h a l f b a k e r yRenovating the wheel
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Hypercubism
Visualise and feel the fourth dimension through sculpture | |
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.
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]
[link]
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I can't really get my head around the description. |
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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. |
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So, sort of an attempt like at the flatlanders looking out of their plane. |
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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. |
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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. |
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But what about the other six dimensions ? Are you just going to ignore them ? |
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[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". |
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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: |
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two or three loop do loops are traversed simultaneously with cars to simulate the wikipedia animation as a 3d actual thing |
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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. |
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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. |
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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. |
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Reflections or tracings aren't a touchable. |
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I was hoping that the curved plexiglass would blur the real world 3D and make the slightly clearer sculpture pop out of our reality. |
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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. |
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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. |
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[+] You had me at the title. |
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// this might or might not be of use to the discussion. |
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