The status of computational theory in ecological psychology has been and continues to be a source of controversy. Over a period of more than 30 years, Robert Shaw and his colleagues have developed a powerful negative critique of computation based in part on the idea that computational theory cannot capture central aspects of the coimplicative structure of the relations between animals and their environments. Two aspects of the Shavian critique are considered in this article: the characterization of the algorist and the problem of complexity. It is argued, contrary to the critique, that computational theory offers a properly constrained formal view of the algorist and is not defeated by complexity. Computational ideas can therefore have a fundamental role to play in the further development of ecological psychology.