Comment by logicallee | Hacker News Reader

Comment by logicallee | Hacker News Reader

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This is a very good point - Aesop Rock, for example, uses one unique word every 5 words (7k unique in 35k), and if this does not stop, maybe he would continue and we would find the same average in 70k or 120k words. After all, you still have to have filler words like "to", "a", "the", "have", etc - he could be saturating the spots where he can put uniques.

So this could substantially underrepresent vocabularies. There are only so many unique words you can put in a sentence. As an extreme, if we looked at the first hundred words of every rapper, we would not find a hundred unique words in any of them: (due to repeats of grammatically common words) even though, clearly, all rappers have a vocabulary over a hundred.

I wonder if this is a fatal flaw? How can we estimate where the distortion stops? (For example, if someone uses 1000 words in their first 35,000, intuitively this seems to imply to me that's most of their stock. But if someone uses 5,000 in 35,000 - that is not so clear at all.)

The paper I linked to in my previous comment uses Zipf's law (briefly, the frequency of word use is inversely proportional to its rank; more at http://en.wikipedia.org/wiki/Zipf%27s_law) to estimate the "distortion." This should produce a better estimate than the naive method, but there are still problems: the plot on the Wikipedia page shows that Zipf's law is not a particularly good fit to word frequency for Wikipedia past the ~10,000th word, and it's not clear that rap music represents a typical natural language corpus. It is probably still possible to devise a correction if one knows how word use frequencies are distributed.

A second related problem that that paper touches on toward the end is that sequential words from the same text are not independent samples from an author's vocabulary. Two artists may have the same vocabulary, but if one artist uses more non-sequiturs, fewer articles, fewer repeated phrases, or generally tries to use more unique words within a given song, then that artist will come out ahead in the measure used here. I'm not sure how much of a problem this really is for comparing lyrics between artists (depending on what is of interest, it may actually be desirable), but it may explain the poor showings for Shakespeare and Melville, since prose is likely to repeat words more frequently than rap lyrics for reasons unrelated to the authors' vocabularies. (FWIW, even conservative estimates put Shakespeare's vocabulary at >15,000 words, which would be hard to measure in a sample of 35,000 words.)

OP here. vocab is non-linear:

mdaniels.com/vocab/scatter.png

so the average would change as your sample size grows.

35K was the threshold where things didn't get garbled (like the 100 word example that you mention).

The threshold is also impacted by who I include. If I went to 50K, I'd lose out on rappers like Drake.

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