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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 jschwartzi 8y ago
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.
- mattkrause 8y agoThere’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.
- jschwartzi 8y agoAnd the dimensionality becomes hard to manage when you go from interpreting it as a spatial dimension to interpreting it as a feature dimension.