In this paper we advance the radical notion that a computational model based on the reals provides a more abstract description of concurrent and reactive systems, than the conventional integers based behavioral model of execution sequences. The real model is studied in the setting of temporal logic, and we illustrate its advantages by providing a fully abstract temporal semantics for a simple concurrent language, and an example of verification of a concurrent program within the real temporal logic defined here. It is shown that, by imposing the crucial condition of finite variability, we achieve a balanced formalism that is insensitive to finite stuttering, but can recognize infinite stuttering, a distinction which is essential for obtaining a fully abstract semantics of non-terminating processes. Among other advantages, going into real-based semantics obviates the need for the controversial representation of concurrency by interleaving, and most of the associated fairness constraints.