When you sit on a swing and a friend twists the swing up and then lets go, you spin around as the swing untwists. If you are spinning fast enough, you'll notice that your extremities seem to get "pulled away" from the axis of rotation. They don't really, of course, it just seems that way because the force you need to exert on them to keep them moving in a circle is towards you just like the force you'd need to exert to counter an outword pulling force.
According to the theory of General Relativity, if you were standing still and all the matter in the universe were rotating around you (with a speed proportional to distance from you), the motions of all this matter would exert the same forces on you that you feel by spinning around in a non-spinning universe. In other words, there is a sort of symmetry between spinning around in a non-spinning universe and staying still in a spinning universe. This line of thinking suggests that in a universe which was completely empty apart from you (if that were possible) you would be able to spin around without experiencing these centrifugal effects.
But the only reason we feel these effects is because you need to exert a force to accelerate things (like limbs) - inertia. This doesn't seem to have anything to do with the rest of the universe. Or does it? Perhaps inertia only happens because of gravitational interactions with the rest of the universe as a whole, and that whenever we experience the relationship between force and acceleration we can infer the existence of the rest of the universe from that. Perhaps there is something in the mystical idea that "all things are connected" after all.