 In passing we would like to mention another important property of K-systems: one can prove that K-systems have positive Kolmogorov-Sinai entropy (KS-entropy); for details see the  Appendix, Section C. The KS-entropy itself does not have an intuitive interpretation, but it relates to three other concepts of dynamical systems theory in an interesting way, and these do have intuitive interpretations. First, Lyapunov exponents are a measure for how fast two originally nearby trajectories diverge on average, and they are often used in chaos theory to characterise the chaotic nature of the dynamics of a system. Under certain circumstances (essentially, the system has to be differentiable and ergodic) one can prove that a dynamical system has a positive KS-entropy if and only if it has positive Lyapounov exponents (Lichtenberg and Liebermann 1992, 304). In such a system initially arbitrarily close trajectories diverge exponentially. This result is known as Pessin’s theorem. Second, the algorithmic complexity of a sequence is the length of the shortest computer programme needed to reproduce the sequence. Some sequences are simple; e.g. a string of a million ‘1’ is simple: the programme needed to reproduce it basically is ‘write ‘1’ a million times’, which is very short. Others are complex: there is no pattern in the sequence 5%8£yu@*mS!}&lt;74^F that one could exploit, and so a programme reproducing that sequence essentially reads ‘write 5%8£yu@*mS!}&lt;74^F’, which is similar in length to the sequence itself. In the discrete case a trajectory can be represented as a sequence of symbols which corresponds to the states of the system along this trajectory.  It is then the case that if a system is a K-system, then its KS-entropy equals the algorithmic complexity of almost all its trajectories (Brudno 1978). This is now known as Brudno’s theorem (Alekseev and Yakobson 1981). Third, the Shannon entropy is a common measure for the uncertainty of a future outcome: the higher the entropy the more uncertain we are about what is going to happen. One can prove that, given certain plausible assumptions, the KS-entropy is equivalent to a generalised version of the Shannon entropy, and can hence be regarded as a measure for the uncertainty of future events given past events (Frigg 2004).