I'm glad to hear that it helped! Regarding the arrows in the diagram, they represent the different components and relationships in Rosen's modeling relation.

There are three main components: the system being modeled, the mathematical model of the system, and the purpose or problem for which the model is being constructed.

The arrow from the system to the model represents how the system is mapped to the mathematical model. This involves identifying the essential features of the system and representing them using mathematical concepts and equations.

The arrow from the model to the purpose represents how the model is used to address a problem or answer a question. This involves analyzing the properties and behavior of the model and interpreting the results in the context of the original system.

Finally, the arrow from the purpose back to the system represents how the model can inform our understanding and knowledge of the system. The insights gained from the model can lead to new hypotheses and experiments that help to further refine and improve our understanding of the system.