Modelling is a way of simplifying the real world to enable us to solve problems. We do it all the time and so easily that we don’t even notice we are doing it. For example, a street directory is a model of a city’s roads, a diagram is a model of how something is made, and even a calendar is a model of a month. People use these models to solve problems, such as ‘What is the shortest route?’, ‘How do I put this together?’, ‘How long until my birthday?’. Mathematics is one of the most important modelling tools. The ancient Egyptians used geometry to model and divide up their farmland. In the 1600s, Isaac Newton developed calculus, a way of mathematically describing moving objects. He used equations to accurately model the motion of the planets – one of the greatest scientific achievements. Today we use sophisticated computer models in many ways; for example, to help predict the weather, simulate climate change, and assess the impact of population on the environment. How does modelling work? Modelling is a five-step process. A simple way to see how the steps work is to imagine that you have been asked to organise a function for 30 people. Your problem is to decide how much to charge each person to cover all the costs.
Step 1. Get a clear picture of the problem.
Step 2. Choose the most appropriate mathematics to solve the problem and then present the problem in mathematical language.
Step 3. Solve the mathematical problem.
Step 4. Translate your answer back into the language of the original problem.
Step 5. Check the solution your mathematics has produced. Is it a good enough answer for your needs? What makes a good model? The aim of a model is to simplify the problem. Using a street directory to find your way around a city is much easier than using trial and error or just heading off in one direction. However you usually have to reach a balance between simplicity and accuracy. Seasons give us a simple model for general weather patterns – hot or cold, wet or dry. But the model may not be accurate on any particular day. Good models must include the most significant factors and describe the most important features of a problem but may omit factors of minor importance. You would expect that temperature measurements might be important for a weather model, and the model should tell you if it will rain or not. But the cost of potato chips is not a factor that should be in a model about weather! Finally, a good model must be accurate enough to make predictions. Your costing of the function is not very useful if no-one could afford to come. Similarly, if a weather model predicts warm sunshine but it snows instead, then the model should be checked. Modelling is important for solving problems, we do it all the time. But there are always more problems, and more ways of making models – great challenges still remain. Related sites
Other boxes Box 3. Global warming and climate change Box 4. International deliberations Box 5. Australia's policy response
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