| Abstract |
As the centenary of the birth of Alan Turing approaches, this proposal may be seen as a continuation and updating of Turing's research agenda focusing on a range of computational questions fundamental still to our understanding of, and engagement with, the world around us. It has been claimed that while the focus in 20th century mathematics was to develop grand formalisms like algebra and topology, the focus in the 21st century will be on extracting data and algorithms. The research topic described below represents foundational work in this direction, and as such is basic to understanding the underlying possibilities within a universe constrained by its algorithmic content.One of the most longstanding and intractable problems in the classical theory of computability is that of characterising the algorithmic content of physical systems and their computability-theoretic infrastructure. This proposal focuses on particular aspects which appear to give a better grip on the problem, and addresses technical challenges basic to further progress in the area. Any such progress is given added significance by new and unexpected relationships being discovered between the Turing universe and its extensions and various epistemological and structural questions in science and beyond. |
