 Even if we accept that randomness, like disorder, is at root a product notion, there are a number of candidates in the vicinity of the set identified by Schnorr’s thesis that might also deserve to be called the set of random sequences. Most obviously, there is Schnorr’s own conception of randomness (§2.1.2; supplement B.1.2). Schnorr (1971) suggests that, for technical and conceptual reasons, Schnorr randomness is to be preferred to Martin-Löf randomness as an account of the intuitive notion. While results that parallel the convergence of ML-randomness and Kolmogorov randomness have been given (Downey and Griffiths 2004), the relevant compressibility notion of randomness for Schnorr randomness was not known until quite recently, and is certainly less intuitively clear than Kolmogorov randomness. Moreover, since the set of ML-random sequences is a strict subset of the set of Schnorr random sequences, any problematic members of the former are equally problematic members of the latter; and of course there will be Schnorr random sequences which fail some Martin-Löf statistical test, which might lead some to reject the viability of Schnorr’s notion from the start.