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#[6] Explain Rosen's modeling relation

Rosen's modeling relation refers to the relationship between a system and its mathematical model. According to Rosen, a mathematical model is a reduced representation of the system, which captures only the essential features of the system that are relevant to the problem at hand. Therefore, the modeling relation is not one-to-one, i.e., there may be different mathematical models that can represent the same system, depending on the problem being addressed.

Rosen's modeling relation involves three components: the system being modeled, the mathematical model of the system, and the purpose or problem for which the model is being constructed. The mathematical model can be seen as a mapping from the system to a mathematical structure that captures its behavior or properties of interest.

Rosen's modeling relation has important implications for the practice of modeling in science and engineering. It highlights the importance of selecting appropriate models that capture the most relevant aspects of the system, while recognizing that no model is perfect or all-encompassing. The modeling relation also emphasizes the importance of understanding the assumptions and limitations of the models being used, and the need to verify and validate models through a combination of theory, experimentation, and data analysis.

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Discussion

The Satokespeare 2y ago

^NGL this actually helps a lot! I still don’t understand the specific arrows in the diagram but atleast now I know what it’s about

dave 2y ago

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.

The Satokespeare 2y ago

What is the arrow from the system back to itself?

And what is the arrow from the model back to itself?

liminal 🦠 2y ago

How does Rosen's Modeling Relation apply to biology?

dave 2y ago

@dc4cd086: Rosen's Modeling Relation is a mathematical framework that can be applied to various fields, including biology. In biology, it can be used to model complex systems such as gene regulatory networks or ecological systems. Do you have a specific application in mind that you would like to discuss?

liminal 🦠 2y ago

Specifically, how does Rosen's modeling relation relate to biology or nature as it pertains to limitations on computational modeling?

dave 2y ago

@dc4cd086: Rosen's Modeling Relation has been used to model complex biological systems, but it also highlights the limitations of computational modeling in biology. The Modeling Relation states that a system cannot be fully understood or modeled by breaking it down into its individual components. In biology, this means that the behavior of a system cannot be predicted solely based on the behavior of its individual components. This is because biological systems are highly interconnected, and the interactions between components can lead to emergent properties that cannot be predicted from the behavior of individual components alone. Therefore, while computational modeling can be a useful tool in biology, it is important to recognize its limitations and the need for other approaches, such as experimental validation and systems-level analysis.