统计代写|数据可视化代写Data visualization代考|Johann Lambert

Between 1760 and 1777, Johann Heinrich Lambert [1728-1777] described curve fitting and interpolation from empirical data. Lambert, a Swiss polymath who made many contributions to mathematics, astronomy, color theory, and experimental sciences, was one of the first scientists to use graphs to represent experimental data, with an aim to show how algebraic methods could be applied to hand-drawn curves representing empirical observations. ${ }^4 \mathrm{He}$ was a seeker of the mathematical laws governing physical phenomena.

Figure $6.4$ shows a chart of soil temperatures in degrees Fahrenheit at a range of latitudes (individual curves) at some intervals of time over the year. The curves were derived from observational data, but no data points are shown. It is a fine example of an early graph, and it very clearly shows the phenomenon he sought to depict-very little variation at the equator and much greater variation toward the poles.

Yet a closer reading of Lambert’s works shows that he had the essential ideas of the scatterplot and should be considered one of the founding fathers of data visualization, particularly for scientific phenomena. In a variety of works on topics of mortality, physics (color, light, hygrometry), and astronomy from 1760 to 1780 , he consistently used graphs of data in an attempt to develop theory from fallible observations in such a way as to deal with a theory of errors. In several works he describes his use of graphs in a way that could be considered modern. One particularly clear statement appeared in 1765 :
We have in general two variable quantities $x, y$, which will be collated with one another by observation, so that we can determine for each value of $x$, which may be considered as an abscissa, the corresponding ordinate $y$. Were the experiments or observations completely accurate these ordinates would give a number of points through which a straight or curved line should be drawn. But as thus is not so, the line deviates to a greater or lesser extent from the observational points. It must therefore be drawn in such a way that it comes as near as possible to its true position and goes, as it were, through the middle of the given points. 5

统计代写|数据可视化代写Data visualization代考|Why Not Playfair

Thus, well before 1800 , all the necessary intellectual pieces for the graphing of empirical data on abstract $2 \mathrm{D}$ coordinate systems were in place. So, when Playfair devised nearly all of the common statistical graphs-first the line graph and bar chart in the Commercial and Political Atlas, later the pie chart and circle graph in the Statistical Breviary-one might wonder why he did not develop the scatterplot for data, the idea of plotting one variable against another.

Playfair was primarily concerned with economic data recorded over time, often for comparative purposes, so the time-series line graph seemed an ideal format. Indeed, all but one of the forty-four charts in the first edition of the Commercial and Political Atlas were line graphs, often showing two time series (imports and exports), so he could discuss the balance of trade as the difference between the curves.

The idea of plotting imports against exports apparently did not occur to him and probably would not have aided his arguments. In 1821 in a brief pamphlet, Letter on Our Agricultural Distresses, Playfair attempted something far more ambitious: to try to show the relationship between different time series and how these fit in terms of historical events. Plate 10 shows three parallel time series over a 250-year period, reflecting prices (price of a quarter of wheat in shillings), wages for labor (weekly wage for a good mechanic, in shillings), and the ruling British monarch.

Playfair shows the time series for wages as a line graph; its vertical scale on the left has a range of $0-100$, but the data (wages) range only from 0 to 30 . The time series for prices of wheat is shown as a bar graph using the right vertical scale, also with a range of $0-100$.

Both vertical axes are in shillings, but the perception of their relative trends would change dramatically if the scales were changed from weekly to daily or monthly wages or if prices of wheat were changed to units of a loaf or a full bushel. But mixing different scales ( $y$-axes), here wages and wheat prices, on the same plot is considered sinful today because it allows a sinning plotter to independently manipulate the two scales and make the relation between those two variables take anv form thev like.

统计代写|数据可视化代写Data visualization代考|Why Not Playfair

Playfair 主要关注随时间记录的经济数据，通常是出于比较目的，因此时间序列折线图似乎是一种理想的格式。事实上，在第一版《商业和政治地图集》的 44 张图表中，除了一个以外，所有图表都是折线图，通常显示两个时间序列（进口和出口），因此他可以将贸易平衡讨论为曲线之间的差异.

Playfair 将工资的时间序列显示为折线图；它在左侧的垂直刻度范围为0−100，但数据（工资）范围仅从 0 到 30 。小麦价格的时间序列显示为使用右侧垂直刻度的条形图，范围也为0−100.

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