Random thought (no pun intended): The surface area vs volume discussion sounds vaguely fractal. Sierpinski gaskets are fractal objects (non-integer dimension) that have surface areas that trend toward a fixed value or value increasing towards infinity depending on its fractal parameters, and volumes trend toward zero. Information tied to surface area not volume prompted me to think of it.
Random thought (no pun intended): The surface area vs volume discussion sounds vaguely fractal. Sierpinski gaskets are fractal objects (non-integer dimension) that have surface areas that trend toward a fixed value or value increasing towards infinity depending on its fractal parameters, and volumes trend toward zero. Information tied to surface area not volume prompted me to think of it.