One early success consistent with this approach was to examine the mathematics of random sequences like coin tosses, but under the assumption that the observer has a limited memory capacity and could only ever see sequences of finite length. That’s why we think tails will come after three heads in a row when tossing a coin — demonstrating that humans do make sensible use of the information we observe. Others have shown that the availability bias, where we overestimate the probability of rare events such as plane crashes, results from a highly efficient way of processing the possible outcomes of a decision. The perception that we are irrational is one unfortunate side effect of the ever growing catalogue of human decision-making biases. But when we apply computational rationality, these biases aren’t seen as evidence of failures, but as windows on to how the brain is solving complex problems, often very efficiently.

Ramsey, young as he was, pulled against Russell, Wittgenstein and the Vienna Circle, who at the time were engaged in a quest for certainty and purity. In the summer of 1924, Ramsey went to Vienna for six months, to be psychoanalysed (he was paralysed about relations with women), and to spend more time with Wittgenstein. The Circle was happy to find the first part of their own answer in Wittgenstein’s idea that the truths of logic are tautologies. While the Circle was discussing ‘The Foundations of Mathematics’, Ramsey was writing a new paper, ‘Facts and Propositions’. But despite this ongoing contact, Schlick and the rest of the Circle seemed to be unaware that Ramsey was moving at speed away from their project, that he was developing a pragmatic outlook that clashed with their attempt to construct the world out of logic and observation.