We are at the beginning of a new age in which artificial entities will perform significant amounts of high-level cognitive processing rivaling and even surpassing human thinking. The future belongs to those who can best collaborate with artificial cognitive entities achieving a high degree of cognitive augmenta-tion. However, we currently lack theoretically grounded fundamental metrics able to describe human or artificial cognition much less augmented and combined cognition. How do we measure thinking, cognition, information, and knowledge in an implementation-independent way? How can we tell how much thinking an artificial entity does and how much is done by a human? How can we measure the combined and possible even emergent effect of humans working together with intelligent artificial entities? These are some of the challenges for research-ers in this field. We first define a cognitive process as the transformation of data, information, knowledge, and wisdom. We then review several existing and emerging information metrics based on entropy, processing effort, quantum physics, emergent capacity, and human concept learning. We then discuss how these fail to answer the above questions and provide guidelines for future re-search.