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Life of Pie: William Playfair and the Impact of the Visual

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Life of Pie: William Playfair and the Impact of the Visual PRESIDENTIAL ESSAY NO. 4: JULY 2021 Life of Pie: William Playfair 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 James Playfair, as well as Scotsman published a circular diagram divided James’s son, William Henry Playfair, 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 Edinburgh’s New Town. And then in central London. 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 Europe, Asia and Africa, and visionary when it came to explaining things rather sloppily coloured by hand. This was the through diagrams. William Playfair, the subject of first pie chart 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 James Watt 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 Euclid’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 John Playfair (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 University of Edinburgh for a moved towards international business, decade, his earlier career in the ministry set economics and visual statistics. 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, Robert Adam and restored by focussing on manufacturing, banking especially James Hutton, whose uniformitarian and trade, rather than on the traditional land- theory of geology 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 Dundee, the eldest but by no means the The first time-series chart and bar chart 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 charts 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 information 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 data 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 Scotland’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 Paris 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.
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