Is conceptual space continuous? The answer to this question depends on how concepts are represented in the brain. Vector space representations, which ground conceptual states in the instantaneous firing rates of neurons, have successfully captured cognitive dynamics in a broad range of domains. There is a growing body of evidence, however, that conceptual information is encoded in spatiotemporal patterns of neural spikes, sometimes called polychronous neuronal groups (PNGs). The use of PNGs to represent conceptual states, rather than employing a continuous vector space, introduces new challenges, including issues of temporally extended representations, meaning through symbol grounding, compositionality, and representational similarity. In this article, we explore how PNGs support discontinuous transitions between concepts. While the continuous dynamics of vector space approaches require such transitions to activate intermediate and blended concepts, PNGs offer the means to change the activation of concepts discretely, introducing a form of conceptual dynamics unavailable to vector space models.