june2012 31© 2012 Robert Cook and Howard Wainer

A c e n t u r y a n d a h a l f o f m o r a l s t a t i s t i c s i n t h e U n i t e d K i n g d o m

Va r i a t i o n s o n J o s e p h F l e t c h e r ’ s t h e m a t i c m a p s

It is a truth universally acknowledged, that any person in possession of a geographic data set, must be in want of a map. (Jane Austen, 1817)

A cave painting from around 25 000 bc in Pavlov in the Czech Republic is thought to show the mountain, rivers and valleys nearby. Maps are the oldest of graphic displays. This is not surpris-ing, for representing space as space is a natural metaphor. Adding a third variable onto a geo-graphic background, however, is a more recent innovation. There were partially thematic maps in China as early as the fourth century bc. A set of seven maps of that date show rivers and roads, but also where different kinds of timber may be gathered, and the distances to reach the sites. But the additional variables that were plotted on such maps were generally geographic variables such as altitude, and were ancillary to the main purpose of the map. A thematic map whose focus was primarily on the additional variable did not appear until the seventeenth century.

Initially, the variables that were plotted on a geographic background were physical ones such as magnetic phenomena, currents and geology. Such maps have obvious and immediate uses. Halley published what is believed to be the first meteorological chart in 1686. And, in 1815, William Smith (1769–1839) prepared a map

depicting the geology of England, which showed that specific fossils were found in correspond-ing layers of rock; so severely did this conflict with the biblical interpretation in which the

rocks were laid down during the Great Flood that Smith’s production has been called the “map that changed the world”1.

The gathering of what might be called social statistics is often dated from John Graunt’s (1662) analysis of the London Bills of Mortality. There were bits and pieces of graphic display of social data in the late 17th and early 18th cen-turies, most notably Christiaan Huygens’ drawing of a survival graph in a letter that he sent to his brother in 1669, but, so far as is known, very few maps of such social subjects as population,

religion or industrial production appeared before 1820. The preparers of the earliest such maps merely wrote the statistic of interest on the map. An example of this practice is Wyld’s 1815 map “Chart of the World Shewing the Religion, Popu-lation and Civilization of Each Country”. Such maps only barely “qualify as thematic since they do not graphically portray the character of the distribution effectively”2. They were hardly an advance on the Chinese maps of 2000 years be-fore. While it is surely true that putting numbers on a map to indicate the location where some-thing is happening conveys more information than would merely listing them in a table, such a practice does not utilise the graphic medium at anywhere near its capability.

More sophisticated use of thematic maps began on November 30th, 1826, when Charles Dupin (1784–1873) gave an address on the topic of popular education and its relation to French prosperity. He used a map shaded according to the proportion of male children in school relative to the size of the population in that départe-ment. This graphic approach was improved upon by Frère de Montizon, who in 1830 produced a map showing the population of France in which he represented the population by dots, with each dot representing 10 000 people. Although no one remarked on it for the better part of a century, it remains perhaps the most important conceptual

Do ignorance and crime go together? And does immorality accompany them? Robert Cook and Howard Wainer tell

of a Victorian pioneer of maps that contain more than geography, and bring his advances up to date.

Merely putting numbers on a map does not use the medium at

anywhere near its capability

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breakthrough in thematic mapping. It was the direct linear antecedent of John Snow’s famous map of the 1854 cholera epidemic in London, reproduced in Significance June 2011. Snow’s map is generally referred to as the beginning of modern epidemiology.

After Montizon’s map there were a number of others between 1830 and 1845 that used shading to convey population. Often they were roughly drawn and clearly meant to be of only secondary importance to the document in which they appeared. But a few were clever, remark-ably polished, displays. Exemplary among these were population maps, designed and prepared by Henry Drury Harness (1804–1883), a young lieutenant in the Royal Engineers, that appeared in an 1837 Atlas as accompaniment to a report prepared by railway commissioners.

Maps of moral statistics started appearing at about the same time; these typically focused on various aspects of crime. Most widely known were those of Adriano Balbi (1782–1848) and André-Michel Guerry (1802–1866), whose 1829 map pairing the popularity of instruction with

the incidence of crimes was but the start of their continuing investigations. Their work was paralleled by the Belgian Adolphe Quetelet (1796–1874) who, in 1831, produced a marvel-lous map of crimes against property in France, in which the shading was continuous across inter-nal boundaries rather than being uniform within département. Guerry expanded his investigation in the 1830s to add three other moral variables (illegitimacy, charity, and suicides) to crime and instruction. Thus, despite graphical display’s English birth, its early childhood was spent on the Continent.

Maps of moral statistics began their return across the Channel in 1847 when a 34-year-old barrister named Joseph Fletcher (1813–1852) published the first of several long papers. This paper was filled with tables and but a single, rudimentary map. In fact, he rejected the use of maps explicitly, suggesting that you could get all you needed by simply perusing the columns of numbers and thus avoid the bother and expense of drafting and printing maps. Two years later he completely changed his approach in two much

longer papers that included many shaded maps that were innovative in both content and format. He gives an evocative hint about the cause of his change of heart: “I have endeavoured to sup-ply the deficiency which H. R. H. Prince Albert was pleased to point out, of the want of more illustrations of this kind.”

We can look at his format first. Fletcher, having a background in statistics, or at least what was thought of as statistics in the mid-nineteenth century, did not plot the raw numbers but instead their deviations from the mean. And so the scale of the tints he used varied from the middle, an approach that is now common. For example, Andrew Gelman, in his remarkable 2008 book explaining that year’s presidential election results3, uses increasing saturations of red to show the proportion of voters who voted Republican in states where they were in the majority and increasing saturations of blue for those states that voted Democratic. The closer the vote came to a 50:50 split between the two parties, the closer the shading was to white, regardless of the final outcome. But in 1849, the

Figure 1. Ignorance in England and Wales taken from Fletcher’s Summary of the Moral Statistics of England and Wales7

Figure 2. Crime in England and Wales, taken from Fletcher’s Summary of the Moral Statistics of England and Wales7

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approach was an innovation. The advantage of centring all variables at zero was that it allowed Fletcher to prepare a number of maps, on very different topics and very different scales, and place them side by side for comparison without

worrying about the location of the scale. He also oriented the shading, as much as possible, in the same way. In his words: “In all the Maps it will be observed that the darker tints and the lower numbers are appropriated to the unfavorable end of the scale.”

Of course, with variables like population den-sity it is hard to know which end is favourable.

He chose lesser population as more favourable because, we speculate, it seemed to accompany favourable outcomes on the other variables.

Although many of Fletcher’s innovations in format were noteworthy, it is the content he chose that makes him special. He did not make maps of obvious physical variables such as wind direction or altitude or even the distribution of the population (although he did make one such map, it was fundamentally for comparative pur-poses). He had more profound purposes in mind. Joseph Fletcher made maps of moral statistics, and opposed these maps with others to suggest causal interpretations to his viewers.

For example, he made a map of ignorance in England and Wales (Figure 1) – his data for ignorance, cunningly, was the proportion who, on marriage certificates, instead of signing their names had to make an X. Next to this plot he put a map of the incidence of crime (Figure 2). He opted for this juxtaposition on the ba-sis of detailed analysis of subsets of the data. For example, he wrote: “We thus find that the decline in total ignorance to be slowest in the most criminal and the most ignorant districts”. He then tied this analysis into the phenomenon

made observable through the juxtaposed maps, stating that “the darkest tints of ignorance go with those of crime, from the more southern of the Midland Manufacturing Counties, through the South Midland and Eastern Agricultural Counties, … and it will be well to observe, as an example of their use, that all four of the tests of moral influences now employed are seen to be on the side of the more instructed districts”. And then, looking into the phenomenon at a more microscopic level, he observed: “The two least criminal regions are at the opposite extremes in this respect (the Celtic and the Scandinavian)” – “Celtic” included Cornwall as well as Wales; by “Scandinavian” he meant the northern counties with Lincolnshire and Yorkshire – “with this important difference, that in the region where there is the greatest decline of absolute igno-rance among the criminals (the Scandinavian), there is not one-half of the amount of it in the population at large which exists in the other”.

In addition to these maps, he also produced parallel plots of bastardy in England and Wales, of improvident marriages, of persons of inde-pendent means, of pauperism, and many other variables that could plausibly be thought of as

Figure 3. Fletcher’s map of ignorance in England and Wales, updated Figure 4. Fletcher’s map of crime in England and Wales, updated

Fletcher produced maps of bastardy, of ignorance, of

crime, of pauperism, and of improvident marriages

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either causes or effects of other variables. His goal in doing this was to generate and test hypotheses, which might then be used to guide social action and policy. One such hypothesis was framed as follows:

The practical resistance of the country or the people in these latter districts to any system of higher economy or better cultivation is as conspicuous on the map as it is on the face of the land itself; the regions occupied by the Celtic populations, forming a class apart, quite beyond all the others in the excess of their population in proportion to the assessable value of the soil which it cultivates. A reference again to Map V [Figure 2] shows that these regions are equally under the average in observed delinquency and to Map IV [Figure 1], that they are equally in excess of ignorance; whence I am induced to draw the conclusion, to be tested by further experience, that an ignorant people, engaged in rural industry, will exhibit a less amount of crime when that industry

is organized on the plan of the small rather than the large husbandry, and, as a necessary corollary, from what has already been shown, that the introduction of an improved economy into the organization of agriculture as of manufacturing labour, demands for its security and the general welfare a higher moral development among the whole population than enables society to exist in its ruder form.

His epistemological viewpoint was both wise and surprisingly modern. Unfortunately, similarly modern robust statistics and colour plotting were not available to Fletcher. Had he been construct-ing these plots today, he would almost certainly have looked at deviations from the median in-stead of the mean, and would likely have fol-lowed the lead of Gelman and others in plotting points above the median in varying saturations of red and points below the median in varying saturations of blue (or vice versa). And, if he had had access to modern plotting software and laser printers he likely would have abandoned the practice of categorising the variables in

favour of using a continuous method of shading. As Bertin4 has taught us, the representation of a variable should match the variable itself. Thus, if a variable is continuous, so too should be its graphical representation.

In Figures 3 and 4 are versions, redone using modern variables and techniques, of Fletcher’s plots of ignorance and crime previously shown as Figures 1 and 2. Careful study will reveal the advantages of the modern approach. Most strik-

Figure 5. Ignorance in England and Wales, 2000 Figure 6. Crime in England and Wales, 2010

An ignorant people engaged in rural industry will exhibit less crime when their industry is on the small scale than on the large

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ingly, the two-colour shading scheme renders his suggested interpretations all the more read-ily observable. Where comparison of Fletcher’s maps may involve careful scrutiny of shading and frequent reference to the legend, at least before thorough familiarisation, the modern versions of the same are interpretable at a glance, needing only to have red matched to red and blue to blue with the maps side by side to quickly get an idea of how the proportion of crime within counties is related to the propor-tion of ignorance.

These thematic mapping techniques can also be employed to see how 150 years of social programmes in the UK, the arguments for many of which were the inspiration for Fletcher’s the-matic maps, have changed the faces of crime and ignorance on the landscape. To this end, let us look at revisions of Figures 3 and 4 using modern data, shown as Figures 5 and 6. With a careful look, we can see that the relationship between ignorance (now defined rather dif-ferently) and crime seems more tenuous. The relationship does appear to hold in the area of highest crime, which is coincidentally home to the better part of London, the biggest urban centre in England. Overall, though, the lack of a strong link between ignorance and crime in the modern data suggests a possible interpretation that effective social programmes have reduced the need of the ignorant to turn to crime in order to survive.

The maps can also be juxtaposed to see if geographical patterns of crime and ignorance have changed over time. As noted, crime rates are highest in the modern data in counties with

major urban centres. This holds historically as well. The 1845 crime map’s two darkest red coun-ties contain London, England’s largest city, and Birmingham, its industrial centre and “the first manufacturing town in the world”5. Beyond that, understanding the geographical shifts of crime in the UK would involve deeper anthropological investigation. Counties with highest rates of ignorance were found primarily in the central latitudes of England and Wales in 1845, whereas

the line of ignorance in the modern map is drawn to create a fairly strict North–South dichotomy. The reasons for this pattern go beyond the scope of this article.

Though some understanding of the relation-ship between crime and ignorance as well as their relationship over time can be attained through the comparison of thematic maps, the process is neither easy nor precise – even using modern analysis and shading techniques. Fletcher’s use of thematic maps was innovative but perhaps not the ideal tool available at the time. Had he had

an interest in astronomy, Fletcher might have come upon a more useful tool for depicting the relationship between these two data sets: the scatterplot. In his “investigation of the orbits of revolving double stars”, published in 1833, Brit-ish astronomer John Frederick William Herschel plotted the positions of stars on one axis against the observation year on the other and drew a smoothed curve between the points to represent the relationship between the two variables; in so doing, he unknowingly staked his claim as inven-tor of the scatterplot6. Such a representation of Fletcher’s 1845 crime and ignorance data more clearly illustrates the relationship between the two variables and is presented here in Figure 7. In Figure 7(a) we show the relationship between ignorance and crime in the United Kingdom in the 1840s and in Figure 7(b) we show the re-lationship between the same variables in con-temporary Britain. Unsurprisingly, the positive relationship Fletcher showed via his maps is made strikingly clear in the scatterplot based on his data. The same positive relationship exists for the contemporary data, though the positions of the individual counties on these variables bear little resemblance to their historical positions. It is interesting that the exceptional relationship be-tween high crime and low ignorance that Fletcher observed in the Celtic counties is considerably weakened, but the positions of the counties rela-tive to one another is nearly perfectly preserved.

The bivariate scatterplot has the power to illuminate other sorts of relationships as well. In Figure 8(a) we compare the distribution of ignorance in the UK in 1844 with that in the present; in Figure 8(b) we do the same thing

Ignorance has reversed, so that the least ignorant counties in

1844 are now the most ignorant, and vice versa

Figure 7. (a) A scatter plot of ignorance against crime for the nineteenth-century data vividly shows the positive relation that Fletcher discusses. It also highlights the unusual character of Middlesex county (home of greater London), as well as the similarity of the Celtic counties (Monmouth, North and South Wales).

(b) A scatter plot of ignorance against crime for contemporary data shows the same positive relationship, but, as we will see in Figure 8, there have been major changes in the positions of the counties on these two variables

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with crime. Ignorance is shown to have reversed such that the least ignorant counties in 1844 are now the most ignorant, and vice versa. There is no such reversal in the distribution of crime between then and now, but the relationship is weak at best, with Middlesex county – modern-day London – being the most notable exception.

That there is a better way to represent the relationship between crime and ignorance in the

UK than by juxtaposition of monochromatic maps does not diminish the ingenuity of Fletcher’s ap-proach in his day. Had he had more sophisticated statistical tools, convenient colour data mapping techniques, and knowledge of the scatterplot, he would no doubt have taken advantage of them in presenting his moral statistics. Given the tools available to him, his use of thematic maps in making his case was ingenious. Having the tools we now have at our access, the use of thematic maps remains an excellent method for represent-ing the geographic distribution of social data. For representing the geographic relationship between two variables, the addition of a scat-

terplot to make clear the exact nature of the relationship is invaluable.

It is fitting that we close with a passage of Fletcher’s on the challenge of being a social scientist, in which he encapsulates the scientific method of testing a hypothesis if possible to destruction7:

The man who studies society, however, labours under a great difficulty in being entirely denied the use of experiment, and limited most rigidly to … observation, of elements most subtilly combined … and wholly beyond his control. Analysis, therefore, in the sense of the chemist, is absolutely impossible; but by exhaustive enumerations of facts … we get a means of detecting the excess or deficiency of certain social elements in definite classes or localities; and by multiplying these lines of observation … we gradually arrive at higher and safe inductions, which will sometimes corroborate principles which we have reached by deductive reasoning … and at others will present irreconcile-able results, which the bigot of theory will despise, but which the man of science knows how to prize as gems.

Acknowledgements

This work was collaborative in all respects and the order of authorship is alphabetical. Figures 1 and 2 are courtesy of the Rare Books Library in the Van Pelt Dietrich Library Center of the

University of Pennsylvania. We are grateful to John Pollack. In addition, we would like to thank Stephen Ferguson and the Rare Books Library of Princeton University for providing access to Fletcher’s original papers. Finally, our updated plots of ignorance and crime in contemporary England and Wales would have been much more difficult without the generosity of Danny Dorling at the University of Sheffield, who made avail-able to us the data used in his books, Human Geography in the UK and Bankrupt Britain: An Atlas of Social Change.

References1. Winchester, S. (2009) The Map that

Changed the World. New York: Harper Perennial.2. Robinson, A. H. (1982) Early Thematic

Mapping in the History of Cartography. Chicago: University of Chicago Press.

3. Gelman, A. (2008) Red State, Blue State, Rich State, Poor State: Why Americans Vote the Way They Do. Princeton, NJ: Princeton University Press.

4. Bertin, J. (1983) Semiology of Graphics. Madison: University of Wisconsin Press.

5. Hopkins, E. (1989) Birmingham: The First Manufacturing Town in the World, 1760–1840. London: Weidenfeld & Nicolson.

6. Friendly, S., & Denis, D. (2005) The early origins and development of the scatterplot. Journal of the History of the Behavioral Sciences, 41(2), 103–130.

7. Fletcher, J. (1849) Summary of the Moral Statistics of England and Wales. Privately printed and distributed.

Robert Cook is at the University of Massachusetts. Howard Wainer is a member of the National Board of Medical Examiners.

Figure 8. (a) A scatter plot of ignorance for the two time periods shows a remarkable shift; the least ignorant counties in the nineteenth century tend to be the most ignorant now and vice versa.

(b) A scatter plot of crime for the two time periods shows only a very modest relationship between the level of criminality in a county over the two time periods depicted; the principal exception to this lack of trend is Middlesex county

We arrive at safe inductions, which the bigot of theory will despise, but

which the man of science knows how to prize as gems