  Disorderly sequences, in the above sense, are highly incompressible. The best effective description we can give of such a sequence—one that would enable someone else, or a computer, to reliably reproduce it—would be to simply list the sequence itself. This feature allows us to characterise the random sequences as those which cannot be produced by a compact algorithm (compact with respect to the length of the target sequence, that is). Given that algorithms can be specified by a list of Turing machine instructions, we have some basic idea on how to characterise the length of an algorithm. We can then say that a random sequence is one such that the shortest algorithm which produces it is approximately (to be explained below) the same length as the sequence itself—no greater compression in the algorithm can be attained. This proposal, suggested by the work of Kolmogorov, Chaitin and Solomonov (KCS), characterises randomness as the algorithmic or informational complexity of a sequence. Comprehensive surveys of complexity and the complexity-based approach to randomness are Li and Vitányi 2008 and Downey and Hirschfeldt 2010: Part I. (See also Chaitin 1975, Dasgupta 2011: §7, Downey et al. 2006: §§1–3, Earman 1986: 141–7, Kolmogorov 1963, Kolmogorov and Uspensky 1988, Smith (1998: ch. 9) and van Lambalgen 1995.)