By Alexander Nunn, The University of Melbourne
The paper plane. The perfect way to demonstrate both your ingenuity and your devil may care attitude towards life and gravity. The graceful and sometimes fleeting moments our folded creations arc through the air might be the only times we grapple with flight. Struggling to send our scrap paper further heavenward we might visualise smooth lines of air flowing over the surface of our plane and tweak an edge. Frustrated by the repeated and dramatic nose-dive of our craft we might think about the balance of the forces of gravity and airflow on the paper. The game of guesswork and visualisation we play as we try to capture within our minds the processes behind the behaviour of our paper plane is called modelling.
In modelling we construct a simplified representation of the natural world or system. Our model imitates and emulates the system allowing us to predict and understand. When we think of atoms as small balls interacting, bouncing around and bound into molecules we are using a model. In reality atoms have complex internal structures and physics which we choose not to include in our ‘ball atom’ model.
The real power of modelling is only realised however when we start to use the framework of mathematics. In mathematical modelling we are able to use the language of mathematics to unambiguously express the behaviour of our system. By reducing our models to mathematical relationships we can start to see similarities between different systems and discover symmetries and patterns present in nature. One great advantage of using mathematics is the predictive ability of mathematical models. There are numerous cases in history when theoretical work using modelling has predicted and discovered behaviour previously unobserved experimentally. The famous physicist Richard Feynman went so far as to say,
“People who wish to analyse nature without mathematics must settle for a reduced understanding.”
Mathematics together with modelling forms an indispensable tool in comprehending the world around us.
Today, mathematical modelling is used in a broad variety of areas and applications from predicting the weather to understanding the spread and transmission of disease. Aided by the advent of high speed computing, mathematical modelling promises many new interesting and profound discoveries in the future. This dynamic and challenging area of research is one I feel privileged to be a part of in some small way.
Alexander Nunn was one of the recipients of a 2016/17 AMSI Vacation Research Scholarship.