Keith and I worked on a problem of what to do to make a computer that was reliable out of extremely unreliable elements. It was a very interesting problem, although the practical motivation disappeared after a while because at that time, we were thinking in terms of very unreliable vacuum tubes and, of course, they were succeeded by extremely reliable transistors. We didn't know that. But at that time, it seemed to be interesting to look at how to improve the performance of a computer made of very unreliable parts. And, of course, it was a very general problem, and so what we did was to purify the outputs by having a majority voting unit so that we would do each problem three times and have a majority vote. And we'd do that over and over and over again, and the assumption was that... we... we made the assumption of going to the extreme, so that the probability of a correct functioning of the individual unit was 50% plus epsilon, where epsilon is very small, and the probability of its doing it wrong was 50% minus epsilon. Then we did an expansion in epsilon and... the... then we connected the various majority voting units in a sort of random pattern. We were trying to prove that doing that we would get an exponential correction in the... exponentially improving correction, as we put in more and more and more of these units. So that we could take individual elements that were very unreliable and make a reliable computer out of them.

Well, John von Neumann came through as our consultant. I'd never met him before although he was at the institute. I'd seen him but I'd never actually interacted with him before, and he was paid by the Control Systems Laboratory to help Keith and me for a day or so. And he was very impressive solving the cubic equation in his head in an expansion in epsilon and so on for the majority voter and all that, but it was mainly fairly mechanical help that he gave. He endorsed the idea of doing an exponential, but he didn't really supply a proof that it would work. We were looking for a rather rigorous proof. Well, years later in a very famous lecture at Caltech which was published – before I got to Caltech by the way – von Neumann repeated all this; asserted that the exponential improvement would be achieved with this random method, and footnoted Brueckner and me for the majority voter – not for the general idea. And, of course, Sid Dancoff had some responsibility for the general idea, too, because he assigned the problem. Well, I was so flattered to be mentioned in a footnote by John von Neumann that it didn't occur to me that he hadn't actually credited us with what we were doing.