In the Ninth Meditation, entitled „O změnách jevů v čase“ (“On Changes in Phenomena in Time”), in the book Meditace o základech vědy (Meditations on the Foundations of Science; Praha, Práh 2001), Petr Vopěnka presents a certain non-traditional conception of experienced time, founded on his new infinite mathematics. The point of departure for his model is the idea of an “atomistic rhythm”, which is a linearly structured discrete sequence of beats. It is assumed that this rhythm is so fine that it runs far (or deeply) beyond our ability to distinguish individual beats from each other, so that it appears to us to be a continual temporal line. In this paper, Vopěnka’s model is interpreted in detail, but in the absence of mathematical formalism, and a view is presented as to how we might, on the basis of this model, formalise intuitive concepts such as past, future, present and the momentary “Now”. The interpretation is accompanied by a detailed analysis of Vopěnka’s approach and a sketching of the prospects for alternatives to it.