Displays of data are necessarily produced on a two-dimensional surface– paper or screen. Yet these are often at worst, misleading, or at best, incomplete. The representation of multidimensional phenomena on a two-dimensional 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.

- Contour Maps
- Three-Dimensional Plots
- Going Forward

## Figure 8.1: Picturing a higher-dimensional 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 data-based 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 ParisLouis-Léger 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 three-dimensional 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. |

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