Classics of Data Visualization on Visualizing.JP

A Country's Extent as the Area of a Circle, the Weight of Its Tax as the Direction of a Dotted Line: Playfair's The Statistical Breviary, Chart 1

Sun, 12 Oct 2025 00:00:00 +0900

In 1801, in Chart 1 of The Statistical Breviary, William Playfair (1759–1823) drew the extent of the countries of Europe as the area of circles. Population and revenue are shown by vertical lines standing on either side of each circle, measured on the same scale. The tops of the two vertical lines are joined by a dotted line. In his text, Playfair writes that which way the dotted line rises shows whether taxes are heavy in proportion to population.

The sources are the book’s preface, pp.13–16, where he explains how to read the chart, and the country-by-country tables. I read the text in the Bodleian Library copy on the Internet Archive. Because the foldout plates were not captured correctly in that scan, I show the chart from the 1802 French translation. How the circles are divided is covered in an article comparing the two circles of 1801 and 1805, and the 1805 chart is covered in an article on the 1805 United States pie chart.

Photograph of the plate of Chart 1 in The Statistical Breviary

Chart 1 in the French translation. Circles are arranged in order of size, from the large Russia at the far left to the United States at the far right. Red and yellow vertical lines stand on either side of each circle, with their tops joined by a dotted line

The whole plate, original drawing by William Playfair, engraved by Adam (French translation, 1802). Source: David Rumsey Map Collection, David Rumsey Map Center, Stanford Libraries / Internet Archive (CC BY-NC-SA 3.0)

Four Charts Born from the Supplement to a Table

According to the preface, it began with helping with someone else’s book. The editor of the English edition of Boetticher’s statistical tables asked him for a table supplying the changes since publication. Partway through that work, he writes, he realized the following (preface p.3).

it occurred to me, that tables are by no means a good form for conveying such information

In short: tables are not at all a good form for conveying this kind of information. On p.4 he says that when proportion and magnitude are at issue, appealing to the eye is the best and quickest way.

The book appeared in London in 1801. According to Chris Pritchard, it runs to 64 pages, most of them tables by country, with four plates. The contents of the four are listed on p.14.

Chart 1: Europe before the French Revolution
Chart 2: Europe as projected by the peace of Lunéville
Chart 3: The populations of the capitals of Europe
Chart 4: The countries of Hindustan

The original wording for Chart 1 is “Exhibits the powers of Europe as they were previous to the French Revolution.” What is drawn is Europe before the Revolution, not Europe as of 1801. 1801 was the middle of the French Revolutionary Wars, and Chart 2 draws the picture after the Treaty of Lunéville in February (Pritchard 2021).

Charts built from lines were not new for Playfair. On p.15 he writes that about fifteen years earlier he had applied lines to commerce and finance; this refers to The Commercial and Political Atlas. The Statistical Breviary came out in Paris the following year, 1802, in a French translation by D.-F. Donnant, and the plates were re-engraved with French text.

The Reading Instructions Are in Two Pages of the Text

Chart 1 has no legend. How to read it is set out in the text, pp.13–14. The key passage about the vertical lines is this.

The yellow lines on the right of each nation represent the revenue in millions of pounds sterling, measured also upon the same divided scale with the population.

The yellow line on the right represents revenue in millions of pounds, measured on the same scale as population. Just before this he writes that the red line on the left represents population in millions, and that the scale, one division per million, is numbered “at both ends.”

Population and revenue are measured on one and the same scale. The numbers appear at the left and right edges of the chart so that either can be read from both sides. It is not a dual axis, with the left for population and the right for revenue.

Turning the text’s explanation into a table of data and appearance gives the following. The example is France (before the Revolution), with figures from the table on p.33.

Data	Appearance	Example: France
Extent of the country (square miles)	Size of the circle; arranged from left in descending order of size	Circle
The extent figure	Number inside the circle	149,000
Population (millions)	Height of the red vertical line to the left of the circle	26
Revenue (millions of pounds)	Height of the yellow vertical line to the right of the circle, on the same scale as population	19
Weight of tax relative to population	Which way the dotted line joining the tops of the two vertical lines rises	Falls to the right
Population density (people per square mile)	Number directly above the circle	174
Maritime or land power	Color of the circle; green for maritime powers, pale red for land powers	—

The number above each circle is population density, not revenue. The text itself gives examples: “5 over Russia, and 14 over Sweden.” If you read France’s 174 as revenue, it is wildly at odds with the table’s £19 million.

In the French translation’s plate, the circles are colored blue and red. France, Spain, Britain and others are blue; Poland, Prussia and others are red. The maritime powers that the English text calls “green” can be read as having become blue in the French translation.

Only the circles for Russia and Turkey are divided inside. In Russia the inner circle is European territory and the outer ring is Asian territory; Turkey is split into sectors by continent. The text does not explain this division. Here the colors stand for continents rather than maritime or land power. It can be read as the colors carrying two different meanings within a single chart.

The circles of the Russian Empire and the Turkish Empire

Making Countries’ Shapes into the Same Circle

Why draw countries as circles? Playfair gives his reason on p.15.

for where forms are not similar, the eye cannot compare them easily nor accurately. From this circumstance it happens, that we have a more accurate idea of the sizes of the planets, which are spheres, than of the nations of Europe which we see on the maps

Where forms are not similar, the eye cannot compare them easily or accurately; so we have a more accurate idea of the sizes of the planets, which are spheres, than of the nations of Europe that we see on maps. In the preface, p.6, he also writes that when the eye sees similar forms it cannot help comparing their sizes.

On how the size of a circle is determined, the text does not say “proportional to area.” The preface’s phrase is “proportional circles.” I measured the plate of the French translation (the image above, 2000px wide): Russia’s circle has a diameter of about 410px and France’s about 68px. Taking France’s diameter as 1, area-proportional circles would give Russia about 5.6, and diameter-proportional circles about 31. The measured ratio is about 6, so the diameter is roughly proportional to the square root of the extent. Even allowing for measurement error, this is a value consistent with area proportionality.

The circles are arranged from left to right in order of size. On p.7 Playfair writes that on seeing this chart one will be struck by the size of Russia and Turkey. He continues that one will also be struck by the smallness of the nations that have moved the world these five hundred years.

He also decides what not to draw. On p.15 he writes that he combined extent, population, and revenue in one chart because they are the foundation of a power that can be accurately measured. He goes on to say that the form of government and the virtue of individuals also affect a nation’s strength, but cannot be shown in a chart.

The Direction of the Dotted Line Divides at “One Pound per Person”

The explanation of the dotted line spans p.13 to p.14.

The dotted lines drawn between the population and revenue, are merely intended to connect together the lines belonging to the same country. The ascent of those lines being from right to left, or from left to right, shews whether in proportion to its population the country is burdened with heavy taxes or otherwise.

The dotted lines are there to connect the two lines belonging to the same country. And which way a dotted line rises shows whether the country is burdened with heavy taxes in proportion to its population. Read only the first half, and the dotted line is merely a connector. It is the second sentence that gives the dotted line meaning.

Because population and revenue are on the same scale, a dotted line rises to the right when the revenue figure exceeds the population figure. That is, it is a country where tax per person exceeds one pound. Let us check against the tables in the text (£1 = 20 shillings).

Country	Population (millions)	Revenue (millions of pounds)	Tax per person in the table	Dotted line
Russia	25	7.3	6s 8d	Falls to the right
France	26	19	14s 8d	Falls to the right
Spain	11	14	£1 5s 5d	Rises to the right
Britain and Ireland	14	27	£1 18s 3d	Rises to the right

The figures are from the tables on pp.19, 33, 35 and 37. In the chart, the dotted line rises to the right for only four countries: Spain, Britain and Ireland, Portugal, and the United States. Those are also the only four countries whose tax per person in the tables exceeds one pound.

The section with Poland, France, Spain, and Britain and Ireland. France’s dotted line falls to the right, those of Spain and Britain rise to the right, and Britain’s rises most steeply

Detail cropped from Chart 1, original drawing by William Playfair, engraved by Adam (French translation, 1802). Source: David Rumsey Map Collection, David Rumsey Map Center, Stanford Libraries / Internet Archive (CC BY-NC-SA 3.0)

It matters that Playfair speaks only of the direction in which the line rises. On a common scale, direction works correctly as a binary split at “one pound per person.” The text’s explanation can be read as promising that much and no more.

The steepness of the slope is a separate matter. The two vertical lines stand touching the left and right edges of the circle, so the horizontal gap between them is the circle’s diameter. The slope of the dotted line is the difference between revenue and population divided by that diameter. Russia has a large difference, but its circle is large, so its dotted line is gentle. Britain has a difference of 13 and a small circle, so its dotted line rises steeply. The country’s extent gets mixed into the steepness of the slope.

How Third Parties Saw the Chart

The David Rumsey Map Collection’s catalog entry for the French translation quotes a comment by Akerman and Karrow. Their view is that the circles for countries’ extent, the sectors of Turkey, and the lines for population and taxes are “a creative combination of different visual forms.”

It was Pritchard (2021) who criticized the slope. He sums up the novelty as three things: the area-proportional circles, the division of Russia and Turkey, and the vertical lines with the sloping lines joining them. He then writes:

a direct comparison of these lines, one country to another, is not possible because each gradient is affected by the radius (and hence the area of the country)

The point is that because the slope depends on the circle’s radius, that is, on the country’s extent, it cannot be compared from one country to another. Jonathan Sachs makes the same point in a note, naming Funkhouser (1937) and others. Incidentally, Pritchard writes that population is read on the left scale and the budget on the right, which conflicts with the text’s “the same divided scale.”

Sachs’s main argument is in the history of ideas. He gives weight to the replacement of irregular national territories with “uniformly scaled circles.” If wealth is measured as revenue, a quantity, then wealth is not the same as the extent of territory. He reads this chart as a rebuttal to those who held that territory and population are wealth.

Juliana Adelman (2018) of The Irish Times focuses on intent. She writes that what Playfair most wanted to show was the advantage of the United Kingdom, which raised large revenue from a small territory and a small population. She then adds that overseas colonies are not counted.

Uses

There are four things to take away from Chart 1.

The first is to put things into the same shape before comparing sizes. On a map, countries’ extents are hard to compare. Playfair replaced them with identical circles and left the work of comparing to the eye.

The second is that putting two quantities on the same scale lets you read the relationship between them. By putting population and revenue, which have different units, on one numerical scale, he made a dividing line of “one pound per person” appear on the chart.

The third is that if you show a derived quantity by slope, you should keep the horizontal gap constant. In Chart 1 the gap is the circle’s diameter, itself data, and the country’s extent got mixed into the weight of tax. If you want to show tax per person, drawing that value directly is more reliable.

The fourth is to put the instructions for reading beside the chart. In Chart 1, the reading instructions exist only in the text. If you cut out the chart alone, you could easily misread the population density above a circle as revenue.

On p.16 Playfair writes that the greatest criterion is what remains in the mind of someone who looks at it for the first few minutes. By my count, Chart 1 tried to show six things in those few minutes: extent, population, revenue, population density, maritime or land power, and the weight of tax. The slope of the dotted line can be read as the awkward part that this cramming produced.

References

Primary sources

William Playfair, The Statistical Breviary; Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe, London, 1801 (Bodleian Library copy, digitized by Google). Internet Archive / Full text / Google Books
William Playfair (trans. D.-F. Donnant), French translation (Paris, 1802), Chart 1, “Carte statistique représentant l’étendue, la population et les revenus des principales nations de l’Europe”. David Rumsey Map Collection. Copy on the Internet Archive

Secondary sources

Chris Pritchard, “Life of Pie: William Playfair and the Impact of the Visual,” Mathematical Association, Presidential Essay No.4, July 2021. PDF
Jonathan Sachs, “1786/1801: William Playfair, Statistical Graphics, and the Meaning of an Event,” BRANCH. Article
Juliana Adelman, “The man with a finger in many pie charts,” The Irish Times, 2018-03-05. Article
Catalog entry of the David Rumsey Map Collection for Chart 1 of the French translation (quoting Akerman & Karrow). Copy on the Internet Archive

The Same Square Miles, Drawn as the Area of a Circle and as the Angle of a Sector: Playfair in 1801 and 1805

Sun, 12 Oct 2025 00:00:00 +0900

William Playfair (1759–1823) drew the same quantity, a country’s extent in square miles, in two ways. In his 1801 chart, he drew it as the area of a separate circle for each country. In his 1805 chart, he drew it as the angle of a sector cut from a single circle. In his own words, the former is meant to show the sizes of countries to the eye, and the latter the proportions among the extents of the provinces.

The 1801 chart is Chart 1 of Playfair’s book The Statistical Breviary. The 1805 chart appears in Statistical Account of the United States of America, Playfair’s English translation of a book by D. F. Donnant. Following the two original books, both readable on the Internet Archive, this article looks at what each circle lets the eye compare and what it does not.

1801: Lining Up Countries by the Size of Circles

Photograph of the plate of Chart 1 in The Statistical Breviary

The Statistical Breviary appeared in London in 1801. Its title page says it is accompanied by stained copper-plate charts. Chart 1, in the text’s own description, shows the countries of Europe before the French Revolution. The image below is the same chart from the French translation published the following year.

Chart 1 in the French translation. The large concentric circle at the far left is Russia, and the circle divided into sectors to its right is Turkey. The circles for the countries get smaller toward the right

The explanation on p.13 of the text is brief. Each circle stands for one country, the countries are arranged in order of extent, and the number inside each circle is that country’s square miles. The preface calls this a way of representing the sizes of countries with “proportional circles.” The reason for using circles is given on p.15.

The present charts are in like manner intended to aid statistical studies, by shewing to the eye the sizes of different countries represented by similar forms, for where forms are not similar, the eye cannot compare them easily nor accurately.

Show the sizes of countries in similar forms: where forms are not similar, the eye cannot compare them easily or accurately. Countries on a map have irregular shapes, he continues, so we have a more accurate idea of the sizes of the planets, which are spheres.

In the text’s table, Russia is 4,650,000 square miles and Turkey is 790,000. Turkey is 0.17 times Russia. When I measured the diameters on the French translation’s plate, Russia came to about 411 pixels and Turkey about 171. The ratio of areas is 0.17, which nearly matches the ratio in the text. The ratio of diameters is 0.42. From this measurement, the circles can be read as drawn so that area, not diameter, is proportional to square miles.

How to read the vertical lines for population and revenue and the like is left to the article reading Chart 1 of 1801.

Cutting Inside the Circle: Russia’s Ring, Turkey’s Sectors, Germany’s Overlapping Circles

The circles of the Russian Empire and the Turkish Empire

In Chart 1, only Russia and Turkey have their circles divided inside. Russia’s circle is double: the inner circle is “European Dominions” and the outer ring is “Asiatic Dominions.” Turkey’s circle is divided by lines from the center into three parts: “European,” “African,” and “Asiatic.”

Turkey’s circle. Lines from the center divide it into three sectors: Europe, Africa, and Asia

Source: William Playfair (1801) / Wikimedia Commons (scan from the Cambridge University Press 2005 reprint). Public domain

The figures for this breakdown appear nowhere in the book. When I measured the French translation’s plate, Russia’s inner circle was about 24% of the area of the outer circle, and Turkey’s European sector was almost a quadrant. But with no numbers to compare against, there is no way to check whether the divisions match the actual extents.

In Chart 2 of the same book (Europe after the Peace of Lunéville), the ways of using circles multiply. According to the explanation around p.50, the whole of the German Empire, the Emperor’s (Austria’s) dominions, and Prussia’s dominions are drawn as three overlapping circles, A, B and C. Red is Austria’s share, yellow is Prussia’s share, and only the remaining green is the German Empire in the true sense. France’s circle is surrounded by a pale red circle that represents the combined extent of the countries under its control.

Part of Chart 2 in the French translation. France’s circle is surrounded by an outer circle, and three circles are drawn overlapping below Germany’s circle

Source: David Rumsey Map Collection, David Rumsey Map Center, Stanford Libraries / Internet Archive (part of Chart 2 of Donnant’s French translation Élémens de statistique, 1802, cropped). CC BY-NC-SA 3.0

In the 1801 book alone, there are at least three ways of dividing within a circle: concentric circles (Russia, France), sectors (Turkey), and overlapping circles (Germany). In Russia and Turkey, the circle’s area remains the extent of the whole country, and a further division is laid over its interior. Germany’s overlapping circles are a different matter. Chris Pritchard (2021) sees this as a diagram of relationships that pays no attention to size (“relationships with carefree attention to scale; they are simply representational”).

Playfair himself does not write why Russia gets a ring and Turkey gets sectors. Pritchard presents one possibility: a theory from an anonymous blog by a company called Geolytix. The circle was small, with no room to color Turkey’s three parts as a triple of concentric rings, so he may have divided it radially just this once. Turkey is the second-largest country in Chart 1, so the point of the story is not the smallness of the country but that there were three parts.

1805: Cutting Up a Single Circle

The plate of the 1805 circle of the United States

In 1802, Donnant published Élémens de statistique in Paris, a French translation of The Statistical Breviary to which he added an account of the United States. Playfair translated that part into English and published it in London in 1805 through Greenland and Norris. According to the translator’s preface, the translation is not literal, and he supplemented it with a “divided circle.” The title page says this circle was drawn “BY A NEW METHOD,” and beneath the figure is the following sentence.

This Newly invented Method is intended to shew the Proportions between the divisions in a Striking Manner

That is, a new method meant to show the ratios among divisions in a way that catches the eye.

The 1805 circle of the United States. The pink sectors in the upper half are the states, the green sectors at the bottom and right are Louisiana and the Western Territory, and the white sector at the left is East and West Florida

Source: William Playfair / Lehigh University Libraries, Special Collections. No Copyright – United States

Below it is “Total Extent 1,929,000 Square Miles or 1224 Millions of Acres.” The extent of the whole United States is given by this sentence, not by the size of the circle.

The extent of each state and region is expressed by the central angle of its sector. They run counterclockwise in descending order of size, starting from Virginia at upper right. According to the Lehigh University exhibit’s explanation, the colors distinguish three things: states, territories, and the East and West Florida held by Spain. Florida is an uncolored sector labeled “East & West Florida not yet united.” The newly acquired territory is drawn as Louisiana, marked “Newly Acquired (in 1804).” The figure on its sector is 725,000 square miles, about 38% of the total. Taken at face value, the angle would be about 135°.

On p.17 of the text, the purpose of the circle is stated as follows.

The divided circle which represents the surface of the country, has been constructed for the purpose of shewing, in an easy and accurate manner, the proportional extent of the different provinces…

It was made to show the proportions among the extents of the provinces simply and accurately. Right after this he goes on to say that the proportions of Virginia and Delaware are too out of balance. This is a comparison of part with part inside the circle. A little earlier on the same page is a sentence saying that even a third-rate province (a third rate province) is as large as France with its enlarged dominions. This comparison with Europe is made in the text, not in the circle.

Note that the data in this figure contains errors. According to David Bellhouse, New York and New Jersey are confused, and the area of each state was obtained by multiplying length by width. The details are covered in the article reading the 1805 United States pie chart.

What the Two Circles Let You Compare, and What They Do Not

The table below shows which appearance corresponds to the same square miles in the two charts.

Data	1801 Chart 1 (countries of Europe)	1805 chart (United States)
Extent of a country, state, or region	Area of a separate circle for each country	Central angle of a sector within a single circle
The extent figure	Written inside the circle	Written inside the sector
Extent of the whole	—	The sentence under the figure; the size of the circle does not represent it
Breakdown	Concentric circles for Russia, sectors for Turkey (no figures)	All sectors
Color	Green = maritime powers, pale red = land powers	Distinguishes states, territories, and East and West Florida

By my own sorting, what the eye can compare divides as follows.

	1801 circles of quantity	1805 divided circle
Number of circles / size of the circle	One per country / data	One / not data
Easy to compare	One country’s extent against another’s	Part with whole, part with part
Cannot be told from the figure alone	Each country’s share of the whole; the values of the Russia and Turkey breakdowns	The ratio of the United States’ extent to other countries'

The 1801 chart can be read as a chart for comparing one country with another. But how much of Europe as a whole Russia takes up cannot be known without adding up all the circles.

The 1805 chart can be read as the reverse. At a glance you can see that Louisiana’s sector is the largest division. But whether the United States is larger or smaller than Russia cannot be told. If drawn on the 1801 scale, the United States’ circle would come to about 0.41 times Russia’s in area and about 0.64 times in diameter. The comparison with France being written in the text can be read as due to the fact that this circle cannot show it.

The 1805 circle takes the size of the circle out of the data and gives meaning only to the divisions. Bellhouse sees Playfair in 1801 as not fully aware of what he had done. From that view, the “newly invented method” of 1805 can be read as pointing to making the angle of the sector the lead.

How Third Parties Saw the Two Circles

Pritchard calls the 1801 Turkey circle the first pie chart. The Wikipedia “Pie chart” entry takes the same position. Pritchard also asks why there were two ways of dividing. He treats the view that likens Germany’s overlapping circles to the later Venn diagram as a reasonable one.

David Bellhouse (2022) draws a different line.

In terms of an actual pie chart, Playfair was not fully aware of what he had done at that point. His fully-fledged pie chart, which appeared in 1805…

His position is that the 1801 chart was only a forerunner and that the real pie chart is the 1805 chart. He then points out the errors in the data seen above.

In the abstract of “No Humble Pie” (2005), Ian Spence writes that the origin of the pie is unclear and that the idea most likely came from the logic diagrams of Llull, Euler, and others.

On p.14, Playfair wrote that the eye compares sizes with almost unrivaled accuracy. Later perception research has produced different results. William S. Cleveland and Robert McGill (1984) proposed a hypothesis that ranks the accuracy of reading a quantity in this order: position on a common scale, length, angle, area, volume. Both the area of 1801 and the angle of 1805 fall on the side that is harder to read than position or length.

Drew Skau and Robert Kosara (2016) examined what the eye relies on in pie charts.

Data is encoded in pie and donut charts in three ways: arc length, center angle, and segment area… Both studies point to angle being the least important visual cue for both charts

Data is encoded in three ways, arc length, center angle, and segment area, and angle turned out to be the least effective cue. When a single circle is cut up, the three have the same ratio, so the proportions do not change whichever you read by.

However, what Playfair was comparing were the irregular shapes of countries on a map against uniform circles. The later studies compare circles with bars and the like. Because the questions differ, they can be read side by side rather than against each other.

Uses

The first is to decide, before drawing, what the reader is to compare with what. If you want items compared with one another, line up separate shapes as in 1801. If you want to show proportions within a whole, cut up a single shape as in 1805. Which one you choose swaps the comparisons that are visible with those that are not.

The second is that if you draw by area, make the area proportional to the data. If you make the diameter proportional, Turkey looks 0.42 times Russia rather than 0.17 times.

The third is that if you layer two roles onto one circle, you should show the interior values too. The Russia and Turkey breakdowns have no figures, so the reader cannot check whether the divisions are right.

The fourth is to be aware that in a divided circle, the size of the circle represents nothing. Add the value of the whole in a sentence, and prepare another means for comparison with outside countries. And even if you draw the angles accurately, errors in the original data are not fixed.

References

Primary sources

William Playfair, The Statistical Breviary; Shewing, on a Principle Entirely New, the Resources of Every State and Kingdom in Europe, London: J. Wallis et al., 1801. (Preface, pp.13–16, the chapters on Russia and Turkey, explanation of Chart 2 around p.50) Internet Archive / OCR text
D. F. Donnant, Statistical Account of the United States of America, translated by William Playfair, London: Greenland and Norris, 1805. (Title page, translator’s preface pp.v–vi, p.17) Internet Archive / OCR text
Lehigh University Libraries, Special Collections, “Statistical Representation of the United States of America” (images of the 1805 chart and title page) Exhibit item / Exhibit “At a Glance” commentary
Plates of Donnant’s translation Élémens de statistique (Paris, 1802), David Rumsey Map Collection (mirrored on the Internet Archive): Chart 1 / Chart 2
Wikimedia Commons, “File:Playfair-piechart.jpg” (Turkey’s circle of 1801) Commons

Secondary sources

Chris Pritchard, “Life of Pie: William Playfair and the Impact of the Visual,” Mathematical Association Presidential Essay No. 4, 2021. PDF
David Bellhouse, “William Playfair’s Statistical Graphs,” CSHPM Notes / Notes de la SMC, 54(1), 2022. PDF
Ian Spence, “No Humble Pie: The Origins and Usage of a Statistical Chart,” Journal of Educational and Behavioral Statistics, 30(4), 2005, pp. 353–368. (Abstract) IDEAS/RePEc / doi:10.3102/10769986030004353
Drew Skau and Robert Kosara, “Arcs, Angles, or Areas: Individual Data Encodings in Pie and Donut Charts,” Computer Graphics Forum, 35(3), 2016, pp. 121–130. eagereyes
William S. Cleveland and Robert McGill, “Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods,” Journal of the American Statistical Association, 79(387), 1984, pp. 531–554. (The ranking is taken from lecture materials) Cornell INFO 3312 lecture slides
Ian Spence and Stephan Lewandowsky, “Displaying Proportions and Percentages,” Applied Cognitive Psychology, 5(1), 1991, pp. 61–77. (Abstract) Introduction by the ISU Graphics Group
Wikipedia, “Pie chart” (History section) Wikipedia / “William Playfair” Wikipedia

Dividing the Size of the United States with One Circle: Playfair's 1805 "Divided Circle"

Sun, 12 Oct 2025 00:00:00 +0900

In 1805, William Playfair translated D. F. Donnant’s (Denis-François Donnant) statistical account of the United States into English and added a figure that divides the area of the states and territories into sectors of a single circle. Beneath the figure he had engraved “This Newly invented Method is intended to shew the Proportions between the divisions in a Striking Manner.” In other words, the method is newly invented, and it is meant to show the ratios between divisions in a striking way.

The book’s title is Statistical Account of the United States of America (London: Greenland and Norris, 1805). “Statistical Representation of the United States of America,” which is often cited as if it were the name of the work, is the title of the plate, not of the book. What follows draws on the images of the copy held by the Lehigh University Libraries and on the text of the Harvard copy at the Internet Archive.

The plate of the 1805 circle of the United States

A Translation with Just One Added Figure

Playfair himself describes how the book came about, in his preface and in the translator’s preface.

In 1801, Playfair publishes the Statistical Breviary.
Donnant in Paris translates it into French and adds an account of the United States.
Donnant sends the French translation to Playfair with an English letter dated November 1802.
Playfair translates the United States part into English, adds the figure, a dedication, and a treatise on trade at the end, and publishes it in 1805.

The title of the French translation is Éléments de statistique (1802). This comes not from the preface but from the bibliography of Bellhouse 2022.

In the translator’s preface, Playfair says the translation is not literal and that he has supplemented the explanations with a divided circle. He also writes that Donnant, who has approved of his own way of showing statistics through geometry, will not take this as an alteration.

Title page of D. F. Donnant, tr. William Playfair, Statistical Account of the United States of America (1805)

Source: Title page of D. F. Donnant, tr. William Playfair, Statistical Account of the United States of America (London, 1805), held by Lehigh University Libraries Special Collections / from Lehigh Library Exhibits (No Copyright – United States)

The title page is printed with “ILLUSTRATED BY A DIVIDED CIRCLE.” It goes on to explain that the engraved, hand-colored figure shows the ratio of the extent of the states, the eastern territories, and the newly acquired Louisiana by a new method. The subtitle is “With an Addition on the Trade to America, for the use of Commercial Men.” The advertisement at the end lists this figure first in the table of contents and describes it as “a Method entirely new, distinct, and EXPEDITIOUS.” The readers he had in mind were people in business.

The dedication is addressed to President Thomas Jefferson. Playfair writes that Jefferson, while in France, approved of his method of using lines for finance, and he urges the government to put effort into collecting statistics. Twenty-five copies were sent to Jefferson (Brinton 1939, Pritchard 2021).

How the Circle Was Divided

Hand-colored figure assigning the areas of the states and territories of the United States to the angles of sectors of a single circle. The states are pink, Florida is white, and the Western Territory and Louisiana are green

Source: William Playfair, “Statistical Representation of the United States of America” (folding plate), in the same book, held by Lehigh University Libraries Special Collections / from Lehigh Library Exhibits (No Copyright – United States)

The figure is a folding plate, and the creases show in the image. The correspondence between data and appearance is as follows. The numbers were read from Lehigh’s high-resolution image, and the spellings are kept as they appear in the figure.

Appearance	Data it encodes	Notation in the figure
The whole circle	Total area of the United States	“Total Extent 1,929,000 Square Miles or 1224 Millions of Acres”
Central angle of a sector	Area of each division (square miles)	Virginia 169,000, Georgia 150,000, and so on. The six small states have names only
Order of the sectors	States in descending order of area	Counterclockwise from Virginia at upper right to Delaware, followed by Florida, Louisiana, and the Western Territory
Color (hand-colored)	Kind of division	Pink = states, white = East & West Florida “not yet united”, green = Western Territory and Louisiana
Lettering along the arc	Grouping of regions	“WESTERN TERRITORY” on the green at right; “Newly Acquired (in 1804)” and “LOUISIANA” on the green at bottom

The Lehigh University Library exhibit explains the three colors as distinguishing states, territories, and the Spanish-held East and West Florida. The Louisiana Purchase treaty was signed on April 30, 1803, but the figure says “in 1804.”

In the 1801 Breviary, what Playfair drew was a row of circles, one per country, to be compared by size. The notation of that figure is covered in a separate article, and the difference between comparing by circle area and dividing by sector angle is covered in the article on the two kinds of circles. This article is about the 1805 circle, which divides a single whole into sectors.

The Line under the Figure, and a Passage in the Text

Two lines of lettering are engraved under the title of the plate. The first is the following sentence, and the second is the line giving the total area.

This Newly invented Method is intended to shew the Proportions between the divisions in a Striking Manner

It means that this newly invented method is meant to show the ratios between divisions in a striking way.

On page 17 of the text, Playfair explains the figure as follows.

The divided circle which represents the surface of the country, has been constructed for the purpose of shewing, in an easy and accurate manner, the proportional extent of the different provinces; and it is scarcely possible to look at it without a few important observations occurring to the mind.

In short, it was made to show the ratios of the extent of the regions easily and accurately, and on looking at it, it is hardly possible for a few important thoughts not to come to mind.

Examples of those thoughts follow. The differences in the size of the divisions are too great, so rearrangements will occur once the population evens out. The western territory will in time be divided into separate states. The ratio between Virginia and Delaware is absurd, and cannot stand as it is. He means the largest state at the upper right of the figure and the state at the far left that is a mere thin line.

The text calls the figure “easy and accurate,” while the engraved line says “Striking.” This can be read as Playfair asking both accuracy and impact of the same figure. The treatise on trade at the end says that the West was three-fifths the size of the United States before the Louisiana Purchase and is now two-thirds, and proposes a company to send British goods to the West. The green sector, which takes up a little over half of the circle, can be read as also serving to make this argument visible.

Checking the Numbers

In 2022, the statistician David R. Bellhouse pointed out errors in this figure. New York and New Jersey are confused. Compared with a map from around 1805, the states’ areas do not match. For each state, Playfair multiplied the length and width that Donnant gave to get an area, ignoring the fact that the states are not rectangles, Bellhouse says.

Left side of the figure. Sectors for Massachussets, South Carolina, and Maryland, six thin states with names only, and the white East & West Florida

Source: An enlargement of the left side of the same plate. Lehigh University Libraries Special Collections / from Lehigh Library Exhibits (No Copyright – United States)

I also measured the sector angles on the Lehigh image. I picked up the radial boundary lines from the center, so an error of about 1° is possible. The table below sets the angle obtained by dividing each printed value by the total area and multiplying by 360° next to my measurement.

Division	Printed in the figure	Angle from the printed value	My measurement
Virginia	169,000	31.5°	about 32°
Georgia	150,000	28.0°	about 27.5°
Kentuckey	115,000	21.5°	about 21.5°
New Jersey	105,000	19.6°	about 19.5°
North Carolina	84,000	15.7°	about 15.5°
Massachussets	73,000	13.6°	about 13.5°
South Carolina	25,000	4.7°	about 8°
Maryland	14,740	2.8°	about 5°
East & West Florida	none	—	about 12.5°
Louisiana	725,000	135.3°	about 111°
Western Territory	450,000	84.0°	about 84°

The six large states and the Western Territory are close to proportional to the printed values. The ones that deviate are South Carolina, Maryland, and Louisiana. Louisiana is about 25° smaller than its printed value, and working back from the angle gives roughly 590,000 square miles.

The total does not close either. The ten divisions with printed values add up to 1,910,740 square miles, only 18,260 short of the total area. Florida and the six small states should fit into that remainder, yet the figure gives them about 23°, the equivalent of about 120,000 square miles. Since a circle closes at 360°, some sector cannot be drawn as printed. In this figure, it can be read as showing up in Louisiana.

There are other discrepancies. The figure names 14 states, and Pennsylvania’s name is missing. Just before the summary table in the text, it says “Since then, the number of States has increased to sixteen.” Louisiana’s 725,000 square miles also differs from the 828,000 square miles that the U.S. National Archives gives for the purchased land.

How Third Parties Saw the Figure

Willard C. Brinton dedicated his 1939 Graphic Presentation to Playfair. In the preface there is a scene in which he leafs through this book at the Huntington Library and exclaims, “This is the first example of a sector chart.” Then he notices the engraved line beneath the one and only figure. On page 81 he writes “one of the first sector charts,” but he also notes that in the 1801 Breviary the Turkish empire’s circle was divided into three, and adds that that one might be the first.

Bellhouse distinguishes the 1801 figure as “An anticipation” and the 1805 figure as a “fully-fledged pie chart.” His view is that in 1801 Playfair was not yet fully aware of what he had done. He cites David S. Moore’s view that a pie chart can be used when emphasizing the relation between parts and a whole, and writes that this figure is an example of that.

Chris Pritchard, in 2021, looks at the figure from the book’s origins and its political context. His assessment is that it shows both the ratios among the states and their ratios to the whole country, and makes plain the effect of the Louisiana Purchase two years earlier. He also writes that one of the 25 copies sent to Jefferson went to Humboldt.

The three accounts have different emphases. Brinton reads the figure as an early sector chart, Bellhouse from the quality of the data, and Pritchard from the context of the purchase.

What to Take Away

Here are the points from this figure that can be carried back into visualization work.

State the whole. With the total area written under the figure, the sectors can be read as quantities relative to the whole.
Decide the order. Going around the circle from the largest state, the gap between Virginia and Delaware shows at a glance.
Use color for kind. The three colors are not about quantity; they distinguish states, unincorporated land, and territory.
Write the numbers on the sectors. Because the values are printed, a reader 200 years later can check them against the angles and find the discrepancies.
Check the total before drawing. If the parts do not add up to the whole, the discrepancy will show up in some sector.

Playfair asked this figure for both “Striking” and “accurate.” The impact comes from color, ordering, and the large green sector. The accuracy cannot be known without checking the numbers one by one. When drawing a pie chart, check these two separately.

References

Primary sources

D. F. Donnant, tr. William Playfair, Statistical Account of the United States of America, London: Greenland and Norris, 1805 (Harvard copy, Internet Archive). archive.org / Full OCR text
Lehigh University Libraries, Special Collections, “Statistical Account of the United States of America.” (Images of the title page and plate from the library’s copy). Lehigh Library Exhibits
Lehigh University Library, “At a Glance: Selected Works in the History of Data Visualization,” Case One: Playfair. Exhibit page
U.S. National Archives, “Louisiana Purchase Treaty (1803).” archives.gov

Secondary sources

Willard C. Brinton, Graphic Presentation, New York: Brinton Associates, 1939 (preface pp. 11–12, p. 81). archive.org
David R. Bellhouse, “William Playfair’s Statistical Graphs,” CMS Notes, 54(1), February 2022. notes.math.ca
Chris Pritchard, “Life of Pie: William Playfair and the Impact of the Visual,” Mathematical Association Presidential Essay No.4, July 2021. PDF

10,000 Men per Millimeter: Minard's 1869 Chart Drawing Napoleon's and Hannibal's Armies by the Same Rule

Mon, 06 Oct 2025 00:00:00 +0900

In 1869, Charles Joseph Minard fixed the width of his bands at “1 mm per 10,000 men” and drew the advance in red and the retreat in black. The chart shows how an army of 422,000 men came back to the border as 10,000, together with the temperatures during the retreat. Minard printed it on the same sheet of paper as a chart of Hannibal’s army, drawn by the same rule.

The title of the chart is “Carte figurative des pertes successives en hommes de l’Armée Française dans la campagne de Russie 1812–1813” (a figurative map of the successive losses of men of the French Army in the Russian campaign of 1812–1813). What follows relies on the legend and figures written into the chart, the impression held by the Bibliothèque nationale de France (BnF), and the introduction Étienne-Jules Marey wrote in 1878.

One sheet printed in Paris on 20 November 1869

Below the title is the line “Paris, le 20 Novembre 1869”. The signature is that of the Ponts et Chaussées (the Corps of Bridges and Roads): “Inspecteur Général … en retraite” (Inspector General, retired). The chart was printed as a lithograph.

Minard was born in Dijon in 1781 and, according to National Geographic, was 88 when he made this chart. According to the biography on Wikipedia, he was a civil engineer who worked on ports, dams, canals, and bridges. Railways were one of his lecture topics, but he was not a “railway engineer.” He became an Inspector General in 1846, retired in 1851 at the age of 70, and only then began making statistical maps in earnest. He produced 51 thematic maps and statistical graphics.

In the BnF impression, this chart is the lower half of a single sheet. The upper half holds a chart of Hannibal’s army, showing its progress from Spain across Gaul into Italy.

One sheet with the chart of Hannibal’s army on top and the chart of Napoleon’s army below. A handwritten note at the top edge reads “pour la Bibliothèque impériale”

Source: Charles Joseph Minard, 1869. Collection of the Bibliothèque nationale de France (BnF) (Gallica btv1b52504201x) / via Wikimedia Commons. Public domain

At the top edge of the sheet is a handwritten note: “pour la Bibliothèque impériale” (for the Imperial Library). The two charts carry the same date and fit within the same frame. Ten months later, in September 1870, in the middle of the Franco-Prussian War, Minard left Paris, and he died in Bordeaux on 24 October.

Band width: 1 mm for 10,000 men

The legend of the Napoleon chart is written below the title. Its first two sentences give the visual rule.

Les nombres d’hommes présents sont représentés par les largeurs des zones colorées à raison d’un millimètre pour dix mille hommes ; ils sont de plus écrits en travers des zones. Le rouge désigne les hommes qui entrent en Russie, le noir ceux qui en sortent.

In other words: the number of men present at a given point is shown by the width of the colored band, with 1 mm standing for 10,000 men. The number is also written across the band. Red marks the men entering Russia, black those leaving it.

The chart of Napoleon’s Russian campaign. A thick band runs from the Niemen on the left to Moscow on the right and returns as a thin black band. A temperature line runs along the bottom

Source: Charles Joseph Minard, 1869 / via Wikimedia Commons (File:Minard.png). Public domain

In this reproduction the advance band looks light brown, but the legend says “rouge” (red). Wikipedia also notes “The red [now brown].” In the BnF impression it looks like a dull red.

Here are the numbers written on the bands, taken in the order of the advance: 422,000 at the Niemen near Kowno, 400,000 at Wilna, 175,000 at Witebsk, 145,000 at Smolensk, 127,100 at Chjat, and 100,000 at Mojaisk and Moscow. The black retreat band falls from 100,000 to 55,000, then to 24,000.

The correspondence between data and appearance is as follows.

Data	Appearance	Concrete example on the chart
Number of men at that point	Band width (1 mm = 10,000 men)	422,000 men at the Niemen; calculated width 42 mm
The same number of men	Figures written along the band	“422.000,” “100.000,” and so on
Advancing or returning	Band color (red = entering, black = leaving)	In the reproduction, the red looks light brown
Route	Position the band takes on the map	Place names such as Kowno, Wilna, Smolensk, MOSCOU
Distance	Scale bar	0–50 French lieues communes
Detached units and their rejoining	Branching of the bands and addition of widths	At Bobr, 20,000 + 30,000 = 50,000
Temperature during the retreat	Height of the line in the lower panel	0 to −30 degrees Réaumur
Date	Text attached to each temperature point	“le 6 Xbre” (6 December), and so on
Link between map and temperature	Thin vertical guide lines	From the temperature points to places on the retreat route

When a branched band rejoins, the widths add up. The 30,000 band that comes down south from near Polotzk joins the main force’s 20,000 at Bobr to make 50,000. At the end, the 4,000 band is joined by 6,000 returning from the north, making 10,000 at the Niemen.

Detail of the black retreat band. The band that came down from Polotzk joins at Bobr, and vertical lines connect it to the temperature line below

Source: Charles Joseph Minard, 1869 (detail) / via Wikimedia Commons (File:Minard.png). Public domain

The last figure on the chart is exactly 10,000, about 2.4% of the 422,000. Because the widths are drawn so that they can be added, the units that split off along the way can be read with the same yardstick. Wikipedia writes that band diagrams of this kind were later called Sankey diagrams.

The temperature panel, and what Minard assumed

The title of the lower panel is “TABLEAU GRAPHIQUE de la température en degrés du thermomètre de Réaumur au dessous de zéro” (a graphic table of the temperature in degrees of the Réaumur thermometer below zero). A scale from 5 to 30 degrees runs along the right edge.

The values written in run from 0 degrees on “le 18 8bre” (18 October) at the right edge, through −21 degrees on 14 November and −30 degrees on 6 December, to −26 degrees on 7 December at the left edge. The lowest value, −30 degrees, is −37.5 °C (1 degree Réaumur = 1.25 °C).

The dates run from right to left. The horizontal position of each point is matched to a place on the retreat route above, and thin vertical lines connect the two. As a result, the horizontal axis is not evenly spaced in time. The dates can be read as text added to an axis of place.

Temperature is drawn only for the black retreat band. The advance has no temperature. By the numbers on the bands, 322,000 of the 422,000 men were already gone before reaching Moscow. The chart holds only head counts and temperatures; it gives no cause of death.

Just before Moscow, the red band narrows suddenly, from 127,100 at Chjat to 100,000 at Mojaisk.

The second half of the legend lists the sources (the works of Thiers, Ségur, Fezensac, and Chambray, and the unpublished diary of Jacob, an army pharmacist) and the simplification Minard added himself.

Pour mieux faire juger à l’œil la diminution de l’armée, j’ai supposé que les corps du Prince Jérôme et du Maréchal Davoust qui avaient été détachés sur Minsk et Mobilow et ont rejoint vers Orscha et Witebsk, avaient toujours marché avec l’armée.

In other words: to let the eye better judge the shrinking of the army, he assumed that the corps of Prince Jérôme and Marshal Davout, which had been detached toward Minsk and Mobilow and rejoined near Orscha and Witebsk, had marched with the army all along. The starting figure of 422,000 also includes this assumption; it is the number “in Minard’s chart.”

On the same sheet as the Hannibal chart

The upper half is a chart of the losses of the army Hannibal led from Spain across Gaul into Italy, drawn after Polybius (Polybe). Here is a transcription of the legend at the upper right.

Les nombres d’hommes restant à Annibal sont représentés par la largeur des zones colorées à raison d’un millimètre pour dix mille hommes, ils sont de plus écrits en travers des zones. Il n’y a pas d’opinion arrêtée sur le point où Annibal a traversé les Alpes, j’ai adopté celle de Larosa sans prétendre la justifier.

In other words: the number of men remaining to Hannibal is shown by band width, with 1 mm for 10,000 men, and the numbers are written across the bands. There is no settled opinion on where Hannibal crossed the Alps, and he adopted Larosa’s view without claiming to justify it. The Crouch Rare Books catalogue explains that Larosa means Larauza.

The band is widest in Spain at the left, and after the Alps it becomes a thin line heading for Turin. Because the width rule is the same, comparing the upper and lower bands lets one set the size and shrinkage of the two armies against the same yardstick.

In 1878, Marey introduced this chart in La méthode graphique dans les sciences expérimentales. Only the Napoleon chart appears there, as Figure 37, and Hannibal’s army gets a single phrase saying that it was drawn “ailleurs” (elsewhere). The widely circulated File:Minard.png on Commons is also a version with only the Napoleon chart. The pair on one sheet, it can be read, has been cut down to its lower half every time it has been introduced.

Richard Taws, at the opening of his article in Grey Room no. 83 (2021), writes that this chart was on the same page as the Hannibal chart. He also mentions that Minard left Paris ten months later, fearing the Prussian army. He then points out that while Tufte’s verdict has been repeated, the chart has hardly been discussed in relation to contemporary visual representations outside the lineage of statistical maps.

How others saw the chart

Among contemporary books, Marey introduced it in 1878. In his introduction of Figure 37, he puts the visual rule directly into words.

Cette figure, construite au moyen de documents statistiques patiemment recueillis à différentes sources, traduit l’amoindrissement graduel de l’armée par le rétrécissement incessant d’une zone dont la largeur exprime le nombre des soldats de Napoléon.

This explains that the chart, built from statistical documents patiently collected from various sources, expresses the gradual diminution of the army through the ceaseless narrowing of a band whose width gives the number of Napoleon’s soldiers. Marey also wrote, however, “Il n’est pas revenu un soldat sur cent” (not even one soldier in a hundred came back). By the chart’s figures it is about 2.4%, so this sentence does not agree with the chart.

The standard modern praise comes from Edward Tufte. On page 40 of The Visual Display of Quantitative Information (1983), he wrote:

It may well be the best statistical graphic ever drawn.

It is a verdict that this may be the best of all statistical graphics ever drawn.

Stephen Kosslyn raised doubts from the burden on the reader. Jorge Camões quoted Kosslyn’s words in a 2008 blog post.

This display has never captivated me for the simple reason that given human processing limitations – I needed several minutes to figure it out. (…) But if you want the facts and want them in a clear, easily understood way, this display is not the solution.

The criticism: human processing has limits, and it took him several minutes to work it out; if you want the facts clearly and easily, this chart is not the answer.

Camões himself questions the choice of what to draw in.

Minard adds detail to explicitly link deaths to cold temperatures during retreat, but around 75% of men died on the way to Moscow and he doesn’t tell us why.

His point: Minard added detail linking deaths during the retreat to cold, yet about 75% died on the way to Moscow, and the chart does not say why.

In a 2021 article, Robert Kosara names what was not drawn. Making the chart work required heavy simplification, and the more famous it became, the more the Russian army and militia who fought the French, and the harm to civilians, have dropped out of sight.

What to take away

What a visualization practitioner can take from this chart is to write the maker’s decisions into the chart itself. There are four concrete points.

Fix one visual feature to carry quantity. Minard shows the number of men by width alone and uses color for direction. For a flow chart, first check whether widths can be added when flows merge.
Write both the width and the number. The width shows the decline, and the number supports reading off values.
Write the simplifications in the legend. Minard wrote into the chart that he had grouped army corps and that he had settled on a single theory for the Alpine crossing.
Draw what you want to compare by the same rule, and put it on the same sheet. When you cut a chart out for use, consider whether to carry along its pair and its legend too.

Camões took issue with Minard drawing temperature only for the retreat. Kosara pointed out that the Russian side and the harm to civilians are not drawn. From the two critiques, it can be read that the choice of where to draw detail and what to leave undrawn becomes, as it stands, the chart’s claim.

References

Primary sources

Charles Joseph Minard, Carte figurative des pertes successives en hommes de l’armée qu’Annibal conduisit d’Espagne en Italie en traversant les Gaules (selon Polybe) / Carte figurative des pertes successives en hommes de l’Armée Française dans la campagne de Russie 1812–1813, Paris, 20 November 1869, lithograph. Impression held by the Bibliothèque nationale de France (BnF) (Gallica btv1b52504201x): Wikimedia Commons
Same, Napoleon chart only (with the French legend and an English translation): Wikimedia Commons, File:Minard.png
Étienne-Jules Marey, La méthode graphique dans les sciences expérimentales, Paris: G. Masson, 1878, pp. 72–73. Internet Archive

Secondary sources

Edward R. Tufte, The Visual Display of Quantitative Information, Graphics Press, 1983, p. 40.
Jorge Camões, “Minard, Tufte, Kosslyn and Godin (and Napoleon),” 2008. excelcharts.com
Robert Kosara, “eagereyesTV: Minard’s famous ‘Napoleon’s March’ chart – what it shows, what it doesn’t,” eagereyes, 2021. eagereyes.org
Richard Taws, “Death from Above in Minard’s Napoleon Map,” Grey Room, no. 83, 2021, pp. 82–111. doi:10.1162/grey_a_00321 / Grey Room
Betsy Mason, “The Underappreciated Man Behind the ‘Best Graphic Ever Produced’,” National Geographic, 2017. nationalgeographic.com
“Charles Joseph Minard,” Wikipedia (biography; based on Chevallier 1871 and Rendgen 2018). en.wikipedia.org
Crouch Rare Books, “From states to statistics” (catalogue; format and the explanation of Larauza). crouchrarebooks.com
HistoryofInformation.com (Jeremy Norman), entry on Minard’s Russian campaign chart (conversion of degrees Réaumur and lieues). historyofinformation.com

Semicircles for Length and Breakdown, Quarter-Circles for Density: The 1880 Transport Routes Map in the Album de statistique graphique

Mon, 15 Sep 2025 00:00:00 +0900

Plate 1 of the 1880 Album de statistique graphique (Album of Graphic Statistics) is a map that places one semicircle on each French département. The area of the semicircle represents the total length of transport routes at the end of 1878. The seven sectors inside the semicircle give the breakdown by type of route, and the two quarter-circles below show length per area and length per inhabitant.

The title is “Carte figurative du développement des voies de communication par département au 31 décembre 1878” (Figurative map of the development of communication routes by département at 31 December 1878). It was made by the Direction des Cartes et Plans (Bureau of Maps and Plans) of the French Ministry of Public Works, and no individual is named on the plate. What follows draws on the plate’s legend and data table, on the album’s preface (reprinted in the 1881 Journal de la Société statistique de Paris), and on the writings of Émile Cheysson, who headed the bureau.

July 1880: An Album of Statistical Charts for Legislators

It began with a ministerial order of March 12, 1878. The order organized the “Bureau of Maps, Plans, Documents and Graphic Statistics,” and Article 2 decided that an album of statistical charts would be published every year. An order of July 3 laid out its contents in detail.

The 1879 edition had 12 plates, and a contemporary review says it was prepared by the Maps and Plans section under Cheysson’s direction. In 1890 Cheysson himself signed as “former head of the Ministry of Public Works’ Bureau of Maps and Plans” and wrote that the 1879 edition was the first application of the order. Some articles mention a “1878 edition” of wall maps, but by his own count the 1879 edition was number one.

This plate is in the second album, the 1880 edition. Its title page reads “July 1880,” and it was published by the Imprimerie nationale in Paris. Of the 16 plates, this map is Plate 1, and Plate 16 depicts the development of railways in the major countries (the article on the railway development map). No source names the author of the 1880 edition; the David Rumsey Map Collection, which holds it, registers the Ministry of Public Works and Cheysson as authors.

A folded plate with a semicircle diagram placed on each département across France, a legend at lower left and a table of figures by département at right

The whole of Plate 1. The legend is at lower left and the table of figures by département is at right

Source: Ministère des Travaux Publics (1880), David Rumsey Map Collection, held at the David Rumsey Map Center, Stanford Libraries (CC BY-NC-SA 3.0)

According to the preface, all 16 plates are large-format, folded in a special way to fit the format of parliamentary documents. The makers dropped lithography in favor of engraving on stone, and shades of the same color are produced by the density of hatching.

The preface ends by naming the readers.

le nouvel album pourra être consulté avec profit par les membres du Parlement, auxquels il est spécialement destiné, par les administrateurs, par les économistes …

In short, the new album is intended especially for members of parliament, and should also be useful to administrators and economists. The reference date of the data is January 1, 1879, and the album was published in July 1880. Cheysson wrote in 1890 that the figures in the albums are normally those of two years before the year of publication.

Reading the Legend: Semicircles, Seven Sectors, Two Quarter-Circles

The conventions are written in the legend at lower left of the plate.

The legend box: explanatory text at the top, a table in the middle matching sector numbers, types of route, colors and scales, and a guide to the data table and the sources at the bottom

The legend (LÉGENDE) of Plate 1

Source: Ministère des Travaux Publics (1880), David Rumsey Map Collection, held at the David Rumsey Map Center, Stanford Libraries (CC BY-NC-SA 3.0)

Chacune de ces longueurs est exprimée par un secteur, qui occupe toujours la même place sur le diagramme, au-dessus du diamètre horizontal, et qui est teinté d’une couleur particulière. L’ensemble de ces secteurs compose un demi-cercle, dont la surface est proportionnelle au développement des voies du Département.

Each length is expressed by a sector that always occupies the same position above the horizontal diameter and is tinted in its own color. The semicircle made of all the sectors has an area proportional to the length of the département’s routes. The legend goes on to say that the two quarter-circles below represent the ratios of length to population and to territory.

The table in the legend, recast as a correspondence between data and appearance, looks like this.

Data	Appearance	Color (as named in the legend)	Scale (legend)
Total length of the département’s transport routes	Area of the upper semicircle	—	Radius 0.025 m = 12,000 km
National roads (Routes nationales)	Area of sector 1 (far left)	Purple	Same as above
Departmental roads (Routes départementales)	Sector 2	Orange	Same as above
Navigable waterways (Voies navigables)	Sector 3	Yellow	Same as above
Railways (Chemins de fer)	Sector 4	Blue	Same as above
Communal roads, long-distance (de grande communication)	Sector 5	Rose, dark	Same as above
Communal roads, common-interest (d’intérêt commun)	Sector 6	Rose, medium	Same as above
Communal roads, ordinary (ordinaires)	Sector 7	Rose, light	Same as above
Total length ÷ area of territory (per km²)	Area of lower left quarter-circle	Blue	Radius 0.005 m = 1
Total length ÷ population (per 100 inhabitants)	Area of lower right quarter-circle	Yellow	Radius 0.007 m = 1
Département	Where the semicircle is placed	—	Within each département

There are seven sectors but only five hues. For the communal roads (chemins vicinaux), the three legal categories are separated by shades of rose. According to a note in the legend, the 12,000 km scale applies to both the semicircle and each sector. Within a département the radius is common, so the angle of a sector is also proportional to its length.

The order is the same in the legend and in the columns of the data table, but the reason is nowhere stated. The base map consists of département boundaries, rivers, coastlines, road and railway lines, and place names, with no depiction of relief. Over the sea, a sample diagram is placed.

A sample diagram of an average département: a semicircle divided into seven colored sectors, with blue and yellow quarter-circles attached below

The sample diagram at sea, “DÉPARTEMENT MOYEN” (average département)

Source: Ministère des Travaux Publics (1880), David Rumsey Map Collection, held at the David Rumsey Map Center, Stanford Libraries (CC BY-NC-SA 3.0)

Below the legend is a column of sources. National roads, departmental roads, and waterways come from the situation tables of the Corps des Ponts et Chaussées (civil engineering corps); communal roads from the situation tables of the Ministry of the Interior; and population and area from the 1879 Annuaire statistique de la France. Only the communal roads have a reference date one year earlier (January 1, 1878). The source of the railway figures is not in this column.

Checking Against the Data Table: National Totals and the Seine Département

The legend also states where the numbers are.

Les chiffres, qui mesurent ces données et dont les diagrammes se bornent à donner la traduction graphique, sont groupés dans un tableau placé à droite de la Carte.

In other words, the diagrams only translate the numbers into pictures, and the numbers are gathered in a table to the right of the map.

The bottom row of the table, “Total and average,” gives national roads 37,279.9 km, departmental roads 38,358.6 km, navigable waterways 13,046.7 km, railways 28,435.0 km, and communal roads 417,264.6 km. The average ratios are 1.01 per km² and 1.45 per 100 inhabitants. Added together, the total is about 534,000 km, of which communal roads are about 78% and railways about 5% (the author’s calculation). Of the semicircle’s 180°, the blue of the railways is only about 10° (the author’s calculation).

Around Paris: below the semicircle of the small Seine département is a large blue quarter-circle, and the yellow quarter-circle is almost invisible. The surrounding départements have large semicircles

Around Paris. The small diagram in the center is the Seine département, and the one at lower left is Seine-et-Oise

Source: Ministère des Travaux Publics (1880), David Rumsey Map Collection, held at the David Rumsey Map Center, Stanford Libraries (CC BY-NC-SA 3.0)

For the Seine département, which includes Paris, the five columns of the table add up to about 1,010 km (the author’s calculation), so the semicircle is small. Meanwhile its length per km² is 2.11, among the highest of all départements, and per 100 inhabitants it is 0.04. Calculated with the scale in the legend, the radius of the blue quarter-circle is about 7.3 mm and that of the yellow about 1.4 mm (the author’s calculation). A large blue attaches below the small semicircle, and the yellow is almost invisible.

In the neighboring Seine-et-Oise, both ratios are 1.29. Even so, the radius of the yellow quarter-circle comes to about 8.0 mm and that of the blue to about 5.7 mm (the author’s calculation), because the scales of the two ratios differ, 0.005 m and 0.007 m. This suggests that the left and right quarter-circles were not made to be compared in size on the same yardstick. What can be compared is left with left and right with right, across départements.

“Fan” and “Foyer”: Reading Through Cheysson’s Words

The preface to the 1880 edition itself explains the type of this plate.

Les planches 1 et 2 ont eu recours aux diagrammes par secteurs diversement coloriés, dont chacun est affecté à la représentation d’un élément distinct et dont l’ensemble constitue une sorte d’éventail.

Differently colored sectors each represent a separate element, and together they form “a sort of fan (éventail).” The preface goes on to say that Plate 1 shows, for each département, progress “in absolute terms and in terms of ratios.”

The preface classifies Plates 1, 2, and 16 as “cartogrammes à foyers diagraphiques” (cartograms with diagraphic foyers). Most of the others are “band cartograms,” in which the width of a band represents the quantity. The name was given by Cheysson in his report on the 1878 Exposition universelle. The method takes the point to be shown as the “foyer” (focal point) and erects a small diagram on it.

In the same 1878 report, Cheysson also touches on the misreading of sectors. A ring diagram from the Marseille Chamber of Commerce represented quantities by the length of the arc.

si la légende n’y mettait ordre, l’esprit serait tenté de faire intervenir dans la mesure des faits, non la largeur des arcs, mais l’aire des secteurs.

His point is that unless the legend set things right, the reader would be tempted to measure by the area of the sectors rather than by the width of the arcs. The legend of Plate 1 makes “area” the convention from the start. It can be read as choosing, as its convention, the quantity that readers naturally look at.

The 1890 commentary cites Plate 34 of the 1886 edition as an example of dividing a semicircle into sectors, saying that the diagram for each département takes the form of a “colored fan.” This can be read as the same construction as Plate 1. The same text also contains a warning.

Il faut surtout se garder de vouloir trop dire de choses à la fois, et de devenir obscur à force d’être complet. … Si un diagramme est touffu au point de n’être plus clair, mieux vaut le tableau de chiffres dont il est la traduction.

Avoid trying to say too much at once and becoming obscure; if a diagram is so dense that it is no longer clear, the table of figures it translates is better. Plate 1 layers four levels on one symbol, yet puts the data table on the same sheet. It can be read as a design that leaves the density to the table.

Cheysson also writes that the purpose of the administration is to prepare material for study and that it has no obligation to draw conclusions. Reading the values of the day from the order of the categories is something the makers themselves held back from, it seems.

How Third Parties Have Viewed This Album

Among contemporary reviews is that of the statistician Toussaint Loua on the 1879 edition. Loua sets length beside average tonnage, writing that waterways, at a third of the length of national roads, carry four times as much in relative terms, and that railway tonnage is nine times that of national roads. This is not a comment on Plate 1, but in a chart of length the railways at about 10° far exceed both waterways and national roads in average tonnage. In the 1880 edition, tonnage is handled by the band maps of Plates 5 to 7 at the same scale.

In his 2008 paper, Michael Friendly places the album as a whole at the peak of the “Golden Age” of statistical graphics. He cites the assessment of Funkhouser (1937).

the Albums present the finest specimens of French graphic work in the century and considerable pride was taken in them by the French people, statisticians and laymen alike.

That is, the albums were the finest specimens of French graphic work of the century, and statisticians and the general public alike took pride in them. Friendly also writes that circles, radial forms, and “pie maps” were favored, but he does not mention Plate 1 itself.

Friendly distinguishes the pie chart as a diagram with “constant radius and varying angle” from the polar area diagram (coxcomb) with “constant angle and varying radius.” The Rumsey catalog annotates this plate with “coxcombs,” but in Plate 1 the sectors share a radius and vary in angle. By Friendly’s definition, it can be read as the semicircle version of a pie chart.

The Rumsey catalog introduces the album as inspired by the work of Charles Joseph Minard. Cheysson himself also begins his 1890 commentary with the name of his predecessor Minard. In 1883 the album, together with the ministry’s statistical bulletin, received the Montyon Prize in Statistics of the Academy of Sciences.

Uses

What we can take away from this plate is how to place conventions when one symbol carries several quantities.

Separate size from breakdown: the size of the semicircle shows the total, and the angles of the sectors show the breakdown.
Fix the positions of the categories: the sectors are placed “always in the same position.” Even if the colors are hard to tell apart, the position lets you read them.
If readers will read by area, say so in the legend: if readers want to measure by area, make that the convention.
If the scales differ, write the scales: when the legend gives numbers, readers can judge which pairs are fair to compare.
Put in a sample: the “average département” becomes a reference that can be applied to the diagram of any département.
Put the data table and sources on the same sheet: even a gap in reference dates (only the communal roads are one year earlier) is written in the legend.

Even so, a chart of length does not show how the routes are used. As Loua set length beside tonnage, quantity and flow have to be handled in separate charts. This presupposes that the title and legend state plainly what was measured.

References

Primary sources

Ministère des Travaux Publics, Direction des Cartes et Plans, “Carte figurative du développement des voies de communication par département au 31 décembre 1878,” Album de statistique graphique, 1880, Pl. 1. David Rumsey Map Collection, List No. 12511.007. David Rumsey Map Collection / IIIF manifest / Internet Archive
“Bibliographie. Notice relative à l’album de statistique graphique [publié par le Ministère des travaux publics en 1880],” Journal de la Société statistique de Paris, 22, 1881, pp. 25–28 (reprint of the preface to the 1880 edition). Numdam
“Notice statistique sur l’album des voies de communication,” Journal de la Société statistique de Paris, 21, 1880, pp. 6–11. Numdam
É. Cheysson, “L’Album de statistique graphique publié par le ministère des travaux publics,” Journal de la Société statistique de Paris, 31, 1890, pp. 11–23. Numdam
É. Cheysson, “Les méthodes de statistique graphique à l’Exposition universelle de 1878,” Journal de la Société statistique de Paris, 19, 1878, pp. 323–333. Numdam
David Rumsey Map Collection, Copyright and Permissions. Terms of use

Secondary sources

T. Loua, “Bibliographie. L’Album de statistique graphique pour 1879,” Journal de la Société statistique de Paris, 20, 1879, p. 308. Numdam
Michael Friendly, “The Golden Age of Statistical Graphics,” Statistical Science, 23(4), 2008, pp. 502–535. doi:10.1214/08-STS268 / arXiv
David Rumsey Map Collection catalog (the plate’s “coxcombs” annotation and the description of the album). Search results

Six Circles Around a Country Chart the Growth of Railways: The 1880 Railway Development Map

Mon, 15 Sep 2025 00:00:00 +0900

In July 1880, the French Ministry of Public Works issued the 1880 edition of the Album de statistique graphique (Album of Graphic Statistics). Its last plate, no. 16, shows each country’s total railway length from 1830 to 1878 as the area of blue circles. The circles for each year are spaced 60 degrees apart around the center of the country. Length per 10,000 inhabitants (green) and per 100 km² (yellow) is added as quarter-circles in the middle.

The original title is “Carte figurative du développement des chemins de fer dans les principaux États de 1830 à 1878”. The catalog names Émile Cheysson as its author. What follows draws on the images that the David Rumsey Map Collection has published (legend, data table, sources) and on the preface to the album. The preface was reprinted in the 1881 Journal de la Société de statistique de Paris.

The whole plate: yearly blue circles for each country lined up along dotted circumferences on a map, with a separate box for the United States and others on the right, a line chart at upper right, and a data table at lower right

Source: Ministère des Travaux Publics (1880) / David Rumsey Map Collection. CC BY-NC-SA 3.0

The Last Plate of the 1880 Album

According to the preface, the album is an annual collection of plates established by a ministerial order of March 12, 1878. The order required that statistics on passenger and freight flows on transport routes, and on their construction and operation, be turned into diagrams and published every year. The 1880 edition is the second. The previous year’s edition had 12 plates; the 1880 edition has 16, all of them large-format. Plate 16 is the last of these, a 49 × 62 cm sheet folded into the album.

The person in charge was Cheysson. According to Michael Friendly, the Ministry’s Bureau of Graphic Statistics was created in March 1878 and headed by Cheysson (1836–1910), an engineer of the École nationale des ponts et chaussées (ENPC). How the album came about, and its plate 1, are covered in the statistical map of the breakdown of transport infrastructure, in the same series.

The preface groups plates 1, 2, and 16 as “cartogrammes à foyers diagraphiques”: maps in which a small diagram is placed around a point (foyer) on the map. The preface notes that plates 1 and 2 use sectors, and it describes plate 16 as follows.

Enfin, la dernière planche n° 16 se rapporte à l’accroissement du réseau ferré des grands États de l’Europe, de dix en dix ans, depuis 1830, et le figure par des cercles proportionnels distribués régulièrement sur une circonférence dont le centre est le chef-lieu de chaque État.

The last plate, no. 16, concerns the growth of the railway networks of the major European states, every ten years since 1830. It represents this with proportional circles spaced evenly along a circumference whose center is each state’s capital.

The preface also names the readers. The album is meant “especially” (auxquels il est spécialement destiné) for members of parliament, and it hopes to be read by administrators and economists as well. It adds that each plate comes with its source, a legend stating the drawing conventions, and a table of the underlying figures. Plate 16 has all three.

What the Legend Says About the Encoding

At lower left of plate 16 is a box titled LÉGENDE. Its first paragraph gives the convention for the blue circles.

A box titled LÉGENDE, with handwritten text giving the convention for the blue circles and quarter-circles, the radius formula, an explanation of the separate boxes, and the sources

Source: Ministère des Travaux Publics (1880), legend detail / David Rumsey Map Collection. CC BY-NC-SA 3.0

Ces 6 phases sont représentées par des cercles dont les centres sont distribués uniformément sur une circonférence en trait noir pointillé, et dont les surfaces teintées en bleu sont proportionnelles au développ.nt du réseau.

These 6 phases are represented by circles whose centers are spread evenly along a circumference drawn as a dotted black line. The surfaces tinted blue are proportional to the length of the network.

A radius formula follows. With the length as n km, the radius is “0,01 √(n / 30 000k)”. The denominator is hard to make out in the image, but the use of the square root is clearly legible. If the radius is made proportional to the square root of the value, the area is proportional to the value. Counting the pixels of the circles in the image, the ratio of France’s 1870 and 1878 areas is 0.77, which roughly matches the ratio of the lengths in the data table, 0.73.

Data	Appearance	Basis
Total railway length of each country (1830, 1840, 1850, 1860, 1870, 1878)	Area of a blue circle	Legend text and radius formula
Which year	Position on the dotted circumference, 60 degrees apart, clockwise	Legend “distribués uniformément”, ring printed with the years
Which country	Center of the circumference (the capital, per the preface)	Preface “le centre est le chef-lieu”
Length per 10,000 inhabitants in 1878	Area of the green quarter-circle at center left-bottom	Legend checked against the data table
Length per 100 km² in 1878	Area of the yellow quarter-circle at center right-bottom	Legend checked against the data table
Countries outside Europe	Separate boxes, removed from their map positions (same scale)	Legend paragraph on “cartouches”

A white ring labeled FRANCE with the years printed on it, six blue circles of different sizes along the dotted circumference around it, and green and yellow quarter-circles in the center

Source: Ministère des Travaux Publics (1880), glyph for France / David Rumsey Map Collection. CC BY-NC-SA 3.0

Let us confirm the orientation on the glyph for France. 1830 is at the 2 o’clock position at upper right, 1840 is at lower right, and 1850 is straight down. 1860 is at lower left, 1870 at upper left, and 1878 comes at the top, at 12 o’clock. The circles grow larger as they go clockwise.

About the quarter-circles at the center, the legend says only that “one is yellow, one is green” and that they represent length relative to territory and to population. The text does not settle which is which, so I compare against the data table. Belgium has 7.5 km per 10,000 inhabitants and 13.5 km per 100 km², and in the plate the yellow one is larger. The United States has 33.9 km and 1.7 km, and the green one is larger while the yellow one is very small. Green is per 10,000 inhabitants, and yellow is per 100 km². The two quarter-circles sit side by side and form a semicircle in the lower half.

The separate box for ÉTATS-UNIS D’AMÉRIQUE. The 1878 blue circle is the largest, and in the center the green quarter-circle is large while the yellow one is very small

Source: Ministère des Travaux Publics (1880), separate box for the United States / David Rumsey Map Collection. CC BY-NC-SA 3.0

Placed 60 Degrees Apart: Ten Years and Eight Years

The six years are not equally spaced, and the legend says so itself. From 1830 to 1878 there are “4 périodes décennales consécutives et une période de 8 ans”: four ten-year periods and one eight-year period. Even so, the circles are placed 60 degrees apart. The preface’s “de dix en dix ans” (every ten years) can be read as a rounded way of describing that last eight-year period.

At upper right of the same plate is a line chart of the world’s total railway length. Its title is “Diagramme figurant le développement des chemins de fer du Monde de 1830 à 1878”.

A line chart titled DIAGRAMME, rising to the right from 1830 to 1878, with the years and lengths in thousands of km below

Source: Ministère des Travaux Publics (1880), line chart of the world’s railway length / David Rumsey Map Collection. CC BY-NC-SA 3.0

The horizontal axis here follows the actual intervals between years. The gap between the ticks for 1875 and 1878 is narrower than the others. The value for 1878 is 330.4 (thousand km), so the world’s railways had reached about 330,000 km.

Within a single sheet, time is handled in two ways. The glyphs line up points in time as “phases” at equal angles, while the line chart measures time as length. Since the legend itself points out the eight-year interval, it can be read as the makers being aware of the difference in intervals and still equalizing the angles of the glyph. What the glyph was meant to show was not the length of time but the difference in size from one phase to the next.

Countries Moved Off the Map, and the Data Table

Countries outside Europe cannot be placed on the map. According to the legend, the major ones gave up the map and were moved to separate boxes (cartouches). The legend states that the boxes have nothing to do with position, but that the conventions and the scale are the same as for the European countries.

The United States, British India, and Canada are in the boxes on the right, while Algeria is drawn at its position in North Africa. Because the scale is shared, the circles in the boxes can be compared in size with the circles on the map.

For the data table at lower right, the legend says that “the map is a translation of these figures into a diagram.” A few countries are extracted below (unit: km; “—” means not recorded).

Country	1830	1870	1878	Per 10,000 inhabitants	Per 100 km²
Great Britain and Ireland	279	24,999	27,552	8.6	8.7
France	37	17,924	24,424	6.6	4.6
Germany	—	18,560	31,556	7.4	5.8
Belgium	—	2,979	3,980	7.5	13.5
Europe, total	316	104,120	158,157	5.3	1.7
United States	65	84,637	131,681	33.9	1.7

The United States in 1878 had about 130,000 km, a little over five times France and close to the roughly 160,000 km of all Europe. The sources of the data are given under “Sources” in the legend: Poor’s Manual (1877), the Ministry’s Situation des chemins de fer (1878), and the Annuaire du Bureau des Longitudes pour 1879.

On a map of Western Europe, glyphs for Great Britain, Belgium, Germany, France, and others stand side by side, and large blue circles spill over the sea and neighboring countries

Source: Ministère des Travaux Publics (1880), Western Europe detail / David Rumsey Map Collection. CC BY-NC-SA 3.0

On the map, the glyphs become larger than the countries. The dotted circumference is about the same size for every country; only the blue circles change. The 1870 and 1878 circles for Great Britain and Germany spill over the sea and neighboring countries. The map seems to serve as a backdrop that shows which country each glyph belongs to, with positional accuracy a secondary concern.

How Third Parties Have Viewed This Album

In his 2008 paper “The Golden Age of Statistical Graphics,” Friendly places the album as a whole at the peak of the golden age of statistical graphics.

These volumes can be considered the pinnacle of the Golden Age, an exquisite sampler of nearly all known graphical forms, and a few that make their first appearance in these volumes.

Friendly names “planetary” diagrams among the new forms that appear in the album, and he shows plate 9 of the 1897 edition as an example. He does not discuss plate 16 itself. However, the Rumsey catalog notes this plate as a “multi-circle, planetary design,” so plate 16 can be read as an early example of that form. Friendly also writes that the album was discontinued in 1897 because of its high production cost.

The geographer Gilles Palsky offered a different view in a 2023 talk at the Ruderman Conference on Cartography.

In the end, it appears that the series of albums did not really meet their objectives, and this despite its high financial cost, which no doubt explains its extinction at the beginning of the twentieth century.

Palsky argues that the series fell short of its aims despite its cost, which likely explains why it ended in the early twentieth century.

Palsky views the album not from the quality of the plates but from its aims and readers. Together with the preface’s naming of members of parliament as the intended readers, this suggests that how well the plates are made and whether their aims were achieved are separate questions.

The third is perceptual research on reading proportional circles. In a 1970 presentation, James J. Flannery reported that even for circles whose areas are properly proportional, readers underestimate the differences in size.

map users consistently underestimated size differences

Map users consistently underestimated the differences in size.

Plate 16 makes the areas proportional exactly as the formula says. In light of Flannery’s result, the difference between the United States and France in 1878 may look smaller than the actual factor of a little over five.

Takeaways

What we can take away from plate 16 is that it hands the reader the rules of the encoding inside the chart itself.

The first is to write the formula in the legend. Plate 16 says that area is proportional to length, and even adds the radius formula. If you use proportional circles or bubbles, you can add one line saying that you scaled by area.

The second is to attach the underlying figures to the chart. Differences in area tend to be underestimated. Plate 16 has a data table, so the difference between the United States and France can be checked in numbers. The meaning of the colors of the quarter-circles was also settled with this table.

The third is to separate absolute and relative quantities by color and position. The outer blue circles are the total length, and the green and yellow at the center are per capita and per area. A country like Belgium, whose total length is small but whose length per area is large, can be read in a single glyph.

The fourth is to decide whether to equalize time by angle or to measure it by length, and to say which. Plate 16 equalizes the angles in the glyph, notes the eight-year interval in the legend, and shows the actual intervals in the line chart. Countries that do not fit were moved to separate boxes at the same scale. When you place small graphs on a map, you can likewise write in the legend what you kept and what you gave up.

References

Primary sources

Ministère des Travaux Publics, Carte figurative du développement des chemins de fer dans les principaux États de 1830 à 1878, 1880 (Album de statistique graphique 1880, pl. 16). David Rumsey Map Collection, List No. 12511.022. Detail page / IIIF manifest / Catalog (search API) / Internet Archive mirror
Album de statistique graphique 1880, table of contents (Table des matières). Internet Archive
Album de statistique graphique 1880, preface (Notice). Page 1 / Page 2
“Bibliographie. Notice relative à l’album de statistique graphique,” Journal de la Société de statistique de Paris, 22, 1881, pp. 25–28 (excerpt from the Bulletin de statistique du Ministère des travaux publics, August 1880). numdam / PDF

Secondary sources

Michael Friendly, “The Golden Age of Statistical Graphics,” Statistical Science, 23(4), 2008, pp. 502–535. DOI: 10.1214/08-STS268. Project Euclid / PDF
Michael Friendly, HistDataVis, Chapter 7. Online version
Gilles Palsky, “Legitimizing administrative statistics in XIXth Century France: The ‘Albums de Statistique Graphique’ in Context, their Aims and Audiences,” Ruderman Conference on Cartography, David Rumsey Map Center, Stanford University, 2023. Abstract
James J. Flannery, “The Relative Effectiveness of Some Common Graduated Point Symbols in the Presentation of Quantitative Data,” 1970 (ERIC ED045469). PDF

What Was Statistics Translated As? Meiji Coinages and the 1889 Debate over the Character Rendering

Sun, 07 Sep 2025 00:00:00 +0900

In Meiji Japan, the English word “statistics” was rendered by several competing terms, among them 政表 seihyō (“government tables”), 表紀 hyōki (“table record”), and 統計 tōkei (“unified counting”). Sugi Kōji (杉亨二), who led the practical work of official statistics, refused to translate the word at all. He built three composite kanji that transcribe the sound of the original, スタチスチク sutachisuchiku, and used them as the title of a lecture record. In 1889, Mori Ōgai (森鷗外) and Imai Takeo (今井武夫) argued in magazines for about ten months over whether the rendering 統計 tōkei was justified. The debate ended in a stalemate, and the term settled on 統計 tōkei.

What follows draws on the Statistics Bureau’s explanatory materials (the Statistics 150 Years special site and the Statistics Museum), Okuzumi Masahiko (奥積雅彦), “Naze ‘Statistics’ wa ’tōkei’ na no ka?” (Why Is “Statistics” “Tōkei”?; Tōkei Today No. 136, 2018), and Hozumi Nobushige (穂積陳重), Hōsō yawa (Night Talks of the Legal Profession, 1916). The titles and issue numbers of the debate pieces follow Okuzumi’s chronology. I have not checked Ōgai’s writings against the original Ōgai zenshū (Complete Works); I rely on passages that Sakai Hironori (酒井弘憲, 2014) quoted in modern orthography.

1860: statistics arrived as seihyō

The first statistical book introduced to Japan was Bankoku seihyō (萬國政表, “Government Tables of All Nations”), published in 1860 (Man’en 1). Okamoto Hakukei (岡本博卿) translated the work of P. A. de Jong, and Fukuzawa Yukichi (福沢諭吉) reviewed it. Its original title was Statistische tafel van alle landen der aarde. It is a book of tables giving the population, area, cities, products, and finances of the countries of the world. The Statistics Bureau’s explanation says: 「スタチスチックスに政表という訳語をつけたのは、本書が最初であった」 (“This book was the first to give statistics the translation 政表 seihyō”).

On February 2, 1872 (Meiji 4, 12th month, 24th day), Sugi Kōji was appointed 大主記 daishuki (chief secretary) of the 政表課 Seihyō-ka (Government Tables Section) in the Dajōkan’s Central Office (太政官正院). This is the post corresponding to today’s Director-General of the Statistics Bureau in the Ministry of Internal Affairs and Communications. In April of the same year, the section issued Shinbi seihyō (辛未政表, “Government Tables for the Shinbi Year”). It is the oldest comprehensive government statistical compilation, and Sugi was its editor in charge. In the first line of the editorial notes, small ruby characters 「スタチスチック」 (sutachisuchikku) stand to the right of the two characters 「政表」 (seihyō).

A page of the editorial notes of Shinbi seihyō. Small katakana ruby, 「スタチスチック」, stands to the right of 「政表」 in the first line

Source: Dajōkan Shikyoku (ed.), Shinbi seihyō (1872), editorial notes, from the Statistics Bureau of Japan, Statistics 150 Years special site, “Historical materials: Shinbi seihyō”. The original is in the public domain; the image is under 公共データ利用規約第1.0版 (Public Data License, version 1.0)

What drew Sugi to this work was translation at the Kaiseijo (開成所, the Bureau for the Study of Western Books). His autobiography says: 「バイエルンの教育の事を書いたものが有た。それに、百人の中で讀み、書きの出來る者が何人、出來ぬ者が何人と云うことが書いてあつた」 (“There was a text on education in Bavaria. It stated how many out of a hundred could read and write, and how many could not.”). Of a Dutch statistical book he also wrote: 「人が何分何厘とは妙な調べだと不思議になった」 (“I wondered at what a strange survey it was, counting people down to tenths and hundredths”).

In 1875, Fukuzawa Yukichi, in Bunmeiron no gairyaku (文明論之概略, An Outline of a Theory of Civilization), called this discipline by its original word, 「スタチスチク」 sutachisuchiku. I quote from the hiragana-converted text in Statistics Library Column No. 0001.

凡そ土地人民の多少、物価賃銭の高低、婚する者、生るゝ者、病に罹る者、死する者等、一々其数を記して表を作り、此彼相比較するときは、世間の事情、これを探るに由なきものも、一目して瞭然たることあり

In English: when one records, item by item, the numbers for the size of land and population, the level of prices and wages, those who marry, those who are born, those who fall ill, those who die, and so on, makes tables of them, and compares this with that, then conditions of the world that could not be explored by any other means can become clear at a glance. Fukuzawa calls this whole procedure sutachisuchiku. It can be read as nearly the same thing we now say about the benefit of visualization.

What each candidate word named

From the 1860s to the 1880s, many renderings stood side by side. Who used which, when, and where? The table below is compiled from the Statistics Bureau’s explanatory materials, Tōkei Today No. 136, and Hōsō yawa. The rightmost column, “What the characters name,” is my own organization.

Term / notation	Who	When and where	What the characters name
政表 seihyō, “government tables”	Translated by Okamoto Hakukei, reviewed by Fukuzawa Yukichi; later the Dajōkan Seihyō-ka	Bankoku seihyō, 1860; Shinbi seihyō, 1872	A table of the state
会計学 kaikeigaku, “science of reckoning”	Kanda Takahira (神田孝平)	Preface to Keizai shōgaku, 1867	Counting things together
統計 tōkei, “unified counting”	Possibly Yanagawa Shunsan (柳河春三); no firm evidence	Around 1869. As an office name, Ministry of Finance Tōkei-shi (統計司), 1871	Gathering under one head and counting
国勢学 kokuseigaku, “science of national conditions” / 国務学 kokumugaku, “science of national affairs”	University regulations / Daigaku Nankō regulations	1870	The state of the nation / the duties of the nation
国誌 kokushi, “national record”; 統計表 tōkeihyō, “statistical tables”; 国誌学 kokushigaku, “science of national records”	Fuon sōzu Eiwa jii (附音挿図英和字彙)	1873	The record of the nation, and its tables
統計学 tōkeigaku, “science of unified counting”	Translated by Mitsukuri Rinshō (箕作麟祥)	Tōkeigaku: ichimei kokusei ryakuron, Ministry of Education, 1874	A science that gathers and counts
表紀 hyōki, “table record” / 政表学 seihyōgaku, “science of government tables”	Translated by Tsuda Mamichi (津田真道)	Hyōki teikō: ichimei seihyōgaku-ron, Dajōkan Seihyō-ka, 1874	The characters mean recording in tables. The definition is a science for knowing the state of the nation
スタチスチク sutachisuchiku (original word)	Fukuzawa Yukichi	Bunmeiron no gairyaku, 1875	Does not translate
表記 hyōki, “recording in tables”	Sugi Kōji and others	Hyōki Gakusha, 1876	Recording in tables
知国学 chikokugaku, “science of knowing the nation”	Possibly devised by Sugi Kōji (according to Sera Taichi (世良太一))	For a time	A science of knowing the nation
Three composite kanji	Sugi Kōji	Lectures at the Kyōritsu Tōkei Gakkō, 1883-84	The sound of the original word

The origin of 統計 tōkei is not clear. By the testimony of Ishibashi Shigetomo (石橋重朝), around 1869 Yanagawa Shunsan compiled a small booklet at the Kaiseijo, either Tōkei nyūmon (統計入門, “Introduction to Tōkei”) or Tōkei benran (統計便覧, “Handbook of Tōkei”). He is said to have used 統計 there and noted that it was imperfect but would stand for the time being. The booklet itself has not been found, and the Statistics Bureau says “no definitive evidence remains.” Sakai (2014) also mentions a theory crediting Fukuchi Gen’ichirō (福地源一郎).

Hozumi Nobushige inferred the origin in Hōsō yawa as follows: 「この『統計』の二字は、恐らくは『英華字典』にスタチスチックに対して『統紀』という訳字を用いておったのに拠って案出したものであろう」 (“These two characters 統計 were probably devised on the basis of the Chinese–English dictionary’s use of 統紀 as the rendering for statistics”). The first office to carry 統計 in its name was the Ministry of Finance’s Tōkei-shi (統計司) on July 27, 1871 (Meiji 4); on August 10 of the same year it was renamed Tōkei-ryō (統計寮).

The Chinese compound 統計 of the time was a word with a different meaning. The enlarged and corrected edition of the Eika jiten (英華字典, English–Chinese dictionary) published in Japan in 1883 translates “Statistics” as 「国紀」 and 「国志」. 統計 appears there as one rendering of “Sum,” meaning a combined number.

There are also cases where the title and the definition disagree. Tsuda Mamichi used 表紀 hyōki in the title, yet defined it in Part 1 this way: 「表紀ノ原語ヲスタチスチキト謂フ其義ヲ直譯スレハ邦國又ハ形勢ト謂フ事ナリ」 (“The original word of hyōki is called statistiek; translated literally, its meaning is the nation, or conditions”). He continues: 「實際ノ形勢ヲ知ル學術」 (“the science of knowing actual conditions”). The editorial notes of Mitsukuri’s Tōkeigaku say: 「其説ク所ハ皆算數ヲ以テ國内百般ノ事ヲ表明シ」 (“What it expounds is all to make plain the many matters within the country by means of arithmetic”).

Laid out in a table, the candidates can be read as falling into three groups: words that name the finished table, words that name the operation of gathering and counting, and words that name the state of the nation one wants to know. 政表 seihyō and 表記 hyōki correspond to the table; 会計学 kaikeigaku and 統計 tōkei to the operation; 国勢学 kokuseigaku and 知国学 chikokugaku to the state of the nation. As for 表紀 hyōki, its characters name the table, but Tsuda’s definition is 「實際ノ形勢ヲ知ル學術」, so it can be read as a word that straddles both the table and the state of the nation. By this division, 統計 tōkei, the term that survived, can be read as the name of an operation.

Sugi Kōji refused to translate

Three composite kanji created by Sugi Kōji

While leading the work of the 政表 seihyō office, Sugi took a different road on the question of the term. In February 1876 (Meiji 9), Sugi and some ten others founded the 表記学社 Hyōki Gakusha (Society for Recording in Tables). In 1878 it was renamed the スタチスチツク社 Sutachisuchitsuku-sha (Statistics Society), and in 1892 it became the 統計学社 Tōkeigakusha. Hōsō yawa writes that the name was chosen because the translated characters were 「区々」 (scattered, inconsistent) and it was better to keep the original word.

In September 1883, Sugi opened the Kyōritsu Tōkei Gakkō (共立統計学校, Joint Statistics School) with volunteers from the Statistics Office (統計院) and became its head instructor. The Statistics Museum’s explanation continues: 「『統計学校』の『統計』という訳語が、スタチスチックの本来の意味を表現していないとしてよしとせず、自ら漢字を創作して使用した」 (“He did not accept that the rendering 統計 in ‘Tōkei Gakkō’ expressed the original meaning of statistics, and created and used characters of his own”). The characters are these three.

Three composite kanji created by Sugi Kōji. From the left, characters combining 寸 and 多, 知 and 寸, and 知 and 久

Source: Sugi Kōji’s invented kanji, from the Statistics Bureau of Japan, Statistics Museum, “Sugi Kōji” (公共データ利用規約第1.0版, Public Data License, version 1.0)

The first character combines 寸 and 多 for “スタ” (suta); the second puts 寸 under 知 for “チス” (chisu); the third puts 久 under 知 for “チク” (chiku). Each packs two sound-bearing kanji into one character, and the three together are read as 「スタチスチク」 (sutachisuchiku). Hōsō yawa says that Sugi “devised and created” these characters in order to “assign” them to the original word (「案出創造せられた」). The Statistics Bureau’s “Naruhodo Tōkei Gakuen” also explains that Sugi argued the word should not be forced into a translation and that 「寸多知寸知久（スタチスチク）」 should be used instead.

In other words, these three characters are not a translation that replaces meaning with Japanese. They are characters for copying the sound of the original word. The notebook of Sugi’s lectures at the Kyōritsu Tōkei Gakkō (1883-84), taken down by Yokoyama Masao (横山雅男), bears this composite kanji title. The Japan Statistical Association reprinted it in 1980. This means the composite kanji were in use before the 1889 debate.

In April 1886 (Meiji 19), the first issue of the Statistics Society’s Sutachisuchikku zasshi (スタチスチック雑誌, Statistics Journal) appeared. In “Sutachisuchikku no hanashi” (スタチスチックの話, “A Talk on Statistics”), Sugi wrote: 「（杉が）知る所にても『スタチスチック』に統計なる意味のあることは未だ曾て見あたらず」 (“As far as he knows, he has never yet found that ‘statistics’ carries the meaning of 統計”). In 1947, Takano Iwasaburō (高野岩三郎) described Sugi as an advocate of “rejecting translated characters and adopting the original word.”

The composite kanji did not take hold. The Statistics Bureau writes that the other candidates, including newly coined characters, “none took hold, and in time faded away.” I have found no source that states why they did not take hold.

1889: Ōgai, Imai Takeo, and ten months of debate

In February 1889 (Meiji 22), Igaku tōkeiron (医学統計論, “On Medical Statistics”), by Oesterlen and translated by Kure Shūzō (呉秀三), was published. The army surgeon Mori Rintarō (森林太郎, Ōgai), then 27, wrote a 「題言」 (daigen, preface remarks) for the book at Kure’s request. The preface also appeared in Tōkyō Iji Shinshi (東京医事新誌, Tokyo Medical News), No. 569. There Ōgai uses 統計 tōkei as the translated term.

An anonymous letter arrived at the editorial office of Tōkyō Iji Shinshi. It asked why 統計 tōkei was used rather than スタチスチック sutachisuchikku. The letter came from Imai Takeo, who belonged to Sugi Kōji’s group. The stage was Tōkyō Iji Shinshi, edited by Ōgai, and the Sutachisuchikku zasshi of the Statistics Society.

Date (Meiji 22 = 1889)	Author	Title	Journal and issue
March	Mori Rintarō	統計ニ就テ (On Tōkei)	Tōkyō Iji Shinshi, No. 573
May	Imai Takeo	統計ニ就テ (On Tōkei)	Sutachisuchikku zasshi, No. 37
June	Mori Rintarō	統計ニ就テノ分疏 (A Defense of “On Tōkei”)	Tōkyō Iji Shinshi, No. 584
July	Imai Takeo	再ビ統計ニ就テ (On Tōkei, Again)	Sutachisuchikku zasshi, No. 39
August	Mori Rintarō (pen name Kojō Itsumin, 湖上逸民)	統計三家論ヲ讀ム (Reading the Three Views on Tōkei)	Tōkyō Iji Shinshi, No. 593
August	Mori Rintarō (pen name Ōgai Gyoshi, 鷗外漁史)	答今井武夫君 (A Reply to Mr. Imai Takeo)	Tōkyō Iji Shinshi, No. 593
September	Imai Takeo	三タビ統計ニ就テ (On Tōkei, a Third Time)	Sutachisuchikku zasshi, No. 41
October	Mori Rintarō (pen name Kojō Itsumin)	讀第三駁義 (Reading the Third Rebuttal)	Tōkyō Iji Shinshi, No. 603
October	Mori Rintarō (pen name Oshigaoka Shōkaku, 忍岡樵客)	「三タビ統計ニ就テ」ヲ讀ム (Reading “On Tōkei, a Third Time”)	Tōkyō Iji Shinshi, No. 604
November	Mori Rintarō (pen name Kojō Itsumin)	統計ノ訳字ハ其定義ニ負カズ (The Translated Term Tōkei Does Not Fall Short of Its Definition)	Tōkyō Iji Shinshi, No. 605
December	Imai Takeo	四タビ統計ニ就テ（未完）(On Tōkei, a Fourth Time; unfinished)	Sutachisuchikku zasshi, No. 44

Source: Okuzumi Masahiko’s chronology (Tōkei Today No. 136). The issue numbers and dates of the Sutachisuchikku zasshi also agree with the bibliographic records in NDL Search (National Diet Library)

Ōgai wrote seven pieces, using his real name and three pen names. Imai wrote four, and the last, “On Tōkei, a Fourth Time,” is unfinished. Okuzumi organizes the points of dispute into three.

Point of dispute	Mori Ōgai	Imai Takeo
Is 統計 tōkei an appropriate rendering?	The rendering “to unify and count” (統べ計る) conveys the meaning	The Chinese word 統計 has no meaning beyond totaling
Is statistics a science or a method?	Not a science but a method	Not only a method that assists other sciences, but a science that studies the phenomena of human society
Can statistics uncover causes?	It cannot be used to find causes or know laws	Examining phenomena in relation to their factors, one can find causes and establish laws

On the first point, Ōgai argued from the meaning of the characters in “統計ニ就テノ分疏.” According to the passages that Sakai (2014) quotes in modern orthography, Ōgai cites the Shuowen (『説文』) on 計: 「“計"は"会也算也”」 (“計 is ’to bring together; to reckon’”). He then writes: 「今含率等物の義ある統字をもって計字の上に加うることはそのスタチスチックの意味を表出することは殆ど余蘊なきを見るなり」 (“Adding the character 統, which carries the sense of containing and governing things, above the character 計 conveys the meaning of statistics, I find, almost without remainder”). He closes with: 「誰か統計の字面を以ってスタチスチックの訳に充つべからずというや」 (“Who would say that the characters 統計 cannot serve as the translation of statistics?”).

Imai’s side replied that the Chinese word 統計 has no meaning beyond a total. It can be read as the same line that Sugi had taken in 1886. Okuzumi describes the outcome of the debate this way: 「両者の見解は平行線をたどり、相交えることはなかったのです」 (“The two views ran in parallel lines and never met”).

How did third parties see the debate?

Okuzumi (2018) draws attention to the timing of the debate. The character 統計 had been spreading gradually: Tōkeigaku in 1874, the Statistics Office in 1881, the Kyōritsu Tōkei Gakkō in 1883. Okuzumi writes: 「この訳字論争が行われたのは明治22年のことであり、逸機の感があります」 (“This debate over the translated term took place in Meiji 22, and one has the sense that the opportunity had already been missed”). At the head of “再ビ統計ニ就テ” in No. 39 of the Sutachisuchikku zasshi was an unusual note saying that this was Imai’s personal view and not the journal’s editorial position. Okuzumi sees in this a “temperature gap” between Imai and Sugi’s group. He concludes: 「今井が森鴎外に一歩も譲らなかったことを忘れてはならないのです」 (“We must not forget that Imai did not yield a single step to Mori Ōgai”).

Nakazawa Satoshi (中澤聡, 2023) investigated the sources of Ōgai’s view of statistics. He compares the 題言, “統計ニ就テ,” and the “分疏” with a 1881 paper by Friedrich Martius. The English abstract reads:

Mori’s view of statistics, owing much to Martius’s paper, can be characterised as a conditional approval à la Bernard that recognises the auxiliary significance of statistics only when the cause cannot be identified using experimental methods.

In short: Ōgai’s view of statistics owes much to Martius. He grants statistics an auxiliary significance only when a cause cannot be identified experimentally, a conditional approval in the manner of Bernard. Ōgai’s stance that “statistics is a method” can be read as coming from the European medical debates of the day.

The Center for Social Science Statistical Information at the Institute of Economic Research, Hitotsubashi University, points out the irony of the ending in an exhibition document. Tōkei tsūron (統計通論, “General Theory of Statistics”), written by Sugi’s disciple Yokoyama Masao, first appeared in 1901 and went through more than forty editions. In the early 1900s, the word 統計 reached China through Yokoyama’s statistics books. The exhibition document says it “may be an irony of history” that the word Sugi disliked enough to build composite kanji against “was spread as far as China by his disciple Yokoyama.” However, the same document states flatly that 統計 was devised by Yanagawa Shunsan, which does not agree with the Statistics Bureau’s view. Today the Chinese word is “统计,” the Korean “통계,” and the Vietnamese “thống kê.”

Sugi himself wrote the following in 1899, in “Tōkei taii” (統計大意, “Outline of Statistics,” Tōkei shūshi No. 223), in summary: the “irresponsible statistics” that takes statistics to be calculation and treats a mere lining up of the numbers of things as statistics is not to be permitted. Takano Iwasaburō in 1947 judged that this point “is one that our statisticians even now should take deeply to heart.” It has not been confirmed whether Sugi touched on the translated term in this piece.

Putting it to use

What this story lets us carry back to visualization work is the question of which part of the work a name points to.

The Meiji terms can be read as dividing into those that name the output, the table; those that name the operation of gathering and counting; and those that name the state of the nation one wants to know. What survived can be read as the name of an operation. Sugi’s reason for objecting in 1886 was that he could find no sense of 統計 in “statistics.” His 1899 warning against “merely lining up the numbers of things” and his 1886 objection to the term can be read as lying on the same line. I have not, however, been able to confirm any text in which Sugi himself linked the two.

Visualization work has the same gap. Requests often arrive under the name of an output: “please make a graph.” The way of proceeding is described as an operation: “aggregate and draw.” Yet, as Fukuzawa wrote, the purpose of making tables and comparing them was to know 「世間の事情」 (the conditions of the world) at a glance. When naming a project, check whether the name points to the output, the operation, or what we want to know. The table of candidate terms can serve as a model for doing so.

References

Primary sources

Hozumi Nobushige (穂積陳重), Hōsō yawa (法窓夜話, Night Talks of the Legal Profession), section 57 “Tōkeigaku” (統計学, Statistics), Yūhikaku, 1916 (Aozora Bunko, based on the Iwanami Bunko edition of 1980). 青空文庫
Statistics Bureau of Japan, Statistics 150 Years special site, “Tōkei no ijintachi: Mori Ōgai” (統計の偉人たち：森鴎外, Great Figures of Statistics: Mori Ōgai). ijin04
Statistics Bureau of Japan, Statistics 150 Years special site, “Tōkei no ijintachi: Sugi Kōji” (統計の偉人たち：杉亨二, Great Figures of Statistics: Sugi Kōji; includes the autobiography quotations). ijin03
Statistics Bureau of Japan, Statistics 150 Years special site, “Tōkei shiryō” (統計史料, Historical Materials): Bankoku seihyō / Shinbi seihyō / Tōkeigaku: ichimei kokusei ryakuron / Hyōki teikō: ichimei seihyōgaku-ron / Sutachisuchikku zasshi
Statistics Bureau of Japan, Statistics 150 Years special site, “Tōkei no rekishi torivia” (統計の歴史トリビア, Statistical History Trivia). trivia03
Statistics Bureau of Japan, Statistics Museum, “Sugi Kōji” (杉亨二; includes the image of the invented kanji). sugi.html
Statistics Bureau of Japan, Naruhodo Tōkei Gakuen, “‘Tōkei’ to iu kotoba no kigen” (「統計」という言葉の起源, The Origin of the Word “Tōkei”). toukei.html
Statistics Bureau of Japan, Naruhodo Tōkei Gakuen Kids, “Tōkei episōdo (1)” (統計エピソード（1）, Statistics Episode 1). ep1.html
Okuzumi Masahiko, “Naze ‘Statistics’ wa ’tōkei’ na no ka? Tōkei no yakuji ga teichaku suru made no keii to Mori Ōgai” (なぜ『Statistics』は『統計』なのか？ー『統計』の訳字が定着するまでの経緯と森鴎外, Why Is “Statistics” “Tōkei”? How the Translated Term Took Hold, and Mori Ōgai), Tōkei Today No. 136, Statistics Bureau, 2018 (cites period dictionaries, Sugi Kōji’s “Sutachisuchikku no hanashi,” 1886, and “Tōkei taii,” 1899). HTML／PDF
Statistics Bureau of Japan, Statistics Library Column No. 0001 (Fukuzawa Yukichi). PDF
Statistics Bureau of Japan, Statistics Library Column No. 0006 (Mori Ōgai and the course of the debate). PDF
Sugi Kōji (lecturer) and Yokoyama Masao (note-taker), [寸多][知寸][知久] Rekishi oyobi riron no bu (History and Theory; 1980 reprint; the title is the author’s composite kanji). 国立国会図書館サーチ
Sutachisuchikku zasshi, No. 1 (1886-04). 国立国会図書館サーチ／No. 37 (1889-05). 国立国会図書館サーチ／No. 44 (1889-12). 国立国会図書館サーチ
Oesterlen, trans. Kure Shūzō, Igaku tōkeiron sōron (医学統計論総論, General Introduction to Medical Statistics), Bunshōdō, 1889. 国立国会図書館サーチ
Dajōkan Shikyoku (ed.), Shinbi seihyō, 1872. 国立国会図書館デジタルコレクション
Statistics Bureau of Japan, “Saito no riyō ni tsuite” (サイトの利用について, About Using This Site; 公共データ利用規約第1.0版, Public Data License, version 1.0). riyou.html

Secondary sources

Nakazawa Satoshi (中澤聡), “Mori Ōgai no tōkeiron no gensen: Furīdorihi Maruchiusu no igaku tōkeiron” (森鷗外の統計論の源泉――フリードリヒ・マルチウスの医学統計論, The Sources of Mori Ōgai’s Theory of Statistics: Friedrich Martius’s Medical Statistics), Kagakushi kenkyū (科学史研究, Journal of the History of Science, Japan) 61(304), 2023, pp. 318-331. doi:10.34336/jhsj.61.304_318／J-STAGE
Okuzumi Masahiko, “Naze ‘Statistics’ wa ’tōkei’ na no ka?” Tōkei Today No. 136, 2018 (the evaluative parts). HTML
Hitotsubashi University, Institute of Economic Research, Center for Social Science Statistical Information, exhibition document “Tōkei tsūron” (統計通論, General Theory of Statistics). PDF
Sakai Hironori (酒井弘憲), “Dai 2 kai: Tōkei no rūtsu o saguru” (第2回統計のルーツを探る, Part 2: Exploring the Roots of Statistics), Farumashia 50(4), 2014, pp. 334-335 (includes passages from Ōgai’s 題言 and “分疏” quoted in modern orthography). J-STAGE
Takagi Shūgen (高木秀玄), “Mori Ōgai no tōkeigaku-kan: Imai Takeo to no ronsō o chūshin to shite” (森鴎外の統計学観：今井武夫との論争を中心として, Mori Ōgai’s View of Statistics: Centering on the Debate with Imai Takeo), Kansai Daigaku keizai ronshū (關西大學經済論集) 19(3), 1969 (bibliographic record only checked). CiNii Research

Switching Inks at the Imperial Average: The German Imperial Statistical Office's Wheat-Yield Map (1905)

Thu, 02 Oct 2025 00:00:00 +0900

The 1905 Vierteljahrshefte zur Statistik des Deutschen Reichs (Quarterly Journal of the Statistics of the German Reich) carries a map of wheat yields for the 1904 harvest. It was made by the Imperial Statistical Office (Kaiserliches Statistisches Amt). The map switches the color of its ink at the imperial average, and within each side, above and below the average, it tells the classes apart by pattern type and line density.

The figure is a single sheet with two maps, one above the other: winter wheat (Winter-Weizen) on top and spring wheat (Sommer-Weizen) below. Below, I read the printed text and legend as the primary source, and set the map beside a figure in the same style from the previous year and another figure showing the same year’s harvest.

Yield maps of winter wheat and spring wheat for the 1904 harvest

1905: A Plate for the Harvest Statistics

At the top of the figure, this is printed.

(Vierteljahrshefte zur Statistik des Deutschen Reichs, 1905. I.) Erntestatistik für das Jahr 1904. No. 1 u. 2.

It means: Part I of the 1905 Vierteljahrshefte, harvest statistics for the year 1904, plates No. 1 and No. 2. 1904 is the year of the harvest, and the publication is from 1905. The Office’s Statistisches Jahrbuch für das Deutsche Reich (Statistical Yearbook for the German Reich), 1905 edition, also gives Part I of the 1905 Vierteljahrshefte as the source of its 1904 harvest tables.

The harvest statistics rest on a resolution of the Bundesrat of 19 January 1899, and the results from 1900 onward appear in Part I of the following year’s Vierteljahrshefte. The Office was the Reich’s central statistical authority, established in 1872.

The title of the figure is “DEUTSCHES REICH. Schematische Karte bearbeitet im Kaiserlichen Statistischen Amt.” Schematische Karte means “schematic map”: instead of drawing the real boundaries of the administrative districts, it lays them out as rectangular blocks. Abbreviations such as Danzig and Posen appear in white inside the blocks. Whether the area of a block is proportional to the real area is not stated. The unit of aggregation is, as the subtitle “Nach preuss. und bayer. Regierungsbezirken, sächs. Kreishauptmannschaften pp.” says, Prussian and Bavarian Regierungsbezirke (governmental districts), Saxon Kreishauptmannschaften, and so on. No individual’s name appears on the figure.

My account of the 1904 figure is based on a scan of the single sheet bearing a holdings stamp of the Bibliothèque nationale de France (BnF). I could not verify the holdings record, so I do not show the image and present the contents of the legend in tables instead.

Switching Inks at the Imperial Average

The title of the legend is “Hectar-Ertrag in Tonnen 1904.” It shows the yield per hectare in tons. The scale runs from 0.61 to 3.40 in steps of 0.2 tons.

The legend is split in two by the line of the imperial average (Reichsdurchschnitt). The vertical label on the upper side reads “Unter Reichsdurchschnitt” (below the imperial average), and the one on the lower side reads “Ueber Reichsdurchschnitt” (at or above the imperial average). The winter wheat map states “Reichsdurchschnitt: 2,00” and prints the below-average classes in orange tones and the at-or-above-average classes in black.

The correspondence between data and appearance is as follows.

Data	Mapped to	Value in the winter wheat map
Position of the administrative district	Placement and abbreviation of the rectangular block	Real boundaries are not drawn
Yield per hectare	Classes in steps of 0.2 tons	14 classes, 0.61 to 3.40
Above or below the imperial average	Switch of ink color	Average 2.00. Below is orange, at or above is black
Rank within the same side	Pattern type, and line weight and density	Dots, diagonal lines, horizontal lines, wavy lines, grids, blocks
Classes that appear on the map	“*” mark to the left of the legend	10 of the 14 classes
Smallest and largest districts	District names and values above and below the legend	Hamburg 1.08 / Danzig 2.96

Reading the winter wheat legend from the top gives the following.

Class (t/ha)	Color	Pattern	Appears on the map
0.61–0.80	Pale orange	Dots	—
0.81–1.00	Pale orange	Fine diagonal lines	—
1.01–1.20	Pale orange	Fine horizontal lines	*
1.21–1.40	Pale orange	Fine wavy lines	*
1.41–1.60	Deep orange	Heavier horizontal lines	*
1.61–1.80	Deep orange	Heavier diagonal lines	*
1.81–2.00	Deep orange	Heavier wavy lines	*
(Imperial average 2.00)
2.01–2.20	Black	Horizontal lines	*
2.21–2.40	Black	Thick diagonal lines	*
2.41–2.60	Black	Coarse diagonal grid	*
2.61–2.80	Black	Fine diagonal grid	*
2.81–3.00	Black	Thick horizontal band	*
3.01–3.20	Black	Blocks separated by white lines	—
3.21–3.40	Black	Larger black blocks	—

There are two layers, “below the average” and “at or above the average,” with no middle layer.

In the spring wheat map the average is “1,93”. The below-average classes are printed in red tones, and the at-or-above-average classes in a dark color close to black. In the scan the dark color looks like a dark brown, redder than black. The scale is the same as for winter wheat, but only the class 1.81–2.00 is split at the average, into 1.81–1.83 and 1.84–2.00. This can be read as a design in which the average of that year and that crop is inserted as a boundary into a fixed ruler with 0.2-ton steps.

Dividing Patterns Above and Below the Average

Color is responsible for whether a value is above or below the average. The rank within the same side is the job of pattern type and line density.

The below-average side has four pale orange classes and three deep orange classes, and it reuses the same kinds of pattern: diagonal lines, horizontal lines, wavy lines. Pattern type in itself has no order of large and small. It can be read that the order is conveyed mainly by the depth of color and by being above or below the average, and that the pattern takes on distinguishing the classes within the same depth. The at-or-above-average side is arranged in order of increasing black area, from lines to grids and from grids to blocks. Here the blackness of the pattern itself can be read as expressing the order of quantity.

The legend also carries a summary of the distribution. To the right of the “*” mark on the left there is an explanation in vertical text.

In dieser Karte vorkommende Stufen.

It means: the classes that occur in this map. Above and below the legend are written the names and values of the smallest and largest districts.

Figure	Classes in legend	Classes on the map	Smallest	Largest
Winter wheat (No. 1)	14	10	Hamburg 1.08	Danzig 2.96
Spring wheat (No. 2)	15 + “not cultivated”	11	Oberpfalz 0.95	Schaumburg-Lippe 2.80

0.61 and 3.40 are the two ends of the scale, not the actual minimum and maximum. The spring wheat legend also has a white box marked “0”, “nicht angebaut” (not cultivated). The smallest value agrees with the yearbook’s table: on p. 27 of the 1905 edition, the 1904 wheat yield of Hamburg is 10.8 dz/ha, that is, 1.08 t/ha.

Legend of the previous year’s winter wheat map: above the line of the imperial average, 1.93, are seven gray-black patterns, and below it eight crimson patterns

Source: Kaiserliches Statistisches Amt, Statistisches Jahrbuch für das Deutsche Reich, 1904 edition, plate No. 1, legend / Mannheim University Library, “Statistische Jahrbücher” (Public Domain Mark 1.0)

This is the legend of a figure in the same style that depicts the harvest of the previous year, 1903. The structure is the same: vertical labels above and below, the “*” on the left, and the smallest and largest districts above and below. The way color is used is different.

Placing It Beside the Previous Year’s Map

This style is not a one-off. The preface of the 1904 yearbook describes the plates at the back of the volume as follows.

Die graphischen Beilagen zeigen in 8 schematischen Karten für die einzelnen Verwaltungsbezirke den Ernteertrag im Jahre 1903 für Winter- und Sommerweizen, Winter- und Sommerroggen, Gerste, Hafer, Kartoffeln und Klee (Heu).

It means: eight schematic maps show the 1903 harvest for each administrative district. The crops are winter and spring wheat, winter and spring rye, barley, oats, potatoes, and clover (hay).

The administrative districts of the German Reich, laid out as rectangular blocks, colored in with gray-black and crimson patterns

Source: Kaiserliches Statistisches Amt, Statistisches Jahrbuch für das Deutsche Reich, 1904 edition, plate No. 1 “Winter-Weizen” / Mannheim University Library, “Statistische Jahrbücher” (Public Domain Mark 1.0). The original is in landscape orientation and has been rotated by 90 degrees.

Compare the winter wheat maps of 1903 and 1904.

	1903 harvest (yearbook 1904)	1904 harvest (Vierteljahrshefte 1905, I)
Below average	Gray-to-black patterns	Orange patterns
At or above average	Crimson patterns	Black patterns
Imperial average	1.93 (class split into 1.81–1.93 / 1.94–2.00)	2.00
Smallest / largest	Birkenfeld 1.16 / Anhalt 2.90	Hamburg 1.08 / Danzig 2.96

In the eight maps of 1903, the below-average classes are printed in gray to black, and the at-or-above-average classes in one color per crop: crimson for winter wheat, salmon for spring wheat, blue for potatoes, green for clover. In the 1903 edition, “color = at or above the average”, and in the 1904 edition, “black = at or above the average”, so the role of color can be read as reversed from year to year.

I have not found any source that explains the use of patterns by printing constraints. The same Office printed the previous year’s eight maps in a different color for each crop, and plate No. 1 at the back of the 1905 yearbook is also multicolor.

A figure showing the yields of five crops by the width and height of rectangles for each region, colored in yellow, orange, and pink by crop

Source: Kaiserliches Statistisches Amt, Statistisches Jahrbuch für das Deutsche Reich, 1905 edition, plate No. 1 / Mannheim University Library, “Statistische Jahrbücher” (Public Domain Mark 1.0)

This figure depicts the same 1904 harvest. Its encoding is written in the subtitle.

(Erntefläche = Grundlinie; Hektarertrag = Höhe; Erntemenge = Rechteck aus Grundlinie × Höhe.)

It means: harvested area corresponds to the width, yield per hectare to the height, and harvest quantity to the area of width times height. The same Office shows the same year’s yields by “above or below the average, and class” in the map, and by “width times height” in this figure. One can read in it the idea of drawing separately the yield as a rate and the harvest as a total.

Through Third-Party Frameworks

I could not find any third-party text that discusses this figure itself. I use three sources that place the method in context.

The first is the number of classes. The English Wikipedia article “Choropleth map,” citing Monmonier (1977), Brewer (1994) and others, says the following.

for shades of gray, tests have shown that when value alone is used (e.g., light to dark, whether gray or any single hue), it is difficult to practically use more than seven classes. … If differences in hue and/or saturation are incorporated, that limit increases significantly to as many as 10-12 classes.

In short: with lightness alone it is hard to go beyond seven classes, and adding hue or saturation raises that to 10–12. The same article calls a color scheme that splits two series around a center such as the average “divergent”. The 14 to 15 classes of the 1904 figure exceed this guideline, and the construction that splits color at the average can be read as the same idea as today’s divergent color schemes. The article also says that the oldest choropleth map is Dupin’s map of 1826, and that color came into wide use after 1850. The 1904 figure is not an early example of the choropleth.

The second is how patterns work. Axis Maps’ “Cartography Guide: Visual Variables,” based on the visual variables of Jacques Bertin, says the following.

Shape is the only one of Bertin’s variables that he thought is never selective, along with orientation when used for area representation (e.g., polygons symbolized by differently angled stripe patterns).

That is, when stripe patterns of different angles are used on areas, orientation, like shape, cannot be picked out at a glance. The same guide also says that size and value have an order that can be seen at a glance, and hue does not. The differences between diagonal and horizontal lines and between straight and wavy lines in the 1904 figure have no order, and the patterns can be read as serving to tell classes apart by checking against the legend.

The third is Germany of the same period. The English Wikipedia article “Cartogram” gives as the oldest known continuous cartograms a pair of maps by Hermann Haack and Hugo Weichel. They depict the results of the 1898 Reichstag election, in preparation for the 1903 election. The schematic map of the Statistical Office is not described as making area proportional to quantity. Even so, it can be read that, in Germany around the same time, attempts to show statistics by simplifying geographic form were happening side by side.

How to Use This

What we can take away is a design that assigns separate jobs to color and pattern.

Split above and below a baseline by color. Use two color families, and write the baseline value into the legend.
Insert the baseline into a fixed ruler. Keep the class widths common across figures, and when the baseline falls in the middle of a class, split that class, as in the spring wheat map.
Use pattern for telling classes apart. Give the order of quantity to depth or to the black area, and use the pattern as a clue for checking against the legend.
Write a summary of the distribution in the legend. Mark the classes that actually occur, and add the names and values of the smallest and largest districts.
In a series, fix the roles of the colors. When the roles are reversed, as between 1903 and 1904, readers have to check the legend every time.

If we were making this today, we could consider reducing the number of classes in line with the guideline above (for the basics, see the article on the choropleth map). Even so, the 1905 legend, which separates the roles of color and pattern, can be read as a model for designing a legend.

References

Primary sources

This figure: Kaiserliches Statistisches Amt, „Schematische Karte" No. 1 Winter-Weizen / No. 2 Sommer-Weizen, Vierteljahrshefte zur Statistik des Deutschen Reichs, 1905, I. (Erntestatistik für das Jahr 1904). Confirmed from a single-sheet scan bearing a BnF holdings stamp. Holdings record not verified
Statistisches Jahrbuch für das Deutsche Reich, 1904, preface p. III: PDF
Same, 1904 edition, plate “Erntestatistik für das Jahr 1903” No. 1 Winter-Weizen: PDF, No. 2 Sommer-Weizen: PDF, No. 7 Kartoffeln: PDF, No. 8 Klee (Heu): PDF
Statistisches Jahrbuch für das Deutsche Reich, 1905, preface p. III: PDF
Same, 1905 edition, list of sources p. XII: PDF, p. XIV (where the harvest statistics are published): PDF
Same, 1905 edition, p. 26 (harvest table for 1904): PDF, p. 27 (yield per hectare): PDF
Same, 1905 edition, plate No. 1 “Erntefläche, Hektarertrag und Erntemenge i.J. 1904”: PDF
Mannheim University Library, “Statistische Jahrbücher” (Public Domain Mark 1.0): Digital edition / Terms of use
Bibliographic record of Vierteljahrshefte zur Statistik des Deutschen Reichs: Internet Archive

Secondary sources

Wikipedia, “Choropleth map”: en.wikipedia.org
Axis Maps, “Cartography Guide: Visual Variables”: axismaps.com
Wikipedia, “Cartogram”: en.wikipedia.org
Wikipedia (German), “Kaiserliches Statistisches Amt”: de.wikipedia.org

Data Analysis Is a Science: What Tukey Wrote to Mathematical Statistics in 1962

Sun, 23 Aug 2026 00:00:00 +0900

In 1962, John W. Tukey published a 67-page paper in the central journal of mathematical statistics. Its title was “The Future of Data Analysis.” It has no theorems and no proofs. In the opening he writes that he had long thought himself a statistician, but that his central interest is data analysis. His main argument is that data analysis is a science.

Half a century later, David Donoho rereads the paper as the starting point of a science that learns from data. David Hand calls Tukey “the first data scientist.” When people today speak of “the beginning of data science,” the event they point to is, first of all, this paper.

The paper itself

The bibliographic details are as follows. John W. Tukey, “The Future of Data Analysis,” The Annals of Mathematical Statistics, Vol. 33, No. 1 (March 1962), pp. 1–67. DOI: 10.1214/aoms/1177704711. The journal was then at the front line of mathematical statistics. The other papers in the same issue are lined with definitions, theorems and proofs. Donoho writes that a public confession was published among them.

The opening is two paragraphs that James R. Thompson called, in 2001, a “manifesto of an intellectual revolution.”

For a long time I have thought I was a statistician, interested in inferences from the particular to the general. But as I have watched mathematical statistics evolve, I have had cause to wonder and to doubt. […] All in all, I have come to feel that my central interest is in data analysis, which I take to include, among other things: procedures for analyzing data, techniques for interpreting the results of such procedures, ways of planning the gathering of data to make its analysis easier, more precise or more accurate, and all the machinery and results of (mathematical) statistics which apply to analyzing data.

In short: he had long thought himself a statistician, interested in inference from the particular to the general. Watching mathematical statistics develop, he came to doubt. What lies at the center, he says, is data analysis, which includes (1) procedures for analyzing data, (2) techniques for interpreting their results, (3) plans for gathering data so that analysis is easier, more precise or more accurate, and (4) the machinery and results of mathematical statistics that apply to analyzing data.

He goes on to write that inference from a sample to a population is a large part but not the whole. Work that picks out signs invisible in the raw data, and work that decides how to allocate effort, are also only parts. “Data analysis is a larger and more varied field than inference, or allocation.” He admits that he is stretching the term beyond its etymology. Peter Huber later judged that this stretching wrapped the whole of statistics inside it.

On page 3, he asks: “Is it not time to seek out novelty in data analysis?”

Three conditions for a science

On pages 4–5, he lists three conditions for being a science. The passage below sets out that argument as he wrote it.

There are diverse views as to what makes a science, but three constituents will be judged essential by most, viz: (a1) intellectual content, (a2) organization into an understandable form, (a3) reliance upon the test of experience as the ultimate standard of validity. By these tests, mathematics is not a science, since its ultimate standard of validity is an agreed-upon sort of logical consistency and provability. As I see it, data analysis passes all three tests, and I would regard it as a science, one defined by a ubiquitous problem rather than by a concrete subject.

Intellectual content. Organization into an understandable form. Reliance on the test of experience as the ultimate standard of validity. Data analysis meets all three. It is, in Tukey’s words, a science defined by a ubiquitous problem rather than by a concrete subject. By the same three conditions, mathematics falls outside science, because its ultimate standard is logical consistency and provability. Where statistics stands depends on whether statisticians side with data analysis or with pure mathematics. He even writes that the two cannot both be the ultimate standard at once.

Standing on the side of science changes one’s attitude as well. These are the points Michael Friendly cites.

(b1) Seek scope and usefulness rather than security.
(b2) Tolerate moderate error, to raise the chance that inadequate evidence will suggest the right answer.
(b3) Use mathematical argument as a basis for judgment, not as a mark of proof or validity.

A famous sentence on page 13 compresses this attitude.

Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.

An approximate answer to the right question is far better than an exact answer to the wrong question, which can always be made precise. Knowledge of data analysis is, at best, only an approximation as to what the problem is. So one has no choice but to proceed by approximation, he continues.

The driving forces number four. Donoho called the list “surprisingly modern.”

Four forces driving data analysis. Statistical theory is only one part

The four influences listed in Tukey 1962, translated from the English as reproduced in Donoho 2017

The formal theory of statistics
Accelerating developments in computers and display devices
The challenge, in many fields, of more and ever larger bodies of data
The emphasis on quantification in a wider variety of disciplines

Item 1 was the shock, Donoho writes, because it implies that statistical theory is one part of the new science, not the whole. Tukey goes as far as to say that data analysis can be more complex than the physical, biological or behavioral sciences, and that demanding dense guidance from formal structure is excessive. “Data analysis can gain much from formal statistics, but only if the connection is kept adequately loose.”

On figures, he writes on page 49 as follows. If one technique had to be named for its power to make many models clear to the mind, it would be the simple graph. It brings out signs of unexpected phenomena. With a single stimulus and a single response, much of the qualitative and a good deal of the quantitative can be put in a graph. Including indirect graphs, the point is that graphs are not a means of avoiding computation but a means of making the results of computation present. Friendly calls 1900–1950 the “modern dark ages” of visualization, and places this paper among the turning points of the 1950–1975 rebirth.

Teaching it as a science

The paper’s argument on education is not only about transmitting facts. It is about returning to the way a science is taught.

Statistics is taught as a part of mathematics (c1). When one studies statistics itself, attention to data analysis is limited (c2). Even in doctoral programs, there is less close contact with practitioners than in physics or mathematics (c3). So there is too little time to learn alongside people who are already analyzing. A science teaches not only facts and established structure but also that science’s way of thinking and its current beliefs and practice. Data analysis is no different, is Tukey’s demand.

What makes the difficulty worse, he also writes, is the view that “the only way to avoid cookbookery and to develop understanding is a mathematical treatment emphasizing proof.” Cookbookery is not peculiar to data analysis. What is peculiar is concentrating the remedy on mathematics and proof. Biochemistry textbooks are written simply to put the facts in. He also proposes that experimental sampling lets a class check facts for itself.

Convey what is known, show current practice, learn beside real data, and verify by experiment. The value of mathematical rigor is limited here.

How it came to be read as a starting point

Tukey’s term is data analysis. Mosteller and Tukey titled their 1968 chapter “Data Analysis, Including Statistics.” The name exploratory data analysis (EDA) spread with the preliminary editions around 1970 and the 1977 “orange book.” Friendly places the origin of EDA in the 1962 paper, as a matter of convenience.

The name data science came after that. In 1997, in his inaugural lecture as Carver Professor at the University of Michigan, “Statistics = Data Science?,” C. F. Jeff Wu argued that statistics should be renamed data science. In 2001, William S. Cleveland explicitly called the expanded field “data science” and proposed how universities should allocate resources. His criterion of value is how much a piece of work helps the learning of the data analyst. It is a text that translates Tukey’s “develop in step with practice” into an organizational plan.

Reading the 1962 paper as the starting point of today’s data science is a verdict of much later years.

Donoho (2017; the talk for Tukey’s 100th birthday was its prototype) writes that Tukey called for reform of academic statistics and pointed to the existence of an unrecognized science of learning from data. His reading is that Tukey foresaw today’s data science moment.
Hand (2023, IMS) calls the 67 pages a tour de force and concludes that Tukey “may be regarded as the first data scientist.”
Thompson (2001) judges it possibly Tukey’s most important work, a call for a revolution in statistical thinking.
Mallows (2006) writes that it redefined the subject and introduced data analysis as the name of what applied statisticians do.
Huber (2010) writes that the influence was ultimately huge but was not recognized immediately, and that it took him several years as well. Donoho sees academic statistics as a whole as not having followed Tukey’s path.

In Donoho’s account of the history, Bell Labs colleagues (Chambers, Cleveland) found it easier than academic statistics to adopt Tukey’s broad view. University statistics kept to the frame of theory. The observation that the 20% Cleveland allotted to theory held 100% of the work of departments at the time is the core of that account. Donoho also notes that its appearance in the Annals was itself anomalous, and was the decision of the editor, Hodges.

Hand picks up even the details of the body of the paper: iteration, new questions, multiple views of a summary, the warning against treating all data the same way, the rebuttal of automation, and the effect of computers as “important but not always fatal.” The context that S, Python and R came decades later is also there. The 1962 paper is not only a manifesto but also a catalog of methods.

Friendly writes that it may have looked to the orthodoxy of the day like Luther’s 95 theses. In the history of visualization, Friendly’s placement is that it was a turn overturning half a century of neglect, the view that pictures cannot state facts to the decimal place. Stephen Stigler states that the direct effect of the EDA orange book itself was small. What had influence was the subject, spread by students and colleagues. We can assume the same structure for the 1962 paper. The manifesto came first, and implementation and education caught up later.

In Friendly’s 2022 article, Huber also writes that today’s data science is distracted by data too large to explore, and leaves exploration to blind batch processing. Reading the paper as a starting point and today’s practice inheriting the paper’s attitude are separate matters. Donoho himself sees today’s university data science programs as a compromise between a statistics master’s and a database master’s rather than as Tukey’s science.

Takeaways

What this paper leaves for visualization work is not the precision of area. It is how to pose a question.

A figure is a device that brings out the unexpected, Tukey writes. Put a rough answer to the right question first. Put the precise wrong answer later. Mathematics is material for judgment, not a mark of validity. Education, too, means conveying what is known, showing current practice and letting students learn beside real data, rather than drilling proofs.

What 1962 has is a declaration that treats the activity of learning from data as a science. The paper itself places the work of drawing figures at the center of that science.

References

Primary sources

John W. Tukey, “The Future of Data Analysis,” The Annals of Mathematical Statistics, 33(1), 1962, pp. 1–67. doi:10.1214/aoms/1177704711 / Project Euclid
Frederick Mosteller and John W. Tukey, “Data Analysis, Including Statistics,” in Handbook of Social Psychology, 2nd ed., 1968.
John W. Tukey, Exploratory Data Analysis, Addison-Wesley, 1977.

Secondary sources

David Donoho, “50 Years of Data Science,” Journal of Computational and Graphical Statistics, 26(4), 2017, pp. 745–766. doi:10.1080/10618600.2017.1384734 (open access)
David J. Hand, “Hand Writing: John Tukey, the first data scientist?,” IMS Bulletin, 2023-09-30. IMS
James R. Thompson, “The Age of Tukey,” Technometrics, 43(3), 2001, pp. 256–265. Rice repository
Colin Mallows, “Tukey’s Paper After 40 Years,” Technometrics, 48(3), 2006, pp. 319–325. doi:10.1198/004017006000000219
Peter J. Huber, Data Analysis: What Can Be Learned From the Past 50 Years, Wiley, 2010.
William S. Cleveland, “Data Science: An Action Plan for Expanding the Technical Areas of the Field of Statistics,” International Statistical Review, 69(1), 2001, pp. 21–26. doi:10.1111/j.1751-5823.2001.tb00477.x
C. F. Jeff Wu, “Statistics = Data Science?,” H. C. Carver Professor inaugural lecture, University of Michigan, 1997. Slides
Michael Friendly, “Remembrances of Things EDA,” Nightingale, 2022-06-16. Article
John M. Chambers, “Greater or Lesser Statistics: A Choice for Future Research,” Statistical Science, 8(2), 1993, pp. 182–186.

Drawing a Boston Merchant's Day as a Single Line: Allan Pred's Space-Time Path (1984)

Sat, 11 Oct 2025 00:00:00 +0900

In 1984, the geographer Allan Pred used Torsten Hägerstrand’s space-time path notation to draw a single diagram. The vertical axis is the time of day, and the base is a street map of Boston. It shows the day of a “typical” Boston merchant between 1783 and 1812, from midnight to midnight, as one line.

The diagram appeared in the paper “Structuration, Biography Formation, and Knowledge: Observations on Port Growth during the Late Mercantile Period” (Environment and Planning D: Society and Space, vol. 2, no. 3). The paper was reprinted in the 1990 collection Making Histories and Constructing Human Geographies. I have not been able to read the body of the 1984 paper. What follows rests on the paper’s bibliographic record, abstract and reference list, and on the figure in the reprinted version. I checked the reprinted figure against a photograph of the book’s page posted by Jeremy Norman on HistoryofInformation.com.

Space-time path diagram of a Boston merchant’s day

One Diagram in a Paper on Port Growth

Pred (1936–2007) was a professor of geography at UC Berkeley and served as department chair from 1979 to 1988. The paper appeared in Environment and Planning D: Society and Space, vol. 2, no. 3, pp. 251–275.

According to the abstract, the paper discusses the growth of ports in the late mercantile period from three sides: a reassessment of Braudel’s account of commercial capitalism, Pred’s own theory that sees place as a “historically contingent process,” and the case of Boston.

Finally, the interplay of biography formation, knowledge acquisition, and the growth of Boston, Massachusetts, between 1783 and 1812 is considered.

In other words, the paper’s last topic is how biography formation, knowledge acquisition and the growth of the city interacted in Boston between 1783 and 1812. These years fall after independence, not in the colonial period. The “Structuration” in the title refers to Anthony Giddens’s structuration theory, and the reference list includes several works by Giddens.

The title of the figure is “Daily path of a ’typical’ Boston merchant capitalist.” It does not record the day of one real merchant. It is a day assembled as a type. The quotation marks around “typical” can be read as a signal that the figure is a constructed image.

Time Upward, a Street Map at the Base

An oblique view of a cylinder. The left and right posts carry a time scale from midnight to midnight; a single thick line rises from a street map of Boston on the base to an ellipse on the top, bending as it passes locations 1 to 6

Source: a figure in Allan Pred, Making Histories and Constructing Human Geographies (Westview Press, 1990), first published in the 1984 paper. Taken from a photograph of the book’s page on HistoryofInformation.com (Jeremy Norman); the figure has been cropped and the show-through from the reverse side of the paper has been lightened.

The diagram has the form of a cylinder seen obliquely. The posts on the left and right are the time scale, with midnight at the bottom and at the top. The ellipse at the base is a street map of central Boston, and the ellipse at the top carries only the location markers.

Visual element	Data or meaning it stands for	Concrete example in this figure
Vertical scales at the left and right edges	Time of day (from midnight at the bottom to midnight at the top)	Evenly spaced, every 3 hours
Ellipse at the base	A street map of central Boston, seen obliquely	Markers and numbers for locations 1 to 6
Ellipse at the top	The same plane, placed at midnight at the end of the day	Markers 1 to 6 sit at the same left-right positions as on the base
Black markers and numbers	Places the merchant visits	(1) home, (2) Faneuil Hall, (3) counting-house, (4) coffee house, (5) ‘Change on State Street, (6) club-meeting site
Thick line	The space-time path of one merchant	Just one
Vertical sections of the line	Staying in the same place	Home from 2:00 to 5:45, for example
Slanted or nearly horizontal sections	Moving from place to place	5:45 to 6:00, for example; roughly 7 to 20 minutes
Numbers at the bends	Times of arrival and departure	8:30, 9:20, 11:30, 12:03, 1:07 and others, 12 in all
Color, changes in line width	Not used	Monochrome

The correspondence between numbers and places comes from the legend printed below the figure in the reprinted version. The ellipse at the top does not stand for “distance,” which is separate from time. It is a lid: the plane of the map, lifted by one day’s worth of height.

Following the line from the bottom, the merchant’s day can be read as follows.

Time of day	Location
Midnight to morning	(1) Home
8:30 to 9:20	(2) Faneuil Hall
9:30 to 11:30	(3) Counting-house
Between leaving the counting-house at 11:30 and returning at 12:03	(4) A stop at a coffee house
12:03 to 1:00	(3) Counting-house
1:07 to 1:40	(5) The ‘Change (exchange) on State Street
2:00 to 5:45	(1) Home
6:00 to 9:00	(6) Club meeting site
Just after 9:00 to midnight	(1) Home

The morning goes back and forth between workplaces, early afternoon brings a stop at the exchange, the afternoon is at home, and the evening is at the club. This timetable was read off the line in the figure. It has not been checked against records of daily life at the time.

Height Alone Does Not Give the Time

This diagram has a point where readers can lose their way. Because the map is seen obliquely, the height on the page mixes two things: the time and the depth of the map.

Location 6 lies farther back on the map than home (location 1). The “6:00” where the line reaches location 6 sits, on the left-hand scale, above 6 PM, at about the height of 8 PM. It is lifted on the page by the amount of the depth.

Pred addresses this in the explanatory note for the reprinted figure.

Thus, the time-scales at the two outermost edges hold only for the corresponding perimeter points that they connect, and one must imagine a separate time-scale line connecting each of the six locations visited.

That is, the time scales at the two outer edges apply only to the perimeter points they connect, and the reader has to imagine a separate time-scale line for each of the six locations visited. The same note also says that 0.44 inch along a vertical line corresponds to 3 hours, and that corresponding points on the base and the top are 3.5 inches apart. I have not confirmed whether the figure in the 1984 paper carried the same note.

Writing a time at each bend of the line can be read as a response to this difficulty. It lets the reader take the numbers directly instead of measuring time from height. The division of labor is this: the scale shows the approximate time of day, and the labels carry the exact times.

The Notation Comes from Hägerstrand

Pred did not invent the way this diagram is drawn. It is the notation of time geography, set out by the Swedish geographer Hägerstrand.

Hägerstrand presented it in 1969 at the European congress of the Regional Science Association in Copenhagen, and published it in 1970 as the paper “What about people in regional science?” Wikipedia quotes the following line from it (pp. 10–11 of the original).

In time-space the individual describes a path

In time-space, in other words, an individual traces a “path.” The notation includes the aquarium, which takes the map as its base and time as its height; the prism, which shows the area that can be reached; and the bundle, in which several paths gather. Drawings are made in axonometric projection. Pred’s diagram consists only of the aquarium and a single path.

The link between Pred and Hägerstrand can be traced through the bibliography.

Year	Pred’s work
1967	Translated Hägerstrand’s doctoral thesis (1953) into English: Innovation Diffusion as a Spatial Process (with Greta Haag)
1977	“The Choreography of Existence,” a commentary on time geography (Economic Geography, vol. 53, no. 2)
1981	Edited the festschrift Space and Time in Geography: Essays Dedicated to Torsten Hägerstrand
1981	Published a diagram of the daily paths of a family of four in Journal of Historical Geography, vol. 7
1984	The Boston merchant diagram. The reference list includes Hägerstrand 1970 and 1974, Lenntorp 1976 and others

Two rectangular boxes stacked vertically. The vertical axis is Time, 0 to 24. In the upper box (a), four lines run almost bundled into one; in the lower box (b), the lines separate and enter different posts

Source: a figure from Allan Pred, Journal of Historical Geography 7 (1981), as reprinted in Making Histories and Constructing Human Geographies (1990). Taken from a photograph of the book’s page on HistoryofInformation.com (Jeremy Norman); cropped in the same way, with the show-through lightened.

The title of the 1981 figure is “Daily paths of a hypothetical family of four under (a) the artisan mode of production and (b) the factory and large-scale shop mode of production.” It compares the days of a hypothetical family of four under an artisan mode of production and under a factory and large-scale shop mode of production. According to Norman, the four black lines running vertically are the movements of each family member.

So the 1984 diagram is not an “early example” of time geography. It applies a notation that Pred himself had already used three years earlier to the history of a port town. The base of the 1981 figure has only place names such as TAVERN and HOME, and no streets. The 1984 figure lays a street map of a real city on the base and writes times to the minute at the bends. It can be read as moving, with the same notation, from a schematic diagram to specific times in a specific city.

How Others Have Seen This Diagram

The first view comes from the side of information history: Jeremy Norman of HistoryofInformation.com.

What interested me was not so much the well-analyzed data discussed in the paper, but the way that Pred mapped the movement of the “merchant” within the 24 hour period.

He says that he was drawn less to the data in the paper than to how Pred mapped the merchant’s movement within 24 hours. Comparing it with the 1981 family diagram, Norman writes that the merchant diagram is “perhaps easier to understand.”

The second comes from the side of geovisualization: Menno-Jan Kraak’s 2003 paper. It revisits the space-time cube as a visualization and explains how to read it, with vertical lines as stays and nearly horizontal lines as movements, and then names the limits of the hand-drawn era.

when the concept was introduced the options to create the graphics were limited to manual methods and the user could only experience the single view created by the draftsperson. An alternative view on the cube would mean to go through a laborious drawing exercise.

With hand drawing, the reader could see only the one viewpoint the draftsperson had chosen, and another angle meant redrawing. The problem of “height alone does not give the time” in Pred’s diagram can also be read as coming from this single viewpoint.

The third is criticism of the notation itself. According to the Wikipedia article “Time geography,” Bo Lenntorp (1999) wrote the following.

The notation system is a very useful tool, but it is a rather poor reflection of a rich world-view.

The notation is useful, he says, but a poor reflection of a rich world-view. In Feminism and Geography (1993), Gillian Rose criticized time geography: it overlaps with feminism in looking at the paths of everyday life, but it is also a form of masculinism in social science. Since then, Mei-Po Kwan (2002) and others have reexamined time geography.

What Pred’s 1984 diagram draws is one day of a male “merchant capitalist.” There are no paths for family, servants or women. Given that in 1981 he had drawn a family of four, reducing the figure to one line can be read as the result of choosing whose day to show. If Rose’s criticism is applied to this diagram, that is where the issue lies.

Uses

There are four things from this diagram that can be carried over into visualization work.

When time is assigned to one axis, staying and moving separate in the shape of the line. Vertical sections are stays and slanted sections are moves, and the length of a stay can be compared by the length of the line. This way of reading also works for activity logs and for delivery and patrol records.
In an oblique view, height gets mixed with depth. Pred writes the time at each bend and shows how to read the figure in the note for the reprinted version. Today, other options are a cube that can be rotated, or placing the map and a band of time side by side.
When drawing a “typical” case, show that it is a constructed image. Pred puts quotation marks around typical in the title.
Choosing whose line to draw is also choosing whose line not to draw. A single path is easy to read, but it leaves other people’s days out of the diagram.

The 1984 diagram is not one that invented a new notation. It borrowed Hägerstrand’s notation and made it concrete, with a map and clock times, for one day in one city.

References

Primary sources

Allan Pred, “Structuration, Biography Formation, and Knowledge: Observations on Port Growth during the Late Mercantile Period,” Environment and Planning D: Society and Space, 2(3), 1984, pp. 251–275. doi:10.1068/d020251 / Crossref (bibliographic record, abstract, references)
Allan Pred, Making Histories and Constructing Human Geographies: The Local Transformation of Practice, Power Relations, and Consciousness, Westview Press, 1990. Bibliographic record at archive.org
Allan Pred, “Biography Formation, Knowledge Acquisition, and the Growth and Transformation of Cities During the Late Mercantile Period: The Case of Boston, 1783-1812” (chapter 2 of the same book in its 2019 Routledge reissue, pp. 41–75). Crossref
Allan Pred, “The Choreography of Existence: Comments on Hägerstrand’s Time-Geography and Its Usefulness,” Economic Geography, 53(2), 1977, pp. 207–221. doi:10.2307/142726
Allan Pred, “Production, Family and Free-time Projects: A Time-Geographic Perspective on the Individual and Societal Change in Nineteenth-Century U.S. Cities,” Journal of Historical Geography, 7, 1981, pp. 3–36. doi:10.1016/0305-7488(81)90082-7
Torsten Hägerstrand, “What about people in regional science?,” Papers of the Regional Science Association, 24(1), 1970, pp. 7–21. doi:10.1111/j.1435-5597.1970.tb01464.x

Secondary sources

Jeremy Norman, “With ‘Time Geography’ Allan Pred Maps the Activity of Individuals and a Family During the Course of a Single Day,” HistoryofInformation.com. Article
Menno-Jan Kraak, “The Space-Time Cube Revisited from a Geovisualization Perspective,” Proceedings of the 21st International Cartographic Conference, 2003. PDF
Wikipedia, “Time geography” (source of the citations of Hägerstrand 1970, Lenntorp 1999 and Rose 1993). Article
Wikipedia, “Torsten Hägerstrand” (Pred’s English translation, the 1981 festschrift). Article
Wikipedia, “Allan Pred” (biography). Article