Displays of data are necessarily produced on a twodimensional surface– paper or screen. Yet these are often at worst, misleading, or at best, incomplete. The representation of multidimensional phenomena on a twodimensional surface was, and remains, graphics greatest challenge. In this chapter we discuss and illustrate some of the approaches that were used to communicate multidimensional phenomena within the practical limitations that we are always faced with.
Figure 8.1: Picturing a higherdimensional plane in 2DKarl Pearson tries to show a solution to the problem of fitting a
plane of closest fit. In 2D, the fitted plane appears as a line. 
Figure 8.2: Contour map of magnetic declinationEdmund Halley drew lines of equal magnetic declination on a map,
possibly the first contour map of a databased variable. The figure
shows the map for the Atlantic Ocean. The curve are the isogonal lines,
with the degree of magnetic declination given as numbers along each. The
thick line is the agonic line of no variation where the compass reading
is true; the dashed line with ships shows the track of Halley’s second
voyage. 
Figure 8.3: Detail showing Halley’s observationsThis figure shows the central portion of Halley’s map with the
locations of his observations. The triangles show the locations of
observations from the first voyage; circles show those from the second
voyage. 
Figure 8.4: Contour map of a bivariate tableThe graph shows the level curves of recordings of soil temperature
measured over time, for months of one year (horizontal axis) by hours of
the day. The maximum temperature occurs in early July, around 3:00 PM.

Figure 8.5: Population density of ParisLouisLéger Vauthier showed the population density of Paris by many
contour levels representing densities of 200 to 1,200 people per unit
area. 
Figure 8.6: Axonometric projection of a 3D surfaceThe labeled points and connecting lines are meant to illustrate how
surfaces and lines appear when projected onto the planes formed by the
coordinate axes. 
Figure 8.7: 3D population pyramidLuigi Perozzo showed the age distributions of the population of
Sweden from 1750 to 1875 as a threedimensional surface. Census years go
from left to right, age is shown front (old) to back (young), and the
height of the surface represents the count of people of that age. 
Figure 8.8: 3D statistical sculpturePerozzo created this 3D model of the population data as a tangible
object, perhaps the first statistical sculpture. 
Plate P.15: Galton’s isochronic chart of travel timeIsolevel contours of equal travel time from London are depicted by
shading. 
Copyright © 2021 Michael Friendly. All rights reserved.
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