In closing, I want to make a few further (and somewhat miscellaneous) observations on the concept of orthogonality in general. First of all, the overall objective of orthogonal design, like that of normalization, is to reduce redundancy and thereby to avoid certain update anomalies that might otherwise occur. In fact, orthogonality complements normalization, in the sense that—loosely speaking—normalization reduces redundancy within relvars, while orthogonality reduces redundancy across relvars.
What’s more, orthogonality complements normalization in another way also. Consider once again the (bad) decomposition of relvar S into its projections SNC and STC, as illustrated in Figure 14-1. As we saw earlier, that decomposition abided by all of the usual normalization principles; in other words, it was orthogonality, not normalization, that told us the design was bad.
My next point is that, like the principles of normalization, The Principle of Orthogonal Design is basically just common sense—but (again like normalization) it’s formalized common sense, and the remarks I made in Chapter 1 in connection with such formalization apply here also. As I said in that chapter:
What design theory does is [formalize] certain commonsense principles, thereby opening the door to the possibility of mechanizing those principles (that is, incorporating them into computerized design tools). Critics of the theory often miss this point; they claim, quite rightly, that the ideas are mostly just common sense, but they don’t seem to realize it’s a significant achievement to state what common sense means in a precise and formal way.
My final point is this: Suppose we start with the usual parts relvar P, but decide for design purposes to decompose that relvar into a set of restrictions, as in the light vs. heavy parts example. Then the orthogonality principle tells us that the restrictions in question should be pairwise disjoint (also, of course, that their union—which will in fact be a disjoint union—should take us back to the original relvar). Note: In previous writings, I’ve referred to a decomposition that meets this requirement as an orthogonal decomposition. However, I now think it would be better to generalize this term and use it to mean any decomposition that abides by the orthogonality principle. This revised definition includes the earlier one as a special case.