(p. ix ) Preface and Acknowledgments

• Just as in the uprooting of wild grasses;
• If not grabbed properly, they cut the hand.
• In ethical training, if there be no proper restrain,
• One is picked for hell through one's own making.

• (Chinese version of) Dharmapada, ch. 30, no. 6

The contents of this essay incorporate the substance of the lectures delivered as the fourth Arne Ryde Lectures on May 24/5 1994, at Trolleholm Castle in Scania, Sweden. I have gone into greater detail in some cases, particularly in Chapters 4 , 6 , 7 , 8 , and 9 , than I was able to do in the delivered lectures because of the obvious time constraints during their actual delivery, although the planned program was substantially the same as the structure of this printed text.

I am greatly indebted to Professor Björn Thalberg for having invited me to give this prestigious series of lectures. My indebtedness to him, however, extends far beyond the acknowledgment of gratitude for this particular invitation. I began life as an academic economist twenty‐seven years ago under his teaching, supervision, and guidance. Whether the work reported here is an adequate partial compensation for his initial faith and investment I do not know. But none of my work would have been possible without his consistent personal and professional support during the whole of the period I have known him.

I was taught by Richard Goodwin that the problems of dynamics, optimization, and computation are inextricably intertwined in the economic sphere. The full significance of his message began to dawn on me only after I understood his idea of computation universality for dynamical systems and the recursion‐theoretic underpinnings of induction. He followed my faltering attempts at synthesizing his vision with sympathy, and even enthusiasm, to almost his last days. I hope something of that great man's teaching comes through in the unspoken message of this book.

I have worked in the general area of computable economics for over two decades. During this period the collaboration with my (p. x ) friend Berc Rustem has meant a great deal to me. He introduced me to the weird and wonderful world of computational complexity theory long before it was fashionable to think about the efficiency of algorithms, using recursion‐theoretic mathematics, in economic contexts.

Bob Clower, Axel Leijonhufvud, Francesco Luna, John McCall, and Stefano Zambelli have also been instrumental in guiding me and helping me to focus on computability issues in economic hypothesis. Their inspired friendship, advice, and help as the written text evolved turned out to be decisive in ways that cannot easily be described.

Almost all the material that has gone into this text was conceived, if not also finalized, during my tenure as associate director of the Centre for Computable Economics (CCE), in the Department of Economics at UCLA. The director, Professor Axel Leijonhufvud, and the CCE's chief benefactor, Dr Spiro Latsis, deserve special thanks for the freedom and facilities they made available to me, through the CCE, for extended periods of time. The challenge of being associated with the establishment and nurturing a research institution was indescribably exciting.

The final version of this text was prepared during my tenure as a member of the Department of Economics at the Queen's University of Belfast. I am grateful to the director of the School of Social Sciences, Professor John Spencer, for having given me unusual latitude to schedule my lectures in ways that made it possible for me to devote extended and continuous periods of time to the preparation of this manuscript.

Viveka, Sumithra, and Aruna, my three daughters, played their usual background music that has sustained my sanity and peace of mind for almost a quarter of a century. Viveka's interest in the music of Bartok, Sumithra's in the history of film, and Aruna's in that of photography gave me perspectives that were, at times, decisive in breaking conceptual and methodological dead‐ends that blocked progress.

Maria Johansson, friend and companion, nursed me through a sequence of personal and professional catastrophes that impinged upon my life from almost the day I began to conceive and pen the thoughts that were to become this book. She was also instrumental in making the final text available for print. She did it with love and care.

Growing up in old Colombo gave me the privilege of basing my ethical training on the twin wisdoms of the Thirukkural and the (p. xi ) Dharmapada. I have chosen, therefore, as an epigraph for this work a verse from the ancient Tamil collection of couplets, the Thirukkural, attributed to the sage Thiruvalluvar. My father instructed me on its interpretations and its wise ambiguities. This work is, in a way, an attempt to extol the virtues of ambiguities in a domain of economic theory replete with pseudo‐formal uncertainties. I hope, however, that the chessmen are not bereft of the chessboard.

More important than that, as taught in the wisdom of the Dharmapada, I hope that I have not extolled the virtues of ambiguities without appropriate restraint.

K.V.

Dervio, Lago di Como

April 1998 (p. xii )