1.1 Systems

“Such knowledge is too wonderful for me; it is high, I cannot attain it.” — Psalm 139:6

To describe nature is tantamount to impossible. The world is too vast to take in all at once, so we focus on a portion of it—a system. It might be a single falling apple, a set of species in a forest, or a group of stars orbiting one another. Within that window, we pick a limited collection characteristic shared by all the members of the system, to evaluate how they interact, and how will the system evolve. Where will the apple fall? Which species will grow the most in the forest?

With a piece of the whole and measurable characteristics serving as parameters, we can then pick one to serve as our independent parameter, meaning that we are describing the other parameters in relation to it, making it the foundation of the model we create to describe the system. The most common independent parameter is time, because it keeps marching, in a uniform way independently of all other parameters in almost all situations, besides very few specific cases.

In our forest example, time moves independently of the size of the forest, and the number of animals, but both size and number of animals can vary in relation to time, allowing us to create models to guess how many animals the forest will have after a period.  Furthermore, those parameters have to be measured through a proper ruler. If we keep track of time in seconds at the beginning, then all of a sudden shift to keeping track through multiples of the time it takes for a train to go from London to Paris, something outside the system we are modelling, therefore impossible to know with our collection of parameters, our model falls apart. The same goes to the number of animals. If we consider at first each animal a single unit, just to shift to multiples of the amount that a 4 year old toddler can count with his finger before he grows bored, our system also falls apart. Keeping a coherent way to keep track of how the parameters of the systems evolve is paramount to making a proper model. That is why keeping track through multiples of padronized units like meters and second is so important. Those units are called a base through which we will build our measurements upon.