Tau

# Tau

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Encyclopedia
Tau is the 19th letter of the Greek alphabet
Greek alphabet
The Greek alphabet is the script that has been used to write the Greek language since at least 730 BC . The alphabet in its classical and modern form consists of 24 letters ordered in sequence from alpha to omega...

. In the system of Greek numerals
Greek numerals
Greek numerals are a system of representing numbers using letters of the Greek alphabet. They are also known by the names Ionian numerals, Milesian numerals , Alexandrian numerals, or alphabetic numerals...

it has a value of 300.

The name in English is pronounced ˈ, but in modern Greek
Modern Greek
Modern Greek refers to the varieties of the Greek language spoken in the modern era. The beginning of the "modern" period of the language is often symbolically assigned to the fall of the Byzantine Empire in 1453, even though that date marks no clear linguistic boundary and many characteristic...

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
Greek orthography
The orthography of the Greek language ultimately has its roots in the adoption of the Greek alphabet in the 9th century BC. Some time prior to that, one early form of Greek, Mycenaean, was written in Linear B, although there was a lapse of several centuries between the time Mycenaean stopped being...

).

Letters that arose from tau include Roman T
T
T is the 20th letter in the basic modern Latin alphabet. It is the most commonly used consonant and the second most common letter in the English language.- History :Taw was the last letter of the Western Semitic and Hebrew alphabets...

and Cyrillic Te
Te (Cyrillic)
Te is a letter of the Cyrillic alphabet.It commonly represents the voiceless alveolar plosive , like the pronunciation of ⟨t⟩ in "tick".-History:...

(Т, τ).

The letter occupies the Unicode
Unicode
Unicode is a computing industry standard for the consistent encoding, representation and handling of text expressed in most of the world's writing systems...

slots U+03C4 (lowercase) and U+03A4 (uppercase). In HTML
HTML
HyperText Markup Language is the predominant markup language for web pages. HTML elements are the basic building-blocks of webpages....

, they can be produced with named entities (&tau; and &Tau;), decimal references
Numeric character reference
A numeric character reference is a common markup construct used in SGML and other SGML-related markup languages such as HTML and XML. It consists of a short sequence of characters that, in turn, represent a single character from the Universal Character Set of Unicode...

(&#964; and &#932;), or hexadecimal references
Numeric character reference
A numeric character reference is a common markup construct used in SGML and other SGML-related markup languages such as HTML and XML. It consists of a short sequence of characters that, in turn, represent a single character from the Universal Character Set of Unicode...

(&#x3C4; and &#x3A4;).

## Modern usage

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

### Mathematics

• The golden ratio
Golden ratio
In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989...

(1.618...), although φ (phi) is more common.
• Ramanujan's tau function in number theory.
• The divisor function
Divisor function
In mathematics, and specifically in number theory, a divisor function is an arithmetical function related to the divisors of an integer. When referred to as the divisor function, it counts the number of divisors of an integer. It appears in a number of remarkable identities, including relationships...

in number theory, also denoted d or σ0.
• Torsion of a curve in differential geometry.
• Kendall's tau rank correlation coefficient as a non-parametric correlation measure in statistics.
• A proposed alternative constant equal to 2
Tau (2π)
Tau is a mathematical constant equal to the ratio of any circle's circumference to its radius, and has a value of approximately 6.28318531. This number also appears in many common formulas, often because it is the period of some very common functions — sine, cosine, , and others that involve...

.

### Physics

• In the physical sciences, tau is sometimes used as time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

variable, to avoid confusing t as temperature.
• The tau lepton
Tau lepton
The tau , also called the tau lepton, tau particle or tauon, is an elementary particle similar to the electron, with negative electric charge and a spin of . Together with the electron, the muon, and the three neutrinos, it is classified as a lepton...

, an elementary particle in particle physics.
• Tau in astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

is a measure of opacity
Opacity (optics)
Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc...

, or how much sunlight cannot penetrate the atmosphere.
• Proper time
Proper time
In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events. The proper time depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a smaller elapsed time between two...

in relativity.
• The symbol for tortuosity
Tortuosity
Tortuosity is a property of curve being tortuous . There have been several attempts to quantify this property. Tortuosity is commonly used to describe diffusion in porous media...

in hydrogeology.
• Torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

, the rotational force in mechanics.
• The lifetime of a spontaneous emission
Spontaneous emission
Spontaneous emission is the process by which a light source such as an atom, molecule, nanocrystal or nucleus in an excited state undergoes a transition to a state with a lower energy, e.g., the ground state and emits a photon...

process.
• The prefix of many stars, via the Bayer
Bayer designation
A Bayer designation is a stellar designation in which a specific star is identified by a Greek letter, followed by the genitive form of its parent constellation's Latin name...

stellar designation system. (Tau Ceti
Tau Ceti
Tau Ceti is a star in the constellation Cetus that is spectrally similar to the Sun, although it has only about 78% of the Sun's mass. At a distance of just under 12 light-years from the Solar System, it is a relatively close star. Tau Ceti is metal-deficient and so is thought to be less likely to...

is such a star.)
• Shear stress
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

in continuum mechanics.
• The time constant
Time constant
In physics and engineering, the time constant, usually denoted by the Greek letter \tau , is the risetime characterizing the response to a time-varying input of a first-order, linear time-invariant system.Concretely, a first-order LTI system is a system that can be modeled by a single first order...

of any device, such as an RC circuit
RC circuit
A resistor–capacitor circuit ', or RC filter or RC network, is an electric circuit composed of resistors and capacitors driven by a voltage or current source...

.

### Biology

• The dose interval in pharmacokinetics
Pharmacokinetics
Pharmacokinetics, sometimes abbreviated as PK, is a branch of pharmacology dedicated to the determination of the fate of substances administered externally to a living organism...

.
• Tau (protein) in biochemistry is a protein associated with microtubules and is implicated in neurodegenerative diseases such as Alzheimer's Disease and FTLD.
• 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.
• The core variable in General Tau Theory
General Tau Theory
General tau theory deals with the guidance of bodily movements. All movements of the body, and within the body, require guided closure of action-gaps. An action-gap, generally defined, is the changing gap between a current state and a goal state...

.

## Symbolism

• In ancient times, Tau was used as a symbol for life
Life
Life is a characteristic that distinguishes objects that have signaling and self-sustaining processes from those that do not, either because such functions have ceased , or else because they lack such functions and are classified as inanimate...

and/or resurrection
Resurrection
Resurrection refers to the literal coming back to life of the biologically dead. It is used both with respect to particular individuals or the belief in a General Resurrection of the dead at the end of the world. The General Resurrection is featured prominently in Jewish, Christian, and Muslim...

, whereas the eighth letter of the Greek alphabet, theta
Theta
Theta is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth...

, was considered the symbol of death
Death
Death is the permanent termination of the biological functions that sustain a living organism. Phenomena which commonly bring about death include old age, predation, malnutrition, disease, and accidents or trauma resulting in terminal injury....

.
• In Biblical times, the Taw
Taw
Taw may refer to:* Taw , the twenty-second letter in many Semitic alphabets* Taw , the collection of all cardinal numbers* the shooter marble in a game of marbles* The River Taw in Devon, England* a method to produce white leather...

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
Voiceless alveolar plosive
The voiceless alveolar plosive is a type of consonantal sound used in many spoken languages. The symbol in the International Phonetic Alphabet that represents voiceless dental, alveolar, and postalveolar plosives is , and the equivalent X-SAMPA symbol is t...

, IPA /t/.
• The symbolism of the cross
Cross
A cross is a geometrical figure consisting of two lines or bars perpendicular to each other, dividing one or two of the lines in half. The lines usually run vertically and horizontally; if they run obliquely, the design is technically termed a saltire, although the arms of a saltire need not meet...

was connected not only to the letter chi
Chi (letter)
Chi is the 22nd letter of the Greek alphabet, pronounced as in English.-Greek:-Ancient Greek:Its value in Ancient Greek was an aspirated velar stop .-Koine Greek:...

, but also to tau, the equivalent of the last letter in the Phoenician
Phoenician alphabet
The Phoenician alphabet, called by convention the Proto-Canaanite alphabet for inscriptions older than around 1050 BC, was a non-pictographic consonantal alphabet, or abjad. It was used for the writing of Phoenician, a Northern Semitic language, used by the civilization of Phoenicia...

and Old Hebrew alphabets, and which was originally cruciform in shape; see Cross of Tau
Cross of Tau
The Cross of Tau, named after the Greek letter it resembles, is suspected to have originated with the Egyptians. When a King was initiatied into the Egyptian mysteries a tau was placed against his lips. It has been a symbol to many cultures before Christianity, including a mention in the Old...

.
• An essay written around 160 AD, attributed to Lucian
Lucian
Lucian of Samosata was a rhetorician and satirist who wrote in the Greek language. He is noted for his witty and scoffing nature.His ethnicity is disputed and is attributed as Assyrian according to Frye and Parpola, and Syrian according to Joseph....

, a mock legal prosecution called The Consonants at Law — Sigma v. Tau in the Court of Seven Vowels contains a reference to the cross 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
Gibbet
A gibbet is a gallows-type structure from which the dead bodies of executed criminals were hung on public display to deter other existing or potential criminals. In earlier times, up to the late 17th century, live gibbeting also took place, in which the criminal was placed alive in a metal cage...

named
stauros after him by men.
• Tau is usually considered as the symbol of Franciscan
Franciscan
Most Franciscans are members of Roman Catholic religious orders founded by Saint Francis of Assisi. Besides Roman Catholic communities, there are also Old Catholic, Anglican, Lutheran, ecumenical and Non-denominational Franciscan communities....

orders due to St. Francis' love for it, symbol of the redemption and of the Cross
Cross
A cross is a geometrical figure consisting of two lines or bars perpendicular to each other, dividing one or two of the lines in half. The lines usually run vertically and horizontally; if they run obliquely, the design is technically termed a saltire, although the arms of a saltire need not meet...

. Almost all Franciscan churches have painted a tau with two crossing arms, both with stigmata
Stigmata
Stigmata are bodily marks, sores, or sensations of pain in locations corresponding to the crucifixion wounds of Jesus, such as the hands and feet...

, the one of Jesus and the other of Francis; usually members of the Secular Franciscan Order
Secular Franciscan Order
thumb|rigth|Lapel pin of Secular Franciscan Order.The Secular Franciscan Order is a community of Catholic men and women, of any of the Rites in communion with Rome , in the world who seek to pattern their lives after Christ in the spirit of St. Francis of Assisi. Secular Franciscans are...

wear a wooden τ in a string with three knots around the neck.