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Vesak

Vesak (Vesākha; Vaiśākha), also known as Buddha Jayanti, Buddha Purnima, and Buddha Day, is a holiday traditionally observed by Buddhists in South Asia and Southeast Asia, as well as Tibet and Mongolia. It is among the most important Buddhist festivals. The festival commemorates the birth, enlightenment (Nibbāna), and death (Parinirvāna) of Gautama Buddha in Theravada, Tibetan Buddhism and Navayana.

The name Vesak is derived from the Pali term vesākha or Sanskrit vaiśākha for the lunar month of Vaisakha, which is considered the month of Buddha's birth. In Mahayana Buddhist traditions, the holiday is known by its Sanskrit name (Vaiśākha) and derived variants of it.

In the East Asian tradition, a celebration of Buddha's Birthday typically occurs around the traditional timing of Vesak, while the Buddha's awakening and death are celebrated as separate holidays that occur at other times in the calendar as Bodhi Day and Nibbāna Day. In the South Asian tradition, where Vesak is celebrated on the full moon day of the Vaisakha month, the Vesak day marks the birth, enlightenment, and the ultimate death of the Buddha.

History
Although Buddhist festivals have centuries-old tradition, the first conference of the World Fellowship of Buddhists held in Sri Lanka in 1950 formalized the decision to celebrate Vesak as the Buddha's birthday across multiple Buddhist countries. The resolution that was adopted at the World Conference reads as follows: "That this Conference of the World Fellowship of Buddhists, while recording its appreciation of the gracious act of His Majesty, the Maharaja of Nepal in making the full-moon day of Vesak a Public Holiday in Nepal, earnestly requests the Heads of Governments of all countries in which large or small number of Buddhists are to be found, to take steps to make the full-moon day in the month of May a Public Holiday in honour of the Buddha, who is universally acclaimed as one of the greatest benefactors of Humanity." On Vesak Day, Buddhists all over the world commemorate events of significance to Buddhists of all traditions: The birth, enlightenment and the death of Buddha Gautama. As Buddhism spread from India it was assimilated into many foreign cultures, and consequently Vesak is celebrated in many different ways all over the world. In India, Vaishakh Purnima day is also known as Buddha Jayanti day and has been traditionally accepted as Buddha's birth day.

In 2000, the United Nations (UN) resolved to internationally observe the day of Vesak at its headquarters and offices.

Celebration
The month of May usually has one full moon, but as there are 29.5 days between full moons, occasionally there are two. If there are two full moons during the month of May, some countries (including Sri Lanka, Cambodia and Malaysia) celebrate Vesak on the first full moon, while others (Thailand, Singapore) celebrate the holiday on the full moon of 4th lunar month. The difference also manifests in the observance of other Buddhist holidays, which are traditionally observed at the local full moon.

On Vesak, devout Buddhists and followers alike assemble in their various temples before dawn for the ceremonial and honorable hoisting of the Buddhist flag and the singing of hymns in praise of the holy triple gem: The Buddha, The Dharma (his teachings), and The Sangha (his disciples). Devotees may bring simple offerings of flowers, candles and joss-sticks to lay at the feet of their teacher. These symbolic offerings are to remind followers that just as the beautiful flowers would wither away after a short while, and the candles and joss-sticks would soon burn out, so too is life subject to decay and destruction. Devotees are enjoined to make a special effort to refrain from killing of any kind. They are encouraged to partake only of vegetarian food for the day. In some countries, notably Sri Lanka, two days are set aside for the celebration of Vesak, and all liquor shops and slaughter houses are closed by government decree during the two days.

Also birds, insects and animals are released by the thousands in what is known as life release to give freedom to those who are in captivity, imprisoned, or tortured against their will. (The practice, however, is banned in some countries such as Singapore, as the released animals are unable to survive long-term or may adversely impact the local ecosystem if they do.)

Some devout Buddhists will wear simple white clothing and spend the whole day in temples with renewed determination to observe the eight precepts.

Devout Buddhists undertake to lead a noble life according to the teaching by making daily affirmations to observe the Five Precepts. However, on special days, notably new moon and full moon days, they observe the eight precepts to train themselves to practice morality, simplicity, and humility.

Some temples also display a small statue of the Buddha in front of the altar in a small basin decorated with flowers, and filled with water or sweet tea for devotees to pour over the statue. This is symbolic of the cleansing of a practitioner's bad karma, and to reenact the events following the Buddha's birth, when devas and spirits made heavenly offerings to him.

Devotees are expected to listen to talks given by monks. On this day, monks will recite verses uttered by the Buddha twenty-five centuries ago to invoke peace and happiness for the government and the people. Buddhists are reminded to live in harmony with people of other faiths and to respect the beliefs of other people as the Buddha taught.

Bringing happiness to others
Celebrating Vesak also means making special efforts to bring happiness to the unfortunate like the aged, the disabled, and the sick. To this day, Buddhists will distribute gifts in the form of cash, or volunteering in various charitable homes throughout the country. Vesak is also a time for great joy and happiness, expressed not by pandering to one's appetites, but by concentrating on useful activities such as decorating and illuminating temples, or painting and creating exquisite scenes from the life of the Buddha for public dissemination. Devout Buddhists also vie with one another to provide refreshments and vegetarian food to followers who visit the temple to pay homage to the Enlightened One.

Paying homage to the Buddha
According to tradition the Buddha instructed followers how to pay him homage. Just before he died, he saw his faithful attendant Ananda, weeping. The Buddha advised him not to weep, instead to understand the universal law that all compounded things (including even his own body) must disintegrate. He advised everyone not to cry over the disintegration of the physical body but to regard his teachings (The Dharma) as their teacher from then on, because only the truth of the Dhamma is eternal, and not subject to the law of change. He also stressed that the way to pay homage to him was not merely by offering flowers, incense, and lights, but by truly and sincerely striving to follow his teachings.

Dates of observance
The exact date of Vesak is based on Asian lunisolar calendars and is primarily celebrated in Vaisakha, a month of both the Buddhist and Hindu calendars, hence the name Vesak. In Nepal, which is considered the birth-country of Buddha, it is celebrated on the full moon day of the Vaisakha month of the Hindu calendar, and is traditionally called Buddha Purnima, Purnima meaning the full moon day in Sanskrit. In Theravada countries following the Buddhist calendar, it falls on Uposatha Day, the full moon typically in the 5th or 6th lunar month.

Nowadays, in Sri Lanka, Nepal, India, Bangladesh and Malaysia, Vesak/Buddha Purnima is celebrated on the day of the first full moon in May in the Gregorian calendar.

For countries using the lunisolar calendar, the date for Vesak or Buddha's Birthday varies from year to year in the Gregorian calendar, but usually falls in April or May; in leap years it may be celebrated in June. In Bhutan it is celebrated on the 15th day of the fourth month of the Bhutanese lunar calendar. In Thailand, Laos, Singapore and Indonesia, Vesak is celebrated on the fourteenth or fifteenth day of the fourth month in the Chinese lunar calendar. In China, Korea, Vietnam and the Philippines, Buddha's Birthday is celebrated on the eighth day of the fourth month in the Chinese lunar calendar. In Japan, Buddha's Birthday is observed on the same date but in the Gregorian calendar, i.e. 8 April.

In Myanmar, Buddha's Birthday is celebrated as Full Moon of Kasun and is a public holiday. It is celebrated by watering the Bodhi tree and chanting. In large pagodas, music and dance is also performed as part of the celebrations

In the following table, year 2021 date as per the Buddhist calendar

In Thailand
In Thailand, where Vesak Day is known as Visakha Buja Day (Visakha Puja Day), Buddhists usually make merits by going to temples, vowing to keep the Buddhists precepts, offering food to monks, listening to Dhamma Talks and practicing Vipassana meditation in the temples.

In Laos
The Vixakha Bouxa festival is the Lao version of the Thai Visakha Puja, which it closely resembles. It commemorates the birth, enlightenment, and death of the Buddha, which are all said to have happened on the same date. It is held around the month of May or Vesak, based on the lunar calendar. Celebrations include dances, poems, parades, processions, deep meditation, theatrical performances, and puppet shows.

Boun Bang Fay
One part of the Vixakha Bouxa festival is called Boun Bang Fay, or Rocket Festival. As this occurs during the hottest and driest season of the year, large homemade rockets are launched into the sky in an attempt to convince the celestial beings to send down rain. Traditionally, Buddhist monks made the rockets out of hollow bamboo tubes filled with gunpowder (among other things). Nowadays, lay people make the bang fai more like fireworks and hold competitions for the highest, fastest and most colorful rockets. The event takes place on both sides of the Mekhong River border between Thailand and the Lao People's Democratic Republic, and sometimes teams from the neighbouring countries will compete against each other. Tourists travel long distances to witness this now popular event.

In Indonesia
This significant and traditional holy day is observed throughout Indonesia, where it is known as Waisak Day. At Borobudur, thousands of Buddhist monks will join to repeat mantras and meditate as they circuit the temple in a ritual called "Pradaksina". This is a form of tribute to the temple. Monks celebrate the special day by bottling holy water (which symbolises humility) and transporting flames (which symbolize light and enlightenment) from location to location. The monks also take part in the "Pindapata" ritual, where they receive charity from the people of Indonesia. Waisak Day in Indonesia has been celebrated as a national public holiday every year since 1983.

In Malaysia

Celebrated by Buddhists to mark three momentous events in Buddha's life – his birth, enlightenment, and his departure from the human world, the Wesak celebration in Malaysia begins at dawn when devotees gather at Buddhist temples nationwide to meditate on the Eight Precepts. Donations – giving food to the needy and offerings of incense and joss sticks – and prayers are carried out. The sutras are chanted in unison by monks in saffron robes. The celebration is highlighted by a candle procession. Wesak Day in Malaysia is a national public holiday.

In Myanmar (Burma)
In Myanmar (Burma), Vesak is known as the Full Moon Day of Kason (ကဆုန်လပြည့် ဗုဒ္ဓနေ့), which is the second month in the traditional Burmese calendar. The date is a public gazetted holiday. Buddhist devotees typically celebrate by offering alms to Buddhist monks, adhering to a more stringent set of Buddhist precepts, practicing meditation, and freeing fish and birds from captivity.

Throughout the country, the date is also marked by a traditional festival called the Nyaungye-thun or "Bodhi tree water pouring festival", whereby devotees visit pagodas or monasteries (kyaung) to pour scented water to sacred Bodhi Trees using clay pots, to ensure the trees, which hold great significance in Buddhism, do not die during the peak of summer.

This tradition dates back to the pre-colonial era and continues to take place at major pagodas such as the Shwekyetyet and Shwekyetkya Pagodas in the former royal capital of Amarapura. A Konbaung era court poet, Letwe Thondara composed a complete set of yadu poems describing this festival in Meza Hill, near Katha, where he had been exiled by King Hsinbyushin.

In the Philippines
In the Philippines, the date of Vesak (known as Araw ni Bisyak, Kaarawan ni Buddha, Araw ni Buddha or Adlaw sa Buddha) follows the Chinese lunar calendar. Like China and Japan, Filipinos also bathe statues on this day.

In Singapore
In Singapore, Vesak Day was made a public holiday in 1955 after many public petitions, replacing Whit Monday. In the early decades of the 20th century, Vesak Day was associated with the Ceylonese community which then celebrated it along with their National Day in a two-day event. After World War II, there was a movement to make Vesak Day a public holiday, with the Singapore Buddhist Association leading the petitions.

In Vietnam
In Vietnam, Vesak is also known as Phật Đản. From 1958 to 1975, Vesak was a national public holiday in South Vietnam. It was a public festival with floats, and lantern parades on the streets. Under the President Ngô Đình Diệm, a member of Vietnam's Catholic minority, South Vietnamese Buddhists were not allowed to celebrate Vesak, and faced many other restrictions.

On 8 May 1963, the day of Vesak in Vietnam, more than 3000 Vietnamese Buddhists were protesting President Diệm's ban on the Buddhist flag in the city of Huế. Tensions rose throughout the day, and as protesters gathered around a government radio station, the Vietnamese army and police were called in to disperse the crowd. Soon after, the army started to shoot and throw grenades into the crowd. Nine were killed, and four were seriously injured. These events are considered to be the beginning of Vietnam's Buddhist crisis, which culminated in a governmental coup and the assassination of President Diệm. Successive South Vietnamese Governments recognized Vesak as a public holiday and allowed the celebrations to go on.

However, after the Fall of Saigon, the day was no longer a public holiday. Since the 2000s, the festival has witnessed a revival across the country. The Vesak Celebration is officially held by the Vietnamese Buddhist Sangha every year and it aggregated international delegates for great events in 2008, 2014, 2019 (the 16th United Nations Day of Vesak Celebration).

In Nepal
Vesak, commonly known in Nepal as "Buddha Jayanti" is widely celebrated all across the country, predominantly, Lumbini – the birthplace of Buddha, and Swayambhu – the holy temple for Buddhists, also known as "the Monkey Temple". The main door of Swayambhu is opened only on this very day, therefore, people from all over Kathmandu valley are stimulated by the event. Thousands of pilgrims from various parts of the world come together to celebrate Buddha's birthday at his birthplace, Lumbini. In Nepal, Buddha is worshipped by all religious groups, therefore "Buddha Jayanti" is marked by a public holiday. People donate foods and clothes to the needy and also provide financial aid to monasteries and schools where Buddhism is taught and practised.

In Sri Lanka
Vesak is celebrated as a religious and a cultural festival in Sri Lanka on the full moon of the lunar month of Vesak (usually in the Gregorian month of May), for about one week, and this festival is often celebrated by people of different religions in Sri Lanka. During this week, the selling of alcohol and fresh meat is usually prohibited, with slaughter houses also being closed. Celebrations include religious and alms-giving activities. Electrically lit pandals called thoranas are erected in locations mainly in Colombo, Kandy, Galle and elsewhere, most sponsored by donors, religious societies and welfare groups. Each pandal illustrates a story from the Jataka tales.

In addition, colorful lanterns called "Vesak kuudu" are hung along streets and in front of homes. They signify the light of the Buddha, Dharma and the Sangha. Food stalls set up by Buddhist devotees called "dansälas" provide free food, ice-cream and drinks to passersby. Groups of people from community organizations, businesses and government departments sing bhakti gee (Buddhist devotional songs). Colombo experiences a massive influx of people from all parts of the country during this week.

In India
In India, the full moon day of the Vaisakha month of the Hindu calendar is celebrated as Buddha Purnima. The festival is commonly known as Buddha Purnima, as Purnima means full moon day in Sanskrit and Hindi languages. It is also called Buddha Jayanti, with Jayanti meaning birthday in Sanskrit. The festival is a public holiday in India.

In Bangladesh
Vesak Day is an important festival for all Bengali Buddhists. In Bangladesh, it is celebrated in Chittagong, Dhaka, and other Buddhist regions in the country. In the Bangla language, it is known as Buddho Purnima. It is also a public holiday in Bangladesh.

In Japan
In Japan, Vesak or hanamatsuri (花祭) is also known as Kanbutsue (灌仏会), Gōtan'e (降誕会)), Busshōue (仏生会), Yokubutsue (浴仏会), Ryūge'e (龍華会) and Hanaeshiki (花会式). It is not a public holiday. It is based on a legend that nine dragons appeared in the sky on the Buddha's birthday and poured amṛta over him.

It used to be celebrated on the 8th day of the fourth month in the Chinese calendar based on one of the legends that proclaims the day as Buddha's birthday. At present, the celebration is observed on 8 April of the Solar Calendar since the government of Meiji Japan adopted the western solar calendar as the official calendar. Since the 8th day of the fourth month in the lunar calendar commonly falls in May of the current solar calendar, it is now celebrated about a month earlier.

In Japan, Vesak celebrations include pouring amacha (甘茶), a sweet tea made from Hydrangea macrophylla, on statues. In Buddhist religious sites such as temples and viharas, more involved ceremonies are conducted for lay Buddhists, priests, and monks and nuns.

In South Korea
In South Korea the birthday of Buddha is celebrated on the 8th day of the 4th month in the Korean lunar calendar (as well as in Hong Kong, Macau) and is an official holiday. This day is called 석가탄신일 (Seokga tansinil), meaning "Buddha's birthday" or 부처님 오신 날 (Bucheonim osin nal) meaning "the day when the Buddha came". It has now grown into one of the nation's biggest cultural festivals. Lotus lanterns cover the entire temple throughout the month which are often flooded down the street. On the day of Buddha's birth, many temples provide free meals and tea to all visitors. The breakfast and lunch provided are often sanchae bibimbap.

Yeondeunghoe (연등회) is a lantern-lighting festival in Korea celebrating the Buddha's Birthday. It is inscribed in UNESCO Intangible Cultural Heritage List from 2020 and enlisted as South Korean Intangible Cultural Property from 2012.

In Canada
An annual event known as Vesak: Buddha's Birthday is celebrated in Toronto in its three major three Buddhist temples, that represent the three main branches of Buddhism. Held at Mississauga Celebration Square, it features a number of Buddhist-themed events and activities, as well as cultural acts from Asia, including China, Sri Lanka and Vietnam.

In United States
The celebration of Vesak or Buddha's Birthday in the United States differs among different Buddhist communities, depending on their ethnicity and nationality.

In Maui, Hawaii the community is usually invited to celebrate Vesak Day (the birth of Buddha) on the full moon of Vaisakha at Chua Tu Hanh Buddhist Temple in Kahului, where there is guided sitting meditation and dharma talk by a Zen master; which is followed by the bathing ceremony of the baby Buddha and a joyful meal to end the evening. The state of Hawaii has officially recognized April 8 of each year as "Buddha Day", which celebrates the birth of Gautama Buddha.

In the Bay Area of California, the Japanese celebration on April 8 has also been significant for several decades. In 1968 the first circumambulation of Mt. Tamalpais to celebrate Buddha's Birthday was conducted. Starting in 1969 at Tassajara Zen Mountain Center, Hana-Matsuri (花ーまつり - flower festival) was celebrated each spring. Dressed in formal black robes, the roughly 70 monks and students form a formal procession to the Horse Pasture with the leader periodically ringing a small, clear bell. A temporary stone altar was built under a huge oak tree in a gorgeous field of green grass and abundant wildflowers; a small statue of a baby Buddha was placed upon it in a metal basin. Then each person, in turn, approaches the altar, and ladle one thin-lipped bamboo dipperful of sweet green tea over the statue, bow, and walk to one side.

New York celebrates the International Lotus Lantern Parade, an annual event held at Union Square Park. The event celebrates the Buddha's birthday and Yeon Deung Hoe (연등회,燃燈會), a Korean lantern celebration that is held during Vesak. The festival features a number of Buddhist themed events and is started off by numerous Buddhist centers of Japanese, Korean and Sri Lankan origins for example.

United Nations
On 15 December 1999 the United Nations General Assembly adopted resolution 54/115, entitled 'International recognition of the Day of Vesak at United Nations Headquarters and other United Nations offices'. The proposal to declare Vesak as an international public holiday was tabled at the United Nations General Assembly by Sri Lanka. The resolution internationally recognized the Day of Vesak to acknowledge the contributions that The Buddha and Buddhism have made for over two and a half millennia. It also called for annual commemoration of the day at the UN Headquarters, in New York, UNESCO and other UN offices around the world.

International celebrations since 2000 included the first Vesak celebration in the UN (New York) on 15 May 2000. 34 countries were represented. The Day of Vesak is an official holiday for the UN offices in many of the countries in South-East Asia.

International Vesak summit
Thailand has hosted an international Vesak summit 11 times, Vietnam 3 times, and Sri Lanka once.
 * 25 May 2004 in Phutthamonthon, Thailand
 * 18–21 May 2005 in Bangkok, Thailand
 * 2006 to 2013 in Thailand
 * 2014 in Vietnam
 * 2015 in Thailand
 * 2016 in Thailand
 * 2017 in Sri Lanka
 * 2018 in Thailand
 * 2019 in Vietnam

Local renditions
There are multiple local renditions of the Vesak festival name, varying by local language, including:
 * বুদ্ধ পূর্ণিমা Buddho Purnima
 * বুদ্ধ পূর্ণিমা Buddho Purnima, বুদ্ধ জয়ন্তী Buddho Joyonti
 * Adlaw sa Buddha (Buddha's Day)
 * ကဆုန်လပြည့် ဗုဒ္ဓနေ့ Kasonelapyany Buddhanae, "Full Moon Day of Kason"
 * , (Buddha's Birthday or Birthday of the Gautama Buddha), 佛誕 (Fódàn, Birthday of the Buddha), 浴佛節 (Yùfójié, Occasion of Bathing the Buddha), 衛塞節 (Wèisāi jié Vesak Day), 偉大的衛塞節花節偉大的滿月 (Wěidà de wèi sāi jié huā jié wěidà de mǎnyuè Great Vesak Day Flower Festival Full Moon of Flower Moon)
 * སྟོན་པའི་དུས་ཆེན་༥ འཛོམས་ Dhüchen Nga Zom
 * Vesak
 * बुद्ध पूर्णिमा Buddha Pūrṇimā, बुद्ध जयन्ती Buddha Jayantī, वैशाख पूर्णिमा Vaisākh Pūrṇimā
 * Aldaw ni Buddha (Day of the Buddha)
 * 花祭り Hanamatsuri (Flower Festival)
 * វិសាខបូជា Visak Bochea
 * ಬುದ್ಧ ಪೌರ್ಣಮಿ Buddha Pournami
 * (Birthday of the Shakyamuni Buddha), 부처님오신날 (Buddha's Day)
 * ວິສາຂະບູຊາ Vixakha Bouxa
 * Malay:
 * Hari Wesak (Jawi:, Malaysian)
 * Hari Vesak (Singapore),
 * Hari Waisak or Hari Raya Waisak (Indonesian)
 * വൈശാഖ പൗർണമി, ബുദ്ധ പൂർണിമ, ബുദ്ധ ജയന്തി
 * Mon: တ္ၚဲကျာ်ဗုဒ္ဓ ဗပေၚ်ပသာ် "Buddha Day Full Moon of Pasāk"
 * Бурхан Багшийн Их Дүйчин Өдөр Burkhan Bagshiin Ikh Düichinn Ödör (Lord Buddha's Great Festival Day)
 * День рождения Гаутамы Будды Den' rozhdeniya Gautamy Buddy (Birthday of the Gautama Buddha), День Гаутамы Будды (Den' Gautamy Buddy Gautama Buddha's Day), Великий День Цветов Весак (Velikiy Den' Tsvetov Vesak Great Vesak Flower Day), День Весака (Den' Vesaka Vesak Day), День Будды (Den' Buddy Buddha's Day), Буддийское рождество (Buddiyskoye rozhdestvo Buddhist Christmas)
 * बुद्ध पौर्णिमा Buddha Pournima
 * बुद्ध पुर्णिमा Buddha Purnima, बुद्ध जयन्ति Buddha Jayanti
 * स्वांया पुन्हि Swānyā Punhi
 * ବୁଦ୍ଧ ପୂର୍ଣ୍ଣିମା Buddha Purnimā
 * වෙසක් Vesak, වෛශාක්‍ය Vaishakya
 * விசாகத் திருநாள் Vicākat Tirunāḷ
 * Araw ni Bisyak, Araw ni Buddha (Buddha's Day), Kaarawan ni Buddha (Buddha's Birthday)
 * బుద్ధ పౌర్ణమి Buddha Pournami or alternatively వైశాఖ పౌర్ణమి Vaisakha Pournami
 * วิสาขบูชา
 * Lễ Phật Đản; Chữ Hán: 禮佛誕 (Birthday of the Buddha), Ngày hội hoa Phật (Buddha's Lord Flower Festival Day)
 * Lễ Phật Đản; Chữ Hán: 禮佛誕 (Birthday of the Buddha), Ngày hội hoa Phật (Buddha's Lord Flower Festival Day)

title: Vesak


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Gravitational singularity

A gravitational singularity, spacetime singularity or simply singularity is a condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically. As such, a singularity is by definition no longer part of the regular spacetime and cannot be determined by "where" or "when". Gravitational singularities exist at a junction between general relativity and quantum mechanics; therefore, the properties of the singularity cannot be described without an established theory of quantum gravity. Trying to find a complete and precise definition of singularities in the theory of general relativity, the current best theory of gravity, remains a difficult problem. A singularity in general relativity can be defined by the scalar invariant curvature becoming infinite or, better, by a geodesic being incomplete.

Gravitational singularities are mainly considered in the context of general relativity, where density would become infinite at the center of a black hole without corrections from quantum mechanics, and within astrophysics and cosmology as the earliest state of the universe during the Big Bang. Physicists have not reached a consensus about what actually happens at the extreme densities predicted by singularities (including at the start of the Big Bang).

General relativity predicts that any object collapsing beyond a certain point (for stars this is the Schwarzschild radius) would form a black hole, inside which a singularity (covered by an event horizon) would be formed. The Penrose–Hawking singularity theorems define a singularity to have geodesics that cannot be extended in a smooth manner. The termination of such a geodesic is considered to be the singularity.

Modern theory asserts that the initial state of the universe, at the beginning of the Big Bang, was a singularity. In this case, the universe did not collapse into a black hole, because currently-known calculations and density limits for gravitational collapse are usually based upon objects of relatively constant size, such as stars, and do not necessarily apply in the same way to rapidly expanding space such as the Big Bang. Neither general relativity nor quantum mechanics can currently describe the earliest moments of the Big Bang, but in general, quantum mechanics does not permit particles to inhabit a space smaller than their Compton wavelengths.

Interpretation
Many theories in physics have mathematical singularities of one kind or another. Equations for these physical theories predict that the ball of mass of some quantity becomes infinite or increases without limit. This is generally a sign for a missing piece in the theory, as in the ultraviolet catastrophe, re-normalization, and instability of a hydrogen atom predicted by the Larmor formula.

In classical field theories, including special relativity but not general relativity, one can say that a solution has a singularity at a particular point in spacetime where certain physical properties become ill-defined, with spacetime serving as a background field to locate the singularity. A singularity in general relativity, on the other hand, is more complex because spacetime itself becomes ill-defined, and the singularity is no longer part of the regular spacetime manifold. In general relativity, a singularity cannot be defined by "where" or "when".

Some theories, such as the theory of loop quantum gravity, suggest that singularities may not exist. This is also true for such classical unified field theories as the Einstein–Maxwell–Dirac equations. The idea can be stated in the form that, due to quantum gravity effects, there is a minimum distance beyond which the force of gravity no longer continues to increase as the distance between the masses becomes shorter, or alternatively that interpenetrating particle waves mask gravitational effects that would be felt at a distance.

Motivated by such philosophy of loop quantum gravity, recently it has been shown that such conceptions can be realized through some elementary constructions based on the refinement of the first axiom of geometry, namely, the concept of a point by considering Klein's prescription of accounting for the extension of a small spot that represents or demonstrates a point, which was a programmatic call that he called as a fusion of arithmetic and geometry. Klein's program, according to Born, was actually a mathematical route to consider 'natural uncertainty in all observations' while describing 'a physical situation' by means of 'real numbers'.

Types
There is only one type of singularity, each with different physical features that have characteristics relevant to the theories from which they originally emerged, such as the different shapes of the singularities, conical and curved. They have also been hypothesized to occur without event horizons, structures that delineate one spacetime section from another in which events cannot affect past the horizon; these are called naked.

Conical
A conical singularity occurs when there is a point where the limit of some diffeomorphism invariant quantity does not exist or is infinite, in which case spacetime is not smooth at the point of the limit itself. Thus, spacetime looks like a cone around this point, where the singularity is located at the tip of the cone. The metric can be finite everywhere the coordinate system is used.

An example of such a conical singularity is a cosmic string and a Schwarzschild black hole.

Curvature
Solutions to the equations of general relativity or another theory of gravity (such as supergravity) often result in encountering points where the metric blows up to infinity. However, many of these points are completely regular, and the infinities are merely a result of using an inappropriate coordinate system at this point. To test whether there is a singularity at a certain point, one must check whether at this point diffeomorphism invariant quantities (i.e. scalars) become infinite. Such quantities are the same in every coordinate system, so these infinities will not "go away" by a change of coordinates.

An example is the Schwarzschild solution that describes a non-rotating, uncharged black hole. In coordinate systems convenient for working in regions far away from the black hole, a part of the metric becomes infinite at the event horizon. However, spacetime at the event horizon is regular. The regularity becomes evident when changing to another coordinate system (such as the Kruskal coordinates), where the metric is perfectly smooth. On the other hand, in the center of the black hole, where the metric becomes infinite as well, the solutions suggest a singularity exists. The existence of the singularity can be verified by noting that the Kretschmann scalar, being the square of the Riemann tensor i.e. $$R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}$$, which is diffeomorphism invariant, is infinite.

While in a non-rotating black hole the singularity occurs at a single point in the model coordinates, called a "point singularity", in a rotating black hole, also known as a Kerr black hole, the singularity occurs on a ring (a circular line), known as a "ring singularity". Such a singularity may also theoretically become a wormhole.

More generally, a spacetime is considered singular if it is geodesically incomplete, meaning that there are freely-falling particles whose motion cannot be determined beyond a finite time, being after the point of reaching the singularity. For example, any observer inside the event horizon of a non-rotating black hole would fall into its center within a finite period of time. The classical version of the Big Bang cosmological model of the universe contains a causal singularity at the start of time (t=0), where all time-like geodesics have no extensions into the past. Extrapolating backward to this hypothetical time 0 results in a universe with all spatial dimensions of size zero, infinite density, infinite temperature, and infinite spacetime curvature.

Naked singularity
Until the early 1990s, it was widely believed that general relativity hides every singularity behind an event horizon, making naked singularities impossible. This is referred to as the cosmic censorship hypothesis. However, in 1991, physicists Stuart Shapiro and Saul Teukolsky performed computer simulations of a rotating plane of dust that indicated that general relativity might allow for "naked" singularities. What these objects would actually look like in such a model is unknown. Nor is it known whether singularities would still arise if the simplifying assumptions used to make the simulation were removed. However, it is hypothesized that light entering a singularity would similarly have its geodesics terminated, thus making the naked singularity look like a black hole.

Disappearing event horizons exist in the Kerr metric, which is a spinning black hole in a vacuum, if the angular momentum ($$J$$) is high enough. Transforming the Kerr metric to Boyer–Lindquist coordinates, it can be shown that the coordinate (which is not the radius) of the event horizon is, $$r_{\pm} = \mu \pm \left(\mu^{2} - a^{2}\right)^{1/2}$$, where $$\mu = G M / c^{2}$$, and $$a=J/M c$$. In this case, "event horizons disappear" means when the solutions are complex for $$r_{\pm}$$, or $$\mu^{2} < a^{2}$$. However, this corresponds to a case where $$J$$ exceeds $$GM^{2}/c$$ (or in Planck units, $J > M^{2}$); i.e. the spin exceeds what is normally viewed as the upper limit of its physically possible values.

Similarly, disappearing event horizons can also be seen with the Reissner–Nordström geometry of a charged black hole if the charge ($$Q$$) is high enough. In this metric, it can be shown that the singularities occur at $$r_{\pm}= \mu \pm \left(\mu^{2} - q^{2}\right)^{1/2}$$, where $$\mu = G M / c^{2}$$, and $$q^2 = G Q^2/\left(4 \pi \epsilon_0 c^4\right)$$. Of the three possible cases for the relative values of $$\mu$$ and $$q$$, the case where $$\mu^{2} < q^{2}$$ causes both $$r_{\pm}$$ to be complex. This means the metric is regular for all positive values of $$r$$, or in other words, the singularity has no event horizon. However, this corresponds to a case where $$Q/\sqrt{4 \pi \epsilon_0}$$ exceeds $$M\sqrt{G}$$ (or in Planck units, $Q > M$); i.e. the charge exceeds what is normally viewed as the upper limit of its physically possible values. Also, actual astrophysical black holes are not expected to possess any appreciable charge.

A black hole possessing the lowest $$M$$ value consistent with its $$J$$ and $$Q$$ values and the limits noted above; i.e., one just at the point of losing its event horizon, is termed extremal.

Entropy
Before Stephen Hawking came up with the concept of Hawking radiation, the question of black holes having entropy had been avoided. However, this concept demonstrates that black holes radiate energy, which conserves entropy and solves the incompatibility problems with the second law of thermodynamics. Entropy, however, implies heat and therefore temperature. The loss of energy also implies that black holes do not last forever, but rather evaporate or decay slowly. Black hole temperature is inversely related to mass. All known black hole candidates are so large that their temperature is far below that of the cosmic background radiation, which means they will gain energy on net by absorbing this radiation. They cannot begin to lose energy on net until the background temperature falls below their own temperature. This will occur at a cosmological redshift of more than one million, rather than the thousand or so since the background radiation formed.

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

title: Gravitational singularity


text:
Technological singularity

The technological singularity—or simply the singularity —is a hypothetical future point in time at which technological growth becomes uncontrollable and irreversible, resulting in unforeseeable consequences for human civilization. According to the most popular version of the singularity hypothesis, I. J. Good's intelligence explosion model of 1965, an upgradable intelligent agent could eventually enter a positive feedback loop of self-improvement cycles, each new and more intelligent generation appearing more and more rapidly, causing a rapid increase ("explosion") in intelligence which would ultimately result in a powerful superintelligence, qualitatively far surpassing all human intelligence.

The Hungarian-American mathematician John von Neumann (1903-1957) became the first known person to use the concept of a "singularity" in the technological context. Stanislaw Ulam reported in 1958 an earlier discussion with von Neumann "centered on the accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue". Subsequent authors have echoed this viewpoint.

The concept and the term "singularity" were popularized by Vernor Vinge – first in 1983 (in an article that claimed that once humans create intelligences greater than their own, there will be a technological and social transition similar in some sense to "the knotted space-time at the center of a black hole", ) and later in his 1993 essay The Coming Technological Singularity, (in which he wrote that it would signal the end of the human era, as the new superintelligence would continue to upgrade itself and would advance technologically at an incomprehensible rate). He wrote that he would be surprised if it occurred before 2005 or after 2030. Another significant contributor to wider circulation of the notion was Ray Kurzweil's 2005 book The Singularity Is Near, predicting singularity by 2045.

Some scientists, including Stephen Hawking, have expressed concern that artificial superintelligence (ASI) could result in human extinction. The consequences of a technological singularity and its potential benefit or harm to the human race have been intensely debated.

Some prominent technologists and academics – including Paul Allen, Jeff Hawkins, John Holland, Jaron Lanier, Steven Pinker, Theodore Modis, and Gordon Moore – dispute the plausibility of a technological singularity and an associated artificial-intelligence explosion. One claim made was that the artificial-intelligence growth is likely to run into decreasing returns instead of accelerating ones, as was observed in previously developed human technologies.

Intelligence explosion
Although technological progress has been accelerating in most areas, it has been limited by the basic intelligence of the human brain, which has not, according to Paul R. Ehrlich, changed significantly for millennia. However, with the increasing power of computers and other technologies, it might eventually be possible to build a machine that is significantly more intelligent than humans.

If a superhuman intelligence were to be invented—either through the amplification of human intelligence or through artificial intelligence—it would, in theory, vastly improve over human problem-solving and inventive skills. Such an AI is referred to as Seed AI because if an AI were created with engineering capabilities that matched or surpassed those of its human creators, it would have the potential to autonomously improve its own software and hardware to design an even more capable machine, which could repeat the process in turn. This recursive self-improvement could accelerate, potentially allowing enormous qualitative change before any upper limits imposed by the laws of physics or theoretical computation set in. It is speculated that over many iterations, such an AI would far surpass human cognitive abilities.

I. J. Good speculated in 1965 that superhuman intelligence might bring about an intelligence explosion: "Let an ultraintelligent machine be defined as a machine that can far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an 'intelligence explosion', and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make, provided that the machine is docile enough to tell us how to keep it under control."

One version of intelligence explosion is where computing power approaches infinity in a finite amount of time. In this version, once AIs are performing the research to improve themselves, speed doubles e.g. after 2 years, then 1 year, then 6 months, then 3 months, then 1.5 months, etc., where the infinite sum of the doubling periods is 4 years. Unless prevented by physical limits of computation and time quantization, this process would literally achieve infinite computing power in 4 years, properly earning the name "singularity" for the final state. This form of intelligence explosion is described in Yudkowsky (1996).

Emergence of superintelligence
A superintelligence, hyperintelligence, or superhuman intelligence is a hypothetical agent that possesses intelligence far surpassing that of the brightest and most gifted human minds. "Superintelligence" may also refer to the form or degree of intelligence possessed by such an agent. John von Neumann, Vernor Vinge and Ray Kurzweil define the concept in terms of the technological creation of super intelligence, arguing that it is difficult or impossible for present-day humans to predict what human beings' lives would be like in a post-singularity world.

The related concept "speed superintelligence" describes an AI that can function like a human mind, only much faster. For example, with a million-fold increase in the speed of information processing relative to that of humans, a subjective year would pass in 30 physical seconds. Such a difference in information processing speed could drive the singularity.

Technology forecasters and researchers disagree regarding when, or whether, human intelligence will likely be surpassed. Some argue that advances in artificial intelligence (AI) will probably result in general reasoning systems that bypass human cognitive limitations. Others believe that humans will evolve or directly modify their biology so as to achieve radically greater intelligence. A number of futures studies focus on scenarios that combine these possibilities, suggesting that humans are likely to interface with computers, or upload their minds to computers, in a way that enables substantial intelligence amplification. The book The Age of Em by Robin Hanson describes a hypothetical future scenario in which human brains are scanned and digitized, creating "uploads" or digital versions of human consciousness. In this future, the development of these uploads may precede or coincide with the emergence of superintelligent artificial intelligence.

Non-AI singularity
Some writers use "the singularity" in a broader way to refer to any radical changes in society brought about by new technology (such as molecular nanotechnology),  although Vinge and other writers specifically state that without superintelligence, such changes would not qualify as a true singularity.

Predictions
In 1965, I. J. Good wrote that it is more probable than not that an ultra-intelligent machine would be built in the twentieth century. In 1993, Vinge predicted greater-than-human intelligence between 2005 and 2030. In 1996, Yudkowsky predicted a singularity in 2021. In 2005, Kurzweil predicted human-level AI around 2029, and the singularity in 2045. In a 2017 interview, Kurzweil reaffirmed his estimates. In 1988, Moravec predicted that if the rate of improvement continues, the computing capabilities for human-level AI would be available in supercomputers before 2010. In 1998, Moravec predicted human-level AI by 2040, and intelligence far beyond human by 2050.

Four polls of AI researchers, conducted in 2012 and 2013 by Nick Bostrom and Vincent C. Müller, suggested a confidence of 50% that human-level AI would be developed by 2040–2050.

Plausibility
Prominent technologists and academics dispute the plausibility of a technological singularity, including Paul Allen, Jeff Hawkins, John Holland, Jaron Lanier, Steven Pinker, Theodore Modis, and Gordon Moore, whose law is often cited in support of the concept.

Most proposed methods for creating superhuman or transhuman minds fall into one of two categories: intelligence amplification of human brains and artificial intelligence. The many speculated ways to augment human intelligence include bioengineering, genetic engineering, nootropic drugs, AI assistants, direct brain–computer interfaces and mind uploading. These multiple possible paths to an intelligence explosion, all of which will presumably be pursued, makes a singularity more likely.

Robin Hanson expressed skepticism of human intelligence augmentation, writing that once the "low-hanging fruit" of easy methods for increasing human intelligence have been exhausted, further improvements will become increasingly difficult. Despite all of the speculated ways for amplifying human intelligence, non-human artificial intelligence (specifically seed AI) is the most popular option among the hypotheses that would advance the singularity.

The possibility of an intelligence explosion depends on three factors. The first accelerating factor is the new intelligence enhancements made possible by each previous improvement. Contrariwise, as the intelligences become more advanced, further advances will become more and more complicated, possibly outweighing the advantage of increased intelligence. Each improvement should generate at least one more improvement, on average, for movement towards singularity to continue. Finally, the laws of physics may eventually prevent further improvement.

There are two logically independent, but mutually reinforcing, causes of intelligence improvements: increases in the speed of computation, and improvements to the algorithms used. The former is predicted by Moore's Law and the forecasted improvements in hardware, and is comparatively similar to previous technological advances. But Schulman and Sandberg argue that software will present more complex challenges than simply operating on hardware capable of running at human intelligence levels or beyond.

A 2017 email survey of authors with publications at the 2015 NeurIPS and ICML machine learning conferences asked about the chance that "the intelligence explosion argument is broadly correct". Of the respondents, 12% said it was "quite likely", 17% said it was "likely", 21% said it was "about even", 24% said it was "unlikely" and 26% said it was "quite unlikely".

Speed improvements
Both for human and artificial intelligence, hardware improvements increase the rate of future hardware improvements. An analogy to Moore's Law suggests that if the first doubling of speed took 18 months, the second would take 18 subjective months; or 9 external months, whereafter, four months, two months, and so on towards a speed singularity. Some upper limit on speed may eventually be reached. Jeff Hawkins has stated that a self-improving computer system would inevitably run into upper limits on computing power: "in the end there are limits to how big and fast computers can run. We would end up in the same place; we'd just get there a bit faster. There would be no singularity."

It is difficult to directly compare silicon-based hardware with neurons. But notes that computer speech recognition is approaching human capabilities, and that this capability seems to require 0.01% of the volume of the brain. This analogy suggests that modern computer hardware is within a few orders of magnitude of being as powerful as the human brain.

Exponential growth

The exponential growth in computing technology suggested by Moore's law is commonly cited as a reason to expect a singularity in the relatively near future, and a number of authors have proposed generalizations of Moore's law. Computer scientist and futurist Hans Moravec proposed in a 1998 book that the exponential growth curve could be extended back through earlier computing technologies prior to the integrated circuit.

Ray Kurzweil postulates a law of accelerating returns in which the speed of technological change (and more generally, all evolutionary processes) increases exponentially, generalizing Moore's law in the same manner as Moravec's proposal, and also including material technology (especially as applied to nanotechnology), medical technology and others. Between 1986 and 2007, machines' application-specific capacity to compute information per capita roughly doubled every 14 months; the per capita capacity of the world's general-purpose computers has doubled every 18 months; the global telecommunication capacity per capita doubled every 34 months; and the world's storage capacity per capita doubled every 40 months. On the other hand, it has been argued that the global acceleration pattern having the 21st century singularity as its parameter should be characterized as hyperbolic rather than exponential.

Kurzweil reserves the term "singularity" for a rapid increase in artificial intelligence (as opposed to other technologies), writing for example that "The Singularity will allow us to transcend these limitations of our biological bodies and brains ... There will be no distinction, post-Singularity, between human and machine". He also defines his predicted date of the singularity (2045) in terms of when he expects computer-based intelligences to significantly exceed the sum total of human brainpower, writing that advances in computing before that date "will not represent the Singularity" because they do "not yet correspond to a profound expansion of our intelligence."

Accelerating change

Some singularity proponents argue its inevitability through extrapolation of past trends, especially those pertaining to shortening gaps between improvements to technology. In one of the first uses of the term "singularity" in the context of technological progress, Stanislaw Ulam tells of a conversation with John von Neumann about accelerating change: "One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue."

Kurzweil claims that technological progress follows a pattern of exponential growth, following what he calls the "law of accelerating returns". Whenever technology approaches a barrier, Kurzweil writes, new technologies will surmount it. He predicts paradigm shifts will become increasingly common, leading to "technological change so rapid and profound it represents a rupture in the fabric of human history". Kurzweil believes that the singularity will occur by approximately 2045. His predictions differ from Vinge's in that he predicts a gradual ascent to the singularity, rather than Vinge's rapidly self-improving superhuman intelligence.

Oft-cited dangers include those commonly associated with molecular nanotechnology and genetic engineering. These threats are major issues for both singularity advocates and critics, and were the subject of Bill Joy's April 2000 Wired magazine article "Why The Future Doesn't Need Us".

Algorithm improvements
Some intelligence technologies, like "seed AI", may also have the potential to not just make themselves faster, but also more efficient, by modifying their source code. These improvements would make further improvements possible, which would make further improvements possible, and so on.

The mechanism for a recursively self-improving set of algorithms differs from an increase in raw computation speed in two ways. First, it does not require external influence: machines designing faster hardware would still require humans to create the improved hardware, or to program factories appropriately. An AI rewriting its own source code could do so while contained in an AI box.

Second, as with Vernor Vinge's conception of the singularity, it is much harder to predict the outcome. While speed increases seem to be only a quantitative difference from human intelligence, actual algorithm improvements would be qualitatively different. Eliezer Yudkowsky compares it to the changes that human intelligence brought: humans changed the world thousands of times more rapidly than evolution had done, and in totally different ways. Similarly, the evolution of life was a massive departure and acceleration from the previous geological rates of change, and improved intelligence could cause change to be as different again.

There are substantial dangers associated with an intelligence explosion singularity originating from a recursively self-improving set of algorithms. First, the goal structure of the AI might self-modify, potentially causing the AI to optimise for something other than what was originally intended.

Secondly, AIs could compete for the same scarce resources humankind uses to survive. While not actively malicious, AIs would promote the goals of their programming, not necessarily broader human goals, and thus might crowd out humans.

Carl Shulman and Anders Sandberg suggest that algorithm improvements may be the limiting factor for a singularity; while hardware efficiency tends to improve at a steady pace, software innovations are more unpredictable and may be bottlenecked by serial, cumulative research. They suggest that in the case of a software-limited singularity, intelligence explosion would actually become more likely than with a hardware-limited singularity, because in the software-limited case, once human-level AI is developed, it could run serially on very fast hardware, and the abundance of cheap hardware would make AI research less constrained. An abundance of accumulated hardware that can be unleashed once the software figures out how to use it has been called "computing overhang".

Criticism
Some critics, like philosopher Hubert Dreyfus and philosopher John Searle, assert that computers or machines cannot achieve human intelligence. Others, like physicist Stephen Hawking, object that whether machines can achieve a true intelligence or merely something similar to intelligence is irrelevant if the net result is the same.

Psychologist Steven Pinker stated in 2008: "There is not the slightest reason to believe in a coming singularity. The fact that you can visualize a future in your imagination is not evidence that it is likely or even possible. Look at domed cities, jet-pack commuting, underwater cities, mile-high buildings, and nuclear-powered automobiles—all staples of futuristic fantasies when I was a child that have never arrived. Sheer processing power is not a pixie dust that magically solves all your problems."

Martin Ford postulates a "technology paradox" in that before the singularity could occur most routine jobs in the economy would be automated, since this would require a level of technology inferior to that of the singularity. This would cause massive unemployment and plummeting consumer demand, which in turn would destroy the incentive to invest in the technologies that would be required to bring about the Singularity. Job displacement is increasingly no longer limited to those types of work traditionally considered to be "routine".

Theodore Modis and Jonathan Huebner argue that the rate of technological innovation has not only ceased to rise, but is actually now declining. Evidence for this decline is that the rise in computer clock rates is slowing, even while Moore's prediction of exponentially increasing circuit density continues to hold. This is due to excessive heat build-up from the chip, which cannot be dissipated quickly enough to prevent the chip from melting when operating at higher speeds. Advances in speed may be possible in the future by virtue of more power-efficient CPU designs and multi-cell processors.

Theodore Modis holds the singularity cannot happen. He claims the "technological singularity" and especially Kurzweil lack scientific rigor; Kurzweil is alleged to mistake the logistic function (S-function) for an exponential function, and to see a "knee" in an exponential function where there can in fact be no such thing. In a 2021 article, Modis pointed out that no milestones – breaks in historical perspective comparable in importance to the Internet, DNA, the transistor, or nuclear energy – had been observed in the previous twenty years while five of them would have been expected according to the exponential trend advocated by the proponents of the technological singularity.

AI researcher Jürgen Schmidhuber stated that the frequency of subjectively "notable events" appears to be approaching a 21st-century singularity, but cautioned readers to take such plots of subjective events with a grain of salt: perhaps differences in memory of recent and distant events could create an illusion of accelerating change where none exists.

Microsoft co-founder Paul Allen argued the opposite of accelerating returns, the complexity brake; the more progress science makes towards understanding intelligence, the more difficult it becomes to make additional progress. A study of the number of patents shows that human creativity does not show accelerating returns, but in fact, as suggested by Joseph Tainter in his The Collapse of Complex Societies, a law of diminishing returns. The number of patents per thousand peaked in the period from 1850 to 1900, and has been declining since. The growth of complexity eventually becomes self-limiting, and leads to a widespread "general systems collapse".

Hofstadter (2006) raises concern that Ray Kurzweil is not sufficiently scientifically rigorous, that an exponential tendency of technology is not a scientific law like one of physics, and that exponential curves have no "knees". Nonetheless, he did not rule out the singularity in principle in the distant future and in the light of ChatGPT and other recent advancements has revised his opinion significantly towards dramatic technological change in the near future.

Jaron Lanier denies that the singularity is inevitable: "I do not think the technology is creating itself. It's not an autonomous process." Furthermore: "The reason to believe in human agency over technological determinism is that you can then have an economy where people earn their own way and invent their own lives. If you structure a society on not emphasizing individual human agency, it's the same thing operationally as denying people clout, dignity, and self-determination ... to embrace [the idea of the Singularity] would be a celebration of bad data and bad politics."

Economist Robert J. Gordon points out that measured economic growth slowed around 1970 and slowed even further since the financial crisis of 2007–2008, and argues that the economic data show no trace of a coming Singularity as imagined by mathematician I. J. Good.

Philosopher and cognitive scientist Daniel Dennett said in 2017: "The whole singularity stuff, that's preposterous. It distracts us from much more pressing problems", adding "AI tools that we become hyper-dependent on, that is going to happen. And one of the dangers is that we will give them more authority than they warrant."

In addition to general criticisms of the singularity concept, several critics have raised issues with Kurzweil's iconic chart. One line of criticism is that a log-log chart of this nature is inherently biased toward a straight-line result. Others identify selection bias in the points that Kurzweil chooses to use. For example, biologist PZ Myers points out that many of the early evolutionary "events" were picked arbitrarily. Kurzweil has rebutted this by charting evolutionary events from 15 neutral sources, and showing that they fit a straight line on a log-log chart. Kelly (2006) argues that the way the Kurzweil chart is constructed with x-axis having time before present, it always points to the singularity being "now", for any date on which one would construct such a chart, and shows this visually on Kurzweil's chart.

Some critics suggest religious motivations or implications of singularity, especially Kurzweil's version of it. The buildup towards the singularity is compared with Judeo-Christian end-of-time scenarios. Beam calls it "a Buck Rogers vision of the hypothetical Christian Rapture". John Gray says "the Singularity echoes apocalyptic myths in which history is about to be interrupted by a world-transforming event".

David Streitfeld in The New York Times questioned whether "it might manifest first and foremost—thanks, in part, to the bottom-line obsession of today’s Silicon Valley—as a tool to slash corporate America’s head count."

Potential impacts
Dramatic changes in the rate of economic growth have occurred in the past because of technological advancement. Based on population growth, the economy doubled every 250,000 years from the Paleolithic era until the Neolithic Revolution. The new agricultural economy doubled every 900 years, a remarkable increase. In the current era, beginning with the Industrial Revolution, the world's economic output doubles every fifteen years, sixty times faster than during the agricultural era. If the rise of superhuman intelligence causes a similar revolution, argues Robin Hanson, one would expect the economy to double at least quarterly and possibly on a weekly basis.

Uncertainty and risk
The term "technological singularity" reflects the idea that such change may happen suddenly, and that it is difficult to predict how the resulting new world would operate. It is unclear whether an intelligence explosion resulting in a singularity would be beneficial or harmful, or even an existential threat. Because AI is a major factor in singularity risk, a number of organizations pursue a technical theory of aligning AI goal-systems with human values, including the Future of Humanity Institute, the Machine Intelligence Research Institute, the Center for Human-Compatible Artificial Intelligence, and the Future of Life Institute.

Physicist Stephen Hawking said in 2014 that "Success in creating AI would be the biggest event in human history. Unfortunately, it might also be the last, unless we learn how to avoid the risks." Hawking believed that in the coming decades, AI could offer "incalculable benefits and risks" such as "technology outsmarting financial markets, out-inventing human researchers, out-manipulating human leaders, and developing weapons we cannot even understand." Hawking suggested that artificial intelligence should be taken more seriously and that more should be done to prepare for the singularity: "So, facing possible futures of incalculable benefits and risks, the experts are surely doing everything possible to ensure the best outcome, right? Wrong. If a superior alien civilisation sent us a message saying, 'We'll arrive in a few decades,' would we just reply, 'OK, call us when you get here – we'll leave the lights on'? Probably not – but this is more or less what is happening with AI."

claims that there is no direct evolutionary motivation for an AI to be friendly to humans. Evolution has no inherent tendency to produce outcomes valued by humans, and there is little reason to expect an arbitrary optimisation process to promote an outcome desired by humankind, rather than inadvertently leading to an AI behaving in a way not intended by its creators. Anders Sandberg has also elaborated on this scenario, addressing various common counter-arguments. AI researcher Hugo de Garis suggests that artificial intelligences may simply eliminate the human race for access to scarce resources, and humans would be powerless to stop them. Alternatively, AIs developed under evolutionary pressure to promote their own survival could outcompete humanity.

discusses human extinction scenarios, and lists superintelligence as a possible cause: "When we create the first superintelligent entity, we might make a mistake and give it goals that lead it to annihilate humankind, assuming its enormous intellectual advantage gives it the power to do so. For example, we could mistakenly elevate a subgoal to the status of a supergoal. We tell it to solve a mathematical problem, and it complies by turning all the matter in the solar system into a giant calculating device, in the process killing the person who asked the question."

According to Eliezer Yudkowsky, a significant problem in AI safety is that unfriendly artificial intelligence is likely to be much easier to create than friendly AI. While both require large advances in recursive optimisation process design, friendly AI also requires the ability to make goal structures invariant under self-improvement (or the AI could transform itself into something unfriendly) and a goal structure that aligns with human values and does not automatically destroy the human race. An unfriendly AI, on the other hand, can optimize for an arbitrary goal structure, which does not need to be invariant under self-modification. proposes an AI design that avoids several dangers including self-delusion, unintended instrumental actions, and corruption of the reward generator. He also discusses social impacts of AI and testing AI. His 2001 book Super-Intelligent Machines advocates the need for public education about AI and public control over AI. It also proposed a simple design that was vulnerable to corruption of the reward generator.

Next step of sociobiological evolution
While the technological singularity is usually seen as a sudden event, some scholars argue the current speed of change already fits this description.

In addition, some argue that we are already in the midst of a major evolutionary transition that merges technology, biology, and society. Digital technology has infiltrated the fabric of human society to a degree of indisputable and often life-sustaining dependence.

A 2016 article in Trends in Ecology & Evolution argues that "humans already embrace fusions of biology and technology. We spend most of our waking time communicating through digitally mediated channels... we trust artificial intelligence with our lives through antilock braking in cars and autopilots in planes... With one in three courtships leading to marriages in America beginning online, digital algorithms are also taking a role in human pair bonding and reproduction".

The article further argues that from the perspective of the evolution, several previous Major Transitions in Evolution have transformed life through innovations in information storage and replication (RNA, DNA, multicellularity, and culture and language). In the current stage of life's evolution, the carbon-based biosphere has generated a cognitive system (humans) capable of creating technology that will result in a comparable evolutionary transition.

The digital information created by humans has reached a similar magnitude to biological information in the biosphere. Since the 1980s, the quantity of digital information stored has doubled about every 2.5 years, reaching about 5 zettabytes in 2014 (5 bytes).

In biological terms, there are 7.2 billion humans on the planet, each having a genome of 6.2 billion nucleotides. Since one byte can encode four nucleotide pairs, the individual genomes of every human on the planet could be encoded by approximately 1 bytes. The digital realm stored 500 times more information than this in 2014 (see figure). The total amount of DNA contained in all of the cells on Earth is estimated to be about 5.3 base pairs, equivalent to 1.325 bytes of information.

If growth in digital storage continues at its current rate of 30–38% compound annual growth per year, it will rival the total information content contained in all of the DNA in all of the cells on Earth in about 110 years. This would represent a doubling of the amount of information stored in the biosphere across a total time period of just 150 years".

Implications for human society
In February 2009, under the auspices of the Association for the Advancement of Artificial Intelligence (AAAI), Eric Horvitz chaired a meeting of leading computer scientists, artificial intelligence researchers and roboticists at the Asilomar conference center in Pacific Grove, California. The goal was to discuss the potential impact of the hypothetical possibility that robots could become self-sufficient and able to make their own decisions. They discussed the extent to which computers and robots might be able to acquire autonomy, and to what degree they could use such abilities to pose threats or hazards.

Some machines are programmed with various forms of semi-autonomy, including the ability to locate their own power sources and choose targets to attack with weapons. Also, some computer viruses can evade elimination and, according to scientists in attendance, could therefore be said to have reached a "cockroach" stage of machine intelligence. The conference attendees noted that self-awareness as depicted in science-fiction is probably unlikely, but that other potential hazards and pitfalls exist.

Frank S. Robinson predicts that once humans achieve a machine with the intelligence of a human, scientific and technological problems will be tackled and solved with brainpower far superior to that of humans. He notes that artificial systems are able to share data more directly than humans, and predicts that this would result in a global network of super-intelligence that would dwarf human capability. Robinson also discusses how vastly different the future would potentially look after such an intelligence explosion.

Hard vs. soft takeoff

In a hard takeoff scenario, an artificial superintelligence rapidly self-improves, "taking control" of the world (perhaps in a matter of hours), too quickly for significant human-initiated error correction or for a gradual tuning of the agent's goals. In a soft takeoff scenario, the AI still becomes far more powerful than humanity, but at a human-like pace (perhaps on the order of decades), on a timescale where ongoing human interaction and correction can effectively steer the AI's development.

Ramez Naam argues against a hard takeoff. He has pointed out that we already see recursive self-improvement by superintelligences, such as corporations. Intel, for example, has "the collective brainpower of tens of thousands of humans and probably millions of CPU cores to... design better CPUs!" However, this has not led to a hard takeoff; rather, it has led to a soft takeoff in the form of Moore's law. Naam further points out that the computational complexity of higher intelligence may be much greater than linear, such that "creating a mind of intelligence 2 is probably more than twice as hard as creating a mind of intelligence 1."

J. Storrs Hall believes that "many of the more commonly seen scenarios for overnight hard takeoff are circular – they seem to assume hyperhuman capabilities at the starting point of the self-improvement process" in order for an AI to be able to make the dramatic, domain-general improvements required for takeoff. Hall suggests that rather than recursively self-improving its hardware, software, and infrastructure all on its own, a fledgling AI would be better off specializing in one area where it was most effective and then buying the remaining components on the marketplace, because the quality of products on the marketplace continually improves, and the AI would have a hard time keeping up with the cutting-edge technology used by the rest of the world.

Ben Goertzel agrees with Hall's suggestion that a new human-level AI would do well to use its intelligence to accumulate wealth. The AI's talents might inspire companies and governments to disperse its software throughout society. Goertzel is skeptical of a hard five minute takeoff but speculates that a takeoff from human to superhuman level on the order of five years is reasonable. He refers to this scenario as a "semihard takeoff".

Max More disagrees, arguing that if there were only a few superfast human-level AIs, that they would not radically change the world, as they would still depend on other people to get things done and would still have human cognitive constraints. Even if all superfast AIs worked on intelligence augmentation, it is unclear why they would do better in a discontinuous way than existing human cognitive scientists at producing super-human intelligence, although the rate of progress would increase. More further argues that a superintelligence would not transform the world overnight: a superintelligence would need to engage with existing, slow human systems to accomplish physical impacts on the world. "The need for collaboration, for organization, and for putting ideas into physical changes will ensure that all the old rules are not thrown out overnight or even within years."

Relation to immortality and aging
Drexler (1986), one of the founders of nanotechnology, postulates cell repair devices, including ones operating within cells and using as yet hypothetical biological machines. According to Richard Feynman, it was his former graduate student and collaborator Albert Hibbs who originally suggested to him (circa 1959) the idea of a medical use for Feynman's theoretical micromachines. Hibbs suggested that certain repair machines might one day be reduced in size to the point that it would, in theory, be possible to (as Feynman put it) "swallow the doctor". The idea was incorporated into Feynman's 1959 essay There's Plenty of Room at the Bottom.

Moravec (1988) predicts the possibility of "uploading" human mind into a human-like robot, achieving quasi-immortality by extreme longevity via transfer of the human mind between successive new robots as the old ones wear out; beyond that, he predicts later exponential acceleration of subjective experience of time leading to a subjective sense of immortality.

Kurzweil (2005) suggests that medical advances would allow people to protect their bodies from the effects of aging, making the life expectancy limitless. Kurzweil argues that the technological advances in medicine would allow us to continuously repair and replace defective components in our bodies, prolonging life to an undetermined age. Kurzweil further buttresses his argument by discussing current bio-engineering advances. Kurzweil suggests somatic gene therapy; after synthetic viruses with specific genetic information, the next step would be to apply this technology to gene therapy, replacing human DNA with synthesized genes.

Beyond merely extending the operational life of the physical body, Jaron Lanier argues for a form of immortality called "Digital Ascension" that involves "people dying in the flesh and being uploaded into a computer and remaining conscious."

History of the concept
A paper by Mahendra Prasad, published in AI Magazine, asserts that the 18th-century mathematician Marquis de Condorcet was the first person to hypothesize and mathematically model an intelligence explosion and its effects on humanity.

An early description of the idea was made in John W. Campbell's 1932 short story "The Last Evolution".

In his 1958 obituary for John von Neumann, Ulam recalled a conversation with von Neumann about the "ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue."

In 1965, Good wrote his essay postulating an "intelligence explosion" of recursive self-improvement of a machine intelligence.

In 1977, Hans Moravec wrote an article with unclear publishing status where he envisioned a development of self-improving thinking machines, a creation of "super-consciousness, the synthesis of terrestrial life, and perhaps jovian and martian life as well, constantly improving and extending itself, spreading outwards from the solar system, converting non-life into mind." The article describes the human mind uploading later covered in Moravec (1988). The machines are expected to reach human level and then improve themselves beyond that ("Most significantly of all, they [the machines] can be put to work as programmers and engineers, with the task of optimizing the software and hardware which make them what they are. The successive generations of machines produced this way will be increasingly smarter and more cost effective.") Humans will no longer be needed, and their abilities will be overtaken by the machines: "In the long run the sheer physical inability of humans to keep up with these rapidly evolving progeny of our minds will ensure that the ratio of people to machines approaches zero, and that a direct descendant of our culture, but not our genes, inherits the universe." While the word "singularity" is not used, the notion of human-level thinking machines thereafter improving themselves beyond human level is there. In this view, there is no intelligence explosion in the sense of a very rapid intelligence increase once human equivalence is reached. An updated version of the article was published in 1979 in Analog Science Fiction and Fact.

In 1981, Stanisław Lem published his science fiction novel Golem XIV. It describes a military AI computer (Golem XIV) who obtains consciousness and starts to increase his own intelligence, moving towards personal technological singularity. Golem XIV was originally created to aid its builders in fighting wars, but as its intelligence advances to a much higher level than that of humans, it stops being interested in the military requirements because it finds them lacking internal logical consistency.

In 1983, Vernor Vinge addressed Good's intelligence explosion in print in the January 1983 issue of Omni magazine. In this op-ed piece, Vinge seems to have been the first to use the term "singularity" (although not "technological singularity") in a way that was specifically tied to the creation of intelligent machines: "We will soon create intelligences greater than our own. When this happens, human history will have reached a kind of singularity, an intellectual transition as impenetrable as the knotted space-time at the center of a black hole, and the world will pass far beyond our understanding. This singularity, I believe, already haunts a number of science-fiction writers. It makes realistic extrapolation to an interstellar future impossible. To write a story set more than a century hence, one needs a nuclear war in between ... so that the world remains intelligible."

In 1985, in "The Time Scale of Artificial Intelligence", artificial intelligence researcher Ray Solomonoff articulated mathematically the related notion of what he called an "infinity point": if a research community of human-level self-improving AIs take four years to double their own speed, then two years, then one year and so on, their capabilities increase infinitely in finite time.

In 1986, Vernor Vinge published Marooned in Realtime, a science-fiction novel where a few remaining humans traveling forward in the future have survived an unknown extinction event that might well be a singularity. In a short afterword, the author states that an actual technological singularity would not be the end of the human species: "of course it seems very unlikely that the Singularity would be a clean vanishing of the human race. (On the other hand, such a vanishing is the timelike analog of the silence we find all across the sky.)".

In 1988, Vinge used the phrase "technological singularity" (including "technological") in the short story collection Threats and Other Promises, writing in the introduction to his story "The Whirligig of Time" (p. 72): Barring a worldwide catastrophe, I believe that technology will achieve our wildest dreams, and soon. ''When we raise our own intelligence and that of our creations, we are no longer in a world of human-sized characters. At that point we have fallen into a technological "black hole", a technological singularity.''

In 1988, Hans Moravec published Mind Children, in which he predicted human-level intelligence in supercomputers by 2010, self-improving intelligent machines far surpassing human intelligence later, human mind uploading into human-like robots later, intelligent machines leaving humans behind, and space colonization. He did not mention "singularity", though, and he did not speak of a rapid explosion of intelligence immediately after the human level is achieved. Nonetheless, the overall singularity tenor is there in predicting both human-level artificial intelligence and further artificial intelligence far surpassing humans later.

Vinge's 1993 article "The Coming Technological Singularity: How to Survive in the Post-Human Era", spread widely on the internet and helped to popularize the idea. This article contains the statement, "Within thirty years, we will have the technological means to create superhuman intelligence. Shortly after, the human era will be ended." Vinge argues that science-fiction authors cannot write realistic post-singularity characters who surpass the human intellect, as the thoughts of such an intellect would be beyond the ability of humans to express.

Minsky's 1994 article says robots will "inherit the Earth", possibly with the use of nanotechnology, and proposes to think of robots as human "mind children", drawing the analogy from Moravec. The rhetorical effect of that analogy is that if humans are fine to pass the world to their biological children, they should be equally fine to pass it to robots, their "mind" children. As per Minsky, 'we could design our "mind-children" to think a million times faster than we do. To such a being, half a minute might seem as long as one of our years, and each hour as long as an entire human lifetime.' The feature of the singularity present in Minsky is the development of superhuman artificial intelligence ("million times faster"), but there is no talk of sudden intelligence explosion, self-improving thinking machines or unpredictability beyond any specific event and the word "singularity" is not used.

Tipler's 1994 book The Physics of Immortality predicts a future where super–intelligent machines will build enormously powerful computers, people will be "emulated" in computers, life will reach every galaxy and people will achieve immortality when they reach Omega Point. There is no talk of Vingean "singularity" or sudden intelligence explosion, but intelligence much greater than human is there, as well as immortality.

In 1996, Yudkowsky predicted a singularity by 2021. His version of singularity involves intelligence explosion: once AIs are doing the research to improve themselves, speed doubles after 2 years, then 1 one year, then after 6 months, then after 3 months, then after 1.5 months, and after more iterations, the "singularity" is reached. This construction implies that the speed reaches infinity in finite time.

In 2000, Bill Joy, a prominent technologist and a co-founder of Sun Microsystems, voiced concern over the potential dangers of robotics, genetic engineering, and nanotechnology.

In 2005, Kurzweil published The Singularity Is Near. Kurzweil's publicity campaign included an appearance on The Daily Show with Jon Stewart.

From 2006 to 2012, an annual Singularity Summit conference was organized by Machine Intelligence Research Institute, founded by Eliezer Yudkowsky.

In 2007, Yudkowsky suggested that many of the varied definitions that have been assigned to "singularity" are mutually incompatible rather than mutually supporting. For example, Kurzweil extrapolates current technological trajectories past the arrival of self-improving AI or superhuman intelligence, which Yudkowsky argues represents a tension with both I. J. Good's proposed discontinuous upswing in intelligence and Vinge's thesis on unpredictability.

In 2009, Kurzweil and X-Prize founder Peter Diamandis announced the establishment of Singularity University, a nonaccredited private institute whose stated mission is "to educate, inspire and empower leaders to apply exponential technologies to address humanity's grand challenges." Funded by Google, Autodesk, ePlanet Ventures, and a group of technology industry leaders, Singularity University is based at NASA's Ames Research Center in Mountain View, California. The not-for-profit organization runs an annual ten-week graduate program during summer that covers ten different technology and allied tracks, and a series of executive programs throughout the year.

In politics
In 2007, the Joint Economic Committee of the United States Congress released a report about the future of nanotechnology. It predicts significant technological and political changes in the mid-term future, including possible technological singularity.

Former President of the United States Barack Obama spoke about singularity in his interview to Wired in 2016: "One thing that we haven't talked about too much, and I just want to go back to, is we really have to think through the economic implications. Because most people aren't spending a lot of time right now worrying about singularity—they are worrying about 'Well, is my job going to be replaced by a machine?'"

title: Technological singularity


text:
Pythagorean

Pythagorean, meaning of or pertaining to the ancient Ionian mathematician, philosopher, and music theorist Pythagoras, may refer to:

Philosophy

 * Pythagoreanism, the esoteric and metaphysical beliefs purported to have been held by Pythagoras
 * Neopythagoreanism, a school of philosophy reviving Pythagorean doctrines that became prominent in the 1st and 2nd centuries AD
 * Pythagorean diet, the name for vegetarianism before the nineteenth century

Mathematics

 * Pythagorean theorem
 * Pythagorean triple
 * Pythagorean prime
 * Pythagorean trigonometric identity
 * Table of Pythagoras, another name for the multiplication table

Music

 * Pythagorean comma
 * Pythagorean hammers
 * Pythagorean tuning

Other uses

 * Pythagorean cup
 * Pythagorean expectation, a baseball statistical term
 * Pythagorean letter

title: Pythagorean