Sigma σ

Sigma is the eighteenth Greek letter, from Phoenician shin ('tooth'); its value is 200. Sigma has a final form (used at the end of words) distinct from its medial form. Its best-known symbolic use, the summation sign of mathematics, is modern; in antiquity it carried no special mystical tradition beyond isopsephy. The Greek letters doubled as numerals in the Milesian (alphabetic) system, in which each letter carried a fixed value; the practice of summing a word's letters into a number, called isopsephy, is the Greek counterpart of Hebrew gematria and appears in inscriptions, the Greek Magical Papyri and early Christian texts. Sigma's Phoenician ancestry places it in a borrowing whose exact point of contact, somewhere among Al Mina, Cyprus, Crete and Euboea in the Aegean world, is still disputed, though the borrowing itself, conventionally dated to around the 8th century BCE, is agreed to be the ancestor of every European alphabet still in use, including the Latin one covered elsewhere in this atlas.

The Greeks' own contribution was to give vowels dedicated letters of their own, something the consonant-only Phoenician script never did. Its isopsephy value of 200 belongs to the Milesian alphabetic numeral system, which also needed three further, otherwise obsolete letters, digamma (also called stigma), koppa and sampi, to cover every value from 1 up to 900; none of the three survives among the 24 letters in ordinary use today.

Sigma is the only Greek letter in ordinary modern use with two distinct lowercase forms depending on its position in a word: the familiar sigma is used everywhere except at the end of a word, where Greek instead uses a separate final form, a distinction fixed by the Byzantine minuscule reform of roughly the 9th century CE and preserved in Greek spelling ever since, unlike most other Greek letters, which kept one lowercase shape regardless of position. That positional split has no equivalent among the Latin letters covered elsewhere in this atlas, though Hebrew final forms, also covered in this atlas, follow a broadly similar principle.

Modern mathematics uses sigma in both its cases for entirely separate technical purposes: a capital sigma denotes summation, adding together a sequence of terms, a notation introduced in the 18th and 19th centuries, while a lowercase sigma denotes standard deviation in statistics, a measure of how spread out a set of values is around its mean.

The Six Sigma quality-management methodology, developed at Motorola in the 1980s, takes its name directly from that statistical sense of the letter. In the Milesian numeral system, discussed elsewhere in this atlas, sigma carries the value two hundred, a role wholly separate from either of its modern mathematical senses.