Stephenson:Neal:Quicksilver:804:in fact it was a vector (Olivier Gerard)

From the Quicksilver Metaweb.

Many of the letters from Leibniz to Daniel Waterhouse contain conceptual or verbal anachronisms, but the occurrence of 'scalar' and 'vector' is notable.

While the Latin word vector existed at the time, Oliver Heaviside and Willard Gibbs actually developed the concept of vector in the 19th century. The Irish mathematician/physicist William Rowan Hamilton developed the concept of the quaternion, about 1850. Quaternions are an extension of the complex numbers. Just as complex numbers provide a compact algebraic notation for expressing 2D geometrical operations, quaternions provide a compact algebraic notation for expressing 4D geometric operations. Vectors eventually replaced quaternions, because vectors are general enough to provide a uniform algebraic method for doing geometric operations and reasoning in any number of dimensions.

Basically, a scalar can be thought of as merely a number, and a vector as a number associated with a direction. The abstract definition of a vector space over a scalar field extends the concept to objects which are not so clearly tied to a geometric interpration, such as sets of functions.