This contribution tries to highlight the importance of Minkowski's “Raum und Zeit” lecture in a “negative” way, where negative is taken in the photographic sense of reversing lights and shades. Indeed, we focus on the “shades” of Minkowski's text, i.e. what is missing, or misunderstood. In particular, we focus on two issues: (i) why are Poincaré's pioneering contributions to four-dimensional geometry not quoted by Minkowski (while he abundantly quoted them a few months before the Cologne lecture)?, and (ii) did Minkowski fully grasp the physical (and existential) meaning of “time” within spacetime? We think that this “negative” approach (and the contrast between Poincaré's and Minkowski's attitudes towards physics) allows one to better grasp the boldness of the revolutionary step taken by Minkowski in his Cologne lecture.