Estimating the number of unseen species: How many words did Shakespeare know?

Shakespeare wrote 31534 different words, of which 14376 appear only once, 4343 twice, etc. The question considered is how many words he knew but did not use. A parametric empirical Bayes model due to Fisher and a nonparametric model due to Good & Toulmin are examined. The latter theory is augmented using linear programming methods. We conclude that the models are equivalent to supposing that Shakespeare knew at least 35000 more words.