Epsilon ε

Epsilon is the fifth Greek letter, from Phoenician he; its value is 5. Its later name 'e psilon' (bare e) distinguishes it from the diphthong 'ai'. Epsilon has a genuinely attested symbolic history: a mysterious letter E was displayed at the temple of Apollo at Delphi, and Plutarch devoted an essay, 'On the E at Delphi', to competing explanations of its meaning.

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. Epsilon'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 5 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.

Epsilon is one of several Greek letters that entered permanent mathematical use only through 19th-century calculus, long after the letter's ancient religious and numerical roots discussed elsewhere in this atlas were fixed. Augustin-Louis Cauchy and, later, Karl Weierstrass formalised the modern definition of a mathematical limit using epsilon to represent an arbitrarily small positive quantity, paired with delta to represent a correspondingly small change in an input variable, a convention now taught to virtually every student of calculus as the epsilon-delta definition.

By extension, mathematicians and scientists more informally use epsilon on its own to mean a negligibly small amount of anything, as in the phrase within epsilon of a value. Because ancient Greek used epsilon for a plain short vowel sound with no special weight, unlike the mother letters and long-vowel letters that carried extra classical significance, its selection for this modern technical role appears to reflect only its position early in the alphabet and its availability as an unclaimed symbol, rather than any inherited meaning; astronomers, following the Bayer star-naming convention of 1603, also use Epsilon to mark a constellation's fifth-brightest star.