geographer Berghaus has drawn up some very curious maps of the world where zoological statistics are established by the representation of the special animals of each country.  Thus the tiger represents India, the camel Arabia, the kangaroo New Holland, the giraffe the center of Africa, etc.

To move from the serious to the humorous, I remember the map of France for the epicure, where the Statistics of the départements are shown by the gastronomic masterpiece of each of them; thus the département of the Bas-Rhine is designated by the pâté de foie gras of Strasbourg, the Meuse by the confections of Bar, the Areyron by the cheese of Roquefort, Saône-Loire by the poularde of Bresse, Lot-et-Garonne by the terrine of Nérac, etc.



Facts similar to each other have been represented by intensities of color; we know the ingenious system of maps of instruction and of criminality in the départements by Senator Dupin, distinguishing each of them by tints more or less dark.  This representation indicates more or less, but not how much.  Because the eye, which can distinguish the resemblances of lengths, is powerless to number the intensities of one color, it cannot tell from two red tints that one is two or three times more red than the other.

I thus sought to remedy the inconvenience, and I imagined the production of diverse tints, like the engravers make by parallel lines, but in exact proportion to the fact that one wants to represent.  The intensity becomes thus a geometrical consequence susceptible to a numerical enunciation.

I presented, in 1866, the first example of my process of tints determined geometrically in a map of the populations of specific provinces of Spain.  [7]



I had imagined graphic tables representing the numbers of travelers circulating on the railways.  On a table published in one hundred copies in 1844, a horizontal line indicates the lengths between the stations, and the height of each rectangle written between two stations represents proportionally the number of travelers that have passed there.

I had also imagined figurative maps indicating the number of travelers passing on the routes by the widths of the colored zones, proportional to the numbers of travelers that pass there annually.

The first map drawn in this system, in two hundred copies, appeared in March 1845, at the Council of Bridges and Roads, at the occasion of the railway projects between Dijon and Mulhouse.  Inspection of the map determined the preference for the valley of Doubs; it does not contain a single figure; it rendered the eye alone judge of the question.

It is said that before my figurative maps, there were other expressive maps; but mine not only speak, even more they count, they calculate by sight: it is this perfection that I introduced with the rectangles in my graphic tables and by the widths of the colored zones in my figurative maps.



One realizes that by substituting goods for travelers, my maps and my graphic tables have spontaneously had numerous commercial applications.  Thus I published in 1845 the first graphic table that has appeared on goods passing on the canal du Centre.  Thus, published during each of the seven years from 1853 to 1862, my figurative maps give the most striking Statistics making distinguishable in plain sight the tonnages which pass on our lines of water and rail, and making it possible to judge next, with the eye and without calculation, the parts where there is the most commercial movement in France.  Figures written transversely to the colored zones give further the exact quantities.  [8]

I applied this process to the special transport of wines, of cereals and of coal in France, and of animals arrived by railroad in Paris in 1862.

Extending my process, I drew figurative and statistical maps of the annual importation of cotton in Europe before, during and after the civil war in the United States of America, making the eye able to judge the quantities arrived by sea from producers of cotton of diverse countries, and showing relative aid that they brought us in the stages of this critical period, the biggest commercial catastrophe in the world.

I had also represented, by this same process, in two figurative and statistical maps, transport by sea: first of the exportations of our wines in 1864; second of the emigrants in 1858; in a third, the movement of travelers on the railways in Europe in 1862, and finally recently, in a fourth, the importation to France of cereals in the year of scarcity, 1867.

The statistical principle of copious applications, their imitation by the Ministers, by the railroad companies, etc., proves their utility; their numerous applications have proved a rapid growth of figurative statistical richness to which I am pleased to have given wings and to have largely contributed.



Among the sciences to which I would like to show that Statistics has been not only useful, I will cite one that is most elevated by the facts it occupies itself with, by the attainments that it requires, and by the immensity to which it extends: I wish to speak of astronomy.

At first glance, one does not see that numeric tables are able to attain truths as sublime as those which result from them.  Yet nothing is more true.

What would we know about the stars and the planets without the observations that Hipparcus recorded two thousand years ago in tables, veritable stellar and planetary statistics of the sky?  [9]

One cannot call into question the utility of these Statistics, when one reads what one of the grandest astronomers of the century wrote about them, speaking of the observations of Hipparcus concerning the moon.  “This result, fruit of immense work on a very large number of observations, is perhaps the most precious monument of ancient astronomy through its exactitude, etc.[5]…”  And later one reads: “Hipparcus undertook a catalog of the stars at the occasion of a new development which appeared in his time… the fruit of this long and laborious enterprise was the important discovery of the precession of the equinoxes.”

Certainly, I do not pretend that this discovery is due to the stellar statistics of the sky; Hipparcus was needed in order to draw a conclusion from them, but without the ordering of the facts, he would not have been driven to the inference.

We only know well a few of the observations of Hipparcus transmitted by Ptolemy in his Almageste; but “their comparison with modern observations made of them recognize their exactitude, and the utility they still have for astronomy makes us regret the loss of others[6].”  There are therefore statistical results the loss of which one regrets; one must remember at the same time the wide usefulness of Statistics applied to astronomy.

Without carrying ourselves too far back in the past, we come to the times of Tycho, of Kepler, of Copernicus.

Tycho, near the end of the sixteenth century made, during twenty-one years, a prodigious number of observations and transmitted to Kepler a precious collection of them.  Through their comparison, this one proceeding from hypotheses within hypotheses and excluding those which deviate too much from the observations, he came to establish his famous laws on the movements of the planets in their orbit: first the areas proportional to the time; second the squares of time between them like the cubes of the great axes of the orbits.  These laws are not the direct results of his observations and those of Tycho, but through them, Kepler was led there as Hipparcus had been led to the precession of the equinoxes by the catalog of the stars, and Kepler ordered his laws in conformity with his observations in the rudolphine tables, forever memorable in astronomy as derived from the statistical facts.  We hasten to say that he [10] finished establishing his laws of the squares of time proportional to the cubes of the large axes of the orbits only after seventeen years of fruitless experiments on the analogy of the conic sections known by the Greeks with the planetary movements.

The utility and application of Statistics to astronomy did not stop with Kepler; more than a century after him, Bradley, who discovered and explained the aberration of the stars, left an immense collection of observations of all the phenomena that the sky presented in his times during ten consecutive years; their large number and their precision make this collection one of the principal foundations of modern astronomy[7].  This judgment of Laplace on the statistical collection of the observations of Bradley is one of the most beautiful eulogies that has been made of Statistics.

Thus observations, and always observations recorded and forming at different times the Statistics of the sky, have accompanied, if not brought about, from century to century discoveries in astronomy; one cannot then refuse to place Statistics in the same rank as geometry, optics and other sciences for usefulness in astronomy.



In history Las Cases devised his chronological tables in order to show the contemporary kingdoms and monarchs; and it is still the best method to make the mind embrace the chronological order of historical events by the statistical method.

It is said that Mailly, professor of history at the College of Dijon in 1787, had preceded him in this idea by placing in the columns at the side of the text the contemporary kings written on the same horizontal line for each epoch.

We find elsewhere an ancient application to history of statistics at once figurative and chronological, in what is called the family tree of a princely family of which the descendants are represented figuratively with a happy analogy by the branches of the tree deriving from the principal trunk and the branches of others like the generations of the same family.

The ideas of statistics are conveyed very differently [11] according to the inclination.  Thus, in the history of facts, we see Raphael adopt in his Bible a figurative statistics showing, in the same engraving: first, Abraham to whom God gives the order to sacrifice Isaac; second, next to that, a little more distant, we see him drawn in a smaller size walking with his son who has the appearance of asking him where the victim is to be sacrificed; third, much more distant in the country, we see him again drawn in a very small size raising the knife in order to sacrifice Isaac and above him an angel restraining his arms and showing him the ram to be substituted for Isaac.  Here is a very singular kind of figurative statistics, where Raphael employed the diminution of the forms in order to represent in the same engraving the different phases of the same story.

Another example of figurative historical statistics is given to us by a very different nation, country and epoch.  A similar tableau of ancient Mexican hieroglyphics tells of the misdemeanors of the governor of a province in revolt, his punishment, that of all of his family, and the vengeance excised by his subjects against the messengers of the state bringing orders from the King[8].

In considering the applications of Statistics to history nothing appears to be inadmissible; but here an Englishman, Henri-Thomas Buckle, gave to it recently (1860) a more elevated scope and attributes to it a very debatable power.  He seeks there the principles of an exact science; he hopes to find facts, which he does not indicate, exposed in a statistical order, the laws which govern history, like those which govern the movement of the stars.  Buckle founded his system on the assumption that the facts which at first appeared not to be subject to laws are found, by the statistical research done on them, to have an unexpected regularity, be it by their number, or by their periodic recurrence.  In the examples of facts which have appeared to escape these laws, and which have come to fall into those indicated by Statistics, he cites the origin of marriages in England of which the number for a century depends on the average of salaries and of profits, instead of following the morals, the thoughts, and the sentiments common to the contracting parties.  He cites the murderers, of which the number, and even the instruments of the crime, are in constant proportion to the population; he adds that even the suicides are among them.  In these examples, one does not see the circumstances, [12] as in the first through which Statistics shows the parallel progress; in the example of the marriages, there is a certain connection: the same salaries, the same profits of the individuals which, by matching them, lead to the marriages.

The law is natural, self-explanatory, and even though this law of marriages was found accidentally, it could have been found in the Statistics of the average salaries and profits, since the idea of a relationship between these and the marriages was natural enough.

But since the Statistics of the yearly murders and suicides were found among several peoples, and their constant proportion to the known population, we still find nothing there which bears the trace of a relationship with the laws of the history of these peoples.

These two examples have been unfruitful in providing support for Buckle’s system in the research of the laws of history that he expects from Statistics, and yet the facts he considers are not without relationship to morals, and consequently, to history.

He cites other examples of which the causes are unknown; among others, the letters thrown into the mailbox without addresses, of which the number is proportional each year to the total number of letters.  Here the example is not a happy one; there is not a law which determines the number of letters without addresses other than the thoughtlessness of those who write the letters; or one can easily believe that in twice as many correspondents there is twice as much thoughtlessness.  It has been a long time since a supposition of the same nature was made for the troops, where one hopes to find two times as many young people of a certain size in twice as many recruits, and in recent times there has been in France some alteration in this proportionality; it has not been researched among them the cause of a change in the physiological laws of the generation; this alteration has been related to a change in the habits of hygiene, nutrition, and exercise to which these young people are subject[9].

Here appears one of the difficulties of Buckle’s system which attempts, the components of Statistics being given, to date back the effects to the causes, which is to say to distinguish, among the many causes which have an effect on history, those which have produced the effect presented by Statistics.

Nonetheless these difficulties did nothing to stop Buckle, and he hopes, [13] with the help of Statistics, that in one hundred years the regularity of the moral world or the laws of history will be established.

But do these laws of history exist, as we have already asked?  And effectively, in the century where we have seen the appearance of steam ships, railways, electric telegraphs, photography and electromagnetism and so many other scientific feats; in a century where we sought so much progress which has had and will have so much influence on the future of humanity, is this not a peculiar time to expect immutable laws of history, statistical facts which would result by themselves from all the changes which are going to take place?

I have expanded a little bit on Buckle’s system, because he offers a curious interpretation of Statistics, even though it appears to me to be chimerical, or at least a very rare success in the consequence that he hopes to elicit from it for history.


Paris, 27 March 1869. [14]

[1]Ampere,” by Babinet, Revue des Deux-Mondes, 1857, 15 April, p. 841.

[2] Eulogy of Montesquieu, by d’Alembert.

[3] P. 382 of the Report.

[4] Regarding the table of Mr. Baudoin I have made another representative in its form, according to information sent to me, of the progressive increase in the number of students showing in that way the approval, by the fathers of the families, of the suppression of the dead languages.

[5] Système du monde [System of the world] by Laplace, 3rd edition, p. 332.

[6] Système du monde [System of the world] by Laplace, p. 334.

[7] Système du monde [System of the world] by Laplace, 3rd edition, p. 367.

[8] Monuments des peoples indigenes de l’Amérique [Monuments of the indigenous peoples of America], by A. Humboldt, p. 225.

[9] Treatise of Mr. Broca, on the supposed degeneracy of the French population.— Revue des cours scientifiques [Review of scientific currents] by Mr. Young and Mr. Algavi, 20 April 1867.


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