Nerve cells differ from other types of cells in an important way: They contain long projections, nerve fibers that consist of axons and dendrites. These nerve fibers are very long and complex. In an animal, they overlap each other in a network whose basic structure is difficult to unravel. For this reason, early biologists had a great deal of trouble determining exactly what it is that constitutes a single nerve cell and how two nerve cells are related to each other.

According to one popular early theory, nerve fibers are actually in contact with each other, and nerve messages are transmitted directly from one fiber to the next, or from one cell to the next. An alternative to this view was suggested in the late 1800s by the German anatomist Wilhelm von Waldeyer-Hartz. Waldeyer-Hartz hypothesized that two nerve cells or nerve fibers are not actually in contact with...