Exponential growth of large self-reproducing machine systems

We address quantitatively the major issues involved in the design of self-reproducing machine systems that are capable of both rapid growth to a very large scale and the accomplishment of correspondingly large tasks. A minimal system that satisfies the growth requirement would consist of a large solar cell array and a colony of diverse and specialized machines. With solar energy, raw dirt, and air as its input, the collective purpose of the colony is to expand the solar cell array and build more machines largely without the aid of man. Once the desired size is attained, the entire production capacity of the system may be diverted to useful applications such as large scale energy collection, control of greenhouse gases in the atmosphere, and fresh water production. We consider the issues of resource availability, the suitability of current automation technology, and the required investment in land area. In the discussion of resources, we propose a high-temperature, metallurgical process for separating useful elements from raw dirt without the use of rare elements. Automation technology is judged by a formal productivity requirement in the production chain of each machine type, which must be satisfied to achieve a given overall growth rate. We estimate the time scale for exponential growth to be on the order of months, so that such a system could reach continental size in less than a decade. An area of 10⁶ km² is enough to provide the key elements of a sustainable world economy. At ten percent efficiency, a solar cell array of this size can collect energy at three times the rate of today's global energy consumption.