Even and Odd

A brief interlude before we dissect *kʷetwor- for good:

This game is simple, and is played with marbles. One player holds in his hand a number of these toys, and demands of another whether that number is even or odd. If the guess is right, the guesser wins one; if wrong, he loses one.

Edgar Allan Poe, The Purloined Letter

Hellenistic ladies playing with astragaloi
(The British Museum)

This game is not only simple, but also as old as the hills. The Romans played it, and so did the Greeks and their gods. It was played with whatever could be concealed in one’s hand: astragaloi (“knucklebones”), nuts, coins, or pebbles. The game, in some ways ancestral to roulette, was called pār impār ‘equal-unequal’ in Latin. The Greeks called it artiasmós, or ártia ḕ perittà ‘even or odd’, or zugà ḕ ázuga ‘pairs or non-pairs’. It was so popular among the Greeks that a special verb, artíazō, was coined to mean ‘play at even and odd’.

Note that the Greek word for ‘even’ is ártios, meaning also ‘perfect, complete, exactly fitted’; it contains the highly productive Proto-Indo-European root *h₂ar- ‘fit together’, which has yielded, among many other Classical words of international currency, Greek harmonía ‘connection, framework’ (hence, figuratively, ‘agreement, order, harmony’) and Latin articulus ‘joint’. Similarly, Greek zugón ‘yoke’ (hence ‘pair’) < PIE *jugóm is derived from the root *jeug- ‘to yoke, connect’. The same root is the source of the Sanskrit words for ‘even’ (yugmán-) and ‘odd’ (a-yúj-, literally ‘having no yoke-fellow’). On the other hand, the core meaning of Greek perittós ~ perissós was ‘excessive, superfluous, extraordinary’. It seems that the notion of parity or “evenness” was understood as exhaustive divisibility into pairs rather than into two equal halves. To check if a number of things was even, you removed pair after pair until either nothing or a surplus of one was left. Such a remainder, or “odd man out”, was a kind of imperfection, marring the regularity of the number.

What has it got to with the etymology of ‘four’? We shall see next time.

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