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Home , Area chart, James Playfair, John Playfair, Pie chart, William Henry Playfair, William Playfair

PRESIDENTIAL ESSAY NO. 4: JULY 2021 Life of Pie: and the Impact of the Visual

By Chris Pritchard ([email protected])

Introduction only talented member of his family. There were his younger brothers, the lawyer Robert Playfair At the dawn of the nineteenth century, a and the architect , as well as Scotsman published a circular divided James’s son, , whose into three parts from the unlikely setting of the architectural legacy is seen in many of the fine Fleet, a debtor’s prison just north of Ludgate Hill buildings in ’s New Town. And then in central . It purported to represent the there was another of John’s brothers, William land mass of the Turkish Empire, with sectors of Playfair, engineer, businessman, political appropriate sizes indicating the fractions of the economist, spy and scoundrel, but also a empire lying in , Asia and , and visionary when it came to explaining things rather sloppily coloured by hand. This was the through . William Playfair, the subject of first pie and the man was William Playfair. this article, is the father of the statistical diagram and hence a beacon for those who believe that understanding in mathematics and science is often enhanced by the visual.

William Playfair (1759–1823) was taught at home by his father until he was twelve (when his father died) and then by his brother John. He showed an early flair for things mechanical, for draughtsmanship and for model construction, and so it was that he became apprenticed to a local millwright. He was still in his teens when he was introduced to Matthew Boulton, co-owner William Playfair’s life: Part 1 with of the Soho Manufactory in Birmingham. Playfair was soon engaged as The Mathematical Association was born out of a Watt’s draftsman and clerk, working on need to teach geometry unshackled from the improved designs for steam-powered machinery, suffocating constraints of ’s Elements and and then in the onsite assembly and installation the associated pedantic pedagogy. In this regard of steam pumping engines. But although this was some progress had been made over the century a very effective way to further his education, he to 1871, including by (1748–1818), found the conservatism of the company stifling: whose 1795 edition of the Elements included there was little ‘research and development’, as algebraic notation for the first time (as well as a we would call it now. So he left the Soho company restatement of the troublesome fifth postulate, and struck out on his own, taking out four patents since known as Playfair’s Axiom). At the time of and starting two companies. And then, out of the the book’s publication he had been Professor of blue, he switched interests altogether, and Mathematics at the for a moved towards international business, decade, his earlier career in the ministry set economics and visual . Prompted by the aside, and he was a key figure in the Scottish loss of the American states, he argued that Enlightenment, brushing shoulders with the likes Britain’s apparently waning power could be of Adam Smith, Joseph Black, and restored by focussing on manufacturing, banking especially , whose uniformitarian and trade, rather than on the traditional land- theory of he promoted. grab. His view was that money should flow, usury should be allowed, and investment and John Playfair was raised in a tiny settlement speculation would surely follow. outside , the eldest but by no the The first time-series chart and publication of 1801, the Statistical Breviary (Playfair, 1801a). From here on in we will use the In the early twentieth century, the phrase ‘a shortened titles, Atlas and Breviary. picture is worth a thousand words’ caught the public imagination. It was invoked in journalism In the Atlas, Playfair’s diagram of choice was and advertising. In fact, similar sentiments had what we now call the time-series chart; in fact, of been expressed widely and over a long period of the 44 the book contains, all but one are time, including, for example, by Ivan Turgenev time-series charts. They include the first who wrote in 1861 that ‘the drawing shows me depictions of a fluctuating balance of trade (i.e. at one glance what might be spread over ten the differences between imports and exports) pages in a book’. Back in 1785, William Playfair between England and its trading partners both recognised the possibility not of reducing words collectively and individually. There are charts to a drawing but of condensing a multitude of comparing the revenues of England and France numbers into a graph or chart designed to have from 1550 onwards, one showing the national maximum visual impact on the reader. Essential debt since the English Revolution, and changes in could be conveyed more quickly, the expenditure on the army and navy and on complex information could be understood by a ordnance back to 1720. Importantly, these are wider audience and at greater speed. The not depictions of a functional relationship. The Commercial and Political Atlas was published in heights of the lines (the value of imports and 1786 as a quarto book of 158 pages in landscape exports) are not a function of time but a trace of orientation. Such was its success, that it was empirical over time. This is the very first of reprinted the following year, with a third edition those time-series charts in Playfair’s book of following in 1801 (Playfair, 1786, 1787, 1801b). 1786: The last of the three piggy-backed another major

Notice that all the good features of a statistical Playfair had incorporated all the necessary graph are in place – title, frame, labelling of the elements from the outset. axes, uniform graduation of the scales, grid lines for ease in estimating values and the use of colour This was all very well when it came to picturing to embolden salient features. We wouldn’t teach England’s economic position over time, but the it any differently today. This is how statistical figures for ’s trade were not so graphs should be drawn and this is how they comprehensive and so, unable to depict changes were drawn from the very first example. Further from year to year, Playfair decided to focus on a finessing was never needed because William single year, and rather than pooling the amounts for different countries he chunked the diagram a dual bar chart because it compares information country by country. In a sense imports and exports in a pair of horizontal bars, Playfair had stumbled across the bar chart country by country. Note that Playfair also took because his data were incomplete. He the trouble to order the countries by the volume commented that ‘this chart … does not of trade for ease of comparison. Particularly comprehend any portion of time, and is much striking is the volume of imports from Catherine inferior in utility to those that do (Playfair, 1786, the Great’s Russia. p.101). Today, we would typically call the

Another book, Lineal Arithmetic, appeared in earlier monograph, Playfair knew this well. The 1798. Privately published and printed by ‘Eden Treaty’ of 1786 had reduced tariffs Alexander in London, it contained 35 between Britain and France, and there was an engraved charts depicting the economic immediate opportunity for trade to flourish performance of England in the eighteenth between the countries. So Playfair took himself century and is very rare. (A copy sold at Christie’s off to Paris and through his contacts there a copy in 2010 for $7500.) Among the conclusions that of the Atlas was passed on to the king, Louis XVI, could be drawn from the charts was the likely who, as Playfair later recalled military capability of a nation and the nature of at once understood the charts and was that capability. Who could put men into the field highly pleased. He said they spoke all and who could afford to produce military languages and were very clear and equipment became clear in a few glances. If easily understood. charts were to be prepared displaying data of a different nature, they too should make Apparently, he was so impressed that when understanding simpler. Playfair thought for Playfair saw an opportunity to build a rolling mill example that they would be excellent for in Paris, the king intimated that he would be youngsters in terms of the ease and the attraction prepared to provide some of the capital. And with of learning. such royal favour, it is no surprise that when Playfair attended the Académie Royale des William Playfair’s life: Part 2 Sciences he was warmly welcomed.

While the new statistical diagrams would make When the Bastille was stormed in July 1789, for ease of understanding, they could also be used Playfair was living close-by and is known to have to change perceptions and to influence policy, attended a meeting to organise a local militia the and having dipped his toe in the water with his day before. He witnessed much of the action and reported on it in detail later. He also wrote a see how they worked, passing on his findings to history of Jacobinism, a movement for which he the Duke of York (remembered as ‘The Grand Old had no sympathy, though he did see its Duke of York’), George III’s second son, then in emergence as an opportunity for a bit of command of British troops in Flanders. adventure, with the possibility of making some money. As tensions rose in the build-up to The second was a scheme Playfair sold to the revolution, the prospect of quitting France for British Government to produce counterfeit safer shores including America seemed a wise assignats in order to further destabilise the option to some, and so it was that Playfair French economy. If the French currency were to became involved in a scam to sell tracts of land become worthless, he argued, France could not on the banks of the Ohio River, land to which he prosecute a war against Britain. No fewer than and his cronies had only tenuous claim. French seventeen outfits in London turned to counterfeit emigrants arrived in the United States by the assignat production. Sure enough, the assignat boatload only to find their title deeds were collapsed completely, though the extent to which invalid; the American government got involved Playfair’s scheme played a part it is hard to tell, right through to President George Washington as is the extent to which the currency’s failure led and Playfair came out of the scandal badly. (For a to Napoleon’s coup later that decade. comprehensive account, see Berkowitz, 2018, chapters 4 and 5.) Counterfeiting was a serious problem in many countries at the end of the eighteenth century. Up Meanwhile in Paris Playfair was running up debts to two-thirds of the coins in circulation in Britain and his creditors were on his tail. Yet he stayed were fake. And so it was that the Bank of England there right through the Revolution, becoming stopped minting copper coins altogether in 1773 more and more disenchanted with leaving a vacuum that was initially taken up by developments. In 1791 he bravely intervened the Parys Mines company on Angelsey which when a friend was slashed repeatedly with minted tokens directly from their own copper. sabres by a mob intent on killing him. By 1792 his But it was Boulton & Watt that took on the concerns about Jacobinism were so great, venture in more earnest, establishing the Soho including the growth of a similar movement back Mint within the Soho Manufactory in the 1780s. home, that he alerted his countrymen to the Playfair had left the company by this point but he dangers in A Letter to the People of England on the would have been aware of the problem with the Revolution in France. It included his analysis of coinage, and the opportunities that the the weaknesses in France’s finances, noting in production of token coins and indeed token notes particular the use of assignats, paper money provided, opportunities to turn a profit on a printed by the revolutionary government in huge personal level but also to flip an economy given quantities in order to maintain liquidity but at the the right circumstances. Accordingly, in the late cost of inflation. Words soon turned to deeds 1790s, Playfair returned to business and when some of his ideas found favour in London; specifically to banking, setting up the Original he was eased into the role of agent for the British Security Bank and an assignat scheme to print in France, at a time when spying was unorganised low denomination banknotes ostensibly backed and ad hoc. by the Bank of England. But the Bank of England cried foul, and this, combined with considerable mismanagement, led to the bank going bust. Playfair found himself in Fleet Prison but, unbroken by his situation, he had a notion to write The Statistical Breviary. As his biographer, Bruce Berkowitz commented (p. 247), ‘Playfair was trying to write his way out of debt. The result: some of the most important works in Two of Playfair’s clandestine activities stand out. statistics, economics, and strategic analysis were The first was the hijacking of the novel written in London’s Fleet Prison’. semaphore telegraph system of communication devised by the French. Following the execution of The first circle and the king in January 1793, the French declared war on Britain, so when they found a way to pass The Breviary arose out of a friend’s project to messages to their army via a line of towers in a gather together and publish descriptive, matter of minutes, it was of huge concern. cartographic and statistical material about a Playfair, learnt of the system on one of his forays number of European countries. The author, John into France and actually built two such towers to Stockdale, also printed and sold books, and he invited Playfair to update a wealth of statistical Playfair did not regain his freedom until a few information compiled by Jakob Boetticher months later following an appeal to a fund (1754–1792) in Königsberg. The outcome was a established to support struggling writers. The series of tables, inauspiciously arrayed. Having book consisted of 64 pages, most of them already produced the Atlas, Playfair realised that displaying tables of data, country by country, but data of this sort could be presented much more with four plates, of which the most famous is that effectively in visual form. One of the keys was showing the first pie chart, ‘Statistical chart deciding which information should be presented showing the extent, the population and revenues in this way and which should be omitted of the principal nations of Europe in the order of altogether. The new book was published in 1801; their magnitude’.

What are the chart’s innovative features? pie chart. (Whilst the radius separating the last two is marked clearly, that separating 1. Circles with areas that are proportional to the first two is not because the sector for the areas of the countries, drawn in Europe is a quadrant and the horizontal grid descending order. Playfair wrote on page 15 line is there anyway.) As to why Playfair that ‘where the forms are not similar, the eye offers two different ways of dividing the cannot compare them easily nor accurately’, circle, one possibility (contained in an effectively arguing that the areas of two or anonymous blog by a company called more countries on a cannot be Geolytix) concerns the practicalities of compared as easily as if those areas are drawing the diagrams. The circles are small; reduced to circles (which are necessarily apparently just big enough in the case of similar). Russia that the annulus approach works but 2. Subdivision of two of the circles, those for too small in the case of the Turkish Empire Russia and Turkey, to indicate the extent to for three bounding concentric circles to be which they straddle two or more continents. drawn and the spaces between them Note here that Playfair uses two different coloured. If this theory is correct, then approaches, and this begs the question, Playfair favoured the concentric circles ‘Why?’ For the Russian Empire, its European approach and adopted the radial division territories appear as a circle while its Asian method only when it broke down, in exactly territories form an annulus wrapped the same way as the bar chart emerging from around. But for the Turkish (Ottoman) a failure to produce a time-series chart. Empire, which encompassed not just 3. Vertical sticks are used to show two modern-day Turkey but Greece, Syria, Iraq quantities: the population in millions and the Caucasus, as well as most of represented by a stick to the left of a circle Mediterranean Africa, there is a single circle, and read using the scale on the left; the proportional in area to the outer circle for budget in millions of pounds sterling Russia but subdivided into sectors for represented by a stick to the right of a circle Europe, Asia and Africa; what we now call a and measured using the right-hand scale. Anticipating Venn diagrams The tops of the pair of sticks for each country are joined with a sloping line. Playfair While Playfair was writing the Breviary, the mistakenly thought that the gradients of fighting in Europe was still in progress. Napoleon these lines would give a measure of the continued to conduct the Revolutionary Wars burden of taxation on the individual, the (specifically, the War of the Second Coalition) steep positive gradient for Britain for against Austria, Russia, Turkey, Britain and other example highlighting just how heavily the countries. But the Austrians, defeated at the British were taxed. In fact, a direct Battle of Marengo, sued for peace and so whilst comparison of these lines, one country to the British fought on, under the Treaty of another, is not possible because each Lunéville in February 1801, the Austrians were gradient is affected by the radius (and hence stripped of territory in Germany and Italy, and the area of the country), so there is some the Holy Roman Empire (bounded by the red fudging of the issue here. outline in the French map below) withered towards secularisation. The first 48 pages of the book survey the historical picture of fourteen states in detail and allude to another twelve. But in the years since the publication of the Atlas, Europe had been in turmoil, the French Revolution itself spilling out into neighbouring countries, the rise of Napoleon and the prosecution of a pan-European war. So while it is possible that it was always Playfair’s intention to finish the study at that point, changing circumstances made that impossible. By Tinodela - Own work, CC BY-SA 3.0, The book was simply brought up-to-date with a https://commons.wikimedia.org/w/index.php?curid further five pages and one plate on the changed =4611703 state of Europe and an addendum on India (termed Hindustan, Persian for the ‘lands of the So Playfair included an updated chart on page 48 Indus’) and more specifically, British India. towards the end of the main section of the Breviary to include the Lunéville settlement.

Here there is an additional pie chart for Germany. unanimity is destroyed from the necessary Playfair wrote (p. 50): and natural operation of opposite interests. … the most interesting situation exhibited is That empire may be considered as divided into that of the German empire; for in the first place three parts, Austria, Prussia and Other German it is diminished in extent; it is in the next place Princes, which make three bodies with so situated politically that all its internal different rather opposite interests. To illustrate this, the three circles A, B, and C, are drawn intersecting each other. The circle A The figure above shows the relevant parts of the represents the German empire as it now is in chart in greater detail. So while the three land its full extent. B represents the dominions of areas in the pie chart are by necessity disjoint, the the emperor, and C the dominions of Prussia. interests of the three parts overlap, so that A and The red part shows how much of the empire B have shared interests, B and C have different belongs to the house of Austria; the yellow shared interests and A and C have no shared portion represents what belongs to Prussia, interests at all. The intersecting circles figure has and consequently the green, which is all that been likened to the later Venn diagram and remains to the other princes, is what may perhaps not unreasonable because it shows alone truly be called the German empire. relationships with carefree attention to scale; they are simply representational. Notice that the sloppiness of the shading here supports the hypothesis about the need to abandon concentric circles for subdivision into three or more parts.

The Breviary was quickly translated into French by Denis-François Donnant, Secretary of the Société Académique des Sciences. This 1802 volume includes a statistical chart of Hindustan, with no pie chart but another annulus diagram and another intersecting circles diagram.

(David Rumsey Map Collection, Stanford Libraries; Creative Commons License 3.0)

Donnant had enhanced what Playfair had done by including data relating to the USA, and so Playfair translated Donnant’s work back into English as The Statistical Account of the United States of America (1805). Its full title finished with ‘illustrated by a divided circle … by a new method, engraved and illuminated’. This was Playfair’s pie chart, drawn to show the areas of the states in relation to each other and to the country as a whole, and making plain the effect of the Louisiana Purchase from France just two years earlier. The book was dedicated by Playfair to Thomas Jefferson whom he’d met in Paris years before and who had just begun his second term as the third US President. He sent him 25 copies, one of which was passed on to Humboldt. Going beyond Adam Smith, anticipating David To Playfair, this was economics, not Riccardo, promoting education for women emancipation, though it perhaps had a small role in what was to become a movement later in the Playfair’s book of 1805, An Inquiry into the nineteenth century. Permanent Causes of the Decline and Fall of Powerful and Wealthy Nations, was the Invention of strategic studies and a missed culmination of his most ambitious project. In his opportunity review of Playfair’s works, Jonathan Sachs explains how the book is linked to Adam Smith’s Playfair lived in times of huge social and political Wealth of Nations (1776) and Edward Gibbon’s upheaval, of countries moving from war to war, Decline and Fall of the Roman Empire (1776– of boundaries drawn and redrawn. Attracted by 1788), the title obviously nodding in those David Hume’s concept of a ‘balance of power’ directions. Essentially he analysed how countries amongst nations, in 1813 Playfair tried to become poor, rather than how they become rich. establish whether such a balance could be Playfair argued that if economic data were elicited from statistics. He saw an imbalance of gathered and suitably displayed so that trends power such as that which led to Napoleon’s were apparent, any signs of decline in a nation exploits to be like water in turmoil and a balance could be measured and corrective measures of power as a calmer and hence desirable taken. The policy of extending a country’s equilibrium. Here, he appears to have been let territories through conquest should be down by his approach for, strangely, instead of abandoned in favour of developing its displaying his data in a suitable chart, he commercial strengths. Sachs believes the book provided the data without a supporting diagram. constitutes the ‘first attempt at a general and The (shown on the next page) is in his comparative theory of the rise and fall of nations’. Outlines of a for a New and Solid Balance of It contains the idea of ‘comparative advantage’, a Power in Europe (another incredibly rare book, a concept in economics to which David Riccardo’s copy of which was sold at Christie’s for $4750 in name is attached despite Playfair’s priority. It 2010). It gives key statistics for each of 15 also emphasised the need for entrepreneurs, that countries (rows) arranged under fourteen they would emerge only through education, and headings (columns) — area, population, since the education of the young was largely in population density, various revenues, the the hands of women they themselves must be strengths of armies and so on. A series of educated to a good standard. Playfair argued that sectional bar charts might have displayed these girls should be educated to the age of thirteen or data well and allowed interested parties to play fourteen. A selection of quotes from the Inquiry with the bars to find suitable balances but (pp. 99-101) will give a flavour of his views: Playfair already had his part-part, part-whole diagram of choice, the pie chart. And among the When they become wives and mothers, when faults of the pie chart are its failure when there the economy of the family, and the education are many subdivisions and also when two or of the younger children depend chiefly on more of the subdivisions have similar magnitude, them, they are then of very great importance partly because length is easier than angle both to to society. Their conduct in that important measure accurately and to judge by eye. situation must be greatly influenced by their

education. Let’s take an example: here are Playfair’s data Female education ought then … to be attended from his ‘Army in war’ column, showing the to in the same manner as the education of numbers of soldiers each country could put in the youth of the other sex. field. The data have been reduced by a factor of 10000 and ordered: There is too much pains taken with adorning the person, and too little with instructing the France 60 Prussia 35 Poland 10 mind. Russia 53 Germanic 26 Sardinia, 10 States Savoy If the women of a nation are badly educated, it Austria 45 Spain 25 Naples, 8 must have a great effect on the education of Sicily their sons. Turkey 30 Sweden 14 Holland 8 Britain, 35 Denmark 13 Portugal 6 The great general error consists in considering Ireland the woman merely in her identical self, without thinking of her influence on others.

Playfair (1813): image taken from Berkowitz, p. 281

Could we create an approximate balance of revolved around whether or not Douglas’s sister power if there were two coalition armies, or and heir, Lady Jane Stewart, had given birth to three coalition armies? Playfair favoured a twins at the age of 50 while in France. The matter Britain-Russia alliance against France with the proved of major public interest with many of the other countries moving from time to time as their notable figures of the day expressing their interests changed. The Russian Tsar, Alexander I, opinion and the verdict led to rioting in to whom the book was dedicated, was much Edinburgh. So it was that in 1816, almost fifty taken with Playfair’s approach to these early years later, William Playfair, once more strapped strategic studies. for cash, attempted to blackmail the Douglas family with the threat to publish papers William Playfair’s life: Part 3 purporting to prove the illegitimacy of the twins and hence of the inheritance. It was a scheme that Having returned to France in 1814 following the failed, though its very existence was not revealed restoration of the monarchy Playfair edited an until 1997 (see Spence and Wainer). Clearly, English-language newspaper but fled following a Playfair was just as content to bend or even break conviction for libellous, disparaging remarks the law towards the end of his life as he was to do resulting in a heavy fine and a three-month jail so as a young man. It is no surprise therefore that sentence that he did not serve. He also got wind in 1822 Playfair again spent several months in of a plan for Napoleon to make an escape from the Fleet. Leaving the prison with a gangrenous exile on Elba, depose Louis XVIII and seize power leg, there was little alternative to amputation but once more and though he took the information the surgery proved ineffective and he survived directly to ministers he was not believed. Had he only a few weeks into 1823. been taken seriously, the perilously close battle of Waterloo would not have been necessary and There are still two matters to be considered in tens of thousands would have been saved from greater detail: death or severe injury.  How a lad from a tiny community outside Dundee came to produce statistical diagrams. Playfair was also a minor figure in the Douglas Where did the ideas come from? Cause, a battle between Archibald Douglas and the seventh Duke of Hamilton. Actually the legal  What did Playfair himself consider to be the shenanigans took place in the 1760s and merits of his diagrams? Playfair’s inspiration 2018 and 1986). In short, it appears that William’s elder brother had some understanding So where did William Playfair’s ideas come from of developments in probability and statistics in and why did he call his approach ‘lineal the middle of the eighteenth century. William’s arithmetic’? Some have argued that they came claim that he was much influenced by his brother from his employment at Boulton & Watt and therefore seems completely plausible. certainly there were design features and The advantages of statistical diagrams automated pressure recordings attached to Watt’s machines that could have made an Playfair’s statistical diagrams, some 177 of them, impression. But if Playfair’s own words are our were published in three clusters over 36 years guide on this matter, then the hand of his elder (Costigan-Eves and Macdonald-Ross, p.319). brother, the mathematician John Playfair, comes From 1786 to 1801, the focus is on time-series into focus, and this takes us back to where we charts to display financial information over time; began. The most overt reference is to be found in from 1801 to 1805, his attention turns to novel a footnote on page xvi of the Inquiry (1805): forms, circles and parts of circles; from 1821 onwards, a return to line graphs. I think it well to embrace this opportunity … of

making some return, (as far as The comparisons that Playfair asked his readers acknowledgement is a return) for an to make were comparisons of areas. This is obligation, of a nature never to be repaid, by obviously the case with circle charts and pie acknowledging publicly that, to the best and charts but not so obvious when it comes to time- most affectionate of brothers, I owe the series charts. But his use of colour or other invention of those Charts. shading (stippling or hatching) between lines is At a very early period of my life, my brother, designed to draw the eye to those regions of the who, in a most exemplary manner, maintained graphs rather than to the lines themselves. It is and educated the family his father left, made the shape of the region which impresses on the me keep a register of a thermometer, eye; as we scan from left to right (the passage of expressing the variations by lines on a divided time) is the region narrowing or widening. scale. He taught me to know that, whatever can be expressed in numbers, may be represented Playfair gave a number of advantages of using by lines. The Chart of the thermometer was on statistical diagrams and by and large, here, we the same principle with those given here; the are following the research findings of Costigan- application only is different. The brother to Eaves and Macdonald-Ross (1990). The main whom I owe this, now fills the Natural four are shown below with examples: Philosophy Chair in the University of 1. Speed of interpretation and attractiveness of Edinburgh. learning John Playfair’s research in meteorology did ‘… no study is less alluring or more dry and indeed generate a huge body of data, which was tedious than statistics, unless the mind and published in the Transactions of the Royal Society imagination are set free to work’ (Breviary, of Edinburgh; they were later quoted by p. 16). Humboldt in his Isothermal Lines and the Distribution of Heat on the Earth (1817). And it is ‘Men of great rank, or active business, can not at all surprising that William called it ‘lineal only pay attention to general outlines, nor arithmetic’. is attention to particulars of use, any farther than they give a general We know that John Playfair was conversant with information … with the assistance of these the writing of Richard Price, a writer on actuarial Charts, such information will be got, science, who was also responsible for bringing without the fatigue and trouble of studying Thomas Bayes’s essay of 1763 to publication. In the particulars of which it is composed’ the main part of the essay Bayes gave us Bayes’s (Atlas, 1786, p. 4). Theorem (for finding the probability of a cause 2. Ease of interpretation from an effect) and Price appended twenty pages of examples (Stigler, 2018). John Playfair also ‘Information, that is imperfectly acquired, knew of David Hartley’s Observations on Man is generally as imperfectly retained; and a which alluded to Bayes’s thinking prior to the man who has carefully investigated a publication of his ideas and he was familiar with printed table, finds, when done, that he has Roger Boscovich’s work, a precursor to Karl only a very faint and partial idea of what he Pearson’s on fitting a straight line to data (Stigler, has read; and that like a figure imprinted on sand, is soon totally erased and defaced. 4. Increased of learning The amount of mercantile transactions in ‘Whatever presents itself quickly and money, and of profit or loss, are capable of clearly to the mind, sets it to work, to being as easily represented in drawing, as reason and think; whereas, it often any part of space, or as the face of a happens, that in learning a number of country; though, till now, it has not been detached facts, the mind is merely passive, attempted. Upon that principle these and makes no effort further than an Charts were made; and while they give a attempt to retain such knowledge’ simple and distinct idea, they are as near (Breviary, 1801, p.7). perfect accuracy as is any way useful. On inspecting any one of these Charts ‘The advantages proposed by this of attentively, a sufficiently distinct representation, are to facilitate the impression will, be made, to remain attainment of information, and aid the unimpaired for a considerable time, and memory in retaining it: which two points the idea which does remain will be simple form the principal business in what we call and complete, at once including the learning, or the acquisition of knowledge’ duration and amount’ (Atlas, 1786, pp. 3- (Breviary, 1801, p.14). 4). Playfair was also aware of how statistical ‘… tables are by no means a good form for diagrams could be designed to mislead. In the conveying such information … I can see no first edition of the Atlas he wrote ‘As to the kind of advantage in that sort of propriety and justness of representing sums of representation …’ (Breviary, Preface). money, and time, by parts of space, tho' very 3. Appeal to the eye readily agreed to by most men, yet a few seem to apprehend there may possibly be some ‘As the eye is the best judge of proportion, deception in it, of which they are not aware ...’ being able to estimate it with more (Atlas, 1786, iii). Written in this way it is difficult quickness and accuracy than any other of to know whether he is saying that some people our organs, it follows, that wherever have seen his graphs and are wary of their relative quantities are in question, a veracity or that he knows how to tweak a scale gradual increase or decrease of any for example to bring out, even exaggerate, a revenue, receipt or expenditure, of money, particular feature. or other value, is to be stated, this mode of

representing it is peculiarly applicable; it Remembering William Playfair gives a simple, accurate, and permanent

idea, by giving form and shape to a number After his death, Playfair’s rather colourful life was of separate ideas, which are otherwise repainted uniformly black, starting with the abstract and unconnected’ (Atlas, 3rd journalist John Goldworth Alger (1836–1907). In edition, p. x.). a number of publications, including the ‘… making an appeal to the eye when Dictionary of National Biography, Alger dismissed proportion and magnitude are concerned, Playfair as a complete rogue and critically for our is the best and readiest method of story made no mention of statistical diagrams. conveying a distinct idea’ (Breviary, p. 4). This judgement and this omission went largely unchallenged until 1983 when In the expanded introduction to the third propelled Playfair’s reputation upwards. The edition of the Atlas Playfair explains on p. xi biographer, Bruce Berkowitz, believes that his ‘lineal arithmetic’ by invoking an Playfair’s reputation as a rogue is exaggerated, imaginary merchant who is paid his work as an agent of the British government exclusively in guineas, the standard gold understated (secrecy is central to tradecraft, coin until 1816. If he were to stack his after all) and his contribution to statistical and guineas for one day, then append stacks on economic graphics without par. He notes that subsequent days until there was a straight there is no image of William Playfair, either in line of such stacks shoulder to shoulder, portrait or statue, that he lived a most interesting then, he wrote, ‘lineal arithmetic … is life never far from penury, and it was that nothing more than those piles of guineas financial insecurity that drove him forward. represented on paper, and on a small scale,

in which an inch (suppose) represents the

thickness of five millions of guineas’.

References Spence, Ian, ‘William Playfair and the psychology of graphs’, Proceedings of the American Statistical Adelman, Juliana, ‘The man with a finger in many Association: Section on pie charts’, The Irish Times (online), 5 March (August 2006), 2426-2436. 2018; accessed 18/02/21. Spence, Ian & Wainer, Howard, ‘William Playfair Berkowitz, Bruce, Playfair: The True Story of the and his graphical inventions: and excerpt from British Secret Agent Who Changed How We See the the introduction to the republication of his Atlas World, George Mason University Press, Fairfax and Statistical Breviary’, The American VA, 2018. 59, 3 (August 2005), 224-229. Costigan-Eves, Patricia and Macdonald-Ross, Stigler, Stephen M., The , Michael, ‘William Playfair, (1759-1823)’, Harvard (Belknap Press), 1986. Statistical Science 5, 3 (1990), 318-326. Stigler, Stephen M., ‘Richard Price, the first Friendly, Michael, ‘A brief history of data Bayesian’, Statist. Sci. 33, 1 (February ’, in Chen, C., Härdle, W. & Unwin, A. 2018), 117-125. https://doi.org/10.1214/17- (eds.), Handbook of Computational Statistics: STS635 III, Springer-Verlag, 2008. Symanzik, Jürgen, William Fischetti and Ian Playfair, James G. (ed.), The Works of John Spence, ‘Editorial: Commemorating William Playfair, Edinburgh: Constable, 1822. Playfair’s 250th birthday’, Computational Statistics 24, 4 (2009); available online at Playfair, William, The Commercial and Political www.researchgate.net/publication/228091935 Atlas, London: Debrett; Robinson; and Sewell, _Commemorating_William_Playfair%27s_250th_ 1786. birthday Playfair, William, The Commercial, Political and Sachs, Jonathan, ‘1786/1801, William Playfair, Parliamentary Atlas, London: Stockdale, 1787. statistical graphics, and the meaning of an event’, Playfair, William, Lineal Arithmetic, London: BRANCH online, at private publication printed by Alexander Paris, www.branchcollective.org/?ps_articles=jonatha 1798. n-sachs-17861801-william-playfair-statistical- graphics-and-the-meaning-of-an-event Playfair, William, The Commercial and Political (retrieved 10 March 2021). Atlas, 3rd edition, London: J. Wallis (1801b). Tufte, Edward R., The Visual Display of Playfair, William, The Statistical Breviary, Quantitative Information, Cheshire CT: Graphics Shewing on a Principle Entirely New, The Press, 1983; second edition, 2007. Resources of Every State and Kingdom in Europe,

Illustrated with Stained Copper-Plate Charts, Representing the Physical Powers of Each Distinct Nation with Ease and Perspicuity, London: T. Bentley (1801a). A digitised version of a copy held in the Bodleian Library, University of Oxford, is at: https://archive.org/details/statisticalbrev00pla ygoog Playfair, William, An Inquiry into the Permanent Causes of the Decline and Fall of Powerful and Wealthy Nations, London: Greenland & Norris, 1805. There is an online copy at www.google.co.uk/books/edition/An_Inquiry_I nto_the_Permanent_Causes_of/uMVAAQAAMAAJ ?hl=en&gbpv=1&printsec=frontcover This is useful for the text, though the charts have been digitised whilst folded and hence remain hidden. Playfair, William, Outlines of a Plan for a New and Solid Balance of Power in Europe, London: Stockdale, 1813.