A physicist loose among the liberal arts

Relative Importance of Hobbit Families

Since it got such a positive response, I’m trying to turn the GIS distribution of names in Britain into a piece of real scholarship.  The first step is collecting and classifying Hobbit names.

Shortly after I started doing that, I was forcibly reminded that some characters just aren’t as important as others. Names that get mentioned a single time won’t be as carefully managed as those of more-important characters (even by JRRT), so they should carry less weight.  I’ll need some kind of quantitative measure for the concept of “importance”.  Searching about the Web for an hour produced nothing.  I see plenty of syllabuses from digital-humanities courses that ought to use such a thing, but no explicit references.  Perhaps it’s too trivial for them to mention. That’s an opportunity: What could be more appropriate for this blog than something too trivial for professors?  Onward!

Principles for quantitative importance of a character:

  1. A character must have a positive number of mentions in the story.  In most books, this would be a trivial requirement, but not in LotR.  There are lots of hobbits who are mentioned only in family trees in the Appendices.  I don’t know enough about them to say anything, so they get dropped.
  2. The difference between being mentioned on one page and being mentioned on ten is a big deal.  The difference between being mentioned on 10 pages and 11 is not so big.  The difference between 10 pages of mentions and 100 is a big deal, comparable to that between 1 and 10.

These two principles are just the definition of a multiplicative scale, like we use for sound.  It would be funny to express importance of characters in units of dBfrodo, but a proper solemnity dictates that we use a more information-theoretic definition:  the importance of a character will be the log2 of the number of pages on which that character is mentioned.  The page mentions are from the index of the 2002 single-volume edition of LotR from Houghton-Mifflin-Harcourt.

Hobbit families by importance: histogram

Fig. 1:Distribution of importance of hobbit families

For hobbit families in The Lord of the Rings, the distribution of importance looks like Figure 1. There are 28 family names mentioned in the story. Four are mentioned much more frequently than the others, which is reassuring.

There is a group of families that are mentioned only once. A larger group is mentioned thrice.  This is due to the repetition for comic effect of the list of Bilbo’s relatives at the Long-Expected Party.  Then there is a smaller group of hobbits who appear on dozens of pages.  These can be good guys or bad guys. [1]

Log plot of importance of families

Fig. 2 Family names ranked by mentions

On the far right are Baggins, Gamgee, Took, and Brandybuck, as expected.  Figure 2 is an attempt to reconcile my desire for a density graph like Figure 1 with the fact that logarithms don’t really mesh well with histograms.  The left-right position is the number of pages, the vertical position of the name is that family’s position in the bin in Figure 1.

I think this measure of importance will work.  It emphasizes the right things:  Farmer Cotton is “the chief person around here”, and his family duly shows up near the top.  It de-emphasizes the right things: Merry gets mentioned about 40% less than Pippin, but that washes out if importance is quoted with no fractional part.  Hobbits who barely exist at all, such as a few families in Bree whose only significance is that there are similar names in the Shire, have zero importance.

[1] Sauron is mentioned on 273 pages, which makes him two notches worse than the Sackville-Bagginses.[back]


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  1. Jeff Snider

    I humbly submit dH as the unit of measurement. I leave it to the reader to decide for themselves whether the H is the initial of *man or *bit.

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