Science 28 April 1995: Vol. 268 no. 5210 pp. 545-548 DOI: 10.1126/science.268.5210.545 Article Computation Beyond the Turing Limit Hava T. Siegelmann + Author Affiliations Department of Information Systems Engineering, Faculty of Industrial Engineering, Technion, Haifa 32000, Israel. E-mail: iehava@ie.technion.ac.il Abstract Extensive efforts have been made to prove the Church-Turing thesis, which suggests that all realizable dynamical and physical systems cannot be more powerful than classical models of computation. A simply described but highly chaotic dynamical system called the analog shift map is presented here, which has computational power beyond the Turing limit (super-Turing); it computes exactly like neural networks and analog machines. This dynamical system is conjectured to describe natural physical phenomena.