Tau

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

Greek alphabet
Α α Alpha	Ν ν Nu
Β β Beta	Ξ ξ Xi
Γ γ Gamma	Ο ο Omicron
Δ δ Delta	Π π ϖ Pi
Ε ε Epsilon	Ρ ρ Rho
Ζ ζ Zeta	Σ σ ς Sigma
Η η Eta	Τ τ Tau
Θ θ Theta	Υ υ Upsilon
Ι ι Iota	Φ φ Phi
Κ κ Kappa	Χ χ Chi
Λ λ Lambda	Ψ ψ Psi
Μ μ Mu	Ω ω Omega
Obsolete letters
Ϝ ϝ Digamma	Ϻ ϻ San
Ϙ ϙ Qoppa	Ϡ ϡ Sampi
Ϛ ϛ Stigma	Ϸ ϸ Sho
diacritics

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 (as the first syllable in "tower"), but in Modern Greek, this letter's name is pronounced tæf. 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" (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.

An essay written around 160 CE, 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.

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

• Torque, the rotational force in mechanics.
• 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.
• 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.
• Number of divisors of highly composite numbers
• a measure of the perceived motion-gap in General Tau Theory of perceptuomotor control.

Other uses of Tau:

• 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 Tau cross was put on men to distinguish those who lamented sin, although newer versions of the Bible have replaced the ancient term “Tau” with "mark" (Ezekiel 9:4). Resonating with this, the Hebrew form of the word Tau is pronounced tov, which means "marking."
• 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.
• The prefix of many stars, via the Bayer stellar designation system.