Perhaps the most important requirements in statistical thinking, however, are the definition of the population about which inferences are to be made, and the need for fair samples from that population. The valid design of sampling in surveys and in experiments is therefore an essential precursor to any application of statistical methods. Review of published scientific papers suggests that as much as 80% of research may be wasted by inefficient, or even invalid, design.

Statistical methodology makes extensive use of mathematical models. Many of these models depend on linear and monotonic relationships, and on variability which is both symmetric and homogeneous. With the increased accessibility to powerful computers, however, the fitting of non-linear models to data with heterogeneous variability, hysteresis, and discontinuities in relationships, has become relatively simple, provided that the initial design of the data collection makes such fitting relevant. Extension of modelling concepts by appeal to topology, networks, fractal geometry and chaos theory have all added a new stimulus to the ways in which numerical information can be integrated into human thinking, and the possibilities are increasing almost exponentially.

Linear dynamic models behave predictably and can be analysed mathemat-ically relatively easily but they are idealisations rarely found in nature. Especially in the environmental and human sciences, therefore, computer simulations that incorporate complex feedback structures, non-linear relationships, and the aggregation of system responses to complex signals are usually the most practical way to study and predict the behaviour of whole systems. Very often, the only way to learn how a system behaves is through accumulated experience of the responses it makes to changes imposed on it, ideally through a planned series of experiments so that the interactions between two or more changes can be explored. Just as airline pilots are trained on simulators - essentially computer models of aircraft flight and control - the only way to learn how to manage complex information may be through computer simulations and computer games.

In practice, models need to be embedded in systems analysis - defined as the orderly and logical organisation of data and information into models, followed by the rigorous testing and exploration of these models necessary for their validation and improvement - if they are to be used successfully in creative thinking.