Additional Math Pages & Resources

Tuesday, February 15, 2011

When is one not one? Part II

Yesterday's blog started a series of posts on the idea that some singular words imply more than one object. Like pair or dozen.

Today I'm going into dangerous territory - the intersection of the English language and math - to talk about other kinds of collective words. Note that these examples are specific to English. Other languages have the same sorts of issues but the examples will vary.

Have you heard of count nouns and mass nouns?

A count noun can be modified by a number (or number word) and the result makes sense.
  • For example, plates on a table. I can have some plates, one plate, ten plates, etc. I need only the noun and the number.
A mass noun cannot be directly modified by a number (or number word). If you try, the result makes no sense. With a mass noun, you must decide on a unit of measure (a measure word) and put a number word in front of your chosen unit, then put both in front of the mass noun.
  • For example, silverware on a table. I can have some forks, one knife, ten spoons, etc. But I only have a mass of some silverware, not three silverware or three silverwares.
  • Another example: water in a pool. I can have some water, but not three waters or seven waters. Using a unit of measure, I can have three gallons of water, or four buckets of water.
Measure words are shown in the preceding examples - gallons and buckets. In addition to formal units (gallons) there are informal measure words that do not represent a metric or standard unit, such as bucket, drop, crumb, grain, etc. Measure words are combined with numbers and mass nouns to describe how much of the "mass" you are interested in.

Another word (concept) - cumulativity - can be used to describe how words work when things are added together.
  • For example, a plate plus a plate equals two plates. Plates becomes plural.
  • Some water plus some water equals more water, not two waters. Waters does not become plural.
  • However, a brush fire plus a forest fire equals two fires, but if they join together, we have a fire again. English is the language full of exceptions. And fire can be singular and plural as needed.
Now we'll look at two Latin phrases, singulare tantum (only singular) and plurale tantum  (only plural). These words have unique forms:
  • For example, dirt, wealth, etc. come only in singular form. You may not say dirts or wealths.
  • For example, scissors, trousers, etc. only come in plural form. You may not say scissor or pajama.
Notice that we could add the measure word "pair" to the plurale tantum word scissors to get one pair of scissors or five pairs of scissors.

I'm going to continue on this theme again tomorrow. This pair of blogs will become a trio? triplet? triad?