Why would it be possible to see a ball inside a closed box in a 4d world but not a 3d world?

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Why would it be possible to see a ball inside a closed box in a 4d world but not a 3d world?

In: Mathematics

Same concept as using a circle in a 2d world. 2d beings would not be able to see what is inside the circle. 3D beings don’t have their line of sight blocked by the edge of the circle.

Let’s reduce the dimensionality of it, and consider the case of a 2D circle inside a 2D square, as viewed by yourself and Mr. Stick Figure, a flatlander.

As a flatlander, Mr. Figure can only see forwards/backwards and up/down. He sees everything as lines that are closer or further away from him, or higher up/lower down than he is. He can also rotate objects only so that they roll towards him or away from him. Left and right do not exist for him, and so if he puts a circle in a square, there is no “other” direction for him to move in to go “around” the walls of his square safe.

Except, as a 3D creature observing Mr. Figure sliding around on your wall, you can clearly see the alternate direction. Mr. Figure is thinner than a piece of paper and can’t even conceptualize something that is off his wall, but you could just reach out and poke the ball inside the safe, since there’s no wall blocking your access from the third dimension.

You could also poke inside of his brains if you wanted, because his skull is just a 2D oval, not a 3D ovoid.

If you’ve got some time, look at https://youtu.be/Mfglluny8Z0?t=2406. I’ve put in a timestamp near the good part of the explanation, but it’s a full movie on the subject if you’re interested.