Jonathan Mayhew at Bemsha Swing takes Nick Piombino to task for writing that

You could multiply the dictionary by a thousand and still not have enough words to describe what most people think and feel in a single day.

Jonathan's comment:

Learning new words, after a certain point, doesn't allow for more expression. It just multiplies the number of choices; like giving a bored child more toys it does not address the real problem; and in fact aggravates the problem. Boredom is not a function of the lack of toys.

My sympathies are with Jonathan. But I wonder if the analogy to children's toys is a fair one. We could also say that giving a restless intellect more books does not address the real problem; and in fact it aggravates the problem. Or that giving a well-dressed person more clothes does not address the real problem. The different analogies evoke different emotions, and none of them are quite right for this case.

Isn't the "real problem" that describing what someone thinks and feels takes more than a one-word message? We often make a game from multiple toys, or read one book in the context of others, or coordinate items of clothing, but words are combinatoric on a whole different scale.

If you can't express what you feel, the problem is probably not too few word choices, and it's probably not too many word choices either. Maybe your real problem is getting in touch with your feelings, or connecting your amygdala to your cerebral cortex, or finding the right metaphor, or coming to terms with the essential ineffability of experience. But as a practical matter, whatever you can do to express yourself will comes down to choosing a sequence of words. And no matter how big your vocabulary is, it's dwarfed by the exponential explosion of combinatoric possibilities when you combine words into phrases.

Jonathan expressed a similar idea this way:

Even a *small* vocabulary of 10,000 words is susceptible to a number of combinations that I am too lazy to calculate right now, but it's a big, big number.

The simple form of the calculation doesn't take much work: there are 10,000^2 = 10^8 = a hundred million two-word sequences; 10,000^3 = 10^12 = one trillion three-word sequences, and so on. Syntactic constraints lower the effective base somewhat -- there aren't really 10,000 choices at every step -- but whatever the base is, as you add more words, the total keeps on growing exponentially.

So Nick Piombino's lament might be parodied like this:

You could use base 10,000 and still not have enough numbers to count the ways that I love you.

Touching, but stupid. There's no number you can express in base 10,000 that you can't also express in base 10, or in base 2 for that matter. That's the genius of a positional number system.

Words are different from numbers, and sometimes a new word is a real help in thinking as well as in communicating. We humans are not cognitively adapted to working in binary -- base 10,000 or base 100,000 is more like it, if you think of different words as crudely analogous to different digits. Still, once your vocabulary gets to a reasonable size, the need for more words is probably not your key conceptual or communicative problem.

As Jonathan suggested in email to me, Piombino's lament is a common kind of linguification, based on the idea that the set of things a language can express is equivalent to the set of definitions in its dictionary. This is the same fallacy that lies behind the "no word for X" and "N words for X" syndromes. But it's also a case where adding one new term to the dictionary does help express what some of us think and feel.

Posted by Mark Liberman at September 21, 2006 06:32 AM