Although the brain has long been considered a potential inspiration for future computing, Moore's Law - the scaling property that has seen revolutions in technologies ranging from supercomputers to smart phones - has largely been driven by advances in materials science. As the ability to miniaturize transistors is coming to an end, there is increasing attention on new approaches to computation, including renewed enthusiasm around the potential of neural computation. This paper describes how recent advances in neurotechnologies, many of which have been aided by computing's rapid progression over recent decades, are now reigniting this opportunity to bring neural computation insights into broader computing applications. As we understand more about the brain, our ability to motivate new computing paradigms with continue to progress. These new approaches to computing, which we are already seeing in techniques such as deep learning and neuromorphic hardware, will themselves improve our ability to learn about the brain and accordingly can be projected to give rise to even further insights. This paper will describe how this positive feedback has the potential to change the complexion of how computing sciences and neurosciences interact, and suggests that the next form of exponential scaling in computing may emerge from our progressive understanding of the brain.