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Answers to the Exercises of Chapter 1
Ex. 1.1 A is false. Modularity has no direct impact on incommensurate scaling. Its
impact on complexity comes from reducing the number of interconnections. B is true.
By eliminating unnecessary interconnections, modularity helps control unexpected
propagation of effects.
Ex. 1.2 A is false. Hierarchy has no direct impact on module size. Instead, it provides
structure for the interconnections among modules. Its primary impact on complexity
comes from constructing stable subassemblies and thus reducing the number of modules
that interact at each assembly point, so B, C, and D all are correct.
Ex. 1.3 Almost certainly false. Although there would be clusters of interconnections,
the existence of mutual friends would provide many non-hierarchical cross-connections.
Ex. 1.4
A. Yes. Digital hardware, which forms the basis for today’s computing, has for several
decades improved dramatically with time.
B. No. A complex system is hard to describe easily, and usually no single person
understands it all.
C. Yes. Interacting requirements and features are usually observed in complex
systems.
D. No. Complex systems often exhibit emergent properties, but more often than not
they come as an unpleasant surprise and it is more typical for them to be the cause
of worse performance than expected.
Ex. 1.5a 16 modules × 100 lines per module = 1600 lines.
Ex. 1.5b Ambiguity: If A calls B and B calls A, we can count that as either one or two
interconnections. Assume two interconnections; the alternative produces numbers half
as large. Each of the 16 modules contains at least 15 intermodule calls (at least one to
each of the other 15 modules), so the number of calls is at least 16 x 15 = 240.
