In this article we will examine how human beings acquire knowledge in science, mathematics, and art. Our focus shall primarily be on the formation of ideas and hypotheses in science and mathematics, since the formal nature of these subjects tends to put the phenomena we are concerned with into particularly clear perspective. We will show that the phenomenon known generally as inspiration is an essential part of the process of acquiring knowledge in modern science and mathematics, as well as in the various creative arts (such as music). We will argue that the phenomenon of inspiration cannot readily be explained by means of mechanistic models of nature consistent with present-day theories of physics and chemistry. As an alternative to these models, a nonmechanistic theoretical framework for the description of nature will be outlined. While providing a direct explanation of inspiration, this general framework is broad enough to include the current theories of physics as a limiting case.