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Visualise and feel the fourth dimension through sculpture
  [vote for,

I am not an artist, so my understanding of this may be flawed. Nonetheless, I think one of the varieties of cubism involved depicting planes intersecting with the objects represented in the scene. Salient features of the objects were then sketched onto the planes. The painting, of course, remains almost two-dimensional. The analysis involved helps viewers to appreciate the true three- dimensional nature of the items more easily.

This technique could be extended to sculpture in order to depict four-dimensional objects in a three-dimensional space. Instead of having planes intersecting with parts of the objects, have solids, perhaps transparent but in any case available for feeling by the "viewer", arranged next to each other in a space. The usual view of four- dimensional shapes is either isometric or involves three-dimensional "slices" of the objects concerned. This is a combination of the two, with the advantage that the distortion of projecting the scene onto three and then two dimensions is reduced, as for each portion the solid concerned is relatively shallow in the ana-kata dimension, and of course the projection is only into a space with one fewer dimensions rather than only half the requisite number.

Thanks to [jscott] for the inspiration.

nineteenthly, Feb 06 2017

Dimensions https://en.wikipedia.org/wiki/Dimension
More than you think ... [8th of 7, Feb 06 2017]

some 3 sphere images at wikipedia https://en.wikipedi...iki/Talk%3A3-sphere
[beanangel, Feb 06 2017]

Could look like toy cars doing loop de loops https://en.wikipedi...:Hopf_Fibration.png
[beanangel, Feb 06 2017]


       I can't really get my head around the description.   

       But, I am imagining a curved plexiglass sheet that when you look through has a two dimension object part imbeded in the sheet that looks three dimensional because of perspective. On the otherside of the plexiglass sheet is the scupture that is the fourth dimentional part of the object. Together the whole object viewing may look 4 dimensional.   

       So, sort of an attempt like at the flatlanders looking out of their plane.
wjt, Feb 06 2017

       That probably arises from my own confusion. I had two images. One was of objects embedded in cubes or other polyhedra of transparent material, and the other was of objects which could actually be handled directly. I'm happy to have both, but for the purposes of simulating a three-dimensional visual field objects embedded in lumps of clear plastic or glass would then need to be accessible to the sense of touch as well as vision. That could possibly be achieved by some other artifice, such as making them a different temperature via heating or refrigeration elements, or varying the texture of the surface according to the proximity of the embedded object to it, like making it smoother or rougher depending on depth.   

       But, you are in the midst of the object and can touch it directly. It's not behind a sheet as that would be a projection, more or less.
nineteenthly, Feb 06 2017

       But what about the other six dimensions ? Are you just going to ignore them ?   

8th of 7, Feb 06 2017

       [Jscott]'s actual picture, which made me think of this, is of a five-dimensional shape rather than a four-dimensional one, and I could've gone there, but there are limits. Having said that, however many dimensions above three, you'd always be one dimension up on a 2-D projection of a projection. Also, right now I'm wondering if the left hand could steer you in the fourth dimension and the right in the fifth. And then it'd be "Up, Up and Away".
nineteenthly, Feb 06 2017

       this might or might not be of use to the discussion. If you go to wikipedia and look up 4d sphere, as well as 3-sphere, there is a synchronized thingy. it might be possible to have a view of plastic toy racecars Where:   

       two or three loop do loops are traversed simultaneously with cars to simulate the wikipedia animation as a 3d actual thing   

       The cars have faceted areas so that the light they reflect has the same path and time order that a 3d secion of a 4d object passing through 3 space would have.   

       translation: I think a three sphere could look like toy cars glittery with mirrors doing synchonized loop de loops to look like part of a higher dimensional thing passing through 3d a la flatland.
beanangel, Feb 06 2017

       Yeah. Actually I agree [beanangel]. The caustic on a parabolic reflecting surface produces an apparently three- dimensional cross-section of a swallowtail catastrophe graph, and what you suggest sounds similar.
nineteenthly, Feb 07 2017

       Reflections or tracings aren't a touchable.   

       I was hoping that the curved plexiglass would blur the real world 3D and make the slightly clearer sculpture pop out of our reality.   

       A trick, where you place your hand through the glass, could be employed to touch points on the sculpture but not in the expected visual places.
wjt, Feb 08 2017

       I thought they should have hypercube and 3-sphere holiday lawn ornaments with racing lights that show a 3d object moving smoothly through them. The more of these holiday ornaments the more people that would learn higher dimensional graphical thinking, preparing generations to produce a better future.
beanangel, Feb 09 2017

       [+] You had me at the title.   

       // this might or might not be of use to the discussion.   

tatterdemalion, Feb 09 2017


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