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Ganges

The Ganges (in India: Ganga, ; in Bangladesh: Padma,  )    is a trans-boundary river of Asia which flows through India and Bangladesh. The 2525 km-long river rises in the western Himalayas in the Indian state of Uttarakhand. It flows south and east through the Gangetic plain of North India, receiving the right-bank tributary, the Yamuna, which also rises in the western Indian Himalayas, and several left-bank tributaries from Nepal that account for the bulk of its flow. In West Bengal state, India, a feeder canal taking off from its right bank diverts 50% of its flow southwards, artificially connecting it to the Hooghly River. The Ganges continues into Bangladesh, its name changing to the Padma. It is then joined by the Jamuna, the lower stream of the Brahmaputra, and eventually the Meghna, forming the major estuary of the Ganges Delta, and emptying into the Bay of Bengal. The Ganges–Brahmaputra–Meghna system is the second-largest river on earth by discharge.

The main stem of the Ganges begins at the town of Devprayag, at the confluence of the Alaknanda, which is the source stream in hydrology on account of its greater length, and the Bhagirathi, which is considered the source stream in all of Hindu mythology.

The Ganges is a lifeline to tens of millions of people who live in its basin and depend on it for their daily needs. It has been important historically, with many former provincial or imperial capitals such as Pataliputra, Kannauj, Sonargaon, Dhaka, Bikrampur, Kara, Munger, Kashi, Patna, Hajipur, Delhi, Bhagalpur, Murshidabad, Baharampur, Kampilya, and Kolkata located on its banks or the banks of tributaries and connected waterways. The river is home to approximately 140 species of fish, 90 species of amphibians, and also reptiles and mammals, including critically endangered species such as the gharial and South Asian river dolphin. The Ganges is the most sacred river to Hindus. It is worshipped as the goddess Ganga in Hinduism.

The Ganges is threatened by severe pollution. This not only poses a danger to humans but also to many species of animals. The levels of fecal coliform bacteria from human waste in the river near Varanasi are more than 100 times the Indian government's official limit. The Ganga Action Plan, an environmental initiative to clean up the river, has been considered a failure which is variously attributed to corruption, a lack of will in the government, poor technical expertise, poor environmental planning, and a lack of support from religious authorities.

Course

The upper phase of the river Ganges begins at the confluence of the Bhagirathi and Alaknanda rivers in the town of Devprayag in the Garhwal division of the Indian state of Uttarakhand. The Bhagirathi is considered to be the source in Hindu culture and mythology, although the Alaknanda is longer, and therefore, hydrologically the source stream. The headwaters of the Alakananda are formed by snow melt from peaks such as Nanda Devi, Trisul, and Kamet. The Bhagirathi rises at the foot of Gangotri Glacier, at Gomukh, at an elevation of 4356 m and was mythologically referred to as residing in the matted locks of Shiva; symbolically Tapovan, which is a meadow of ethereal beauty at the feet of Mount Shivling, just 5 km away.

Although many small streams comprise the headwaters of the Ganges, the six longest and their five confluences are considered sacred. The six headstreams are the Alaknanda, Dhauliganga, Nandakini, Pindar, Mandakini and Bhagirathi. Their confluences, known as the Panch Prayag, are all along the Alaknanda. They are, in downstream order, Vishnuprayag, where the Dhauliganga joins the Alaknanda; Nandprayag, where the Nandakini joins; Karnaprayag, where the Pindar joins; Rudraprayag, where the Mandakini joins; and finally, Devprayag, where the Bhagirathi joins the Alaknanda to form the Ganges.

After flowing for 256.90 km through its narrow Himalayan valley, the Ganges emerges from the mountains at Rishikesh, then debouches onto the Gangetic Plain at the pilgrimage town of Haridwar. At Haridwar, a headworks diverts some of its water into the Ganges Canal, which irrigates the Doab region of Uttar Pradesh, whereas the river, whose course has been roughly southwest until this point, now begins to flow southeast through the plains of northern India.

The Ganges river follows a 900 km arching course passing through the cities of Bijnor, Kannauj, Farukhabad, and Kanpur. Along the way it is joined by the Ramganga, which contributes an average annual flow of about 495 m3/s to the river. The Ganges joins the 1444 km long River Yamuna at the Triveni Sangam at Prayagraj(previously Allahabad), a confluence considered holy in Hinduism. At their confluence the Yamuna is larger than the Ganges contributing about 58.5% of the combined flow, with an average flow of 2948 m3/s.

Now flowing east, the river meets the 400 km long Tamsa River (also called Tons), which flows north from the Kaimur Range and contributes an average flow of about 187 m3/s. After the Tamsa, the 625 km long Gomti River joins, flowing south from the Himalayas. The Gomti contributes an average annual flow of about 234 m3/s. Then the 1156 km long Ghaghara River (Karnali River), also flowing south from the Himalayas of Tibet through Nepal joins. The Ghaghara (Karnali), with its average annual flow of about 2991 m3/s, is the largest tributary of the Ganges by discharge. After the Ghaghara confluence, the Ganges is joined from the south by the 784 km long Son River, which contributes about 1008 m3/s. The 814 km long Gandaki River, then the 729 km long Kosi River, join from the north flowing from Nepal, contributing about 1654 m3/s and 2166 m3/s, respectively. The Kosi is the third largest tributary of the Ganges by discharge, after Ghaghara (Karnali) and Yamuna. The Kosi merges into the Ganges near Kursela in Bihar.

Along the way between Prayagraj and Malda, West Bengal, the Ganges river passes the towns of Chunar, Mirzapur, Varanasi, Ghazipur, Ara, Patna, Chapra, Hajipur, Mokama, Begusarai, Munger, Sahibganj, Rajmahal, Bhagalpur, Ballia, Buxar, Simaria, Sultanganj, and Farakka. At Bhagalpur, the river begins to flow south-southeast and at Farakka, it begins its attrition with the branching away of its first distributary, the 408 km long Bhāgirathi-Hooghly, which goes on to become the Hooghly River. Just before the border with Bangladesh the Farakka Barrage controls the flow of Ganges, diverting some of the water into a feeder canal linked to the Hooghly for the purpose of keeping it relatively silt-free. The Hooghly River is formed by the confluence of the Bhagirathi River and Ajay River at Katwa, and Hooghly has a number of tributaries of its own. The largest is the Damodar River, which is 625 km long, with a drainage basin of 25820 km2. The Hooghly River empties into the Bay of Bengal near Sagar Island. Between Malda and the Bay of Bengal, the Hooghly river passes the towns and cities of Murshidabad, Nabadwip, Kolkata and Howrah.

After entering Bangladesh, the main branch of the Ganges river is known as the Padma. The Padma is joined by the Jamuna River, the largest distributary of the Brahmaputra. Further downstream, the Padma joins the Meghna River, the converged flow of Surma-Meghna River System taking on the Meghna's name as it enters the Meghna Estuary, which empties into the Bay of Bengal. Here it forms the 1430 by Bengal Fan, the world's largest submarine fan, which alone accounts for 10–20% of the global burial of organic carbon.

The Ganges Delta, formed mainly by the large, sediment-laden flows of the Ganges and Brahmaputra rivers, is the world's largest delta, at about 64000 km2. It stretches 400 km along the Bay of Bengal.

Only the Amazon and Congo rivers have a greater average discharge than the combined flow of the Ganges, the Brahmaputra, and the Surma-Meghna river system. In full flood only the Amazon is larger.

Geology
The Indian subcontinent lies atop the Indian tectonic plate, a minor plate within the Indo-Australian Plate. Its defining geological processes commenced seventy-five million years ago, when, as a part of the southern supercontinent Gondwana, it began a northeastwards drift—lasting fifty million years—across the then unformed Indian Ocean. The subcontinent's subsequent collision with the Eurasian Plate and subduction under it, gave rise to the Himalayas, the planet's highest mountain ranges. In the former seabed immediately south of the emerging Himalayas, plate movement created a vast trough, which, having gradually been filled with sediment borne by the Indus and its tributaries and the Ganges and its tributaries, now forms the Indo-Gangetic Plain.

The Indo-Gangetic Plain is geologically known as a foredeep or foreland basin.

Hydrology
Major left-bank tributaries include the Gomti River, Ghaghara River, Gandaki River and Kosi River; major right-bank tributaries include the Yamuna River, Son River, Punpun and Damodar. The hydrology of the Ganges River is very complicated, especially in the Ganges Delta region. One result is different ways to determine the river's length, its discharge, and the size of its drainage basin.

The name Ganges is used for the river between the confluence of the Bhagirathi and Alaknanda rivers, in the Himalayas, and the first bifurcation of the river, near the Farakka Barrage and the India-Bangladesh Border. The length of the Ganges is frequently said to be slightly over 2600 km long, about 2601 km, 2525 km or 2650 km. In these cases the river's source is usually assumed to be the source of the Bhagirathi River, Gangotri Glacier at Gomukh and its mouth being the mouth of the Meghna River on the Bay of Bengal. Sometimes the source of the Ganges is considered to be at Haridwar, where its Himalayan headwater streams debouch onto the Gangetic Plain.

In some cases, the length of the Ganges is given by its Hooghly River distributary, which is longer than its main outlet via the Meghna River, resulting in a total length of about 2704 km, if taken from the source of the Bhagirathi, or 2321.50 km, if from Haridwar to the Hooghly's mouth. In other cases the length is said to be about 2304 km, from the source of the Bhagirathi to the Bangladesh border, where its name changes to Padma.

For similar reasons, sources differ over the size of the river's drainage basin. The basin covers parts of four countries, India, Nepal, China, and Bangladesh; eleven Indian states, Himachal Pradesh, Uttarakhand, Uttar Pradesh, Madhya Pradesh, Chhattisgarh, Bihar, Jharkhand, Punjab, Haryana, Rajasthan, West Bengal, and the Union Territory of Delhi. The Ganges basin, including the delta but not the Brahmaputra or Meghna basins, is about 1080000 km2, of which 861000 km2 is in India (about 80%), 140000 km2 in Nepal (13%), 46000 km2 in Bangladesh (4%), and 33000 km2 in China (3%). Sometimes the Ganges and Brahmaputra–Meghna drainage basins are combined for a total of about 1600000 km2 or 1621000 km2. The combined Ganges-Brahmaputra-Meghna basin (abbreviated GBM or GMB) drainage basin is spread across Bangladesh, Bhutan, India, Nepal, and China.

The Ganges basin ranges from the Himalaya and the Transhimalaya in the north, to the northern slopes of the Vindhya range in the south, from the eastern slopes of the Aravalli in the west to the Chota Nagpur plateau and the Sunderbans delta in the east. A significant portion of the discharge from the Ganges comes from the Himalayan mountain system. Within the Himalaya, the Ganges basin spreads almost 1,200 km from the Yamuna-Satluj divide along the Simla ridge forming the boundary with the Indus basin in the west to the Singalila Ridge along the Nepal-Sikkim border forming the boundary with the Brahmaputra basin in the east. This section of the Himalaya contains 9 of the 14 highest peaks in the world over 8,000m in height, including Mount Everest which is the high point of the Ganges basin. The other peaks over 8,000m in the basin are Kangchenjunga, Lhotse, Makalu, Cho Oyu, Dhaulagiri, Manaslu, Annapurna and Shishapangma. The Himalayan portion of the basin includes the south-eastern portion of the state of Himachal Pradesh, the entire state of Uttarakhand, the entire country of Nepal and the extreme north-western portion of the state of West Bengal.

The discharge of the Ganges also differs by source. Frequently, discharge is described for the mouth of the Meghna River, thus combining the Ganges with the Brahmaputra and Meghna. This results in a total average annual discharge of about 38000 m3/s, or 42470 m3/s. In other cases the average annual discharges of the Ganges, Brahmaputra, and Meghna are given separately, at about 16650 m3/s for the Ganges, about 19820 m3/s for the Brahmaputra, and about 5100 m3/s for the Meghna.

The maximum peak discharge of the Ganges, as recorded at Hardinge Bridge in Bangladesh, exceeded 70000 m3/s. The minimum recorded at the same place was about 180 m3/s, in 1997.

The hydrologic cycle in the Ganges basin is governed by the Southwest Monsoon. About 84% of the total rainfall occurs in the monsoon from June to September. Consequently, streamflow in the Ganges is highly seasonal. The average dry season to monsoon discharge ratio is about 1:6, as measured at Hardinge Bridge. This strong seasonal variation underlies many problems of land and water resource development in the region. The seasonality of flow is so acute it can cause both drought and floods. Bangladesh, in particular, frequently experiences drought during the dry season and regularly suffers extreme floods during the monsoon.

In the Ganges Delta, many large rivers come together, both merging and bifurcating in a complicated network of channels. The two largest rivers, the Ganges and Brahmaputra, both split into distributary channels, the largest of which merge with other large rivers before themselves joining the Bay of Bengal. But this current channel pattern was not always the case. Over time the rivers in Ganges Delta have often changed course, sometimes altering the network of channels in significant ways.

Before the late 12th century the Bhagirathi-Hooghly distributary was the main channel of the Ganges and the Padma was only a minor spill-channel. The main flow of the river reached the sea not via the modern Hooghly River but rather by the Adi Ganga. Between the 12th and 16th centuries, the Bhagirathi-Hooghly and Padma channels were more or less equally significant. After the 16th century, the Padma grew to become the main channel of the Ganges. It is thought that the Bhagirathi-Hooghly became increasingly choked with silt, causing the main flow of the Ganges to shift to the southeast and the Padma River. By the end of the 18th century, the Padma had become the main distributary of the Ganges. One result of this shift to the Padma was that the Ganges now joined the Meghna and Brahmaputra rivers before emptying into the Bay of Bengal. The present confluence of the Ganges and Meghna was formed very recently, about 150 years ago.

Also near the end of the 18th century, the course of the lower Brahmaputra changed dramatically, significantly altering its relationship with the Ganges. In 1787 there was a great flood on the Teesta River, which at the time was a tributary of the Ganges-Padma River. The flood of 1787 caused the Teesta to undergo a sudden change course, an avulsion, shifting east to join the Brahmaputra and causing the Brahmaputra to shift its course south, cutting a new channel. This new main channel of the Brahmaputra is called the Jamuna River. It flows south to join the Ganges-Padma. During ancient times, the main flow of the Brahmaputra was more easterly, passing by the city of Mymensingh and joining the Meghna River. Today this channel is a small distributary but retains the name Brahmaputra, sometimes Old Brahmaputra. The site of the old Brahmaputra-Meghna confluence, in the locality of Langalbandh, is still considered sacred by Hindus. Near the confluence is a major early historic site called Wari-Bateshwar.

In the rainy season of 1809, the lower channel of the Bhagirathi, leading to Kolkata, had been entirely shut; but in the following year it opened again and was nearly of the same size as the upper channel but both however suffered a considerable diminution, owing probably to the new communication opened below the Jalanggi on the upper channel.

Discharge
Discharge of the Ganges River at Farakka Barrage (period from 1998/01/01 to 2023/12/31):

History
The first European traveller to mention the Ganges was the Greek envoy Megasthenes (ca. 350–290 BCE). He did so several times in his work Indica: "India, again, possesses many rivers both large and navigable, which, having their sources in the mountains which stretch along the northern frontier, traverse the level country, and not a few of these, after uniting with each other, fall into the river called the Ganges. Now this river, which at its source is 30 stadia broad, flows from north to south, and empties its waters into the ocean forming the eastern boundary of the Gangaridai, a nation which possesses a vast force of the largest-sized elephants." (Diodorus II.37).

In 1951 a water sharing dispute arose between India and East Pakistan (now Bangladesh) after India declared its intention to build the Farakka Barrage. The original purpose of the barrage, which was completed in 1975, was to divert up to 1100 m3/s of water from the Ganges to the Bhagirathi-Hooghly distributary to restore navigability at the Port of Kolkata. It was assumed that during the worst dry season the Ganges flow would be around 1400 to 1600 m3/s, thus leaving 280 to 420 m3/s for the then East Pakistan. East Pakistan objected and a protracted dispute ensued. In 1996 a 30-year treaty was signed with Bangladesh. The terms of the agreement are complicated, but in essence, they state that if the Ganges flow at Farakka was less than 2000 m3/s then India and Bangladesh would each receive 50% of the water, with each receiving at least 1000 m3/s for alternating ten-day periods. However, within a year the flow at Farakka fell to levels far below the historic average, making it impossible to implement the guaranteed sharing of water. In March 1997, flow of the Ganges in Bangladesh dropped to its lowest ever, 180 m3/s. Dry season flows returned to normal levels in the years following, but efforts were made to address the problem. One plan is for another barrage to be built in Bangladesh at Pangsha, west of Dhaka. This barrage would help Bangladesh better utilize its share of the waters of the Ganges.

Embodiment of sacredness
The Ganges is a sacred river to Hindus along every fragment of its length. All along its course, Hindus bathe in its waters, paying homage to their ancestors and their gods by cupping the water in their hands, lifting it, and letting it fall back into the river; they offer flowers and rose petals and float shallow clay dishes filled with oil and lit with wicks (diyas). On the journey back home from the Ganges, they carry small quantities of river water with them for use in rituals; Ganga Jal, literally "the water of the Ganges".

The Ganges is the embodiment of all sacred waters in Hindu mythology. Local rivers are said to be like the Ganges and are sometimes called the local Ganges. The Godavari River of Maharashtra in Western India is called the Ganges of the South or the 'Dakshin Ganga'; the Godavari is the Ganges that was led by the sage Gautama to flow through Central India. The Ganges is invoked whenever water is used in Hindu ritual and is therefore present in all sacred waters. Despite this, nothing is more stirring for a Hindu than a dip in the actual river, which is thought to remit sins, especially at one of the famous tirthas such as Varanasi, Gangotri, Haridwar, or the Triveni Sangam at Prayagraj. The symbolic and religious importance of the Ganges is one of the few things that Hindus, even their skeptics, have agreed upon. Jawaharlal Nehru, a religious iconoclast himself, asked for a handful of his ashes to be thrown into the Ganges. "The Ganga", he wrote in his will, "is the river of India, beloved of her people, round which are intertwined her racial memories, her hopes and fears, her songs of triumph, her victories and her defeats. She has been a symbol of India's age-long culture and civilization, ever-changing, ever-flowing, and yet ever the same Ganga."

Avatarana – Descent of Ganges

In late May or early June every year, Hindus celebrate the karunasiri and the rise of the Ganges from earth to heaven. The day of the celebration, Ganga Dashahara, the Dashami (tenth day) of the waxing moon of the Hindu calendar month Jyestha, brings throngs of bathers to the banks of the river. A dip in the Ganges on this day is said to rid the bather of ten sins (dasha = Sanskrit "ten"; hara = to destroy) or ten lifetimes of sins. Those who cannot journey to the river, however, can achieve the same results by bathing in any nearby body of water, which, for the true believer, takes on all the attributes of the Ganges.

The karunasiri is an old theme in Hinduism with a number of different versions of the story. In the Vedic version, Indra, the Lord of Swarga (Heaven) slays the celestial serpent, Vritra, releasing the celestial liquid, soma, or the nectar of the gods which then plunges to the earth and waters it with sustenance.

In the Vaishnava version of the myth, the heavenly waters were then a river called Vishnupadi (Sanskrit: "from the foot of Vishnu"). As Lord Vishnu as the avatar Vamana completes his celebrated three strides —of earth, sky, and heaven— he stubs his toe on the vault of heaven, punches open a hole and releases the Vishnupadi, which until now had been circling the cosmic egg. Flowing out of the vault, she plummets down to Indra's heaven, where she is received by Dhruva, once a steadfast worshipper of Vishnu, now fixed in the sky as the Pole star. Next, she streams across the sky forming the Milky Way and arrives on the moon. She then flows down earthwards to Brahma's realm, a divine lotus atop Mount Meru, whose petals form the earthly continents. There, the divine waters break up, with one stream, the Bhagirathi, flowing down one petal into Bharatvarsha (India) as the Ganges.

It is Shiva, however, among the major deities of the Hindu pantheon, who appears in the most widely known version of the avatarana story. Told and retold in the Ramayana, the Mahabharata and several Puranas, the story begins with a sage, Kapila, whose intense meditation has been disturbed by the sixty thousand sons of King Sagara. Livid at being disturbed, Kapila sears them with his angry gaze, reduces them to ashes, and dispatches them to the netherworld. Only the waters of the Ganges, then in heaven, can bring the dead sons their salvation. A descendant of these sons, King Bhagiratha, anxious to restore his ancestors, undertakes rigorous penance and is eventually granted the prize of Ganges's descent from heaven. However, since her turbulent force would also shatter the earth, Bhagiratha persuades Shiva in his abode on Mount Kailash to receive the Ganges in the coils of his tangled hair and break her fall. The Ganges descends, is tamed in Shiva's locks, and arrives in the Himalayas. She is then led by the waiting Bhagiratha down into the plains at Haridwar, across the plains first to the confluence with the Yamuna at Prayag and then to Varanasi, and eventually to Ganges Sagar (Ganges delta), where she meets the ocean, sinks to the netherworld, and saves the sons of Sagara. In honour of Bhagirath's pivotal role in the avatarana, the source stream of the Ganges in the Himalayas is named Bhagirathi, (Sanskrit, "of Bhagiratha").

Redemption of the Dead
As the Ganges had descended from heaven to earth, she is also considered the vehicle of ascent, from earth to heaven. As the Triloka-patha-gamini, (Sanskrit: triloka = "three worlds", patha = "road", gamini = "one who travels") of the Hindu tradition, she flows in heaven, earth, and the netherworld, and, consequently, is a "tirtha" or crossing point of all beings, the living as well as the dead. It is for this reason that the story of the avatarana is told at Shraddha ceremonies for the deceased in Hinduism, and Ganges water is used in Vedic rituals after death. Among all hymns devoted to the Ganges, there are none more popular than the ones expressing the worshipper's wish to breathe his last surrounded by her waters. The Gangashtakam expresses this longing fervently: "O Mother! ... Necklace adorning the worlds! Banner rising to heaven! I ask that I may leave of this body on your banks, Drinking your water, rolling in your waves, Remembering your name, bestowing my gaze upon you." No place along her banks is more longed for at the moment of death by Hindus than Varanasi, the Great Cremation Ground, or Mahashmshana. Those who are lucky enough to die in Varanasi, are cremated on the banks of the Ganges, and are granted instant salvation. If the death has occurred elsewhere, salvation can be achieved by immersing the ashes in the Ganges. If the ashes have been immersed in another body of water, a relative can still gain salvation for the deceased by journeying to the Ganges, if possible during the lunar "fortnight of the ancestors" in the Hindu calendar month of Ashwin (September or October), and performing the Shraddha rites.

Hindus also perform pinda pradana, a rite for the dead, in which balls of rice and sesame seed are offered to the Ganges while the names of the deceased relatives are recited. Every sesame seed in every ball thus offered, according to one story, assures a thousand years of heavenly salvation for each relative. Indeed, the Ganges is so important in the rituals after death that the Mahabharata, in one of its popular ślokas, says, "If only (one) bone of a (deceased) person should touch the water of the Ganges, that person shall dwell honoured in heaven." As if to illustrate this truism, the Kashi Khanda (Varanasi Chapter) of the Skanda Purana recounts the remarkable story of Vahika, a profligate and unrepentant sinner, who is killed by a tiger in the forest. His soul arrives before Yama, the Lord of Death, to be judged for the afterworld. Having no compensating virtue, Vahika's soul is at once dispatched to hell. While this is happening, his body on earth, however, is being picked at by vultures, one of whom flies away with a foot bone. Another bird comes after the vulture, and in fighting him off, the vulture accidentally drops the bone into the Ganges below. Blessed by this event, Vahika, on his way to hell, is rescued by a celestial chariot which takes him instead to heaven.

The Purifying Ganges
Hindus consider the waters of the Ganges to be both pure and purifying. Regardless of all scientific understanding of its waters, the Ganges is always ritually and symbolically pure in Hindu culture. Nothing reclaims order from disorder more than the waters of the Ganga. Moving water, as in a river, is considered purifying in Hindu culture because it is thought to both absorb impurities and take them away. The swiftly moving Ganga, especially in its upper reaches, where a bather has to grasp an anchored chain to not be carried away, is especially purifying. What the Ganges removes, however, is not necessarily physical dirt, but symbolic dirt; it wipes away the sins of the bather, not just of the present, but of a lifetime.

A popular paean to the Ganga is the Ganga Lahiri composed by a 17th-century poet Jagannatha who, legend has it, was turned out of his Hindu Brahmin caste for carrying on an affair with a Muslim woman. Having attempted futilely to be rehabilitated within the Hindu fold, the poet finally appeals to Ganga, the hope of the hopeless, and the comforter of last resort. Along with his beloved, Jagannatha sits at the top of the flight of steps leading to the water at the famous Panchganga Ghat in Varanasi. As he recites each verse of the poem, the water of the Ganges rises one step until in the end it envelops the lovers and carries them away. "I come to you as a child to his mother", begins the Ganga Lahiri. "I come as an orphan to you, moist with love. I come without refuge to you, giver of sacred rest. I come a fallen man to you, uplifter of all. I come undone by disease to you, the perfect physician. I come, my heart dry with thirst, to you, ocean of sweet wine. Do with me whatever you will."

Consort, Shakti, and Mother
Ganga is a consort to all three major male deities of Hinduism. As Brahma's partner she always travels with him in the form of water in his kamandalu (water-pot). She is also Vishnu's consort. Not only does she emanate from his foot as Vishnupadi in the avatarana story, but is also, with Sarasvati and Lakshmi, one of his co-wives. In one popular story, envious of being outdone by each other, the co-wives begin to quarrel. While Lakshmi attempts to mediate the quarrel, Ganga and Sarasvati, heap misfortune on each other. They curse each other to become rivers, and to carry within them, by washing, the sins of their human worshippers. Soon their husband, Vishnu, arrives and decides to calm the situation by separating the goddesses. He orders Sarasvati to marry Brahma, Ganga to marry Shiva, and Lakshmi, as the blameless conciliator, to remain as his own wife. Ganga and Sarasvati, however, are so distraught at this dispensation, and wail so loudly, that Vishnu is forced to take back his words. Consequently, in their lives as rivers they are still thought to be with him.

It is Shiva's relationship with Ganga, that is the best-known in Ganges mythology. Her descent, the avatarana is not a one-time event, but a continuously occurring one in which she is forever falling from heaven into his locks and being forever tamed. Shiva, is depicted in Hindu iconography as Gangadhara, the "Bearer of the Ganga", with Ganga, shown as spout of water, rising from his hair. The Shiva-Ganga relationship is both perpetual and intimate. Shiva is sometimes called Uma-Ganga-Patiswara ("Husband and Lord of Uma (Parvati) and Ganga"), and Ganga often arouses the jealousy of Shiva's better-known consort.

Ganga is the shakti or the moving, restless, rolling energy in the form of which the otherwise reclusive and unapproachable Shiva appears on earth. As water, this moving energy can be felt, tasted, and absorbed. The war-god Skanda addresses the sage Agastya in the Kashi Khand of the Skanda Purana in these words: "One should not be amazed ... that this Ganges is really Power, for is she not the Supreme Shakti of the Eternal Shiva, taken in the form of water? This Ganges, filled with the sweet wine of compassion, was sent out for the salvation of the world by Shiva, the Lord of the Lords. Good people should not think this Triple-Pathed River to be like the thousand other earthly rivers, filled with water."

The Ganga is also the mother, the Ganga Mata (mata="mother") of Hindu worship and culture, accepting all and forgiving all. Unlike other goddesses, she has no destructive or fearsome aspect, destructive though she might be as a river in nature. She is also a mother to other gods. She accepts Shiva's incandescent seed from the fire-god Agni, which is too hot for this world and cools it in her waters. This union produces Skanda, or Kartikeya, the god of war. In the Mahabharata, she is married to Shantanu, and the mother of heroic warrior-patriarch, Bhishma. When Bhishma is mortally wounded in battle, Ganga comes out of the water in human form and weeps uncontrollably over his body.

The Ganges is the distilled lifeblood of the Hindu tradition, of its divinities, holy books, and enlightenment. As such, her worship does not require the usual rites of invocation (avahana) at the beginning and dismissal (visarjana) at the end, required in the worship of other gods. Her divinity is immediate and everlasting.

Ganges in classical Indian iconography
Early in ancient Indian culture, the river Ganges was associated with fecundity, its redeeming waters, and its rich silt providing sustenance to all who lived along its banks. A counterpoise to the dazzling heat of the Indian summer, the Ganges came to be imbued with magical qualities and to be revered in anthropomorphic form. By the 5th century CE, an elaborate mythology surrounded the Ganges, now a goddess in her own right, and a symbol for all rivers of India. Hindu temples all over India had statues and reliefs of the goddess carved at their entrances, symbolically washing the sins of arriving worshippers and guarding the gods within. As protector of the sanctum sanctorum, the goddess soon came to be depicted with several characteristic accessories: the makara (a crocodile-like undersea monster, often shown with an elephant-like trunk), the kumbha (an overfull vase), various overhead parasol-like coverings, and a gradually increasing retinue of humans.

Central to the goddess's visual identification is the makara, which is also her vahana, or mount. An ancient symbol in India, it pre-dates all appearances of the goddess Ganga in art. The makara has a dual symbolism. On the one hand, it represents the life-affirming waters and plants of its environment; on the other, it represents fear, both fear of the unknown which it elicits by lurking in those waters, and real fear which it instils by appearing in sight. The earliest extant unambiguous pairing of the makara with Ganga is at the Udayagiri Caves in Central India (circa 400 CE). Here, in the Cave V, flanking the main figure of Vishnu shown in his boar incarnation, two river goddesses, Ganga and Yamuna appear atop their respective mounts, makara and kurma (a turtle or tortoise).

The makara is often accompanied by a gana, a small boy or child, near its mouth, as, for example, shown in the Gupta period relief from Besnagar, Central India, in the left-most frame above. The gana represents both posterity and development (udbhava). The pairing of the fearsome, life-destroying makara with the youthful, life-affirming gana speaks to two aspects of the Ganges herself. Although she has provided sustenance to millions, she has also brought hardship, injury, and death by causing major floods along her banks. The goddess Ganga is also accompanied by a dwarf attendant, who carries a cosmetic bag, and on whom she sometimes leans, as if for support. (See, for example, frames 1, 2, and 4 above.)

The purna kumbha or full pot of water is the second most discernible element of the Ganga iconography. Appearing first also in the relief in the Udayagiri Caves (5th century), it gradually appeared more frequently as the theme of the goddess matured. By the 7th century it had become an established feature, as seen, for example, in the Dashavatara temple, Deogarh, Uttar Pradesh (7th century), the Trimurti temple, Badoli, Chittorgarh, Rajasthan, and at the Lakshmaneshwar temple, Kharod, Bilaspur, Chhattisgarh, (9th or 10th century), and seen very clearly in frame 3 above and less clearly in the remaining frames. Worshipped even today, the full pot is emblematic of the formless Brahman, as well as of woman, of the womb, and of birth. Furthermore, The river goddesses Ganga and Saraswati were both born from Brahma's pot, containing the celestial waters.

In her earliest depictions at temple entrances, the goddess Ganga appeared standing beneath the overhanging branch of a tree, as seen as well in the Udayagiri caves. However, soon the tree cover had evolved into a chatra or parasol held by an attendant, for example, in the 7th-century Dasavatara temple at Deogarh. (The parasol can be clearly seen in frame 3 above; its stem can be seen in frame 4, but the rest has broken off.) The cover undergoes another transformation in the temple at Kharod, Bilaspur (9th or 10th century), where the parasol is lotus-shaped, and yet another at the Trimurti temple at Badoli where the parasol has been replaced entirely by a lotus.

As the iconography evolved, sculptors, especially in central India, were producing animated scenes of the goddess, replete with an entourage and suggestive of a queen en route to a river to bathe. A relief similar to the depiction in frame 4 above, is described in as follows: "A typical relief of about the ninth century that once stood at the entrance of a temple, the river goddess Ganga is shown as a voluptuously endowed lady with a retinue. Following the iconographic prescription, she stands gracefully on her composite makara mount and holds a water pot. The dwarf attendant carries her cosmetic bag, and a ... female holds the stem of a giant lotus leaf that serves as her mistress's parasol. The fourth figure is a male guardian. Often in such reliefs, the makara tail is extended with great flourish into a scrolling design symbolizing both vegetation and water."

Kumbh Mela

Kumbh Mela is a mass Hindu pilgrimage in which Hindus gather at the Ganges River. The normal Kumbh Mela is celebrated every 3 years, the Ardh (half) Kumbh is celebrated every six years at Haridwar and Prayagraj, the Purna (complete) Kumbh takes place every twelve years at four places (Triveni Sangam (Prayagraj), Haridwar, Ujjain, and Nashik). The Maha (great) Kumbh Mela which comes after 12 'Purna Kumbh Melas', or 144 years, is held at Prayagraj.

The major event of the festival is ritual bathing at the banks of the river. Other activities include religious discussions, devotional singing, mass feeding of holy men and women and the poor, and religious assemblies where doctrines are debated and standardized. Kumbh Mela is the most sacred of all the pilgrimages. Thousands of holy men and women attend, and the auspiciousness of the festival is in part attributable to this. The sadhus are seen clad in saffron sheets with ashes and powder dabbed on their skin per the requirements of ancient traditions. Some called naga sanyasis, may not wear any clothes.

Irrigation
The Ganges and its all tributaries, especially the Yamuna, have been used for irrigation since ancient times. Dams and canals were common in the Gangetic plain by the 4th century BCE. The Ganges-Brahmaputra-Meghna basin has a huge hydroelectric potential, on the order of 200,000 to 250,000 megawatts, nearly half of which could easily be harnessed. As of 1999, India tapped about 12% of the hydroelectric potential of the Ganges and just 1% of the vast potential of the Brahmaputra.

Canals
Megasthenes, a Greek ethnographer who visited India during the 3rd century BCE when Mauryans ruled India described the existence of canals in the Gangetic plain. Kautilya (also known as Chanakya), an advisor to Chandragupta Maurya, the founder of Maurya Empire, included the destruction of dams and levees as a strategy during the war. Firuz Shah Tughlaq had many canals built, the longest of which, 240 km, was built in 1356 on the Yamuna River. Now known as the Western Yamuna Canal, it has fallen into disrepair and been restored several times. The Mughal emperor Shah Jahan built an irrigation canal on the Yamuna River in the early 17th century. It fell into disuse until 1830, when it was reopened as the Eastern Yamuna Canal, under British control. The reopened canal became a model for the Upper Ganges Canal and all following canal projects. The first British canal in India (which did not have Indian antecedents) was the Ganges Canal built between 1842 and 1854. Contemplated first by Col. John Russell Colvin in 1836, it did not at first elicit much enthusiasm from its eventual architect Sir Proby Thomas Cautley, who balked at the idea of cutting a canal through extensive low-lying land to reach the drier upland destination. However, after the Agra famine of 1837–38, during which the East India Company's administration spent Rs. 2,300,000 on famine relief, the idea of a canal became more attractive to the company's budget-conscious Court of Directors. In 1839, the Governor General of India, Lord Auckland, with the Court's assent, granted funds to Cautley for a full survey of the swath of land that underlay and fringed the projected course of the canal. The Court of Directors, moreover, considerably enlarged the scope of the projected canal, which, in consequence of the severity and geographical extent of the famine, they now deemed to be the entire Doab region.

The enthusiasm, however, proved to be short-lived. Auckland's successor as Governor-General, Lord Ellenborough, appeared less receptive to large-scale public works, and for the duration of his tenure, withheld major funds for the project. Only in 1844, when a new Governor-General, Lord Hardinge, was appointed, did official enthusiasm and funds return to the Ganges canal project. Although the intervening impasse had seemingly affected Cautley's health and required him to return to Britain in 1845 for recuperation, his European sojourn gave him an opportunity to study contemporary hydraulic works in the United Kingdom and Italy. By the time of his return to India even more supportive men were at the helm, both in the North-Western Provinces, with James Thomason as Lt. Governor, and in British India with Lord Dalhousie as Governor-General. Canal construction, under Cautley's supervision, now went into full swing. A 350 mi long canal, with another 300 mi of branch lines, eventually stretched between the headworks in Haridwar, splitting into two branches below Aligarh, and its two confluences with the Yamuna (Jumna in map) mainstem in Etawah and the Ganges in Kanpur (Cawnpore in map). The Ganges Canal, which required a total capital outlay of £2.15 million, was officially opened in 1854 by Lord Dalhousie. According to historian Ian Stone: "It was the largest canal ever attempted in the world, five times greater in its length than all the main irrigation lines of Lombardy and Egypt put together, and longer by a third than even the largest USA navigation canal, the Pennsylvania Canal."

Dams and barrages
A major barrage at Farakka was opened on 21 April 1975, It is located close to the point where the main flow of the river enters Bangladesh, and the tributary Hooghly (also known as Bhagirathi) continues in West Bengal past Kolkata. This barrage, which feeds the Hooghly branch of the river by a 26 mi long feeder canal, and its water flow management has been a long-lingering source of dispute with Bangladesh. Indo-Bangladesh Ganges Water Treaty signed in December 1996 addressed some of the water sharing issues between India and Bangladesh. There is Lav Khush Barrage across the River Ganges in Kanpur.

Tehri Dam was constructed on Bhagirathi River, a tributary of the Ganges. It is located 1.5 km downstream of Ganesh Prayag, the place where Bhilangana meets Bhagirathi. Bhagirathi is called the Ganges after Devprayag. Construction of the dam in an earthquake-prone area was controversial.

Bansagar Dam was built on the Sone River, a tributary of the Ganges for both irrigation and hydroelectric power generation. Ganges floodwaters along with Brahmaputra waters can be supplied to most of its right side basin area along with central and south India by constructing a coastal reservoir to store water on the Bay of Bengal sea area.

Economy

The Ganges Basin with its fertile soil is instrumental to the agricultural economies of India and Bangladesh. The Ganges and its tributaries provide a perennial source of irrigation to a large area. Chief crops cultivated in the area include rice, sugarcane, lentils, oil seeds, potatoes, and wheat. Along the banks of the river, the presence of swamps and lakes provides a rich growing area for crops such as legumes, chillies, mustard, sesame, sugarcane, and jute. There are also many fishing opportunities along the river, though it remains highly polluted. Also, the major industrial towns of Unnao and Kanpur, situated on the banks of the river with the predominance of tanning industries add to the pollution.

Tourism
Tourism is another related activity. Three towns holy to Hinduism—Haridwar, Prayagraj, and Varanasi—attract millions of pilgrims to its waters to take a dip in the Ganges, which is believed to cleanse oneself of sins and help attain salvation. The rapids of the Ganges are also popular for river rafting in the town of Rishikesh, attracting adventure seekers in the summer months. Several cities such as Kanpur, Kolkata and Patna have also developed riverfront walkways along the banks to attract tourists.

Ecology and environment
Human development, mostly agriculture, has replaced nearly all of the original natural vegetation of the Ganges basin. More than 95% of the upper Gangetic Plain has been degraded or converted to agriculture or urban areas. Only one large block of relatively intact habitat remains, running along the Himalayan foothills and including Rajaji National Park, Jim Corbett National Park, and Dudhwa National Park. As recently as the 16th and 17th centuries the upper Gangetic Plain harboured impressive populations of wild Asian elephants (Elephas maximus), Bengal tigers (Panthera t. tigris), Indian rhinoceros (Rhinoceros unicornis), gaurs (Bos gaurus), barasinghas (Rucervus duvaucelii), sloth bears (Melursus ursinus) and Indian lions (Panthera leo leo). In the 21st century there are few large wild animals, mostly deer, wild boars, wildcats, and small numbers of Indian wolves, golden jackals, and red and Bengal foxes. Bengal tigers survive only in the Sundarbans area of the Ganges Delta. The Sundarbands freshwater swamp ecoregion, however, is nearly extinct. The Sundarbans mangroves (Heritiera fomes) also grow in the Sundarbans area of the Ganges Delta. Threatened mammals in the upper Gangetic Plain include the tiger, elephant, sloth bear, and four-horned antelope (Tetracerus quadricornis).

Many types of birds are found throughout the basin, such as myna, Psittacula parakeets, crows, kites, partridges, and fowls. Ducks and snipes migrate across the Himalayas during the winter, attracted in large numbers to wetland areas. There are no endemic birds in the upper Gangetic Plain. The great Indian bustard (Ardeotis nigriceps) and lesser florican (Sypheotides indicus) are considered globally threatened.

The natural forest of the upper Gangetic Plain has been so thoroughly eliminated it is difficult to assign a natural vegetation type with certainty. There are a few small patches of forest left, and they suggest that much of the upper plains may have supported a tropical moist deciduous forest with sal (Shorea robusta) as a climax species.

A similar situation is found in the lower Gangetic Plain, which includes the lower Brahmaputra River. The lower plains contain more open forests, which tend to be dominated by Bombax ceiba in association with Albizzia procera, Duabanga grandiflora, and Sterculia vilosa. There are early seral forest communities that would eventually become dominated by the climax species sal (Shorea robusta) if forest succession was allowed to proceed. In most places forests fail to reach climax conditions due to human causes. The forests of the lower Gangetic Plain, despite thousands of years of human settlement, remained largely intact until the early 20th century. Today only about 3% of the ecoregion is under natural forest and only one large block, south of Varanasi, remains. There are over forty protected areas in the ecoregion, but over half of these are less than 100 km2. The fauna of the lower Gangetic Plain is similar to the upper plains, with the addition of a number of other species such as the smooth-coated otter (Lutrogale perspicillata) and the large Indian civet (Viverra zibetha).

Fish

It has been estimated that about 350 fish species live in the entire Ganges drainage, including several endemics. In a major 2007–2009 study of fish in the Ganges basin (including the river itself and its tributaries, but excluding the Brahmaputra and Meghna basins), a total of 143 fish species were recorded, including 10 non-native introduced species. The most diverse orders are Cypriniformes (barbs and allies), Siluriformes (catfish) and Perciformes (perciform fish), each comprising about 50%, 23% and 14% of the total fish species in the drainage.

There are distinct differences between the different sections of the river basin, but Cyprinidae is the most diverse throughout. In the upper section (roughly equalling the basin parts in Uttarakhand) more than 50 species have been recorded and Cyprinidae alone accounts for almost 80% those, followed by Balitoridae (about 15.6%) and Sisoridae (about 12.2%). Sections of the Ganges basin at altitudes above 2400-3000 m above sea level are generally without fish. Typical genera approaching this altitude are Schizothorax, Tor, Barilius, Nemacheilus and Glyptothorax. About 100 species have been recorded from the middle section of the basin (roughly equalling the sections in Uttar Pradesh and parts of Bihar) and more than 55% of these are in family Cyprinidae, followed by Schilbeidae (about 10.6%) and Clupeidae (about 8.6%). The lower section (roughly equalling the basin in parts of Bihar and West Bengal) includes major floodplains and is home to almost 100 species. About 46% of these are in the family Cyprinidae, followed by Schilbeidae (about 11.4%) and Bagridae (about 9%).

The Ganges basin supports major fisheries, but these have declined in recent decades. In the Prayagraj region in the middle section of the basin, catches of carp fell from 424.91 metric tons in 1961–1968 to 38.58 metric tons in 2001–2006, and catches of catfish fell from 201.35 metric tons in 1961–1968 to 40.56 metric tons in 2001–2006. In the Patna region in the lower section of the basin, catches of carp fell from 383.2 metric tons to 118, and catfish from 373.8 metric tons to 194.48. Some of the fish commonly caught in fisheries include catla (Catla catla), golden mahseer (Tor putitora), tor mahseer (Tor tor), rohu (Labeo rohita), walking catfish (Clarias batrachus), pangas catfish (Pangasius pangasius), goonch catfish (Bagarius), snakeheads (Channa), bronze featherback (Notopterus notopterus) and milkfish (Chanos chanos).

The Ganges basin is home to about 30 fish species that are listed as threatened with the primary issues being overfishing (sometimes illegal), pollution, water abstraction, siltation and invasive species. Among the threatened species is the critically endangered Ganges shark (Glyphis gangeticus). Several fish species migrate between different sections of the river, but these movements may be prevented by the building of dams.

Crocodilians and turtles

The main sections of the Ganges River are home to the gharial (Gavialis gangeticus) and mugger crocodile (Crocodylus palustris), and the Ganges delta is home to the saltwater crocodile (C. porosus). Among the numerous aquatic and semi-aquatic turtles in the Ganges basin are the northern river terrapin (Batagur baska; only in the lowermost section of the basin), three-striped roofed turtle (B. dhongoka), red-crowned roofed turtle (B. kachuga), black pond turtle (Geoclemys hamiltonii), Brahminy river turtle (Hardella thurjii), Indian black turtle (Melanochelys trijuga), Indian eyed turtle (Morenia petersi), brown roofed turtle (Pangshura smithii), Indian roofed turtle (Pangshura tecta), Indian tent turtle (Pangshura tentoria), Indian flapshell turtle (Lissemys punctata), Indian narrow-headed softshell turtle (Chitra indica), Indian softshell turtle (Nilssonia gangetica), Indian peacock softshell turtle (N. hurum) and Cantor's giant softshell turtle (Pelochelys cantorii; only in the lowermost section of Ganges basin). Most of these are seriously threatened.

Ganges river dolphin
The river's most famed faunal member is the freshwater Ganges river dolphin (Platanista gangetica gangetica), which has been declared India's national aquatic animal.

This dolphin used to exist in large schools near urban centres in both the Ganges and Brahmaputra rivers but is now seriously threatened by pollution, dam construction and improper fishing methods. Their numbers have now dwindled to a quarter of their numbers of fifteen years before, and they have become extinct in the Ganges' main tributaries. A recent survey by the World Wildlife Fund found only 3,000 left in the water catchment of both river systems.

The Ganges river dolphin is one of only five true freshwater dolphins in the world. The other four are the baiji (Lipotes vexillifer) of the Yangtze River in China, now likely extinct; the Indus River dolphin of the Indus River in Pakistan; the Amazon river dolphin of the Amazon River in South America; and the Araguaian river dolphin (not considered a separate species until 2014 ) of the Araguaia–Tocantins basin in Brazil. There are several marine dolphins whose ranges include some freshwater habitats, but these five are the only dolphins who live only in freshwater rivers and lakes.

Effects of climate change
The Tibetan Plateau contains the world's third-largest store of ice. Qin Dahe, the former head of the China Meteorological Administration, said that the recent fast pace of melting and warmer temperatures will be good for agriculture and tourism in the short term; but issued a strong warning:

"Temperatures are rising four times faster than elsewhere in China, and the Tibetan glaciers are retreating at a higher speed than in any other part of the world. ... In the short term, this will cause lakes to expand and bring floods and mudflows ... In the long run, the glaciers are vital lifelines for Asian rivers, including the Indus and the Ganges. Once they vanish, water supplies in those regions will be in peril."

In 2007, the Intergovernmental Panel on Climate Change (IPCC), in its Fourth Report, stated that the Himalayan glaciers which feed the river were at risk of melting by 2035. The IPCC has now withdrawn that prediction, as the original source admitted that it was speculative and the cited source was not a peer-reviewed finding. In its statement, the IPCC stands by its general findings relating to the Himalayan glaciers being at risk from global warming (with consequent risks to water flow into the Gangetic basin). Many studies have suggested that climate change will affect the water resources in the Ganges river basin including increased summer (monsoon) flow, and peak runoff could result in an increased risk of flooding.

Pollution and environmental concerns

The Ganges suffers from extreme pollution levels, caused by the 400 million people who live close to the river. Sewage from many cities along the river's course, industrial waste and religious offerings wrapped in non-degradable plastics add large amounts of pollutants to the river as it flows through densely populated areas. The problem is exacerbated by the fact that many poorer people rely on the river on a daily basis for bathing, washing, and cooking. The World Bank estimates that the health costs of water pollution in India equal three percent of India's GDP. It has also been suggested that eighty percent of all illnesses in India and one-third of deaths can be attributed to water-borne diseases.

Varanasi, a city of one million people that many pilgrims visit to take a "holy dip" in the Ganges, releases around 200 million liters of untreated human sewage into the river each day, leading to large concentrations of fecal coliform bacteria. According to official standards, water safe for bathing should not contain more than 500 fecal coliforms per 100 ml, yet upstream of Varanasi's ghats the river water already contains 120 times as much, 60,000 fecal coliform bacteria per 100 ml.

After the cremation of the deceased at Varanasi's ghats, the bones and ashes are immersed into the Ganges. However, in the past thousands of uncremated bodies were thrown into the Ganges during cholera epidemics, spreading the disease. Even today, holy men, pregnant women, people with leprosy or chicken pox, people who have been bitten by snakes, people who have committed suicide, the poor, and children under 5 are not cremated at the ghats but are left to float free, to decompose in the waters. In addition, those who cannot afford the large amount of wood needed to incinerate the entire body, leave behind many half-burned body parts.

After passing through Varanasi, and receiving 32 streams of raw sewage from the city, the concentration of fecal coliforms in the river's waters rises from 60,000 to 1.5 million, with observed peak values of 100 million per 100 ml. Drinking and bathing in its waters therefore carries a high risk of infection.

Between 1985 and 2000, Rs. 10 billion, around US$226 million, or less than 4 cents per person per year, were spent on the Ganga Action Plan, an environmental initiative that was "the largest single attempt to clean up a polluted river anywhere in the world". The Ganga Action Plan has been described variously as a "failure" and a "major failure".

According to one study, The Ganga Action Plan, which was taken on priority and with much enthusiasm, was delayed for two years. The expenditure was almost doubled. But the result was not very appreciable. Much expenditure was done on political propaganda. The concerning governments and the related agencies were not very prompt to make it a success. The public of the areas was not taken into consideration. The release of urban and industrial wastes in the river was not controlled fully. The flowing of dirty water through drains and sewers were not adequately diverted. The continuing customs of burning dead bodies, throwing carcasses, washing of dirty clothes by washermen, and immersion of idols and cattle wallowing were not checked. Very little provision of public latrines was made and the open defecation of lakhs of people continued along the riverside. All these made the Action Plan a failure.

The failure of the Ganga Action Plan has also been variously attributed to "environmental planning without proper understanding of the human-environment interactions", Indian "traditions and beliefs", "corruption and a lack of technical knowledge" and "lack of support from religious authorities".

In December 2009 the World Bank agreed to loan India US$1 billion over the next five years to help save the river. According to 2010 Planning Commission estimates, an investment of almost Rs. 70 billion (Rs. 70 billion, approximately US$1.5 billion) is needed to clean up the river.

In November 2008, the Ganges, alone among India's rivers, was declared a "National River", facilitating the formation of a National Ganga River Basin Authority that would have greater powers to plan, implement and monitor measures aimed at protecting the river.

In July 2014, the Government of India announced an integrated Ganges-development project titled Namami Gange Programme and allocated ₹2,037 crore for this purpose. The main objectives of the Namami Gange project is to improve the water quality by the abatement of pollution and rejuvenation of river Ganga by creating infrastructures like sewage treatment plants, river surface cleaning, biodiversity conservation, afforestation, and public awareness.

In March 2017 the High Court of Uttarakhand declared the Ganges River a legal "person", in a move that according to one newspaper, "could help in efforts to clean the pollution-choked rivers". , the ruling has been commented on in Indian newspapers to be hard to enforce, that experts do not anticipate immediate benefits, that the ruling is "hardly game changing", that experts believe "any follow-up action is unlikely", and that the "judgment is deficient to the extent it acted without hearing others (in states outside Uttarakhand) who have stakes in the matter."

The incidence of water-borne and enteric diseases—such as gastrointestinal disease, cholera, dysentery, hepatitis A and typhoid—among people who use the river's waters for bathing, washing dishes and brushing teeth is high, at an estimated 66% per year.

Recent studies by Indian Council of Medical Research (ICMR) say that the river is so full of killer pollutants that those living along its banks in Uttar Pradesh, Bihar, and Bengal are more prone to cancer than anywhere else in the country. Conducted by the National Cancer Registry Programme under the ICMR, the study throws up shocking findings indicating that the river is thick with heavy metals and lethal chemicals that cause cancer. According to Deputy Director-General of NCRP A. Nandkumar, the incidence of cancer was highest in the country in areas drained by the Ganges and stated that the problem would be studied deeply and with the findings presented in a report to the health ministry.

Apart from that, many NGOs have come forward to rejuvenate the river Ganges. Vikrant Tongad, an Environmental specialist from SAFE Green filed a petition against Simbhaoli Sugar Mill (Hapur UP) to NGT. NGT slapped a fine of Rs. 5 crores to Sugar Mill and a fine of Rs. 25 lakhs to Gopaljee Dairy for discharging untreated effluents into the Simbhaoli drain.

Water shortages
Along with ever-increasing pollution, water shortages are getting noticeably worse. Some sections of the river are already completely dry. Around Varanasi, the river once had an average depth of 60 m, but in some places, it is now only 10 m.

"To cope with its chronic water shortages, India employs electric groundwater pumps, diesel-powered tankers, and coal-fed power plants. If the country increasingly relies on these energy-intensive short-term fixes, the whole planet's climate will bear the consequences. India is under enormous pressure to develop its economic potential while also protecting its environment—something few, if any, countries have accomplished. What India does with its water will be a test of whether that combination is possible."

Mining
Illegal mining in the Ganges river bed for stones and sand for construction work has long been a problem in Haridwar district, Uttarakhand, where it touches the plains for the first time. This is despite the fact that quarrying has been banned in Kumbh Mela area zone covering 140 km2 area in Haridwar.

In art and literature

 * A painting of the Ganges entering the plains near Haridwar by William Purser with a poetical illustration by Letitia Elizabeth Landon in Fisher's Drawing Room Scrap Book, 1838.
 * A painting of the Ganges near Kahalgaon by J. M. W. Turner with a poetical illustration by Letitia Elizabeth Landon in Fisher's Drawing Room Scrap Book, 1839.

title: Ganges


text:
Mobile Suit Gundam Wing

Mobile Suit Gundam Wing, also known in Japan as New Mobile Report Gundam Wing (新機動戦記ガンダム), is a 1995 Japanese mecha anime series directed by Masashi Ikeda and written by Katsuyuki Sumizawa. It is the sixth installment in the Gundam franchise, taking place in the "After Colony" timeline. As with the original series, the plot of Gundam Wing centers on a war in the future (specifically, the year After Colony 195) between Earth and its orbital colonies in the Earth-Moon system.

The series aired in Japan on the terrestrial TV Asahi network. It ran for 49 episodes, beginning on April 7, 1995, and ending on March 29, 1996. It received multiple manga adaptations, as well as video games. Four original video animation (OVA) episodes were produced including a retelling of the series, Operation Meteor, and a direct sequel, Endless Waltz. In 2010, Sumizawa started writing the novel Frozen Teardrop, another sequel to the series. While the series fared modestly well in Japan, it found greater success in the United States and single-handedly popularized the Gundam franchise in the West.

Plot
In the distant future, Mankind has colonized space, with clusters of space colonies at each of the five Earth-Moon Lagrange points. Down on the Earth, the nations have come together to form the United Earth Sphere Alliance. This Alliance oppresses the colonies with its vast military might. The colonies wishing to be free, joined together in a movement headed by the pacifist Heero Yuy. In the year After Colony 175, Yuy is shot dead by an assassin, forcing the colonies to search for other paths to peace. The assassination prompts five disaffected scientists from the Organization of the Zodiac, more commonly referred to as OZ, to turn rogue upon the completion of the mobile suit prototype Tallgeese.

The story of Gundam Wing begins in the year After Colony 195, with the start of "Operation Meteor": the scientists' plan for revenge against OZ. The operation involves five teenage boys, who have each been chosen and trained by each of the five scientists, then sent to Earth independently in extremely advanced mobile suits (one designed by each of the scientists) known as "Gundams" (called such because they are constructed from a rare and astonishingly durable material called Gundanium alloy, which can only be created in outer space). Each Gundam is sent from a different colony, and the pilots are unaware of each other's existence.

The series focuses primarily on the five Gundam pilots: Heero Yuy (an alias, not to be confused with the martyred pacifist), Duo Maxwell, Trowa Barton, Quatre Raberba Winner and Chang Wufei. Their mission is to use their Gundams to attack OZ directly, to rid the Alliance of its weapons, and to free the colonies from its oppressive rule. The series also focuses on Relena Peacecraft, heir to the pacifist Sanc Kingdom, who becomes an important political ally to the Gundam pilots (particularly Heero) throughout the series.

Production
The making of Gundam Wing was influenced by Mobile Fighter G Gundam with the idea of having five main characters. Originally, the series was meant to be titled Gundam Meteor after "Operation Meteor." Bandai suggested having a Gundam with the ability of transforming into a plane-like form (which led to the creation of the Wing Gundam and its "Bird Mode"). The writers worked together for one week conceptualizing the characters, mobile suits and first 40 episodes. Director Masashi Ikeda reacted to their work comparing it to the first Gundam series, Zeta and G all at once. The series was more focused on drama than mecha, which the staff credits as one of the reasons for the show's popularity within the female demographic.

Writer Katsuyuki Sumizawa expressed difficulties in the making of the story as opposed to his work in novels due to the fact he relayed duties to other members. However, the handling of the five characters was made easy due to the setting. Early sketches of the protagonists by Ikeda were handled by character designer Shuko Murase. He was cast due to his work with Ikeda in Samurai Troopers. The director wanted the designs to appeal to the female demographic. Originally, Duo Maxwell was set as the protagonist but was replaced by Heero Yuy. The staff members noted Heero was too different from previous Gundam protagonists and were afraid he would be unpopular. The voice casting was more difficult to do than the ones from previous series due to the different atmosphere.

Following the series' ending, the staff members were asked by the studio to make a sequel due to its popularity. Neither Ikeda nor executive producer Hideyuki Tomioka intended to make a sequel for Gundam Wing. However, Sumizawa was bothered by the finale as he felt the series ended abruptly. Tomioka asked Sumizawa if he could write a continuation, which he agreed to do.

Anime
Gundam Wing was not the first series in the Gundam franchise to be dubbed and distributed in the U.S. (the compilation film version of the original Mobile Suit Gundam, as well as the OVAs War in the Pocket and Stardust Memory, preceded it by about two years), but it is well known as the first Gundam series to be aired on American television. This dub was licensed by Sunrise and the voice work was done by Ocean Productions. The series aired on Cartoon Network's weekday afternoon after-school programming block Toonami, premiering on March 6, 2000. In the first extended promo leading up to the series' premiere, voice actor Peter Cullen narrated the back story, evoking memories of Voltron's opening credits. The promo was said to be so riveting that Bandai decided to use it as the official promo for the series. Gundam Wing was a huge ratings winner for Toonami (often outperforming veteran series such as Dragon Ball Z and Sailor Moon) and became, for a time, not only the highest rated series on Toonami but on all of Cartoon Network.

It was broadcast in two formats: an edited version shown in the daytime on Toonami and an uncut version shown past midnight as part of Toonami's "Midnight Run." Examples of the edits included the removal of blood, profanity, atheism, and the word "kill" being replaced with the word "destroy" (this was extended to Duo's nickname, "The God of Death," changed to "The Great Destroyer," forcing the alteration of two episode titles), though the word "death" was mostly left intact. All Gundam Wing episodes have been released to VHS and DVD in the U.S. Differences between the two video systems is that the VHS episodes contain the edited version while the DVD episodes contain the uncut version.

Due to the closure of Bandai Entertainment, the series was out-of-print for some time. On October 11, 2014 at their 2014 New York Comic Con panel, Sunrise announced they will be releasing all of the Gundam franchise, including Gundam Wing in North America though distribution from Right Stuf Inc., beginning in Spring 2015. Right Stuf released the series on Blu-ray and DVD in two sets in November 2017. In addition, a collector's edition set containing the complete series, Endless Waltz, Operation Meteor and the Frozen Teardrop picture drama was released in December 2017.

OVAs
After the series ended, four original video animation (OVA) episodes, compiling various scenes from the series along with a few minutes of new footage, were released in 1996 as Gundam Wing: Operation Meteor I and II.

A three-part OVA titled Gundam Wing: Endless Waltz was produced in 1997 as a sequel to the TV series; plot-wise, it brought the "After Colony" timeline to a close. The OVA was also notable for its massive redesigns of all the Gundams by Hajime Katoki, such as the Wing Gundam Zero's new "angel-winged" appearance. A compilation film version of Endless Waltz (featuring additional footage, alterations of the music score and a different ending theme) was later released in Japan on August 1, 1998. Endless Waltz premiered on Cartoon Network in the U.S. on November 10, 2000. Both the OVA and film versions of Endless Waltz were later released together on DVD. Right Stuf released both OVAs on Blu-ray and DVD in December 2017 (though Operation Meteor remains un-dubbed).

Manga
In addition to manga adaptations of the series and Endless Waltz, several manga sidestories have also been produced. Episode Zero is a prequel, detailing the events leading up to series; the stories have been collected in a volume that also contains one brief open-ended interlude, Preventer 5, that details an operation that occurs after Endless Waltz. A coincident storyline to the series is presented in Last Outpost (G-Unit). Several sequel manga, occurring between Gundam Wing and Endless Waltz, have also been written: Blind Target, Ground Zero and Battlefield of Pacifists.

The Gundam Wing, Battlefield of Pacifists and Endless Waltz manga series were published in English by Tokyopop, while Blind Target, Ground Zero and Episode Zero were published by Viz Communications. Another sequel manga detailing the future of the colonies entitled Tiel's Impulse was printed in 1998 and has not been published in the United States.

In September 2010, Gundam Ace magazine began serializing a manga titled New Mobile Report Gundam Wing Endless Waltz: The Glory of Losers that retells the events of the anime while incorporating facts from Episode Zero and the novel Frozen Teardrop. The manga ended in November 2017 and was compiled into fourteen volumes. The manga also uses Hajime Katoki's Gundam redesigns from Endless Waltz and other subsequent media, instead of the original Kunio Okawara designs featured in the anime. Vertical published English editions of the manga volumes under the title Mobile Suit Gundam Wing Endless Waltz: Glory of the Losers from July 2017 to November 2019.

Novel sequel
In early 2010, Gundam Ace magazine announced they would serialize a "New Gundam Wing Project". The project was eventually revealed to be a novel, titled New Mobile Report Gundam Wing: Frozen Teardrop. Written by Katsuyuki Sumizawa, the novel begins a new timeline, following the "Mars Century" calendar ("MC") which was the successor of the previous "After Colony" calendar. According to an interview with the author, the novel spans backwards into the AC century and the Gundam pilots, Relena, and their children make appearances.

Other media
A fighting video game titled Shin Kidō Senki Gundam Wing: Endless Duel was developed by Natsume Co., Ltd. and released for the Super Famicom in Japan on March 29, 1996. A second fighting game titled Shin Kidō Senki Gundam Wing: The Battle was developed by Natsume Co., Ltd. and released for the PlayStation in Japan on October 11, 2002 as the 13th volume of the Simple Characters 2000 series. Gundam Wing characters and mecha have also appeared in several other video game series including Super Robot Wars, Gundam Battle Assault, Another Century's Episode, Mobile Suit Gundam: Extreme Vs. and Dynasty Warriors: Gundam.

Upon the series' debut in North America, Gundam Wing received a large roster of licensees for merchandise including wallscrolls, apparel, school supplies, skateboards, trading cards, model kits and action figures.

Soundtracks

 * Openings:
 * "Just Communication" by Two-Mix (ep. 1–40) (YTV Broadcast: 1–49)
 * "Rhythm Emotion" by Two-Mix (ep. 41–49)

 * Ending:
 * "It's Just Love!" by Rumi Ohishi (ep. 1–49)
 * "Just Communication" (Instrumental Version) by Kow Otani (Toonami Broadcast, ep. 1–49; the credits aired over a shortened version of the show's first opening animation)

 * Insert songs:
 * "Just Communication" by Two-Mix (eps. 3 & 49)
 * "Rhythm Emotion" by Two-Mix (eps. 36, 38, 39, and 41)

Reception
Gundam Wing was only a modest success in Japan during its initial run; it, along with G Gundam, was the only Gundam series of the 1990s that managed an average television rating over four percent. It was ranked number two in Animage magazine's Anime Grand Prix in 1996 and was also ranked number 76 in the publication's list of the 100 most important anime of all time. The series is infamous within dōjinshi where authors tend to depict romantic relationships between several of the protagonists.

Gundam Wing was a greater success in North America, however, and is credited by John Oppliger on Animation Anime News Blog with single-handedly popularizing the Gundam franchise among American audiences. Just over a week after its premiere on Cartoon Network on March 6, 2000, the series was the top rated program in all age groups. During the summer of 2000, it remained as the first or second top-rated show among kids and teens during its twelve airings per week on the Toonami block. Gundam Wing was ranked the 73rd best animated series by IGN, calling the series "so good that even those opposed to anime have to give the show its due credit".

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Mobile Suit Gundam Wing


text:
Gödel's completeness theorem

Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic.

The completeness theorem applies to any first-order theory: If T is such a theory, and φ is a sentence (in the same language) and every model of T is a model of φ, then there is a (first-order) proof of φ using the statements of T as axioms. One sometimes says this as "anything true in all models is provable". (This does not contradict Gödel's incompleteness theorem, which is about a formula φu that is unprovable in a certain theory T but true in the "standard" model of the natural numbers: φu is false in some other, "non-standard" models of T. )

The completeness theorem makes a close link between model theory, which deals with what is true in different models, and proof theory, which studies what can be formally proven in particular formal systems.

It was first proved by Kurt Gödel in 1929. It was then simplified when Leon Henkin observed in his Ph.D. thesis that the hard part of the proof can be presented as the Model Existence Theorem (published in 1949). Henkin's proof was simplified by Gisbert Hasenjaeger in 1953.

Preliminaries
There are numerous deductive systems for first-order logic, including systems of natural deduction and Hilbert-style systems. Common to all deductive systems is the notion of a formal deduction. This is a sequence (or, in some cases, a finite tree) of formulae with a specially designated conclusion. The definition of a deduction is such that it is finite and that it is possible to verify algorithmically (by a computer, for example, or by hand) that a given sequence (or tree) of formulae is indeed a deduction.

A first-order formula is called logically valid if it is true in every structure for the language of the formula (i.e. for any assignment of values to the variables of the formula). To formally state, and then prove, the completeness theorem, it is necessary to also define a deductive system. A deductive system is called complete if every logically valid formula is the conclusion of some formal deduction, and the completeness theorem for a particular deductive system is the theorem that it is complete in this sense. Thus, in a sense, there is a different completeness theorem for each deductive system. A converse to completeness is soundness, the fact that only logically valid formulas are provable in the deductive system.

If some specific deductive system of first-order logic is sound and complete, then it is "perfect" (a formula is provable if and only if it is logically valid), thus equivalent to any other deductive system with the same quality (any proof in one system can be converted into the other).

Statement
We first fix a deductive system of first-order predicate calculus, choosing any of the well-known equivalent systems. Gödel's original proof assumed the Hilbert-Ackermann proof system.

Gödel's original formulation
The completeness theorem says that if a formula is logically valid then there is a finite deduction (a formal proof) of the formula.

Thus, the deductive system is "complete" in the sense that no additional inference rules are required to prove all the logically valid formulae. A converse to completeness is soundness, the fact that only logically valid formulae are provable in the deductive system. Together with soundness (whose verification is easy), this theorem implies that a formula is logically valid if and only if it is the conclusion of a formal deduction.

More general form
The theorem can be expressed more generally in terms of logical consequence. We say that a sentence s is a syntactic consequence of a theory T, denoted $$T\vdash s$$, if s is provable from T in our deductive system. We say that s is a semantic consequence of T, denoted $$T\models s$$, if s holds in every model of T. The completeness theorem then says that for any first-order theory T with a well-orderable language, and any sentence s in the language of T,

Since the converse (soundness) also holds, it follows that $$T\models s$$ if and only if $$T\vdash s$$, and thus that syntactic and semantic consequence are equivalent for first-order logic.

This more general theorem is used implicitly, for example, when a sentence is shown to be provable from the axioms of group theory by considering an arbitrary group and showing that the sentence is satisfied by that group.

Gödel's original formulation is deduced by taking the particular case of a theory without any axiom.

Model existence theorem
The completeness theorem can also be understood in terms of consistency, as a consequence of Henkin's model existence theorem. We say that a theory T is syntactically consistent if there is no sentence s such that both s and its negation ¬s are provable from T in our deductive system. The model existence theorem says that for any first-order theory T with a well-orderable language,

Another version, with connections to the Löwenheim–Skolem theorem, says:

Given Henkin's theorem, the completeness theorem can be proved as follows: If $$T \models s$$, then $$T\cup\lnot s$$ does not have models. By the contrapositive of Henkin's theorem, then $$T\cup\lnot s$$ is syntactically inconsistent. So a contradiction ($$\bot$$) is provable from $$T\cup\lnot s$$ in the deductive system. Hence $$(T\cup\lnot s) \vdash \bot$$, and then by the properties of the deductive system, $$T\vdash s$$.

As a theorem of arithmetic
The model existence theorem and its proof can be formalized in the framework of Peano arithmetic. Precisely, we can systematically define a model of any consistent effective first-order theory T in Peano arithmetic by interpreting each symbol of T by an arithmetical formula whose free variables are the arguments of the symbol. (In many cases, we will need to assume, as a hypothesis of the construction, that T is consistent, since Peano arithmetic may not prove that fact.) However, the definition expressed by this formula is not recursive (but is, in general, Δ2).

Consequences
An important consequence of the completeness theorem is that it is possible to recursively enumerate the semantic consequences of any effective first-order theory, by enumerating all the possible formal deductions from the axioms of the theory, and use this to produce an enumeration of their conclusions.

This comes in contrast with the direct meaning of the notion of semantic consequence, that quantifies over all structures in a particular language, which is clearly not a recursive definition.

Also, it makes the concept of "provability", and thus of "theorem", a clear concept that only depends on the chosen system of axioms of the theory, and not on the choice of a proof system.

Relationship to the incompleteness theorems
Gödel's incompleteness theorems show that there are inherent limitations to what can be proven within any given first-order theory in mathematics. The "incompleteness" in their name refers to another meaning of complete (see model theory – Using the compactness and completeness theorems): A theory $$T$$ is complete (or decidable) if every sentence $$S$$ in the language of $$T$$ is either provable ($$T\vdash S$$) or disprovable ($$T\vdash \neg S$$).

The first incompleteness theorem states that any $$T$$ which is consistent, effective and contains Robinson arithmetic ("Q") must be incomplete in this sense, by explicitly constructing a sentence $$S_T$$ which is demonstrably neither provable nor disprovable within $$T$$. The second incompleteness theorem extends this result by showing that $$S_T$$ can be chosen so that it expresses the consistency of $$T$$ itself.

Since $$S_T$$ cannot be proven in $$T$$, the completeness theorem implies the existence of a model of $$T$$ in which $$S_T$$ is false. In fact, $$S_T$$ is a Π1 sentence, i.e. it states that some finitistic property is true of all natural numbers; so if it is false, then some natural number is a counterexample. If this counterexample existed within the standard natural numbers, its existence would disprove $$S_T$$ within $$T$$; but the incompleteness theorem showed this to be impossible, so the counterexample must not be a standard number, and thus any model of $$T$$ in which $$S_T$$ is false must include non-standard numbers.

In fact, the model of any theory containing Q obtained by the systematic construction of the arithmetical model existence theorem, is always non-standard with a non-equivalent provability predicate and a non-equivalent way to interpret its own construction, so that this construction is non-recursive (as recursive definitions would be unambiguous).

Also, if $$T$$ is at least slightly stronger than Q (e.g. if it includes induction for bounded existential formulas), then Tennenbaum's theorem shows that it has no recursive non-standard models.

Relationship to the compactness theorem
The completeness theorem and the compactness theorem are two cornerstones of first-order logic. While neither of these theorems can be proven in a completely effective manner, each one can be effectively obtained from the other.

The compactness theorem says that if a formula φ is a logical consequence of a (possibly infinite) set of formulas Γ then it is a logical consequence of a finite subset of Γ. This is an immediate consequence of the completeness theorem, because only a finite number of axioms from Γ can be mentioned in a formal deduction of φ, and the soundness of the deductive system then implies φ is a logical consequence of this finite set. This proof of the compactness theorem is originally due to Gödel.

Conversely, for many deductive systems, it is possible to prove the completeness theorem as an effective consequence of the compactness theorem.

The ineffectiveness of the completeness theorem can be measured along the lines of reverse mathematics. When considered over a countable language, the completeness and compactness theorems are equivalent to each other and equivalent to a weak form of choice known as weak Kőnig's lemma, with the equivalence provable in RCA0 (a second-order variant of Peano arithmetic restricted to induction over Σ01 formulas). Weak Kőnig's lemma is provable in ZF, the system of Zermelo–Fraenkel set theory without axiom of choice, and thus the completeness and compactness theorems for countable languages are provable in ZF. However the situation is different when the language is of arbitrary large cardinality since then, though the completeness and compactness theorems remain provably equivalent to each other in ZF, they are also provably equivalent to a weak form of the axiom of choice known as the ultrafilter lemma. In particular, no theory extending ZF can prove either the completeness or compactness theorems over arbitrary (possibly uncountable) languages without also proving the ultrafilter lemma on a set of the same cardinality.

Completeness in other logics
The completeness theorem is a central property of first-order logic that does not hold for all logics. Second-order logic, for example, does not have a completeness theorem for its standard semantics (though does have the completeness property for Henkin semantics), and the set of logically-valid formulas in second-order logic is not recursively enumerable. The same is true of all higher-order logics. It is possible to produce sound deductive systems for higher-order logics, but no such system can be complete.

Lindström's theorem states that first-order logic is the strongest (subject to certain constraints) logic satisfying both compactness and completeness.

A completeness theorem can be proved for modal logic or intuitionistic logic with respect to Kripke semantics.

Proofs
Gödel's original proof of the theorem proceeded by reducing the problem to a special case for formulas in a certain syntactic form, and then handling this form with an ad hoc argument.

In modern logic texts, Gödel's completeness theorem is usually proved with Henkin's proof, rather than with Gödel's original proof. Henkin's proof directly constructs a term model for any consistent first-order theory. James Margetson (2004) developed a computerized formal proof using the Isabelle theorem prover. Other proofs are also known.

title: Gödel's completeness theorem


text:
Global Boundary Stratotype Section and Point

A Global Boundary Stratotype Section and Point (GSSP), sometimes referred to as a golden spike, is an internationally agreed upon reference point on a stratigraphic section which defines the lower boundary of a stage on the geologic time scale. The effort to define GSSPs is conducted by the International Commission on Stratigraphy, a part of the International Union of Geological Sciences. Most, but not all, GSSPs are based on paleontological changes. Hence GSSPs are usually described in terms of transitions between different faunal stages, though far more faunal stages have been described than GSSPs. The GSSP definition effort commenced in 1977. As of 2024, 79 of the 101 stages that need a GSSP have a ratified GSSP.

Rules
A geologic section has to fulfill a set of criteria to be adapted as a GSSP by the ICS. The following list summarizes the criteria:

 * A GSSP has to define the lower boundary of a geologic stage.
 * The lower boundary has to be defined using a primary marker (usually first appearance datum of a fossil species).
 * There should also be secondary markers (other fossils, chemical, geomagnetic reversal).
 * The horizon in which the marker appears should have minerals that can be radiometrically dated.
 * The marker has to have regional and global correlation in outcrops of the same age.
 * The marker should be independent of facies.
 * The outcrop has to have an adequate thickness.
 * Sedimentation has to be continuous without any changes in facies.
 * The outcrop should be unaffected by tectonic and sedimentary movements, and metamorphism.
 * The outcrop has to be accessible to research and free to access.
 * This includes that the outcrop has to be located where it can be visited quickly (International airport and good roads), has to be kept in good condition (ideally a national reserve), in accessible terrain, extensive enough to allow repeated sampling and open to researchers of all nationalities.

Agreed-upon Global Boundary Stratotype Section and Points
Once a GSSP boundary has been agreed upon, a 'golden spike' is driven into the geologic section to mark the precise boundary for future geologists (though in practice the 'spike' need neither be golden nor an actual spike). As such, GSSPs are also sometimes referred to as golden spikes. The first stratigraphic boundary was defined in 1972 by identifying the Silurian-Devonian boundary with a bronze plaque at a locality called Klonk, northeast of the village of Suchomasty in the Czech Republic.

Fortune Head GSSP
The Precambrian-Cambrian boundary GSSP at Fortune Head, Newfoundland is a typical GSSP. It is accessible by paved road and is set aside as a nature preserve. A continuous section is available from beds that are clearly Precambrian into beds that are clearly Cambrian. The boundary is set at the first appearance of a complex trace fossil Treptichnus pedum that is found worldwide. The Fortune Head GSSP is unlikely to be washed away or built over. Nonetheless, Treptichnus pedum is less than ideal as a marker fossil as it is not found in every Cambrian sequence, and it is not assured that it is found at the same level in every exposure. In fact, further eroding its value as a boundary marker, it has since been identified in strata 4m below the GSSP. However, no other fossil is known that would be preferable. There is no radiometrically datable bed at the boundary at Fortune Head, but there is one slightly above the boundary in similar beds nearby. These factors have led some geologists to suggest that this GSSP is in need of reassigning.

Global Standard Stratigraphic Ages
Because defining a GSSP depends on finding well-preserved geologic sections and identifying key events, this task becomes more difficult as one goes farther back in time. Before 630 million years ago, boundaries on the geologic timescale are defined simply by reference to fixed dates, known as "Global Standard Stratigraphic Ages" (GSSAs).

As of March 2024, there are two "formalized" GSSAs, one for the base of the Hadean (ratified October 2022), and the other for the base of the Archean and Eoarchean (ratified in mid-late 2023). These are defined based on dates obtained from physical samples, and can have associated physical stratotypes. This is in contrast to non-formalized GSSAs, which are arbitrary age estimates with no imprecision.