We have defined the Conscious Turing Machine (CTM) for the purpose of investigating a Theoretical Computer Science (TCS) approach to consciousness. For this, we have hewn to the TCS demand for simplicity and understandability. The CTM is consequently and intentionally a simple machine. It is not a model of the brain, though its design has greatly benefited - and continues to benefit - from neuroscience and psychology. The CTM is a model of and for consciousness. Although it is developed to understand consciousness, the CTM offers a thoughtful and novel guide to the creation of an Artificial General Intelligence (AGI). For example, the CTM has an enormous number of powerful processors, some with specialized expertise, others unspecialized but poised to develop an expertise. For whatever problem must be dealt with, the CTM has an excellent way to utilize those processors that have the required knowledge, ability, and time to work on the problem, even if it is not aware of which ones these may be.

We consider the paradoxical concept of free will from the perspective of Theoretical Computer Science (TCS), a branch of mathematics concerned with understanding the underlying principles of computation and complexity, including the implications and surprising consequences of resource limitations, particularly the fact that computation takes time. The concept of free will is paradoxical.

The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. This paper studies consciousness from the perspective of theoretical computer science. It formalizes the Global Workspace Theory (GWT) originated by cognitive neuroscientist Bernard Baars and further developed by him, Stanislas Dehaene, and others. Our major contribution lies in the precise formal definition of a Conscious Turing Machine (CTM), also called a Conscious AI. We define the CTM in the spirit of Alan Turing's simple yet powerful definition of a computer, the Turing Machine (TM). We are not looking for a complex model of the brain nor of cognition but for a simple model of (the admittedly complex concept of) consciousness. After formally defining CTM, we give a formal definition of consciousness in CTM. We then suggest why the CTM has the feeling of consciousness. The reasonableness of the definitions and explanations can be judged by how well they agree with commonly accepted intuitive concepts of human consciousness, the breadth of related concepts that the model explains easily and naturally, and the extent of its agreement with scientific evidence.