SQL and Relational Theory, 2nd Edition

RELATIONS ARE n-DIMENSIONAL

I’ve stressed the point several times that, while a relation can be pictured as a table, it isn’t a table. (To say it yet again, a picture of a thing isn’t the same as the thing.) Of course, it can be very convenient to think of a relation as a table; after all, tables are user friendly; indeed, as noted in Chapter 1, it’s the fact that we can think of relations, informally, as tables—sometimes more explicitly as “flat” or “two-dimensional” tables—that makes relational systems intuitively easy to understand and use, and makes it intuitively easy to reason about the way such systems behave. In other words, it’s a very nice property of the relational model that its basic data structure, the relation, has such an intuitively attractive pictorial representation.

Unfortunately, however, many people seem to have been blinded by that attractive pictorial representation into thinking that relations as such are “flat” or “two-dimensional.” But they’re not. Rather, if relation r has n attributes, then each tuple in r represents a point in a certain n-dimensional space (and the relation overall represents a set of such points). For example, each of the five tuples appearing in our usual suppliers relation represents a certain point in a certain 4-dimensional space (the four dimensions corresponding, of course, to the four attributes of that relation), and the relation overall can thus be said to be 4-dimensional. Thus, relations are n-dimensional, not two-dimensional. ...