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About a week ago I randomly watched part of Carl Sagan's Cosmos on youtube. Relevant part starts around 4:57

Which got me thinking about what a real tesseract would look like in 4D since the shadow is what we know as a tesseract (cube inside a cube with connections on each corner) is just the shadow of a 4D tesseract. I want to imagine what it would really look like as explained in the video.

I also got to thinking about shadows, if 3D objects make 2D shadows (are shadows actually 2D?) do 4D objects create 3D shadows and if they do how would that work? Would it be like a dark foggy area? Could 3D shadows be seen/interacted with by humans?

Is there a pattern to how the dimensional downgrade works (assuming that is what happens)? If so can we use this in reverse to know what higher dimensional objects actually look like?
 
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