Production of Ideas by Means of Ideas

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 complexity 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, persistent and increasing emergence of new discoveries as well as periods of explosive evolutions followed by stasis periods.