In mathematics:

The eighteenth letter of the Greek alphabet, capital form Σ and lower-case σ . At the end of a word a different lower-case form ς is used. The HTML codes for these are Σ and σ and ς

It derives from a Semitic letter such as Hebrew ש sin, though the name sigma is perhaps influenced by that of a different sibilant, ס samekh. It occupies the position of sin. It gave rise to the Roman letter S.

The basic sound was S in Ancient Greek, and continues to be S in Modern Greek. The only significant variation was before voiced consonants such as B, G, L, M, N: so Lesbos and Smyrna were pronounced Lezbos, Zmyrna. This also continues in Modern Greek. It was also voiced before D but the combination ZD was usually written as ζ zeta.

Where most dialects had it doubled, SS, the Attic dialect of Athens used ττ TT. This probably derived from an original TT that changed in all other dialects, and would have had an intermediate value like TS at some point before the classical period, but there is no evidence that Attic σσ was anything other than a normal doubled SS in pronunciation.

Note that the group GM was pronounced ngm as in hangman in Ancient Greek (see agma), so the name was actually said singma.

An old variant form of the capital letter was C, which gave rise to the Cyrillic letter of that shape, representing S, as in CCCP for the USSR. This must not be confused with the unrelated Roman letter C, a derivative of Γ gamma.

Ancient Greek S came from Proto-Indo-European S in some positions, such as the end of a word (noun ending -ος -os) and before consonants (αστηρ astêr = English star = Latin stella from ster-la). However, S before a vowel changed to H long before the classical period (even before Mycenaean), and disappeared between vowels. So hex-, herpet-, hemi- are the Greek elements for 'six, serpent, half' (Latin semi-).

The old genitive ending was -osyo (cf. Sanskrit -asya). In Homeric Greek this has changed to -oio, and it later went to -oo then classical -ou.

Instances of sigma before vowels in classical Greek derive from other sources, such as tw, tj, thj (earlier dhj), and sw, or borrowings: the second person pronoun συ su corresponds to Latin tu, English thou. The word sêma 'sign' is related to Sanskrit dhyâman 'thought'. The word selênê 'moon' comes from earlier swelannâ. (Actually, sw also lost its s normally, but the origin of selênê was confirmed to me by Miguel Carrasquer Vidal, the linguist I most respect.)

In the Laconian dialect sigma was used where other dialects have theta. It is possible that this was pronounced not S but Th as in thin. The letter theta later changed to this value throughout Greek, so perhaps Laconian was the first to use it.

Sigma is the evil robotic mastermind in the Mega Man X series of video games. Like Dr. Wily no matter how many times Mega Man X destroys one incarnation of Sigma, he always returns for another fight. Sigma's first appearance was in Mega Man X. The story goes that Sigma was once the leader of a group of Reploid police forces, but one day for some unknown reason he rebelled against the other Reploids and began to lead a battle to destroy humanity so that robots could become the dominant species in society. Reploids that turn against humanity are known as Mavericks. The Mavericks take their orders from Sigma, and members of his force wear a capital sigma Σ somewhere on their bodies. Maverick machinery also bears this insignia. At the end of the first game in the series X destroyed Sigma, but after the credits a transmission from Sigma appeared and he claimed that someday he'll be back.

True to his word he reappeared in Mega Man X2. This time around Sigma had ordered a group of three Mavericks, known as the X Hunters, to destroy X and recover the three pieces of X's best friend and fellow fighter, Zero. X's actions in the game shape the outcome of the ending. If X recovers all three pieces, then Zero appears at the end of the game to assist X. If the X Hunters get the pieces, however, Zero appears at the end of the game at Sigma's side, forcing Zero and X to engage in battle. Also, just to make things more interesting, Sigma claims that he knows Zero's "secret". X eventually destroys Sigma again.

Mega Man X3 established that Sigma's true form is not of a robot, but of a computer virus. Reploids that are infected become Mavericks. Aided by the Reploid-turned-Maverick scientist Dr. Doppler, Sigma acquired a massive battle armor. Just as X was cornered by the Maverick leader, some help arrives (either Zero or Dr. Doppler, depending on the outcome of other plot elements in the game) and infects Sigma with an anti-virus. Sigma is once again presumed dead.

When the Repliforce began to turn rebelious in Mega Man X4, X and Zero were dispatched to investigate the cause and destroy their former team members. In the end it was revealed that Sigma was pulling the strings behind the scenes, but X and Zero caught up to him and blew his latest form to bits. Unfortunately it wasn't long before Sigma returned and launched a direct attack on Reploid headquarters in Mega Man X5. X and Zero destroyed him, but then discovered that the attack was a trap. By blowing up Sigma's latest form, the Sigma Virus spread to all corners of the planet. There are a number of outcomes for this game, but the one that is considered to have "really" happened is that after Sigma was destroyed (again) he engages a self-distruct program on his latest body, blasting Zero to pieces and causing major damage to X. Both are discovered and repaired by the time Mega Man X6 rolls around and the seemingly endless battle takes place again with Sigma coming out the loser.

Sigma has also appeared in the two Game Boy Color games in the Mega Man X series, Mega Man Xtreme and Mega Man Xtreme 2. These games are composed of elements from their console cousins and consist of minimal plot elements. In the first Xtreme Sigma hacks into the Repliforce computer and begins to destroy data, so X enters cyberspace to find and eliminate him. In Xtreme 2 Sigma is extracting the DNA souls of Reploids and using them to create new weapons for his fighting force. After X destroys Sigma all of the stolen souls return to the Reploid victims.

Sigma is a main fixture of the Mega Man X series, so it's almost guarenteed that he'll return for future battles.

Sig"ma (?), n.; pl. Sigmas (#). [L., from Gr. , .]

The Greek letter S, or s). It originally had the form of the English C.


© Webster 1913.

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