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What is a Model?

Model-building is a fundamental human activity. For our purposes, a model can be defined as any form of computation that predicts the behavior of a physical object or phenomenon based on its initial state and any ``input'' forces. Our first successful models occurred in our heads [186]. By mentally predicting future effects of seasonal climate change, for example, we were able to plan for winter food supplies. Current theories of human evolution postulate that increased brain size came about as an adaptation to larger scale climate changes, including centuries of drought. Mental simulation was later extended by mathematical simulation, enabling, for example, accurate prediction of astronomical events and physical phenomena at all scales. A mathematical physical theory, such as Newton's laws of motion, gives us a mathematical model that readily predicts the outcome of any physical experiment in the real world for which the theory is applicable. More recently, our brains have been supplemented even further by computer simulation, enabling formerly intractable problems to be simulated as well, thereby further extending our ability to predict. For example, it is now possible to predict even the weather some days into the future with a useful degree of accuracy.

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2023-08-20 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University