Conceptual Science

From the geometry of arrows to the mathematics of motion, Richard Feynman explores how vectors can be combined, transformed and differentiated while retaining their essential character. Introduction: More than three numbers There is something deceptively simple about a vector. We draw an arrow, give it a length and a direction, and use it to represent quantities such as displacement, velocity and force. Yet beneath this familiar geometrical picture lies a rather more interesting mathematical idea. In the preceding sections of Chapter 11, Feynman has established that a vector is not simply a collection of three numbers. It is a quantity whose components change in a particular, mathematically prescribed way when we rotate our coordinate system. This distinction is fundamental. It is what separates a genuine physical vector from an arbitrary collection of numerical values. In this section, Feynman begins to develop the algebra of vectors. How can we add them? What does it mean to multi...