title: Price elasticity of demand

text: Price elasticities are negative except in special cases. If a good is said to have an elasticity of 2, it almost always means that the good has an elasticity of −2 according to the formal definition. The phrase "more elastic" means that a good's elasticity has greater magnitude, ignoring the sign. Veblen and Giffen goods are two classes of goods which have positive elasticity, rare exceptions to the law of demand. Demand for a good is said to be "inelastic" when the elasticity is less than one in absolute value: that is, changes in price have a relatively small effect on the quantity demanded. Demand for a good is said to be "elastic" when the elasticity is greater than one. A good with an elasticity of −2 has elastic demand because quantity falls twice as much as the price increase; an elasticity of −0.5 has inelastic demand because the quantity response is half the price increase.


title: Price elasticity of demand

text: Revenue is maximised when price is set so that the elasticity is exactly one. The good's elasticity can be used to predict the incidence (or "burden") of a tax on that good. Various research methods are used to determine price elasticity, including test markets, analysis of historical sales data and conjoint analysis.


title: Price elasticity of demand

text: The variation in demand in response to a variation in price is called price elasticity of demand. It may also be defined as the ratio of the percentage change in quantity demanded to the percentage change in price of particular commodity. The formula


title: Price elasticity of demand

text: where formula_3 is the price of the good demanded, formula_4 is how much it changed, formula_5 is the quantity of the good demanded, and formula_6 is how much it changed. In other words, we can say that the price elasticity of demand is the percentage change in demand for a commodity due to a given percentage change in the price. If the quantity demanded falls 20 tons from an initial 200 tons after the price rises $5 from an initial price of $100, then the quantity demanded has fallen 10% and the price has risen 5%, so the elasticity is (−10%)/(+5%) = −2.


title: Price elasticity of demand

text: The price elasticity of demand is ordinarily negative because quantity demanded falls when price rises, as described by the "law of demand". Two rare classes of goods which have elasticity greater than 0 (consumers buy more if the price is "higher") are Veblen and Giffen goods. Since the price elasticity of demand is negative for the vast majority of goods and services (unlike most other elasticities, which take both positive and negative values depending on the good), economists often leave off the word "negative" or the minus sign and refer to the price elasticity of demand as a positive value (i.e., in absolute value terms). They will say "Yachts have an elasticity of two" meaning the elasticity is −2. This is a common source of confusion for students.


title: Price elasticity of demand

text: unitary elastic demand (= 1). If demand is elastic, the quantity demanded is very sensitive to price, e.g. when a 1% rise in price generates a 10% decrease in quantity. If demand is inelastic, the good's demand is relatively insensitive to price, with quantity changing less than price. If demand is unitary elastic, the quantity falls by exactly the percentage that the price rises. Two important special cases are perfectly elastic demand (= ∞), where even a small rise in price reduces the quantity demanded to zero; and perfectly inelastic demand (= 0), where a rise in price leaves the quantity unchanged.


title: Price elasticity of demand

text: The above measure of elasticity is sometimes referred to as the "own-price" elasticity of demand for a good, i.e., the elasticity of demand with respect to the good's own price, in order to distinguish it from the elasticity of demand for that good with respect to the change in the price of some other good, i.e., an independent, complementary, or substitute good. That two-good type of elasticity is called a "cross"-price elasticity of demand. If a 1% rise in the price of gasoline causes a 0.5% fall in the quantity of cars demanded, the cross-price elasticity is formula_7


title: Price elasticity of demand

text: As the size of the price change gets bigger, the elasticity definition becomes less reliable for a combination of two reasons. First, a good's elasticity is not necessarily constant; it varies at different points along the demand curve because a 1% change in price has a quantity effect that may depend on whether the initial price is high or low. Contrary to common misconception, the price elasticity is not constant even along a linear demand curve, but rather varies along the curve. A linear demand curve's slope is constant, to be sure, but the elasticity can change even if formula_8 is constant. There does exist a nonlinear shape of demand curve along which the elasticity is constant: formula_9, where formula_10 is a shift constant and formula_11 is the elasticity.


title: Price elasticity of demand

text: Second, percentage changes are not symmetric; instead, the percentage change between any two values depends on which one is chosen as the starting value and which as the ending value. For example, suppose that when the price rises from $10 to $16, the quantity falls from 100 units to 80. This is a price increase of 60% and a quantity decline of 20%, an elasticity of formula_12 for that part of the demand curve. If the price falls from $16 to $10 and the quantity rises from 80 units to 100, however, the price decline is 37.5% and the quantity gain is 25%, an elasticity of formula_13 for the same part of the curve. This is an example of the index number problem.


title: Price elasticity of demand

text: Two refinements of the definition of elasticity are used to deal with these shortcomings of the basic elasticity formula: "arc elasticity" and "point elasticity".


title: Price elasticity of demand

text: Arc elasticity was introduced very early on by Hugh Dalton. It is very similar to an ordinary elasticity problem, but it adds in the index number problem. Arc Elasticity is a second solution to the asymmetry problem of having an elasticity dependent on which of the two given points on a demand curve is chosen as the "original" point will and which as the "new" one is to compute the percentage change in P and Q relative to the "average" of the two prices and the "average" of the two quantities, rather than just the change relative to one point or the other. Loosely speaking, this gives an "average" elasticity for the section of the actual demand curve—i.e., the "arc" of the curve—between the two points. As a result, this measure is known as the "arc elasticity", in this case with respect to the price of the good. The arc elasticity is defined mathematically as:


title: Price elasticity of demand

text: This method for computing the price elasticity is also known as the "midpoints formula", because the average price and average quantity are the coordinates of the midpoint of the straight line between the two given points. This formula is an application of the midpoint method. However, because this formula implicitly assumes the section of the demand curve between those points is linear, the greater the curvature of the actual demand curve is over that range, the worse this approximation of its elasticity will be.


title: Price elasticity of demand

text: The point elasticity of demand method is used to determine change in demand within the same demand curve, basically a very small amount of change in demand is measured through point elasticity. One way to avoid the accuracy problem described above is to minimize the difference between the starting and ending prices and quantities. This is the approach taken in the definition of "point" elasticity, which uses differential calculus to calculate the elasticity for an infinitesimal change in price and quantity at any given point on the demand curve:


title: Price elasticity of demand

text: In other words, it is equal to the absolute value of the first derivative of quantity with respect to price formula_16 multiplied by the point's price ("P") divided by its quantity ("Q"). However, the point elasticity can be computed only if the formula for the demand function, formula_17, is known so its derivative with respect to price, formula_18, can be determined.


title: Price elasticity of demand

text: In terms of partial-differential calculus, point elasticity of demand can be defined as follows: let formula_19 be the demand of goods formula_20 as a function of parameters price and wealth, and let formula_21 be the demand for good formula_22. The elasticity of demand for good formula_21 with respect to price formula_24 is


title: Price elasticity of demand

text: Together with the concept of an economic "elasticity" coefficient, Alfred Marshall is credited with defining "elasticity of demand" in "Principles of Economics", published in 1890. Alfred Marshall invented price elasticity of demand only four years after he had invented the concept of elasticity. He used Cournot's basic creating of the demand curve to get the equation for price elasticity of demand. He described price elasticity of demand as thus: "And we may say generally:— the elasticity (or responsiveness) of demand in a market is great or small according as the amount demanded increases much or little for a given fall in price, and diminishes much or little for a given rise in price". He reasons this since "the only universal law as to a person's desire for a commodity is that it diminishes ... but this diminution may be slow or rapid. If it is slow... a small fall in price will cause a comparatively large increase in his purchases. But if it is rapid, a small fall in price will cause only a very small increase in his purchases. In the former case... the elasticity of his wants, we may say, is great. In the latter case... the elasticity of his demand is small." Mathematically, the Marshallian PED was based on a point-price definition, using differential calculus to calculate elasticities.


title: Price elasticity of demand

text: The overriding factor in determining the elasticity is the willingness and ability of consumers after a price change to postpone immediate consumption decisions concerning the good and to search for substitutes ("wait and look"). A number of factors can thus affect the elasticity of demand for a good:


title: Price elasticity of demand

text: Goods that are more addictive in nature tend to have an inelastic PED (absolute value of PED < 1). Examples of such include cigarettes, heroin and alcohol. This is because consumers treat such goods as necessities and hence are forced to purchase them, despite even significant price changes.


title: Price elasticity of demand

text: On a graph with both a demand curve and a marginal revenue curve, demand will be elastic at all quantities where marginal revenue is positive. Demand is unit elastic at the quantity where marginal revenue is zero. Demand is inelastic at every quantity where marginal revenue is negative.


title: Price elasticity of demand

text: A firm considering a price change must know what effect the change in price will have on total revenue. Revenue is simply the product of unit price times quantity:


title: Price elasticity of demand

text: For inelastic goods, because of the inverse nature of the relationship between price and quantity demanded (i.e., the law of demand), the two effects affect total revenue in opposite directions. But in determining whether to increase or decrease prices, a firm needs to know what the net effect will be. Elasticity provides the answer: The percentage change in total revenue is approximately equal to the percentage change in quantity demanded plus the percentage change in price. (One change will be positive, the other negative.) The percentage change in quantity is related to the percentage change in price by elasticity: hence the percentage change in revenue can be calculated by knowing the elasticity and the percentage change in price alone.


title: Price elasticity of demand

text: Hence, as the accompanying diagram shows, total revenue is maximized at the combination of price and quantity demanded where the elasticity of demand is unitary.


title: Price elasticity of demand

text: It is important to realize that price-elasticity of demand is "not" necessarily constant over all price ranges. The linear demand curve in the accompanying diagram illustrates that changes in price also change the elasticity: the price elasticity is different at every point on the curve.


title: Price elasticity of demand

text: Demand elasticity, in combination with the price elasticity of supply can be used to assess where the incidence (or "burden") of a per-unit tax is falling or to predict where it will fall if the tax is imposed. For example, when demand is "perfectly inelastic", by definition consumers have no alternative to purchasing the good or service if the price increases, so the quantity demanded would remain constant. Hence, suppliers can increase the price by the full amount of the tax, and the consumer would end up paying the entirety. In the opposite case, when demand is "perfectly elastic", by definition consumers have an infinite ability to switch to alternatives if the price increases, so they would stop buying the good or service in question completely—quantity demanded would fall to zero. As a result, firms cannot pass on any part of the tax by raising prices, so they would be forced to pay all of it themselves.


title: Price elasticity of demand

text: In practice, demand is likely to be only "relatively" elastic or relatively inelastic, that is, somewhere between the extreme cases of perfect elasticity or inelasticity. More generally, then, the "higher" the elasticity of demand compared to PES, the heavier the burden on producers; conversely, the more "inelastic" the demand compared to supply, the heavier the burden on consumers. The general principle is that the party (i.e., consumers or producers) that has "fewer" opportunities to avoid the tax by switching to alternatives will bear the "greater" proportion of the tax burden. In the end the whole tax burden is carried by individual households since they are the ultimate owners of the means of production that the firm utilises (see Circular flow of income).


title: Price elasticity of demand

text: PED and PES can also have an effect on the deadweight loss associated with a tax regime. When PED, PES or both are inelastic, the deadweight loss is lower than a comparable scenario with higher elasticity.


title: Price elasticity of demand

text: Among the most common applications of price elasticity is to determine prices that maximize revenue or profit.


title: Price elasticity of demand

text: If one point elasticity is used to model demand changes over a finite range of prices, elasticity is implicitly assumed constant with respect to price over the finite price range. The equation defining price elasticity for one product can be rewritten (omitting secondary variables) as a linear equation.


title: Price elasticity of demand

text: Similarly, the equations for cross elasticity for formula_34 products can be written as a set of formula_34 simultaneous linear equations.


title: Price elasticity of demand

text: This form of the equations shows that point elasticities assumed constant over a price range cannot determine what prices generate maximum values of formula_40; similarly they cannot predict prices that generate maximum formula_5 or maximum revenue.


title: Price elasticity of demand

text: Constant elasticities can predict optimal pricing only by computing point elasticities at several points, to determine the price at which point elasticity equals −1 (or, for multiple products, the set of prices at which the point elasticity matrix is the negative identity matrix).


title: Price elasticity of demand

text: If the definition of price elasticity is extended to yield a quadratic relationship between demand units (formula_5) and price, then it is possible to compute prices that maximize formula_40, formula_5, and revenue. The fundamental equation for one product becomes


title: Price elasticity of demand

text: Excel models are available that compute constant elasticity, and use non-constant elasticity to estimate prices that optimize revenue or profit for one product or several products.


title: Price elasticity of demand

text: In most situations, such as those with nonzero variable costs, revenue-maximizing prices are not profit-maximizing prices. For these situations, using a technique for Profit maximization is more appropriate.


title: Price elasticity of demand

text: Various research methods are used to calculate the price elasticities in real life, including analysis of historic sales data, both public and private, and use of present-day surveys of customers' preferences to build up test markets capable of modelling such changes. Alternatively, conjoint analysis (a ranking of users' preferences which can then be statistically analysed) may be used. Approximate estimates of price elasticity can be calculated from the income elasticity of demand, under conditions of preference independence. This approach has been empirically validated using bundles of goods (e.g. food, healthcare, education, recreation, etc.).


title: Price elasticity of demand

text: Though elasticities for most demand schedules vary depending on price, they can be modeled assuming constant elasticity. Using this method, the elasticities for various goods—intended to act as examples of the theory described above—are as follows. For suggestions on why these goods and services may have the elasticity shown, see the above section on determinants of price elasticity.


title: Computer-generated imagery

text: Computer-generated imagery (CGI) is the use of computer graphics to create or contribute to images in art, printed media, video games, simulators, and visual effects in films, television programs, shorts, commercials, and videos. The images may be static (still images) or dynamic (moving images), in which case CGI is also called "computer animation". CGI may be two-dimensional (2D), although the term "CGI" is most commonly used to refer to the 3-D computer graphics used for creating characters, scenes and special effects in films and television, which is described as "CGI animation".


title: Computer-generated imagery

text: The first feature film to make use of CGI was the 1973 film "Westworld". Other early films that incorporated CGI include "Star Wars" (1977), "Tron" (1982), "" (1983), "The Last Starfighter" (1984), "Young Sherlock Holmes" (1985) and "Flight of the Navigator" (1986). The first music video to use CGI was Dire Straits' award-winning "Money for Nothing" (1985), whose success was instrumental in giving the process mainstream exposure.


title: Computer-generated imagery

text: The evolution of CGI led to the emergence of virtual cinematography in the 1990s, where the vision of the simulated camera is not constrained by the laws of physics. Availability of CGI software and increased computer speeds have allowed individual artists and small companies to produce professional-grade films, games, and fine art from their home computers.


title: Computer-generated imagery

text: The term virtual world refers to agent-based, interactive environments, which can be created with CGI.


title: Computer-generated imagery

text: Not only do animated images form part of computer-generated imagery; natural looking landscapes (such as fractal landscapes) are also generated via computer algorithms. A simple way to generate fractal surfaces is to use an extension of the triangular mesh method, relying on the construction of some special case of a de Rham curve, e.g. midpoint displacement. For instance, the algorithm may start with a large triangle, then recursively zoom in by dividing it into four smaller Sierpinski triangles, then interpolate the height of each point from its nearest neighbors. The creation of a Brownian surface may be achieved not only by adding noise as new nodes are created but by adding additional noise at multiple levels of the mesh. Thus a topographical map with varying levels of height can be created using relatively straightforward fractal algorithms. Some typical, easy-to-program fractals used in CGI are the "plasma fractal" and the more dramatic "fault fractal".


title: Computer-generated imagery

text: Many specific techniques been researched and developed to produce highly focused computer-generated effects — e.g., the use of specific models to represent the chemical weathering of stones to model erosion and produce an "aged appearance" for a given stone-based surface.


title: Computer-generated imagery

text: Modern architects use services from computer graphic firms to create 3-dimensional models for both customers and builders. These computer generated models can be more accurate than traditional drawings. Architectural animation (which provides animated movies of buildings, rather than interactive images) can also be used to see the possible relationship a building will have in relation to the environment and its surrounding buildings. The processing of architectural spaces without the use of paper and pencil tools is now a widely accepted practice with a number of computer-assisted architectural design systems.


title: Computer-generated imagery

text: Architectural modeling tools allow an architect to visualize a space and perform "walk-throughs" in an interactive manner, thus providing "interactive environments" both at the urban and building levels. Specific applications in architecture not only include the specification of building structures (such as walls and windows) and walk-throughs but the effects of light and how sunlight will affect a specific design at different times of the day.


title: Computer-generated imagery

text: Architectural modeling tools have now become increasingly internet-based. However, the quality of internet-based systems still lags behind that of sophisticated in-house modeling systems.


title: Computer-generated imagery

text: In some applications, computer-generated images are used to "reverse engineer" historical buildings. For instance, a computer-generated reconstruction of the monastery at Georgenthal in Germany was derived from the ruins of the monastery, yet provides the viewer with a "look and feel" of what the building would have looked like in its day.


title: Computer-generated imagery

text: Computer generated models used in skeletal animation are not always anatomically correct. However, organizations such as the Scientific Computing and Imaging Institute have developed anatomically correct computer-based models. Computer generated anatomical models can be used both for instructional and operational purposes. To date, a large body of artist produced medical images continue to be used by medical students, such as images by Frank H. Netter, e.g. Cardiac images. However, a number of online anatomical models are becoming available.


title: Computer-generated imagery

text: A single patient X-ray is not a computer generated image, even if digitized. However, in applications which involve CT scans a three-dimensional model is automatically produced from many single-slice x-rays, producing "computer generated image". Applications involving magnetic resonance imaging also bring together a number of "snapshots" (in this case via magnetic pulses) to produce a composite, internal image.


title: Computer-generated imagery

text: In modern medical applications, patient-specific models are constructed in 'computer assisted surgery'. For instance, in total knee replacement, the construction of a detailed patient-specific model can be used to carefully plan the surgery. These three-dimensional models are usually extracted from multiple CT scans of the appropriate parts of the patient's own anatomy. Such models can also be used for planning aortic valve implantations, one of the common procedures for treating heart disease. Given that the shape, diameter, and position of the coronary openings can vary greatly from patient to patient, the extraction (from CT scans) of a model that closely resembles a patient's valve anatomy can be highly beneficial in planning the procedure.


title: Computer-generated imagery

text: To date, making the clothing of a digital character automatically fold in a natural way remains a challenge for many animators.


title: Computer-generated imagery

text: In addition to their use in film, advertising and other modes of public display, computer generated images of clothing are now routinely used by top fashion design firms.


title: Computer-generated imagery

text: The finest visible features such as fine wrinkles and skin pores are the size of about 100 µm or 0.1 millimetres. Skin can be modeled as a 7-dimensional bidirectional texture function (BTF) or a collection of bidirectional scattering distribution function (BSDF) over the target's surfaces.


title: Computer-generated imagery

text: Interactive visualization is the rendering of data that may vary dynamically and allowing a user to view the data from multiple perspectives. The applications areas may vary significantly, ranging from the visualization of the flow patterns in fluid dynamics to specific computer aided design applications. The data rendered may correspond to specific visual scenes that change as the user interacts with the system — e.g. simulators, such as flight simulators, make extensive use of CGI techniques for representing the world.


title: Computer-generated imagery

text: At the abstract level, an interactive visualization process involves a "data pipeline" in which the raw data is managed and filtered to a form that makes it suitable for rendering. This is often called the "visualization data". The visualization data is then mapped to a "visualization representation" that can be fed to a rendering system. This is usually called a "renderable representation". This representation is then rendered as a displayable image. As the user interacts with the system (e.g. by using joystick controls to change their position within the virtual world) the raw data is fed through the pipeline to create a new rendered image, often making real-time computational efficiency a key consideration in such applications.


title: Computer-generated imagery

text: While computer-generated images of landscapes may be static, "computer animation" only applies to dynamic images that resemble a movie. However, in general, the term computer animation refers to dynamic images that do not allow user interaction, and the term virtual world is used for the interactive animated environments.


title: Computer-generated imagery

text: Computer animation is essentially a digital successor to the art of stop motion animation of 3D models and frame-by-frame animation of 2D illustrations. Computer generated animations are more controllable than other more physically based processes, such as constructing miniatures for effects shots or hiring extras for crowd scenes, and because it allows the creation of images that would not be feasible using any other technology. It can also allow a single graphic artist to produce such content without the use of actors, expensive set pieces, or props.


title: Computer-generated imagery

text: To create the illusion of movement, an image is displayed on the computer screen and repeatedly replaced by a new image which is similar to the previous image, but advanced slightly in the time domain (usually at a rate of 24 or 30 frames/second). This technique is identical to how the illusion of movement is achieved with television and motion pictures.


title: Computer-generated imagery

text: A virtual world is a simulated environment, which allows the user to interact with animated characters, or interact with other users through the use of animated characters known as avatars. Virtual worlds are intended for its users to inhabit and interact, and the term today has become largely synonymous with interactive 3D virtual environments, where the users take the form of avatars visible to others graphically. These avatars are usually depicted as textual, two-dimensional, or three-dimensional graphical representations, although other forms are possible (auditory and touch sensations for example). Some, but not all, virtual worlds allow for multiple users.


title: Computer-generated imagery

text: Computer-generated imagery has been used in courtrooms, primarily since the early 2000s. However, some experts have argued that it is prejudicial. They are used to help judges or the jury to better visualize the sequence of events, evidence or hypothesis. However, a 1997 study showed that people are poor intuitive physicists and easily influenced by computer generated images. Thus it is important that jurors and other legal decision-makers be made aware that such exhibits are merely a representation of one potential sequence of events.


title: Computer-generated imagery

text: Weather visualizations were the first application of CGI in television. It has now become common in weather casting to display full motion video of images captured in real-time from multiple cameras and other imaging devices. Coupled with 3D graphics symbols and mapped to a common virtual geospatial model, these animated visualizations constitute the first true application of CGI to TV.


title: Computer-generated imagery

text: CGI has become common in sports telecasting. Sports and entertainment venues are provided with see-through and overlay content through tracked camera feeds for enhanced viewing by the audience. Examples include the yellow "first down" line seen in television broadcasts of American football games showing the line the offensive team must cross to receive a first down. CGI is also used in association with football and other sporting events to show commercial advertisements overlaid onto the view of the playing area. Sections of rugby fields and cricket pitches also display sponsored images. Swimming telecasts often add a line across the lanes to indicate the position of the current record holder as a race proceeds to allow viewers to compare the current race to the best performance. Other examples include hockey puck tracking and annotations of racing car performance and snooker ball trajectories. Sometimes CGI on TV with correct alignment to the real world has been referred to as augmented reality.


title: Computer-generated imagery

text: Computer-generated imagery is often used in conjunction with motion-capture to better cover the faults that come with CGI and animation. Computer-generated imagery is limited in its practical application by how realistic it can look. Unrealistic, or badly managed computer-generated imagery can result in the Uncanny Valley effect. This effect refers to the human ability to recognize things that look eerily like humans, but are slightly off. Such ability is a fault with normal computer-generated imagery which, due to the complex anatomy of the human-body, can often fail to replicate it perfectly. This is where motion-capture comes into play. Artists can use a motion-capture rig to get footage of a human performing an action and then replicate it perfectly with computer-generated imagery so that it looks normal.


title: Computer-generated imagery

text: The lack of anatomically correct digital models contributes to the necessity of motion-capture as it is used with computer-generated imagery. Because computer-generated imagery reflects only the outside, or skin, of the object being rendered, it fails to capture the infinitesimally small interactions between interlocking muscle groups used in fine motor-control, like speaking. The constant motion of the face as it makes sounds with shaped lips and tongue movement, along with the facial expressions that go along with speaking are difficult to replicate by hand. Motion capture can catch the underlying movement of facial muscles and better replicate the visual that goes along with the audio, like Josh Brolin's Thanos.


title: Mahayana

text: Mahāyāna (; "Great Vehicle") is a term for a broad group of Buddhist traditions, texts, philosophies, and practices. Mahāyāna Buddhism developed in India (c. 1st century BCE onwards) and is considered one of the two main existing branches of Buddhism (the other being "Theravāda"). Mahāyāna accepts the main scriptures and teachings of early Buddhism but also recognizes various doctrines and texts that are not accepted by Theravada Buddhism as original. These include the Mahāyāna Sūtras and their emphasis on the "bodhisattva" path and "Prajñāpāramitā". "Vajrayāna" or Mantra traditions are a subset of Mahāyāna, which make use of numerous tantric methods considered to be faster and more powerful at achieving Buddhahood by Vajrayānists.


title: Mahayana

text: "Mahāyāna" also refers to the path of the bodhisattva striving to become a fully awakened Buddha ("samyaksaṃbuddha") for the benefit of all sentient beings, and is thus also called the "Bodhisattva Vehicle" ("Bodhisattvayāna"). Mahāyāna Buddhism generally sees the goal of becoming a Buddha through the bodhisattva path as being available to all and sees the state of the arhat as incomplete. Mahāyāna also includes numerous Buddhas and bodhisattvas that are not found in Theravada (such as "Amitābha" and Vairocana). Mahāyāna Buddhist philosophy also promotes unique theories, such as the Madhyamaka theory of emptiness ("śūnyatā"), the "Vijñānavāda" doctrine, and the "Buddha-nature" teaching.


title: Mahayana

text: Although it was initially a small movement in India, Mahāyāna eventually grew to become an influential force in Indian Buddhism. Large scholastic centers associated with Mahāyāna such as Nalanda and Vikramashila, thrived between the seventh and twelfth centuries. In the course of its history, Mahāyāna Buddhism spread throughout South Asia, Central Asia, East Asia, and Southeast Asia. It remains influential today in China, Mongolia, Hong Kong, Korea, Japan, Singapore, Vietnam, the Philippines, Nepal, Malaysia, Taiwan, and Bhutan.


title: Mahayana

text: The Mahāyāna tradition is the largest major tradition of Buddhism existing today (with 53% of Buddhists belonging to East Asian Mahāyāna and 6% to Vajrayāna), compared to 36% for Theravada (survey from 2010).


title: Mahayana

text: According to Jan Nattier, the term "Mahāyāna" ("Great Vehicle") was originally an honorary synonym for "Bodhisattvayāna" ("Bodhisattva Vehicle"), the vehicle of a bodhisattva seeking buddhahood for the benefit of all sentient beings. The term "Mahāyāna" (which had earlier been used simply as an epithet for Buddhism itself) was therefore adopted at an early date as a synonym for the path and the teachings of the bodhisattvas. Since it was simply an honorary term for "Bodhisattvayāna", the adoption of the term "Mahāyāna" and its application to Bodhisattvayāna did not represent a significant turning point in the development of a Mahāyāna tradition.


title: Mahayana

text: The earliest Mahāyāna texts, such as the "Lotus Sūtra", often use the term "Mahāyāna" as a synonym for "Bodhisattvayāna", but the term "Hīnayāna" is comparatively rare in the earliest sources. The presumed dichotomy between "Mahāyāna" and "Hīnayāna" can be deceptive, as the two terms were not actually formed in relation to one another in the same era.


title: Mahayana

text: Among the earliest and most important references to "Mahāyāna" are those that occur in the "Lotus Sūtra" (Skt. "Saddharma Puṇḍarīka Sūtra") dating between the 1st century BCE and the 1st century CE. Seishi Karashima has suggested that the term first used in an earlier Gandhāri Prakrit version of the "Lotus Sūtra" was not the term "mahāyāna" but the Prakrit word "mahājāna" in the sense of "mahājñāna" (great knowing). At a later stage when the early Prakrit word was converted into Sanskrit, this "mahājāna", being phonetically ambivalent, may have been converted into "mahāyāna", possibly because of what may have been a double meaning in the famous Parable of the Burning House, which talks of three vehicles or carts (Skt: "yāna").


title: Mahayana

text: In Chinese, Mahāyāna is called ("dacheng"), which is a calque of "maha" (great ) "yana" (vehicle ). There is also the transliteration . The term appeared in some of the earliest Mahāyāna texts, including Emperor Ling of Han's translation of the Lotus Sutra. It also appears in the Chinese Āgamas, though scholars like Yin Shun argue that this is a later addition. Some Chinese scholars also argue that the meaning of the term in these earlier texts is different than later ideas of Mahāyāna Buddhism.


title: Mahayana

text: The origins of Mahāyāna are still not completely understood and there are numerous competing theories. The earliest Western views of Mahāyāna assumed that it existed as a separate school in competition with the so-called "Hīnayāna" schools. Some of the major theories about the origins of Mahāyāna include the following:


title: Mahayana

text: The lay origins theory was first proposed by Jean Przyluski and then defended by Étienne Lamotte and Akira Hirakawa. This view states that laypersons were particularly important in the development of Mahāyāna and is partly based on some texts like the "Vimalakirti Sūtra", which praise lay figures at the expense of monastics. This theory is no longer widely accepted since numerous early Mahāyāna works promote monasticism and asceticism.


title: Mahayana

text: The Mahāsāṃghika origin theory, which argues that Mahāyāna developed within the Mahāsāṃghika tradition. This is defended by scholars such as Hendrik Kern, A.K. Warder and Paul Williams who argue that at least some Mahāyāna elements developed among Mahāsāṃghika communities (from the 1st century BCE onwards), possibly in the area along the Kṛṣṇa River in the Āndhra region of southern India. The Mahāsāṃghika doctrine of the supramundane ("lokottara") nature of the Buddha is sometimes seen as a precursor to Mahāyāna views of the Buddha. Some scholars also see Mahāyāna figures like Nāgārjuna, Dignaga, Candrakīrti, Āryadeva, and Bhavaviveka as having ties to the Mahāsāṃghika tradition of Āndhra. However, other scholars have also pointed to different regions as being important, such as Gandhara and northwest India.


title: Mahayana

text: The Mahāsāṃghika origins theory has also slowly been shown to be problematic by scholarship that revealed how certain Mahāyāna sutras show traces of having developed among other "nikāyas" or monastic orders (such as the Dharmaguptaka). Because of such evidence, scholars like Paul Harrison and Paul Williams argue that the movement was not sectarian and was possibly pan-buddhist. There is no evidence that Mahāyāna ever referred to a separate formal school or sect of Buddhism, but rather that it existed as a certain set of ideals, and later doctrines, for aspiring bodhisattvas.


title: Mahayana

text: The "forest hypothesis" meanwhile states that Mahāyāna arose mainly among "hard-core ascetics, members of the forest dwelling ("aranyavasin") wing of the Buddhist Order", who were attempting to imitate the Buddha's forest living. This has been defended by Paul Harrison, Jan Nattier and Reginald Ray. This theory is based on certain sutras like the "Ugraparipṛcchā Sūtra" and the "Mahāyāna Rāṣṭrapālapaṛiprcchā" which promote ascetic practice in the wilderness as a superior and elite path. These texts criticize monks who live in cities and denigrate the forest life.


title: Mahayana

text: Jan Nattier's study of the "Ugraparipṛcchā Sūtra, A few good men" (2003) argues that this sutra represents the earliest form of Mahāyāna, which presents the bodhisattva path as a 'supremely difﬁcult enterprise' of elite monastic forest asceticism. Boucher's study on the "Rāṣṭrapālaparipṛcchā-sūtra" (2008) is another recent work on this subject.


title: Mahayana

text: The cult of the book theory, defended by Gregory Schopen, states that Mahāyāna arose among a number of loosely connected book worshiping groups of monastics, who studied, memorized, copied and revered particular Mahāyāna sūtras. Schopen thinks they were inspired by cult shrines where Mahāyāna sutras were kept. Schopen also argued that these groups mostly rejected stupa worship, or worshiping holy relics.


title: Mahayana

text: David Drewes has recently argued against all of the major theories outlined above. He points out that there is no actual evidence for the existence of book shrines, that the practice of sutra veneration was pan-Buddhist and not distinctly Mahāyāna. Furthermore, Drewes argues that "Mahāyāna sutras advocate mnemic/oral/aural practices more frequently than they do written ones." Regarding the forest hypothesis, he points out that only a few Mahāyāna sutras directly advocate forest dwelling, while the others either do not mention it or see it as unhelpful, promoting easier practices such as "merely listening to the sutra, or thinking of particular Buddhas, that they claim can enable one to be reborn in special, luxurious 'pure lands' where one will be able to make easy and rapid progress on the bodhisattva path and attain Buddhahood after as little as one lifetime."


title: Mahayana

text: Drewes states that the evidence merely shows that "Mahāyāna was primarily a textual movement, focused on the revelation, preaching, and dissemination of Mahāyāna sutras, that developed within, and never really departed from, traditional Buddhist social and institutional structures." Drewes points out the importance of "dharmabhanakas" (preachers, reciters of these sutras) in the early Mahāyāna sutras. This figure is widely praised as someone who should be respected, obeyed ('as a slave serves his lord'), and donated to, and it is thus possible these people were the primary agents of the Mahāyāna movement.


title: Mahayana

text: The earliest textual evidence of "Mahāyāna" comes from sūtras ("discourses", scriptures) originating around the beginning of the common era. Jan Nattier has noted that some of the earliest Mahāyāna texts, such as the "Ugraparipṛccha Sūtra" use the term "Mahāyāna", yet there is no doctrinal difference between Mahāyāna in this context and the early schools. Instead, Nattier writes that in the earliest sources, "Mahāyāna" referred to the rigorous emulation of Gautama Buddha's path to Buddhahood.


title: Mahayana

text: Some important evidence for early Mahāyāna Buddhism comes from the texts translated by the Indoscythian monk Lokakṣema in the 2nd century CE, who came to China from the kingdom of Gandhāra. These are some of the earliest known Mahāyāna texts. Study of these texts by Paul Harrison and others show that they strongly promote monasticism (contra the lay origin theory), acknowledge the legitimacy of arhatship, do not recommend devotion towards 'celestial' bodhisattvas and do not show any attempt to establish a new sect or order. A few of these texts often emphasize ascetic practices, forest dwelling, and deep states of meditative concentration ("samadhi").


title: Mahayana

text: Indian Mahāyāna never had nor ever attempted to have a separate Vinaya or ordination lineage from the early schools of Buddhism, and therefore each bhikṣu or bhikṣuṇī adhering to the Mahāyāna formally belonged to one of the early Buddhist schools. Membership in these "nikāyas", or monastic orders, continues today, with the Dharmaguptaka nikāya being used in East Asia, and the Mūlasarvāstivāda nikāya being used in Tibetan Buddhism. Therefore, Mahāyāna was never a separate monastic sect outside of the early schools.


title: Mahayana

text: Paul Harrison clarifies that while monastic Mahāyānists belonged to a nikāya, not all members of a nikāya were Mahāyānists. From Chinese monks visiting India, we now know that both Mahāyāna and non-Mahāyāna monks in India often lived in the same monasteries side by side. It is also possible that, formally, Mahāyāna would have been understood as a group of monks or nuns within a larger monastery taking a vow together (known as a ""kriyākarma"") to memorize and study a Mahāyāna text or texts.


title: Mahayana

text: The earliest stone inscription containing a recognizably Mahāyāna formulation and a mention of the Buddha Amitābha (an important Mahāyāna figure) was found in the Indian subcontinent in Mathura, and dated to around 180 CE. Remains of a statue of a Buddha bear the Brāhmī inscription: "Made in the year 28 of the reign of King Huviṣka, ... for the Blessed One, the Buddha Amitābha." There is also some evidence that the Kushan Emperor Huviṣka himself was a follower of Mahāyāna. A Sanskrit manuscript fragment in the Schøyen Collection describes Huviṣka as having "set forth in the Mahāyāna." Evidence of the name "Mahāyāna" in Indian inscriptions in the period before the 5th century is very limited in comparison to the multiplicity of Mahāyāna writings transmitted from Central Asia to China at that time.


title: Mahayana

text: Based on archeological evidence, Gregory Schopen argues that Indian Mahāyāna remained "an extremely limited minority movement – if it remained at all – that attracted absolutely no documented public or popular support for at least two more centuries." Likewise, Joseph Walser speaks of Mahāyāna's "virtual invisibility in the archaeological record until the fifth century." Schopen also sees this movement as being in tension with other Buddhists, "struggling for recognition and acceptance". Their "embattled mentality" may have led to certain elements found in Mahāyāna texts like Lotus sutra, such as a concern with preserving texts.


title: Mahayana

text: Schopen, Harrison and Nattier also argue that these communities were probably not a single unified movement, but scattered groups based on different practices and sutras. One reason for this view is that Mahāyāna sources are extremely diverse, advocating many different, often conflicting doctrines and positions, as Jan Nattier writes:Thus we find one scripture (the "Aksobhya-vyuha") that advocates both srávaka and bodhisattva practices, propounds the possibility of rebirth in a pure land, and enthusiastically recommends the cult of the book, yet seems to know nothing of emptiness theory, the ten bhumis, or the trikaya, while another (the "P’u-sa pen-yeh ching") propounds the ten bhumis and focuses exclusively on the path of the bodhisattva, but never discusses the paramitas. A Madhyamika treatise (Nagarjuna's "Mulamadhyamika-karikas") may enthusiastically deploy the rhetoric of emptiness without ever mentioning the bodhisattva path, while a Yogacara treatise (Vasubandhu's "Madhyanta-vibhaga-bhasya") may delve into the particulars of the trikaya doctrine while eschewing the doctrine of ekayana. We must be prepared, in other words, to encounter a multiplicity of Mahayanas flourishing even in India, not to mention those that developed in East Asia and Tibet.In spite of being a minority in India, Indian Mahāyāna was an intellectually vibrant movement, which developed various schools of thought during what Jan Westerhoff has been called "The Golden Age of Indian Buddhist Philosophy" (from the beginning of the first millennium CE up to the 7th century). Some major Mahāyāna traditions are Prajñāpāramitā, Mādhyamaka, Yogācāra, Buddha-nature ("Tathāgatagarbha"), and the school of Dignaga and Dharmakirti as the last and most recent. Major early figures include Nagarjuna, Āryadeva, Aśvaghoṣa, Asanga, Vasubandhu, and Dignaga. Mahāyāna Buddhists seem to have been active in the Kushan Empire (30–375 CE), a period that saw great missionary and literary activities by Buddhists. This is supported by the works of the historian Taranatha.


title: Mahayana

text: The Mahāyāna movement (or movements) remained quite small until it experienced much growth in the fifth century. Very few manuscripts have been found before the fifth century (the exceptions are from Bamiyan). According to Walser, "the fifth and sixth centuries appear to have been a watershed for the production of Mahāyāna manuscripts." Likewise it is only in the 4th and 5th centuries CE that epigraphic evidence shows some kind of popular support for Mahāyāna, including some possible royal support at the kingdom of Shan shan as well as in Bamiyan and Mathura.


title: Mahayana

text: Still, even after the 5th century, the epigraphic evidence which uses the term Mahāyāna is still quite small and is notably mainly monastic, not lay. By this time, Chinese pilgrims, such as Faxian (337–422 CE), Xuanzang (602–664), Yijing (635–713 CE) were traveling to India, and their writings do describe monasteries which they label 'Mahāyāna' as well as monasteries where both Mahāyāna monks and non-Mahāyāna monks lived together.


title: Mahayana

text: After the fifth century, Mahāyāna Buddhism and its institutions slowly grew in influence. Some of the most influential institutions became massive monastic university complexes such as Nalanda (established by the 5th-century CE Gupta emperor, Kumaragupta I) and Vikramashila (established under Dharmapala c. 783 to 820) which were centers of various branches of scholarship, including Mahāyāna philosophy. The Nalanda complex eventually became the largest and most influential Buddhist center in India for centuries. Even so, as noted by Paul Williams, "it seems that fewer than 50 percent of the monks encountered by Xuanzang (Hsüan-tsang; c. 600–664) on his visit to India actually were Mahāyānists."


title: Mahayana

text: Over time Indian Mahāyāna texts and philosophy reached Central Asia and China through trade routes like the Silk Road, later spreading throughout East Asia. Over time, Central Asian Buddhism became heavily influenced by Mahāyāna and it was a major source for Chinese Buddhism. Mahāyāna works have also been found in Gandhāra, indicating the importance of this region for the spread of Mahāyāna. Central Asian Mahāyāna scholars were very important in the Silk Road Transmission of Buddhism. They include translators like Lokakṣema (c. 167–186), Dharmarakṣa (c. 265–313), Kumārajīva (c. 401), and Dharmakṣema (385–433). The site of Dunhuang seems to have been a particularly important place for the study of Mahāyāna Buddhism.


title: Mahayana

text: By the fourth century, Chinese monks like Faxian (c. 337–422 CE) had also begun to travel to India (now dominated by the Guptas) to bring back Buddhist teachings, especially Mahāyāna works. These figures also wrote about their experiences in India and their work remains invaluable for understanding Indian Buddhism. In some cases Indian Mahāyāna traditions were directly transplanted, as with the case of the East Asian Madhymaka (by Kumārajīva) and East Asian Yogacara (especially by Xuanzang). Later, new developments in Chinese Mahāyāna led to new Chinese Buddhist traditions like Tiantai, Huayen, Pure Land and Chan Buddhism (Zen). These traditions would then spread to Korea, Vietnam and Japan.


title: Mahayana

text: Forms of Mahāyāna Buddhism which are mainly based on the doctrines of Indian Mahāyāna sutras are still popular in East Asian Buddhism, which is mostly dominated by various branches of Mahāyāna Buddhism. Paul Williams has noted that in this tradition in the Far East, primacy has always been given to the study of the Mahāyāna sūtras.


title: Mahayana

text: Beginning during the Gupta (c. 3rd century CE–575 CE) period a new movement began to develop which drew on previous Mahāyāna doctrine as well as new Pan-Indian tantric ideas. This came to be known by various names such as Vajrayāna (Tibetan: "rdo rje theg pa"), Mantrayāna, and Esoteric Buddhism or "Secret Mantra" ("Guhyamantra"). This new movement continued into the Pala era (8th century–12th century CE), during which it grew to dominate Indian Buddhism. Possibly led by groups of wandering tantric yogis named mahasiddhas, this movement developed new tantric spiritual practices and also promoted new texts called the Buddhist Tantras. Philosophically, Vajrayāna Buddhist thought remained grounded in the Mahāyāna Buddhist ideas of Madhyamaka, Yogacara and Buddha-nature. Tantric Buddhism generally deals with new forms of meditation and ritual which often makes use of the visualization of Buddhist deities (including Buddhas, bodhisattvas, dakinis, and fierce deities) and the use of mantras. Most of these practices are esoteric and require ritual initiation or introduction by a tantric master ("vajracarya") or guru.


title: Mahayana

text: The source and early origins of Vajrayāna remain a subject of debate among scholars. Some scholars like Alexis Sanderson argue that Vajrayāna derives its tantric content from Shaivism and that it developed as a result of royal courts sponsoring both Buddhism and Saivism. Sanderson argues that Vajrayāna works like the Samvara and Guhyasamaja texts show direct borrowing from Shaiva tantric literature. However, other scholars such as Ronald M. Davidson question the idea that Indian tantrism developed in Shaivism first and that it was then adopted into Buddhism. Davidson points to the difficulties of establishing a chronology for the Shaiva tantric literature and argues that both traditions developed side by side, drawing on each other as well as on local Indian tribal religion.


title: Mahayana

text: Whatever the case, this new tantric form of Mahāyāna Buddhism became extremely influential in India, especially in Kashmir and in the lands of the Pala Empire. It eventually also spread north into Central Asia, the Tibetan plateau and to East Asia. Vajrayāna remains the dominant form of Buddhism in Tibet, in surrounding regions like Bhutan and in Mongolia. Esoteric elements are also an important part of East Asian Buddhism where it is referred to by various terms. These include: "Zhēnyán" (Chinese: 真言, literally "true word", referring to mantra), "Mìjiao" (Chinese: 密教; Esoteric Teaching), "Mìzōng" (密宗; "Esoteric Tradition") or "Tángmì" (唐密; "Tang (Dynasty) Esoterica") in Chinese and Shingon, Tomitsu, Mikkyo, and Taimitsu in Japanese.


title: Mahayana

text: Few things can be said with certainty about Mahāyāna Buddhism in general other than that the Buddhism practiced in China, Indonesia, Vietnam, Korea, Tibet, Mongolia and Japan is Mahāyāna Buddhism. Mahāyāna can be described as a loosely bound collection of many teachings and practices (some of which are seemingly contradictory). Mahāyāna constitutes an inclusive and broad set of traditions characterized by plurality and the adoption of a vast number of new sutras, ideas and philosophical treatises in addition to the earlier Buddhist texts.


title: Mahayana

text: Broadly speaking, Mahāyāna Buddhists accept the classic Buddhist doctrines found in early Buddhism (i.e. the "Nikāya" and Āgamas), such as the Middle Way, Dependent origination, the Four Noble Truths, the Noble Eightfold Path, the Three Jewels, the Three marks of existence and the "bodhipakṣadharmas" (aids to awakening). Mahāyāna Buddhism further accepts some of the ideas found in Buddhist Abhidharma thought. However, Mahāyāna also adds numerous Mahāyāna texts and doctrines, which are seen as definitive and in some cases superior teachings. D.T. Suzuki described the broad range and doctrinal liberality of Mahāyāna as "a vast ocean where all kinds of living beings are allowed to thrive in a most generous manner, almost verging on a chaos."


title: Mahayana

text: Paul Williams refers to the main impulse behind Mahāyāna as the vision which sees the motivation to achieve Buddhahood for sake of other beings as being the supreme religious motivation. This is way that Atisha defines Mahāyāna in his "Bodhipathapradipa". As such, according to Williams, "Mahāyāna is not as such an institutional identity. Rather, it is inner motivation and vision, and this inner vision can be found in anyone regardless of their institutional position." Thus, instead of a specific school or sect, Mahāyāna is a "family term" or a religious tendency, which is united by "a vision of the ultimate goal of attaining full Buddhahood for the benefit of all sentient beings (the 'bodhisattva ideal') and also (or eventually) a belief that Buddhas are still around and can be contacted (hence the possibility of an ongoing revelation)."


title: Mahayana

text: Buddhas and bodhisattvas (beings on their way to Buddhahood) are central elements of Mahāyāna. Mahāyāna has a vastly expanded cosmology and theology, with various Buddhas and powerful bodhisattvas residing in different worlds and buddha-fields ("buddha kshetra"). Buddhas unique to Mahāyāna include the Buddhas Amitābha ("Infinite Light"), Akṣobhya ("the Imperturbable"), Bhaiṣajyaguru ("Medicine guru") and Vairocana ("the Illuminator"). In Mahāyāna, a Buddha is seen as a being that has achieved the highest kind of awakening due to his superior compassion and wish to help all beings.


title: Mahayana

text: An important feature of Mahāyāna is the way that it understands the nature of a Buddha, which differs from non-Mahāyāna understandings. Mahāyāna texts not only often depict numerous Buddhas besides Sakyamuni, but see them as transcendental or supramundane ("lokuttara") beings with great powers and huge lifetimes. The "White Lotus Sutra" famously describes the lifespan of the Buddha as immeasurable and states that he actually achieved Buddhahood countless of eons ("kalpas") ago and has been teaching the Dharma through his numerous avatars for an unimaginable period of time.


title: Mahayana

text: Furthermore, Buddhas are active in the world, constantly devising ways to teach and help all sentient beings. According to Paul Williams, in Mahāyāna, a Buddha is often seen as "a spiritual king, relating to and caring for the world", rather than simply a teacher who after his death "has completely 'gone beyond' the world and its cares". Buddha Sakyamuni's life and death on earth are then usually understood docetically as a "mere appearance", his death is a show, while in actuality he remains out of compassion to help all sentient beings. Similarly, Guang Xing describes the Buddha in Mahāyāna as an omnipotent and almighty divinity "endowed with numerous supernatural attributes and qualities."


title: Mahayana

text: The idea that Buddhas remain accessible is extremely influential in Mahāyāna and also allows for the possibility of having a reciprocal relationship with a Buddha through prayer, visions, devotion and revelations. Through the use of various practices, a Mahāyāna devotee can aspire to be reborn in a Buddha's pure land or buddha field ("buddhakṣetra"), where they can strive towards Buddhahood in the best possible conditions. Depending on the sect, liberation into a buddha-field can be obtained by faith, meditation, or sometimes even by the repetition of Buddha's name. Faith-based devotional practices focused on rebirth in pure lands are common in East Asia Pure Land Buddhism.


title: Mahayana

text: The influential Mahāyāna concept of the three bodies ("trikāya") of a Buddha developed to make sense of the transcendental nature of the Buddha. This doctrine holds that the "bodies of magical transformation" ("nirmāṇakāyas") and the "enjoyment bodies" ("saṃbhogakāya") are emanations from the ultimate Buddha body, the "Dharmakaya," which is none other than the ultimate reality itself, i.e. emptiness or "Thusness".


title: Mahayana

text: The Mahāyāna bodhisattva path ("mārga") or vehicle ("yāna") is seen as being the superior spiritual path by Mahāyānists, over and above the paths of those who seek arhatship or "solitary buddhahood" for their own sake ("Śrāvakayāna" and "Pratyekabuddhayāna"). Mahāyāna Buddhists generally hold that pursuing only the personal release from suffering i.e. nirvāṇa is a smaller or inferior aspiration (called ""hinayana""), because it lacks the wish and resolve to liberate all other sentient beings from saṃsāra (the round of rebirth) by becoming a Buddha.""


title: Mahayana

text: This wish to help others is called "bodhicitta". One who engages in this path to complete buddhahood is called a bodhisattva. High level bodhisattvas are seen as extremely powerful supramundane beings which are objects of devotion and prayer throughout Mahāyāna lands. Popular bodhisattvas which are revered across Mahāyāna include Avalokiteshvara, Manjushri, Tara and Maitreya. Bodhisattvas could reach the personal nirvana of the arhats, but they reject this goal and remain in saṃsāra to help others out of compassion.


title: Mahayana

text: According to eighth-century Mahāyāna philosopher Haribhadra, the term "bodhisattva" can technically refer to those who follow any of the three vehicles, since all are working towards "bodhi" (awakening) and hence the technical term for a Mahāyāna bodhisattva is a "mahāsattva" (great being) "bodhisattva". According to Paul Williams, a Mahāyāna bodhisattva is best defined as:that being who has taken the vow to be reborn, no matter how many times this may be necessary, in order to attain the highest possible goal, that of Complete and Perfect Buddhahood. This is for the benefit of all sentient beings.


title: Mahayana

text: There are two models for the nature of the bodhisattvas, which are seen in the various Mahāyāna texts. One is the idea that a bodhisattva must postpone their awakening until Buddhahood is attained. This could take eons and in the meantime, they will help countless beings. After reaching Buddhahood, they do pass on to nirvāṇa. The second model is the idea that there are two kinds of nirvāṇa, the nirvāṇa of an arhat and a superior type of nirvāṇa called "apratiṣṭhita" (non-abiding, not-established) that allows a Buddha to remain forever engaged in the world. As noted by Paul Williams, the idea of "apratiṣṭhita nirvāṇa" may have taken some time to develop and is not obvious in some of the early Mahāyāna literature.


title: Mahayana

text: In most classic Mahāyāna sources (as well as in non-Mahāyāna sources on the topic), the bodhisattva path is said to take three or four "asaṃkheyyas" ("incalculable eons"), requiring a huge number of lifetimes of practice. However, certain practices are sometimes held to provide shortcuts to Buddhahood (these vary widely by tradition). According to the "Bodhipathapradīpa" ("A Lamp for the Path to Awakening") by the Indian master Atiśa, the central defining feature of a bodhisattva's path is the universal aspiration to end suffering for themselves and all other beings, i.e. "bodhicitta".


title: Mahayana

text: The bodhisattva's spiritual path is traditionally held to begin with the revolutionary event called the "arising of the Awakening Mind" ("bodhicittotpāda"), which is the wish to become a Buddha in order to help all beings. This is achieved in different ways, such as the meditation taught by the Indian master Shantideva in his "Bodhicaryavatara" called "equalising self and others and exchanging self and others." Other Indian masters like Atisha and Kamalashila also teach a meditation in which we contemplate how "all" beings have been our close relatives or friends in past lives. This contemplation leads to the arising of deep love ("maitrī") and compassion ("karuṇā") for others, and thus bodhicitta is generated. According to the Indian philosopher Shantideva, when great compassion and bodhicitta arises in a person's heart, they cease to be an ordinary person and become a "son or daughter of the Buddhas".


title: Mahayana

text: The idea of the bodhisattva is not unique to Mahāyāna Buddhism and it is found in Theravada and other early Buddhist schools. However, these schools held that becoming a bodhisattva required a prediction of one's future Buddhahood in the presence of a living Buddha. In Mahāyāna a bodhisattva is applicable to any person from the moment they intend to become a Buddha (i.e. the arising of bodhicitta) and without the requirement of a living Buddha. Some Mahāyāna sūtras like the "Lotus Sutra", promote the bodhisattva path as being universal and open to everyone. Other texts disagree with this.


title: Mahayana

text: The generation of bodhicitta may then be followed by the taking of the bodhisattva vows to "lead to Nirvana the whole immeasurable world of beings" as the "Prajñaparamita" "sutras" state. This compassionate commitment to help others is the central characteristic of the Mahāyāna bodhisattva. These vows may be accompanied by certain ethical guidelines or bodhisattva precepts. Numerous sutras also state that a key part of the bodhisattva path is the practice of a set of virtues called "pāramitās" (transcendent or supreme virtues). Sometimes six are outlined: giving, ethical discipline, patient endurance, diligence, meditation and transcendent wisdom. Other sutras (like the "Daśabhūmika") give a list of ten, with the addition of "upāya" (skillful means), "praṇidhāna" (vow, resolution), "Bala" (spiritual power) and "Jñāna" (knowledge). "Prajñā" (transcendent knowledge or wisdom) is arguably the most important virtue of the bodhisattva. This refers to an understanding of the emptiness of all phenomena, arising from study, deep consideration and meditation.


title: Mahayana

text: Various texts associate the beginning of the bodhisattva practice with what is called the "path of accumulation" or equipment ("saṃbhāra-mārga"), which is the first path of the classic five paths schema.


title: Mahayana

text: The "Daśabhūmika Sūtra" as well as other texts also outline a series of bodhisattva levels or spiritual stages ("bhūmis" ) on the path to Buddhahood. The various texts disagree on the number of stages however, the "Daśabhūmika" giving ten for example (and mapping each one to the ten paramitas), the "Bodhisattvabhūmi" giving seven and thirteen and the "Avatamsaka" outlining 40 stages.


title: Mahayana

text: In later Mahāyāna scholasticism, such as in the work of Kamalashila and Atiśa, the five paths and ten "bhūmi" systems are merged and this is the progressive path model that is used in Tibetan Buddhism. According to Paul Williams, in these systems, the first "bhūmi" is reached once one attains "direct, nonconceptual and nondual insight into emptiness in meditative absorption", which is associated with the path of seeing ("darśana-mārga"). At this point, a bodhisattva is considered an "ārya" (a noble being).


title: Mahayana

text: Skillful means or Expedient techniques (Skt. "upāya") is another important virtue and doctrine in Mahāyāna Buddhism. The idea is most famously expounded in the "White Lotus Sutra", and refers to any effective method or technique that is conducive to spiritual growth and leads beings to awakening and nirvana. This doctrine states that the Buddha adapts his teaching to whoever he is teaching to out of compassion. Because of this, it is possible that the Buddha may teach seemingly contradictory things to different people. This idea is also used to explain the vast textual corpus found in Mahāyāna.


title: Mahayana

text: A closely related teaching is the doctrine of the One Vehicle ("ekayāna"). This teaching states that even though the Buddha is said to have taught three vehicles (the disciples' vehicle, the vehicle of solitary Buddhas and the bodhisattva vehicle, which are accepted by all early Buddhist schools), these actually are all skillful means which lead to the same place: Buddhahood. Therefore, there really are not three vehicles in an ultimate sense, but one vehicle, the supreme vehicle of the Buddhas, which is taught in different ways depending on the faculties of individuals. Even those beings who think they have finished the path (i.e. the arhats) are actually not done, and they will eventually reach Buddhahood.


title: Mahayana

text: This doctrine was not accepted in full by all Mahāyāna traditions. The Yogācāra school famously defended an alternative theory that held that not all beings could become Buddhas. This became a subject of much debate throughout Mahāyāna Buddhist history.


title: Mahayana

text: Some of the key Mahāyāna teachings are found in the "Prajñāpāramitā" ("Transcendent Knowledge" or "Perfection of Wisdom") texts, which are some of the earliest Mahāyāna works. Prajñāpāramitā is a deep knowledge of reality which Buddhas and bodhisattvas attain. It is a transcendent, non-conceptual and non-dual kind of knowledge into the true nature of things. This wisdom is also associated with insight into the emptiness ("śūnyatā") of dharmas (phenomena) and their illusory nature ("māyā"). This amounts to the idea that all phenomena ("dharmas") without exception have "no essential unchanging core" (i.e. they lack "svabhāva," an essence or inherent nature), and therefore have "no fundamentally real existence." These empty phenomena are also said to be conceptual constructions.


title: Mahayana

text: Because of this, all "dharmas" (things, phenomena), even the Buddha's Teaching, the Buddha himself, Nirvāṇa and all living beings, are like "illusions" or "magic" ("māyā") and "dreams" ("svapna"). This emptiness or lack of real existence applies even to the apparent arising and ceasing of phenomena. Because of this, all phenomena are also described as unarisen ("anutpāda"), unborn ("ajata"), "beyond coming and going" in the Prajñāpāramitā literature. Most famously, the "Heart Sutra" states that "all phenomena are empty, that is, without characteristic, unproduced, unceased, stainless, not stainless, undiminished, unfilled." The Prajñāpāramitā texts also use various metaphors to describe the nature of things, for example, the "Diamond Sutra" compares phenomena to: "A shooting star, a clouding of the sight, a lamp, an illusion, a drop of dew, a bubble, a dream, a lightning's flash, a thunder cloud."


title: Mahayana

text: Prajñāpāramitā is also associated with not grasping, not taking a stand on or "not taking up" ("aparigṛhīta") anything in the world. The "Aṣṭasāhasrikā Prajñāpāramitā Sūtra" explains it as "not grasping at form, not grasping at sensation, perception, volitions and cognition." This includes not grasping or taking up even correct Buddhist ideas or mental signs (such as "not-self", "emptiness", bodhicitta, vows), since these things are ultimately all empty concepts as well.


title: Mahayana

text: Attaining a state of fearless receptivity ("ksanti") through the insight into the true nature of reality ("Dharmatā") in an intuitive, non-conceptual manner is said to be the "prajñāpāramitā," the highest spiritual wisdom. According to Edward Conze, the "patient acceptance of the non-arising of dharmas" ("anutpattika-dharmakshanti") is "one of the most distinctive virtues of the Mahāyānistic saint." The Prajñāpāramitā texts also claim that this training is not just for Mahāyānists, but for all Buddhists following any of the three vehicles.


title: Mahayana

text: The Mahāyāna philosophical school termed Madhyamaka (Middle theory or Centrism, also known as "śūnyavāda," 'the emptiness theory') was founded by the second-century figure of Nagarjuna. This philosophical tradition focuses on refuting all theories which posit any kind of substance, inherent existence or intrinsic nature ("svabhāva").


title: Mahayana

text: In his writings, Nagarjuna attempts to show that any theory of intrinsic nature is contradicted by the Buddha's theory of dependent origination, since anything that has an independent existence cannot be dependently originated. The "śūnyavāda" philosophers were adamant that their denial of "svabhāva" is not a kind of nihilism (against protestations to the contrary by their opponents).


title: Mahayana

text: Using the two truths theory, Madhyamaka claims that while one can speak of things existing in a conventional, relative sense, they do not exist inherently in an ultimate sense. Madhyamaka also argues that emptiness itself is also "empty", it does not have an absolute inherent existence of its own. It is also not to be understood as a transcendental absolute reality. Instead, the emptiness theory is merely a useful concept that should not be clung to. In fact, for Madhyamaka, since everything is empty of true existence, all things are just conceptualizations ("prajñapti-matra"), including the theory of emptiness, and all concepts must ultimately be abandoned in order to truly understand the nature of things.


title: Mahayana

text: "Vijñānavāda" ("the doctrine of consciousness", a.k.a. "vijñapti-mātra," "perceptions only" and "citta-mātra" "mind only") is another important doctrine promoted by some Mahāyāna sutras which later became the central theory of a major philosophical movement which arose during the Gupta period called Yogācāra. The primary sutra associated with this school of thought is the "Saṃdhinirmocana Sūtra," which claims that "śūnyavāda" is not the final definitive teaching ("nītārtha") of the Buddha. Instead, the ultimate truth ("paramārtha-satya") is said to be the view that all things ("dharmas") are only mind ("citta"), consciousness ("vijñāna") or perceptions ("vijñapti") and that seemingly "external" objects (or "internal" subjects) do not really exist apart from the dependently originated flow of mental experiences.


title: Mahayana

text: When this flow of mentality is seen as being empty of the subject-object duality we impose upon it, one reaches the non-dual cognition of "Thusness" ("tathatā"), which is nirvana. This doctrine is developed through various theories, the most important being the eight consciousnesses and the three natures. The "Saṃdhinirmocana" calls its doctrine the 'third turning of the dharma wheel"'." The "Pratyutpanna sutra" also mentions this doctrine, stating: "whatever belongs to this triple world is nothing but thought ["citta-mātra"]. Why is that? It is because however I imagine things, that is how they appear".


title: Mahayana

text: The most influential thinkers in this tradition were the Indian brothers Asanga and Vasubandhu, along with an obscure figure termed Maitreyanātha. Yogācāra philosophers developed their own interpretation of the doctrine of emptiness which also criticized Madhyamaka for falling into nihilism.


title: Mahayana

text: The doctrine of "Tathāgata embryo" or "Tathāgata womb (Tathāgatagarbha)," also known as "Buddha-nature, matrix" or "principle" (Skt: "Buddha-dhātu") is important in all modern Mahāyāna traditions, though it is interpreted in many different ways. Broadly speaking, Buddha-nature is concerned with explaining what allows sentient beings to become Buddhas. The earliest sources for this idea may include the "Tathāgatagarbha Sūtra" and the "Mahāyāna Mahāparinirvāṇa Sūtra". The "Mahāyāna Mahāparinirvāṇa" refers to "a sacred nature that is the basis for [beings] becoming buddhas", and it also describes it as the 'Self' ("atman").


title: Mahayana

text: David Seyfort Ruegg explains this concept as the base or support for the practice of the path, and thus it is the "cause" ("hetu") for the fruit of Buddhahood. The "Tathāgatagarbha Sūtra" states that within the defilements is found "the tathagata's wisdom, the tathagata's vision, and the tathagata's body...eternally unsullied, and...replete with virtues no different from my own...the tathagatagarbhas of all beings are eternal and unchanging".


title: Mahayana

text: The ideas found in the Buddha-nature literature are a source of much debate and disagreement among Mahāyāna Buddhist philosophers as well as modern academics. Some scholars have seen this as an influence from Brahmanic Hinduism, and some of these sutras admit that the use of the term 'Self' is partly done in order to win over non-Buddhist ascetics (in other words, it is a skillful means). According to some scholars, the Buddha-nature discussed in some Mahāyāna sūtras does not represent a substantial self ("ātman") which the Buddha critiqued; rather, it is a positive expression of emptiness ("śūnyatā") and represents the potentiality to realize Buddhahood through Buddhist practices. Similarly, Williams thinks that this doctrine was not originally dealing with ontological issues, but with "religious issues of realising one's spiritual potential, exhortation, and encouragement."


title: Mahayana

text: The Buddha-nature genre of sūtras can be seen as an attempt to state Buddhist teachings using positive language while also maintaining the middle way, to prevent people from being turned away from Buddhism by a false impression of nihilism. This is the position taken by the "Laṅkāvatāra Sūtra", which states that the Buddhas teach the doctrine of "tathāgatagarbha" (which sounds similar to an atman) in order to help those beings who are attached to the idea of anatman. However, the sutra goes on to say that the "tathāgatagarbha" is empty and is not actually a substantial self.


title: Mahayana

text: A different view is defended by various modern scholars like Michael Zimmermann. This view is the idea that Buddha-nature sutras such as the "Mahāparinirvāṇa" and the "Tathāgatagarbha Sūtra" teach an affirmative vision of an eternal, indestructible Buddhic Self. Shenpen Hookham, a western scholar and lama sees Buddha-nature as a True Self that is real and permanent. Similarly, C. D. Sebastian understands the "Ratnagotravibhāga's" view of this topic as a transcendental self that is "the unique essence of the universe".


title: Mahayana

text: Indian Mahāyāna Buddhists faced various criticisms from non-Mahāyānists regarding the authenticity of their teachings. The main critique they faced was that Mahāyāna teachings had not been taught by the Buddha, but were invented by later figures. Numerous Mahāyāna texts discuss this issue and attempt to defend the truth and authenticity of Mahāyāna in various ways.


title: Mahayana

text: One idea that Mahāyāna texts put forth is that Mahāyāna teachings were taught later because most people were unable to understand the Mahāyāna sūtras at the time of the Buddha and that people were ready to hear the Mahāyāna only in later times. Certain traditional accounts state that Mahāyāna sutras were hidden away or kept safe by divine beings like Nagas or bodhisattvas until the time came for their dissemination.


title: Mahayana

text: Similarly, some sources also state that Mahāyāna teachings were revealed by other Buddhas, bodhisattvas and devas to a select number of individuals (often through visions or dreams). Some scholars have seen a connection between this idea and Mahāyāna meditation practices which involve the visualization of Buddhas and their Buddha-lands.


title: Mahayana

text: Another argument that Indian Buddhists used in favor of the Mahāyāna is that its teachings are true and lead to awakening since they are in line with the Dharma. Because of this, they can be said to be "well said" ("subhasita)", and therefore, they can be said to be the word of the Buddha in this sense. This idea that whatever is "well spoken" is the Buddha's word can be traced to the earliest Buddhist texts, but it is interpreted more widely in Mahāyāna. From the Mahāyāna point of view, a teaching is the "word of the Buddha" because it is in accord with the Dharma, not because it was spoken by a specific individual (i.e. Gautama). This idea can be seen in the writings of Shantideva (8th century), who argues that an "inspired utterance" is the Buddha word if it is "connected with the truth", "connected with the Dharma", "brings about renunciation of kleshas, not their increase" and "it shows the laudable qualities of nirvana, not those of samsara."


title: Mahayana

text: The modern Japanese Zen Buddhist scholar D. T. Suzuki similarly argued that while the Mahāyāna sūtras may not have been directly taught by the historical Buddha, the "spirit and central ideas" of Mahāyāna derive from the Buddha. According to Suzuki, Mahāyāna evolved and adapted itself to suit the times by developing new teachings and texts, while maintaining the spirit of the Buddha.


title: Mahayana

text: Mahāyāna often sees itself as penetrating further and more profoundly into the Buddha's Dharma. An Indian commentary on the "Mahāyānasaṃgraha", gives a classification of teachings according to the capabilities of the audience:


title: Mahayana

text: There is also a tendency in Mahāyāna sūtras to regard adherence to these sūtras as generating spiritual benefits greater than those that arise from being a follower of the non-Mahāyāna approaches. Thus the "Śrīmālādevī Siṃhanāda Sūtra" claims that the Buddha said that devotion to Mahāyāna is inherently superior in its virtues to following the śrāvaka or pratyekabuddha paths.


title: Mahayana

text: The commentary on the "Abhidharmasamuccaya" gives the following seven reasons for the "greatness" of the Mahayana:


title: Mahayana

text: Mahāyāna Buddhist practice is quite varied. A common set of virtues and practices which is shared by all Mahāyāna traditions are the six perfections or transcendent virtues ("pāramitā").


title: Mahayana

text: A central practice advocated by numerous Mahāyāna sources is focused around "the acquisition of merit, the universal currency of the Buddhist world, a vast quantity of which was believed to be necessary for the attainment of Buddhahood".


title: Mahayana

text: Another important class of Mahāyāna Buddhist practice is textual practices that deal with listening to, memorizing, reciting, preaching, worshiping and copying Mahāyāna sūtras.


title: Mahayana

text: Mahāyāna sūtras, especially those of the "Prajñāpāramitā" genre, teach the practice of the six transcendent virtues or perfections ("pāramitā") as part of the path to Buddhahood. Special attention is given to transcendent knowledge ("prajñāpāramitā"), which is seen as a primary virtue. According to Donald S. Lopez Jr., the term "pāramitā" can mean "excellence" or "perfection" as well as "that which has gone beyond" or "transcendence".


title: Mahayana

text: This list is also mentioned by the Theravāda commentator Dhammapala, who describes it as a categorization of the same ten perfections of Theravada Buddhism. According to Dhammapala, "Sacca" is classified as both "Śīla" and "Prajñā", "Mettā" and "Upekkhā" are classified as "Dhyāna", and "Adhiṭṭhāna" falls under all six. Bhikkhu Bodhi states that the correlations between the two sets show there was a shared core before the Theravada and Mahayana schools split.


title: Mahayana

text: Mahāyāna Buddhism teaches a vast array of meditation practices. These include meditations which are shared with the early Buddhist traditions, including mindfulness of breathing; mindfulness of the unattractivenes of the body; loving-kindness; the contemplation of dependent origination; and mindfulness of the Buddha. In Chinese Buddhism, these five practices are known as the "five methods for stilling or pacifying the mind" and support the development of the stages of "dhyana".


title: Mahayana

text: The "Yogācārabhūmi-Śāstra" (compiled c. 4th century), which is the most comprehensive Indian treatise on Mahāyāna practice, discusses classic Buddhist numerous meditation methods and topics, including the four "dhyānas", the different kinds of "samādhi", the development of insight ("vipaśyanā") and tranquility ("śamatha"), the four foundations of mindfulness ("smṛtyupasthāna"), the five hindrances ("nivaraṇa"), and classic Buddhist meditations such as the contemplation of unattractiveness, impermanence ("anitya"), suffering ("duḥkha"), and contemplation death ("maraṇasaṃjñā").


title: Mahayana

text: Other works of the Yogācāra school, such as Asaṅga's "Abhidharmasamuccaya," and Vasubandhu's "Madhyāntavibhāga-bhāsya" also discuss meditation topics such as mindfulness, "smṛtyupasthāna," the 37 wings to awakening"," and "samadhi".


title: Mahayana

text: A very popular Mahāyāna practice from very early times involved the visualization of a Buddha while practicing mindfulness of a Buddha ("buddhānusmṛti") along with their Pure Land. This practice could lead the meditator to feel that they were in the presence of the Buddha and in some cases it was held that it could lead to visions of the Buddhas, through which one could receive teachings from them.


title: Mahayana

text: This meditation is taught in numerous Mahāyāna sūtras such as the Pure Land sutras, the "Akṣobhya-vyūha" and the "Pratyutpanna Samādhi". The "Pratyutpanna" states that through mindfulness of the Buddha meditation one may be able to meet this Buddha in a vision or a dream and learn from them.


title: Mahayana

text: Similarly, the "Samādhirāja Sūtra" for states that:Those who, while walking, sitting, standing, or sleeping, recollect the moon-like Buddha, will always be in Buddha's presence and will attain the vast nirvāṇa. His pure body is the colour of gold, beautiful is the Protector of the World. Whoever visualizes him like this practises the meditation of the bodhisattvas.


title: Mahayana

text: In the case of Pure Land Buddhism, it is widely held that the practice of reciting the Buddha's name (called "nianfo" in Chinese and "nembutsu" in Japanese) can lead to rebirth in a Buddha's Pure Land, as well as other positive outcomes. In East Asian Buddhism, the most popular Buddha used for this practice is Amitabha.


title: Mahayana

text: East Asian Mahāyāna Buddhism also developed numerous unique meditation methods, including the Chan (Zen) practices of huatou, koan meditation, and silent illumination (Jp. "shikantaza"). Tibetan Buddhism also includes numerous unique forms of contemplation, such as "tonglen" ("sending and receiving") and "lojong" (""mind training"").


title: Mahayana

text: There are also numerous meditative practices that are generally considered to be part of a separate category rather than general or mainstream Mahāyāna meditation. These are the various practices associated with Vajrayāna (also termed Mantrayāna, Secret Mantra, Buddhist Tantra, and Esoteric Buddhism). This family of practices, which include such varied forms as Deity Yoga, Dzogchen, Mahamudra, the Six Dharmas of Nāropa, the recitation of mantras and dharanis, and the use of mudras and mandalas, are very important in Tibetan Buddhism as well as in some forms of East Asian Buddhism (like Shingon and Tendai).


title: Mahayana

text: Mahāyāna Buddhism takes the basic teachings of the Buddha as recorded in early scriptures as the starting point of its teachings, such as those concerning karma and rebirth, anātman, emptiness, dependent origination, and the Four Noble Truths. Mahāyāna Buddhists in East Asia have traditionally studied these teachings in the Āgamas preserved in the Chinese Buddhist canon. "Āgama" is the term used by those traditional Buddhist schools in India who employed Sanskrit for their basic canon. These correspond to the Nikāyas used by the Theravāda school. The surviving Āgamas in Chinese translation belong to at least two schools. Most of the Āgamas were never translated into the Tibetan canon, which according to Hirakawa, only contains a few translations of early sutras corresponding to the Nikāyas or Āgamas. However, these basic doctrines are contained in Tibetan translations of later works such as the "Abhidharmakośa" and the "Yogācārabhūmi-Śāstra."


title: Mahayana

text: In addition to accepting the essential scriptures of the early Buddhist schools as valid, Mahāyāna Buddhism maintains large collections of sūtras that are not recognized as authentic by the modern Theravāda school. The earliest of these sutras do not call themselves 'Mahāyāna', but use the terms "vaipulya" (extensive) sutras, or "gambhira" (profound) sutras. These were also not recognized by some individuals in the early Buddhist schools. In other cases, Buddhist communities such as the Mahāsāṃghika school were divided along these doctrinal lines. In Mahāyāna Buddhism, the Mahāyāna sūtras are often given greater authority than the Āgamas. The first of these Mahāyāna-specific writings were written probably around the 1st century BCE or 1st-century CE. Some influential Mahāyāna sutras are the "Prajñaparamita sutras" such as the "Aṣṭasāhasrikā Prajñāpāramitā Sūtra," the "Lotus Sutra," the "Pure Land sutras," the "Vimalakirti Sutra," the "Golden Light Sutra," the "Avatamsaka Sutra," the "Sandhinirmocana Sutra" and the "Tathāgatagarbha sūtras."


title: Mahayana

text: According to David Drewes, Mahāyāna sutras contain several elements besides the promotion of the bodhisattva ideal, including "expanded cosmologies and mythical histories, ideas of purelands and great, 'celestial' Buddhas and bodhisattvas, descriptions of powerful new religious practices, new ideas on the nature of the Buddha, and a range of new philosophical perspectives." These texts present stories of revelation in which the Buddha teaches Mahāyāna sutras to certain bodhisattvas who vow to teach and spread these sutras after the Buddha's death. Regarding religious praxis, David Drewes outlines the most commonly promoted practices in Mahāyāna sutras were seen as means to achieve Buddhahood quickly and easily and included "hearing the names of certain Buddhas or bodhisattvas, maintaining Buddhist precepts, and listening to, memorizing, and copying sutras, that they claim can enable rebirth in the pure lands Abhirati and Sukhavati, where it is said to be possible to easily acquire the merit and knowledge necessary to become a Buddha in as little as one lifetime." Another widely recommended practice is "anumodana", or rejoicing in the good deeds of Buddhas and Bodhisattvas.


title: Mahayana

text: The practice of meditation and visualization of Buddhas has been seen by some scholars as a possible explanation for the source of certain Mahāyāna sutras which are seen traditionally as direct visionary revelations from the Buddhas in their pure lands. Paul Harrison has also noted the importance of dream revelations in certain Mahāyāna sutras such as the "Arya-svapna-nirdesa" which lists and interprets 108 dream signs.


title: Mahayana

text: As noted by Paul Williams, one feature of Mahāyāna sutras (especially earlier ones) is "the phenomenon of laudatory self-reference – the lengthy praise of the sutra itself, the immense merits to be obtained from treating even a verse of it with reverence, and the nasty penalties which will accrue in accordance with karma to those who denigrate the scripture." Some Mahāyāna sutras also warn against the accusation that they are not the word of the Buddha ("buddhavacana)," such as the "Astasāhasrikā (8,000 verse) Prajñāpāramitā," which states that such claims come from Mara (the evil tempter). Some of these Mahāyāna sutras also warn those who would denigrate Mahāyāna sutras or those who preach it (i.e. the "dharmabhanaka") that this action can lead to rebirth in hell.


title: Mahayana

text: Another feature of some Mahāyāna sutras, especially later ones, is increasing sectarianism and animosity towards non-Mahāyāna practitioners (sometimes called "sravakas", "hearers") which are sometimes depicted as being part of the 'hīnayāna' (the 'inferior way') who refuse to accept the 'superior way' of the Mahāyāna. As noted by Paul Williams, earlier Mahāyāna sutras like the "Ugraparipṛcchā Sūtra" and the "Ajitasena sutra" do not present any antagonism towards the hearers or the ideal of arhatship like later sutras do. Regarding the bodhisattva path, some Mahāyāna sutras promote it as a universal path for everyone, while others like the "Ugraparipṛcchā" see it as something for a small elite of hardcore ascetics.


title: Mahayana

text: In the 4th-century Mahāyāna Abhidharma work "Abhidharmasamuccaya", Asaṅga refers to the collection which contains the āgamas as the "Śrāvakapiṭaka" and associates it with the śrāvakas and pratyekabuddhas. Asaṅga classifies the Mahāyāna sūtras as belonging to the "Bodhisattvapiṭaka", which is designated as the collection of teachings for bodhisattvas.


title: Mahayana

text: Mahāyāna Buddhism also developed a massive commentarial and exegetical literature, many of which are called "śāstra" (treatises) or "vrittis" (commentaries). Philosophical texts were also written in verse form ("karikās"), such as in the case of the famous "Mūlamadhyamika-karikā" (Root Verses on the Middle Way) by Nagarjuna, the foundational text of Madhyamika philosophy. Numerous later Madhyamika philosophers like Candrakirti wrote commentaries on this work as well as their own verse works.


title: Mahayana

text: Mahāyāna Buddhist tradition also relies on numerous non-Mahayana commentaries (śāstra), a very influential one being the "Abhidharmakosha" of Vasubandhu, which is written from a non-Mahayana Sarvastivada–Sautrantika perspective.


title: Mahayana

text: Vasubandhu is also the author of various Mahāyāna Yogacara texts on the philosophical theory known as "vijñapti-matra" (conscious construction only). The Yogacara school philosopher Asanga is also credited with numerous highly influential commentaries. In East Asia, the "Satyasiddhi śāstra" was also influential.


title: Mahayana

text: Another influential tradition is that of Dignāga's Buddhist logic whose work focused on epistemology. He produced the "Pramānasamuccaya", and later Dharmakirti wrote the "Pramānavārttikā", which was a commentary and reworking of the Dignaga text.


title: Mahayana

text: Dating back at least to the "Saṃdhinirmocana Sūtra" is a classification of the corpus of Buddhism into three categories, based on ways of understanding the nature of reality, known as the "Three Turnings of the Dharma Wheel". According to this view, there were three such "turnings":


title: Mahayana

text: Some traditions of Tibetan Buddhism consider the teachings of Esoteric Buddhism and Vajrayāna to be the third turning of the Dharma Wheel. Tibetan teachers, particularly of the Gelugpa school, regard the second turning as the highest teaching, because of their particular interpretation of Yogācāra doctrine. The Buddha Nature teachings are normally included in the third turning of the wheel.


title: Mahayana

text: The different Chinese Buddhist traditions have different schemes of doctrinal periodization called "panjiao" which they use to organize the sometimes bewildering array of texts.


title: Mahayana

text: Scholars have noted that many key Mahāyāna ideas are closely connected to the earliest texts of Buddhism. The seminal work of Mahāyāna philosophy, Nāgārjuna's "Mūlamadhyamakakārikā", mentions the canon's "Katyāyana Sūtra" (SA 301) by name, and may be an extended commentary on that work. Nāgārjuna systematized the Mādhyamaka school of Mahāyāna philosophy. He may have arrived at his positions from a desire to achieve a consistent exegesis of the Buddha's doctrine as recorded in the canon. In his eyes, the Buddha was not merely a forerunner, but the very founder of the Mādhyamaka system. Nāgārjuna also referred to a passage in the canon regarding "nirvanic consciousness" in two different works.


title: Mahayana

text: Yogācāra, the other prominent Mahāyāna school in dialectic with the Mādhyamaka school, gave a special significance to the canon's "Lesser Discourse on Emptiness" (MA 190). A passage there (which the discourse itself emphasizes) is often quoted in later Yogācāra texts as a true definition of emptiness. According to Walpola Rahula, the thought presented in the Yogācāra school's "Abhidharma-samuccaya" is undeniably closer to that of the Pali Nikayas than is that of the Theravadin Abhidhamma.


title: Mahayana

text: Both the Mādhyamikas and the Yogācārins saw themselves as preserving the Buddhist Middle Way between the extremes of nihilism (everything as unreal) and substantialism (substantial entities existing). The Yogācārins criticized the Mādhyamikas for tending towards nihilism, while the Mādhyamikas criticized the Yogācārins for tending towards substantialism.


title: Mahayana

text: Key Mahāyāna texts introducing the concepts of bodhicitta and Buddha nature also use language parallel to passages in the canon containing the Buddha's description of "luminous mind" and appear to have evolved from this idea.


title: Mahayana

text: There are also some minor Mahāyāna traditions practiced by minority groups, such as Newar Buddhism practiced by the Newar people (Nepal) and Azhaliism practiced by the Bai people (Yunnan).


title: Mahayana

text: Furthermore, there are also various new religious movements which either see themselves as Mahāyāna or are strongly influenced by Mahāyāna Buddhism. Examples of these include Hòa Hảo, Won Buddhism, Triratna Buddhist Community and Sōka Gakkai.


title: Mahayana

text: Lastly, some religious traditions such as Bon and Shugendo are strongly influenced by Mahāyāna Buddhism, though they may not be considered as being "Buddhist" per se.


title: Mahayana

text: Most of the major forms of contemporary Mahāyāna Buddhism are also practiced by Asian immigrant populations in the West and also by western convert Buddhists. For more on this topic see: Buddhism in the West.


title: Mahayana

text: Contemporary Chinese Mahāyāna Buddhism (also known as Han Buddhism) is practiced through many varied forms, such as Chan, Pure land, Tiantai, Huayan and mantra practices. This group is the largest population of Buddhists in the world. There are between 228 and 239 million Mahāyāna Buddhists in the People's Republic of China (this does not include the Tibetan and Mongolian Buddhists who practice Tibetan Buddhism).


title: Mahayana

text: Harvey also gives the East Asian Mahāyāna Buddhist population in other nations as follows: Taiwanese Buddhists, 8 million; Malaysian Buddhists, 5.5 million; Singaporean Buddhists, 1.5 million; Hong Kong, 0.7 million; Indonesian Buddhists, 4 million, The Philippines: 2.3 million. Most of these are Han Chinese populations.


title: Mahayana

text: Chinese Buddhism can be divided into various different traditions ("zong"), such as Sanlun, Faxiang, Tiantai, Huayan, Pure Land, Chan, and Zhenyan. However, historically, most temples, institutions and Buddhist practitioners usually did not belong to any single "sect" (as is common in Japanese Buddhism), but draw from the various different elements of Chinese Buddhist thought and practice. This non-sectarian and eclectic aspect of Chinese Buddhism as a whole has persisted from its historical beginnings into its modern practice. The modern development of an ideaology called Humanistic Buddhism (Chinese: 人間佛教; pinyin: "rénjiān fójiào, more literally" "Buddhism for the Human World") has also been influential on Chinese Buddhist leaders and institutions. In addition, Chinese Buddhists may also practice some form of religious syncretism with other Chinese religions, such as Taoism. In modern China, the reform and opening up period in the late 20th century saw a particularly significant increase in the number of converts to Chinese Buddhism, a growth which has been called "extraordinary". Outside of mainland China, Chinese Buddhism is also practiced in Taiwan and wherever there are Chinese diaspora communities.


title: Mahayana

text: Korean Buddhism consists mostly of the Korean Seon school (i.e. Zen), primarily represented by the Jogye Order and the Taego Order. Korean Seon also includes some Pure Land practice. It is mainly practiced in South Korea, with a rough population of about 10.9 million Buddhists. There are also some minor schools, such as the Cheontae (i.e. Korean Tiantai), and the esoteric Jingak and Chinŏn schools.