Category: Abstract/Art/Design

Prayer is an invocation or act that seeks to activate a rapport with an object of worship through deliberate communication. In the narrow sense, the term refers to an act of supplication or intercession directed towards a deity or a deified ancestor. More generally, prayer can also have the purpose of thanksgiving or praise, and in comparative religion is closely associated with more abstract forms of meditation and with charms or spells.^[1]

Prayer can take a variety of forms: it can be part of a set liturgy or ritual, and it can be performed alone or in groups. Prayer may take the form of a hymn, incantation, formal creedal statement, or a spontaneous utterance in the praying person.

The act of prayer is attested in written sources as early as five thousand years ago. Today, most major religions involve prayer in one way or another; some ritualize the act, requiring a strict sequence of actions or placing a restriction on who is permitted to pray, while others teach that prayer may be practised spontaneously by anyone at any time.

Scientific studies regarding the use of prayer have mostly concentrated on its effect on the healing of sick or injured people. The efficacy of prayer in faith healing has been evaluated in numerous studies, with contradictory results.

Etymology[edit]

The English term prayer is from Medieval Latin: precaria, lit. 'petition, prayer'.^[2] The Vulgate Latin is oratio, which translates Greek προσευχή^[3] in turn the Septuagint translation of Biblical Hebrew תְּפִלָּה tĕphillah.^[4]

Act of prayer[edit]

Various spiritual traditions offer a wide variety of devotional acts. There are morning and evening prayers, graces said over meals, and reverent physical gestures. Some Christians bow their heads and fold their hands. Some Native Americans regard dancing as a form of prayer.^[5] Hindus chant mantras.^[6] Jewish prayer may involve swaying back and forth and bowing.^[7] Muslim prayer involves bowing, kneeling and prostration, while some Sufis whirl.^[8] Quakers often keep silent.^[9] Some pray according to standardized rituals and liturgies, while others prefer extemporaneous prayers; others combine the two.

Typologies and modalities[edit]

Christian circles often look to Friedrich Heiler (1892-1967), whose systematic Typology of Prayer lists six types of prayer: primitive, ritual, Greek cultural, philosophical, mystical, and prophetic.^[10] Some forms of prayer require a prior ritualistic form of cleansing or purification, such as in ghusl and wudhu.^[11]

Prayer may occur privately and individually (sometimes called affective prayer),^[12] or collectively, shared by or led on behalf of fellow-believers of either a specific faith tradition or a broader grouping of people.^[13] Prayer can be incorporated into a daily "thought life", in which one is in constant communication with a god. Some people pray throughout all that is happening during the day and seek guidance as the day progresses. This is actually regarded as a requirement in several Christian denominations,^[14] although enforcement is neither possible nor desirable.^[opinion] There can be many different answers to prayer, just as there are many ways to interpret an answer to a question, if there in fact comes an answer.^[14] Some may experience audible, physical, or mental epiphanies. If indeed an answer comes, the time and place it comes is considered random.^{[citation needed]}

Some traditions distinguish between contemplative and meditative prayer.^[15]

Outward acts that may accompany prayer include anointing with oil;^[16] ringing a bell;^[17] burning incense or paper;^[18] lighting a candle or candles; facing a specific direction (e.g., towards Mecca^[19] or the East);^[20] and making the sign of the cross. One less noticeable act related to prayer is fasting.

A variety of body postures may be assumed, often with specific meaning (mainly respect or adoration) associated with them: standing; sitting; kneeling; prostrate on the floor; eyes opened; eyes closed; hands folded or clasped; hands upraised; holding hands with others; a laying on of hands and others. Prayers may be recited from memory, read from a book of prayers, or composed spontaneously or "impromptu".^[21] They may be said, chanted, or sung. They may or may not have a musical accompaniment. There may be a time of outward silence while prayers are offered mentally. Often, there are prayers to fit specific occasions, such as the blessing of a meal, the birth or death of a loved one, other significant events in the life of a believer, or days of the year that have special religious significance. Details corresponding to specific traditions are outlined below.

Origins and early history[edit]

Anthropologically, the concept of prayer is closely related to that of surrender and supplication. The traditional posture of prayer in medieval Europe is kneeling or supine with clasped hands, in antiquity more typically with raised hands. The early Christian prayer posture was standing, looking up to heaven, with outspread arms and bare head. This is the pre-Christian, pagan prayer posture (except for the bare head, which was prescribed for males in I Corinthians 11:4, in Roman paganism, the head had to be covered in prayer). Certain Cretan and Cypriote figures of the Late Bronze Age, with arms raised, have been interpreted as worshippers. Their posture is similar to the "flight" posture, a crouching posture with raised hands related to the universal "hands up" gesture of surrender. The kneeling posture with clasped hands appears to have been introduced only with the beginning high medieval period, presumably adopted from a gesture of feudal homage.^[23]

Although prayer in its literal sense is not used in animism, communication with the spirit world is vital to the animist way of life. This is usually accomplished through a shaman who, through a trance, gains access to the spirit world and then shows the spirits' thoughts to the people. Other ways to receive messages from the spirits include using astrology or contemplating fortune tellers and healers.^[24]

Some of the oldest extant literature, such as the Kesh temple hymn (c. 26th century BC), is liturgy addressed to deities and thus technically "prayer". The Egyptian Pyramid Texts of about the same period similarly contain spells or incantations addressed to the gods. In the loosest sense, in the form of magical thinking combined with animism, prayer has been argued as representing a human cultural universal, which would have been present since the emergence of behavioral modernity, by anthropologists such as Sir Edward Burnett Tylor and Sir James George Frazer.^[25]

Reliable records are available for the polytheistic religions of the Iron Age, most notably Ancient Greek religion, which strongly influenced Roman religion. These religious traditions were direct developments of the earlier Bronze Age religions. Ceremonial prayer was highly formulaic and ritualized.^[26][27]

In ancient polytheism, ancestor worship is indistinguishable from theistic worship (see also euhemerism). Vestiges of ancestor worship persist, to a greater or lesser extent, in modern religious traditions throughout the world, most notably in Japanese Shinto, Vietnamese folk religion, and Chinese folk religion. The practices involved in Shinto prayer are heavily influenced by Buddhism; Japanese Buddhism has also been strongly influenced by Shinto in turn. Shinto prayers quite frequently consist of wishes or favors asked of the kami, rather than lengthy praises or devotions. The practice of votive offering is universal and is attested at least since the Bronze Age. In Shinto, this takes the form of a small wooden tablet, called an ema.

Prayers in Etruscan were used in the Roman world by augurs and other oracles long after Etruscan became a dead language. The Carmen Arvale and the Carmen Saliare are two specimens of partially preserved prayers that seem to have been unintelligible to their scribes and whose language is full of archaisms and difficult passages.^[28]

Roman prayers and sacrifices were envisioned as legal bargains between deity and worshipper. The Roman principle was expressed as do ut des: "I give, so that you may give." Cato the Elder's treatise on agriculture contains many examples of preserved traditional prayers; in one, a farmer addresses the unknown deity of a possibly sacred grove, and sacrifices a pig in order to placate the god or goddess of the place and beseech his or her permission to cut down some trees from the grove.^[29]

Celtic, Germanic and Slavic religions are recorded much later, and much more fragmentarily, than the religions of classical antiquity. They nevertheless show substantial parallels to the better-attested religions of the Iron Age. In the case of Germanic religion, the practice of prayer is reliably attested, but no actual liturgy is recorded from the early (Roman era) period. An Old Norse prayer is on record in the form of a dramatization in skaldic poetry. This prayer is recorded in stanzas 2 and 3 of the poem Sigrdrífumál, compiled in the 13th century Poetic Edda from earlier traditional sources, where the valkyrie Sigrdrífa prays to the gods and the earth after being woken by the hero Sigurd.^[30] A prayer to Odin is mentioned in chapter 2 of the Völsunga saga where King Rerir prays for a child. In stanza 9 of the poem Oddrúnargrátr, a prayer is made to "kind wights, Frigg and Freyja, and many gods,^[31] In chapter 21 of Jómsvíkinga saga, wishing to turn the tide of the Battle of Hjörungavágr, Haakon Sigurdsson eventually finds his prayers answered by the goddesses Þorgerðr Hölgabrúðr and Irpa.^[32] Folk religion in the medieval period produced syncretisms between pre-Christian and Christian traditions. An example is the 11th-century Anglo-Saxon charm Æcerbot for the fertility of crops and land, or the medical Wið færstice.^[33] The 8th-century Wessobrunn Prayer has been proposed as a Christianized pagan prayer and compared to the pagan Völuspá^[34] and the Merseburg Incantations, the latter recorded in the 9th or 10th century but of much older traditional origins.^[35]

In Australian Aboriginal mythology, prayers to the "Great Wit" are performed by the "clever men" and "clever women", or kadji.^{[citation needed]} These Aboriginal shamans use maban or mabain, the material that is believed to give them their powers.^[36] The Pueblo Indians are known to have used prayer sticks, that is, sticks with feathers attached as supplicatory offerings. The Hopi Indians used prayer sticks as well, but they attached to it a small bag of sacred meal.^[37]

Approaches to prayer[edit]

Direct petitions[edit]

There are different forms of prayer. One of them is to directly appeal to a deity to grant one's requests.^[38] Some have termed this as the social approach to prayer.^[39]

Atheist arguments against prayer are mostly directed against petitionary prayer in particular. Daniel Dennett argued that petitionary prayer might have the undesirable psychological effect of relieving a person of the need to take active measures.^[40]

This potential drawback manifests in extreme forms in such cases as Christian Scientists who rely on prayers instead of seeking medical treatment for family members for easily curable conditions which later result in death.^[41]

Christopher Hitchens (2012) argued that praying to a god which is omnipotent and all-knowing would be presumptuous. For example, he interprets Ambrose Bierce's definition of prayer by stating that "the man who prays is the one who thinks that god has arranged matters all wrong, but who also thinks that he can instruct god how to put them right."^[42]

Educational approach[edit]

In this view, prayer is not a conversation. Rather, it is meant to inculcate certain attitudes in the one who prays, but not to influence. Among Jews, this has been the approach of Rabbenu Bachya, Rabbi Yehuda Halevi, Joseph Albo, Samson Raphael Hirsch, and Joseph B. Soloveitchik. This view is expressed by Rabbi Nosson Scherman in the overview to the Artscroll Siddur (p. XIII).

Among Christian theologians, E.M. Bounds stated the educational purpose of prayer in every chapter of his book, The Necessity of Prayer. Prayer books such as the Book of Common Prayer are both a result of this approach and an exhortation to keep it.^[43]

Rationalist approach[edit]

In this view, the ultimate goal of prayer is to help train a person to focus on divinity through philosophy and intellectual contemplation (meditation). This approach was taken by the Jewish scholar and philosopher Maimonides^[44] and the other medieval rationalists.^[45] It became popular in Jewish, Christian, and Islamic intellectual circles, but never became the most popular understanding of prayer among the laity in any of these faiths. In all three of these faiths today, a significant minority of people still hold to this approach.

In a rationalist approach, praying encompasses three aspects. First, 'logos', as the "idea" of the sender, secondly 'rhemata' as the words to express the idea, and thirdly 'rhemata' and 'logos', to where the idea is sent (e.g. to God, Allah). Thus praying is not a conversation with God, or Jesus but a one-way direction to the divine.^[46] Among the Abrahamic religions, Islam, Orthodox Christianity and Hasidic Judaism are likely most adhering to this concept, also because it does not allow secondary mythologies, and has taken its spiritual roots from Hellenistic philosophy, particularly from Aristotle.^[47]

Similarly in Hinduism, the different divinities are manifestations of one God with associated prayers. However, many Indians – particularly Hindus – believe that God can be manifest in people, including in people of lower castes, such as Sadhus.^[48]

Experiential approach[edit]

In this approach, the purpose of prayer is to enable the person praying to gain a direct experience of the recipient of the prayer (or as close to direct as a specific theology permits). This approach is very significant in Christianity and widespread in Judaism (although less popular theologically). In Eastern Orthodoxy, this approach is known as hesychasm. It is also widespread in Sufi Islam, and in some forms of mysticism. It has some similarities with the rationalist approach, since it can also involve contemplation, although the contemplation is not generally viewed as being as rational or intellectual.

Christian and Roman Catholic traditions also include an experiential approach to prayer within the practice of lectio divina. Historically a Benedictine practice, lectio divina involves the following steps: a short scripture passage is read aloud; the passage is meditated upon using the mind to place the listener within a relationship or dialogue with the text; recitation of a prayer; and concludes with contemplation. The Catechism of the Catholic Church describes prayer and meditation as follows:^[49]

Meditation engages thought, imagination, emotion, and desire. This mobilization of faculties is necessary in order to deepen our convictions of faith, prompt the conversion of our heart, and strengthen our will to follow Christ. Christian prayer tries above all to meditate on the mysteries of Christ, as in lectio divina or the rosary. This form of prayerful reflection is of great value, but Christian prayer should go further: to the knowledge of the love of the Lord Jesus, to union with him.

The experience of God within Christian mysticism has been contrasted with the concept of experiential religion or mystical experience because of a long history or authors living and writing about experience with the divine in a manner that identifies God as unknowable and ineffable, the language of such ideas could be characterized paradoxically as "experiential", as well as without the phenomena of experience.^[50]

The notion of "religious experience" can be traced back to William James, who used a term called "religious experience" in his book, The Varieties of Religious Experience.^{[51][citation not found]} The origins of the use of this term can be dated further back.

In the 18th, 19th, and 20th centuries, several historical figures put forth very influential views that religion and its beliefs can be grounded in experience itself. While Kant held that moral experience justified religious beliefs, John Wesley in addition to stressing individual moral exertion thought that the religious experiences in the Methodist movement (paralleling the Romantic Movement) were foundational to religious commitment as a way of life.^[52] According to catholic doctrine, Methodists lack a ritualistic and rational approach to praying but rely on individualistic and moralistic forms of worship in direct conversation

A rainbow is an optical phenomenon caused by refraction, internal reflection and dispersion of light in water droplets resulting in a continuous spectrum of light appearing in the sky.^[1] The rainbow takes the form of a multicoloured circular arc.^[2] Rainbows caused by sunlight always appear in the section of sky directly opposite the Sun. Rainbows can be caused by many forms of airborne water. These include not only rain, but also mist, spray, and airborne dew.

Rainbows can be full circles. However, the observer normally sees only an arc formed by illuminated droplets above the ground,^[3] and centered on a line from the Sun to the observer's eye.

In a primary rainbow, the arc shows red on the outer part and violet on the inner side. This rainbow is caused by light being refracted when entering a droplet of water, then reflected inside on the back of the droplet and refracted again when leaving it.

In a double rainbow, a second arc is seen outside the primary arc, and has the order of its colours reversed, with red on the inner side of the arc. This is caused by the light being reflected twice on the inside of the droplet before leaving it.

Visibility[edit]

Rainbows can be observed whenever there are water drops in the air and sunlight shining from behind the observer at a low altitude angle. Because of this, rainbows are usually seen in the western sky during the morning and in the eastern sky during the early evening. The most spectacular rainbow displays happen when half the sky is still dark with raining clouds and the observer is at a spot with clear sky in the direction of the Sun. The result is a luminous rainbow that contrasts with the darkened background. During such good visibility conditions, the larger but fainter secondary rainbow is often visible. It appears about 10° outside of the primary rainbow, with inverse order of colours.

The rainbow effect is also commonly seen near waterfalls or fountains. In addition, the effect can be artificially created by dispersing water droplets into the air during a sunny day. Rarely, a moonbow, lunar rainbow or nighttime rainbow, can be seen on strongly moonlit nights. As human visual perception for colour is poor in low light, moonbows are often perceived to be white.^[4]

It is difficult to photograph the complete semicircle of a rainbow in one frame, as this would require an angle of view of 84°. For a 35 mm camera, a wide-angle lens with a focal length of 19 mm or less would be required. Now that software for stitching several images into a panorama is available, images of the entire arc and even secondary arcs can be created fairly easily from a series of overlapping frames.

From above the Earth such as in an aeroplane, it is sometimes possible to see a rainbow as a full circle. This phenomenon can be confused with the glory phenomenon, but a glory is usually much smaller, covering only 5–20°.

The sky inside a primary rainbow is brighter than the sky outside of the bow. This is because each raindrop is a sphere and it scatters light over an entire circular disc in the sky. The radius of the disc depends on the wavelength of light, with red light being scattered over a larger angle than blue light. Over most of the disc, scattered light at all wavelengths overlaps, resulting in white light which brightens the sky. At the edge, the wavelength dependence of the scattering gives rise to the rainbow.^[5]

The light of a primary rainbow arc is 96% polarised tangential to the arc.^[6] The light of the second arc is 90% polarised.

Number of colours in a spectrum or a rainbow[edit]

For colours seen by the human eye, the most commonly cited and remembered sequence is Isaac Newton's sevenfold red, orange, yellow, green, blue, indigo and violet,^[7][a] remembered by the mnemonic Richard Of York Gave Battle In Vain, or as the name of a fictional person (Roy G. Biv). The initialism is sometimes referred to in reverse order, as VIBGYOR. More modernly, the rainbow is often divided into red, orange, yellow, green, cyan, blue and violet.^[9] The apparent discreteness of main colours is an artefact of human perception and the exact number of main colours is a somewhat arbitrary choice.

Newton, who admitted his eyes were not very critical in distinguishing colours,^[10] originally (1672) divided the spectrum into five main colours: red, yellow, green, blue and violet. Later he included orange and indigo, giving seven main colours by analogy to the number of notes in a musical scale.^[7][b][11] Newton chose to divide the visible spectrum into seven colours out of a belief derived from the beliefs of the ancient Greek sophists, who thought there was a connection between the colours, the musical notes, the known objects in the Solar System, and the days of the week.^[12][13] Scholars have noted that what Newton regarded at the time as "blue" would today be regarded as cyan, and what Newton called "indigo" would today be considered blue.^[8][9][14]

The colour pattern of a rainbow is different from a spectrum, and the colours are less saturated. There is spectral smearing in a rainbow owing to the fact that for any particular wavelength, there is a distribution of exit angles, rather than a single unvarying angle.^[15] In addition, a rainbow is a blurred version of the bow obtained from a point source, because the disk diameter of the sun (0.5°) cannot be neglected compared to the width of a rainbow (2°). Further red of the first supplementary rainbow overlaps the violet of the primary rainbow, so rather than the final colour being a variant of spectral violet, it is actually a purple. The number of colour bands of a rainbow may therefore be different from the number of bands in a spectrum, especially if the droplets are particularly large or small. Therefore, the number of colours of a rainbow is variable. If, however, the word rainbow is used inaccurately to mean spectrum, it is the number of main colours in the spectrum.

Moreover, rainbows have bands beyond red and violet in the respective near infrared and ultraviolet regions, however, these bands are not visible to humans. Only near frequencies of these regions to the visible spectrum are included in rainbows, since water and air become increasingly opaque to these frequencies, scattering the light. The UV band is sometimes visible to cameras using black and white film.^[16]

The question of whether everyone sees seven colours in a rainbow is related to the idea of linguistic relativity. Suggestions have been made that there is universality in the way that a rainbow is perceived.^[17][18] However, more recent research suggests that the number of distinct colours observed and what these are called depend on the language that one uses, with people whose language has fewer colour words seeing fewer discrete colour bands.^[19]

Explanation[edit]

Light rays enter a raindrop from one direction (typically a straight line from the Sun), reflect off the back of the raindrop, and fan out as they leave the raindrop. The light leaving the rainbow is spread over a wide angle, with a maximum intensity at the angles 40.89–42°. (Note: Between 2 and 100% of the light is reflected at each of the three surfaces encountered, depending on the angle of incidence. This diagram only shows the paths relevant to the rainbow.)

White light separates into different colours on entering the raindrop due to dispersion, causing red light to be refracted less than blue light.

When sunlight encounters a raindrop, part of the light is reflected and the rest enters the raindrop. The light is refracted at the surface of the raindrop. When this light hits the back of the raindrop, some of it is reflected off the back. When the internally reflected light reaches the surface again, once more some is internally reflected and some is refracted as it exits the drop. (The light that reflects off the drop, exits from the back, or continues to bounce around inside the drop after the second encounter with the surface, is not relevant to the formation of the primary rainbow.) The overall effect is that part of the incoming light is reflected back over the range of 0° to 42°, with the most intense light at 42°.^[20] This angle is independent of the size of the drop, but does depend on its refractive index. Seawater has a higher refractive index than rain water, so the radius of a "rainbow" in sea spray is smaller than that of a true rainbow. This is visible to the naked eye by a misalignment of these bows.^[21]

The reason the returning light is most intense at about 42° is that this is a turning point – light hitting the outermost ring of the drop gets returned at less than 42°, as does the light hitting the drop nearer to its centre. There is a circular band of light that all gets returned right around 42°. If the Sun were a laser emitting parallel, monochromatic rays, then the luminance (brightness) of the bow would tend toward infinity at this angle if interference effects are ignored (see Caustic (optics)). But since the Sun's luminance is finite and its rays are not all parallel (it covers about half a degree of the sky) the luminance does not go to infinity. Furthermore, the amount by which light is refracted depends upon its wavelength, and hence its colour. This effect is called dispersion. Blue light (shorter wavelength) is refracted at a greater angle than red light, but due to the reflection of light rays from the back of the droplet, the blue light emerges from the droplet at a smaller angle to the original incident white light ray than the red light. Due to this angle, blue is seen on the inside of the arc of the primary rainbow, and red on the outside. The result of this is not only to give different colours to different parts of the rainbow, but also to diminish the brightness. (A "rainbow" formed by droplets of a liquid with no dispersion would be white, but brighter than a normal rainbow.)

The light at the back of the raindrop does not undergo total internal reflection, and most of the light emerges from the back. However, light coming out the back of the raindrop does not create a rainbow between the observer and the Sun because spectra emitted from the back of the raindrop do not have a maximum of intensity, as the other visible rainbows do, and thus the colours blend together rather than forming a rainbow.^[22]

A rainbow does not exist at one particular location. Many rainbows exist; however, only one can be seen depending on the particular observer's viewpoint as droplets of light illuminated by the sun. All raindrops refract and reflect the sunlight in the same way, but only the light from some raindrops reaches the observer's eye. This light is what constitutes the rainbow for that observer. The whole system composed by the Sun's rays, the observer's head, and the (spherical) water drops has an axial symmetry around the axis through the observer's head and parallel to the Sun's rays. The rainbow is curved because the set of all the raindrops that have the right angle between the observer, the drop, and the Sun, lie on a cone pointing at the sun with the observer at the tip. The base of the cone forms a circle at an angle of 40–42° to the line between the observer's head and their shadow but 50% or more of the circle is below the horizon, unless the observer is sufficiently far above the earth's surface to see it all, for example in an aeroplane (see below).^[23][24] Alternatively, an observer with the right vantage point may see the full circle in a fountain or waterfall spray.^[25]

Mathematical derivation[edit]

It is possible to determine the perceived angle which the rainbow subtends as follows.^[26]

Given a spherical raindrop, and defining the perceived angle of the rainbow as 2φ, and the angle of the internal reflection as 2β, then the angle of incidence of the Sun's rays with respect to the drop's surface normal is 2β − φ. Since the angle of refraction is β, Snell's law gives us

sin(2β − φ) = n sin β,

where n = 1.333 is the refractive index of water. Solving for φ, we get

φ = 2β − arcsin(n sin β).

The rainbow will occur where the angle φ is maximum with respect to the angle β. Therefore, from calculus, we can set dφ/dβ = 0, and solve for β, which yields

${displaystyle eta _{ ext{max}}=arccos left({frac {2{sqrt {-1+n^{2}}}}{{sqrt {3}}n}} ight)approx 40.2^{circ }.}$

Substituting back into the earlier equation for φ yields 2φ_max ≈ 42° as the radius angle of the rainbow.

For red light (wavelength 750nm, n = 1.330 based on the dispersion relation of water), the radius angle is 42.5°; for blue light (wavelength 350nm, n = 1.343), the radius angle is 40.6°.

Variations[edit]

Double rainbows[edit]

A secondary rainbow, at a greater angle than the primary rainbow, is often visible. The term double rainbow is used when both the primary and secondary rainbows are visible. In theory, all rainbows are double rainbows, but since the secondary bow is always fainter than the primary, it may be too weak to spot in practice.

Secondary rainbows are caused by a double reflection of sunlight inside the water droplets. Technically the secondary bow is centred on the sun itself, but since its angular size is more than 90° (about 127° for violet to 130° for red), it is seen on the same side of the sky as the primary rainbow, about 10° outside it at an apparent angle of 50–53°. As a result of the "inside" of the secondary bow being "up" to the observer, the colours appear reversed compared to those of the primary bow.

The secondary rainbow is fainter than the primary because more light escapes from two reflections compared to one and because the rainbow itself is spread over a greater area of the sky. Each rainbow reflects white light inside its coloured bands, but that is "down" for the primary and "up" for the secondary.^[27] The dark area of unlit sky lying between the primary and secondary bows is called Alexander's band, after Alexander of Aphrodisias, who first described it.^[28]

Twinned rainbow[edit]

Unlike a double rainbow that consists of two separate and concentric rainbow arcs, the very rare twinned rainbow appears as two rainbow arcs that split from a single base.^[29] The colours in the second bow, rather than reversing as in a secondary rainbow, appear in the same order as the primary rainbow. A "normal" secondary rainbow may be present as well. Twinned rainbows can look similar to, but should not be confused with supernumerary bands. The two phenomena may be told apart by their difference in colour profile: supernumerary bands consist of subdued pastel hues (mainly pink, purple and green), while the twinned rainbow shows the same spectrum as a regular rainbow. The cause of a twinned rainbow is believed to be the combination of different sizes of water drops falling from the sky. Due to air resistance, raindrops flatten as they fall, and flattening is more prominent in larger water drops. When two rain showers with different-sized raindrops combine, they each produce slightly different rainbows which may combine and form a twinned rainbow.^[30] A numerical ray tracing study showed that a twinned rainbow on a photo could be explained by a mixture of 0.40 and 0.45 mm droplets. That small difference in droplet size resulted in a small difference in flattening of the droplet shape, and a large difference in flattening of the rainbow top.^[31]

Meanwhile, the even rarer case of a rainbow split into three branches was observed and photographed in nature.^[32]

Full-circle rainbow[edit]

In theory, every rainbow is a circle, but from the ground, usually only its upper half can be seen. Since the rainbow's centre is diametrically opposed to the Sun's position in the sky, more of the circle comes into view as the sun approaches the horizon, meaning that the largest section of the circle normally seen is about 50% during sunset or sunrise. Viewing the rainbow's lower half requires the presence of water droplets below the observer's horizon, as well as sunlight that is able to reach them. These requirements are not usually met when the viewer is at ground level, either because droplets are absent in the required position, or because the sunlight is obstructed by the landscape behind the observer. From a high viewpoint such as a high building or an aircraft, however, the requirements can be met and the full-circle rainbow can be seen.^[33][34] Like a partial rainbow, the circular rainbow can have a secondary bow or supernumerary bows as well.^[35] It is possible to produce the full circle when standing on the ground, for example by spraying a water mist from a garden hose while facing away from the sun.^[36]

A circular rainbow should not be confused with the glory, which is much smaller in diameter and is created by different optical processes. In the right circumstances, a glory and a (circular) rainbow or fog bow can occur together. Another atmospheric phenomenon that may be mistaken for a "circular rainbow" is the 22° halo, which is caused by ice crystals rather than liquid water droplets, and is located around the Sun (or Moon), not opposite it.

Supernumerary rainbows [edit]

In certain circumstances, one or several narrow, faintly coloured bands can be seen bordering the violet edge of a rainbow; i.e., inside the primary bow or, much more rarely, outside the secondary. These extra bands are called supernumerary rainbows or supernumerary bands; together with the rainbow itself the phenomenon is also known as a stacker rainbow. The supernumerary bows are slightly detached from the main bow, become successively fainter along with their distance from it, and have pastel colours (consisting mainly of pink, purple and green hues) rather than the usual spectrum pattern.^[37] The effect becomes apparent when water droplets are involved that have a diameter of about 1 mm or less; the smaller the droplets are, the broader the supernumerary bands become, and the less saturated their colours.^[38] Due to their origin in small droplets, supernumerary bands tend to be particularly prominent in fogbows.^[39]

Supernumerary rainbows cannot be explained using classical geometric optics. The alternating faint bands are caused by interference between rays of light following slightly different paths with slightly varying lengths within the raindrops. Some rays are in phase, reinforcing each other through constructive interference, creating a bright band; others are out of phase by up to half a wavelength, cancelling each other out through destructive interference, and creating a gap. Given the different angles of refraction for rays of different colours, the patterns of interference are slightly different for rays of different colours, so each bright band is differentiated in colour, creating a miniature rainbow. Supernumerary rainbows are clearest when raindrops are small and of uniform size. The very existence of supernumerary rainbows was historically a first indication of the wave nature of light, and the first explanation was provided by Thomas Young in 1804.^[40]

Reflected rainbow, reflection rainbow[edit]

When a rainbow appears above a body of water, two complementary mirror bows may be seen below and above the horizon, originating from different light paths. Their names are slightly different.

A reflected rainbow may appear in the water surface below the horizon.^[41] The sunlight is first deflected by the raindrops, and then reflected off the body of water, before reaching the observer. The reflected rainbow is frequently visible, at least partially, even in small puddles.

A reflection rainbow may be produced where sunlight reflects off a body of water before reaching the raindrops, if the water body is large, quiet over its entire surface, and close to the rain curtain. The reflection rainbow appears above the horizon. It intersects the normal rainbow at the horizon, and its arc reaches higher in the sky, with its centre as high above the horizon as the normal rainbow's centre is below it. Reflection bows are usually brightest when the sun is low because at that time its light is most strongly reflected from water surfaces. As the sun gets lower the normal and reflection bows are drawn closer together. Due to the combination of requirements, a reflection rainbow is rarely visible.

Up to eight separate bows may be distinguished if the reflected and reflection rainbows happen to occur simultaneously: the normal (non-reflection) primary and secondary bows above the horizon (1, 2) with their reflected counterparts below it (3, 4), and the reflection primary and secondary bows above the horizon (5, 6) with their reflected counterparts below it (7, 8).^[42][43]

Monochrome rainbow[edit]

Occasionally a shower may happen at sunrise or sunset, where the shorter wavelengths like blue and green have been scattered and essentially removed from the spectrum. Further scattering may occur due to the rain, and the result can be the rare and dramatic monochrome or red rainbow.^[44]

Higher-order rainbows[edit]

In addition to the common primary and secondary rainbows, it is also possible for rainbows of higher orders to form. The order of a rainbow is determined by the number of light reflections inside the water droplets that create it: One reflection results in the first-order or primary rainbow; two reflections create the second-order or secondary rainbow. More internal reflections cause bows of higher orders—theoretically unto infinity.^[45] As more and more light is lost with each internal reflection, however, each subsequent bow becomes progressively dimmer and therefore increasingly difficult to spot. An additional challenge in observing the third-order (or tertiary) and fourth-order (quaternary) rainbows is their location in the direction of the sun (about 40° and 45° from the sun, respectively), causing them to become drowned in its glare.^[46]

For these reasons, naturally occurring rainbows of an order higher than 2 are rarely visible to the naked eye. Nevertheless, sightings of the third-order bow in nature have been reported, and in 2011 it was photographed definitively for the first time.^[47][48] Shortly after, the fourth-order rainbow was photographed as well,^[49][50] and in 2014 the first ever pictures of the fifth-order (or quinary) rainbow were published.^[51] The quinary rainbow lies partially in the gap between the primary and secondary rainbows and is far fainter than even the secondary. In a laboratory setting, it is possible to create bows of much higher orders. Felix Billet (1808–1882) depicted angular positions up to the 19th-order rainbow, a pattern he called a "rose of rainbows".^[52][53][54] In the laboratory, it is possible to observe higher-order rainbows by using extremely bright and well collimated light produced by lasers. Up to the 200th-order rainbow was reported by Ng et al. in 1998 using a similar method but an argon ion laser beam.^[55]

Tertiary and quaternary rainbows should not be confused with "triple" and "quadruple" rainbows—terms sometimes erroneously used to refer to the (much more common) supernumerary bows and reflection rainbows.

Rainbows under moonlight[edit]

Like most atmospheric optical phenomena, rainbows can be caused by light from the Sun, but also from the Moon. In case of the latter, the rainbow is referred to as a lunar rainbow or moonbow. They are much dimmer and rarer than solar rainbows, requiring the Moon to be near-full in order for them to be seen. For the same reason, moonbows are often perceived as white and may be thought of as monochrome. The full spectrum is present, however, but the human eye is not normally sensitive enough to see the colours. Long exposure photographs will sometimes show the colour in this type of rainbow.^[56]

Fogbow[edit]

Fogbows form in the same way as rainbows, but they are formed by much smaller cloud and fog droplets that diffract light extensively. They are almost white with faint reds on the outside and blues inside; often one or more broad supernumerary bands can be discerned inside the inner edge. The colours are dim because the bow in each colour is very broad and the colours overlap. Fogbows are commonly seen over water when air in contact with the cooler water is chilled, but they can be found anywhere if the fog is thin enough for the sun to shine through and the sun is fairly bright. They are very large—almost as big as a rainbow and much broader. They sometimes appear with a glory at the bow's centre.^[57]

Fog bows should not be confused with ice halos, which are very common around the world and visible much more often than rainbows (of any order),^[58] yet are unrelated to rainbows.

Sleetbow[edit]

A sleetbow forms in the same way as a typical rainbow, with the exception that it occurs when light passes through falling sleet (ice pellets) instead of liquid water. As light passes through the sleet, the light is refracted causing the rare phenomena. These have been documented across United States with the earliest publicly documented and photographed sleetbow being seen in Richmond, Virginia on 21 December 2012.^[59] Just like regular rainbows, these can also come in various forms, with a monochrome sleetbow being documented on 7 January 2016 in Valparaiso, Indiana.^{[citation needed]}

Circumhorizontal and circumzenithal arcs[edit]

Posted on December 7, 2007

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Look up Underground or underground in Wiktionary, the free dictionary.

Underground most commonly refers to:

• Subterranea (geography), the regions beneath the surface of the Earth

Underground may also refer to:

Places[edit]

• Buenos Aires Underground, a rapid transit system
• London Underground, a rapid transit system
• The Underground (Boston), a music club in the Allston neighborhood of Boston
• The Underground (Stoke concert venue), a club/music venue based in Hanley, Stoke-on-Trent
• Underground (Manhattan), a music club (1980—1989) in Manhattan
• Underground Atlanta, a shopping and entertainment district in the Five Points neighborhood of downtown Atlanta, Georgia
• Underground City, Montreal
• Underground city, a series of linked subterranean spaces
• Underground living, modes of living below the ground's surface

Arts, entertainment, and media[edit]

Films[edit]

• Underground (1928 film), a drama by Anthony Asquith
• Underground (1941 film), a war drama by Vincent Sherman
• Underground (1970 film), a war drama starring Robert Goulet
• Underground (1976 film), a documentary about the radical organization the Weathermen
• Underground (1989 film), a film featuring Melora Walters
• Underground (1995 film), a film by Emir Kusturica
• The Underground (1997 film), a cop must stop the killings of rap stars
• Underground (2007 film), a British independent film starring Mark Strange
• Underground (2011 film), a horror film starring Adrian R'Mante
• Underground (2020 film), a/k/a Souterrain, a drama film directed by Sophie Dupuis
• Underground: The Julian Assange Story, a 2012 Australian television film on Julian Assange for Network Ten

Games[edit]

• Underground (role-playing game), a satirical superhero game
• Underground, an expansion pack for Tom Clancy's The Division
• Medal of Honor: Underground, a 2000 first-person shooter
• Need for Speed: Underground, a 2003 racing video game
• Need for Speed: Underground 2, a 2004 racing video game
• Tony Hawk's Underground, a 2003 skateboarding video game
• Tony Hawk's Underground 2, a 2004 skateboarding video game
• Underground Zone, the first level in Sonic the Hedgehog 2 (8-bit)

Literature[edit]

• Underground (Dreyfus book), a 1997 nonfiction book about computer hacking
• Underground (McGahan novel), by Andrew McGahan
• Underground (Murakami book), a 1998 collection of interviews about the Tokyo sarin gas attack
• The Underground (Animorphs), by K. A. Applegate
• The Underground (Left Behind: The Kids), by Jerry B. Jenkins and Tim LaHaye
• Underground comix

Music[edit]

Albums[edit]

• Underground (The Electric Prunes album), 1967
• Underground (Thelonious Monk album), 1968
• Underground (Twinkle Brothers album), ?
• Underground (Phil Keaggy album), 1983
• Underground (Graham Bonnet album), 1997
• Underground (Jayo Felony album), 1999
• Underground (Courtney Pine album), 1997
• Underground (Chris Potter album), 2006
• Underground (soundtrack), by Goran Bregović, 2000
• Underground, by Analog Pussy, ?
• Underground Vol. 1: 1991–1994, a compilation album by Three 6 Mafia, 1999
• Underground Vol. 2: Club Memphis, a compilation album by Three 6 Mafia, 1999

Songs[edit]

• "Underground", a song by Curtis Mayfield from Roots, 1970
• "Underground", a song by Gentle Giant from Civilian
• "Underground", a song by Tom Waits from Swordfishtrombones
• "Underground", song by Men at Work from Business as Usual, 1980s
• "Underground" (David Bowie song), featured in the film Labyrinth
• "Underground" (Ben Folds Five song), 1995
• "Underground" (Evermore song), 2010
• "Underground", a song by Adam Lambert from The Original High, 2015
• "Underground", a song by Circa Zero from Circus Hero
• "Underground", a song by Decadence from Undergrounder, 2017
• "Underground", a song by Eminem from Relapse
• "Underground", a song by Jane's Addiction from The Great Escape Artist
• "Underground", a song by Pokey LaFarge from Something In The Water
• "Underground", a song by The Tea Party from Triptych
• "The Underground", a song by Mani Spinx

Other uses in music[edit]

• Underground music, a variety of music subgenres

Television[edit]

• Underground (TV series), a 2016 American television drama series
• TCM Underground, a weekly cult-film showcase
• The Underground (TV series), a sketch comedy show
• "Underground" (1958 TV play), a British television drama, part of Armchair Theatre
• "Underground" (Stargate Atlantis), an episode of Stargate Atlantis
• "Underground" (BoJack Horseman), an episode of BoJack Horseman
• "Underground", a Transformers: Armada episode

Other uses in arts, entertainment, and media[edit]

• Underground (play), by Michael Sloane
• Underground press, independent counterculture publications
• Underground producciones, an Argentine producer of TV series

Groups and organizations[edit]

• Narodnaya Volya, an underground group in late 19th-century Russia
• Resistance movement
  • Resistance during World War II, with some groups sometimes referred to informally as "The Underground"
    • Polish Underground State (Polish: Polskie Państwo Podziemne), 1939-1945
• Weather Underground, a clandestine far-left terrorist group which operated in the United States of America between 1969 and 1977

Other uses[edit]

• Underground economy, a market system operating outside of legal regulations
• UK underground, a counter-cultural movement in the United Kingdom
• Underground Railroad, an informal network of secret routes and safe houses
• The Underground (roller coaster), a wooden roller coaster at Adventureland (Iowa)
• Underground mining (hard rock), removal of valuable minerals from below the Earth's surface

See also[edit]

• Rapid transit, rail-based transportation systems, which often operate in tunnels
• Underground culture (disambiguation)
• Underground 2 (disambiguation)
• 6 Underground (disambiguation)
• Overground (disambiguation)

This disambiguation page lists articles associated with the title Underground.
If an internal link led you here, you may wish to change the link to point directly to the intended article.

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Military" – news · newspapers · books · scholar · JSTOR (August 2008) (Learn how and when to remove this message)

A military, also known collectively as an armed forces, are a heavily armed, highly organized force primarily intended for warfare. Militaries are typically authorized and maintained by a sovereign state, with their members identifiable by a distinct military uniform. They may consist of one or more military branches such as an army, navy, air force, space force, marines, or coast guard. The main task of a military is usually defined as defence of their state and its interests against external armed threats.

In broad usage, the terms "armed forces" and "military" are often synonymous, although in technical usage a distinction is sometimes made in which a country's armed forces may include other paramilitary forces such as armed police.

A nation's military may function as a discrete social subculture, with dedicated infrastructure such as military housing, schools, utilities, logistics, hospitals, legal services, food production, finance, and banking services. Beyond warfare, the military may be employed in additional sanctioned and non-sanctioned functions within the state, including internal security threats, crowd control, promotion of political agendas, emergency services and reconstruction, protecting corporate economic interests, social ceremonies, and national honour guards.^[1]

The profession of soldiering is older than recorded history.^[2] Some images of classical antiquity portray the power and feats of military leaders. The Battle of Kadesh in 1274 BC from the reign of Ramses II, features in bas-relief monuments. The first Emperor of a unified China, Qin Shi Huang, created the Terracotta Army to represent his military might.^[3] The Ancient Romans wrote many treatises and writings on warfare, as well as many decorated triumphal arches and victory columns.

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