Alan Turing: The Enigma

Part One: The Logical

1. Esprit de Corps (to 13 February 1930)

• Alan was slow to learn that indistinct line that separated initiative from disobedience and resisted the duties of childhood.
• He had identified the crucial point, that Einstein doubted the axioms. Not for Alan the 'obvious duties', for nothing was obvious to him.

2. The Spirit of Truth (to 14 April 1936)

• For a person with a mathematical mind, an ability to deal with very abstract relations and symbols as thought with tangible everyday objects...
• He had thought deeply about Einstein and had broken the rules to do so.
• For science, to Alan Turing, was thinking for himself, and seeing for himself, and not a collection of facts. Science was doubting the axioms. He had the pure mathematical approach to the subject, allowing a free rein to thought, and seeing afterwards whether or not it had application to the physical world.
• The distinction between science and mathematics had only been clarified in the late 19th C. Until then it might be supposed that mathematics necessarily represented the relations of numbers and quantities appearing in the physical world, although this point of view had really been doomed as soon as such concepts as the 'negative numbers" were developed. The 19th C however, had seen developments in many branches of mathematics towards an abstract point of view. Mathematical symbols became less and less obliged to correspond directly with physical entities.
• One remarkable thing about Gödel's special assertion was that since it was not provable, it was, in a sense, true. But to say it was true required an observer who could, as it were, look at the system from outside. It could not be shown by working within the axiomatic system.