On the size of machines

In this paper, the methods of recursive function theory are used to study the size (or cost or complexity) of machines. A positive result of this study shows that to a remarkable degree, the relative size of two machines is independent of the particular way in which machine size is measured. Another result suggests that in order for programs to be of economical size, the programming language must be powerful enough to compute arbitrary general recursive functions, rather than some restricted subset such as the primitive recursive functions. Finally, a kind of speedup theorem is proved which is curiously independent of whether the measure of complexity be the size or the number of steps taken by the machines that compute the functions