From the crow's nest of a sailing ship you can see the surface of the ocean for about 35 km (20 miles). A ship farther from land than this will have to sail its course on a featureless waterscape without landmarks or direction. Of course, the sun and stars can give guidance, but require some understanding of astronomy, since the celestial positions vary with time and season; and the knowledge is useless when the sky is overcast with clouds. The discovery of the compass must have been a wonderful revelation, that made sailing a course possible and liberated trade and exploration from the need to stay within sight of land.

A compass depends on the existence of the earth's magnetic field. Conveniently, magnetic north (the direction that a compass points) is not too different from astronomical north (the axis of rotation of the earth).

The magnetic field starts out as an abstract idea: it is the direction a compass would point if there was a compass present to determine this. But in the description of electricity and magnetism that is used in physics, these patterns of lines and arrows come to have a meaning and a reality of their own. Instead of having to explain how a magnet here can affect another magnet at a distance from it, we describe how the field of one magnet fills the space around it, and how that field affects the second magnet. Light turns out to be described as a wave in the electromagnetic field, in which the field rapidly changes in time -- all the little arrows are waving at once in a complicated pattern.

The section on the magnetic field