Graphic Discovery

Graphic Discovery: A Trout in the Milk and Other Visual Adventures

Copyright Date: 2005
Pages: 208
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  • Book Info
    Graphic Discovery
    Book Description:

    Good graphs make complex problems clear. From the weather forecast to the Dow Jones average, graphs are so ubiquitous today that it is hard to imagine a world without them. Yet they are a modern invention. This book is the first to comprehensively plot humankind's fascinating efforts to visualize data, from a key seventeenth-century precursor--England's plague-driven initiative to register vital statistics--right up to the latest advances. In a highly readable, richly illustrated story of invention and inventor that mixes science and politics, intrigue and scandal, revolution and shopping, Howard Wainer validates Thoreau's observation that circumstantial evidence can be quite convincing, as when you find a trout in the milk.

    The story really begins with the eighteenth-century origins of the art, logic, and methods of data display, which emerged, full-grown, in William Playfair's landmark 1786 trade atlas of England and Wales. The remarkable Scot singlehandedly popularized the atheoretical plotting of data to reveal suggestive patterns--an achievement that foretold the graphic explosion of the nineteenth century, with atlases published across the observational sciences as the language of science moved from words to pictures.

    Next come succinct chapters illustrating the uses and abuses of this marvelous invention more recently, from a murder trial in Connecticut to the Vietnam War's effect on college admissions. Finally Wainer examines the great twentieth-century polymath John Wilder Tukey's vision of future graphic displays and the resultant methods--methods poised to help us make sense of the torrent of data in our information-laden world.

    eISBN: 978-1-4008-4927-7
    Subjects: Mathematics

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-xii)
  3. Preface
    (pp. xiii-xvi)
  4. Introduction
    (pp. 1-4)

    Let me begin with a few kind words about the bubonic plague. In 1538, Thomas Cromwell, the Earl of Essex (1485–1540),* issued an injunction (one of seventeen) in the name of Henry VIII that required the registration of all christenings and burials in every English parish. The London Company of Parish Clerks compiled weekly Bills of Mortality from such registers. This record of burials provided a way to monitor the incidence of plague within the city. Initially, these Bills were circulated only to government officials, principal among them the Lord Mayor and members of the King’s Council.† They were...

  5. Part I William Playfair and the Origins of Graphical Display
    • [Part I Introduction]
      (pp. 5-8)

      The graphic explosion of the nineteenth century that manifested itself in the publication of atlases in all aspects of the observational sciences had its origin in the intellectual turbulence of the eighteenth century. The hundred-year span between 1750 and 1850 saw a shift in the language of science from words to pictures.*

      This shift began with the historical time charts of Jacques Barbeau-Dubourg (see chapter 7), which were followed closely by similar efforts from the Scottish philosopher Adam Ferguson and twelve years later from Joseph Priestley (chapter 5). Indeed, this idea proved so useful that Thomas Jefferson even used it...

    • 1 Why Playfair?
      (pp. 9-19)

      “Getting information from a table is like extracting sunbeams from a cucumber” (Farquhar and Farquhar).* This evocative indictment of data tables by two nineteenth-century economists comes as no great insight to anyone who has ever tried to draw inferences from such a data display. For most purposes we almost always prefer a graphical representation. Indeed, graphs are ubiquitous now; hence it is hard to imagine a world before they existed. Yet data graphs are a human invention, indeed a relatively modern one. Data-based graphics began to make an appearance in the mid-seventeenth century but their full value and great popularity...

    • 2 Who Was Playfair?
      (pp. 20-23)
      Ian Spence and Howard Wainer

      The Cartesian tradition of graphical representation of mathematical functions worked against the use of graphs to depict empirical regularities. The switch to the view that a graph can help us formulate an understanding of nature by plotting data points and looking for patterns required, in Thomas Kuhn’s terms, a change in paradigm. A person who might effect such a change would not only have to be in the right place at the right time, but would also have to be an iconoclast of the first order. In all aspects William Playfair fits the bill. In this chapter we sketch some...

    • 3 William Playfair: A Daring Worthless Fellow
      (pp. 24-27)
      Ian Spence and Howard Wainer

      In 1816, William Playfair sought to blackmail Lord Douglas. The latter had been at the focus of the longest legal proceeding in Scottish history, known familiarly as the Douglas Cause. The events precipitating the Cause occurred around the time of Douglas’s birth, several years before Playfair’s own, and are at the heart of the attempted extortion. The episode illuminates an aspect of Playfair’s personality that arguably played a fundamental role in both the invention and the delay in adoption of statistical graphs.

      Between 1786 and 1801, Playfair invented the pie chart and was also first to apply the line and...

    • 4 Scaling the Heights (and Widths)
      (pp. 28-38)

      Playfair used graphs to inform and to convince. His understanding of the capacity of this new medium was remarkably deep. To gain a full appreciation for his skill, it is helpful to compare the polished displays he produced with the more rudimentary ones of his predecessors (a sampling of those appeared in chapter 1). We need not confine our comparisons to his predecessors, however, for Playfair’s work does not suffer when placed side by side with those of more modern graphers.

      Let us consider a simple table (table 4.1) that compares wages with living expenses over the 250-year span from...

    • 5 A Priestley View of International Currency Exchanges
      (pp. 39-43)

      As middle age and its associated onrushing senescence swoop down on me, I have come to appreciate the wisdom of the Talmudic midrash attributed to Rabban Yohanan ben Zakkai: “If there be a plant in your hand when they say to you, Behold the Messiah!, go and plant the plant, and afterward go out to greet him.” The scientific establishment regularly discovers new sources of redemption—this year’s promise is that computer-aided design will save us all—but I suspect that the Lord is best served by scientists who find salvation in the routine transactions of their daily work.


    • 6 Tom’s Veggies and the American Way
      (pp. 44-46)

      When Buck Mulligan began James Joyce’s Ulysses by looking into the broken mirror of Irish art, he provided a powerful image of how the character of a society reflects itself in all forms of expression. The brash, revolutionary, democratic structure of America has shown itself in all forms. Tom Wolfe, in the lead essay of The Kandy-Kolored Tangerine-Flake Streamline Baby, maintained that there were only two cities in the world that had completely coherent architectural themes: Versailles and Las Vegas. Versailles was built in the classical favored by seventeenth-century French aristocracy; Las Vegas in what Wolfe termed “MacDonald’s Parabola Modern.”...

    • 7 The Graphical Inventions of Dubourg and Ferguson: Two Precursors to William Playfair
      (pp. 47-51)

      Eighteenth-century Europe was a hotbed of invention and discovery. It was the time of Bayes and Bernoulli, of DeMoivre and Euler, of Lagrange, Laplace, and Legendre. And although he did not begin publishing until the nineteenth century, the eighteenth century gets credit for the birth of Gauss. During this time, despite the absence of the kinds of modern communication we have all come to depend on, there seems to have been a tight network of communication among the intellectual elite of Europe. This network even expanded wide enough to include some of the brighter lights of the new world. This...

    • 8 Winds across Europe: Francis Galton and the Graphic Discovery of Weather Patterns
      (pp. 52-56)

      The old adage about everyone talking about the weather but nobody doing anything about it needs to be generalized. Historically, people not only talked about the weather but also graphed it. Indeed, the development of graphic displays of data has been intertwined with the study of the weather for more than three hundred years. Christopher Wren (ca. 1663) developed an intricate weather clock that graphically recorded wind direction (in polar coordinates) and temperature (in rectangular coordinates) on a common time axis, as well as segregating hourly rainfall collections.* Twenty years later, Martin Lister presented various versions of graphical summaries of...

  6. Part II Using Graphical Displays to Understand the Modern World
    • [Part II Introduction]
      (pp. 57-58)

      The twenty-first century is overrun with data, often complex and more often voluminous.* The study of statistics, because it is crucial in the understanding of the modern world, has become much more common than in the past and is now taught widely in high schools (see figure II.1). As we have seen, graphic display fits snuggly with statistical data to allow us to see what we were not expecting. As with most things graphical, Playfair understood that viewers could understand a complex phenomenon presented graphically that might elude them if presented any other way. Hence when he tried to point...

    • 9 A Graphical Investigation of the Scourge of Vietnam
      (pp. 59-62)

      When I moved from Princeton to Philadelphia, I raised the average income in both places. Those unfamiliar with statistical artifact may have to ponder momentarily how such an event might come to pass. But once one has done so, the implication is clear. In this chapter, I point out a similar result—specifically, how the Vietnam War managed to lower the average ability both inside and outside the American military.

      Yogi Berra pointed out, “You can see a lot just by looking.” I’m sure that Yogi Berra had other things on his mind when he uttered his now famous line,...

    • 10 Two Mind-Bending Statistical Paradoxes
      (pp. 63-71)

      In 1998, Ian Westbrooke described how New Zealand indigenous Maoris appeared to be overrepresented on juries in New Zealand: 9.5 percent of people living within the jury districts were Maori, compared with 10.1 percent of Maori in the pool of potential jurors.¹ Yet, upon looking more closely, Westbrooke found that “in every single local area Maori were underrepresented—often substantially.” Such anomalies are not restricted to New Zealand.

      Recently I have noticed a number of empirical results reported in the newspaper, like the one above, that seem, at least on the surface, to be self-contradictory. When I ask friends about...

    • 11 Order in the Court
      (pp. 72-77)

      Because we are almost never interested in seeing Alabama first, it is astonishing how often data displays use alphabetical order as the organizing principle of choice. The only reason I can think of is that organizing by this trivial aspect of the data is easy and obvious. Yet the benefits derived from ordering a display alphabetically are usually so modest and the gains from reordering so large that one would expect wiser alternatives to prevail. But typically they do not.*

      Consider the function shown in figure 11.1 that relates various foods to their cost. The order of the foods along...

    • 12 No Order in the Court
      (pp. 78-80)

      In chapter 11 we illustrated why we are not usually interested in Alabama first. Alphabetical order may be important for some limited set of purposes, but much more often another ordering is likely to be far more useful. The examples in chapter 11 demonstrated how reordering helps us to understand the deep structure that may underlie the data in the display. Sometimes it also helps us to see exactly what is in the display.

      The benefits associated with the proper ordering arose dramatically on March 17, 1998, in a murder trial, when State v. Gibbs began in Connecticut Superior Court....

    • 13 Like a Trout in the Milk
      (pp. 81-85)

      During a dairymen’s strike in New England, some suspected that the limited supplies of milk were being watered down for wider distribution. Commenting on the worth of the evidence being cited, Henry David Thoreau wrote in his journal (November 11, 1850): “Sometimes circumstantial evidence can be quite convincing; like when you find a trout in the milk.”

      Oftentimes a statistical graphic provides the evidence for a plausible story, and the evidence, though perhaps only circumstantial, can be quite convincing. For example, in figure 13.1 we cannot help but note the obvious causal implications in the simple swooping line that bemoans...

    • 14 Scaling the Market
      (pp. 86-89)

      Placing a fact within a context increases its value greatly. “Our town has two doctors” is a fact, but appending the phrase “but most towns our size have sixteen doctors” tells us so much more. An efficacious way to add context to statistical facts is by embedding them in a graphic. Sometimes the most helpful context is geographical, and shaded maps come to mind as examples. Sometimes the most helpful context is temporal, and time-based line graphs are the obvious choice. But how much time? The ending date (today) is usually clear, but where do you start? The starting point...

    • 15 Sex, Smoking, and Life Insurance: A Graphical View
      (pp. 90-96)

      My mailbox, like those of most American adults, is often filled to overflowing with ads and solicitations of various sorts. Strategically located between my mailbox and my back door is the paper recycling barrel; hence most of this capitalist detritus rarely makes it into the house. But sometimes, either because the topic strikes a chord of interest, or, more likely, because the unrequested commercial message has been hidden inside some more worthy missive, a solicitation makes it inside for more careful examination. I strongly suspected the latter when I found on my mail pile an ad for Jackson National’s ten-year...

    • 16 There They Go Again!
      (pp. 97-102)

      I am addicted to the New York Times and feel restive if I miss it for even a day; after two days I become seriously out of sorts; longer periods of abstinence are almost intolerable. When the Times makes an error, I feel the same sort of disappointment that one would evince at the discovery of a flaw in any loved one. In the past I have tried gently to point out graphical flaws in Times reportage,¹ in the hope that the errors would be corrected. It is hard to measure the effect that my efforts have had.

      In general,...

    • 17 Sex and Sports: How Quickly Are Women Gaining?
      (pp. 103-108)

      Over the past century, women’s participation in competitive sports has increased markedly. At the same time the disparities in performance between men and women seem to have shrunk substantially. One cannot help but suspect that the former is a principal cause of the latter.* We can see this effect clearly in data from the Boston Marathon, which has been run over essentially the same course for more than a century. A plot of winning times is shown in figure 17.1.

      Such evocative plots have led the unwary to predict that women runners will soon be overtaking their male counterparts and,...

    • 18 Clear Thinking Made Visible: Redesigning Score Reports for Students
      (pp. 109-114)

      Edward Albee, in his one-act play Zoo Story, points out that sometimes you need to go far out of your way to come back a short distance correctly. While what follows may seem to meander, please stay with me.

      In 1980, when I began working at the Educational Testing Service, my boss, Paul Holland, gave me some important advice: “An effective memo should have at most one point.” Over time, whenever I have violated this advice I have never been happy with the result. I think the lesson explicit in Holland’s Rule can be broadened.

      I have had a thirty-seven-year-long...

  7. Part III Graphical Displays in the Twenty-first Century
    • [Part III Introduction]
      (pp. 115-116)

      Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading . . . spirits of coming generations will strive? What new methods and new facts in the wide and rich field of [scientific] thought will the new centuries disclose?

      History teaches the continuity of the development of science. We know that every age has its own problems, which the following age either...

    • 19 John Wilder Tukey: The Father of Twenty-first-Century Graphical Display
      (pp. 117-124)

      Our ability to see patterns in data has been improved by the light shed by a number of brilliant contributors. I discussed some of the early stars in part I, with a focus on William Playfair, whose contributions dominated all others of his time. The twentieth century, too, had important contributors to the growing science of effective data display, but John Wilder Tukey (1915–2000) stands out. Moreover, just as Playfair’s work, completed during the cusp of the eighteenth and nineteenth centuries, carried over to have its greatest effect in the twentieth century, so too I suspect will Tukey’s carry...

    • 20 Graphical Tools for the Twenty-first Century: I. Spinning and Slicing
      (pp. 125-133)

      It has been more than thirty years since I first stumbled into the University of Chicago’s Green Hall and began teaching a course in exploratory data analysis (EDA). A great deal has changed since then, but a great deal remains the same. Although the tools of EDA at that time were primarily built for hand manipulation, we found that a computer program we wrote (even a batch processed mainframe program) was enormously helpful.¹ Computing has changed profoundly in those intervening thirty years, but most of the EDA tools that John Tukey laid out in his wonderful 1977 book remain broadly...

    • 21 Graphical Tools for the Twenty-first Century: II. Nearness and Smoothing Engines
      (pp. 134-141)

      The previous chapter discussed two graphical engines that can profitably be used to aid in computer-assisted graphical data analysis. I complete this discussion with two more. The four engines do not overlap appreciably in their capabilities—what one does, the others do not—but they do span a space of considerable dimensionality in their capabilities. I considered including other tools (e.g., a flashing capability, in which a sequence of points could be alternated on the screen and through their apparent movement yield information) but decided that these four, when properly implemented and coupled with automated versions of the traditional graphical...

    • 22 Epilogue: A Selection of Selection Anomalies
      (pp. 142-149)

      The focus of this book has been on displaying data and, except in chapter 10, I have spent very little effort discussing the quality of what is being displayed. In good conscience I cannot end without at least providing a modest caveat. The consideration of the quality of the data that we plot is a side trip of this particular voyage, so I have opted to use the space necessary for only a few short stories to illustrate the often subtle concerns that can yield potentially profound consequences. And last, I am unable to resist the opportunity to preach a...

  8. Conclusion
    (pp. 150-150)

    In 1923, Edna St. Vincent Millay, applauding the growth of good data while simultaneously decrying the lack of good techniques for exploratory data analysis, wrote:

    Upon this gifted age in its dark hour

    Falls from the sky a meteoric shower

    Of facts. They lie, unquestioned, uncombined.

    Wisdom enough to leach us of our ills is daily spun,

    But there exists no loom to weave it into fabric.

    This book celebrates more than two centuries of progress toward the construction of a glorious loom....

  9. Dramatis Personae
    (pp. 151-172)
  10. Notes
    (pp. 173-176)
  11. References
    (pp. 177-184)
  12. Index
    (pp. 185-192)