This article examines the ways in which art and aesthetics provide powerful and rich models for inquiry and connection, facilitating fresh perception, conceptualization, and engagement in qualitative research. The very engagement with research parallels the engagement with the arts. In this engagement, problem setting and problem solving, the conceptual and the embodied, the analytic and the holistic, are interconnected and interdependent. This article discusses a specific pedagogy used in the author's research courses to develop and nurture this inquiring mindset: a museum activity around consonant and dissonant artworks ("bounded systems") that targets the skills of observation and conceptualization, the identification of relevant contexts for inquiry, and the generation of directions for further inquiry.