November 27, 2003

Six nouns deep or more

It did cross my mind (I confess it) that Mark Liberman and Bill Poser might be making up their exotic-looking noun-noun-noun-noun-noun-noun compounds ( Volume Feeding Management Success Formula Award and East-ward Communist-Party Lifestyle Consultation Center and so on); but yesterday I found that I was being required to write a letter of formal response to the Narrative[1] Evaluation[2] Student[3] Grievance[4] Hearing[5] Committee[6] on my campus. This was because of a couple of students who objected to the F grades I gave them after a winter[1] quarter[2] undergraduate[3] computer[4] science[5] course[6] assignment[7] plagiarism[8] incident[9]. They really are all around us, these compounds that are six nouns deep or more.

Incidentally, if you want to know how to work out how many different bracketings there are for a string of N nouns, the answer is given by the function f such that f(1) = 1 and for each N > 0 you compute f(N) by taking the sum of all the products of all the f(i) values for all the non-singleton sequences of nonzero choices of i that add up to N.

For 2 this comes to 1, because the only list of positive integers that has more than one item and adds up to 2 is <1, 1>, and f(1) times f(1) = 1. For 3, the value of f comes out to 3, because we have 3 different lists of positive integers that add up to 3: <1, 1, 1>, <1, 2>, and <2, 1>; and when we take the products of all the f(i) for the integers i in each list we get f(1) times f(1) times f(1) = 1, and f(1) times f(2) = 1, and f(2) times f(1) = 1, and when we sum the products we get 1 + 1 + 1 = 3. This corresponds to the fact there are three bracketings for lifestyle consultation center: [lifestyle consultation center], [[lifestyle consultation] center], and [lifestyle [consultation center]].

To work out f(N) for N = 6, and thus the bracketings for volume feeding management success formula award or Narrative Evaluation Student Grievance Hearing Committee, just make a table of all the values of f for numbers from 1 up to 5; then make a list of all the lists of numbers that sum to 6; then take the value of f for each number in each list and write down those lists; then take the product of the numbers in each list and record those; and then sum all the products. This may take a while. In fact, for Americans it will entirely solve the problem of what to do with the long dull afternoons of the current four-day Thanksgiving holiday. Have a good one.

Posted by Geoffrey K. Pullum at November 27, 2003 12:07 PM