Picture a line running between a person and the world, the line that carries cold, pain, danger, praise. Insensible is what you say when nothing comes along that line. The useful thing about the word is that it never says which end is at fault. Usually it is the person: the hands stop reporting the cold, the warning does not land, or the body is out altogether and every line is dead at once. But the same shape works from the other end, where the person is fine and the thing is simply too small or too slow for any sense to catch. One old branch leaves the body behind and follows the other meaning of sense — not what you feel, but what words mean — so a document nobody can read a meaning into is insensible too.