The concept of emergence evolved to capture our intuition that when a large number of entities interact, the resulting system can display features and behaviours which are not displayed by the individual constituents. The human body possesses behaviours and functions which are not expressed by our individual cells; metals show properties not displayed by individual atoms; societies undergo dynamics which transcend individuals.

Despite a vast literature, going back several decades, no agreement can be found on a definition, nor on a framework for its study, nor on whether emergence is a 'real' natural phenomenon or merely a by-product of our perception, or a convenient way to make sense of processes otherwise too hard to comprehend.

Why should a process which appears so widespread, obvious and at times even easy to model prove so hard to define and conceptualise?

The fundamental reason is that in an emergent process it is very hard to discriminate 'who does what'. When I decide to listen to music, is it my 'emergent' self which takes the decision or my cells? My body depends on cellular activity for its functioning, so cells must be the controlling entities. However, no cell decides to listen to music since listening to music is not something cells 'do'. This leads straight into old and unsolved philosophical problems of causality, determinism and freewill.

Crucially, this is also a technological problem. Today, probably for the first time in history, technological developments in many applications depend on the understanding of emergent phenomena. Advances in Information Technology, Epidemiology, Ecosystem Management, Health Science, just to name a few, depend on approaches which go beyond traditional reductionism and address the understanding of how emergent properties arise, what they 'do' and how they can be controlled.

Despite the philosophical halo of the above discussion, the aim of our research is utterly practical. In a scientific culture in which understanding is increasingly synonymous with computer modelling, we ask what forms of emergence can be studied by simulation and what we can gain from doing so. We will see that computational and 'causal' barriers are strongly related. This may lead to new insights into the limitations and future of the computer modelling of complex processes.