Michael Conrad was a pioneer in investigating biological information processing. He believed that there are fundamental lessons to be learned from the structure and behavior of biological brains that we are far from understanding or have implemented in our computers. Accumulation of advances in several fields have confirmed his views in broad outline but not necessarily in some of the strong forms he had tried to establish. For example, his assertion that programmable computers are intrinsically incapable of the brain's efficient and adaptive behavior has not received much examination. Yet, this is clearly a direction that could afford much insight into fundamental differences between brain and machine. In this paper, we pay tribute to Michael, by examining his pioneering thoughts on the brain-machine disanalogy in some depth and from the hindsight of a decade later. We argue that as long as we stay within the frame of reference of classical computation, it is not possible to confirm that programmability places a fundamental limitation on computing power, although the resources required to implement a programmable interface leave fewer resources for actual problem-solving work. However, if we abandon the classical computational frame and adopt one in which the user interacts with the system (artificial or natural) in real time, it becomes easier to examine the key attributes that Michael believed place biological brains on a higher plane of capability than artificial ones. While we then see some of these positive distinctions confirmed (e.g. the limitations of symbol manipulation systems in addressing real-world perception problems), we also see attributes in which the implementation in bioware constrains the behavior of real brains. We conclude by discussing how new insights are emerging, that look at the time-bound problem-solving constraints under which organisms have had to survive and how their so-called 'fast and frugal' faculties are tuned to the environments that coevolved with them. These directions open new paths for a multifaceted understanding of what biological brains do and what we can learn from them. We close by suggesting how the discrete event modeling and simulation paradigm offers a suitable medium for exploring these paths.