The limit of four
In practice, when we want to distinguish a quantity we have recourse to our memories and/or to acquired techniques such as comparison, splitting, mental grouping, or, best of all, actual counting.
Everyone can see the sets of one, of two, and of three objects and most people can see the set of four. But that's about the limit of
our natural ability to numerate. Beyond four, quantities are vague, and our eyes alone cannot tell us how many things there are. Are there fifteen or twenty plates in that pile? Thirteen or fourteen cars parked along the street? Eleven or twelve bushes in that garden. ten or fifteen steps on this staircase, nine, eight or six windows in the front of that house? The correct answers cannot be just seen. We have to count to find out!
The eye is simply not a sufficiently precise measuring tool: its natural number-ability virtually never exceeds four.
There are many traces of the "limit of four" in different languages and cultures. There are several Oceanic languages, for example, which distinguish between nouns in the singular, the dual, the triple, the quadruple, and the plural (as if in English we were to say one bird, two birdo, three birdi, four birdu, many birds).
In Latin, the names of the first four numbers (unus, duos, tres, quatuor) decline at least in part like other nouns and adjectives, but from five (quinque), Latin numerical terms are invariable. Similarly, Romans gave "ordinary" names to the first four of their sons (names like Marcus, Servius, Appius, etc.), but the fifth and subsequent sons were named only by a numeral: Quintus (the fifth), Sixtus (the sixth), Septimus (the seventh), and so on. In the original Roman calendar (the so-called "calendar of Romulus"), only the first four months had names (Martius, Aprilis, Maius, Junius), the fifth to tenth being referred to by their order-number: Quintilis, Sextilis, September, October, November, December.
Think about the almost universal counting-device called (in England) the "five-barred gate". It is used by innkeepers keeping
a tally or "slate" of drinks ordered, by card-players totting up scores, by prisoners keeping count of their days in jail, even by examiners working out the mark-distribution of a cohort of students:
