Many problems in connection with the analysis of complex, political issues are related to the questions of what factors are causing a specific desirable or undesirable development. One example might be to ask how environmental factors are affecting security issues. A traditional way of analysing this problem is to compare histories of each of the parameters and perform statistical analysis to measure how dependent or independent these factors are.
Thus one can show, for example, that environmental problems, in a statistical sense,
are very poorly correlated with security issues. One could naïvely draw the conclusion
that environmental variables should not be relevant for decisions relating to security
problems. How dangerous such conclusions might be in the context of nonlinear chaotic,
systems is illustrated in the following example: Assume we observe three time series
(each one appropriately normalized) with apparent erratic time dependence. Visual
inspection of the time series suggests that these time-series might not be independent.
(fig.3.a). When we calculate the corresponding correlation between pairs of the
three variables we find the results shown in fig.3.b: Indeed, the x and y
variables are highly correlated (up to 90%) whereas neither the x nor the y
variable show any significant correlation with the third, z-variable. (Note the
correlation is computed with a relative time-shift of 
.)
Fig.3:
(a) Times-series of the (normalized) x,y,z-coordinates of the standard Lorenz system.
(b) Pair-correlation between each of the time-series of (a) with a relative time-shift.
Coming back to our initial example, let us now assume that the z-variable corresponds to a factor describing some environmental parameter. From the interpretation mentioned above we would expect that decisions, which would have an effect on the z-parameter would not make much difference on the variables x or y.