Big data and deep learning are the memes of the day, as we shift from a world where data was rare, precious, and expensive to one where it is ubiquitous, commonplace, and inexpensive. Massive digital data (from scientific instruments and IoT devices), powerful multilayer classification networks, and inexpensive hardware accelerators are bringing new data-driven approaches, challenging some long held beliefs and illuminating old questions in new ways. Like any new tool or technology, big data challenges and reshapes both our social and technical expectations. Likewise, the end of semiconductor Dennard scaling poses new technology challenges in designing ever-faster computing systems. This talk will examine the challenges of continuum computing, fusing edge sensors and machine learning with exascale computing and big data analytics, when computations must increasingly respond to real-time events. As an example, consider the research and scholarship questions that might be explored via powerful analytics applied to data streaming from thousands of sensors placed on human structures (buildings, public utility poles, automobiles) and the environment (air, water, soil, …).