tau n : the 19th letter of the Greek alphabet

This article is about the letter of the Greek alphabet. For other uses, see Tau (disambiguation).

Tau (uppercase Τ, lowercase τ; []) is the 19th letter of the Greek alphabet. In the system of Greek numerals it has a value of 300. This letter in English is pronounced [taʊ], but in Modern Greek, this letter's name is pronounced [tuf]. This is because the pronunciation of the combination of Greek letters αυ has changed from ancient to modern times from one of /aʊ/ to either /av/ or /af/ (see Greek language#Orthography).

The symbolism of the cross was connected not only to the letter chi, but also to tau, the equivalent of the last letter in the Phoenician and Old Hebrew alphabets, and which was originally cruciform in shape.

Scientific uses

The lower-case letter τ is used as a symbol for:

• The perceived motion-gap in General Tau Theory, a psychological principle of perception.
• Torque, the rotational force in mechanics.
• Tuning and Analysis Utilities (TAU) performance evaluation tool, computer science http://tau.uoregon.edu
• The elementary tau lepton particle in particle physics.
• The lifetime of a spontaneous emission process.
• The time constant of any device, such as an RC circuit.
• Proper time in relativity.
• The symbol of continuity in electro-flux resonance.
• A coefficient of correlation — see Kendall's tau.
• The Golden ratio 1.618... (although φ (phi) is more common)
• Ramanujan's tau function in number theory.
• Tau in astronomy is a measure of opacity, or how much sunlight cannot penetrate the atmosphere.
• Tau in biochemistry is a protein associated to microtubules.
• Shear stress in continuum mechanics.
• Divisor function in number theory.
• Number of divisors of highly composite numbers
• The prefix of many stars, via the Bayer stellar designation system. (Tau Ceti is such a star.)

Other uses

• In ancient times, a symbol for life and/or resurrection, whereas the 8th letter of the Greek alphabet, theta, was considered the symbol of death.
• In Biblical times, the Taw was put on men to distinguish those who lamented sin, although newer versions of the Bible have replaced the ancient term “Taw” with "mark" (Ezekiel 9:4) or "signature" (Job 31:35). Its original sound value is a voiceless alveolar plosive, IPA /t/,

• Tau is usually considered as the symbol of Franciscan orders due to St. Francis' love for it, symbol of the redemption and of the Cross. Almost all Franciscan churches have painted a tau with two crossing arms, both with stigmata, the one of Jesus and the other of Francis; usually members of the Secular Franciscan Order wear a wooden τ in a string with three knots around the neck.
• Tau mission, a proposal to send a space probe to a thousand astronomical units from the Earth and Sun.
• The Tau Empire, one of the playable races in Warhammer 40K universe.
• In Freelancer, the Tau systems make up much of the Border Worlds.
• Surname for Chinese family
• Hyundai Motors uses "Tau" to identify their recently introduced V8 engine.

Miscellaneous

An essay written around 160 AD, attributed to Lucian, a mock legal prosecution called The Consonants at Law — Sigma v. Tau in the Court of Seven Vowels contains a reference to the attribution. Sigma petitions the court to sentence Tau to death by crucifixion, saying:

Men weep, and bewail their lot, and curse Cadmus with many curses for introducing Tau into the family of letters; they say it was his body that tyrants took for a model, his shape that they imitated, when they set up structures on which men are crucified. Stauros'' (cross) the vile engine is called, and it derives its vile name from him. Now, with all these crimes upon him, does he not deserve death, nay, many deaths? For my part I know none bad enough but that supplied by his own shape — that shape which he gave to the gibbet named stauros after him by men.''