What is the role of the brain's ongoing activity for cognition? The predominant perspectives associate ongoing brain activity with resting state, the default-mode network (DMN), and internally oriented mentation. This triad is often contrasted with task states, non-DMN brain networks, and externally oriented mentation, together comprising a "dual model" of brain and cognition. In opposition to this duality, however, we propose that ongoing brain activity serves as a neuronal baseline; this builds upon Raichle's original search for the default mode of brain function that extended beyond the canonical default-mode brain regions. That entails what we refer to as the "baseline model." Akin to an internal biological clock for the rest of the organism, the ongoing brain activity may serve as an internal point of reference or standard by providing a shared neural code for the brain's rest as well as task states, including their associated cognition. Such shared neural code is manifest in the spatiotemporal organization of the brain's ongoing activity, including its global signal topography and dynamics like intrinsic neural timescales. We conclude that recent empirical evidence supports a baseline model over the dual model; the ongoing activity provides a global shared neural code that allows integrating the brain's rest and task states, its DMN and non-DMN, and internally and externally oriented cognition.