In the book, the Narrator describes the "Romantic" approach to life of his friend, John Sutherland, who chooses not to learn how to maintain his expensive new motorcycle. John simply hopes for the best with his bike, and when problems do occur he often becomes frustrated, and is forced to rely on professional mechanics to repair it. In contrast, the "classical" Narrator has an older motorcycle which he is usually able to diagnose and repair himself through the use of rational problem solving skills.
In an example of the classical approach, Pirsig explains to the reader that one must pay continual attention: when the Narrator and his friends came into Miles City, Montana [3] he notices that the "engine idle is loping a little," a possible indication that the fuel/air mixture is too rich. The next day he is thinking of this as he is going through his ritual to adjust the valves on his cycle's engine. During the adjustment, he notes that both spark plugs are black, confirming a rich mixture. He recognizes that the feel-good-higher-altitude-mountain-air is causing the engine to run rich. New jets are purchased, and installed, and with the valves adjusted, the engine runs well again.
With this, the book details two types of personalities: those who are interested mostly in gestalts (romantic viewpoints, such as Zen, focused on being "In the moment", and not on rational analysis), and those who seek to know the details, understand the inner workings, and master the mechanics (classic viewpoints with application of rational analysis, vis-a-vis motorcycle maintenance) and so on.