"String theory... resolves the central dilemma confronting contemporary physics—the incompatibility between quantum mechanics and general relativity—and that unifies our understanding of all of nature's fundamental material constituents and forces. But to accomplish these feats, ...string theory requires that the universe have extra space dimensions. ... Physicists have found that a key signal that a quantum mechanical theory has gone haywire is that particular calculations yield "probabilities" that are not within... acceptable range. For instance... infinite probabilities. ...string theory cures these infinities. ...a residual ...problem remains. In the early days ...calculations yielded negative probabilities ...so string theory appeared to be awash in its own quantum-mechanical hot water. ... Physicists found that the troublesome calculations were highly sensitive to the number of independent directions to which a string can vibrate. ...if strings could vibrate in nine independent spatial directions, all of the negative probabilities would cancel out. ... Kaluza and Klein provide a loophole... in addition to our familiar three... there are six other curled-up... rather than just postulating the existence of extra dimensions, as had been done by Kaluza, Klein, and their followers, string theory requires them."