Traditional mathematical modelling is oriented towards describing the behaviour of devices or systems that resemble conventional computers, whose reliability of operation can be taken on trust, and whose mode of interaction with its environment is preconceived and circumscribed. To meet such challenges as are encountered in programming reactive systems, reliable patterns of interaction between system components have to be identified, exploited and monitored throughout the programming process. For this purpose, we need rigorous computer-based modelling methods that take account of an evolving real-world situation and enable us to combine principles of mathematical modelling with the open-ended nature of observation and experiment.
The choice of the epithet "empirical" reflects the fact that our methods are rooted in observation and experiment, and accordingly approach system development from a very different perspective from that associated with formal methods and traditional mathematical models. As when constructing a spreadsheet model, the primary emphasis is upon identifying the dependencies between real-world observables, and on obtaining a representation of state that is sufficiently faithful to be useful in "what if" experiments. Its explicit emphasis upon modelling state as directly experienced, rather than behaviours as circumscribed, distinguishes our approach from traditional techniques of computer-based modelling. Our modelling process gives useful insight into how we presume to gain reliable comprehensive knowledge about a system from experimental evidence.