I analyze the long dialog that Eugene Wigner (1902-1995) and Michael Polanyi (1891–1976) carried out on Polanyi’s concept of tacit knowledge and its meaning for the measurement problem in quantum physics, focusing in particular on their ten-year correspondence between 1961 and 1971 on these subjects and the related mind-body problem. They differed in their interpretations, epistemologies, and ontologies, and consequently never resolved their differences on the measurement and mind-body problems. Nonetheless, their long dialog is significant and opens up avenues for exploring these problems further.