B.5.TU:10 - Architectural Rationale

The method joins two directions of reasoning. Working backward from the question reveals the needed contribution. Working forward through the theory tests whether the available objects and operations actually supply it. Returning the consequence to use exposes conditions a correct internal calculation can leave unresolved.

B.5.RC and B.5.RA recover constructions and arguments. Here they contribute to assembling an application whose meaning and needed output may still be unsettled. C.29 constructs and tests mathematical correspondence; it can start before a mathematical object has been selected. This method adds recovery of how the unfamiliar theoretical account becomes usable at that point. A theory can also be used within its own mathematical setting, as in the composition case.

A complete explanation of the theory can be the appropriate learning project. For one urgent use, however, an adequate supplied application or bounded specialist result may settle the question sooner. The choice depends on the work the receiver must perform, including any need to criticize or change the method later.

A small successful application provides something to use and a basis for further inquiry. Broader generalization requires its own argument. If the application exposes a limitation in the theory, the resulting construction or counterexample can become material for developing its objects, rules or questions.