Turing's Normal Numbers: Towards Randomness

VERÓNICA BECHER

Cambridge

Conferencia; Turing Centenary Conference CiE 2012; 2012

University of Cambridge, UK

Turing´s Normal Numbers: Towards Randomness (Invited talk) In a manuscript entitled "A note on normal numbers´´ and written presumably in 1938 Alan Turing gave an algorithm that produces real numbers normal to every integer base. This proves, for the first time, the existence of computable instances and it is the best solution to date to Borel´s problem on giving examples of normality. Furthermore, with this work Turing pioneers the theory of randomness and shows that he had the insight, ahead of his time, that traditional mathematical concepts, like measure or continuity, could be made computational. In this talk I will highlight the ideas in these achievements of Turing, which are largely unknown because his manuscript remained unpublished until it appeared in his Collected Works in 1992.