  It might seem initially that giving a rigorous characterisation of disorder and patternlessness is a hopeless task, made even more difficult by the fact that we need to characterise it without using the notion of chance. (Otherwise we make CT trivial.) Yet a series of mathematical developments in the theory of algorithmic randomness, culminating in the early 1970s, showed that a satisfactory characterisation of randomness of a sequence of outcomes was possible. This notion has shown its theoretical fruitfulness not only in the foundations of statistics and scientific inference, but also in connection with the development of information theory and complexity theory. The task of this section is to introduce the mathematical approach to the definition of random sequences, just as we introduced the philosophical consensus on chance in the previous section. We will then be in a position to evaluate the Commonplace Thesis, when made precise using theoretically fruitful notions of chance and randomness.