One of the oldest canards in the “map to a common identifier/model” game is the allegation of a lurking combinatorial explosion.
It goes something like this: If you have identifiers A, B, and C, for a single subject, there are mappings to and from each identifier, hence:
- A -> B
- A -> C
- B -> A
- B -> C
- C -> A
- C -> B
Since no identifier maps to itself, the number of mappings is given by N * (N-1).
To avoid the overhead of tracking an ever increasing number of mappings between identifiers, the “cure” is to map all identifiers for a subject to a single identifier.
If something doesn’t feel right, congratulations! You’re right, something isn’t right. As Sam Hunting observed when I forwarded a draft of this post to him, if the mapping argument were true, it would not be possible to construct a thesaurus.
But it is possible to construct a thesaurus. So how to reconcile both the observed mappings and the existence of thesauri? The trick is that a thesaurus has only implicit mappings between identifiers for a subject. That assumption is glossed over in the combinatorial explosion argument. If mappings between the identifiers is left implied, the potential combinatorial explosion is defused. (You could also say the identifiers are collocated with each other. A term I will return to in other posts.)
Multiple identifiers for a subject lead to convenience and ease of use, not combinatorial explosions.