Mathematical and algorithmic models

  • Frames

Anyone who wants to show how forces work in inanimate nature gets a long way by assuming that laws are universal and unchanging. This assumption often makes it possible to translate findings into the language of mathematics — the language of numbers. This has advantages and disadvantages. An advantage is that you can write down universal relationships like

E=MC^{2}

at least when you assume that it is clear what E, M and C mean and that you can determine all three values ​​at a single particular moment.

Unlike in high school, there are few situations in which knowing universally valid laws is sufficient. The formula shows that energy is equivalent to mass, but does not provide insight into how, if desired, the transformation of a paper clip into energy (or vice versa) can be achieved. If you want to write something like that down, you need a different language and different assumptions. A language that connects contingencies (input value[s]) via mechanism[s] with output value[s]. In abstracto:

Here the formula has been loosely translated into a diagram, in which the mass of an object and the speed of light serve as input for a method (if it exists), a sequence of actions that de facto convert this mass into energy. The description of such a mechanism is an algorithm and requires means of expression other than numbers and arithmetic operators alone. Diagrams and algorithms are networks.