On the face of it, the premise seems wrong. For any finite number of dimensions, there will be a finite number of objects in the cube, which means you aren’t getting any infinity shenanigans—it’s just high-dimensional geometry. And in no non-shenanigans case will the hypervolume of a thing be greater than a thing it is entirely inside of.
On the face of it, the premise seems wrong. For any finite number of dimensions, there will be a finite number of objects in the cube, which means you aren’t getting any infinity shenanigans—it’s just high-dimensional geometry. And in no non-shenanigans case will the hypervolume of a thing be greater than a thing it is entirely inside of.
Are you sure, it’s entirely inside?
OK, that’s an angle (pun intended) I didn’t catch upon first consideration.
High-dimensional cubes are really thin and spiky.
They are counterintuitive. A lot is counterintuitive in higher dimensions. Especially something, I may write about in the future.
This 1206 business is even Googleable. Which I have learned only after I have calculated the actual number 1206.
https://sbseminar.wordpress.com/2007/07/21/spheres-in-higher-dimensions/