Wouldn’t it be great to reach your arm into a fourth dimension of space? You could then liberate yourself from the shackles of ordinary geometry. Hopelessly tangled extension cords would slip apart with ease. A left-handed glove could be flipped over to replace the right-handed one your dog ate. Dentists could do root canals without drilling or even asking you to open your mouth.
As fantastic as extra dimensions of space sound, they might really exist. From the relative weakness of gravity to the deep affinity among seemingly distinct particles and forces, various mysteries of the world around us give the impression that the known universe is but the shadow of a higher-dimensional reality. If so, the Large Hadron Collider (LHC) near Geneva could smash particles together and release enough energy to break the shackles that keep particles in three dimensions and let us reach into that mind-blowing realm.