@RSessions kindly gave me a quick overview of his SIP methodology, and how he calculates the complexity of a system of systems, based on the number of elements in each system and the number of connections between systems. The internal complexity of each system increases in a non-linear manner with the number of elements, and the external complexity increases with the number of connections between the systems, so the trick is to find a structure that optimizes the overall complexity.
Obviously we have to be clear as to what counts as an element (for example functions), and what counts as a connection. Using the SIP lens, it is possible to see how certain architectural styles (including those popular in the SOA world, such as hub-and-spoke or layered) only deliver simplicity (and the benefits of simplicity) if we can assume that only certain kinds of connection are significant. Roger's view is that this assumption is unwarranted and invalid.
In general, the so-called functional requirements are associated with the elements and the logical connections between them. In my view, architects also need to pay attention to the nature of the connections (coupling) because these will have important consequences on the structure and behaviour of the system as a whole. For example, synchronous versus asynchronous. At present, Roger's complexity calculations don't differentiate between different kinds of connection, so it would be interesting to investigate the costs and risks associated with different kinds of connections, to see how much difference it could make.
Roger's primary interest is in IT systems, but the same principles would appear to apply to processes and organizations. If you are running a factory, you have an architectural choice about the connection between say the moulding shop and the paint shop. With an asynchronous flow you have two loosely coupled operations separated by a buffer of work-in-progress; with a synchronous flow you have two tightly-coupled operations connected on a just-in-time basis. The former is a lot easier to manage, but it has an overhead in terms of inventory cost, storage cost, increased elapsed time, slower response to changes in demand, and so on. The latter may be more efficient under certain conditions, but it can be more volatile and the impact is much greater when something goes wrong anywhere in the process.
Intuitively, there seems to be a difference in complexity between these two solutions. The first is simpler, because the connection between the two systems is weaker; the second is more complex. With greater complexity comes greater power but also greater risk. Surely this is exactly the kind of architectural trade-off that enterprise architects should be qualified to consider. Roger's SIP methodology does give the architect a very simple lens to try and understand system-of-system complexity. Not everyone agrees with Roger's definition of complexity, and we can find some radically different notions of complexity for example in the Cynefin world, but at least Roger is raising some important issues. The EA world certainly needs to pay a lot more attention to questions like these.