—Richard Feynman Language, a human invention, is a mirror for the soul. It is through language that a good novel, play, or poem teaches us about our own humanity. Mathematics, on the other hand, is the language of nature and so provides a mirror for the physical world. It is precise, clean, diverse, and rock-solid. While these very qualities make it ideal for describing the workings of nature, they are the same qualities that appear to make it ill suited to the foibles of the human drama. So arises the central dilemma of the “two cultures.” Like it or not, numbers are a central part of physics. Everything we do, including the way we think about the physical world, is affected by the way we think about numbers. Thankfully, the way we think about them is completely dependent upon how these quantities arise in the physical world. Thus, physicists think about numbers very differently than do mathematicians. Physicists use numbers to extend their physical intuition, not to bypass it. Mathematicians deal with idealized structures, and they really don’t care where, or whether, they might actually arise in nature.
