# 统计代写|数据可视化代写Data visualization代考|BINF7003

## 统计代写|数据可视化代写Data visualization代考|Escaping Flatland

In his much loved 1884 book Flatland: A Romance of Many Dimensions, Edwin Abbot described the mental sensation of taking a geometrical idea to one more dimension through movement:

In One Dimension, did not a moving Point produce a Line with two terminal points?
In Two Dimensions, did not a moving Line produce a Square with four terminal points?
In Three Dimensions, did not a moving Square produce – did not the eyes of mine behold it -that blessed being, a Cube, with eight terminal points?
Thus, the inhabitants of Flatland had to contemplate a three-dimensional world that might exist outside the confines of the purely two-dimensional world of their perception and experience

In Flatland, a moving square could produce a blessed being, something that could only be “seen” in visual imagination, but nonetheless it provided an opening into a new world. Escaping flatland was yet another essential step in the development of visual thinking.

Indeed, but more abstractly, in both statistics and in data visualization, much of the progress can be thought of as an expansion in the number of dimensions contemplated,
$$1 D \rightarrow 2 D \rightarrow 3 D \approx n D$$
representing univariate, bivariate, and then multivariate problems. ${ }^1$ The essential insight, initially in statistics, was that once you had solved some three-dimensional problem, a solution for the general, multidimensional case was not far behind.

## 统计代写|数据可视化代写Data visualization代考|Contour Maps

Maps start with a two-dimensional surface defined by latitude and longitude. After geographic features such as rivers, cities, and towns had been inscribed, it was natural for cartographers to want to show features of elevation, and landforms such as mountains and plateaus, in what came to be called topographic maps. This idea was a natural initial impetus for 3D thinking and visual depiction.

The first large-scale topographic map of an entire country was the Carte géométrique de la France, by the French astronomer and surveyor CésarFrançis Cassini de Thury [1714-1784], ${ }^2$ completed in 1789. But well before these precise determinations of altitude were made, map makers began to try to show topographical features using contour lines of equal elevation on their maps. These were useful for finding the way through a mountain range as well as for military defense.

Beyond wayfinding and route navigation, thematic maps use the features of geography to show something more: how some quantity of interest varies from place to place. Figure $3.3$ by Balbi and Guerry is a nice example of the use of shaded (choropleth) maps of France to display the geographic distribution of crimes and compare this with the distribution of literacy. But this and similar maps treat geographic regions as discrete, and simply shade the entire arca in rclation to a variable of interest.

The language and symbolism of maps expanded to display more abstract quantitative phenomena that varied systematically over geographical space. This was technically a small step from topographic maps that showed elevation of terrain using either color shading or iso-curves (lines of equal magnitude), but the impact was profound in scientific investigation. It was essentially what Galton had done in mapping the contours of equal barometric pressure across Europe (see Plate 12).

This idea, of drawing level curves or contours on a map to show a data variable, began much earlier. Perhaps the first complete example ${ }^3$ is the 1701 map by Edmund Halley, showing lines of equal magnetic declination (isogons) for the world, shown here in Figure 8.2. It was titled, in a style that tried to tell the whole story on the frontispiece, The Description and Uses of a New, and Correct Sea-Chart of the Whole World, Shewing Variations of the Compass.

## 统计代写|数据可视化代写数据可视化代考|逃离平面

.

$$1 D \rightarrow 2 D \rightarrow 3 D \approx n D$$

## 统计代写|数据可视化代写数据可视化代考|等高线地图

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