March 20, 2012
So I’m reading Turing’s Cathedral, and hve greatly enjoyed the first couple of chapters. The Guardian’s review prompted me to get a copy. There is a mixture of history and technical theory in theis book, as Spufford pointed out in his review. Dyson is drawing out the connections between the bomb project and early computing development too, which is fascinating. I’m sure I’ll be struck by parallels with the development of financial pricing models as I read. In chapter one Dyson decribes how MANIAC’s memory was built out of 40 cathode ray tubes, each of which could store 1024 bits, giving 40K bits of addressable storage. He then comments: “Since a 10 bit order code, combined with 10 bits specifying a memory address, returned a string of 40 bits, the result was a chain reaction analogous to the two-for-one fission of neutrons within the core of an atomic bomb. All hell broke loose as a result. Random-access memory gave the world of machines access to the powers of numbers – and gave the world of numbers access to the powers of machines.”
Fundamentally, Dyson is describing a mechanism for indirection. As I read his desription I was struck by the parallel with Godel numbering, and how it allows mathematical statements to be turned into numbers, which can then be quantified over by further statements. That opens up the possibility of a self referential statement, which enables Godel to prove the incompleteness theorem.