PRODUCTION OF IDEAS BY MEANS OF IDEAS: A TURING MACHINE METAPHOR Stefano Zambelli* Aalborg University (Revised December 2002) ABSTRACT In this paper production of knowledge is modelled in terms of Turing machines or compositions of Turing machines. The input tape and the output tape of the machines are seen as the encoding of ideas generated by Turing machines. This allows us, among other things, to define and measure the com- plexity of ideas and knowledge in the simple terms of algorithmic and computational complexity. Moreover the very existence of the halting problem allows for the introduction of a non-stochastic notion of uncertainty. Consequently uncertainty may be modelled not as the outcome of a predefined probability distribution, but in terms of the randomness associated with the halting problem. In this way the ‘frequency distribution of innovations’ is endogenously generated by the choices of the Turing machines. It is shown that a vast variety of alternative dynamic behaviours in knowledge evolution and hence in productivity can be generated. One can observe clusters of emerging innovations, per- sistent and increasing emergence of new discoveries as well as periods of explosive evolutions followed by stasis periods. 1. INTRODUCTION The question of the proper modelling of the evolution of knowledge, inno- vations and production is a traditional one, but it has been revitalized by the amount of research generated after the contributions of Nelson and Winter (1982), Romer (1986, 1990), Aghion and Howitt (1998) and Arthur (1989). In the present paper a simple model for the evolution of ideas using the formalism of Turing machines is presented. In section 2 the Romer (1993) metaphor of the toy chemistry set is discussed. Section 3 presents, following Davis (1958), the simple formalism of the Turing machine and a case is made to consider these machines as ideas-generating machines. Section 4 shows how a model of knowledge evolution can be constructed; here the halting Metroeconomica 55:2 & 3 (2004) 155–179 © Blackwell Publishing Ltd 2004, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. * I would like to express my gratitude to Professor K.Velupillai for all the help and friendly support given and for being an inexhaustible source of original, profound and ‘productive’ ideas.