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A Brief History of Data Visualization

Michael Friendly

Psychology Department and Statistical Consulting Service

York University

4700 Keele Street, Toronto, ON, Canada M3J 1P3

in: Handbook of Computational Statistics: Data Visualization. See also BIBTEXentry below.

BIBTEX:

@InCollection{Friendly:06:hbook,

author = {M. Friendly},

title = {A Brief History of Data Visualization},

year = {2006},

publisher = {Springer-Verlag},

address = {Heidelberg},

booktitle = {Handbook of Computational Statistics: Data Visualization},

volume = {III},

editor = {C. Chen and W. H\"ardle and A Unwin},

pages = {???--???},

note = {(In press)},

}

© copyright by the author(s)

document created on: March 21, 2006

created from ﬁle: hbook.tex

cover page automatically created with CoverPage.sty

(available at your favourite CTAN mirror)

A brief history of data visualization

Michael Friendly∗

March 21, 2006

Abstract

It is common to think of statistical graphics and data visualization as relatively modern

developments in statistics. In fact, the graphic representation of quantitative information

has deep roots. These roots reach into the histories of the earliest map-making and visual

depiction, and later into thematic cartography, statistics and statistical graphics, medicine,

and other ﬁelds. Along the way, developments in technologies (printing, reproduction)

mathematical theory and practice, and empirical observation and recording, enabled the

wider use of graphics and new advances in form and content.

This chapter provides an overview of the intellectual history of data visualization from

medieval to modern times, describing and illustrating some signiﬁcant advances along the

way. It is based on a project, called the Milestones Project, to collect, catalog and document

in one place the important developments in a wide range of areas and ﬁelds that led to mod-

ern data visualization. This effort has suggested some questions of the use of present-day

methods to analyze and understand this history, that I discuss under therubric of “statistical

historiography.”

1 Introduction

The only new thing in the world is the history you don’t know. —Harry S Truman

It is common to think of statistical graphics and data visualization as relatively modern de-

velopments in statistics. In fact, the graphic portrayal of quantitative information has deep roots.

These roots reach into the histories of the earliest map-making and visual depiction, and later

into thematic cartography, statistics and statistical graphics, with applications and innovations

in many ﬁelds of medicine and science that are often intertwined with each other. They also

connect with the rise of statistical thinking and widespread data collection for planning and

commerce up through the 19th century. Along the way, a variety of advancements contributed

to the widespread use of data visualization today. These include technologies for drawing and

reproducing images, advances in mathematics and statistics, and new developments in data col-

lection, empirical observation and recording.

From above ground, we can see the current fruit and anticipate future growth; we must look

below to understand their germination. Yet the great variety of roots and nutrients across these

∗This paper was prepared for the Handbook of Computational Statistics on Data Visualization. Michael Friendly

is Professor, Psychology Department, York University, Toronto, ON, M3J 1P3 Canada, E-mail: friendly@yorku.ca.

This work is supported by Grant 8150 from the National Sciences and Engineering Research Council of Canada. I

am grateful to the archivists of many libraries and to les Chevaliers des Album de Statistique Graphique: Antoine

de Falguerolles, Ruddy Ostermann, Gilles Palsky, Ian Spence, Antony Unwin, and Howard Wainer for historical

information, images, and helpful suggestions.

1

domains, that gave rise to the many branches we see today, are often not well known, and have

never been assembled in a single garden, to be studied or admired.

This chapter provides an overview of the intellectual history of data visualization from me-

dieval to modern times, describing and illustrating some signiﬁcant advances along the way. It

is based on what I call the Milestones Project, an attempt to provide a broadly comprehensive

and representative catalog of important developments in all ﬁelds related to the history of data

visualization.

There are many historical accounts of developments within the ﬁelds of probability (Hald,

1990), statistics (Pearson,1978,Porter,1986,Stigler,1986), astronomy (Riddell,1980), car-

tography (Wallis and Robinson,1987), which relate to, inter alia, some of the important de-

velopments contributing to modern data visualization. There are other, more specialized ac-

counts, which focus on the early history of graphic recording (Hoff and Geddes,1959,1962),

statistical graphs (Funkhouser,1936,1937,Royston,1970,Tilling,1975), ﬁtting equations to

empirical data (Farebrother,1999), economics and time-series graphs (Klein,1997), cartogra-

phy (Friis,1974,Kruskal,1977) and thematic mapping (Robinson,1982,Palsky,1996), and

so forth; Robinson (Robinson,1982, Ch. 2) presents an excellent overview of some of the im-

portant scientiﬁc, intellectual, and technical developments of the 15th–18th centuries leading

to thematic cartography and statistical thinking. Wainer and Velleman (2001) provide a recent

account of some of the history of statistical graphics.

But there are no accounts that span the entire development of visual thinking and the visual

representation of data, and which collate the contributions of disparate disciplines. In as much

as their histories are intertwined, so too should be any telling of the development of data vi-

sualization. Another reason for interweaving these accounts is that practitioners in these ﬁelds

today tend to be highly specialized, and unaware of related developments in areas outside their

domain, much less their history.

2 Milestones Tour

Every picture tells a story. —Rod Stewart, 1971

In organizing this history, it proved useful to divide history into epochs, each of which

turned out to be describable by coherent themes and labels. This division is, of course somewhat

artiﬁcial, but it provides the opportunity to characterize the accomplishments in each period in a

general way, before describing some of them in more detail. Figure 1, discussed in Section 3.2,

provides a graphic overview of the epochs I describe in the subsections below, showing the

frequency of events considered milestones in the periods of this history. For now, it sufﬁces to

note the labels attached to these epochs, a steady rise from the early 18th century to the late 19th

century, with a curious wiggle thereafter.

In the larger picture— recounting the history of data visualization— it turns out that many

of the milestones items have a story to be told: What motivated this development? What was the

communication goal? How does it relate to other developments— What were the pre-cursors?

How has this idea been used or re-invented today? Each section below tries to illustrate the gen-

eral themes with a few exemplars. In particular, this account attempts to tell a few representative

stories of these periods, rather than to try to be comprehensive.

For reasons of economy, only a limited number of images could be printed here, and these

only in black and white. Others are referred to by web links, mostly from the Milestones

2

Early maps

& diagrams Measurement

& Theory

New graphic

forms Begin modern

period

Golden age

Modern dark

ages

Re-birth

High-D Vis

Milestones: Time course of developments

Density

0.000

0.001

0.002

0.003

0.004

0.005

Year

1500 1600 1700 1800 1900 2000

Figure 1: The time distribution of events considered milestones in the history of data visualiza-

tion, shown by a rug plot and density estimate.

Project, http://www.math.yorku.ca/SCS/Gallery/milestone/, where a color

version of this chapter will also be found.

2.1 Pre-17th Century: Early maps and diagrams

The earliest seeds of visualization arose in geometric diagrams, in tables of the positions of stars

and other celestial bodies, and in the making of maps to aid in navigation and exploration. The

idea of coordinates was used by ancient Egyptian surveyors in laying out towns, earthly and

heavenly positions were located by something akin to latitude and longitude at least by 200 BC,

and the map projection of a spherical earth into latitude and longitude by Claudius Ptolemy [c.

85–c. 165] in Alexandria would serve as reference standards until the 14th century.

Among the earliest graphical depictions of quantitative information is an anonymous 10th

century multiple time-series graph of the changing position of the seven most prominent heav-

enly bodies over space and time (Figure 2), described by Funkhouser (1936) and reproduced

in Tufte (1983, p. 28). The vertical axis represents the inclination of the planetary orbits, the

horizontal axis shows time, divided into thirty intervals. The sinusoidal variation, with different

periods is notable, as is the use of a grid, suggesting both an implicit notion of a coordinate

system, and something akin to graph paper, ideas that would not be fully developed until the

1600–1700s.

In the 14th century, the idea of a plotting a theoretical function (as a proto bar graph), and

3

Figure 2: Planetary movements shown as cyclic inclinations over time, by an unknown as-

tronomer, appearing in a 10th century appendix to commentaries by A. T. Macrobius on Cicero’s

In Somnium Scripionus. Source: Funkhouser (1936, p. 261).

the logical relation between tabulating values and plotting them appeared in a work by Nicole

Oresme [1323–1382] Bishop of Liseus1(Oresme,1482,1968), followed somewhat later by the

idea of a theoretical graph of distance vs. speed by Nicolas of Cusa.

By the 16th century, techniques and instruments for precise observation and measurement

of physical quantities, and geographic and celestial position were well-developed (for example,

a “wall quadrant” constructed by Tycho Brahe [1546–1601], covering an entire wall in his ob-

servatory). Particularly important were the development of triangulation and other methods to

determine mapping locations accurately (Frisius,1533,Tartaglia,1556). As well, we see ini-

tial ideas for capturing images directly (the camera obscura, used by Reginer Gemma-Frisius in

1545 to record an eclipse of the sun), the recording of mathematical functions in tables (trigono-

metric tables by Georg Rheticus, 1550), and the ﬁrst modern cartographic atlas (Teatrum Orbis

Terrarum by Abraham Ortelius, 1570). These early steps comprise the beginnings of data visu-

alization.

2.2 1600-1699: Measurement and theory

Among the most important problems of the 17th century were those concerned with physical

measurement— of time, distance, and space— for astronomy, surveying, map making, naviga-

tion and territorial expansion. This century also saw great new growth in theory and the dawn

of practical application— the rise of analytic geometry and coordinate systems (Descartes and

1Funkhouser (1936, p. 277) was sufﬁciently impressed with Oresme’s grasp of the relation between functions

and graphs that he remarked, “if a pioneering contemporary had collected some data and presented Oresme with

actual ﬁgures to work upon, we might have had statistical graphs four hundred years before Playfair.”

4

Fermat), theories of errors of measurement and estimation (initial steps by Galileo in the anal-

ysis of observations on Tycho Brahe’s star of 1572 (Hald,1990, §10.3)), the birth of probability

theory (Pascal and Fermat), and the beginnings of demographic statistics (John Graunt) and

“political arithmetic” (William Petty)— the study of population, land, taxes, value of goods,

etc. for the purpose of understanding the wealth of the state.

Early in this century, Christopher Scheiner (1630, recordings from 1611) introduced an idea

Tufte (1983) would later call the principle of “small multiples” to show the changing conﬁgu-

rations of sunspots over time, shown in Figure 3. The multiple images depict the recordings of

sunpots from 23 October 1611 until 19 December of that year. The large key in the upper left

identiﬁes seven groups of sunspots by the letters A–F. These groups are similarly identiﬁed in

the 37 smaller images, arrayed left-to-right and top-to-bottom below.

Figure 3: Scheiner’s 1626 representation of the changes in sunspots over time. Source: Scheiner

(1630).

Another noteworthy example (Figure 4) shows a 1644 graphic by Michael Florent van Lan-

gren [1600–1675], a Flemish astronomer to the court of Spain, believed to be the ﬁrst visual

representation of statistical data (Tufte,1997, p. 15). At that time, lack of a reliable means to

determine longitude at sea hindered navigation and exploration.2This 1D line graph shows all

2For navigation, latitude could be ﬁxed from star inclinations, but longitude required accurate measurement of

time at sea, an unsolved problem until 1765 with the invention of a marine chronometer by John Harrison. See Sobel

(1996) for a popular account.

5

12 known estimates of the difference in longitude between Toledo and Rome, and the name of

the astronomer (Mercator, Tycho Brahe, Ptolemy, etc.) who provided each observation.

Figure 4: Langren’s 1644 graph of determinations of the distance, in longitude, from Toledo to

Rome. The correct distance is 16◦300. Source: Tufte (1997, p. 15).

What is notable is that van Langren could have presented this information in various tables—

ordered by author to show provenance, by date to show priority, or by distance. However, only a

graph shows the wide variation in the estimates; note that the range of values covers nearly half

the length of the scale. Van Langren took as his overall summary the center of the range, where

there happened to be a large enough gap for him to inscribe “ROMA.” Unfortunately, all of the

estimates were biased upwards; the true distance (16◦300) is shown by the arrow. Van Langren’s

graph is also a milestone as the earliest-known exemplar of the principle of “effect ordering for

data display” (Friendly and Kwan,2003).

In the 1660s, the systematic collection and study of social data began in various European

countries, under the rubric of “political arithmetic” (John Graunt 1662 and William Petty 1665),

with the goals of informing the state about matters related to wealth, population, agricultural

land, taxes and so forth,3as well as for commercial purposes such as insurance and annuities

based on life tables (Jan de Witt, 1671). At approximately the same time, the initial statements

of probability theory around 1654 (see Ball (1908)) together with the idea of coordinate systems

were applied by Christiaan Huygens in 1669 to give the ﬁrst graph of a continuous distribution

function4(from Gaunt’s life table based on the bills of mortality). The mid 1680s saw the ﬁrst

bivariate plot derived from empirical data, a theoretical curve relating barometric pressure to

altitude, and the ﬁrst known weather map,5showing prevailing winds on a map of the earth

(Halley,1686).

By the end of this century, the necessary elements for the development of graphical methods

were at hand— some real data of signiﬁcant interest, some theory to make sense of them, and a

few ideas for their visual representation. Perhaps more importantly, one can see this century as

giving rise to the beginnings of visual thinking, as illustrated by the examples of Scheiner and

van Langren.

3For example, Graunt (1662) used his tabulations of London births and deaths from parish records and the bills

of mortality to estimate the number of men the king would ﬁnd available in the event of war (Klein,1997, 43–47).

4Image: http://math.yorku.ca/SCS/Gallery/images/huygens-graph.gif

5Image: http://math.yorku.ca/SCS/Gallery/images/halleyweathermap-1686.jpg

6

2.3 1700-1799: New graphic forms

With some rudiments of statistical theory, data of interest and importance, and the idea of

graphic representation at least somewhat established, the 18th century witnessed the expansion

of these aspects to new domains and new graphic forms. In cartography, map-makers began to

try to show more than just geographical position on a map. As a result, new data representations

(isolines and contours) were invented, and thematic mapping of physical quantities took root.

Towards the end of this century, we see the ﬁrst attempts at the thematic mapping of geologic,

economic, and medical data.

Abstract graphs, and graphs of functions became more widespread, along with the early

beginnings of statistical theory (measurement error) and systematic collection of empirical data.

As other (economic and political) data began to be collected, some novel visual forms were

invented to portray them, so the data could ‘speak to the eyes.’

For example, the use of isolines to show contours of equal value on a coordinate grid (maps

and charts) was developed by Edmund Halley (1701). Figure 5, showing isogons— lines of

equal magnetic declination— is among the ﬁrst examples of thematic cartography, overlay-

ing data on a map. Contour maps and topographic maps were introduced somewhat later by

Phillippe Buache (1752) and Marcellin du Carla-Boniface (1782).

Figure 5: A portion of Edmund Halley’s New and Correct Sea Chart Shewing the Variations

in the Compass in the Western and Southern Ocean, 1701. Source:Halley (1701), image from

Palsky (1996, p. 41).

Timelines, or “cartes chronologiques” were ﬁrst introduced by Jacques Barbeu-Dubourg in

7

the form of an annotated chart of all of history (from Creation) on a 54-foot scroll (Ferguson,

1991). Joseph Priestley, presumably independently, used a more convenient form to show ﬁrst a

timeline chart of biography (lifespans of 2,000 famous people, 1200 B.C. to 1750 A.D., Priestley

(1765)), and then a detailed chart of history (Priestley,1769).

The use of geometric ﬁgures (squares or rectangles) and cartograms to compare areas or de-

mographic quantities by Charles de Fourcroy6(1782) and August F.W. Crome (1785) provided

another novel visual encoding for quantitative data using superimposed squares to compare the

areas of European states.

As well, several technological innovations provided necessary ingredients for the produc-

tion and dissemination of graphic works. Some of these facilitated the reproduction of data

images, such as three-color printing, invented by Jacob le Blon in 1710 and lithography by

Aloys Senefelder in 1798. Of the latter, Robinson (1982, p. 57) says “the effect was as great as

the introduction [of the Xerox machine].” Yet, likely due to expense, most of these new graphic

forms appeared in publications with limited circulation, unlikely to attract wide attention.

A prodigious contributor to the use of the new graphical methods, Johann Lambert [1728–

1777] introduced the ideas of curve ﬁtting and interpolation from empirical data points. He used

various sorts of line graphs and graphical tables to show periodic variation, for example, in air

and soil temperature.7

William Playfair [1759–1823] is widely considered the inventor of most of the graphical

forms widely used today— ﬁrst the line graph and bar chart (Playfair,1786), later the pie chart

and circle graph (Playfair,1801). Figure 6shows a creative combination of different visual

forms: circles, pies and lines, re-drawn from Playfair (1801, Plate 2).

The use of two separate vertical scales for different quantities (population and taxes) is

today considered a sin in statistical graphics (you can easily jiggle either scale to show different

things). But Playfair used this device to good effect here to try to show taxes per capita in various

nations and argue that the British were overtaxed, compared with others. But alas, showing

simple numbers by a graph was hard enough for Playfair— he devoted several pages of text in

Playfair (1786) describing how to read and understand a line graph. The idea of calculating and

graphing rates and other indirect measurements was still to come.

In this ﬁgure the left axis and line on each circle/pie graph shows population, while the

right axis and line shows taxes. Playfair intended that the slope of the line connecting the two

would depict the rate of taxation directly to the eye; but, of course, the slope also depends on

the diameters of the circles. Playfair’s graphic sins can perhaps be forgiven here, because the

graph clearly shows the slope of the line for Britain to be in the opposite direction of those for

the other nations.

A somewhat later graph (Playfair,1821), shown in Figure 7, exempliﬁes the best that Play-

fair had to offer with these graphic forms. Playfair used three parallel time series to show the

price of wheat, weekly wages, and reigning monarch over a ∼250 year span from 1565 to 1820,

and used this graph to argue that workers had become better off in the most recent years.

By the end of this century (1794), the utility of graphing in scientiﬁc applications prompted a

Dr. Buxton in London to patent and market printed coordinate paper; curiously, a patent for lined

notepaper was not issued until 1815. The ﬁrst known published graph using coordinate paper

is one of periodic variation in barometric pressure (Howard,1800). Nevertheless, graphing of

6Image: http://math.yorku.ca/SCS/Gallery/images/palsky/defourcroy.jpg

7Image: http://www.journals.uchicago.edu/Isis/journal/demo/v000n000/000000/

fg7.gif

8

Figure 6: Re-drawn version of a portion of Playfair’s 1801 pie-circle-line chart, comparing

population and taxes in several nations.

data would remain rare for another 30 or so years,8perhaps largely because there wasn’t much

data (apart from widespread astronomical, geodetic, and physical measurement) of sufﬁcient

complexity to require new methods and applications. Ofﬁcial statistics, regarding population

and mortality, and economic data were generally fragmentary and often not publicly available.

This would soon change.

2.4 1800-1850: Beginnings of modern graphics

With the fertilization provided by the previous innovations of design and technique, the ﬁrst half

of the 19th century witnessed explosive growth in statistical graphics and thematic mapping, at

a rate which would not be equalled until modern times.

In statistical graphics, all of the modern forms of data display were invented: bar and pie

charts, histograms, line graphs and time-series plots, contour plots, scatterplots, and so forth.

In thematic cartography, mapping progressed from single maps to comprehensive atlases, de-

picting data on a wide variety of topics (economic, social, moral, medical, physical, etc.), and

introduced a wide range of novel forms of symbolism. During this period graphical analysis

of natural and physical phenomena (lines of magnetism, weather, tides, etc.) began to appear

regularly in scientiﬁc publications as well.

In 1801, the ﬁrst geological maps were introduced in England by William Smith [1769–

1839], setting the pattern for geological cartography or “stratigraphic geology” (Smith,1815).

8William Herschel (1833), in a paper that describes the ﬁrst instance of a modern scatterplot, devoted three pages

to a description of plotting points on a grid.

9

Figure 7: William Playfair’s 1821 time series graph of prices, wages, and ruling monarch over

a 250 year period. Source:Playfair (1821), image from Tufte (1983, p. 34)

These and other thematic maps soon led to new ways to show quantitative information on maps,

and, equally importantly, to new domains for graphically-based inquiry.

In the 1820s, Baron Charles Dupin [1784–1873] invented the use of continuous shadings

(from white to black) to show the distribution and degree of illiteracy in France (Dupin,1826)—

the ﬁrst unclassed choropleth map,9and perhaps the ﬁrst modern-style thematic statistical map

(Palsky,1996, p. 59). Later given the lovely title, “Carte de la France obscure et la France

´

eclair´

ee,” it attracted wide attention, and was also perhaps the ﬁrst application of graphics in the

social realm.

More signiﬁcantly, in 1825, the Ministry of Justice in France instituted the ﬁrst centralized

national system of crime reporting, collected quarterly from all departments and recording the

details of every charge laid before the French courts. In 1833, Andr´

e-Michel Guerry, a lawyer

with a penchant for numbers used this data (along with other data on literacy, suicides, donations

to the poor and other “moral” variables) to produce a seminal work on the moral statistics of

France (Guerry,1833)— a work that (along with Quetelet (1831,1835)) can be regarded as the

foundation of modern social science.10

Guerry used maps in a style similar to Dupin to compare the ranking of departments on

pairs of variables, notably crime vs. literacy, but other pairwise variable comparisons were

made.11 He used these to argue that the lack of an apparent (negative) relation between crime

9Image: http://math.yorku.ca/SCS/Gallery/images/dupin2.gif

10Guerry showed that rates of crime, when broken down by department, type of crime, age and gender of the

accused and other variables, remained remarkably consistent from year to year, yet variedwidely across departments.

He used this to argue that such regularity implied the possibility of establishing social laws, much as the regularity

of natural phenomena implied physical ones. Guerry also pioneered the study of suicide, with tabulations of suicides

in Paris, 1827–1830, by sex, age, education, profession, etc. and a content analysis of suicide notes as to presumed

motives.

11Today, one would use a scatterplot, but that graphic form was only just invented (Herschel,1833) and would not

10

and literacy contradicted the arm-chair theories of some social reformers who had argued that

the way to reduce crime was to increase education.12 Guerry’s maps and charts made somewhat

of an academic sensation both in France and the rest of Europe; he later exhibited several of

these at the 1851 London Exhibition, and carried out a comparative study of crime in England

and France (Guerry,1864), for which he was awarded the Moynton Prize in statistics by the

French Academy of Sciences.13 But Guerry’s systematic and careful work was unable to shine

in the shadows cast by Adolphe Quetelet, who regarded moral and social statistics as his own

domain.

Figure 8: A portion of Dr. Robert Baker’s cholera map of Leeds, 1833, showing the districts

affected by cholera. Source: Gilbert (1958, Fig. 2).

In October 1831, the ﬁrst case of asiatic cholera occurred in Great Britain, and over 52,000

enter common usage for another 50 years; see Friendly and Denis (2005).

12Guerry seemed reluctant to take sides. He also contradicted the social conservatives who argued for the need to

build more prisons or impose more severe criminal sentences. See Whitt (2002).

13Among the 17 plates in this last work, seven pairs of maps for England and France each included sets of small

line graphs to show trends over time, decompositions by subtype of crime and sex, distributions over months of the

year, and so forth. The ﬁnal plate, on general causes of crime is an incredibly detailed and complex multivariate

semi-graphic display attempting to relate various types of crimes to each other, to various social and moral aspects

(instruction, religion, population) as well as to their geographic distribution.

11

people died in the epidemic that ensued over the next 18 months or so (Gilbert,1958). Sub-

sequent cholera epidemics in 1848–1849 and 1853–1854 produced similarly large death tolls,

but the water-born cause of the disease was unknown until 1855 when Dr. John Snow produced

his famous dot map14 (Snow,1855) showing deaths due to cholera clustered around the Broad

Street pump in London. This was indeed a landmark graphic discovery, but it occurred at the

end of the period, roughly 1835–1855, that marks a high-point in the application of thematic

cartography to human (social, medical, ethnic) topics. The ﬁrst known disease map of cholera

(Figure 8), due to Dr. Robert Baker (1833), shows the districts of Leeds “affected by cholera”

in the particularly severe 1832 outbreak.

I show this ﬁgure to make another point— why Baker’s map did not lead to a “eureka”

experience, while John Snow’s did. Baker used a town plan of Leeds that had been divided

into districts. Of a population of 76,000 in all of Leeds, Baker mapped the 1800 cholera cases

by hatching in red “the districts in which the cholera had prevailed.” In his report, he noted

an association between the disease and living conditions: “how exceedingly the disease has

prevailed in those parts of the town where there is a deﬁciency, often an entire want of sewage,

drainage, and paving” (Baker,1833, p. 10). Baker did not indicate the incidence of disease on

his map, nor was he equipped to display rates of disease (in relation to population density)15

and his knowledge of possible causes, while deﬁnitely on the right track, was both weak and

implicit (not analyzed graphically or by other means). It is likely that some, perhaps tenuous,

causal indicants or evidence were available to Baker, but he was unable to connect the dots, or

see a geographically distributed outcome in relation to geographic factors in even the simple

ways that Guerry had tried.

At about the same time, ∼1830–1850, the use of graphs began to become recognized in

some ofﬁcial circles for economic and state planning— where to build railroads and canals?

what is the distribution of imports and exports? This use of graphical methods is no better illus-

trated than in the works of Charles Joseph Minard [1781–1870], whose prodigious graphical

inventions led Funkhouser (1937) to call him the Playfair of France. To illustrate, we choose

(with some difﬁculty) an 1844 “tableau-graphique” (Figure 9) by Minard, an early progenitor of

the modern mosaic plot (Friendly,1994). On the surface, mosaic plots descend from bar charts,

but Minard introduced two simultaneous innovations: the use of divided and proportional-width

bars so that area had a concrete visual interpretation. The graph shows the transportation of com-

mercial goods along one canal route in France by variable-width, divided bars (Minard,1844).

In this display the width of each vertical bar shows distance along this route; the divided bar

segments have height ∼amount of goods of various types (shown by shading), so the area of

each rectangular segment is proportional to cost of transport. Minard, a true visual engineer

(Friendly,2000), developed such diagrams to argue visually for setting differential price rates

for partial vs. complete runs. Playfair had tried to make data ‘speak to the eyes,’ but Minard

wished to make them ‘calculer par l’œil’ as well.

It is no accident that, in England, outside the numerous applications of graphical methods

in the sciences, there was little interest in or use of graphs among statisticians (or “statists” as

14 Image: http://www.math.yorku.ca/SCS/Gallery/images/snow4.jpg

15The German geographer Augustus Petermann produced a “Cholera map of the British Isles” in 1852 us-

ing national data from the 1831–1832 epidemic, (image: http://images.rgs.org/webimages/0/0/

10000/1000/800/S0011888.jpg) shaded in proportion to the relative rate of mortality using class intervals

(<1/35,1/35 : 1/100,1/100 : 1/200,... ). No previous disease map allowed determination of the range of

mortality in any given area.

12

Figure 9: Minard’s Tableau Graphique, showing the transportation of commercial goods along

the Canal du Centre (Chalon–Dijon). Intermediate stops are spaced by distance, and each bar

is divided by type of goods, so the area of each tile represents the cost of transport. Arrows

show the direction of transport. Source: ENPC:5860/C351 (Col. et clich´

e ENPC; used by

permission).

they called themselves). If there is a continuum ranging from “graph people” to “table people,”

British statisticians and economists were philosophically more table-inclined, and looked upon

graphs with suspicion up to the time of William Stanley Jevons around 1870 (Maas and Morgan,

2005). Statistics should be concerned with the recording of “facts relating to communities of

men which are capable of being expressed by numbers” (Mouat,1885, p.15), leaving the gen-

eralization to laws and theories to others. Indeed, this view was made abundantly clear in the

logo of the Statistical Society of London (now the Royal Statistical Society): a banded sheaf of

wheat, with the motto Aliis Exterendum— to others to ﬂail the wheat. Making graphs, it seemed,

was too much like bread-making.

2.5 1850–1900: The Golden Age of statistical graphics

By the mid-1800s, all the conditions for the rapid growth of visualization had been established—

a “perfect storm” for data graphics. Ofﬁcial state statistical ofﬁces were established throughout

13

Europe, in recognition of the growing importance of numerical information for social plan-

ning, industrialization, commerce, and transportation. Statistical theory, initiated by Gauss and

Laplace, and extended to the social realm by Guerry and Quetelet, provided the means to make

sense of large bodies of data.

What started as the Age of Enthusiasm (Funkhouser,1937,Palsky,1996) for graphics ended

with what can be called the Golden Age, with unparalleled beauty and many innovations in

graphics and thematic cartography. So varied were these developments, that it is difﬁcult to be

comprehensive, but a few themes stand out.

2.5.1 Escaping ﬂatland

Although some attempts to display more than two variables simultaneously had occurred earlier

in multiple time-series (Playfair,1801,Minard,1826), contour graphs (Vauthier,1874) and a

variety of thematic maps, (e.g., Berghaus (1838)) a number of signiﬁcant developments ex-

tended graphics beyond the conﬁnes of a ﬂat piece of paper. Gustav Zeuner [1828–1907] in

Germany (Zeuner,1869), and later Luigi Perozzo [?–1875] in Italy (Perozzo,1880) constructed

3D surface plots of population data.16 The former was an axonometric projection showing var-

ious slices, while the latter (a 3D graph of population in Sweden from 1750–1875 by year and

age group) was printed in red and black and designed as a stereogram.17

Contour diagrams, showing iso-level curves of 3D surfaces, had also been used earlier in

mapping contexts (Nautonier,1604,Halley,1701,von Humboldt,1817), but the range of prob-

lems and data to which they were applied expanded considerably over this time in attempts

to understand relations among more than two data-based variables, or where the relationships

are statistical, rather than functional or measured with little error. It is more convenient to de-

scribe these under Galton, below. By 1884, the idea of visual and imaginary worlds of varying

number of dimensions found popular expression in Edwin Abbott’s (1884)Flatland, implicitly

suggesting possible views in four and more dimensions.

2.5.2 Graphical innovations

With the usefulness of graphical displays for understanding complex data and phenomena es-

tablished, many new graphical forms were invented and extended to new areas of inquiry, par-

ticularly in the social realm.

Minard (1861) developed the use of divided circle diagrams on maps (showing both a total,

by area, and sub-totals, by sectors, with circles for each geographic region on the map). Later

he developed to an art form the use of ﬂow lines on maps of width proportional to quantities

(people, goods, imports, exports) to show movement and transport geographically. Near the

end of his life, the ﬂow map would be taken to its highest level in his famous depiction of the

fate of the armies of Napoleon and Hannibal, in what Tufte (1983) would call the “best graphic

ever produced.” See Friendly (2002) for a wider appreciation of Minard’s work.

The social and political uses of graphics is also evidenced in the polar area charts (called

“rose diagrams” or “coxcombs”) invented by Florence Nightingale [1820–1910] to wage a

16 Image: http://math.yorku.ca/SCS/Gallery/images/stereo2.jpg

17Zeuner used one axis to show year of birth and another to show present age, with number of surviving persons

on the third, vertical axis, giving a 3D surface. One set of curves thus showed the distribution of population for a

given generation; the orthogonal set of curves showed the distributions across generations at a given point in time,

e.g., at a census.

14

campaign for improved sanitary conditions in battleﬁeld treatment of soldiers (Nightingale,

1857). They left no doubt that many more soldiers died from disease and the consequences

of wounds than at the hands of the enemy. From around the same time, Dr. John Snow [1813–

1858] is remembered for his use of a dot map of deaths from cholera in an 1854 outbreak in

London the cholera deaths in London. Plotting the residence of each deceased provided the in-

sight for his conclusion that the source of the outbreak could be localized to contaminated water

from a pump on Broad Street, the founding innovation for modern epidemiological mapping.

Figure 10: Lallemand’s L’abaque du bateau Le Triomphe, allowing determination of magnetic

deviation at sea without calculation. Source: courtesy Mme. Marie-No¨

elle Maisonneuve, Les

fonds anciens de la biblioth`

eque de l’Ecole des Mines de Paris.

Scales and shapes for graphs and maps were also transformed for a variety of purposes,

leading to semi-logarithmic graphs (Jevons,1863,1958) to show percentage change in com-

modities over time, log-log plots to show multiplicative relations, anamorphic maps by ´

Emile

Cheysson (Palsky,1996, Fig. 63-64) using deformations of spatial size to show a quantita-

tive variable (e.g., the decrease in time to travel from Paris to various places in France over 200

years), and alignment diagrams or nomograms using sets of parallel axes. We illustrate this slice

of the golden age with Figure 10, a tour-de-force graphic for determination of magnetic devia-

tion at sea in relation to latitude and longitude without calculation (“L’Abaque Triomphe”) by

15

Charles Lallemand (1885), director general of the geodetic measurement of altitudes throughout

France, that combines many variables into a multi-function nomogram, using 3D, juxtaposition

of anamorphic maps, parallel coordinates and hexagonal grids.

2.5.3 Galton’s contributions

Special note should be made of the varied contributions of Francis Galton [1822-1911] to data

visualization and statistical graphics. Galton’s role in the development of the ideas of correlation

and regression are well-known. Less well-known is the role that visualization and graphing

played in his contributions and discoveries.

Galton’s statistical insight (Galton,1886)— that, in a bivariate (normal) distribution (say,

height of child against height of parent), (a) the isolines of equal frequency would appear as

concentric ellipses, and (b) that the locus of the (regression) lines of means of y|xand of x|y

were the conjugate diameters of these ellipses — was based largely on visual analysis from

the application of smoothing to his data. Karl Pearson would later say, “that Galton should

have evolved all this from his observations is to my mind one of the most noteworthy scientiﬁc

discoveries arising from pure analysis of observations.” (Pearson,1920, p. 37). This was only

one of Galton’s discoveries based on graphical methods.

In earlier work, Galton had made wide use of isolines, contour diagrams and smoothing

in a variety of areas. An 1872 paper showed the use of “isodic curves” to portray the

joint effects of wind and current on the distance ships at sea could travel in any direction. An

1881 “isochronic chart” (Galton,1881) showed the time it took to reach any destination in the

world from London by means of colored regions on a world map. Still later, he analyzed rates

of fertility in marriages in relation to the ages of father and mother using “isogens,” curves of

equal percentage of families having a child (Galton,1894).

But perhaps the most notable non-statistical graphical discovery was that of the “anti-cyclonic”

(counter-clockwise) pattern of winds around low-pressure regions, combined with clockwise ro-

tations around high-pressure zones. Galton’s work on weather patterns began in 1861 and was

summarized in Meteorographica (1863). It contained a variety of ingenious graphs and maps

(over 600 illustrations in total) one of which is shown in Figure 11. This remarkable chart, one

of a two-page trellis-style display, shows observations on barometric pressure, wind direction,

rain and temperature from 15 days in December 1861.18 For each day, the 3×3grid shows

schematic maps of Europe, mapping pressure (row 1), wind and rain (row 2) and temperature

(row 3), in the morning, afternoon and evening (columns). One can clearly see the series of

black areas (low pressure) on the barometric charts for about the ﬁrst half of the month, corre-

sponding to the counter-clockwise arrows in the wind charts, followed by a shift to red areas

(high pressure) and more clockwise arrows. Wainer (2005, p. 56) remarks, “Galton did for the

collectors of weather data what Kepler did for Tycho Brahe. This is no small accomplishment.”

2.5.4 Statistical Atlases

The collection, organization and dissemination of ofﬁcial government statistics on population,

trade and commerce, social, moral and political issues became widespread in most of the coun-

18 In July 1861, Galton distributed a circular to meterologists throughout Europe, asking them to record these data

synchonously, three times a day for the entire month of December, 1861. About 50 weather stations supplied the

data; see Pearson (1930, p. 37–39).

16

Figure 11: One page of Galton’s 1863 multivariate weather chart of Europe showing barometric

pressure, wind direction, rain, and temperature for the month of December, 1861. Source:

Pearson (1930, pl. 7).

tries of Europe from about 1825 to 1870 (Westergaard,1932). Reports containing data graphics

were published with some regularity in France, Germany, Hungary, and Finland, and with tabu-

lar displays in Sweden, Holland, Italy and elsewhere. At the same time, there was an impetus to

develop standards for graphical presentation at the International Statistical Congresses that had

begun in 1853 in Belgium (organized by Quetelet), and these congresses were closely linked

with state statistical bureaus. The main participants in the graphics section included Georg

von Mayr, Hermann Schwabe, Pierre ´

Emile Levasseur and ´

Emile Cheysson. Among other rec-

ommendations was one from the 7th Statistical Congress in 1869 that ofﬁcial publications be

accompanied by maps and diagrams. The state-sponsored statistical atlases that ensued provide

additional justiﬁcation to call this period the Golden Age of Graphics, and some of its most

impressive exemplars.

The pinnacle of this period of state-sponsored statistical albums is undoubtedly the Albums

de Statistique Graphique published annually by the French ministry of public works from 1879-

1897 under the direction of ´

Emile Cheysson.19 They were published as large-format books

19Cheysson had been one of the major participants in committees on the standardization of graphical methods at

17

(about 11 x 17 in.), and many of the plates folded out to four- or six-times that size, all printed

in color and with great attention to layout and composition. We concur with Funkhouser (1937,

p.336) that “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.”

The subject matter of the albums largely concerned economic and ﬁnancial data related to

the planning, development and administration of public works— transport of passengers and

freight, by rail, on inland waterways and through seaports, but also included such topics as

revenues in the major theaters of Paris, attendance at the universal expositions of 1867, 1878

and 1889, changes in populations of French departments over time, and so forth.

More signiﬁcantly for this account the Albums can also be viewed as an exquisite sampler of

all the graphical methods known at the time, with signiﬁcant adaptations to the problem at hand.

The majority of these graphs used and extended the ﬂow map pioneered by Minard. Others used

polar forms— variants of pie and circle diagrams, star plots and rose diagrams, often overlaid

on a map and extended to show additional variables of interest. Still others used sub-divided

squares in the manner of modern mosaic displays (Friendly,1994) to show the breakdown of

a total (passengers, freight) by several variables. It should be noted that in almost all cases

the graphical representation of the data was accompanied by numerical annotations or tables,

providing precise numerical values.

The Albums are discussed extensively by Palsky (1996), who includes seven representative

illustrations. It is hard to choose a single image here, but my favorites are surely the recursive,

multi-mosaic of rail transportation for the 1884–1886 volumes, the ﬁrst of which is shown in

Figure 12. This cartogram uses one large mosaic (in the lower left) to show the numbers of

passengers and tons of freight shipped from Paris from the four principal train stations. Of the

total leaving Paris, the amounts going to each main city are shown by smaller mosaics, colored

according to railway lines; of those amounts, the distribution to smaller cities is similarly shown,

connected by lines along the rail routes.

Among the many other national statistical albums and atlases, those from the U.S. Cen-

sus bureau also deserve special mention. The Statistical Atlas of the Ninth Census, produced in

1872–1874 under the direction of Francis A. Walker [1840–1897] contained 60 plates, including

several novel graphic forms. The ambitious goal was to present a graphic portrait of the nation,

and covered a wide range of physical and human topics: geology, minerals, weather; population

by ethnic origin, wealth, illiteracy, school attendance and religious afﬁliation; death rates by

age, sex, race and cause, prevalence of blindness, deaf mutism and insanity, and so forth. “Age

pyramids” (back-to-back, bilateral frequency histograms and polygons) were used effectively to

compare age distributions of the population for two classes (gender, married/single, etc.). Sub-

divided squares and area-proportional pies of various forms were also used to provide com-

parisons among the states on multiple dimensions simultaneously (employed/unemployed, sex,

schooling, occupational categories). The desire to provide for easy comparisons among states

and other categorizations was expressed by arranging multiple sub-ﬁgures as “small multiples”

in many plates.

Following each subsequent decennial census for 1880 to 1900, reports and statistical atlases

were produced with more numerous and varied graphic illustrations. The 1898 volume from

the Eleventh Census (1890), under the direction of Henry Gannett [1846–1914] contained over

400 graphs, cartograms and statistical diagrams. There were several ranked parallel coordinate

the International Statistical Congresses from 1872 on. He was trained as an engineer at the ENPC, and later became

a professor of political economy at the ´

Ecole des Mines.

18

Figure 12: Mouvement des voyageurs et des marchandises dans les principales stations de

chemins de fer en 1882. Scale: 2mm2= 10,000 passengers or tons of freight. Source: Album,

1884, Plate 11 (author’s collection).

19

plots comparing states and cities over all censuses from 1790–1890. Trellis-like collections

of shaded maps showed interstate migration, distributions of religious membership, deaths by

known causes, and so forth.

The 1880 and 1890 volumes produced under Gannett’s direction are also notable for (a) the

multi-modal combination of different graphic forms (maps, tables, bar charts, bilateral poly-

gons) in numerous plates, and (b) the consistent use of effect-order sorting (Friendly and Kwan,

2003) to arrange states or other categories in relation to what was to be shown, rather than for

lookup (e.g., Alabama–Wyoming).

Figure 13: Interstate migration shown by back-to-back bar charts, sorted by emigration. Source:

Statistical Atlas of the Eleventh Census, 1890, diagram 66, p. 23 (author’s collection).

For example, Figure 13 shows interstate immigration in relation to emigration for the 49

states and territories in 1890. The right side shows population loss sorted by emigration, ranging

from NY, Ohio, Penn. and Illinois at the top to Idaho, Wyoming and Arizona at the bottom. The

left side shows where the emigrants went: Illinois, Missouri, Kansas and Texas had the biggest

gains, Virginia the biggest net loss. It is clear that people were leaving the eastern states and

were attracted to those of the midwest Mississippi valley. Other plates showed this data in

map-based formats.

However, the Age of Enthusiasm and the Golden Age were drawing to a close. The French

Albums de Statistique Graphique were discontinued in 1897 due to the high cost of production;

statistical atlases appeared in Switzerland in 1897 and 1914, but never again. The ﬁnal two U.S.

Census atlases, issued after the 1910 and 1920 censuses, “were both routinized productions,

largely devoid of color and graphic imagination” (Dahmann,2001).

2.6 1900-1950: The modern dark ages

If the late 1800s were the “golden age” of statistical graphics and thematic cartography, the early

1900s can be called the “modern dark ages” of visualization (Friendly and Denis,2000).

There were few graphical innovations, and, by the mid-1930s, the enthusiasm for visualiza-

tion which characterized the late 1800s had been supplanted by the rise of quantiﬁcation and

20

formal, often statistical, models in the social sciences. Numbers, parameter estimates, and, es-

pecially, those with standard errors were precise. Pictures were— well, just pictures: pretty or

evocative, perhaps, but incapable of stating a “fact” to three or more decimals. Or so it seemed

to many statisticians.

But it is equally fair to view this as a time of necessary dormancy, application, and popu-

larization, rather than one of innovation. In this period statistical graphics became main stream.

Graphical methods entered English20 textbooks (Bowley,1901,Peddle,1910,Haskell,1919,

Karsten,1925), the curriculum (Costelloe,1915,Warne,1916), and standard use in government

(Ayres,1919), commerce (Gantt charts and Shewart’s control charts) and science.

These textbooks contained rather detailed descriptions of the graphic method, with an appre-

ciative and often modern ﬂavor. For example, Sir Arthur Bowley’s (1901)Elements of Statistics

devoted two chapters to graphs and diagrams, and discussed frequency and cumulative fre-

quency curves (with graphical methods for ﬁnding the median and quartiles), effects of choice

of scales and baselines on visual estimation of differences and ratios, smoothing of time-series

graphs, rectangle diagrams in which three variables could be shown by height, width and area

of bars, and “historical diagrams” in which two or more time series could be shown on a single

chart for comparative views of their histories.

Bowley’s (1901, p. 151-154) example of smoothing (see Figure 14) illustrates the character

of his approach. Here he plotted the total value of exports from Britain and Ireland over 1855–

1899. At issue was whether exports had become stationary in the most recent years and the

conclusion by Sir Robert Giffen (1899), based solely on tables of averages for successive ﬁve

year periods,21 that “the only sign of stationariness is an increase at a less rate in the last periods

than in the earlier periods” (p. 152). To answer this, he graphed the raw data, together with

curves of the moving average over three, ﬁve and ten year periods. The three- and ﬁve-year

moving averages show strong evidence of an approximately 10 year cycle, and he noted, “no

argument can stand which does not take account of the cycle of trade, which is not eliminated

until we take decennial averages” (p. 153). To this end, he took averages of successive 10-year

periods starting 1859 and drew a freehand curve “keeping as close [to the points] as possible,

without making sudden changes in curvature,” giving the thick curve in Figure 14.22 Support

for Sir Robert’s conclusion and the evidence for a 10-year cycle owe much to this graphical

treatment.

Moreover, perhaps for the ﬁrst time, graphical methods proved crucial in a number of new

insights, discoveries, and theories in astronomy, physics, biology, and other sciences. Among

these, one may refer to (a) E. W. Maunder’s (1904) “butterﬂy diagram” to study the variation of

sunspots over time, leading to the discovery that they were markedly reduced in frequency from

1645–1715; (b) the Hertzsprung-Russell diagram (Hertzsprung,1911,Spence and Garrison,

1993), a log-log plot of luminosity as a function of temperature for stars, used to explain the

changes as a star evolves and laying the groundwork for modern stellar physics; (c) the dis-

20The ﬁrst systematic attempt to survey, describe, and illustrate available graphic methods for experimental data

was ´

Etienne Jules Marey’s (1878)La M´

ethode Graphique. Marey [1830–1904] also invented several devices for

visual recording, including the sphymograph and chronophotography to record motion of birds in ﬂight, people

running, and so forth.

21Giffen, an early editor of The Statist, also wrote a statistical text published posthumously in 1913; it contained

an entire chapter on constructing tables, but not a single graph (Klein,1997, p. 17).

22A reanalysis of the data using a loess smoother shows that this is in fact over-smoothed, and corresponds closely

to a loess window width of f= 0.50. The optimal smoothing parameter, minimizing AICCis f= 0.16, giving a

smooth more like Bowley’s three- and ﬁve-year moving averages.

21

Figure 14: Arthur Bowley’s demonstration of methods of smoothing a time series graph. Mov-

ing averages of three, ﬁve and ten years are compared with a freehand curve drawn through four

points representing the averages of successive ten year periods. Source: Bowley (1901, opposite

p. 151).

covery of the concept of atomic number by Henry Moseley (1913) based largely on graphical

analysis. See (Friendly and Denis,2005) for more detailed discussion of these uses.

As well, experimental comparisons of the efﬁcacy of various graphics forms were begun

(Eells,1926,von Huhn,1927,Washburne,1927), a set of standards and rules for graphic presen-

tation was ﬁnally adopted by a joint committee (Joint Committee on Standards for Graphic Presentation,

1914), and a number of practical aids to graphing were developed. In the latter part of this pe-

riod, new ideas and methods for multi-dimensional data in statistics and psychology would

provide the impetus to look beyond the 2D plane.

Graphic innovation was also awaiting new ideas and technology: the development of the

machinery of modern statistical methodology, and the advent of the computational power and

display devices which would support the next wave of developments in data visualization.

22

2.7 1950–1975: Re-birth of data visualization

Still under the inﬂuence of the formal and numerical zeitgeist from the mid-1930s on, data

visualization began to rise from dormancy in the mid 1960s. This was spurred largely by three

signiﬁcant developments:

• In the USA, John W. Tukey [1915–2000], in a landmark paper, The Future of Data Anal-

ysis (Tukey,1962), issued a call for the recognition of data analysis as a legitimate branch

of statistics distinct from mathematical statistics; shortly, he began the invention of a wide

variety of new, simple, and effective graphic displays, under the rubric of “Exploratory

Data Analysis” (EDA)— stem-leaf plots, boxplots, hanging rootograms, two-way table

displays, and so forth, many of which entered the statistical vocabulary and software im-

plementation. Tukey’s stature as a statistician and the scope of his informal, robust, and

graphical approach to data analysis were as inﬂuential as his graphical innovations. Al-

though not published until 1977, chapters from Tukey’s EDA book (Tukey,1977) were

widely circulated as they began to appear in 1970–1972, and began to make graphical

data analysis both interesting and respectable again.

• In France, Jacques Bertin [1918–] published the monumental Semiologie Graphique

(Bertin,1967). To some, this appeared to do for graphics what Mendeleev had done for

the organization of the chemical elements, that is, to organize the visual and perceptual

elements of graphics according to the features and relations in data. In a parallel but sep-

arate steam, an exploratory and graphical approach to multidimensional data (“L’analyse

des donn´

ees”) begun by Jean-Paul Benz´

ecri [1932–] provided French and other European

statisticians with an alternative, visually-based view of what statistics was about.

• But the skills of hand-drawn maps and graphics had withered during the dormant “mod-

ern dark ages” of graphics (though nearly every ﬁgure in Tukey’s EDA (Tukey,1977)

was, by intention, hand-drawn). Computer processing of statistical data began in 1957

with the creation of FORTRAN, the ﬁrst high-level language for computing. By the late

1960s, widespread mainframe university computers offered the possibility to construct

old and new graphic forms by computer programs. Interactive statistical applications,

e.g., Fowlkes (1969), Fishkeller et al. (1974) and true high-resolution graphics were de-

veloped, but would take a while to enter common use.

By the end of this period signiﬁcant intersections and collaborations would begin: (a) com-

puter science research (software tools, C language, UNIX, etc.) at Bell Laboratories (Becker,

1994) and elsewhere would combine forces with (b) developments in data analysis (EDA, psy-

chometrics, etc.) and (c) display and input technology (pen plotters, graphic terminals, digitizer

tablets, the mouse, etc.). These developments would provide new paradigms, languages and

software packages for expressing statistical ideas and implementing data graphics. In turn, they

would lead to an explosive growth in new visualization methods and techniques.

Other themes began to emerge, mostly as initial suggestions: (a) various novel visual repre-

sentations of multivariate data (Andrews’ (1972) Fourier function plots, Chernoff (1973) faces,

star plots, clustering and tree representations); (b) the development of various dimension-

reduction techniques (biplot (Gabriel,1971), multidimensional scaling, correspondence analy-

sis), providing visualization of of multidimensional data in a 2D approximation; (c) animations

23

of a statistical process; and (d) perceptually-based theory and experiments related to how graphic

attributes and relations might be rendered to better convey the data visually.

By the close of this period, the ﬁrst exemplars of modern GIS and interactive systems for

2D and 3D statistical graphics would appear. These would set goals for future development and

extension.

2.8 1975–present: High-D, interactive and dynamic data visualization

During the last quarter of the 20th century data visualization has blossomed into a mature, vi-

brant and multi-disciplinary research area, as may be seen in this Handbook, and software tools

for a wide range of visualization methods and data types are available for every desktop com-

puter. Yet, it is hard to provide a succinct overview of the most recent developments in data

visualization, because they are so varied, have occurred at an accelerated pace, and across a

wider range of disciplines. It is also more difﬁcult to highlight the most signiﬁcant develop-

ments, that may be seen as such in a subsequent history focusing on this recent period.

With this disclaimer, a few major themes stand out:

• the development of highly interactive statistical computing systems. Initially, this meant

largely command-driven, directly programmable systems (APL, S), as opposed to com-

piled, batch processing;

• new paradigms of direct manipulation for visual data analysis (linking, brushing (Becker and Cleveland,

1987), selection, focusing, etc.);

• new methods for visualizing high-dimensional data (the grand tour (Asimov,1985), scat-

terplot matrix (Tukey and Tukey,1981), parallel coordinates plot (Inselberg,1985,Wegman,

1990), spreadplots (Young,1994a), etc.);

• the invention (or re-invention) of graphical techniques for discrete and categorical data;

• the application of visualization methods to an ever-expanding array of substantive prob-

lems and data structures, and

• substantially increased attention to the cognitive and perceptual aspects of data display.

These developments in visualization methods and techniques arguably depended on ad-

vances in theoretical and technological infrastructure, perhaps more so than in previous periods.

Some of these are:

• large-scale statistical and graphics software engineering, both commercial (e.g., SAS)

and non-commercial (e.g., Lisp-Stat, the R project). These have often been signiﬁcantly

leveraged by open-source standards for information presentation and interaction (e.g.,

Java, Tcl/Tk);

• extensions of classical linear statistical modeling to ever wider domains (generalized lin-

ear models, mixed models, models for spatial/geographical data, and so forth).

• vastly increased computer processing speed and capacity, allowing computationally in-

tensive methods (bootstrap methods, Bayesian MCMC analysis, etc.), access to massive

data problems (measured in terabytes) and real-time streaming data. Advances in this area

continue to press for new visualization methods.

From the early 1970s to mid 1980s, many of the advances in statistical graphics concerned

static graphs for multidimensional quantitative data, designed to allow the analyst to see rela-

tions in progressively higher dimensions. Older ideas of dimension reduction techniques (prin-

24

cipal component analysis, multidimensional scaling, discriminant analysis, etc.) led to gener-

alizations of projecting a high-D dataset to “interesting” low-D views, as expressed by various

numerical indices that could be optimized (projection pursuit) or explored interactively (grand

tour).

The development of general methods for multidimensional contingency tables began in the

early 1970s, with Leo Goodman (1970), Shelly Haberman (1973) and others (Bishop et al.,

1975) laying out the fundamentals of log-linear models. By the mid 1980s, some initial, spe-

cialized techniques for visualizing such data were developed (fourfold display (Fienberg,1975),

association plot (Cohen,1980), mosaic plot (Hartigan and Kleiner,1981) and sieve diagram

(Riedwyl and Sch¨

upbach,1983)), based on the idea of displaying frequencies by area (Friendly,

1995). Of these, extensions of the mosaic plot (Friendly,1994,1999) have proved most gener-

ally useful, and are now widely implemented in a variety of statistical software, most completely

in the vcd package (Meyer et al.,2005) in R.

It may be argued that the greatest potential for recent growth in data visualization came from

the development of dynamic graphic methods, allowing instantaneous and direct manipulation

of graphical objects and related statistical properties. One early instance was a system for in-

teracting with probability plots (Fowlkes,1969) in realtime, choosing a shape parameter of a

reference distribution and power transformations by adjusting a control. The ﬁrst general

system for manipulating high-dimensional data was PRIM-9, developed by Fishkeller, Fried-

man and Tukey (1974), and providing dynamic tools for Projecting, Rotating (in 3D), Isolating

(identifying subsets) and Masking data in up to 9 dimensions. These were quite inﬂuential, but

remained one-of-a-kind, “proof of concept” systems. By the mid 1980s, as workstations and

display technology became cheaper and more powerful, desktop software for dynamic graphics

became more widely available (e.g., MacSpin, Xgobi). Many of these developments to that

point are detailed in the chapters of Dynamic Graphics for Statistics (Cleveland and McGill,

1988).

In the 1990s, a number of these ideas were brought together to provide more general systems

for dynamic, interactive graphics, combined with data manipulation and analysis in coherent and

extensible computing environments. The combination of all these factors was more powerful

and inﬂuential than the sum of their parts. Lisp-Stat (Tierney,1990) and its progeny (Arc,

Cook and Weisberg (1999); ViSta, Young (1994b)), for example, provided an easily extensible

object-oriented environment for statistical computing. In these systems, widgets (sliders, se-

lection boxes, pick lists, etc.), graphs, tables, statistical models and the user all communicated

through messages, acted upon by whomever was a designated “listener,” and had a method to re-

spond. Most of the ideas and methods behind present day interactive graphics are described and

illustrated in Young et al. (2006). Other chapters in this Handbook provide current perspectives

on other aspects of interactive graphics.

3 Statistical historiography

As mentioned at the outset, this review is based on the information collected for the Milestones

Project, which I regard (subject to some caveats) as a relatively comprehensive corpus of the

signiﬁcant developments in the history of data visualization. As such, it is of interest to consider

what light modern methods of statistics and graphics can shed on this history, a self-referential

question we call “statistical historiography” (Friendly,2005). In return, this offers other ways

25

to view this history.

3.1 History as “data”

Historical events, by their nature, are typically discrete, but marked with dates or ranges of

dates, and some description— numeric, textual, or classiﬁed by descriptors (who, what, where,

amount, and so forth). Among the ﬁrst to recognize that history could be treated as data and

Figure 15: A specimen version of Priestley’s Chart of Biography.Source:Priestley (1765).

portrayed visually, Joseph Priestley (1765,1769) developed the idea of depicting the lifespans

of famous people by horizontal lines along a time scale. His enormous (2’ by 3’) and detailed

Chart of Biography showed two thousand names from 1200 BC to 1750 AD by horizontal lines

from birth to death, using dots at either end to indicate ranges of uncertainty. Along the vertical

dimension, Priestly classiﬁed these individuals, e.g., as statesmen or men of learning. A small

fragment of this chart is shown in Figure 15.

Priestley’s graphical representations of time and duration apparently inﬂuenced Playfair’s

introduction of time-series charts and bar charts (Funkhouser,1937, p. 280). But these inven-

tions did not inspire the British statisticians of his day, as noted earlier; historical events and

statistical facts were seen as separate, rather than as data arrayed along a time dimension. In

1885 at the Jubilee meeting of the Royal Statistical Society, Alfred Marshall (1885) argued that

the causes of historical events could be understood by the use of statistics displayed by “histori-

cal curves” (time-series graphs): “I wish to argue that that the graphic method may be applied as

to enable history to do this work better than it has hitherto” (p. 252). Maas and Morgan (2005)

discuss these issues in more detail.

3.2 Analyzing Milestones data

The information collected in the Milestone Project is rendered in print and web forms as a

chronological list, but is maintained as a relational database (historical items, references, im-

ages) in order to be able to work with it as “data.” The simplest analyses examine trends over

26

time. Figure 1shows a density estimate for the distribution of 248 milestones items from 1500

to the present, keyed to the labels for the periods in history. The bumps, peaks and troughs all

seem interpretable: note particularly the steady rise up to ∼1880, followed by a decline through

the “modern dark ages” to ∼1945, then the steep rise up to the present. In fact, it is slightly

surprising to see that the peak in the Golden Age is nearly as high as that at present, but this

probably just reﬂects under-representation of the most recent events.23

Other historical patterns can be examined by classifying the items along various dimensions

(place, form, content, and so forth). If we classify the items by place of development (Europe

vs. North America, ignoring Other), interesting trends appear (Figure 16). The greatest peak

in Europe around 1875–1880 coincided with a smaller peak in North America. The decline in

Europe following the Golden Age was accompanied by an initial rise in North America, largely

due to popularization (e.g., text books) and signiﬁcant applications of graphical methods, then a

steep decline as mathematical statistics held sway.

Early maps Measurement

& Theory

New graphic

forms Begin modern

period

Golden age

Modern dark

ages

High-D Vis

n=162 Europe

n= 83

N. America

Milestones: Places of development

Relative density

0.00

0.01

0.02

Year

1500 1600 1700 1800 1900 2000

Figure 16: The distribution of milestone items over time, comparing trends in Europe and North

America.

Finally, Figure 17 shows two mosaic plots for the milestones items classiﬁed by Epoch,

Subject matter and Aspect. Subject was classed as having to do with human (e.g., mortality,

disease), physical or mathematical characteristics of what was represented in the innovation.

Aspect classed each item according to whether it was primarily map-based, a diagram or statis-

23Technical note: In this ﬁgure an optimal bandwidth for the kernel density estimate was selected (using the

Sheather-Jones plugin estimate) for each series separately. The smaller range and sample size of the entries for

Europe vs. North America gives a smaller bandwidth for the former, by a factor of aabout 3. Using a common band-

width, ﬁxed to that determined for the whole series (Figure 1) undersmooths the more extensive data on European

developments and oversmooths the North American ones. The details differ, but most of the points made in the

discussion about what was happening when and where hold.

27

tical innovation or a technological one. The left mosaic shows the shifts in Subject over time:

Most of the early innovations concerned physical subjects, while the later periods shift heavily

to mathematical ones. Human topics are not prevalent overall, but were dominant in the 19th

century. The right mosaic, for Subject ×Aspect indicates that, unsurprisingly, map-based in-

novations were mainly about physical and human subjects, while diagrams and statistical ones

were largely about mathematical subjects. Historical classiﬁcations clearly rely on more detailed

deﬁnitions than described here, however, it seems reasonable to suggest that such analyses of

history as “data” are a promising direction for future work.

-1600 17th C 18th C 19th C 1900-50 1950-75 1975+

Epoch

Physical Human Mathematical

Subject

Maps Diagrams Technology

Aspect

Physical Human Mathematical

Subject

Figure 17: Mosaic plots for milestones items, classiﬁed by Subject, Aspect and Epoch.

3.3 What was he thinking?: Understanding through reproduction

Historical graphs were created using available data, methods, technology, and understanding

current at the time. We can often come to a better understanding of intellectual, scientiﬁc, and

graphical questions by attempting a re-analysis from a modern perspective.

Earlier, we showed Playfair’s time-series graph (Figure 7) of wages and prices, and noted

that Playfair wished to show that workers were better off at the end of the period shown than

at any earlier time. Presumably he wished to draw the reader’s eye to the narrowing of the gap

between the bars for prices and the line graph for wages. Is this what you see?

What this graph shows directly is quite different than Playfair’s intention. It appears that

wages remained relatively stable, while the price of wheat varied greatly. The inference that

wages increased relative to prices is indirect and not visually compelling.

We cannot resist the temptation to give Playfair a helping hand here—by graphing the ratio

of wages to prices (labor cost of wheat), as shown in Figure 18. But this would not have occurred

to Playfair, because the idea of relating one time series to another by ratios (index numbers)

would not occur for another half-century (due to Jevons). See Friendly and Denis (2005) for

further discussion of Playfair’s thinking.

As another example, we give a brief account of an attempt to explore Galton’s discovery of

regression and the elliptical contours of the bivariate normal surface, treated in more detail in

28

Labour cost of wheat (Weeks/Quarter)

1

2

3

4

5

6

7

8

9

10

Year

1560 1580 1600 1620 1640 1660 1680 1700 1720 1740 1760 1780 1800 1820

Figure 18: Redrawn version of Playfair’s time series graph showing the ratio of price of wheat

to wages, together with a loess smoothed curve.

Friendly and Denis (2005). Galton’s famous graph showing these relations (Figure 19) portrays

the joint frequency distribution of the height of children and the average height of their parents.

It was produced from a “semi-graphic table” in which Galton averaged the frequencies in each

set of four adjacent cells, drew iso-curves of equal smoothed value, and noted that these formed

“concentric and similar ellipses.”

A literal transcription of Galton’s method, using contour curves of constant average fre-

quency, and showing the curves of the means of y|xand x|yis shown in Figure 20. It is not

immediately clear that the contours are concentric ellipses, nor that the curves of means are

essentially linear and have horizontal and vertical tangents to the contours.

A modern data analyst following the spirit of Galton’s method might substitute a smoothed

bivariate kernel density estimate for Galton’s simple average of adjacent cells. The result, using

sunﬂower symbols to depict the cell frequencies, and a smoothed loess curve to show E(y|x)is

shown in Figure 21. The contours now do emphatically suggest concentric similar ellipses, and

the regression line is near the points of vertical tangency. A reasonable conclusion from these

ﬁgures is that Galton did not slavishly interpolate iso-frequency values as is done in the contour

plot shown in Figure 20. Rather, he drew his contours to the smoothed data by eye and brain

(as he had done earlier with maps of weather patterns), with knowledge that he could, as one

might say today, trade some increase in bias for a possible decrease in variance, and so achieve

a greater smoothing.

4 Final thoughts

This chapter is titled “A brief history ...” out of recognition that it it impossible to do full

justice to the history of data visualization in such a short account. This is doubly so because I

29

Figure 19: Galton’s smoothed correlation diagram for the data on heights of parents and chil-

dren, showing one ellipse of equal frequency. Source: (Galton,1886, Plate X.).

have attempted to present a broad view spanning the many areas of application in which data

visualization took root and developed. That being said, it is hoped that this overview will lead

modern readers and developers of graphical methods to appreciate the rich history behind the

latest hot new methods. As we have seen, almost all current methods have a much longer

history than is commonly thought. Moreover, as I have surveyed this work and traveled to many

libraries to view original works and read historical sources, I have been struck withthe exquisite

beauty and attention to graphic detail seen in many of these images, particularly those from the

19th century. We would be hard-pressed to recreate many of these today.

From this history one may also see that most of the innovations in data visualization arose

from concrete, often practical goals: the need or desire to see phenomena and relationships

in new or different ways. It is also clear that the development of graphic methods depended

fundamentally on parallel advances in technology, data collection and statistical theory. Finally,

I believe that the application of modern methods of data visualization to its own history, in this

self-referential way I call “statistical historiography,” offers some interesting views of the past

and challenges for the future.

30

Mid-parent height

61

63

65

67

69

71

73

75

Child height

61 63 65 67 69 71 73 75

7

7

3

0

3

0

5

2

7

4

96

1

18

Figure 20: Contour plot of Galton’s smoothed data, showing the curves of ¯y|x(ﬁlled circles,

solid line), ¯x|y(open circles, solid line) and the corresponding regression lines (dashed).

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39

Index

Abbott, Edwin, 14

age pyramid, 18

analysis

discriminant, 25

principal component, 25

arithmetic

political, 5,6

atlascartographic, 4

statistical, 17,20

atomic number, 21

Baker, Robert, 12

bar chart, 8,20,26

divided, 12

Barbeu-Dubourg, Jacques, 7

Bell Laboratories, 23

Benz´

ecri, Jean-Paul, 23

Bertin, Jacques, 23

bilateral frequency polygon, 18

bills of mortality, 6

biplot, 23

bivariate normal surface, 28

bootstrap, 24

Bowley, Arthur, 21,22

boxplot, 23

Brahe, Tycho, 4–6,16

brushing, 24

Buache, Phillippe, 7

C, 23

camera obscura, 4

chartbar, 8,12,20,26

control, 21

Gantt, 21

isochronic, 16

pie, 8

time-series, 26

Cheysson, ´

Emile, 15,17

clustering, 23

continuous distribution function, 6

coordinate

parallel, 16

coordinate paper, 8

coordinate systems, 6

correlation, 16

coxcomb, 14

Crome, August F.W., 8

curve

contour, 29

cumulative frequency, 21

freehand, 21

frequency, 21

historical, 26

isodic, 16

isogen, 16

loess, 29

curve ﬁtting, 8

Cusa, Nicolas of, 4

datamultivariate, 23

de Fourcroy, Charles, 8

de Witt, Jan, 6

density estimation, 29

Descartes, Ren´

e, 5

diagram

alignment, 16

butterﬂy, 21

cartogram, 8,18

Chernoff faces, 23

circle, 18

contour, 14,16

coxcomb, 14

divided circle, 14

geometric, 3

Hertzsprung-Russell, 21

historical, 21

nomogram, 16

pie, 18

rose, 14,18

sieve, 25

statistical, 18

stereogram, 14

tree, 23

dimension

40

3, 16

display

fourfold, 25

trellis, 16

two-way table, 23

du Carla-Boniface, Marcellin, 7

Dupin, Charles, 10

dynamic graphics, 25

Fermat, Pierre, 5

ﬁgure

geometric, 8

ﬂow map, 14,18

FORTRAN, 23

Friendly, Michael, 25

Galilei, Galileo, 5

Galton, Francis, 16,17,28–29

Gannett, Henry, 18

Gauss, Carl Friedrich, 14

Gemma-Frisius, Reginer, 4

Giffen, Robert, 21

Golden Age, 13,27

Goodman, Leo, 25

grand tour, 24

graph

age pyramid, 18

bilateral polygon, 20

circle, 8

hanging rootogram, 23

high-resolution, 23

line, 5,8

time-series, 3,8,26,28

graph paper, 8

Graunt, John, 5,6

grid coordinate, 7

hexagonal, 16

Guerry, Andr´

e-Michel, 10,14

Haberman, Shelly, 25

Halley, Edmund, 7

Harrison, John, 5

Herschel, William, 9

Huygens, Christiaan, 6

interactive graphics, 25

interpolation, 8

isoline, 16

Java, 24

Jevons, William Stanley, 13

Lallemand, Charles, 16

Lambert, Johann, 8

Laplace, Pierre Simon, 14

le Blon, Jacob, 8

Levasseur, Pierre ´

Emile, 17

life table, 6

line contour, 7

isogon, 7

isoline, 7,16

slope as rate, 8

timeline, 7

line graph

1D, 5

linking, 24

Lisp-Stat, 24,25

lithography, 8

longitude, 6

MacSpin, 25

mapanamorphic, 16

cartography, 7

chloropleth, 10

contour, 7

disease, 12

epidemiological, 15

ﬂow, 14,18

geological, 9

shaded, 20

thematic, 7,14

topographic, 7

weather, 6,17

Marey, ´

Etienne Jules, 21

Marshall, Alfred, 26

matrix

scatterplot, 24

Maunder, E. W., 21

measurement

physical, 5

measurement error, 7

41

Minard, Charles Joseph, 12,14

model

generalized linear, 24

mixed, 24

mosaic plot, 12,25,28

Moseley, Henry, 22

multidimensional scaling, 23,25

Nightingale, Florence, 14

nomogram, 16

Oresme, Nicole, 4

Ortelius, Abraham, 4

parallel coordinates plot, 24

Pascal, Blaise, 5

Pearson, Karl, 16

Perozzo, Luigi, 14

Petermann, Augustus, 12

Petty, William, 5,6

pie chart, 8

Playfair, William, 8,26,28

plot association, 25

bivariate, 6

Fourier function, 23

log-log, 16,21

mosaic, 12,25,28

parallel coordinate, 18

probability, 25

star, 18,23

stem-leaf, 23

political arithmetic, 6

Priestley, Joseph, 8,26

PRIM-9, 25

printing

three-colour, 8

probability theory, 6

projection

axonometric, 14

Ptolemy, Claudius, 3,6

Quetelet, Adolphe, 11,14,17

R, 24,25

regression, 16,29

Rheticus, Georg, 4

Royal Statistical Society, 13,26

SAS, 24

scaling

multidimensional, 23,25

scatterplot matrix, 24

Scheiner, Christopher, 5

Schwabe, Hermann, 17

Senefelder, Aloys, 8

sieve diagram, 25

small multiple, 18

small multiples, 5

Smith, William, 9

smoothing, 21,29

Snow, John, 12,15

spreadplot, 24

star plot, 18,23

statistical atlas, 17

statistics

demographic, 5

moral, 10

stem-leaf plot, 23

stereogram, 14

stratigraphic geology, 9

symbol

sunﬂower, 29

tablegraphical, 8

life, 6

semi-graphic, 29

tableau-graphique, 12

Tcl/Tk, 24

thematic cartography, 7

time-series, 8

multiple, 14

timeline, 7,26

tour grand, 24

triangulation, 4

Tufte, Edward, 5

Tukey, John W., 23

two-way table, 23

UNIX, 23

van Langren, Michael F., 5

42