When you use them long enough though, you realize that eventually they form an extension of your body and senses... and are as alive as a limb of yours.
Which motorbike rider does not "feel" the loss of traction when you overcook it on a bend? Which sawyer does not flinch when the saw teeth hit a nail embedded in a log? (and it's exactly the same jarring feeling that you get when you crunch down on a stone with your teeth). Valentino Rossi talks to his bike before a race... perhaps that's why his Yamaha overhauls Hondas which are much more powerful. Wacky, but true. Let he who can out-race Rossi question this!
Musicians should be in touch with this feeling often, as their instruments become directly wired to their mind as it were with the fingers just an intermediary.
Dawkins explains in "The extended phenotype" that the distinction of what a living organisms body is, is quite vague and blurred, shows examples of creatures whose body and environment are overlapped.
The feeling of embodied-ness because of direct physical connection by tissue is just one of the channels of sense. The other senses too do connect us to the world at different ranges and intensities. Is a network any less of a network because it's wireless? Mirror neurons produce in our brain the states of the those things we see in the world. An especially empathetic person will flinch even when shown cartoonish violence.
How far can this go?If you attune your senses with practice, eventually you can no longer be hit by someone than you can punch your own face. I believe the most expert of martial artistes build this level of awareness - as if they are connected to the world they perceive.
V S Ramachandran describes a body-awareness experiment where a persons nose can be made to seem elongated a la Pinnocchio, and another where a person reacts neurologically as if s/he were actually struck by a hammer when it was just a table that was struck.
Perhaps an ultimate extension of this is what the Buddhist meant when he said to the hot-dog vendor : "Make me one with everything!"