Tau

Greek alphabet
Αα	Alpha	Νν	Nu
Ββ	Beta	Ξξ	Xi
Γγ	Gamma	Οο	Omicron
Δδ	Delta	Ππ	Pi
Εε	Epsilon	Ρρ	Rho
Ζζ	Zeta	Σσς	Sigma
Ηη	Eta	Ττ	Tau
Θθ	Theta	Υυ	Upsilon
Ιι	Iota	Φφ	Phi
Κκ	Kappa	Χχ	Chi
Λλ	Lambda	Ψψ	Psi
Μμ	Mu	Ωω	Omega
Other characters
	Digamma		Stigma
	Heta		San
	Qoppa		Sampi
Greek diacritics

Tau (uppercase Τ, lowercase τ; Greek: Ταυ [ˈtaf]) is the 19th letter of the Greek alphabet. In the system of Greek numerals it has a value of 300. The name in English is pronounced /ˈtaʊ/, but in Modern Greek it is [ˈtaf]. This is because the pronunciation of the combination of Greek letters αυ has changed from ancient to modern times from one of [au] to either [av] or [af], depending on what follows (see Greek orthography).

Letters that arose from tau include Roman T and Cyrillic Te (Т, τ).

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 circle constant of one turn, the ratio of a circle circumference to its radius, 6.283...^[1], equal to 2π
• The perceived motion-gap in General Tau Theory, a psychological principle of perception.
• Torque, the rotational force in mechanics.
• In Calorimetry, tau is used as time variable, to avoid confusing t as temperature.
• Tuning and Analysis Utilities (TAU) performance evaluation tool, computer science ^[2]
• The elementary tau lepton particle in particle physics.
• The lifetime of a spontaneous emission process.
• The specific tax amount.
• The time constant of any device, such as an RC circuit.
• The dose interval in pharmacokinetics.
• Proper time in relativity.
• The symbol of continuity in electro-flux resonance.
• The symbol for tortuosity in hydrogeology.
• 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 with microtubules and is implicated in neurodegenerative diseases such as Alzheimer's Disease and FTLD.
• Shear stress in continuum mechanics.
• Divisor function in number theory.
• Sequence A002183 in the OEIS: Number of divisors of highly composite numbers
• The prefix of many stars, via the Bayer stellar designation system. (Tau Ceti is such a star.)
• The expressed period of the freerunning rhythm of an animal (circadian rhythm terminology), i.e., the length of the daily cycle of an animal when kept in constant light or constant darkness
• Kendall's tau rank correlation coefficient as a non-parametric correlation measure in statistics.

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.
• Hyundai Motors uses "Tau" to identify their recently introduced V8 engine.
• In Mobile Suit Gundam 00, imitation-solar furnaces used to power the three Throne Gundams and later the United Nations' GN-X and Alvatore are referred to as GN Drives Tau, as opposed to the original drives used by Celestial Being.
• In the game Half Life 2, the buggy uses a mounted Tau Cannon which fires bolts of electricity in rapid succession. It can also charge up a powered current.

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.

References