NOTES ON THE MATHEMATICAL FOUNDATIONS OF ANALOGUE

♣ The issues discussed in this paper are based on work that has been central to the Computable Economics research project initiated by Stefano Zambelli and myself over a quarter of a century ago. Two of the central mathematical concepts that have informed the theoretical framework of Computable Economics are the Church-Turing Thesis and Universal Computation. The contents of this paper are a first foray into an investigation into the `computability ' properties of the Phillips Machine, considered as a special kind of General Purpose Analog Computer (GPAC). That I am deeply indebted to Stefano Zambelli, for invaluable intellectual companionship, for over a period of over twenty five years, goes without saying. The problem, however, is that I am unable to blame him for the obviously remaining infelicities in the paper-- nor can I blame our competent graduate students, Kao Selda and V. Ragupathy for those very infelicities. Digital computing has its mathematical foundations in (classical) recursion theory and constructive mathematics. The implicit, working, assumption of those who practice the noble art of analog computing may well be that the mathematical foundations of their subject is as sound as the foundations of the real analysis. That, in turn, implies a reliance on the soundness of set theor