We propose a hypothetical classification of different types of public understanding of science and discuss how these types relate to risk perception. Empirically, an increasing understanding of science may lead to acceptance of risks as well as to polarization and strong rejection; on the other hand, a lack of understanding is often associated with uncritical acceptance, a phenomenon that we call the magic of incomprehensibility. We propose a taxonomy of different modes and paths of scientific (in-)comprehension: From a zone of (a) ignorance and indifference, one path leads to (b) familiarity and acceptance, a second path to (c) fragility and polarization, and a third path to (d) the magic of incomprehensibility. We describe the characteristics of risk domains that affect which path is taken in public discourse, and we discuss implications for science communication.