Make even more misleading figures by using higher spatial dimensions: the ultimate secret in displaying numeric results the way you want them to look!

The Issue:

When creating figures, it can be tempting to use misleading techniques in order to bolster one’s own agenda.

But it can be hard to create a misleading figure while technically representing the facts correctly, at least from a certain point of view (Figure 1). 

Fig. 1:
The addition of a third dimension (right) to this pie chart really helps the blue stand out. It’s gone from a quarter of the “ink” on the page to over half! Misleading: yes. Factually incorrect: plausibly debatable!


A popular—yet rarely formally acknowledged—method of creating misleading figures is to add additional spatial dimensions to them. Specifically, this allows us to vastly inflate the visual interpretation of a figure while technically keeping the numbers correct (Figure 2).

Fig. 2: These cubes purport to show the values 1 (left), 2 (middle), and 3 (right). But the rightmost cube has (33) = 27 times the volume of the leftmost cube, even though its individual side lengths are only 3 times larger. One could imagine a figure of this nature being used in an ethically-questionable document extolling the growth rate of a business that had tripled in size.

If we don’t need to use all three dimensions to inflate the apparent size of some numeric results, we can also just use two dimensions (Figure 3).

Fig. 3: In this hypothetical news example, we can see that the number of hamburger-related catastrophes in a major metropolitan area have gone from 1/year to 3/year. This can be misleadingly plotted in two dimensions (top, in orange) or misleadingly-plotted in three dimensions (bottom) by using some spherical-hamburger clipart. Anyone reading a figure like this would definitely support a crackdown on hamburgers.

PROS: Provides misleading figures with plausible deniability. Use it on your clickbait blog today!

CONS: Unfortunately, four-dimensional (and beyond) figures are not practical to display to humans, so it isn’t possible to, say, inflate a 20% increase to a 700x-increase (≈ 1.2036) by displaying it in the 36th spatial dimension.

P.S. Regrettably, it appears that this exact topic was covered in the 1954 book How to Lie with Statistics.