Immersion in a creative task can be an intimate experience. It can feel like a mystery: intangible, inexplicable, and beyond the reach of science. However, science is making exciting headway into understanding creativity. While the mind of a highly uncreative individual consists of a collection of items accumulated through direct experience and enculturation, the mind of a creative individual is self-organizing and self-mending; thus, experiences and items of cultural knowledge are thought through from different perspectives such that they cohere together into a loosely integrated whole. The reweaving of items in memory is elicited by perturbations: experiences that increase psychological entropy because they are inconsistent with ones web of understandings. The process of responding to one perturbation often leads to other perturbations, i.e., other inconsistencies in ones web of understandings. Creative thinking often requires the capacity to shift between divergent and convergent modes of thought in response to the ever-changing demands of the creative task. Since uncreative individuals can reap the benefits of creativity by imitating creators, using their inventions, or purchasing their artworks, it is not necessary that everyone be creative. Agent based computer models of cultural evolution suggest that society functions best with a mixture of creative and uncreative individuals. The ideal ratio of creativity to imitation increases in times of change, such as we are experiencing now. Therefore it is important to educate the next generation in ways that foster creativity. The chapter concludes with suggestions for how educational systems can cultivate creativity.