Not to sound sarcastic but can you do it in real life? It'd scare the "brown gravy" out of me if I looked at the back of your head and noticed you could stair right back at me 0_0
Sure you can, you don't need eyes in the back of your head to sense something approaching from behind. I'm sure most people can hear a lumbering beast approaching from behind, see an unusual shadow cast on the floor, and such. I do it all the time at work. Sometimes I can easily hear people approaching, sometimes I have to rely on the reflections of certain objects around me to track their movements. Or even if they do sneak up on me I notice that my area sounds stuffier and perhaps feels warmer, probably because the person's body is insulating the heat and sound in the area.
Of course, FO3 isn't exactly a simulation, so you probably wont hear a Deathclaw coming or see a dynamic shadow cast across the ground. That's where the perception/radar indicator comes in.