Hypothesis Follow Up #2

1 Escaping Flatland

Even though we navigate daily through a perceptual world of three spatial dimensions and reason occasionally about higher dimensional arenas with mathematical ease, the world portrayed on our informa- tion displays is caught up in the two-dimensionality of the endless flatlands of paper and video screen.' All communication between the readers of an image and the makers of an image must now take place on a two-dimensional surface. Escaping this flatland is the essential task of envisioning information—for all the interesting worlds (physical, biological, imaginary, human) that we seek to understand are inevitably and happily multivariate in nature. Not flatlands.

1 The idea of “flatland” is based on the classic by A. Square [Edwin A. Abbott], Flatland: A Romance of Many Dimensions (London, 1884). A recent statement from an artist’s viewpoint (How can modern painting, abstractionism, escape flatland?) is found in Frank Stella, Working Space (Cambridge, 1986).

Turs chapter outlines a variety of design strategies that sharpen the information resolution, the resolving power, of paper and video

screen. In particular, these methods work to increase (1) the number of dimensions that can be represented on plane surfaces and (2) the data density (amount of information per unit area).

In this Japanese travel guide, an engaging hybrid of design technique, the abrupt shift from friendly perspective to hard flatland shows the loss suffered by giving in to the arbitrary data~compression of paper surfaces. A bird’s-eye view with detailed perspective describes local areas near the architecturally renowned Ise Shrine; then, on the right

margin, a very flat map delineates the national railroad system linking the shrine to major cities, somewhat compensating for loss of a visual dimension with a broad overview. A change in design accommodates a change in the scale of the map, and local detail is shown in national

context, a mixed landscape of refuge and overview. The horizontal

layout combines harmoniously with the vertical orientation of the language, so that the stand-up labels point precisely to each location.

3

Guide for Visitors to Ise Shrine (Ise, Japan; no date; published between October 1948 and April 1954, according to The Library, Ise Shrine, Mie Prefecture).

14 ENVISIONING INFORMATION

Mary C. Dickerson, The Frog Book: North American Toads and Frogs, with a Study of the Habits and Life Histories of those of the North- eastern States (New York, 1906), pp. 74-75.

2 John White, The Birth and Rebirth of Pic- torial Space (London, 1957); and Lawrence ‘Wright, Perspective in Perspective (London, 1983). See also the remarkable book by Kim Veltman, Linear Perspective and the

When the toad (Bufo americanus Le Conte) sheds its skin upon the Visual Diversions of Science ‘aid Art © Seales occasion of a quarterly moulting, the suit leaves life’s spaceland and on Leonardo da Vinci I (Miinchen, 1986). collapses into flatland, not unlike our information displays.

3 Redrawn from Emil v. Zmaczynski, “Periodic System of the Elements in a New Form,” Journal of Chemical Education, 12 (1935), 265-267; Frank Austin Gooch and Claude Frederic Walker, Outline of Inorganic Chemistry, II (London, 1903), pp. 8-9; and Andreas von Antropoff, “Eine neue Form des periodischen Systems der Elemente,” Zeitschrift fir Angewandte Chemie, 39 (1926), 722-728; Edward Mazurs, Types of Graphic Representation of the Periodic System of Chem-

ical Elements (La Grange, Ilinois, 1957).

All sorts of techniques for doing better than flattened-out toad suits have evolved during some 500 years of information design.? Since the

1sth-century Italian Renaissance, when Florentine architects perfected 4 the necessary geometry, conventional perspective drawing has enriched le representations of physical objects. And, for more abstract multivariate i information not residing in our three-space reality, several enterprising methods have evolved—nearly silently, often to be found in workaday ete diagrams of those confronted with an overwhelming quantity of data. ig tice A few such techniques are well documented; for example, the elaborate Mato) structuring of the periodic table of chemical elements’ (with several wae “\ oink

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hundred arrangements proposed to capture the assorted complexities). Some recently perfected statistical graphics, selfconsciously multi- variate, enrich flatland with the dynamics of rotating point clouds on

computer screens—a marvel, although navigation in three-dimensional

scatterplots is not a trivial matter.* Another approach, here on the right,

slices and projects data from many angles onto six of the twelve surfaces of a pentagonal dodecahedron (only six faces are needed, since opposite parallel faces show identical views).

Nearly every escape from flatland demands extensive compromise,

trading off one virtue against another; the literature consists of partial,

arbitrary, and particularistic solutions; and neither clever idiosyncratic

nor conventionally adopted designs solve the inherent general difficul- ties of dimensional compression. Even our language, like our paper, often lacks immediate capacity to communicate a sense of dimensional complexity. Paul Klee wrote to this point:

It is not easy to arrive at a conception of a whole which is constructed from. parts belonging to different dimensions. And not only nature, but also art, her

transformed image, is such a whole.

It is difficult enough, oneself, to survey this whole, whether nature or art, but still more difficult to help another to such a comprehensive view.

This is due to the consecutive nature of the only methods available to us for conveying a clear three-dimensional concept of an image in space, and results from deficiencies of a temporal nature in the spoken word.

For, with such a medium of expression, we lack the means of discussing in its constituent parts, an image which possesses simultancously a number of dimensions.>

And perspective projection is a simple extension of a two-surface,

made unmistakable by everyday experience in three-space itself. Yet

much of our data—and nature’s pattern—have far greater complexity. What, then, are general strategies for extending the dimensional and

informational reach of display flatlands? And what specific techniques

effectively document and envision multivariate worlds? Why are some

performances better than others?

To begin, a series of splendid examples.

ESCAPING FLATLAND I5

4 Andrew W. Donoho, David L. Donoho, Miriam Gasko, MacsPIN Graphical Data Analysis Software (Austin, Texas, 1985), illustration at p. 35 (redrawn); and the

important 1974 paper by Mary Anne Fish- erkeller, Jerome H. Friedman, and John W. Tukey, “prrm-g: An Interactive Mul- tidimensional Data Display and Analysis System,” in William S. Cleveland, ed., The Collected Works of John W.. Tukey, Volume V, Graphics: 1965-1985 (Pacific Grove, California, 1988), 308-327. For a report of some diffi- culties, see Peter J. Huber, “Experiences with Three-Dimensional Scatterplots,”

Journal of the American Statistical Association ,

82 (June 1987), 448-453.

Showing the oft-plotted Anderson data

for Iris setosa -, Iris versicolor « , and Iris virginica - , redrawn from Paul A. Tukey and John W. Tukey, “Preparation; Pre~ chosen Sequences of Views,” in V. Barnett, ed., Interpreting Multivariate Data (New York, 1981), pp. 205-206.

5 Paul Klee, On Modem Art (London, 1948), p. 15, translated by Paul Findlay from Uber die moderne Kunst (Bern, 1945). Recent computer adventures seck to give dimen- sionality and nonlinearity to text. See E. J.

Conklin, “Hypertext: An Introduction and

Survey,” Computer (September 1987), 17-41.

So all their angles there 10yned toge- : ther,make a folide angle. And for the better fight thereof, I haue {et \ here a figure wherby ye fhall more eafily conceiue it, the bafe of the

figure is a triangle namely,A B C,if on euery fide of the triangle AB C,ye rayfe vp a triangle,as vpon the fide AB,ye raife vp the triangle AFB,and vpon the fide A C the triangle A F C, and vpon the fide B

Direct methods for the display of three dimensions include making models, as in this 1570 edition of Euclid’s Elements, where little paper

constructions teach solid geometry. Models pleasingly represent the smooth surfaces of three-space, as in architectural miniatures and math- ematical solids; more obstreperous statistical data however, call for

computer analysis of data point clouds. Narratives of the universe were impressively cranked up in orreries,

simulations of our solar system (as known in 1800), with planets and their satellites rotating and orbiting. Although a triumph of gear ratios, the machines did commit a grave sin of information design—Pridefully Obvious Presentation—by directing attention more toward miraculous contraptionary display than to planetary motion.

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C,the triangle B F C,and fo bowing the triangles raifed vp,that their toppes,namely the pointes F meete and ioyne together in one point, ye thal eafily and plainly fee how thefe three fuperficiall angles A F B BFC,CF A,ioyne and clofe together, touching the one the other in the point F,and fo make a folide angle.

Euclid, The Elements of Geometrie (London, 1570), with preface by John Dee, English translation by Henry Billingsley, fol. 314. A fine guide to various extra-dimensional elaborations in book design is Gay Walker, Eccentric Books (New Haven: Yale Univer-

sity Library, 1988).

‘William Pearson, “Planetary Machines,”

in Abraham Rees, ed., The Cyclopaedia; or, Universal Dictionary of Arts, Sciences, and Literature, Plates, Vol. rv (London, 1820),

plate x1; and Henry C. King with John R. Millburn, Geared to the Stars; The Evolution

of Planetariums, Orreries, and Astronomical Clocks (Toronto, 1978).

Particularly intriguing are stereo illustrations, which deliver vivid

three-dimensional scenes by means of paired images (one for each eye), which are then fused mentally by viewers, Aerial landscapes, molecular structures, and other worldly objects are commonly portrayed; repre- sentations of more abstract and ragged quantitative data are rarely seen. Many viewers must struggle (and some fail) to fuse the images; even experienced eyes may require several minutes of vacant staring before obtaining the splendid stereo view.* Recent work on computer visual- izations, stereo images, holograms, and so on hint at an increasing depth

and pace to analytic displays, perhaps eventually without all the para-

phernalia accompanying current methods.”

ESCAPING FLATLAND 17

Color stereopair of Bonaduz, Canton of Grisons, Switzerland, October, 1975, photographs taken with Wild Leitz aerial camera RCIO. Scale about 1:11,000.

©Stereoscopic viewers will assist in obtain- ing threc-dimensional images. The effects can be seen without optical devices by some, however. The views here are arranged for the wide-eyed or pie-cyed method of viewing stereograms; those using the popular cross- eyed method will see sunken mountains and raised rivers. Sce Thomas Avery and Graydon Berlin, Interpretation of Aerial Photographs (Minneapolis, 4th edition, 1985), pp. 25-90.

7 Promising results are D. B. Carr, W. L. Nicholson, R. J. Littlefield, and D. L. Hall, “Interactive Color Display Methods for Multivariate Data,” and K. R. Gabricl and C. L. Odoroff, “Ilustrations of Model Diag- nosis by Means of Three-Dimensional Bi- plots,” in Edward J. Wegman and Douglas J. DePriest, Statistical Image Processing and Graphics (New York, 1986), 215-250, 258— 2743; Thomas V. Papathomas, James A. Schiavone, and Bela Julesz, “Stereo Ani- mation for Very Large Data Bases,” Com- puter Graphics and Applications (September, 1987), 18-27; and William S. Cleveland and Marylyn E. McGill, eds., Dynamic Graphies Jor Statistics (Belmont, California, 1988).

18 ENVISIONING INFORMATION

Sunspors were examined in detail by telescope in the early 1600s, after some 200 years of repeated viewing by unaided eyes in Athens,

China, Japan, and Russia, It was difficult for Europeans to see sunspots

at all because Aristotle had said that celestial bodies were perfect and

without blemish, a fancy which became official church doctrine in the

middle ages, Then, in 1610-1612, Galileo and others made detailed

telescopic observations of sunspots.

Galileo marked spots directly onto paper flatland, maintaining the

proper image plane while drawing a large diagram of a spotted sun:

The method is this: Direct the telescope upon the sun as if you were going to observe that body. Having focused and steadied it, expose a flat white sheet of paper about a foot from the concave lens; upon this will fall a circular image of the sun’s disk, with all spots that are on it arranged with exactly the same symmetry as in the sun. The more the paper is moved away from the tube, the larger this image will become, and the better the spots will be depicted. Thus they will all be seen without damage to the eye, even the smallest of them— which, when observed through the telescope, can scarcely be perceived, and only with fatigue and injury to the eyes.

In order to picture them accurately, | first describe on the paper a circle of the size that best suits me, and then by moving the paper towards or away from the tube I find the exact place where the image of the sun is enlarged to the measure of the circle I have drawn. This also serves me as a norm and rule for getting the plane of the paper right, so that it will not be tilted to the luminous cone of sunlight that emerges from the telescope. For if the paper is oblique, the section will be oval and not circular, and therefore will not perfectly fit the circumference drawn on the paper. By tilting the paper the proper position is easily found, and then with a pen one may mark out spots in their right sizes, shapes, and positions. But one must work dextrously, following the movement of the sun and frequently moving the telescope, which must be kept directly on the sun.?

® George Sarton, “Early Observations of the Sunspots,” Isis, 37 (May 1947), 69-71; for the fall history, D. Justin Schove, ed., Sunspot Cyeles (Stroudsburg, Pennsylvania, 1983).

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° Galileo Galilei, History and Demonstrations Concerning Sunspots and Their Phenomena (Rome, 1613), translated by Stillman Drake, Discoveries and Opinions of Galileo (Garden City, New York, 1957), pp. 115-116.

ESCAPING FLATLAND 19

As more observations were collected daily, small multiple diagrams recorded the data indexed on time (a design simultaneously enhancing dimensionality and information density), with the labeled sunspots parading along alphabetically. This profoundly multivariate analysis— showing sunspot location in two-space, time, labels, and shifting relative

orientation of the sun in our sky—reflects data complexities that arise because a rotating sun is observed from a rotating and orbiting earth:

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For some astronomers, particularly those seeking to reconcile data

with doctrine, it was unclear just where sunspots were located. Surely not on the surface of that perfect sphere; perhaps satellites orbited the sun, or even planets were in transit across the sun’s face—speculations soon demolished by Galileo. Through an elegant chain of visual reason- ing and with characteristic sardonic bluntness, Galileo, writing from

Florence in August 1612, converts empirical observation into focused

evidence supporting conclusions. His argument unfolds the raw data (“what the eye of the forehead” registers) into a luminous explanation of mechanism (“what the eye of the mind” envisions),"° a deeply visual

logic that produced precise insights far beyond those achieved by others who had also observed sunspots in the early 1600s. Indeed, “it was more

than 150 years before any important addition was made’’** to Galileo’s results, as reported in 1613:

I therefore repeat and more positively confirm to Your Excellency that the dark spots seen in the solar disk by means of the telescope are not at all distant from its surface, but are either contiguous to it or separated by an interval so small as to be quite imperceptible, Nor are they stars or other permanent bodies, but some are

Ilustrations from Christopher Scheiner (writing under the pseudonym “Apelles”), De Maculis Solaribus (Rome, 1613), pp. 14— 15; and his Rosa Ursina sive Sol (Bracciani, 1626-1630), p. 63. On the dispute between Galileo and Scheiner concerning sunspots, see William Shea, Galileo's Intellectual Revolution (New York, 1972), pp. 48-74.

40 The persistent relationship between attistic capacity for visualization and ex- traordinary scientific achievement is de~ scribed in Robert Scott Root-Bernstein, “Visual Thinking: The Art of Imagining Reality,” Transactions of the American Philo- sophical Society, 75 (1983), 50-67. For farther evidence about Galileo, see Erwin Panofsky, Galileo as a Critic of the Arts (The Hague, 1954), p. 5: “An excellent draughtsman, Galileo loved and understood ‘with perfect taste’ all the ‘arts subordinated to design’ . . he was originally inclined to study painting rather than mathematics, and one of his most intimate and faithful friends was the outstanding painter of their native Florence, Ludovico Cigoli.”

41 R. J, Bray and R. E. Loughhead, Sunspots (London, 1964), p. 2. Galileo’s analysis at- tained special longevity because of its in- sight and also the nearly complete absence

of observable sunspots from 1645 until 1715! John A. Eddy, “The Maunder Minimum,” ‘Science, 192 (June 18, 1976), 1189-1202.

20 ENVISIONING INFORMATION

always being produced and others dissolved. They vary in duration from one or two days to thirty or forty. For the most part they are of most irregular shape, and their shapes continually change, some quickly and violently, others more slowly and moderately,

They also vary in darkness, appearing sometimes to condense and sometimes to spread out and rarefy. In addition to changing shape, some of them divide into three or four, and often several unite into one; this happens less at the edge of the sun’s disk than in its central parts. Besides all these disordered movements they have in common a general uniform motion across the face of the sun in parallel lines. From special characteristics of this motion one may learn that the sun is

absolutely spherical, that it rotates from west to east around its own center, carries the spots along with it in parallel circles, and completes an entire revolution in about one lunar month. Also worth noting is the fact that the spots always fall in one zone of the solar body, lying between the two circles which bound the declinations of the planets—that is, they fall within 28° or 29° of the sun’s equator.

The different densities and degrees of darkness of the spots, their changes of shape, and their collecting and separating are evident directly to our sight, without any need of reasoning, as a glance at the diagrams which I am enclosing will show. But that the spots are contiguous to the sun and are carried around by its rotation can only be deduced and concluded by reasoning from certain particular events which our observations yield.

First, to see twenty or thirty spots at a time move with one common movement is

a strong reason for believing that each does not go wandering about by itself, in the manner of the planets going around the sun. . .. To begin with, the spots at their first appearance and final disappearance near the edges of the sun generally seem to have very little breadth, but to have the same length that they show in the central parts of the sun’s disk. Those who understand what is meant by foreshortening on a spherical surface will see this to be a manifest argument that the sun is a globe, that the spots are close to its surface, and that as they are carried on that surface toward the center they will always grow in breadth while preserving the same length. . . . this maximum thinning, it is clear, takes place at the point of greatest

foreshortening. .. .

Ihave since been much impressed by the courtesy of nature, which thousands of years ago arranged a means by which we might come to notice these spots, and through them to discover things of greater consequence. For without any instru- ments, from any little hole through which sunlight passes, there emerges an image of the sun with its spots, and at a distance this becomes stamped upon any surface opposite the hole, It is true that these spots are not nearly as sharp as those seen through the telescope, but the majority of them may nevertheless be seen. If in church some day Your Excellency sees the light of the sun falling upon the pave- ment at a distance from some broken window pane, you may catch this light upon a flat white sheet of paper, and there you will perceive the spots. I might add that nature has been so kind that for our instruction she has sometimes marked the sun

with a spot so large and dark as to be seen merely by the naked eye, though the false and inveterate idea that the heavenly bodies are devoid of all mutation or al- teration has made people believe that such a spot was the planet Mercury coming between us and the sun, to the disgrace of past astronomers.‘

12 Galileo Galilei, History and Demonstrations

Concerning Sunspots and Their Phenomena (Rome, 1613), translated by Stillman Drake, Discoveries and Opinions of Galileo (Garden City, New York, 1957), pp. 106-107, 116— 117. Galileo had been through all this once

before when he first saw craters on the moon, another supposedly perfect celestial sphere. One of Galileo’s opponents, “who admitted the surface of the moon looked

rugged, maintained that it was actually quite smooth and spherical as Aristotle had

said, reconciling the two ideas by saying that the moon was covered with a smooth transparent material through which moun- tains and craters inside it could be discerned.

Galileo, sarcastically applauding the ingenu- ity of this contribution, offered to accept it

gladly—provided that his opponent would do him the equal courtesy of allowing him then to assert that the moon was even more

rugged than he had thought before, its sur- face being covered with mountains and.

craters of this invisible substance ten times as high as any he had seen. At Pisa the Ieading philosopher had refused even to look through the telescope; when he died a few

months afterward, Galileo expressed the hope that since he had neglected to look at

the new celestial objects while on earth, he

would now see them on his way to hea- ven.” Stillman Drake, “Introduction: Sec- ond Part,” Discoveries and Opinions of Galileo

(Garden City, New York, 1957), p. 73-

With continuing observation, indexing each image afresh grew

cumbersome. Christopher Scheiner’s Rosa Ursina sive Sol, completed in 1630, arrays the apparent path of spots across a stationary disk,

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an ingenious method for tracking simple sunspot structures but tending to jumble up complex data. Symbols of Scheiner’s patron and religious order decorate those areas without spots in a hundred such diagrams, a reminder of Jonathan Swift’s indictment of 17th-century cartographers who substituted embellishment for data:

With savage pictures fill their gaps,

And o'er unhabitable downs,

Place elephants for want of towns

These symbols, similar to a modern trademark or logotype, may have served as a seal of validation for the readers of 1630. Today they appear somewhat strident, contradicting nature’s rich pattern.

ESCAPING FLATLAND 21

Christopher Scheiner, Rosa Ursina sive Sol (Bracciani, 1626-1630), pp. 317, 325, 333, and 339.

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22 ENVISIONING INFORMATION

Years and years of daily mapping led to this superb visualization,

sunspot distribution in latitude, recorded for long time periods. The sunspot’s two areal dimensions are reduced to one content-relevant dimension, as the immense quantity of data provoked design mastery. E.W. Maunder’s 1904 butterfly diagram aggregates the micro-detail of

individual observations into a macro-view, portraying a distributional

cycle of sunspots moving from the center of each hemisphere toward the equator, as Galileo had noted.’ Only an interval + 40° sun latitude

is plotted, for little activity is seen in more extreme latitudes:

13, W. Maunder, “Notes on the Distribu- tion of Sun-Spots in Heliographic Latitude, 1874 to 1902,” Royal Astronomical Society Monthly Notices, 64.(1904), 747-761. The data compression here consists of taking only the vertical dimension of the sunspot, measured in degrees latitude.

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The fine detail of this sunspot diagram merges into a repeated typical

pattern; and, as the data march along over time, the foremost result is a

visual measure of variation around that average. Measured assessments of

variability are at the heart of quantitative reasoning. R.A. Fisher, the founder of modern statistics, wrote in 1925:

The populations which are the object of statistical study always display variation in one or more respects. To speak of statistics as the study of variation also serves to emphasize the contrast between the aims of modern statisticians and those of their predecessors. For until comparatively recent times, the vast majority of workers in this field appear to have had no other aim than to ascertain aggregate, or average, values. The variation itself was not an object of study, but was recognized rather as a troublesome circumstance which detracted from the value of the average. The

Sun Latitude

Percent of area of sun covered by sunspots

error curve of the mean of a normal sample has been familiar for a century, but that of the standard deviation was the object of researches up to 1915. Yet, from the modern point of view, the study of the causes of variation of any variable phenomenon, from the yield of wheat to the intellect of [people], should be begun by the examination and measurement of the variation which presents itself.

Compared to Maunder’s original picture, the modern butterfly dia- gram increases the data density tenfold, reporting now a full century of solar memoirs. And, moving in parallel with the fapping wings, the

lower time-series restores an areal measure of sunspot activity.1® The

display method used here, parallel sequencing, enhances dimensionality

and density, although showing the variables one-at-a-time-in-parallel is unrevealing of complex interrelated structure. (As statisticians explain, marginal distributions are not wholly informative with regard to joint distributions.) Portrayal of nine full cycles here enforces comfortable comparisons of between- and within-cycle variation, and also exposes

an apparent growth trend (perhaps it is merely improved observation) in the wingspan of recent cycles.

1900 1920 1940

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Note all the different techniques for displaying sunspots during 380 years of data analysis—from Galileo’s first precious observation of the solar disk, to small multiple images, to dimensionality and data com-

pression, and finally to micro/macro displays combining pattern and detail, average and variation. Exactly the same design strategies are found,

again and again, in the work of those faced with a flood of data and images, as they scramble to reveal, within the cramped limits of flatland, their detailed and

complex information. These design strategies are surprisingly widespread, albeit little appreciated, and occur quite independently of the content of the data.

ESCAPING FLATLAND 23

14 Ronald A. Fisher, Statistical Methods for Research Workers (Edinburgh, 1925; 13th edition, 1958), p. 3.

15 Since the sunspots appear symmetric about the sun’s equator, the wings may be folded over to show the distribution of the sun latitude of spots without distinction be- tween northerly and southerly sunspots. W. Gleissberg and T. Damboldt, “A New Approach to the Butterfly Diagram of Sun spots,” Journal of the British Astronomical Association, 81 (1971), 271-276.

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At top, a Maunder diagram from 1880 to 1980, with the sine of the latitude marking sunspot placement. Color coding (the lighter, the larger) reflects the logarithm of the area covered by sunspots within each areal bin of data. The lower time-series, by

summing over all latitudes, shows the total

area of the sun’s surface covered by sunspots at any given time during the hundred-year sequence. Diagrams produced by David H. Hathaway, George C. Marshall Space Flight Center, National Aeronautics and Space Administration.

24 ENVISIONING INFORMATION

oilit a . . lear |y Ree ey ‘Wonprousty complex is this graphic timetable for a Java railroad line, (5]| eay-ewone alle ara aT & Soerabaja-Djokjakarta, drawn in November 1937 (annotated in Dutch, | WA ce Eh + then in Japanese). By smoothly suppressing a dimension first here and sis “fe then several times there, finessing perspective treatments entirely, and al

changing the focus, this 24-hour railroad plan abstractly traces out mul- MI, ee ening tiple paths through three-space and time, in a four-dimensional tour with a dozen other variables carried along.

The time scale is read across the top; towns on the railroad route are indicated by names stacked down the column at left. Diagonal lines running from upper left to lower right show trains heading down \\ , return trains by diagonals going from lower left to upper right // . The first train from the top station, Soerabajakotta, leaves at about 4:50 in the morning (at the « dot), and then reaches the first stop just a few minutes later, and so on, Steeper lines are the faster trains. When trains going opposite directions pass by, an X appears. The arrangement repays meticulous study: + Graphical timetables turn the three spatial dimensions of our daily world into one train-relevant dimension by measuring distance along the track itself. Horizontal grid lines, marking towns and station stops, are spaced approximately in proportion to their distance apart along the rails (yielding straight-line diagonals, assuming trains run more or less at constant speed over the entire route), - The left margin of the timetable reflects another viewpoint, with a profile (at an enlarged vertical scale) of all the valleys and mountains crossed by rail. This visual depiction is accompanied by quantitative details, to the right of the profile, where columns of numbers describe the grade and path. Note how the vertical has been used repeatedly to

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26 ENVISIONING INFORMATION

+ Within each station, still another view—for what is important here is activity on the flat ground. Aerial views of the intricate networks of station switching tracks are shown, encoded with symbols, icons, and dingbats describing the local facilities:

x 3s sp. Rablick on Gasfabriak NS Nf ye

34 “Ook h Me

a ‘ onneyt

Onw lr Dfor

+ The train diagonals cleverly multiple-function,'* as those marks record six variables all at once: the location of a train between towns, time of that position, direction, train type, relative speed (comparing slopes of diagonals), and yearly pattern of operation. A two-dimensional matrix organizes lines by type and seasonality, encoding the diagonal path of the train through the space-time field:

regular seasonal irregular special

RAAB | RH AB | ez | esl we Hea = Bae 9 = =S RRB 0 =e BA —

” (BpaR) [tre] ete ee] ete | eee

MBH HB | atereeesen se |ememorearerae | ececerseneeee|-—

This 16-variable schedule served as an internal planning document for the Java Railroad; it was then obtained by agents working for Japan preparing for their military invasion of Java during 1942.17 In the upper righthand corner, this railroad timetable is classified “secret” (jie). The spy graphical timetable portrays detailed operations of an intricate and irregular system and, at a more distant view, the overall structure and pattern of the railroad—a dual micro and macro reading. It is very much like an excellent map, but with many dimensions breaking free of direct analogy to conventional cartographic flatland.

DC cargo unloading platform

CS livestock loading platform

en

water supply pump tower

cargo unloading facilities

@® directional change platform

‘Ut car repair platform

toc standby engines on relief car

Spa closed areas

18 The idea of double-functioning elements

appears in architectural criticism; Robert Venturi, Complexity and Contradiction in

Architecture (New York, 2nd edition, 1977), ch. 5. Venturi in turn cites Wylie Sypher, Four Stages of Renaissance Style (Garden City, New York, 1955). For statistical graphics, see “Multifunctioning Graphical Elements,” in Edward R. Tufte, The Visual

Display of Quantitative Information (Cheshire, Connecticut, 1983), pp. 139-159.

17 Indonesia ni okeru nihon gunsei no genkyu [A Study of Japanese Occupation in Indonesia], Okuma Social Science Center at Waseda University (Tokyo, 1959).

” Fifizcle or Cheon. aa

oe as as Se

Lrxz the tour-guides for the Ise Shrine and sunspots, movements are

again depicted on a perspective map, but now in four dimensions—the

flatland of floor, coded gestures in dance notation of body motion, and

time sequence. (Symbolically encoded because “any serious system of

movement notation avoids words because they are a strong deterrent to international communication.”**) The floor plan is linked to the airy

music (two dimensions there, time and tone) by numbers, with varying

steps for varying sounds. The numbers double-function, simultaneously

sequencing steps and relating movement to music. Note the enlarged

dance-floor notation for the partner on our right, since he takes a front

route in switching sides. Often the redundancy of bilateral symmetry

consumes space better devoted to fresh information; but here the inte-

grated complexity of dual movements, as the dancers’ paths weave and

intermingle, requires symmetric repetition. The two, pulled apart by

their mirrored pairing, become visually integrated through their nearly

touching hands, mutual postures, overlapping paths of movement, and

convergence of perspective lines radiating from the flatland floor to a

vanishing point exactly midway between their outstretched hands.

A subtle, graceful, profoundly simple design, with a straightforward

complexity, a forerunner of modern dance and movement notation.

ESCAPING FLATLAND 27

Kellom Tomlinson, The Art of Dancing, Explained by Reading and Figures (London, 1735), book 1, plate x11.

18 Ann Hutchinson Guest, Dance Notation: The Process of Recording Movement on Paper (London, 1984), p. 14. This book also makes a surprising demonstration that abstract,

symbolic methods of movement notation

are preferable to film and stick figure por- trayals, at least from a dancer’s viewpoint.

Margaret Morris, The Notation of Movement (London, 1928), pp. 103-104.

28 ENVISIONING INFORMATION

migratory anticyclone cirrocumulus eryeney

cirrus altostratus stratocumulus strat

a 6km

Dba B® Lom A Th z = @ BR £E 3 i i) a Bik zl a 2 oo Be § eo =: Poy ter 2a 4 ~- # e te a 26

2 x 4

Harz gray contours tracing out constant temperatures at 0° and -10° c stretch through the clouds in a side profile of Japan, an ocean-eye view. Forecasts for 15 areas annotate the cross-section of this unusual weather map from a daily newspaper. How easily the design reads, compared to traditional weather maps that commit both their visual dimensions to a planview of latitude and longitude, suppressing the vertical. Of course the arrangement works best for long, thin countries.

The next graphic, plotted by a computer, reports four times daily the levels of three air pollutants fuming over southern California. Nitrogen oxides (top row) are emitted by power plants, refineries, and vehicles. Refineries along the coast produce post-midnight peaks shown in the first panel; cars and power plants send daytime levels up. The morning traffic generates carbon monoxide, with high concentrations where five freeways converge in downtown Los Angeles, Reactive hydrocarbons (bottom row) emanate from refineries after midnight and then increase

REACTIVE HYDROCARBONS

Va

oon to.3 pm

covering Japan

tocumulus nimbostratus

~ ln Gf 4 %o ig

2 q “

bee & 2 8 oe : z 3 £

Redrawn from Akahata [Red Flag], Tokyo, March 7, 1985. English translation added here. Note the changing weather reported for some cities, for example, Sapporo at the far right of the map.

Redrawn. See G. J. McRae, W. R. Goodin, and J. H. Seinfeld, “Development of a Sec- ond-Generation Mathematical Model for Urban Air Pollution. I. Model Formula tion,” Atmospheric Environment, 16 (1982), 679-696.

3pm to 6 pm

ESCAPING FLATLAND 29.

with daily traffic. The twelve time-space-pollutant maps add up smog INTERETS CoMPOSES A TROIS POUR CENT,

observations on a spatial grid of 2,400 squares (each five kilometers on a carrrat, | 1. Annee. 2.8 an

side), for a total of 28,800 readings, except for those masked by peaks— Bilge bes| ave

a high density arrangement of data, abounding with variables and with : ue ae pe

observations on those variables. i na ia iG

This air pollution display is a small multiple, with the same design $ eal gael «| eS structure repeated for all the images. An economy of perception results; 2 eh ya 7s

once viewers decode and comprehend the design for one slice of data, 2 eo gay ae

they have familiar access to data in all the other slices. As our eye moves 2 Seeds gel vane from one image to the next, this constancy of design allows viewers to fe guagle as ie oy By

focus on changes in information rather than changes in graphical com- - non oral ill se-49 position. A steady canvas makes for a clearer picture. Note how papet’s fo oe a eee

two dimensions are put to work here, twice over. Each small map re- bpel eseo|) 98 cg] 198 2%

ports on the two-space location of a third quantity; those maps become $e | Bea ee] fib a2) gan 8

entries themselves in another matrix arraying time of day by type of pe eee, eee 516 3%

pollution, for a grand total of five variables. f ele we is ze 3°

Tabular arrays of numbers similarly confront flatland, with design O88 |: 987 09] | 1984 4] 1988 ts

solutions identical to graphical displays. These compound interest tables 3000 24060 00 23 tat Bo 38 & record a third variable located on the two-surface, and then repeat each LESS Unseen ee

array, small multiple style, at levels of a fourth variable. Entries show

capital plus interest, entabled for sequenced amounts of capital and time. INTERETS composts A QUATRE POUR CENT.

oo : : carirar, ane That grid is then repeated, indexed on the annual rate of interest. ee cules

Data entries located on a plane surface can themselves multiply, as in & ete

the notorious applicant/admit tables for law school admissions. Knitting i iz

together all combinations of college grades and test scores, the bivariate 4 44s

grid registers both the number of applicants and, from those candidates, $ : u

the number then actually admitted by this law school. The margins on 8 a . : : «: * : . 9

the right and bottom sum up to univariate distributions, with grand ae B a

totals shown at lower right. This table could in turn become an entry in = es

another two-space, a multiple comparison over time of various schools. oe e z

And when that array itself becomes another entry... p ER a a ror 33

190 112 48 200 224 99

LAW SCHOOL APTITUDE TEST (LSAT) PERCENTILE 300 337 45 ee 030 31-40 41-50 51-60 61-70 71-80 81-90___91-99_— TOTALS ae err GPA) 700 728 oo| 757 12] 787 ho

>37s | 70 70 133 180 341 71-9 151-36 449-345 750-394 See eee eee 1,000 | 1,040 00] 1,081 60 | 1,124 86

3.75 | 21-1 26-4 38-6 54-0 94-0 206-14 358-19 791-436 1588-480 25000 | 2,080 00| 2,163 20] 2,249 72 3,000 | 35320 00] 3,244 80] 3,394 59

3.50 | 57-4 37-4 53-5 65-2. 136-5 228-8 ~=— 369-6 798-148 1743-182

3.25 | 88-0 59-5 61-0 96-5 131-8 193-7 289-12 504-44 1421-81 ‘Baréme Universel (Paris, 1822), pp. 382-390.

3.00 | 93-0 46-0 46-0 53-0 79-1 89-3. 122-2 204-7 732-13 Law School Admission Council and the Association of American Law Schools, Pre-

<2.15 | 174-0 55-0 44-0 51-0 530 740 80-0 113-2 644-2 Law Handbook 1983-84 (Washington, D.C., 1983). The table shown is for the School of

TOTALS | 440-5 230-13 255-14 337-7 527-15 861-41 1369-75 2859-982 6878-1152 Law, New York University. Redrawn.

30 ENVISIONING INFORMATION

Small multiples work as efficient and convincing summaries of data or The New York Times, March 14, 1987, p. 1. an argument, making the same point again and again by offering comple-

mentary variations on the major substantive theme. Here is the colorful story of one such chart:

GOTT! IS ACQUITTED BY A FEDERAL JURY IN CONSPIRACY CASE

NEW CHARGES ARE LIKELY

Verdict is the First Setback in

Recent Government Drive

Against Mafia Leaders

By LEONARD BUDER

John Gotti was acquitted of Federal racketeering and conspiracy charges yesterday in the Government's first major setback in its recent assault on organized crime.

Mr. Gotti, who the Government says is the leader of the nation’s most powerful Mafia family, and six co-de- fendants were found not guilty of charges they took part in a criminal en- terprise. They were accused of carry- ing out illegal gambling and loan- sharking operations, armed hijackings and at least two murders over an 18-

year period. Despite yesterday’s verdict, Federal

investigators said the 46-year-old Mr. Gotti might face indictment on new charges as head of the Gambino crime family. “I can’t comment but I won’t deny it,” said Thomas L. Sheer, head of the Federal Bureau of Investigation in New York, when asked if the F.B.I. was building up another case against Mr. Gotti.

“We'll Be Starting Again’ “They'll be ready to frame us again

in two weeks,” Mr. Gotti told a reporter before leaving the Brooklyn courthouse in a gray Cadillac that was waiting for him. “In three weeks we’ll be starting again, just watch.”

Until yesterday, Federal prosecutors in the Southern and Eastern Districts of New York had recorded a string of successes in major organized-crime cases.

Within the last six months, the heads of the city’s four other Mafia families have been convicted after trials in Manhattan and Brooklyn. They, like Mr. Gotti and his co-defendants, had been charged under the Federal Rack- eteer Influenced and Corrupt Organi- zations Act, or RICO.

Key Witnesses Were Criminals “Obviously they perceived there was

something wrong with the evidence,” said Andrew J. Maloney, the United States Attorney in Brooklyn, referring to the jury. Many of the Government’s key wit-

nesses were criminals who testified for the prosecution under grants of im- munity or in return for payments and other benefits.

The last piece of evidence requested by the jury for re-examination was a chart introduced by the defense that showed the criminal backgrounds of seven prosecution witnesses. It listed 69 crimes, including murder, drug pos- session and sales and kidnapping.

Mr. Gotti’s lawyer, Bruce Cutler, said the jury showed “courage” be- cause “‘it’s not easy to say no to a Fed- eral prosecutor.” He said the jury had not been impressed with the testimony of “paid Government informants who lie, who use drugs, who kill people.”

The verdict, which came on the sev- enth day of jury deliberations after a trial that lasted almost seven months, surprised many in the packed court. room. Friends of the defendants cheered and applauded; the Govern- ment prosecutors, Diane F. Giacalone and John Gleeson, looked glum.

Mr. Gotti, who has been dubbed “Dapper Don’ because of his expen- sive attire and impeccable grooming, and his co-defendants hugged and kissed each other and their lawyers.

Then they stood and applauded as the 12 members of the jury — whose identities had been kept secret to pre- vent possible tampering — left the room escorted by Federal marshals.

‘The New York Times John Gotti

A Weakness

In Gotti Case

Major U.S. Witnesses

Viewed as Unreliable

By SELWYN RAAB Many lawyers and prosecutors who

followed events in the seven-month trial of John Gotti said the underlying weakness of the prosecution’s case was its apparent reliance on turncoat ca-

reer criminals as key wit- nesses against Mr. Gotti and six co-defendants.

A signal that the cred- ibility of the prosecution’s

principal witnesses was in doubt came yesterday morning when the jury, in its final request before acquitting the de- fendants of all charges, reviewed an exhibit introduced by the defense.

It was a chart listing the lengthy criminal records of seven prosecution witnesses who had obtained promises of leniency and other favors from the Government in return for their testi- mony against Mr. Gotti...

News Analysis

ESCAPING FLATLAND 31

The chart invites reading both horizontally and vertically; neither

direction enhances the reputations of those testifying against Mr. Gotti

and his colleagues, as the eye detects curious patterns and unbroken runs

of X’s. Mr. Polisi, for example, has something of a streak going. Those

marks indicating each crime by each witness are not modest or shy, and

they dominate the spreadsheet grid (although only 37 percent of all the possible combinations are marked). Placement of particularly obnoxious Pati ara Det agp ta

activities at the top (murder) and bottom of the list (pistol whipping a nople di ie andl Brae Gua ae

priest) exploits the visual prominence of those positions. Susan G. Kellman.

CRIMINAL ACTIVITY OF GOVERNMENT INFORMANTS }

CRIME CARDINALE LOFARO MALONEY POLISI SENATORE FORONJY — CURRO MURDER,

ATTEMPTED MURDER HEROIN POSSESSION AND SALE

COCAINE POSSESSION AND SALE MARIJUANA POSSESSION AND SALE

GAMBLING BUSINESS ARMED ROBBERIES

LOANSHARKING KIDNAPPING EXTORTION

ASSAULT POSSESSION OF DANGEROUS WEAPONS

PERJURY, COUNTERFEITING

BANK ROBBERY ARMED HIJACKING

STOLEN FINANCIAL DOCUMENTS TAX EVASION BURGLARIES

BRIBERY THEFT: AUTO, MONEY, OTHER

BAIL JUMPING AND ESCAPE INSURANCE FRAUDS

FORGERIES PISTOL WHIPPING A PRIEST SEXUAL ASSAULT ON MINOR

RECKLESS ENDANGERMENT

Such displays are likely to be especially persuasive and memorable 19 For visual displays in the courtroom,

in situations where most information communicated consists of spoken see are, Gillen ed Pictesr bls and Maps : ; i . Go to Court (Washington, D.C.: American

words—as in a trial.t? Courtroom graphics can overcome the linear, Society for Photogrammetry and Remote

nonreversible, one-dimensional sequencing of talk talk talk, allowing Sensing, 1986); and Gregory P. Joseph, + : Modern Visual Evide (New York, 1989).

members of a jury to reason about an array of data at their own pace ser el ee (New ont) |

and in their own manner. Visual displays of information encourage a | diversity of individual viewer styles and rates of editing, personalizing,

reasoning, and understanding. Unlike speech, visual displays are simul-

taneously a wideband and a perceiver-controllable channel.

ENVISIONING INFORMATION 32

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Small multiples, whether tabular or pictorial, move to the heart of Redrawn from Yumi Takahashi and Ikuyo

visual reasoning —to see, distinguish, choose (even among children’s Sab aan G clon Conainatiors (LOY, : 5 see b ae 1985), pp. 114-115.

shirts). Their multiplied smallness enforces local comparisons within

our eyespan, relying on an active eye to select and make contrasts rather

than on bygone memories of images scattered over pages and pages.

We envision information in order to reason about, communicate, doc-

ument, and preserve that knowledge—activities nearly always carried

out on two-dimensional paper and computer screen. Escaping this flat-

land and enriching the density of data displays are the essential tasks of

information design. Such escapes grow more difficult as ties of data to

our familiar three-space world weaken (with more abstract measures)

and as the number of dimensions increases (with more complex data). Still, all the history of information displays and statistical graphics—

indeed of any communication device—is entirely a progress of methods

for enhancing density, complexity, dimensionality, and even sometimes

beauty. Some of these methods, identified and described in the chapters

that follow, include micro/macro readings of detail and panorama, lay-

ering and separation of data, multiplying of images, color, and narratives

of space and time.

By giving the focus over to data rather than data-containers, these

design strategies are transparent and self-effacing in character. Designs

so good that they are invisible. Too many data presentations, alas, seek

to attract and divert attention by means of display apparatus and orna-

ment. Chartjunk has come to corrupt all sorts of information exhibits

and computer interfaces, just like the “ducks” of modern architecture:

‘When Modem architects righteously abandoned ornament on buildings, they unconsciously designed buildings that were ornament. In promoting Space and Articulation over symbolism and ornament, they distorted the whole building into a duck. They substituted for the innocent and inexpensive practice of applied

34 ENVISIONING INFORMATION

decoration on a conventional shed the rather cynical and expensive distortion of program and structure to promote a duck. .. , It is now time to reevaluate the once-horrifying statement of John Ruskin that architecture is the decoration of construction, but we should append the warning of Pugin: Itis all right to decorate construction but never construct decoration.2°

Consider this unsavory exhibit at right—chockablock with cliché

and stereotype, coarse humor, and a content-empty third dimension.

Itis the product of a visual sensitivity in which a thigh-graph with a

fishnet-stocking grid counts as a Creative Concept. Everything counts,

but nothing matters. The data-thin (and thus uncontextual) chart mixes

up changes in the value of money with changes in diamond prices, a

crucial confusion because the graph chronicles a time of high inflation.

Lurking behind chartjunk is contempt both for information and for

the audience. Chartjunk promoters imagine that numbers and details

are boring, dull, and tedious, requiring ornament to enliven. Cosmetic

decoration, which frequently distorts the data, will never salvage an

underlying lack of content.” If the numbers are boring, then you've got

the wrong numbers. Credibility vanishes in clouds of chartjunk; who would trust a chart that looks like a video game???

Worse is contempt for our audience, designing as if readers were

obtuse and uncaring. In fact, consumers of graphics are often more intelligent about the information at hand than those who fabricate the data decoration. And, no matter what, the operating moral premise of information design should be that our readers are alert and caring; they may be busy, eager to get on with it, but they are not stupid. Clarity and simplicity are completely opposite simple-mindedness. Disrespect for the audience will leak through, damaging communication. What E.B. White said of writing is equally true for information design: “No

Big Duck, Flanders, New York; photo- graph by Edward Tufte, July 2000.

20 Robert Venturi, Denise Scott Brown, and Steven Izenour, Learning from Las Vegas (Cambridge, 1977), p. 163.

+}$80;006)

$20,000

21 For detailed evidence, see Edward R.

Tufte, The Visual Display of Quantitative Information (Cheshire, Connecticut, 1983),

PP. 52-87.

22 Paul Rand writes, “Readers of a report should be unaware of its ‘design.’ Rather,

they should be enticed into reading it by interesting content, logical arrangement

and simple presentation. The printed page should appear natural and authoritative, avoiding gimmicks which might get in the way of its documentary character.” Paul Rand, “Design,” in Speaking Out on Annual Reports (New York, 1983).

one can write decently who is distrustful of the reader’s intelligence, or

whose attitude is patronizing.”

Standards of excellence for information design are set by high quality

maps, with diverse bountiful detail, several layers of close reading com-

bined with an overview, and rigorous data from engineering surveys.

In contrast, the usual chartjunk performances look more like posters

than maps. Posters are meant for viewing from a distance, with their

strong images, large type, and thin data densities. Thus poster design

provides very little counsel for making diagrams that are read more

intensely. Display of closely-read data surely requires the skilled craft

of good graphic and poster design: typography, object representation,

layout, color, production techniques, and visual principles that inform criticism and revision. Too often those skills are accompanied by the

ideology of chartjunk and data posterization; excellence in presenting

information requires mastering the craft and spurning the ideology.**

Tue ducks of information design are false escapes from flatland, adding

pretend dimensions to impoverished data sets, merely fooling around

with information. They don’t work, just as this royal dining table,

caught up in flatland, fails to hold the pots and plates. The king and

queen watch in exasperation and exclaim, as their meal slides off,

“It’s the way they draw these wretched tables!”

ESCAPING FLATLAND 35

23 William Strunk, Jr. and E. B. White, The Elements of Style (New York, 1959), p. 70. An effective trial lawyer, Joe Jamail, noted “If you use too many pictures and make it like a circus or going to a matinee, jurors will think you think they’re stupid.” Susan Ayala, “Legal-Graphics Firms,” The Wall

Street Journal, July 21, 1988, p. 19.

24 Our philosophy of information design— self-effacing displays intensely committed to rich data—parallels Balanchine’s approach to dance. Lincoln Kirstein, in his 1972 essay “Balanchine’s Fourth Dimension,” describes an attitude governing the nature of dancing: “A committed Balanchine dancer (with a

small ‘d’) comes to realize that Personality

(with an enormous ‘P’) is a bundle of hap-

hazard characteristics frozen in a pleasing mask for immediate identification and nego- tiable prestige. No matter what is danced— and it makes little difference—stardom dims

the dancing. What is danced is perforce secondary. There are two types of ballet companies: those interested in selling stars

and those occupied in demonstrating and extending the dance, as such. . . . Physicality in the tense relationships of Balanchine’s

dancers kept under so strict a discipline in so free an exercise pushes the spectacle to a high pressure point. Everything is so fo- cused, compressed, packed, playful that it is as if the entire design were patterned on coiled steel or explosive fuels. Combinations

of music in motion approach a fourth dimen- sion that cannot be verbally defined.” Vogue, 160 (December 1972), 118-129, 203-206; and Lincoln Kirstein, Ballet: Bias and Belief (New York, 1983), 111-119.

Harvey, The Bulletin, Sydney, Australia, ca. 19508, as reproduced in E. H. Gombrich, The Image and the Eye (Oxford, 1982), p. 21