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It is possible to visualize 3 dimensional data (like a scatter plot) by projecting it on a 2 dimensional screen in a way that allows to interact with it in an intuitive way.

Is it possible to visualize 4 dimensional data (like a scatter plot) by projecting it on a virtual 3D space in a way that allows to interact with it in an intuitive way or at least in a fashion that one can get used to?

Comments on the italic written wordings:

  • 'virtual 3D space' means a 3D space created in your brain by suggesting a different perspective to your eyes by means of shutter goggles for example.

  • 'in a fashion that one can get used to' is adressing the fact that the projection of a 3D space onto a 2D space uses concepts from 3 dimensional vision like perspective, blurred edges, shadows, ... such concepts are not trivially applicable when going from 3D to 4D.

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Not intended to be an answer, but… how do you define a “projection”? When I visualized quaternion multiplication, I resorted to a bizarre and clumsy pseudo-3D presentation of S³, but I feel it offers more insight than, say, orthogonal projections from ℍ to ℝ³ could. –  Incnis Mrsi Nov 2 at 16:18

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