Published online by Cambridge University Press: 03 December 2009
Maybe we oughta help him see,
The future ain't what it used to be.
Tom PettyIntroduction
Predictability evolves. The relation between our models and reality is one of similarity, not identity, and predictability takes form only within the context of our models. Thus predictability is a function of our understanding, our technology and our dedication to the task. The imperfection of our models implies that theoretical limits to predictability in the present may be surpassed; they need not limit predictability in the future. How then are we to exploit probabilistic forecasts extracted from our models, along with observations of the single realisation corresponding to each forecast, to improve the structure and formulation of our models? Can we exploit observations as one agent of a natural selection and happily allow our understanding to evolve without any ultimate goal, giving up the common vision of slowly approaching the Perfect Model? This chapter addresses these questions in a rather applied manner, and it adds a fourth: Might the mirage of a Perfect Model actually impede model improvement?
Given a mathematical dynamical system, a measurement function that translates between states of this system and observations, and knowledge of the statistical characteristics of any observational noise, then in principle we can quantify predictability quite accurately. But this situation describes the perfect model scenario (PMS), not the real world. In the real world we define the predictability of physical systems through our mathematical theories and our in silico models.
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