The connection of 2D areas gives rise to three-dimensional volumes, which gives the additional dimension of ‘depth’ in encoding.

I omit the coverage of 3D data graphs due to the inherent difficulties in visual decoding. Several software, like Stata, purposefully choose not to support 3D graphs because they are the most inaccurate form of visualisation when it comes to decoding and should be avoided altogether (the only exception I can think of is a rotating 3D density for understanding surface variation).

Note that use of quotation marks around ‘depth’ above. This is because we do not see actually ‘depth’ – we perceive depth. The dimension of depth is a clever reconstruction of our surroundings by our brain as it learns over time and experience. Our brain actually puts together several 2D images of overlapping shapes of different scale and converging lines to extrapolate perspective and depth. This is known as stereopsis (or stereoscopic vision). To understand this better consider the following visual illusion:

What do you see? Do you see a cubic space at the top and a cube protruding outwards at the bottom? Probably you see both, continuously alternating, as your brain cannot decide which is which, because both interpretations appear equally likely. It does not matter how long you look at this picture, your brain will still not be able to resolve the conflict.

It is a generally a very bad idea to visualise data using 3D graphs. An excellent resource to learn more why this is so is Colin Ware’s Visual Thinking for Design. See also the discussion on ambiguous visual illusions.

Indeed, this is not new advice. We have been told more than 100 years ago that it is best to “represent quantities by liner magnitude as areas or volumes are more likely to be misrepresented.” This advice is a standard that was issued by the Joint Committee on Standards for Graphic Presentation for the American Statistical Association in 1915:

Thus, we need to find ways to encode data in a 2D plane, and for that we can employ strategies from the tools provided by visual implantations and retinal variables.

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Demetris Christodoulou