CityReads│How to Lie with Maps
This book has explored the variety of ways maps can lie to promote a healthy skepticism about maps.
Mark Monmonier, 1996. How to lie with maps, 2th edition. University of Chicago Press.
Source:http://www.press.uchicago.edu/ucp/books/book/chicago/H/bo3696845.html
Not only is it easy to lie with maps, it's essential. To portray meaningful relationships for a complex, three-dimensional world on a flat sheet of paper or a video screen, a map must distort reality.There's no escape from the cartographic paradox: to present a useful and truthful picture, an accurate map must tell white lies.
The potential for cartographic mischief extends beyond the deliberate suppression used by some cartographer-politicians and the electronic blunders made by the cartographically ignorant. If any single caveat can alert map users, it is that a single map is but one of an indefinitely large number of maps that might be produced for the same situation or from the same data.
The purpose of this book is to promote a healthy skepticism about maps. Maps are authored collections of information and are subject to distortions arising from ignorances, greed, ideological blindness, or malice.
IElements of the Map
Maps have three basic attributes: scale,projection, and symbolization. Each element is a source of distortion.
Maps can state their scale in three ways:as a ratio, as a short sentence, and as a simple graph. Small-scale maps have a smaller capacity for truth than large-scale maps.
FIGURE 1 Types of map scales
Map projections transform the curved,three-dimensional surface of the planet into a flat, two-dimensional plane.It can be treated as two-stage process. Stage one shrinks the earth to a globe, for which the ratio scale is valid everywhere and in all directions. Stage two projects symbols from the globe onto a flat tenable surface, such as a plane, a cone, or a cylinder. On flat maps, the scale is constant along the standard lines. Scale distortion increases with distance from the standard line.
The common developable surfaces-plane,cone, and cylinder-allow the mapmaker to minimize distortion by centering the projection in or near the region featured on the map. World maps commonly use a cylindrical projection, centered on the equator. Conic projections are well suited to large mid-latitude areas and secant conic projections offer less average distortion than tangent conic projections. Azimuthal projections are used most commonly for maps of polar regions.
For each developable surface, the mapmaker can choose among a variety of projections. Equivalent or equal-area projections allow the mapmaker to preserve areal relationships. As equal-area projections preserve areas,conformal projections preserve local angles.
FIGURE 2 Developable surfaces in the second stage of map projection
FIGURE 3 Secant(above) and tangent (below) cylindrical projections
Map projections distort five geographic relationships: areas,
angles, gross shapes, distances, and irections. Any map projection is a compromise solution.Perhaps the most striking trade-off in map projection is between con formality and equivalence. No projection can be both conformal and equivalent.The two properties are mutually exclusive.
By describing and differentiating features and places, map symbols serve as a graphic code for storing and retrieving datain a two-dimensional geographic framework.
Map symbols include three geometric categories and six visual variables.
Symbols on flat maps are either point, line or area symbols. Point symbols mark the locations of landmarks and villages,line symbols show the lengths and shapes of rivers and roads, and area symbols depict the form and size of state parks and major cities.
Map symbols can differ in size, shape,graytone value, texture, orientation, and hue. Shape, texture, and hue are effective in showing qualitative differences. For quantitative differences,size is more suited to showing variation in amount or count, whereas graytone value is preferred for portraying differences in rate or intensity. Symbols varying in orientation are useful for representing winds, migration streams, and other directional occurrences.
FIGURE 4 The six principal visual variables
IIWhite Lies of Map Generalization
A good map tells white lies; it suppresses truth to help the user see what needs to be seen. Reality is three-dimensional and far too factual to allow a complete two-dimensional graphic scale model. A map that did not generalize would be useless. But the value of a map depends on how well its generalized geometry and content reflect a chosen aspect of reality.
Map generalization includes geometric generalization and content generalization.
Geometric generalization seeks graphic clarity by avoiding overlapping symbols. Point, line, and area symbols require different kinds of generalization.
Selection and displacement of point features avoid graphic interference when too many close symbols might overlap.When displacement moves a label far from the feature it names, graphic association with a tie line or a numeric code might be needed to link the label with its symbol. Abbreviation is another strategy for generalizing labels on congested small-scale maps. Aggregation is useful where many equivalent features might overwhelm the map.
FIGURE 5 Elementary geometric operations in the generalization of point features and map labels
There are five fundamental processes of geometric line: selection,simplication, displacement,smooth, and enhancement.
FIGURE 6 Elementary geometric operations in the generalization of line features
Area features require the largest set ofgeneralization operators because area boundaries are subject to aggregation and point conversion and all five elements of line generalization as well as to several operators unique to areas: aggregation, dissolve, segementation, point conversion and line conversion.
FIGURE 7 Elementary geometric operations in the generalization of area features
Maps that meet the standards show only planimetric d istance,
that is, distance measured in a plane. A planimetric map compresses the three-dimensional land surface onto a two-dimensional sheet by projecting each point perpendicularly onto a horizontal plane. For two points at different elevations, the map distance between their"planimetrically accurate" positions underestimates both overland distance across the land surface and straight-line distance in three dimensions. Yet this portrayal of planimetric distance is a geometric generalization essential for large-scale flat maps.
For some maps, though, geometric accuracy is less important than linkages, adjacency, and relative position. Among the more effective highly generalized maps are the linear cartograms portraying subway and rapid transit systems. Scale is relatively large for the inner city.In contrast, toward the fringes of the city, scale can be smaller.
Content generalization promotes clarity of purpose or meaning by filtering out details irrelevant to the map's function ortheme.Content generalization has two essential elements, selection and classification. Selection, which serves geometric generalization by suppressing some information, promotes content generalization by choosing only relevant features. Classification makes the map informative as well as usable by recognizing similarities among the features chosen so that a single type ofsymbol can represent a group of similar features.
Content generalization reflect choices,values and biases of the cartographer.Choropleth maps portray geographic patterns for regions composed of areal units. The breaks between these categories can affect the mapped pattern.
First, a single choropleth map presents only one of many possible views of a geographic variable. Second, the white lies of map generalization might also mask the real lies of the political propagandist.
FIGURE 8 Different sets of class breaks applied to the same data yield different-looking choropleth maps
FIGURE 9 Class breaks can be manipulated to yield choropleth maps supporting politically divergent interpretations
In viewing maps it is essential to remember that a particular view of reality (or a future reality) is not the only viewand is not necessarily a good approximation of truth.
IIIHow to lie with Map Projection?
Some map projections can help the propagandist by making small areas bigger and large areas bigger still. Designed specifically to aid navigators, the Mercator projection vastl yenlarges poleward areas so that straight lines can serve as lines ofconstant geographic direction. The projection shows little of the area withinthe Arctic Circle and the Antarctic Circle because its poles are infinitely farfrom its equator.
For decades the John Birch Society andother political groups intimidated by Communist ideology and Stalinist atrocities have reveled in the Mercator's cartographic enhancement of the Soviet Union. Birch Society lecturers warning of the Red menace commonly shared the stage with a massive Mercator map of the world with China and Russia printed in a provocative, symbolically rich red.
FIGURE 10 Mercator world map showing the bearing angle O for a rhumb line from A to B and the areal exaggeration of Red China and in particular the USSR. Designed to aid navigators, the Mercator also has served political propagandists seeking to magnify the Communist threat
In the early 1970s this geopolitical propaganda served as a convenient straw man for German historian Arno Peters,who published a "new" world map based on an equal-area projection similar to one described in 1855 by the Reverend James Gall, a Scottish clergyman.
Peters held a press conference to condemnthe Mercator world view and to tout his projection's"fidelity of area" and more accurate, "more egalitarian"representation of the globe. Peters called attention to the Mercator's slighted portrayal of most Third World nations. Religious and international development organizations welcomed this "new cartography".
FIGURE 11 The Peters projection or, more accurately, the Gall-Peters projection
The Gall-Peters projection gives tropical continents a mildly attenuated, stretched look, which explains why geographersand cartographers have adopted more plausible equal-area maps. U.S. Geological Survey cartographic expert John Snyder offered another equal-area projection tounderscore that an equal-area map is not necessarily a good map. Snyder'shourglass equal-area projection does what the Peters projection does and theMercator doesn't-it preserves areal relationships. But it demonstrates thatareal fidelity does not mean shape fidelity.
FIGURE 12 Like all equal-area projetions, this hourglass equal-area map projection John Snyder devised as a joke has area fidelity but distorts shape
Maps can be good or bad, depending on who'sholding them, who they're aimed at, how they're used, and why.
IVHow to lie with Data Maps？
A single set of numerical data can yield dissimilar maps. Different areal aggregation can affect geographic pattern. By manipulating breaks between categories of a choropleth map, a mapmaker can create different spatial patterns. Thus a single map is one of many maps that might be prepared. Map authors and readers need to know how maps based on census data can yield useful information as well as flagrant distortions.
Different areal aggregations of the data might yield different patterns, the analyst should explain the type of geographic unit used. Values at the county-unit level generally show a different trend with values at state-level data.
A real aggregation can have a striking effect on the mapped patterns of rates and ratios. A ratio such as the average number of television sets per household might produce radically different maps when the data are aggregated separately by counties and by thetowns.
FIGURE 13 Town-unit number tables showing number of televison (top left),number of house holds(top right), and average number of televisons per household(bottom) for twenty-eight hypothetical towns
FIGURE 14 County-unit number tables of number of televisions(left), number of households (middle), and average number of televisons per household (right) for a three-county aggregation of the twenty-eight hypothetical towns in FIGURE 13
Another example illustrates how areal aggregation can affect geographic pattern. Whereas figure 9.3 demonstrates that different aggregations of towns into counties can yield different county-level patterns. It is important not to assume that a trend apparent at one level of aggregation exists at other levels.
FIGURE 15 County-unit number tables based on other aggregations of the twenty-eight towns into counties
Map readers should avoid the ecological fallacy: if the careless analyst or naive reader leaps from a pattern based on a real units to conclusions based on individual households. Aggregated census data provide an average for the place but say little about individual residents.
Map makers should know the area and the data, experiment with data for a variety of levels of aggregation, and qualifyall con clusions. The skeptical map user should look for and compare maps with different levels of detail, and be wary of cartographic manipulators who choosethe level of aggregation that best proves their point.
Data classification introduces the risk of a mapped pattern that distorts spatial trends. Arbitrary selection of breaks between categories might mask a clear coherent trend with a needlessly fragmented map or over simplify a intricate pattern with an excessively smoothed view.
The two most common default classing options include the equal-intervals scheme and the quartile scheme.
When data values are uniformly distributed across the range, the equal-interval classification works fine. When data values are not uniformly distributed, this classification might assign most of the region to a single category.
In contrast, the quartile scheme ranks the data values and then divides them so that all categories have the same number of areal units. Only an approximately equal balance is possible when the numberof areas is not a multiple of four. The map based on these four quartilecategories does have meaning for the viewer interested in the locations of towns in the highest and lowest quarters of the data values.
FIGURE 16 Two common classing schemes used as "defaults" by choropleth mapping software yield radically different four-catagory patterns for the data in previous figure
How are the data distributed through out their range? And what, if any, class breaks might have particular meaning to the map viewer? The answer to this second question depends on the data and on whether the map author deems useful a comparison with the national or regional average.
The conscientious map author might then plot a number line. A horizontal scale with tick marks and labels represents the range of the data. The resulting graph reveals natural breaks and clusters of homogeneous data values. Number lines allow the map author to visualize the distribution of data values and to choose an appropriate number of categories and positions for class breaks.
How to deal with the extremely high or extremely low values isolated from the rest of the distribution? No simple,standard solution addresses all outliers. The map author should know the data,know whether these deviant values are real or improbable, and know whether a large difference between outliers really matters. Also important is the relation of outliers to the theme of the map and the interests of map viewers.
FIGURE 17 Number line for the town-level televison-ownership rates in previous figure
Choropleth maps distort geographic relationships between two distributions. Hastily selected or deliberately manipulated categories can diminish the visual similarity of two essentially identical trends or force an apparent similarity between two differentpatterns.
The spatial correspondence of the darkest,most eye-catching symbols strongly influences judgments of map by naive map viewers. The careful map viewer never judges numerical correlation by the Similarity in map pattern alone.
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FIGURE 18 Choropleth maps with identical patterns for television ownership rate and average number of children per household
FIGURE 19 Distinctly different choropleth maps suggest minimal correlation between television ownership and family size
FIGURE 20 Similarity among large areas can distort visual estimates of correlation by masking significant dissimilartiy among small areas. Numerical data and mapping catagories are identical to those for the more obviously dissimilar pair of maps in FIGURE 19
To avoid estimates of correlation biased by the size of areal units, the analyst will inspect the more egalitarian scatterplot.
FIGURE 21 Scatterplots and trend lines for varioius types of correlation
Maps, scatterplots, and correlation coefficients are complementary. The correlation coefficient, which provides a comparison for a pair of variables, measures only linear correlation. Yet a scatterplot quickly reveals a strong curvilinear relationship. Scatterplotsal so show outliers. But scatterplots can not compare strengths of relationships. Moreover, scatterplots and correlation coefficients tell us nothing about the locations of places, whereas maps, which present spatial trends, can offer unreliable estimates of correlation.
Maps also show a different kind of correlation, a geographic correlatiml distinct from the statistical correlation of the scatterplot and correlation coefficient. Statistical correlation is a spatialand reveals nothing about spatial trends. Figures show two map pairs distinctin spatial pattern yet identical inscatterplot and correlation coefficient.
FIGURE 22 Two pairs of variables with identical scatterplots, correlation coefficients(r=.93), and class breaks, yet distinctly different map patterns
Often the map author has a single theme in mind and has several variables to choose from. Some variables are markedly more optimistic in tone or pattern than others, and the name of the index can cast a favorable or an unfavorable impression in the map title. "Labor Force Participation," for instance, sounds optimistic, whereas "Job Losses" clearly is a pessimist's term.
When a single variable might yield many different maps, which one is right? the skeptical viewer must question the represent ativeness of a single graphic. Guard against not only the cartographic manipulator, but also the careless map author unaware of the effects of aggregation and classification.
VConclusion
This book has explored the variety of waysmaps can lie: why maps usually must tell some white lies, how maps can beexploited to tell manipulative lies, and why maps often distort the truth when a well-intentioned map author fails to understand cartographic generalization and graphic principles. The wise map user is a skeptic, wary of confusing or misleading distortions conceived by ignorant or diabolical map authors. However,the map's demonstrated ability to distort and mislead should detract from anappreciation of the map's power to explore and explain geographic facts.Cartographic abstraction has costs as well as benefits. If not harnessed by knowledge and honest intent, the power of maps can get out of control.