COMPLEX (Knowledge Based Climate Mitigation Systems for a Low Carbon Economy) - EU FP7 project (2012 - 2016). The science of complex systems distinguishes linear from non-linear dynamics. Simpler systems can often be satisfactory described by linear models, but complex systems require non-linear models that can capture more of the characteristics of such systems, such as thresholds, feedback loops, avalanche effects, and irreversibility. Linear systems can be validated by aligning models to the past and using the model to predict the future. Non-linear systems, however, are often time-asymmetric - they can be explained with the wisdom of hindsight, but are not always predictable. For example, systems may respond sharply to minor perturbations, and the quality of this response is a measure of the system resilience. In practice, non-linear dynamics are significant both at the micro-scale of small history and at the macro-scale of deep time. The brilliant young scientist, for example, may experience a series of epiphanies that change his/her understanding and behaviour in an unpredictable and irreversible way. The scientific community as a whole may experience an innovation-cascade that has a similar effect on a much larger scale.