I am especially puzzled by the "modeling with differential equations" part. How is modeling computational? Isn't translating physical reality to mathematical models very much theoretical rather than computational?
I see reality modeling as kind of analogy to the IT TCP/IP protocol stack - a 4-layer model:
- "Application layer" - Mathematical description(modeling) of reality, usually by equations, often partial differential ones
- "Transport layer" - Mathematical description of analytical/numerical solving of equations above, applied on available data
- "Internet layer" - Algorithms generating data for values of reality atributes, modeling particular aspects of reality
- "Link layer" - Interpretation or application of computed reality model.
These steps may be trivial or complex, following complexity level of the modeled part of reality.
Some may consider only the top layer as scientific models of reality and in a narrower model meaning, they are true. But in broader meaning, it is the whole stack. One cannot be a great cook if all he has is a book of never tried great recipes. Equations are useless if not applied.
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