Turing's Cathedral: ... Brueckner and Gell-Mann were able to show that even with logical components that had "a 51% probability of being right and a 49% probability of being wrong," they could design circuits so that "the signal was gradually improved." They were trying to show exponential improvement, and were getting close. "... The project hired various consultants, including von Neumann (vN) for one day" Gell-Mann adds ...
In late 1951, vN wrote up these ideas in a short manuscript, "Reliable Organization of Unreliable Elements," and in January 1952 he gave a series of five lectures at Caltech, later published as Probabilistic Logic and the Synthesis of Reliable Organisms from Unreliable Components, in which he began to formulate a theory of reliability, in his characteristic, axiomatic way. ... He thanked Brueckner and Gell-Mann for "some important stimuli on this subject," but not in any detail. ... Gell-Mann: "I thought, my God, this great man is referring to me in the footnote. I'm in the footnote! I was so flattered, and I suppose Keith was, too."AIP Oral History (primarily on JASON) with Brueckner.
In the introduction to Probabilistic Logic and the Synthesis of Reliable Organisms from Unreliable Components (see also here), von Neumann writes:
Our present treatment of error is unsatisfactory and ad hoc. It is the author’s conviction, voiced over many years, that error should be treated by thermodynamical methods and be the subject of a thermodynamical theory, as information has been by the work of L. Szilard and C.E. Shannon.