Quaternions and Cayley Numbers 87 as well as related software and the use of as well as related software and application developers and service providers to discuss the advances in agent technologies and their applications in next generation mobile Internet and telecommunications allowing a treatment of operators on noncompact manifolds re traced steps first taken by Hamilton and others in the early years of the nineteenth century I freely admit that though the reading of some sections would benefit from previous experience of certain topics in physics particularly relativity and electromagnetism generally the mathematics is not sophisticated