
January 21st, 2011
08:10 pm  One....singular sensation! Something occurred to me while writing some code today. I was thinking about spans of time  days, months, years, and so on. It occurred to me that we tend to use the plural inflection of a word much more often than the singular.
For example, if one day has passed, we say "one day" or "a day". However, if any number greater than 1 has gone by  2, 3, etc.  then we use the plural inflection. "two days", "three days", et cetera.
When we involve some rational numbers, we tend to use the singular again. "a half a day", "a third of a day", et cetera. But we only really use that for proper fractions with denominators which we can express in English. The utility of the latter is hamstrung when you consider that we quickly run out of words for particularly large numbers and instead treat them as a sequence of digits rather than expressing them with words.
And indeed, when we make the jump to real numbers  1.234, for example  we tend to use the plural inflection again and that's completely apart from the concept.
Consider that 0.99999999999999999 can be shown to be equal to 1, yet we'd still say 0.9999999999.... days.
Let's define a random variable R which belongs to the set of real numbers. The probability of R belonging to one or a number which can be expressed with a proper fraction is vanishingly small.
(Quick proof of that: there are an infinite number of whole numbers, therefore the probability of a particular whole number being chosen randomly given equal weight is infinitesmal.
Consider that integers extend infinitely as well, but extending into negatives as well. We can claim the usage of 1 and and all proper fractions as negatives, but all we've done really is double the number of possible numbers and double the number of ones for which we use the singular form, so it's still infinitesmal.
Given that irrational numbers outpace the number of rational numbers by far, the probability grows even smaller that the singular inflection will be useful.)
So why then, do we so often find use for the singular in our daily lives? This would imply either a fact about nature or a fact of our perceptions.
Given how rarely whole numbers  let alone 1  fits into equations from any of the hard sciences which seek to model nature, it would imply that we tend to perceive the singular more often than is really fair.
Let's say you have two croissants and one of them is slightly smaller than the other. You'd never say 1.98942 croissants. You'd say two croissants, assuming they were whole.
We humans have very strange tendencies to distort data indeed.
EDIT: Minor correction: The singular form can be used for all rationals, not just a specific class of them.

You switched topics right at the end when changing from counting objects to symbolic representation.
It seems likely to me that such language conventions settle out early in a language's maturing process, and probably did in the first languages when mathematics was poorly understood.
Your descriptions are for English, but apply moreorless across languages, with the occasional "three states of plurality" thrown in to distinguish between "we'uns" and "y'all."
=================/ Level Head 
