Mathematical models are all around us. We may not think about it, but we engage in mathematical 'modeling' all the time.
'It looks like we may get rain. Should I bring an umbrella? But if I do, I may forget it on the bus or at the restaurant... Perhaps bring a coat instead? On the other hand...'
We are constantly doing these calculations, often with incomplete or uncertain data, indirectly pondering upon probabilities and finally arriving at a decision. We model all the time, and how could we not?
Models are deliberate simplifications of reality, providing us value by allowing the 'main' properties of something to stand out from the noise. Sometimes, the models can then serve us better than reality itself.
Bird guide books are examples of this. Instead of using actual photographs of birds, they often contain hand-drawn pictures where an illustrator has reduced the less useful information and just slightly exaggerated the character traits of a species, for enabling simpler identification. Similarly, a caricature of the famous Swedish author August Strindberg may be found, also by his close friends, to better depict and capture the person than an actual photograph would.
Comparably, bio-mathematical fatigue models provide a cleaner and more refined representation of a more complex phenomena. They make the known 'nature' of the effects of the crew roster 'stand out' to be observed and actioned. We know that reality, the full picture, is something different. Reality has many more facets to it and also varies more from person to person. We would need a massive amount of data to capture this accurately and model the 'reality' as it plays out. But that level of detail would not necessarily help us much. It more often serves us better to take a step back and have the defining features in clear view.
Read more about models? Please consider the book 'Scientific models: red atoms, white lies and black boxes in a yellow book' by Philip Gerlee and Torbjörn Lundh from 2016 (link).
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