Using mathematical models to deal with the complexity in IT

You’ve probably seen the anticomplexity patent we recently got for the Simple Iterative Partitions (SIP) methodology. […] Our methodology uses a mathematical approach to finding the best possible balance between […] making the system small and minimizing functionality related complexity and keeping the system large and minimizing dependency related complexity.

We are actually already using mathematical models without realizing it. For example, Service-Oriented Architectures (SOA) are mathematically described as partitions, which is part of set theory. But typically we build SOA without understanding how partitions behave mathematically. So we don’t use a mathematical approach to find the best possible partitions and then translate those partitions into SOAs. Instead we design our SOAs through decompositional design. Decompositional design is highly arbitrary. It is a process that is mathematically defined as irrational. There are literally trillions of ways of decomposing a problem and the vast majority of these are sub optimal. So many large SOAs end up in the failure bin.
This patent also uses partitioning to build an SOA, but not with highly arbitrary decompositional design. Instead we drive the partitioning with equivalence relations. Unlike decompositional design, with its effectively random results, equivalence relation analysis is a highly directed process. It leads you to one and only one solution. And we can show mathematically that this solution is the simplest possible solution. It will also be the cheapest solution and the solution that will most likely line up with the business needs

Roger Sessions, CTO of ObjectWatch and an expert in software architecture, in a NetworkWorld interview.

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