Tangential, but I noticed the same thing with visual information when testing data visualizations: people have a hard time processing information beyond 4-5 variables.

 Most humans can only really understand 2D (2 variables). That is why visual representation of data are almost always 2d. Graphs, charts, scatter plots.
 What are you claiming?That in a picture with line graphs varying X, Y, people can't understand if the lines are different colours or the same colours (a third dimension)?That people can't play 3D games because they can't understand that the image is depicting length, width and depth?That people can't use windowing GUIs with overlapping windows, because they can't understand the Z-order of which window is "in front"?It seems intuitive that people can cope with more than 2 variables and more than 2 "dimensions" spatially or otherwise.What do you mean when you say they can't - what, specifically, can't people do?
 I think they're claiming that people have enormous amounts of trouble reasoning formally about graphs with 3 or more dimensions. Anecdotally this is bourne out by my experience, where it's easy to read an X-Y plot and speak to how the X value influences the Y value(EG linear, cubic, quartic, grows to infinity in one direction, etc). Add a third or 4th dimension and I start to have a lot of trouble making general statements because I have to juggle the impact of the third dimension on the X-Y plot slices.Please note that I'm not saying it's impossible for people to intuitively understand 3 or more dimensions. Indeed as you say we do it every day. This is not the same as reasoning about it in a general way, which is much harder.
 There’s a confound here between an extra “spatial dimension” (x, y, z) and an extra “feature dimension” (x vs y for plain and star-bellied sneeches). Very few people have trouble with the latter, but the former is tricky to plot and interpret.
 And the dimensionality becomes hard to manage when you go from interpreting it as a spatial dimension to interpreting it as a feature dimension.
 Certainly 3 variables is common place? https://i0.wp.com/flowingdata.com/wp-content/uploads/2018/08...4 is pretty common too, but I agree that 4-5 is tricker to make sense of.
 The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information https://en.m.wikipedia.org/wiki/The_Magical_Number_Seven,_Pl...

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