In this column we begin a two-part discussion of the fundamental principles that lead to equations of motion for acoustic, elastic, and poroelastic waves. It is an interesting story that reaches back over 300 years of physics. By necessity, this involves some mathematics. I would encourage the reader who finds the math too difficult to follow the expert who finds it too simple—skip it. Mathematics is a kind of extreme shorthand. Or, better yet, if the physics is a soup then mathematics is the thick roux that remains when all that is superfluous boils away. But when the writer has done the job right, the story is told equally well by reading between the equations.