"... a solid differs from a liquid because its crystal structure breaks the translational and rotational symmetries of space. Moreover, solids with different crystal structures should be viewed as different phases of matter because they break these symmetries in different ways. Perhaps more surprisingly, liquids and gases break no such symmetries and so should be viewed as the same phase. When you include further symmetries, such as rotations of spins in a magnet or more subtle quantum counterparts, this classification opens up a wide range of possibilities that allows us to understand almost all the known forms of matter... First, we can be sure that any attempt to change a material from one symmetry class to another will necessarily involve a violent phase transition. Second, it turns out that understanding the symmetries of a system will immediately determine many of its properties, especially at low temperature."