Hypercomputation, which is the general concept embracing all methods of computation and machinery capable of carrying out tasks more powerful than Turing Machines and beyond the Turing Limit, has implications for various fields including mathematics, physics, computer science and philosophy. This book points to a relation between hypercomputation and agent causation theory of free will by exploring that theory’s alleged infinite regress problem. In order to cope with this problem, a certain hypercomputer, viz. reverse Zeus machine, is proposed. Reverse Zeus machines have the same working principle as accelerating Turing machines, which are abstract machines performing temporal patterning in an accelerating manner by executing each step in half the time required for previous step. This allows them to compute infinitely many operations in finite time. In this book, it is showed that Reverse Zeus machines can help to understand and explain the infinite regress problem of agent causation better than other Turing machines.