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William Playfair and the Psychology of Graphs WilliamWilliam PlayfairPlayfair andand thethe PsychologyPsychology ofof GraphsGraphs Figures and letters may express with accuracy, but they can never represent either number or space. William Playfair, Atlas, 1st Ed., 1786, p.3. Ian Spence University of Toronto [email protected] http://psych.utoronto.ca/~spence JSM 2006, Seattle, WA, August 6, 2006 Playfair’sPlayfair’s Atlas and Breviary “As the eye is the best judge of proportion … it follows, that wherever relative quantities are in question, a gradual increase or decrease of any … value, is to be stated, this mode of representing it is peculiarly applicable … giving form and shape to a number of separate ideas, which are otherwise abstract and unconnected.” New York, NY: Cambridge University Press, 2005. Edited by Howard Wainer and Ian Spence. Information Visualization “… visual system is a pattern seeker of enormous power and subtlety. The eye and visual cortex … form a massively parallel processor that provides the highest-bandwidth channel into human cognitive centers … perception and cognition are closely interrelated which is why the words understanding and seeing are synonymous ” New York, NY: MIT Press, 2004. Graphs before Playfair (1786) Rarely published At most a score of isolated and often peculiar examples Often rudimentary or primitive Lacking elements customary today (notably data) Similar to (Cartesian) graphs of mathematical functions Generally display data from “natural philosophy” Rarely “statistical” data Halley:Halley: PressurePressure vs.vs. AltitudeAltitude (1686)(1686) Huygens:Huygens: ChartChart ofof MortalityMortality (1669)(1669) Christian Huygens’ “ligne de vie” in a letter of 1669. This graph plotted the expected number of survivors as a function of age, based on Lodewijk Huygens’ calculations from Graunt’s mortality tables. Also, in the letter, was a diagram entitled “reste de vie de chaqu’aage” Lambert:Lambert: SoilSoil TemperaturesTemperatures (1779)(1779) PlatePlate 4,4, AtlasAtlas 11st Ed.,Ed., 17861786 Title Labelled Ordinate Frame Color Labelled Abscissa Caption Grid Labels Lines LowLow--LevelLevel VisualVisual ProcessingProcessing Luminance processing (opponent-process channels, inhibition, receptive fields) Edge detection (receptive fields) Orientation detection (receptive fields) Color processing (opponent process channels, trichromacy) Segmentation (luminance, texture, colour, etc) Playfair’s designs are constructed in such a fashion that low- level processes are easily completed by the human visual system. HigherHigher--LevelLevel ProcessingProcessing Higher-level cognitive processes operate under the control of selective attention. Selective attention Visual working memory Verbal working memory Limited capacity (3-5 items) Playfair’s charts are (almost) always constructed so that comparisons in different domains (lines, colors, labels, etc) do not exceed attentional/working memory capacity. InformationInformation ProcessingProcessing (Visual) Query Statistical World graph Low-level visual processing Edges, slopes, (preattentive processing) areas, colors, etc. Selective visual processing (attention-driven processing) Objects, labels, etc. Visual Working Verbal Working Estimation, Memory Memory comparison, etc. Long-term memory Knowledge We Learn to Read Graphs Lower-level processes are not (consciously) learned. Since higher-level processes are learned, consistency is important “To those who have studied geography, or any branch of mathematics, these charts will be perfectly intelligible. To such, however, as have not, a short explanation may be necessary.” Atlas, 3rd Ed., 1801, p. ix, PerceptionPerception andand CognitionCognition Perceptual attributes supporting cognitive operations: Color to code (and compare) categories Slope to code (and compare) trends Length to code (and compare) quantities Similar figures (areas) to code (and compare) quantities Area to code accumulated quantities PlatePlate 16,16, AtlasAtlas,, 33rd Ed.,Ed., 18011801 PlatePlate 19,19, AtlasAtlas,, 33rd Ed.,Ed., 18011801 Color to Code Categories W. Playfair, An inquiry into the permanent causes of the decline and fall of powerful and wealthy nations. 1805 Length to Code Quantity VisualVisual Query:Query: Differences?Differences? Plate 7, Atlas, 2nd Ed., 1787 VisualVisual Query:Query: DifferencesDifferences Cleveland & McGill’s (1984) Demonstration VisualVisual Query:Query: DifferencesDifferences VisualVisual Query:Query: DifferencesDifferences oror Accumulations?Accumulations? Comparisons “… the eye cannot look on similar forms without involuntarily … comparing their magnitudes. So that what in the usual [tabular] mode was attended with some difficulty, becomes not only easy, but … unavoidable” Breviary, 1801, p.6 “The present charts are … intended to aid statistical studies, by showing to the eye the sizes of different countries represented by similar forms, for where forms are not similar, the eye cannot compare them easily nor accurately.” Breviary, 1801, p.15 Areas (Similar Figures) to Code Quantity Breviary, 1801, Plate 2 Comparisons 10 5 Area of Circle of Area 0 0 500000 1000000 Population Area of circle represents population size (land area in previous) Orders circles by area (population or land area) Unaware that we overestimate small areas and underestimate large ones (not appreciated until 20th C.) Cleveland suggested a dot plot for these data Memory “Information, that is imperfectly acquired, is generally as imperfectly retained; and a man who has carefully investigated a printed table, finds, when done, that he has only a very faint and partial idea of what he has read;” Atlas, 1st Ed., 1786, p. 3 “… as much information may be obtained in five minutes as would require whole days to imprint on the memory, in a lasting manner, by a table of figures.” Atlas, 3rd Ed., 1801, p. xii “The advantages proposed by this mode of representation, are to facilitate the attainment of information, and aid the memory in retaining it.” Breviary, 1801, p. 14 Memory “On inspecting any one of these Charts attentively, a sufficiently distinct impression will be made, to remain unimpaired for a considerable time, and the idea which does remain will be simple and complete, at once including the duration and the amount.” Atlas, 1st Ed., 1786, p.4 Visualizations before the Late 18th C Visualizations of the real world (Pictures) Maps and nautical charts (data) Landscapes (real and imagined) Natural history (seen and unseen) Mechanical diagrams, etc. (actual and imagined) Visualizations of abstractions (Relatively novel) Graphs and charts (data) Diagrams (theory) Playfair’s Insights Original ideas? Natural selection. Imitation/adaptation. Synthesis. Major Early Influences Thomas Reid Joseph Priestley (Dugald Stewart) (Lunar Society) James/John Andrew James Playfair Meikle Watt Scotland England FranceEngland France England Atlas Breviary WP American War of French Independence Revolution 1760 1770 1780 1790 1800 1810 1820 JohnJohn PlayfairPlayfair (1748(1748--1819)1819) Professor of Mathematics and later Professor of Natural Philosophy at the University of Edinburgh Illustrations of the Huttonian Theory of the Earth (1802) Alternative formulation of Euclid's parallel postulate (Playfair's axiom) “He taught me to know, that, whatever can be expressed in numbers, may be represented by lines.” WP, Decline … , 1805 Dugald Stewart (1753-1828) “… I have a very favourable opinion … [WP] professes a great deal both of mathematical & mechanical information … he has strong natural abilities, and has acquired a considerable stock of facts … I found his conversation extremely instructive. Indeed I know very few who have been more attentive & intelligent observers both of men & things …” Letter to Benjamin Vaughan, 1786 ThomasThomas ReidReid (1710(1710--1796)1796) AndrewAndrew MeikleMeikle (1736(1736--1811)1811) Drum Threshing Machine JamesJames WattWatt (1736(1736--1819)1819) JosephJoseph PriestleyPriestley (1733(1733--1804)1804) “ … a longer or a shorter space of time may be most commodiously and advantageously represented by a longer or a shorter line” Influence of Maps and Patents Cartesian Geometry? Tufte, E.R. (1983). The visual display of quantitative information. Cheshire, CT: Graphics Press. Biderman, A.D. (1990). The Playfair enigma: The development of the schematic representation of statistics. Information Design Journal, 6, 3-25 Influence of Maps The Commercial and Political Atlas (use of word “chart”) “The amount of mercantile transactions in money can be as easily represented in drawing . as the face of a country” Influence of Patent Drawings Drawing/Shading/Framing/Labeling/Engraving/Printing TheThe InfluenceInfluence ofof ChartsCharts andand MapsMaps City map (Turkey), ca. 6200 BC Timothy Pont, ca. 1580, Dundee Willem Janszoon Blaeu, 1640 Charles Delamarche, 1785 JohnJohn Ainslie,Ainslie, Playfair’sPlayfair’s FirstFirst EngraverEngraver Scotland, 1783 JohnJohn Ainslie,Ainslie, Playfair’sPlayfair’s FirstFirst EngraverEngraver Liff & Benvie, 1783 SamuelSamuel JohnJohn NeeleNeele,, Playfair’sPlayfair’s EngraverEngraver South America, 1790 SamuelSamuel JohnJohn NeeleNeele,, Playfair’sPlayfair’s EngraverEngraver Crimea, 1797 Playfair’s Insights WP was keenly aware of the importance of psychology He frequently refers to “eye”, “mind”, “memory”, “learning”, “understanding”, etc. His charts have stood the test of time (natural selection) His choice of graphical elements satisfies psychological principles (discovered much later) Major figures of the Scottish Enlightenment (Stewart, Reid, Hume) influenced his conception of psychology He acquired the needed technical skills from the foremost practitioners (John Playfair, Meikle, Watt, Ainslie, Neele) Most importantly, WP was a great adapter and synthesizer Playfair’sPlayfair’s Atlas and Breviary William Playfair's Commercial and Political Atlas and Statistical Breviary New York: NY, Cambridge University Press, 2005. Edited by Howard Wainer and Ian Spence. Introduction by Ian Spence and Howard Wainer.
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