I think there is a fallacy comparing the 2d world as the size of a TV screen or book. The 2d or 3d world would still be linked to all higher dimensions and thus part of the higher dimensional structure. My guess is there would be greater volume with a higher dimension universe but not...
Assume a TV screen or a book page represents 2D information viewable within our 3D world. From our 3D world, we see the entirety of the 2d world...all of it.
Now imagine if somehow we lived within the 2D TV or book page. From our 2D world, we would be incapable of viewing, interacting or...