Design presumes that PQRST are already known well enough to proceed. However, in the process of design any of PQRST may change. It is useful therefore to maintain a trace of the connection between conclusions and the PQRST that lead to them[Dasgupta 91, Gravell 90]. In USA DoD projects this traceability is a mandated requirement.
Notice that (in theory) P can be expressed as
Notice that since this is a model of systems rather than a model of designs, specifications, and implementations it is not natural to make a model of the relation (1st) implements (2nd). Instead the set of systems that are in P and/or R may be described by a separate universe of documentation and the (1st) implements (2nd) connects systems with their documentation. Thus a hierarchy of refinements may or may not exist between documentation, bot between systems. Loe Freijs has presented an interesting theory of this relation and the structure of designs[ Freijs 93].
My focus here is on the essence of the engineering ethic: making something more effective.
By Knaster-Tarski Theorem
Knaster 29
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Assume that costs and qualities accumulate as successive changes are made.
A triple in S><T><S can model a particular change to the system, and can have a value associated with it by:
??{Arrow's theorem|-real projects will have conflicts}?
We have an induced relation between systems:
The Travelling Salesperson Problem demonstrates that finding an optimal design is an NP-complete problem. The Busy Beaver problem for Turing Machines is an optimization problem as well (longest time), so it is clear that some Optimization problems are unsolvable.
If we can treat S as a topological space with
Simon's Satisficing heuristic - good enough now, is better than the best never[Simon 69, Dasgupta 91].
(14): F==>&{R, P, &[ q:Q]{s1 || t:T(s1 in t(s0) & v(s0,t,s1)(q) in V(q))} }.
A solution is stable with respect to a given quality if all changes can make it worse.
By analogy with Parieto's economic analysis there is probably a system from which all changes decrease some quality:
However some equilibria are not optimal.
Another attempt to optimize complex systems leads to the paradoxical trap of sub-optimization. In sub-optimization the problem is decomposed into parts and each part optimized separately. Although this is often successful there is no reason to expect the whole to be optimal as well. ...
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A design is structurally stable with respect to a factor if small changes in that factor leave the structure unchanged. Values of factors where this is not so are said to be on a 'catastrophe'[Thom, ...].
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