title: Okta, Inc.

text: On March 9, 2021, hacking collective "Advanced Persistent Threat 69420" breached an Okta office network through a security failure in the company's Verkada camera setup. They were able to download security footage from the cameras. One member of the group, Tillie Kottmann, also revealed that the group had gained root shell access to the network. In a blog post the next day, Okta Chief Security Officer David Bradbury minimized the root shell as an "internal support tool" of the camera manufacturer Verkada. However, the shell would have given the hackers full access to run any commands on the network, and Cloudflare admitted that an identical hack by the group on that company's network had given them that level of access. Bradbury also said that the threat was contained to an isolated network.


title: Okta, Inc.

text: On March 22, 2022, the hacking group LAPSUS$ posted screenshots claiming to be from Okta internal systems. The next day, Okta concluded that a maximum of 366 of their customers data may potentially have been impacted, further stating that the breach originated with a computer used by one of Okta's third-party customer support engineers to which the hackers had access.


title: Molecular orbital

text: In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms "atomic orbital" and "molecular orbital" were introduced by Robert S. Mulliken in 1932 to mean "one-electron orbital wave functions". At an elementary level, they are used to describe the "region" of space in which a function has a significant amplitude.


title: Molecular orbital

text: In an isolated atom, the orbital electrons' location is determined by functions called atomic orbitals. When multiple atoms combine chemically into a molecule, the electrons' locations are determined by the molecule as a whole, so the atomic orbitals combine to form molecular orbitals. The electrons from the constituent atoms occupy the molecular orbitals. Mathematically, molecular orbitals are an approximate solution to the Schrödinger equation for the electrons in the field of the molecule's atomic nuclei. They are usually constructed by combining atomic orbitals or hybrid orbitals from each atom of the molecule, or other molecular orbitals from groups of atoms. They can be quantitatively calculated using the Hartree–Fock or self-consistent field (SCF) methods.


title: Molecular orbital

text: Molecular orbitals are of three types: "bonding orbitals" which have an energy lower than the energy of the atomic orbitals which formed them, and thus promote the chemical bonds which hold the molecule together; "antibonding orbitals" which have an energy higher than the energy of their constituent atomic orbitals, and so oppose the bonding of the molecule, and "non-bonding orbitals" which have the same energy as their constituent atomic orbitals and thus have no effect on the bonding of the molecule.


title: Molecular orbital

text: A molecular orbital (MO) can be used to represent the regions in a molecule where an electron occupying that orbital is likely to be found. Molecular orbitals are approximate solutions to the Schrödinger equation for the electrons in the electric field of the molecule's atomic nuclei. However calculating the orbitals directly from this equation is far too intractable a problem. Instead they are obtained from the combination of atomic orbitals, which predict the location of an electron in an atom. A molecular orbital can specify the electron configuration of a molecule: the spatial distribution and energy of one (or one pair of) electron(s). Most commonly a MO is represented as a linear combination of atomic orbitals (the LCAO-MO method), especially in qualitative or very approximate usage. They are invaluable in providing a simple model of bonding in molecules, understood through molecular orbital theory.


title: Molecular orbital

text: Most present-day methods in computational chemistry begin by calculating the MOs of the system. A molecular orbital describes the behavior of one electron in the electric field generated by the nuclei and some average distribution of the other electrons. In the case of two electrons occupying the same orbital, the Pauli principle demands that they have opposite spin. Necessarily this is an approximation, and highly accurate descriptions of the molecular electronic wave function do not have orbitals (see configuration interaction).


title: Molecular orbital

text: Molecular orbitals are, in general, delocalized throughout the entire molecule. Moreover, if the molecule has symmetry elements, its nondegenerate molecular orbitals are either symmetric or antisymmetric with respect to any of these symmetries. In other words, application of a symmetry operation S (e.g., a reflection, rotation, or inversion) to molecular orbital ψ results in the molecular orbital being unchanged or reversing its mathematical sign: Sψ = ±ψ. In planar molecules, for example, molecular orbitals are either symmetric (sigma) or antisymmetric (pi) with respect to reflection in the molecular plane. If molecules with degenerate orbital energies are also considered, a more general statement that molecular orbitals form bases for the irreducible representations of the molecule's symmetry group holds. The symmetry properties of molecular orbitals means that delocalization is an inherent feature of molecular orbital theory and makes it fundamentally different from (and complementary to) valence bond theory, in which bonds are viewed as localized electron pairs, with allowance for resonance to account for delocalization.


title: Molecular orbital

text: In contrast to these symmetry-adapted "canonical" molecular orbitals, localized molecular orbitals can be formed by applying certain mathematical transformations to the canonical orbitals. The advantage of this approach is that the orbitals will correspond more closely to the "bonds" of a molecule as depicted by a Lewis structure. As a disadvantage, the energy levels of these localized orbitals no longer have physical meaning. (The discussion in the rest of this article will focus on canonical molecular orbitals. For further discussions on localized molecular orbitals, see: natural bond orbital and sigma-pi and equivalent-orbital models.)


title: Molecular orbital

text: Molecular orbitals arise from allowed interactions between atomic orbitals, which are allowed if the symmetries (determined from group theory) of the atomic orbitals are compatible with each other. Efficiency of atomic orbital interactions is determined from the overlap (a measure of how well two orbitals constructively interact with one another) between two atomic orbitals, which is significant if the atomic orbitals are close in energy. Finally, the number of molecular orbitals formed must be equal to the number of atomic orbitals in the atoms being combined to form the molecule.


title: Molecular orbital

text: For an imprecise, but qualitatively useful, discussion of the molecular structure, the molecular orbitals can be obtained from the "Linear combination of atomic orbitals molecular orbital method" ansatz. Here, the molecular orbitals are expressed as linear combinations of atomic orbitals.


title: Molecular orbital

text: Molecular orbitals were first introduced by Friedrich Hund and Robert S. Mulliken in 1927 and 1928. The linear combination of atomic orbitals or "LCAO" approximation for molecular orbitals was introduced in 1929 by Sir John Lennard-Jones. His ground-breaking paper showed how to derive the electronic structure of the fluorine and oxygen molecules from quantum principles. This qualitative approach to molecular orbital theory is part of the start of modern quantum chemistry.


title: Molecular orbital

text: Linear combinations of atomic orbitals (LCAO) can be used to estimate the molecular orbitals that are formed upon bonding between the molecule's constituent atoms. Similar to an atomic orbital, a Schrödinger equation, which describes the behavior of an electron, can be constructed for a molecular orbital as well. Linear combinations of atomic orbitals, or the sums and differences of the atomic wavefunctions, provide approximate solutions to the Hartree–Fock equations which correspond to the independent-particle approximation of the molecular Schrödinger equation. For simple diatomic molecules, the wavefunctions obtained are represented mathematically by the equations


title: Molecular orbital

text: where formula_3 and formula_4 are the molecular wavefunctions for the bonding and antibonding molecular orbitals, respectively, formula_5 and formula_6 are the atomic wavefunctions from atoms a and b, respectively, and formula_7 and formula_8 are adjustable coefficients. These coefficients can be positive or negative, depending on the energies and symmetries of the individual atomic orbitals. As the two atoms become closer together, their atomic orbitals overlap to produce areas of high electron density, and, as a consequence, molecular orbitals are formed between the two atoms. The atoms are held together by the electrostatic attraction between the positively charged nuclei and the negatively charged electrons occupying bonding molecular orbitals.


title: Molecular orbital

text: When atomic orbitals interact, the resulting molecular orbital can be of three types: bonding, antibonding, or nonbonding.


title: Molecular orbital

text: The type of interaction between atomic orbitals can be further categorized by the molecular-orbital symmetry labels σ (sigma), π (pi), δ (delta), φ (phi), γ (gamma) etc. These are the Greek letters corresponding to the atomic orbitals s, p, d, f and g respectively. The number of nodal planes containing the internuclear axis between the atoms concerned is zero for σ MOs, one for π, two for δ, three for φ and four for γ.


title: Molecular orbital

text: A MO with σ symmetry results from the interaction of either two atomic s-orbitals or two atomic p-orbitals. An MO will have σ-symmetry if the orbital is symmetric with respect to the axis joining the two nuclear centers, the internuclear axis. This means that rotation of the MO about the internuclear axis does not result in a phase change. A σ* orbital, sigma antibonding orbital, also maintains the same phase when rotated about the internuclear axis. The σ* orbital has a nodal plane that is between the nuclei and perpendicular to the internuclear axis.


title: Molecular orbital

text: A MO with π symmetry results from the interaction of either two atomic p orbitals or p orbitals. An MO will have π symmetry if the orbital is asymmetric with respect to rotation about the internuclear axis. This means that rotation of the MO about the internuclear axis will result in a phase change. There is one nodal plane containing the internuclear axis, if real orbitals are considered.


title: Molecular orbital

text: A π* orbital, pi antibonding orbital, will also produce a phase change when rotated about the internuclear axis. The π* orbital also has a second nodal plane between the nuclei.


title: Molecular orbital

text: A MO with δ symmetry results from the interaction of two atomic d or d orbitals. Because these molecular orbitals involve low-energy d atomic orbitals, they are seen in transition-metal complexes. A δ bonding orbital has two nodal planes containing the internuclear axis, and a δ* antibonding orbital also has a third nodal plane between the nuclei.


title: Molecular orbital

text: Theoretical chemists have conjectured that higher-order bonds, such as phi bonds corresponding to overlap of f atomic orbitals, are possible. There is no known example of a molecule purported to contain a phi bond.


title: Molecular orbital

text: For molecules that possess a center of inversion (centrosymmetric molecules) there are additional labels of symmetry that can be applied to molecular orbitals.


title: Molecular orbital

text: If inversion through the center of symmetry in a molecule results in the same phases for the molecular orbital, then the MO is said to have gerade (g) symmetry, from the German word for even.


title: Molecular orbital

text: If inversion through the center of symmetry in a molecule results in a phase change for the molecular orbital, then the MO is said to have ungerade (u) symmetry, from the German word for odd.


title: Molecular orbital

text: For a bonding MO with σ-symmetry, the orbital is σ (s' + s<nowiki>"</nowiki> is symmetric), while an antibonding MO with σ-symmetry the orbital is σ, because inversion of s' – s<nowiki>"</nowiki> is antisymmetric.


title: Molecular orbital

text: For a bonding MO with π-symmetry the orbital is π because inversion through the center of symmetry for would produce a sign change (the two p atomic orbitals are in phase with each other but the two lobes have opposite signs), while an antibonding MO with π-symmetry is π because inversion through the center of symmetry for would not produce a sign change (the two p orbitals are antisymmetric by phase).


title: Molecular orbital

text: The qualitative approach of MO analysis uses a molecular orbital diagram to visualize bonding interactions in a molecule. In this type of diagram, the molecular orbitals are represented by horizontal lines; the higher a line the higher the energy of the orbital, and degenerate orbitals are placed on the same level with a space between them. Then, the electrons to be placed in the molecular orbitals are slotted in one by one, keeping in mind the Pauli exclusion principle and Hund's rule of maximum multiplicity (only 2 electrons, having opposite spins, per orbital; place as many unpaired electrons on one energy level as possible before starting to pair them). For more complicated molecules, the wave mechanics approach loses utility in a qualitative understanding of bonding (although is still necessary for a quantitative approach).


title: Molecular orbital

text: The general procedure for constructing a molecular orbital diagram for a reasonably simple molecule can be summarized as follows:


title: Molecular orbital

text: 3. Arrange the SALCs of each molecular fragment in increasing order of energy, first noting whether they stem from "s", "p", or "d" orbitals


title: Molecular orbital

text: 4. Combine SALCs of the same symmetry type from the two fragments, and from N SALCs form N molecular orbitals.


title: Molecular orbital

text: 5. Estimate the relative energies of the molecular orbitals from considerations of overlap and relative energies of the parent orbitals, and draw the levels on a molecular orbital energy level diagram (showing the origin of the orbitals).


title: Molecular orbital

text: 6. Confirm, correct, and revise this qualitative order by carrying out a molecular orbital calculation by using commercial software.


title: Molecular orbital

text: Molecular orbitals are said to be degenerate if they have the same energy. For example, in the homonuclear diatomic molecules of the first ten elements, the molecular orbitals derived from the p and the p atomic orbitals result in two degenerate bonding orbitals (of low energy) and two degenerate antibonding orbitals (of high energy).


title: Molecular orbital

text: When the energy difference between the atomic orbitals of two atoms is quite large, one atom's orbitals contribute almost entirely to the bonding orbitals, and the other atom's orbitals contribute almost entirely to the antibonding orbitals. Thus, the situation is effectively that one or more electrons have been transferred from one atom to the other. This is called an (mostly) ionic bond.


title: Molecular orbital

text: The bond order, or number of bonds, of a molecule can be determined by combining the number of electrons in bonding and antibonding molecular orbitals. A pair of electrons in a bonding orbital creates a bond, whereas a pair of electrons in an antibonding orbital negates a bond. For example, N, with eight electrons in bonding orbitals and two electrons in antibonding orbitals, has a bond order of three, which constitutes a triple bond.


title: Molecular orbital

text: Bond strength is proportional to bond order—a greater amount of bonding produces a more stable bond—and bond length is inversely proportional to it—a stronger bond is shorter.


title: Molecular orbital

text: There are rare exceptions to the requirement of molecule having a positive bond order. Although Be has a bond order of 0 according to MO analysis, there is experimental evidence of a highly unstable Be molecule having a bond length of 245 pm and bond energy of 10 kJ/mol.


title: Molecular orbital

text: The highest occupied molecular orbital and lowest unoccupied molecular orbital are often referred to as the HOMO and LUMO, respectively. The difference of the energies of the HOMO and LUMO is called the HOMO-LUMO gap. This notion is often the matter of confusion in literature and should be considered with caution. Its value is usually located between the fundamental gap (difference between ionization potential and electron affinity) and the optical gap. In addition, HOMO-LUMO gap can be related to a bulk material band gap or transport gap, which is usually much smaller than fundamental gap.


title: Molecular orbital

text: Homonuclear diatomic MOs contain equal contributions from each atomic orbital in the basis set. This is shown in the homonuclear diatomic MO diagrams for H, He, and Li, all of which containing symmetric orbitals.


title: Molecular orbital

text: As a simple MO example, consider the electrons in a hydrogen molecule, H (see molecular orbital diagram), with the two atoms labelled H' and H". The lowest-energy atomic orbitals, 1s' and 1s", do not transform according to the symmetries of the molecule. However, the following symmetry adapted atomic orbitals do:


title: Molecular orbital

text: The symmetric combination (called a bonding orbital) is lower in energy than the basis orbitals, and the antisymmetric combination (called an antibonding orbital) is higher. Because the H molecule has two electrons, they can both go in the bonding orbital, making the system lower in energy (hence more stable) than two free hydrogen atoms. This is called a covalent bond. The bond order is equal to the number of bonding electrons minus the number of antibonding electrons, divided by 2. In this example, there are 2 electrons in the bonding orbital and none in the antibonding orbital; the bond order is 1, and there is a single bond between the two hydrogen atoms.


title: Molecular orbital

text: On the other hand, consider the hypothetical molecule of He with the atoms labeled He' and He". As with H, the lowest energy atomic orbitals are the 1s' and 1s", and do not transform according to the symmetries of the molecule, while the symmetry adapted atomic orbitals do. The symmetric combination—the bonding orbital—is lower in energy than the basis orbitals, and the antisymmetric combination—the antibonding orbital—is higher. Unlike H, with two valence electrons, He has four in its neutral ground state. Two electrons fill the lower-energy bonding orbital, σ(1s), while the remaining two fill the higher-energy antibonding orbital, σ*(1s). Thus, the resulting electron density around the molecule does not support the formation of a bond between the two atoms; without a stable bond holding the atoms together, the molecule would not be expected to exist. Another way of looking at it is that there are two bonding electrons and two antibonding electrons; therefore, the bond order is 0 and no bond exists (the molecule has one bound state supported by the Van der Waals potential).


title: Molecular orbital

text: Dilithium Li is formed from the overlap of the 1s and 2s atomic orbitals (the basis set) of two Li atoms. Each Li atom contributes three electrons for bonding interactions, and the six electrons fill the three MOs of lowest energy, σ(1s), σ*(1s), and σ(2s). Using the equation for bond order, it is found that dilithium has a bond order of one, a single bond.


title: Molecular orbital

text: Considering a hypothetical molecule of He, since the basis set of atomic orbitals is the same as in the case of H, we find that both the bonding and antibonding orbitals are filled, so there is no energy advantage to the pair. HeH would have a slight energy advantage, but not as much as H + 2 He, so the molecule is very unstable and exists only briefly before decomposing into hydrogen and helium. In general, we find that atoms such as He that have full energy shells rarely bond with other atoms. Except for short-lived Van der Waals complexes, there are very few noble gas compounds known.


title: Molecular orbital

text: While MOs for homonuclear diatomic molecules contain equal contributions from each interacting atomic orbital, MOs for heteronuclear diatomics contain different atomic orbital contributions. Orbital interactions to produce bonding or antibonding orbitals in heteronuclear diatomics occur if there is sufficient overlap between atomic orbitals as determined by their symmetries and similarity in orbital energies.


title: Molecular orbital

text: In hydrogen fluoride HF overlap between the H 1s and F 2s orbitals is allowed by symmetry but the difference in energy between the two atomic orbitals prevents them from interacting to create a molecular orbital. Overlap between the H 1s and F 2p orbitals is also symmetry allowed, and these two atomic orbitals have a small energy separation. Thus, they interact, leading to creation of σ and σ* MOs and a molecule with a bond order of 1. Since HF is a non-centrosymmetric molecule, the symmetry labels g and u do not apply to its molecular orbitals.


title: Molecular orbital

text: To obtain quantitative values for the molecular energy levels, one needs to have molecular orbitals that are such that the configuration interaction (CI) expansion converges fast towards the full CI limit. The most common method to obtain such functions is the Hartree–Fock method, which expresses the molecular orbitals as eigenfunctions of the Fock operator. One usually solves this problem by expanding the molecular orbitals as linear combinations of Gaussian functions centered on the atomic nuclei (see linear combination of atomic orbitals and basis set (chemistry)). The equation for the coefficients of these linear combinations is a generalized eigenvalue equation known as the Roothaan equations, which are in fact a particular representation of the Hartree–Fock equation. There are a number of programs in which quantum chemical calculations of MOs can be performed, including Spartan.


title: Molecular orbital

text: Simple accounts often suggest that experimental molecular orbital energies can be obtained by the methods of ultra-violet photoelectron spectroscopy for valence orbitals and X-ray photoelectron spectroscopy for core orbitals. This, however, is incorrect as these experiments measure the ionization energy, the difference in energy between the molecule and one of the ions resulting from the removal of one electron. Ionization energies are linked approximately to orbital energies by Koopmans' theorem. While the agreement between these two values can be close for some molecules, it can be very poor in other cases.


title: Carnival game

text: A carnival game is a game of chance or skill that can be seen at a traveling carnival, charity fund raiser, amusement arcade and amusement park, or on a state and county fair midway. They are also commonly played on holidays such as Mardi Gras, Saint Patrick's Day, and Oktoberfest.


title: Carnival game

text: Carnival games are usually operated on a "pay per play" basis. Prices may range from a small amount, for example 25 cents, to a few dollars per play. Most games offer a small prize to the winner. Prizes may include items like stuffed animals, toys, or posters. Continued play is encouraged as multiple small prizes may be traded in for a larger prize. Multiplayer games—the "Watergun" game is one example—may change the size of the prize with the number of players. In a more difficult game, including the "Baseball and Basket" or "Stand the Bottle", a large prize may be awarded to any winner.


title: Carnival game

text: Carnival games have a poor reputation in some areas. This may be that some carnival games utilize optical illusions or physical relationships that make it hard for a player to judge the game's difficulty. Also, some operators have run games that are rigged to take advantage of unsuspecting players. In many areas, these games are tested by local law enforcement to find unfairly run games.


title: Carnival game

text: At amusement parks, the carnival games are usually owned and operated by the park owner. The games are usually installed in permanent buildings stationed around the park. A traveling carnival may, however, be made up of multiple independent game concession owners. These independents owners contract their games with the carnival operator. Carnival games of this type are mounted to towable trailers that enable the game to be moved from site to site. However, there are still some free-standing game booths that are assembled on site. These carnival games are usually set up in rows along the midway area along with the rides.


title: Carnival game

text: Games of chance are favorite carnival games. A random outcome gives all players the chance of winning a prize. An example of a carnival game of chance is the "Dime Pitch" game. The objective is to toss a coin (typically a dime or quarter) onto a horizontal board that has random marks on it. The marks on the board are the same diameter as the coin thrown. By completely covering the mark on the board with the coin, the player wins. Another example of a game of chance is the "Birthday" game. Players place their bets on a rail mounted strip that has months, colors and holidays written on it. Many players choose the month of their birth for their bet. A random player is then selected to throw a large multisided die into a designated center area (play area) of the booth. The die thrown has corresponding months, colors and holidays written on the different sides. The month, color or holiday that shows on the top of the thrown die, when it stops, will indicate the winner.


title: Carnival game

text: In "Pingpong Ball and Fish Bowl" players throw pingpong balls at a table filled with rows of empty small fish bowls. If the player gets a ball in the bowl, they usually win a goldfish. A game like "Duck Pond," which is geared for young children, may offer a winner every time. The player selects a rubber duck that is floating at random in water. Writing on the bottom of the duck reveals the prize won.


title: Carnival game

text: Games of skill are another favorite carnival game. These games may test a players aim at hitting a target with either a ball or a weapon. Some games of this type are the "Cross Bow Shoot", the "Milk Bottle" game, or the "Balloon and Dart" game.


title: Carnival game

text: Other skill testing games challenge the physical abilities of the player. One example of this type of game is the "Rope Ladder Climb". In this game, the player must keep their balance while climbing an angled rope ladder that can pivot and invert the player. The object of the game is to climb the ladder, without falling off, and ring a bell at the end of the climb. Another game that tests the physical abilities of the player is "Ring the Bell". The player uses a large mallet to strike a pivot board on the game, this causes an indicator to be driven vertically up an indicator scale board. By hitting the pivot hard enough, the indicator will ring a bell mounted at the top of the indicator scale board indicating a win. Cover the spot is a game that involves covering a giant red spot with five smaller discs dropped by hand; all red (or color) must be covered to win.


title: Carnival game

text: Carnival games are often viewed or portrayed as dishonest, due to past history that may not necessarily apply to modern-day games and operators. The term "mark" (meaning sucker) originated with the carnival.


title: Carnival game

text: When dishonest carnival game operators found someone who they could entice to keep playing their rigged (slang term: "gaffed") game, they would then "mark" the individual by patting their back with a hand that had chalk on it. Other game operators would then look for these chalk marks and entice the individuals to also play their rigged game.


title: Carnival game

text: Rigging a carnival game may be done in many different manners depending on the game. For example, the "Ball and Basket" game may be rigged by moving the "A" frame onto which the basket is mounted. This would change the trajectory of the ball. Another method has the operator leaving a ball in the basket for the demonstration which absorbs the energy of the tossed ball, enabling the ball to stay in the basket, and then remove it when the mark plays, which makes the ball much more susceptible to bouncing out. In a game like "Ring Toss", the blocks that the prizes are attached to are cut in such a way as to ensure the ring will not fit. The "Balloon and Dart" game can be rigged by underinflating the balloons or by using dull point darts. Some games may be rigged to play honestly or dishonestly and can be switched by the game operator. The "Milk Bottle" game can be rigged this way. On a rigged game, one of the milk bottles is heavier than the others. Depending on how the bottles are stacked will determine if the player will win.


title: Carnival game

text: Some games are simply impossible to win. One such game is the "Push 'em Up" (or "Stand the Bottle") game, which requires the player to stand up a bottle with a 2-tine plastic fork, was featured in episode 5 of Penn & Teller Tell a Lie. The bottles used in the game are weighted on one side, which makes it impossible to stand the bottles upright without tipping them over when the heavier side is rotated to the top. The "Bottle Up," often confused with this game, is simply a skill game where the player uses a fishing pole with a ring attached to the end of the string to stand up the bottle.


title: Carnival game

text: In many areas, local law enforcement will test the carnival games prior to and during the carnival to help eliminate rigged games. However, there are still some dishonest game operators. One method they use to avoid law enforcement is to give legitimate instruments or make the carnival game "fair-and-square" during testing, but rig it for other people.


title: Carnival game

text: In the United States, there was a longtime tradition of carnival games the point of which was to hurt, dehumanize or denigrate Black people. Such games included "African dodger" or "bean-em", where a Black person would stick their head through a curtain to be pelted with beanbags, eggs or baseballs, or "dunk tanks" that would drop a Black person into a tank of water if fairgoers hit a target with a ball. In her 2020 book , Isabel Wilkerson describes these games as part of "a culture of cruelty [that] made violence and mockery seem mundane and amusing", teaching and reinforcing the U.S. racial caste system through entertainment.


title: Île de Ré

text: Île de Ré (; variously spelled Rhé or Rhéa; Poitevin: "ile de Rét"; , ) is an island off the Atlantic coast of France near La Rochelle, Charente-Maritime, on the northern side of the Pertuis d'Antioche strait.


title: Île de Ré

text: Its highest point has an elevation of . It is long and wide. The Île de Ré bridge, completed in 1988, connects it to La Rochelle on the mainland.


title: Île de Ré

text: Administratively, the island is part of the Charente-Maritime department, Nouvelle-Aquitaine (before 2015: Poitou-Charentes). The island is also a part of the Charente-Maritime's 1st constituency.


title: Île de Ré

text: Located in the arrondissement of La Rochelle, Île de Ré includes two cantons: Saint-Martin-de-Ré eastwards and Ars-en-Ré westwards. The island is divided into 10 communes, from East to West: Rivedoux-Plage, La Flotte, Sainte-Marie-de-Ré, Saint-Martin-de-Ré, Le Bois-Plage-en-Ré, La Couarde-sur-Mer, Loix, Ars-en-Ré, Saint-Clément-des-Baleines, Les Portes-en-Ré.


title: Île de Ré

text: During Roman times, Île de Ré was an archipelago consisting of three small islands. The space between the islands was progressively filled by a combination of human activity (salt fields gained from the sea) and silting.


title: Île de Ré

text: In the seventh and eighth centuries the island, along with Oléron, formed the "Vacetae Insulae" or Vacetian Islands, according to the "Cosmographia". Since "Vaceti" is another name for the Vascones, this reference is evidence of Basque (Gascon) settlement or control of the islands by that date. In 745, Hunald, the Duke of Aquitaine, retired to a monastery on the island. In the mid-twelfth century, a Cistercian monastery was founded on the isle, where the Abbot Isaac of Stella sojourned amid the Becket controversy.


title: Île de Ré

text: The island became English in 1154, when Eleanor of Aquitaine became queen of England through her marriage with Henry Plantagenet. The island reverted to France in 1243, when Henry III of England returned it to Louis IX through a treaty. In 1360, however, with the Treaty of Brétigny, Île de Ré briefly became English again, until the 1370s.


title: Île de Ré

text: The first fishing locks were constructed between the 13th and 15th centuries. The locks consist of fixed fish traps which become submerged at high tide and retain the fish when the tide goes out.


title: Île de Ré

text: In February 1625, the Protestant Duke of Soubise led a Huguenot revolt against the French king Louis XIII, and after publishing a manifesto, invaded and occupied the island of Ré. He seized Ré with 300 soldiers and 100 sailors. From there he sailed up to Brittany, where he led his successful attack on the royal fleet in Blavet, although he could not take the fort after a three-week siege. Soubise then returned to Ré with 15 ships and soon occupied the Ile d'Oléron as well, thus giving him command of the Atlantic coast from Nantes to Bordeaux. Through these actions, he was recognized as the head of the reform, and named himself "Admiral of the Protestant Church". A few months later, in September 1625, Charles, Duke of Guise, organized a landing in order to recapture the islands, with the support of the Dutch (20 ships) and English navies. The fleet of La Rochelle was defeated, as was Soubise with 3,000 men, when he led a counter-attack against the royal troops who had landed on the island. The island was invested forcing Soubise to flee to England.


title: Île de Ré

text: In 1627, an English invasion force under the command of George Villiers, Duke of Buckingham, attacked the island in order to relieve the Siege of La Rochelle. After three months of combat in the Siege of Saint-Martin-de-Ré against the French under Marshal Toiras, the Duke was forced to withdraw. The English lost more than 4,000 out of 7,000 troops during the campaign.


title: Île de Ré

text: The main port, Saint-Martin, was fortified by Vauban in 1681 as a component of the belt of forts and citadels built to protect the military harbour of Rochefort. It was later used as a depot for convicts on their way to the penal settlements of New Caledonia and French Guiana. Prisoners included Alfred Dreyfus, en route to the penal colony of Devil's Island after his conviction for treason.


title: Île de Ré

text: The old city of Saint-Martin, within the walls of the citadel, was added in 2008 to the World Heritage Site list, along with 11 others Fortifications of Vauban across France.


title: Île de Ré

text: During World War II, the beaches of the Île de Ré were fortified by German forces with bunkers, in order to block a possible seaward invasion. Many of the bunkers are still visible, in a more or less derelict state. Several scenes of the 1962 movie "The Longest Day" were filmed on the beaches of the island.


title: Île de Ré

text: In 1987, a bridge was built to connect the island to the mainland. Previously, the island was connected through roll-on roll-off ferries (called ""bacs""), which could accommodate vehicles and passengers. In peak summer time periods, the waiting time to board a ferry could reach several hours. The bridge was built by Bouygues. Since then, tourism on the island has developed considerably, with real estate prices reaching high levels. The easier transportation system has stimulated the purchase of holiday homes by people from as far as Paris, who can visit for week-ends, mostly in spring and summer. Using the bridge requires the payment of a toll (either €8 or €16 return for a normal car depending on the season) and makes it the most expensive road to use per kilometre in France. The Paris-La Rochelle high-speed train (TGV) trip takes around three hours, and then taxis or buses can be taken to the island. Île de Ré can also be reached from Paris by plane. It takes 85 minutes to fly from Paris to La Rochelle airport.


title: Île de Ré

text: The area is a popular tourist destination. It has approximately the same number of hours of sunshine as the southern coast of France. The island has a constant light breeze, and the water temperature is generally cool. The island is surrounded with sandy beaches.


title: Île de Ré

text: The island has a year-round resident population of approximately 17,650 residents and a summer resident population of about 220,000. The island has a network of cycle tracks, with many residents rarely using cars for transportation.


title: Île de Ré

text: American celebrities, including Johnny Depp, Katy Perry, and British actor Orlando Bloom, have vacationed there.


title: Île de Ré

text: Visiting French celebrities include Charles Aznavour, Claude Nougaro, Bernard Giraudeau, Claude Rich, Carole Bouquet, Philippe Sollers, and Caroline of Monaco. French politicians, including Jean Monnet and ex-Prime Minister Lionel Jospin, have lived on the island.


title: Île de Ré

text: Oysters and fresh fish are caught year-round. A tradition sees fishermen sell a small quantity of their catch directly on the quays after a harvest, enabling them to buy a drink. Markets are open in the main towns.


title: Île de Ré

text: The island is known for donkeys wearing (trousers), originally a bite prevention method but now a tourist attraction.


title: Île de Ré

text: Nearby Fort Boyard, a Napoleonic maritime fort, is currently used for a television game show series of the same name.


title: Susan Cooper

text: Susan Mary Cooper (born 23 May 1935) is an English author of children's books. She is best known for "The Dark Is Rising", a contemporary fantasy series set in England and Wales, which incorporates British mythology such as the Arthurian legends and Welsh folk heroes. For that work, in 2012 she won the lifetime Margaret A. Edwards Award from the American Library Association, recognizing her contribution to writing for teens. In the 1970s two of the five novels were named the year's best English-language book with an "authentic Welsh background" by the Welsh Books Council.


title: Susan Cooper

text: Cooper was born in 1935 in Burnham, Buckinghamshire, to Ethel May ("née" Field) and her husband John Richard Cooper. Her father had worked in the reading room of the Natural History Museum until going off to fight in the Second World War, from which he returned with a wounded leg. He then pursued a career in the offices of the Great Western Railway. Her mother was a teacher of ten-year-olds and eventually became deputy head of a large school. Her younger brother Roderick also grew up to become a writer.


title: Susan Cooper

text: Cooper lived in Buckinghamshire until she was 21, when her parents moved to her grandmother's village of Aberdyfi in Wales. She attended Slough High School and then earned a degree in English at Somerville College at the University of Oxford, where she was the first woman to edit the undergraduate newspaper "Cherwell" with her co-editor Patrick Nobes.


title: Susan Cooper

text: After graduating, she worked as a reporter for "The Sunday Times" (London) under Ian Fleming and wrote in her spare time. During that period she began work on the series "The Dark Is Rising" and finished her debut novel, the science fiction "Mandrake", published by Hodder & Stoughton in 1964.


title: Susan Cooper

text: Cooper emigrated to the United States in 1963 to marry Nicholas J. Grant, a Professor of Metallurgy at the Massachusetts Institute of Technology, and a widower with three teenage children. She had two children with him, Jonathan Roderick Howard Grant (b. 1965) and Katharine Mary Grant (b. 1966; later Katharine Glennon). She then became a full-time writer, focusing on "The Dark Is Rising" and on "Dawn of Fear" (1970), a novel based on her experiences of the Second World War. Eventually she wrote fiction for both children and adults, a series of picture books, film screenplays, and works for the stage.


title: Susan Cooper

text: Around the time of writing "Seaward" (1983), both of her parents died, and her marriage to Grant was dissolved.


title: Susan Cooper

text: In July 1996, she married the Canadian-American actor and her sometime co-author Hume Cronyn, the widower of Jessica Tandy. (Cronyn and Tandy had starred in the Broadway production of "Foxfire", written by Cooper and Cronyn and staged in 1982.)


title: Susan Cooper

text: After Cronyn's death in 2003, she moved back to Massachusetts, building a house facing the North River in Marshfield, and also living in Cambridge. The history of the Marshfield area was the basis for her 2013 book "Ghost Hawk", in which the spirit of a Wampanoag, whose people were decimated by European disease, witnesses the transformation of Massachusetts by the Plymouth Colony.


title: Susan Cooper

text: From 2006 to 2012, Cooper was on the Board of the National Children's Book and Literacy Alliance (NCBLA), a US nonprofit organization that advocates for literacy, literature, and libraries.


title: Susan Cooper

text: In April 2017, Cooper gave the fifth annual Tolkien Lecture at Pembroke College, Oxford, speaking on the role of fantasy literature in contemporary society.


title: Susan Cooper

text: In 2019 she published "The Shortest Day", based on her performance poem of the same title written for the Cambridge Christmas "Revels" in the 1970s.


title: Susan Cooper

text: For her lifetime contribution as a children's writer, Cooper was U.S. nominee in 2002 for the biennial, international Hans Christian Andersen Award, the highest international recognition available to creators of children's books.


title: Susan Cooper

text: The American Library Association's Margaret A. Edwards Award recognises one writer and a particular body of work for "significant and lasting contribution to young adult literature". Cooper won the award in 2012 citing the five Dark Is Rising novels, published 1965 to 1977. The citation observed, "In one of the most influential epic high fantasies in literature, Cooper evokes Celtic and Arthurian mythology and masterly world-building in a high-stakes battle between good and evil, embodied in the coming of age journey of Will Stanton."


title: Susan Cooper

text: Cooper wrote four screenplays produced for television, one supernatural tale for children and three more adaptations of books about Appalachia (as "Foxfire").


title: Madhyamaka

text: Mādhyamaka ("middle way" or "centrism"; ; Tibetan: དབུ་མ་པ ; "dbu ma pa"), otherwise known as Śūnyavāda ("the emptiness doctrine") and Niḥsvabhāvavāda ("the no "svabhāva" doctrine"), refers to a tradition of Buddhist philosophy and practice founded by the Indian Buddhist monk and philosopher Nāgārjuna (c. 150 – c. 250 CE). The foundational text of the Mādhyamaka tradition is Nāgārjuna's "Mūlamadhyamakakārikā" ("Root Verses on the Middle Way"). More broadly, Mādhyamaka also refers to the ultimate nature of phenomena as well as the non-conceptual realization of ultimate reality that is experienced in meditation.


title: Madhyamaka

text: Mādhyamaka thought had a major influence on the subsequent development of the Mahāyāna Buddhist tradition. It is the dominant interpretation of Buddhist philosophy in Tibetan Buddhism and has also been influential in East Asian Buddhist thought.


title: Madhyamaka

text: According to the classical Indian Mādhyamika thinkers, all phenomena ("dharmas") are empty ("śūnya") of "nature," of any "substance" or "essence" ("svabhāva") which could give them "solid and independent existence," because they are dependently co-arisen. But this "emptiness" itself is also "empty": it does not have an existence on its own, nor does it refer to a transcendental reality beyond or above phenomenal reality.


title: Madhyamaka

text: "Madhya" is a Sanskrit word meaning "middle". It is cognate with Latin "med-iu-s" and English "mid". The "-ma" suffix is a superlative, giving "madhyama" the meaning of "mid-most" or "medium". The "-ka" suffix is used to form adjectives, thus "madhyamaka" means "middling". The "-ika" suffix is used to form possessives, with a collective sense, thus "mādhyamika" mean "belonging to the mid-most" (the "-ika" suffix regularly causes a lengthening of the first vowel and elision of the final "-a").


title: Madhyamaka

text: In a Buddhist context, these terms refer to the "middle path" ("madhyama pratipada"), which refers to right view ("samyagdṛṣṭi") which steers clear of the metaphysical extremes of annihilationism ("ucchedavāda") and eternalism ("śassatavāda"). For example, the Sanskrit "Kātyāyanaḥsūtra" states that though the world "relies on a duality of existence and non-existence", the Buddha teaches a correct view which understands that:Arising in the world, Kātyayana, seen and correctly understood just as it is, shows there is no non-existence in the world. Cessation in the world, Kātyayana, seen and correctly understood just as it is, shows there is no permanent existence in the world. Thus avoiding both extremes the Tathāgata teaches a dharma by the middle path ("madhyamayā pratipadā"). That is: this being, that becomes; with the arising of this, that arises. With ignorance as condition there is volition ... [to be expanded with the standard formula of the 12 links of dependent origination]”Though all Buddhist schools saw themselves as defending a middle path in accord with the Buddhist teachings, the name "madhyamaka" refers to a school of Mahayana philosophy associated with Nāgārjuna and his commentators. The term "mādhyamika" refers to adherents of the madhyamaka school.


title: Madhyamaka

text: Central to madhyamaka philosophy is "śūnyatā", "emptiness", and this refers to the central idea that dharmas are empty of "svabhāva". This term has been translated variously as essence, intrinsic nature, inherent existence, own being and substance. Furthermore, according to Richard P. Hayes, svabhava can be interpreted as either "identity" or as "causal independence". Likewise, Westerhoff notes that "svabhāva" is a complex concept that has ontological and cognitive aspects. The ontological aspects include "svabhāva" as essence, as a property which makes an object what it is, as well as "svabhāva" as substance, meaning, as the madhyamaka thinker Candrakirti defines it, something that does "not depend on anything else".


title: Madhyamaka

text: It is substance-"svabhāva", the objective and independent existence of any object or concept, which madhyamaka arguments mostly focus on refuting. A common structure which madhyamaka uses to negate "svabhāva" is the "catuṣkoṭi" ("four corners" or tetralemma), which roughly consists of four alternatives: a proposition is true; a proposition is false; a proposition is both true and false; a proposition is neither true nor false. Some of the major topics discussed by classical madhyamaka include causality, change, and personal identity.


title: Madhyamaka

text: Madhyamaka's denial of "svabhāva" does not mean a nihilistic denial of all things, for in a conventional everyday sense, madhyamaka does accept that one can speak of "things", and yet "ultimately" these things are empty of inherent existence. Furthermore, "emptiness" itself is also "empty": it does not have an existence on its own, nor does it refer to a transcendental reality beyond or above phenomenal reality.


title: Madhyamaka

text: "Svabhāva"'s cognitive aspect is merely a superimposition ("samāropa") that beings make when they perceive and conceive of things. In this sense then, emptiness does not exist as some kind of primordial reality, but it is simply a corrective to a mistaken conception of how things exist. This idea of "svabhāva" that madhyamaka denies is then not just a conceptual philosophical theory, but it is a cognitive distortion that beings automatically impose on the world, such as when we regard the five aggregates as constituting a single self. Candrakirti compares it to someone who suffers from vitreous floaters that cause the illusion of hairs appearing in their visual field. This cognitive dimension of "svabhāva" means that just understanding and assenting to madhyamaka reasoning is not enough to end the suffering caused by our reification of the world, just like understanding how an optical illusion works does not make it stop functioning. What is required is a kind of cognitive shift (termed "realization") in the way the world appears and therefore some kind of practice to lead to this shift. As Candrakirti says:


title: Madhyamaka

text: For one on the road of cyclic existence who pursues an inverted view due to ignorance, a mistaken object such as the superimposition ("samāropa") on the aggregates appears as real, but it does not appear to one who is close to the view of the real nature of things.


title: Madhyamaka

text: Much of madhyamaka philosophy centers on showing how various essentialist ideas have absurd conclusions through "reductio ad absurdum" arguments (known as "prasanga" in Sanskrit). Chapter 15 of Nāgārjuna's "Mūlamadhyamakakārikā" centers on the words svabhava parabhava bhava and abhava. According to Peter Harvey:


title: Madhyamaka

text: An important element of madhyamaka refutation is that the classical Buddhist doctrine of dependent arising (the idea that every phenomena is dependent on other phenomena) cannot be reconciled with "a conception of self-nature or substance" and that therefore essence theories are contrary not only to the Buddhist scriptures but to the very ideas of causality and change. Any enduring essential nature would prevent any causal interaction, or any kind of origination. For things would simply always have been, and will always continue to be, without any change. As Nāgārjuna writes in the MMK:


title: Madhyamaka

text: We state that conditioned origination is emptiness. It is mere designation depending on something, and it is the middle path. (24.18)


title: Madhyamaka

text: Beginning with Nāgārjuna, madhyamaka discerns two levels of truth, conventional truth (everyday commonsense reality) and ultimate truth (emptiness). Ultimately, madhyamaka argues that all phenomena are empty of "svabhava" and only exist in dependence on other causes, conditions and concepts. Conventionally, madhyamaka holds that beings do perceive concrete objects which they are aware of empirically. In madhyamaka this phenomenal world is the limited truth - "saṃvṛti satya," which means "to cover", "to conceal", or "obscure." (and thus it is a kind of ignorance) Saṃvṛti is also said to mean "conventional", as in a customary, norm based, agreed upon truth (like linguistic conventions) and it is also glossed as "vyavahāra-satya" (transactional truth). Finally, Chandrakirti also has a third explanation of saṃvṛti, which is “mutual dependence” ("parasparasaṃbhavana").


title: Madhyamaka

text: This seeming reality does not "really" exist as the highest truth realized by wisdom which is "paramartha satya" ("parama" is literally "supreme or ultimate," and "artha" means "object, purpose, or actuality"), and yet it has a kind of conventional reality which has its uses for reaching liberation. This limited truth includes everything, including the Buddha himself, the teachings (dharma), liberation and even Nāgārjuna's own arguments. This two truth schema which did not deny the importance of convention allowed Nāgārjuna to defend himself against charges of nihilism; understanding both correctly meant seeing the middle way:


title: Madhyamaka

text: "Without relying upon convention, the ultimate fruit is not taught. Without understanding the ultimate, nirvana is not attained."


title: Madhyamaka

text: The limited, perceived reality is an experiential reality or a nominal reality which beings impute on the ultimate reality. It is not an ontological reality with substantial or independent existence. Hence, the two truths are not two metaphysical realities; instead, according to Karl Brunnholzl, "the two realities refer to just what is experienced by two different types of beings with different types and scopes of perception." As Candrakirti says:


title: Madhyamaka

text: This means that the distinction between the two truths is primarily epistemological and dependent on the cognition of the observer, not ontological. As Shantideva writes, there are "two kinds of world," "the one of yogins and the one of common people." The seeming reality is the world of samsara because conceiving of concrete and unchanging objects leads to clinging and suffering. As Buddhapalita states: "unskilled persons whose eye of intelligence is obscured by the darkness of delusion conceive of an essence of things and then generate attachment and hostility with regard to them."


title: Madhyamaka

text: According to Hayes, the two truths may also refer to two different goals in life: the highest goal of nirvana, and the lower goal of "commercial good". The highest goal is the liberation from attachment, both material "and" intellectual.


title: Madhyamaka

text: According to Paul Williams, Nāgārjuna associates emptiness with the ultimate truth but his conception of emptiness is not some kind of Absolute, but rather it is the very absence of true existence with regards to the conventional reality of things and events in the world. Because the ultimate is itself empty, it is also explained as a "transcendence of deception" and hence is a kind of apophatic truth which experiences the lack of substance.


title: Madhyamaka

text: Because the nature of ultimate reality is said to be empty, empty even of "emptiness" itself, both the concept of "emptiness" and the very framework of the two truths are also mere conventional realities, not part of the ultimate. This is often called "the emptiness of emptiness" and refers to the fact that even though madhyamikas speak of emptiness as the ultimate unconditioned nature of things, this emptiness is itself empty of any real existence.


title: Madhyamaka

text: The two truths themselves are therefore just a practical tool used to teach others, but do not exist within the actual meditative equipoise that realizes the ultimate. As Candrakirti says: "the noble ones who have accomplished what is to be accomplished do not see anything that is delusive or not delusive." From within the experience of the enlightened ones there is only one reality which appears non-conceptually, as Nāgārjuna says in the Sixty stanzas on reasoning: "that nirvana is the sole reality, is what the Victors have declared." Bhāvaviveka's "Madhyamakahrdayakārikā" describes the ultimate truth through a negation of all four possibilities of the "catuskoti":


title: Madhyamaka

text: Its character is neither existent, nor nonexistent, / Nor both existent and nonexistent, nor neither. / Centrists should know true reality / That is free from these four possibilities.


title: Madhyamaka

text: Atisha describes the ultimate as "here, there is no seeing and no seer, no beginning and no end, just peace... It is nonconceptual and nonreferential ... it is inexpressible, unobservable, unchanging, and unconditioned." Because of the non-conceptual nature of the ultimate, according to Brunnholzl, the two truths are ultimately inexpressible as either "one" or "different."


title: Madhyamaka

text: As noted by Roger Jackson, some non-Buddhist writers, like some Buddhist writers both ancient and modern, have argued that the madhyamaka philosophy is nihilistic. This claim has been challenged by others who argue that it is a Middle Way ("madhyamāpratipad") between nihilism and eternalism. Madhyamaka philosophers themselves explicitly rejected the nihilist interpretation from the outset: Nāgārjuna writes: "through explaining true reality as it is, the seeming "samvrti" does not become disrupted." Candrakirti also responds to the charge of nihilism in his "Lucid Words":


title: Madhyamaka

text: Therefore, emptiness is taught in order to completely pacify all discursiveness without exception. So if the purpose of emptiness is the complete peace of all discursiveness and you just increase the web of discursiveness by thinking that the meaning of emptiness is nonexistence, you do not realize the purpose of emptiness [at all].


title: Madhyamaka

text: This although some scholars (e.g., Murti) interpret emptiness as described by Nāgārjuna as a Buddhist transcendental absolute, other scholars (such as David Kalupahana) consider this claim a mistake, since then emptiness teachings could not be characterized as a middle way.


title: Madhyamaka

text: Madhyamaka thinkers also argue that since things have the nature of lacking true existence or own being ("niḥsvabhāva"), all things are mere conceptual constructs ("prajñaptimatra") because they are just impermanent collections of causes and conditions. This also applies to the principle of causality itself, since "everything" is dependently originated. Therefore, in madhyamaka, phenomena appear to arise and cease, but in an ultimate sense they do not arise or remain as inherently existent phenomena. This tenet is held to show that views of absolute or eternalist existence (such as the Hindu ideas of Brahman or "sat-dravya") and nihilism are both equally untenable. These two views are considered to be the "two extremes" that madhyamaka steers clear from. The first is "essentialism" or "eternalism" (sastavadava) -- a belief that things inherently or substantially exist and are therefore efficacious objects of craving and clinging; Nagarjuna argues that we naively and innately perceive things as substantial, and it is this predisposition which is the root delusion that lies at the basis of all suffering. The second extreme is "nihilism" or "annihilationism" (ucchedavada) -- encompassing views that could lead one to believe that there is no need to be responsible for one's actions -- such as the idea that one is annihilated at death or that nothing has causal effects -- but also the view that absolutely nothing exists.


title: Madhyamaka

text: In madhyamaka, reason and debate are understood as a means to an end (liberation), and therefore they must be founded on the wish to help oneself and others end suffering. Reason and logical arguments, however (such as those employed by classical Indian philosophers, i.e., "pramana"), are also seen as being empty of any true validity or reality. They serve only as conventional remedies for our delusions. Nāgārjuna's "Vigrahavyāvartanī" famously attacked the notion that one could establish a valid cognition or epistemic proof ("pramana"):


title: Madhyamaka

text: If your objects are well established through valid cognitions, tell us how you establish these valid cognitions. If you think they are established through other valid cognitions, there is an infinite regress. Then, the first one is not established, nor are the middle ones, nor the last. If these [valid cognitions] are established even without valid cognition, what you say is ruined. In that case, there is an inconsistency, And you ought to provide an argument for this distinction.


title: Madhyamaka

text: Candrakirti comments on this statement by stating that madhyamaka does not completely deny the use of pramanas conventionally, and yet ultimately they do not have a foundation:


title: Madhyamaka

text: Therefore we assert that mundane objects are known through the four kinds of authoritative cognition. They are mutually dependent: when there is authoritative cognition, there are objects of knowledge; when there are objects of knowledge, there is authoritative cognition. But neither authoritative cognition nor objects of knowledge exist inherently.


title: Madhyamaka

text: To the charge that if Nāgārjuna's arguments and words are also empty they therefore lack the power to refute anything, Nāgārjuna responds that:


title: Madhyamaka

text: My words are without nature. Therefore, my thesis is not ruined. Since there is no inconsistency, I do not have to state an argument for a distinction.Nāgārjuna goes on:


title: Madhyamaka

text: Just as one magical creation may be annihilated by another magical creation, and one illusory person by another person produced by an illusionist, this negation is the same.Shantideva makes the same point: "thus, when one's son dies in a dream, the conception "he does not exist" removes the thought that he does exist, but it is also delusive." In other words, madhyamaka thinkers accept that their arguments, just like all things, are not "ultimately" valid in some foundational sense. But one is still able to use the opponent's own reasoning apparatus in the conventional field to refute their theories and help them see their errors. This remedial deconstruction does not replace false theories of existence with other ones, but simply dissolves all views, including the very fictional system of epistemic warrants ("pramanas") used to establish them. The point of madhyamaka reasoning is not to establish any abstract validity or universal truth, it is simply a pragmatic project aimed at ending delusion and suffering.


title: Madhyamaka

text: Nāgārjuna also argues that madhyamaka only negates things conventionally, since ultimately, there is nothing there to negate: "I do not negate anything and there is also nothing to be negated." Therefore, it is only from the perspective of those who cling to the existence of things that it seems as if something is being negated. In truth, madhyamaka is not annihilating something, merely elucidating that this so-called existence never existed in the first place.


title: Madhyamaka

text: Thus, madhyamaka uses language to make clear the limits of our concepts. Ultimately, reality cannot be depicted by concepts. According to Jay Garfield, this creates a sort of tension in madhyamaka literature, since it has use some concepts to convey its teachings.


title: Madhyamaka

text: For madhyamaka, the realization of emptiness is not just a satisfactory theory about the world, but a key understanding which allows one to reach liberation or nirvana. As Nāgārjuna's Mūlamadhyamakakārikā ("Root Verses on the Middle Way") puts it:


title: Madhyamaka

text: With the cessation of ignorance, formations will not arise. Moreover, the cessation of ignorance occurs through right understanding. Through the cessation of this and that, this and that will not come about. The entire mass of suffering thereby completely ceases.


title: Madhyamaka

text: The words "this" and "that" allude to the mind's profound addiction to dualism, but also and more specifically to the mind that has not yet grasped the reality of dependent origination. The insight of dependent origination -- that nothing arises or happens independently, that everything is rooted in or "made of" something else, and conditioned by other things, each of which are likewise made of and conditioned by other things in the same way, so that nothing at all "is" independently -- is central to the fundamental Buddhist analysis of the arising of suffering and the liberation from it. Therefore, according to Nāgārjuna, the cognitive shift which sees the nonexistence of "svabhāva" leads to the cessation of the first link in this chain of suffering, which then leads to the ending of the entire chain of causes and thus, of all suffering. Nāgārjuna adds:


title: Madhyamaka

text: Liberation ("moksa") results from the cessation of actions ("karman") and defilements ("klesa"). Actions and defilements result from representations ("vikalpa"). These [come] from false imagining ("prapañca"). False imagining stops in emptiness ("sunyata"). (18.5)


title: Madhyamaka

text: Therefore, the ultimate aim of understanding emptiness is not philosophical insight as such, but the actualization of a liberated mind which does not cling to anything. To encourage this awakening, meditation on emptiness may proceed in stages, starting with the emptiness of self, of objects and of mental states, culminating in a "natural state of nonreferential freedom."


title: Madhyamaka

text: Moreover, the path to understanding ultimate truth is not one that negates or invalidates relative truths (especially truths about the path to awakening). Instead it is only through properly understanding and using relative truth that the ultimate can be attained, as Bhāvaviveka maintains:


title: Madhyamaka

text: In order to guide beginners a method is taught, comparable to the steps of a staircase that leads to perfect Buddhahood. Ultimate reality is only to be entered once we have understood seeming reality.


title: Madhyamaka

text: Nāgārjuna is famous for arguing that his philosophy was not a view, and that he in fact did not take any position ("paksa") or thesis ("pratijña") whatsoever since this would just be another form of clinging to some form of existence. In his "Vigrahavyāvartanī" , Nāgārjuna states:


title: Madhyamaka

text: If I had any position, I thereby would be at fault. Since I have no position, I am not at fault at all. If there were anything to be observed through direct perception and the other instances [of valid cognition], it would be something to be established or rejected. However, since no such thing exists, I cannot be criticized.


title: Madhyamaka

text: Likewise in his "Sixty Stanzas on Reasoning", Nāgārjuna says: "By taking any standpoint whatsoever, you will be snatched by the cunning snakes of the afflictions. Those whose minds have no standpoint will not be caught."


title: Madhyamaka

text: Randall Collins argues that for Nāgārjuna, ultimate reality is simply the idea that "no concepts are intelligible", while Ferrer emphasizes that Nāgārjuna criticized those whose mind held any "positions and beliefs", "including" the view of emptiness. As Nāgārjuna says: "The Victorious Ones have announced that emptiness is the relinquishing of all views. Those who are possessed of the view of emptiness are said to be incorrigible." Aryadeva echoes this idea in his Four Hundred Verses:


title: Madhyamaka

text: "First, one puts an end to what is not meritorious. In the middle, one puts an end to identity. Later, one puts an end to all views. Those who understand this are skilled."


title: Madhyamaka

text: Other writers, however, do seem to affirm emptiness as a specific madhyamaka thesis or view. Shantideva for example says "one cannot uphold any faultfinding in the thesis of emptiness" and Bhavaviveka's "Blaze of Reasoning" says: "as for our thesis, it is the emptiness of nature, because this is the nature of phenomena." Jay Garfield notes that Nāgārjuna and Candrakirti both make positive arguments, and cites both the Mūlamadhyamakakārikā ("Root Verses on the Middle Way") --"There does not exist anything that is not dependently arisen. Therefore there does not exist anything that is not empty" -- and Candrakirti's commentary on it: "We assert the statement, 'Emptiness itself is a designation.'"


title: Madhyamaka

text: These positions are not really in contradiction, however, since madhyamaka can be said to have the "thesis of emptiness" only conventionally, in the context of debating or explaining it. According to Karl Brunnholzl, even though madhyamaka thinkers may express a thesis pedagogically, what they deny is that "they have any thesis that involves real existence or reference points, or any thesis that is to be defended from their own point of view."


title: Madhyamaka

text: Brunnholzl underlines that madhyamaka analysis applies to all systems of thought, ideas and concepts, including madhyamaka itself. This is because the nature of madhyamaka is "the deconstruction of any system and conceptualization whatsoever, including itself". In the Root verses on the Middle Way, Nāgārjuna illustrates this point:


title: Madhyamaka

text: By the flaw of having views about emptiness, those of little understanding are ruined, just as when incorrectly seizing a snake or mistakenly practicing an awareness-mantra.


title: Madhyamaka

text: The madhyamaka school is usually considered to have been founded by Nāgārjuna, though it may have existed earlier. Various scholars have noted that some of themes in the work of Nāgārjuna can also be found in earlier Buddhist sources.


title: Madhyamaka

text: It is well known that the only sutra that Nāgārjuna explicitly cites in his "Mūlamadhyamakakārikā" (Chapter 15.7) is the "Advice to Kātyāyana.". He writes, "according to the Instructions to Kātyāyana, both existence and nonexistence are criticized by the Blessed One who opposed being and non-being." This appears to have been a Sanskrit version of the "Kaccānagotta Sutta" (Saṃyutta Nikāya ii.16-17 / SN 12.15, with parallel in the Chinese "Saṃyuktāgama" 301). The "Kaccānagotta Sutta" itself says:


title: Madhyamaka

text: This world, Kaccāna, for the most part depends on a duality–upon the notion of existence and the notion of nonexistence. But for one who sees the origin of the world as it really is with correct wisdom, there is no notion of nonexistence in regard to the world. And for one who sees the cessation of the world as it really is with correct wisdom, there is no notion of existence in regard to the world.


title: Madhyamaka

text: Joseph Walser also points out that verse six of chapter 15 contains an allusion to the ""Mahahatthipadopama sutta"", another early sutra of the "Nidanavagga", the collection which also contains the "Kaccānagotta," and which contains various sutras that focus on the avoidance of extreme views, which are all held to be associated with either the extreme of eternality ("sasvata") or the extreme of disruption ("uccheda"). Another allusion to an early Buddhist text noted by Walser occurs in Nāgārjuna's "Ratnavali" chapter 1, where he makes reference to a statement in the "Kevaddha sutta."


title: Madhyamaka

text: Some scholars, like Tillman Vetter and Luis Gomez, have also seen some passages from the early "Aṭṭhakavagga" (Pali, "Octet Chapter") and the "Pārāyanavagga" (Pali, "Way to the Far Shore Chapter"), which focusing on letting go of all views, as teaching a kind of "Proto-Mādhyamika." Other scholars such as Paul Fuller and Alexander Wynne have rejected the arguments of Gomez and Vetter.


title: Madhyamaka

text: Finally, the "Dazhidulun", a text attributed to Nāgārjuna in the Chinese tradition (though this attribution has been questioned), cites the Sanskrit "Arthavargīya sūtra" (which parallels the "Aṭṭhakavagga") in its discussion of ultimate truth.


title: Madhyamaka

text: The madhyamaka school has been perhaps simplistically regarded as a reaction against the development of Buddhist abhidharma, however according to Joseph Walser, this is problematic. In abhidharma, dharmas are characterized by defining traits ("lakṣaṇa") or own-existence ("svabhāva"). The "Abhidharmakośabhāṣya" states for example: ""dharma" means 'upholding,' [namely], upholding intrinsic nature ("svabhāva")", while the "Mahāvibhāṣā" states "intrinsic nature is able to uphold its own identity and not lose it". However this does not mean that all abhidharma systems hold that dharmas exist independently in an ontological sense, since all Buddhist schools hold that (most) dharmas are dependently originated, this doctrine being a central core Buddhist view. Therefore, in abhidharma, "svabhāva" is typically something which arises dependent on other conditions and qualities.


title: Madhyamaka

text: "Svabhāva" in the early abhidharma systems then, is not a kind of ontological essentialism, but it is a way to categorize dharmas according to their distinctive characteristics. According to Noa Ronkin, the idea of "svabhava" evolved towards ontological dimension in the Sarvāstivādin Vaibhasika school's interpretation, which began to also use the term "dravya" which means "real existence". This then, may have been the shift which Nagarjuna sought to attack when he targets certain Sarvastivada tenets.


title: Madhyamaka

text: However, the relationship between madhyamaka and abhidharma is complex, as Joseph Walser notes, "Nagarjuna's position vis-à-vis abhidharma is neither a blanket denial nor a blanket acceptance. Nagarjuna's arguments entertain certain abhidharmic standpoints while refuting others." One example can be seen in Nagarjuna's "Ratnavali" which supports the study of a list of 57 moral faults which Nagarjuna takes from the "Ksudravastuka" (an abhidharma texts that is part of the Sarvastivada "Dharmaskandha")"." Abhidharmic analysis figures prominently in madhyamaka treatises, and authoritative commentators like Candrakīrti emphasize that abhidharmic categories function as a viable (and favored) system of conventional truths - they are more refined than ordinary categories, and they are not dependent on either the extreme of eternalism or on the extreme view of the discontinuity of karma, as the non-Buddhist categories of the time did.


title: Madhyamaka

text: Walser also notes that Nagarjuna's theories have much in common with the view of a sub-sect of the Mahasamgikas called the Prajñaptivadins, who held that suffering was "prajñapti" (designation by provisional naming) "based on conditioned entities that are themselves reciprocally designated" ("anyonya prajñapti"). David Burton argues that for Nagarjuna, "dependently arisen entities have merely conceptually constructed existence ("prajñaptisat")". Commenting on this, Walser writes that "Nagarjuna is arguing for a thesis that the Prajñaptivádins already held, using a concept of prajñapti that they were already using."


title: Madhyamaka

text: According to David Seyfort Ruegg, the main canonical Mahāyāna sutra sources of the Madhyamaka school are the "Prajñāpāramitā", "Ratnakūṭa" and "Avataṃsaka" literature. Other sutras which were widely cited by Madhamikas include the "Vimalakīrtinirdeṣa", the "Śuraṃgamasamādhi," the "Saddharmapuṇḍarīka", the "Daśabhūmika", the "Akṣayamatinirdeśa", the "Tathāgataguhyaka", and the "Kāśyapaparivarta".


title: Madhyamaka

text: Ruegg notes that in Candrakīrti's "Prasannapadā" and "Madhyamakāvatāra", in addition to the "Prajñāpāramitā", "we find the "Akṣayamatinirdeśa, Anavataptahradāpasaṃkramaṇa, Upāliparipṛcchā, Kāśyapaparivarta, Gaganagañja, Tathāgataguhya, Daśabhūmika, Dṛḍhādhyāśaya, Dhāraṇīśvararāja, Pitāputrasamāgama, Mañjuśrīparipṛcchā, Ratnakūṭa, Ratnacūḍaparipṛcchā, Ratnamegha, Ratnākara, Laṅkāvatāra, Lalitavistara, Vimalakirtinirdesa, Śālistamba, Satyadvayāvatāra", "Saddharmapuṇḍarīka", "Samādhirāja" ("Candrapradīpa"), and "Hastikakṣya"."


title: Madhyamaka

text: Madhyamaka thought is also closely related to a number of Mahāyāna sources; traditionally, the "Prajñāpāramitā" sūtras are the literature most closely associated with madhyamaka – understood, at least in part, as an exegetical complement to those Sūtras. Traditional accounts also depict Nāgārjuna as retrieving some of the larger Prajñāpāramitā sūtras from the world of the Nāgas (explaining in part the etymology of his name). Prajñā or 'higher cognition' is a recurrent term in Buddhist texts, explained as a synonym of abhidharma, 'insight' (vipaśyanā) and 'analysis of the dharmas' ("dharmapravicaya"). Within a specifically Mahāyāna context, Prajñā figures as the most prominent in a list of Six Pāramitās ('perfections' or 'perfect masteries') that a Bodhisattva needs to cultivate in order to eventually achieve Buddhahood.


title: Madhyamaka

text: Madhyamaka offers conceptual tools to analyze all possible elements of existence, allowing the practitioner to elicit through reasoning and contemplation the type of view that the Sūtras express more authoritatively (being considered word of the Buddha) but less explicitly (not offering corroborative arguments). The vast Prajñāpāramitā literature emphasizes the development of higher cognition in the context of the Bodhisattva path; thematically, its focus on the emptiness of all dharmas is closely related to the madhyamaka approach. Allusions to the prajñaparamita sutras can be found in Nagarjuna's work. One example is in the opening stanza of the MMK, which seem to allude to the following statement found in two prajñaparamita texts:And how does he wisely know conditioned co-production? He wisely knows it as neither production, nor stopping, neither cut off nor eternal, neither single nor manifold, neither coming nor going away, as the appeasement of all futile discoursings, and as bliss.The first stanza of Nagarjuna's MMK meanwhile, state:I pay homage to the Fully Enlightened One whose true, venerable words teach dependent-origination to be the blissful pacification of all mental proliferation, neither production, nor stopping, neither cut off nor eternal, neither single nor manifold, neither coming, nor going away.


title: Madhyamaka

text: Because of the high degree of similarity between madhyamaka and Pyrrhonism, Thomas McEvilley and Matthew Neale suspect that Nāgārjuna was influenced by Greek Pyrrhonist texts imported into India. Pyrrho of Elis (c. 360-c. 270 BCE), who is credited with founding this school of skeptical philosophy, was himself influenced by Buddhist philosophy during his stay in India with Alexander the Great's army.


title: Madhyamaka

text: As Jan Westerhoff notes, while Nāgārjuna is "one of the greatest thinkers in the history of Asian philosophy...contemporary scholars agree on hardly any details concerning him". This includes exactly when he lived (it can be narrowed down some time in the first three centuries CE), where he lived (Joseph Walser suggests Amarāvatī in east Deccan) and exactly what constitutes his written corpus.


title: Madhyamaka

text: Numerous texts are attributed to him, but it is at least agreed by some scholars that what is called the "Yukti" (analytical) corpus is the core of his philosophical work. These texts are the "Root verses on the Middle way" ("Mūlamadhyamakakārikā," MMK), the "Sixty Stanzas on Reasoning" ("Yuktiṣāṣṭika"), the "Dispeller of Objections" ("Vigrahavyāvartanī"), the "Treatise on Pulverization" ("Vaidalyaprakaraṇa") and the "Precious Garland" ("Ratnāvalī"). However, even the attribution of each one of these has been question by some modern scholars, except for the MMK which is by definition seen as his major work.


title: Madhyamaka

text: Nāgārjuna's main goal is often seen by scholars as refuting the essentialism of certain Buddhist abhidharma schools (mainly "Vaibhasika") which posited theories of "svabhava" (essential nature) and also the Hindu Nyāya and Vaiśeṣika schools which posited a theory of ontological substances ("dravyatas"). In the MMK he used "reductio ad absurdum" arguments ("prasanga") to show that any theory of substance or essence was unsustainable and therefore, phenomena ("dharmas") such as change, causality, and sense perception were empty ("sunya") of any essential existence. Nāgārjuna also famously equated the emptiness of "dharmas" with their dependent origination.


title: Madhyamaka

text: Because of his philosophical work, Nāgārjuna is seen by some modern interpreters as restoring the Middle Way of the Buddha, which had become challenged by absolutist metaphysical tendencies in certain philosophical quarters.


title: Madhyamaka

text: Rāhulabhadra was an early madhyamika, sometimes said to be either a teacher of Nagarjuna or his contemporary and follower. He is most famous for his verses in praise of the "Prajñāpāramitā" (Skt. "Prajñāpāramitāstotra") and Chinese sources maintain that he also composed a commentary on the MMK which was translated by Paramartha.


title: Madhyamaka

text: Nāgārjuna's pupil Āryadeva (3rd century CE) wrote various works on madhyamaka, the most well known of which is his "400 verses". His works are regarded as a supplement to Nāgārjuna's, on which he commented. Āryadeva also wrote refutations of the theories of non-Buddhist Indian philosophical schools.


title: Madhyamaka

text: There are also two commentaries on the MMK which may be by Āryadeva, the "Akutobhaya" (which has also been regarded as an auto-commentary by Nagarjuna) as well as a commentary which survives only in Chinese (as part of the "Chung-Lun", "Middle treatise", Taisho 1564) attributed to a certain "Ch'ing-mu" (aka Pin-lo-chieh, which some scholars have also identified as possibly being Aryadeva). However, Brian C. Bocking, a translator of the "Chung-Lung", also states that it is likely the author of this commentary was a certain Vimalāksa, who was Kumarajiva's old Vinaya-master from Kucha.


title: Madhyamaka

text: An influential commentator on Nāgārjuna was Buddhapālita (470–550) who has been interpreted as developing the prāsaṅgika approach to Nāgārjuna's works in his "Madhyamakavṛtti" (now only extant in Tibetan) which follows the orthodox Madhyamaka method by critiquing essentialism mainly through reductio ad absurdum arguments. Like Nāgārjuna, Buddhapālita's main philosophical method is to show how all philosophical positions are ultimately untenable and self-contradictory, a style of argumentation called "prasanga".


title: Madhyamaka

text: Buddhapālita's method is often contrasted with that of Bhāvaviveka (c. 500 – c. 578), who argued in his "Prajñāpadīpa" (Lamp of Wisdom) for the use of logical arguments using the "pramana" based epistemology of Indian logicians like Dignāga. In what would become a source of much future debate, Bhāvaviveka criticized Buddhapālita for not putting madhyamaka arguments into proper "autonomous syllogisms" ("svatantra"). Bhāvaviveka argued that mādhyamika's should always put forth syllogistic arguments to prove the truth of the madhyamaka thesis. Instead of just criticizing other's arguments, a tactic called "vitaṇḍā" (attacking) which was seen in bad form in Indian philosophical circles, Bhāvaviveka held that madhyamikas must positively prove their position using sources of knowledge (pramanas) agreeable to all parties. He argued that the position of a madhyamaka was simply that phenomena are devoid of an inherent nature. This approach has been labeled the "svātantrika" style of madhyamaka by Tibetan philosophers and commentators.


title: Madhyamaka

text: Another influential commentator, Candrakīrti (c. 600–650), sought to defend Buddhapālita and critique Bhāvaviveka's position (and Dignāga) that one "must" construct independent ("svatantra") arguments to positively prove the madhyamaka thesis, on the grounds this contains a subtle essentialist commitment. He argued that madhyamikas do not "have" to argue by "svantantra", but can merely show the untenable consequences ("prasaṅga") of all philosophical positions put forth by their adversary. Furthermore, for Candrakīrti, there is a problem with assuming that the madhyamika and the essentialist opponent can begin with the same shared premises that are required for this kind of syllogistic reasoning because the essentialist and the madhyamaka do not share a basic understanding of what it means for things to exist in the first place.


title: Madhyamaka

text: Candrakīrti also criticized the Buddhist yogācāra school, which he saw as positing a form of subjective idealism due to their doctrine of "appearance only" ("vijñaptimatra"). Candrakīrti faults the yogācāra school for not realizing that the nature of consciousness is also a conditioned phenomenon, and for privileging consciousness over its objects ontologically, instead of seeing that "everything" is empty. Candrakīrti wrote the "Prasannapadā" (Clear Words), a highly influential commentary on the "Mūlamadhyamakakārikā" as well as the "Madhyamakāvatāra," an introduction to madhyamaka. His works are central to the understanding of madhyamaka in Tibetan Buddhism.


title: Madhyamaka

text: A later "svātantrika" figure is Avalokitavrata (seventh century), who composed a "tika" (sub-commentary) on Bhāvaviveka's "Prajñāpadīpa" and who mentions important figures of the era such as Dharmakirti and Candrakīrti.


title: Madhyamaka

text: Another commentator on Nagarjuna is Bhikshu Vaśitva ("Zizai") who composed a commentary on Nagarjuna's "Bodhisaṃbhāra" that survives in a translation by Dharmagupta in the Chinese canon.


title: Madhyamaka

text: Śāntideva (end 7th century – first half 8th century) is well known for his philosophical poem discussing the bodhisattva path and the six paramitas, the "Bodhicaryāvatāra". He united "a deep religiousness and joy of exposure together with the unquestioned Madhyamaka orthodoxy". Later in the 10th century, there were commentators on the works of prasangika authors such as Prajñakaramati who wrote a commentary on the "Bodhicaryāvatāra" and Jayananda who commented on Candrakīrti's "Madhyamakāvatāra."


title: Madhyamaka

text: A lesser known treatise on the six paramitas associated with the madhyamaka school is Ārya Śūra's "Pāramitāsamāsa," unlikely to be the same author as that of the "Garland of Jatakas."


title: Madhyamaka

text: Other lesser known madhyamikas include Devasarman (fifth to sixth centuries) and Gunamati (the fifth to sixth centuries) both of whom wrote commentaries on the MMK that exist only in Tibetan fragments.


title: Madhyamaka

text: According to Ruegg, possibly the earliest figure to work with the two schools was Vimuktisena (early sixth century), a commentator on the "Abhisamayalamkara" and also is reported to have been a pupil of Bhāvaviveka as well as Vasubandhu.


title: Madhyamaka

text: The seventh and eighth centuries saw a synthesis of the Buddhist yogācāra tradition with madhyamaka, beginning with the work of Śrigupta, Jñānagarbha (Śrigupta's disciple) and his student Śāntarakṣita (8th-century) who, like Bhāvaviveka, also adopted some of the terminology of the Buddhist pramana tradition, in their time best represented by Dharmakīrti.


title: Madhyamaka

text: Like the classical madhyamaka, yogācāra-madhyamaka approaches ultimate truth through the prasaṅga method of showing absurd consequences. However, when speaking of conventional reality they also make positive assertions and autonomous arguments like Bhāvaviveka and Dharmakīrti. Śāntarakṣita also subsumed the yogācāra system into his presentation of the conventional, accepting their idealism on a conventional level as a preparation for the ultimate truth of madhyamaka.


title: Madhyamaka

text: By relying on the Mind Only ("cittamatra"), know that external entities do not exist. And by relying on this [madhyamaka] system, know that no self at all exists, even in that [mind]. Therefore, due to holding the reigns of logic as one rides the chariots of the two systems, one attains [the path of] the actual Mahayanist.


title: Madhyamaka

text: Śāntarakṣita and his student Kamalaśīla (known for his text on self development and meditation, the "Bhavanakrama") were influential in the initial spread of madhyamaka Buddhism to Tibet. Haribhadra, another important figure of this school, wrote an influential commentary on the "Abhisamayalamkara."


title: Madhyamaka

text: The madhyamaka philosophy continued to be of major importance during the period of Indian Buddhism when the tantric Vajrayana Buddhism rose to prominence. One of the central Vajrayana madhyamaka philosophers was Arya Nagarjuna (also known as the "tantric Nagarjuna", 7th-8th centuries) who may be the author of the "Bodhicittavivarana" as well as a commentator on the "Guhyasamāja Tantra". Other figures in his lineage include Nagabodhi, Vajrabodhi, Aryadeva-pada and Candrakirti-pada.


title: Madhyamaka

text: Later figures include Bodhibhadra (c. 1000), a Nalanda university master who wrote on philosophy and yoga and who was a teacher of Atiśa Dīpaṃkara Śrījñāna (982 - 1054 CE) who was an influential figure in the transmission of Buddhism to Tibet and wrote the influential "Bodhipathapradīpa" (Lamp for the Path to Awakening).


title: Madhyamaka

text: Madhyamaka philosophy obtained a central position in all the main Tibetan Buddhist schools, all whom consider themselves to be madhyamikas. Madhyamaka thought has been categorized in various ways in India and Tibet.


title: Madhyamaka

text: Influential early figures who are important in the transmission of madhyamaka to Tibet include the yogacara-madhyamika Śāntarakṣita (725–788), and his students Haribhadra and Kamalashila (740-795) as well as the later Kadampa figures of Atisha (982–1054) and his pupil Dromtön (1005–1064) who taught madhyamaka by using the works of Bhāviveka and Candrakīrti.


title: Madhyamaka

text: The early transmission of Buddhism to Tibet saw these two main strands of philosophical views in debate with each other. The first was the camp which defended the yogacara-madhyamaka interpretation (and thus, svatantrika) centered on the works of the scholars of the Sangphu monastery founded by Ngog Loden Sherab (1059-1109) and also includes Chapa Chokyi Senge (1109-1169).


title: Madhyamaka

text: The second camp was those who championed the work of Candrakirti over the yogacara-madhyamaka interpretation, and included Sangphu monk Patsab Nyima Drag (b. 1055) and Jayananda (fl 12th century). According to John Dunne, it was the madhyamaka interpretation and the works of Candrakirti which became dominant over time in Tibet.


title: Madhyamaka

text: Another very influential figure from this early period is Mabja Jangchub Tsöndrü (d. 1185), who wrote an important commentary on Nagarjuna's "Mūlamadhyamakakārikā". Mabja was a student of both the Dharmakirtian Chapa and the Candrakirti scholar Patsab and his work shows an attempt to steer a middle course between their views. Mabja affirms the conventional usefulness of Buddhist pramāṇa, but also accepts Candrakirti's prasangika views. Mabja's Madhyamaka scholarship was very influential on later Tibetan Madhyamikas such as Longchenpa, Tsongkhapa, Gorampa, and Mikyö Dorje.


title: Madhyamaka

text: In Tibetan Buddhist scholarship, a distinction began to be made between the Autonomist ("Svātantrika, rang rgyud pa") and Consequentialist ("Prāsaṅgika, Thal 'gyur pa") approaches to madhyamaka reasoning. The distinction was one invented by Tibetans, and not one made by classical Indian madhyamikas. Tibetans mainly use the terms to refer to the logical procedures used by Bhavaviveka (who argued for the use of "svatantra-anumana" or autonomous syllogisms) and Buddhapalita (who held that one should only use "prasanga", or "reductio ad absurdum"). Tibetan Buddhism further divides "svātantrika" into sautrantika svātantrika madhyamaka (applied to Bhāviveka), and yogācāra svātantrika madhyamaka (śāntarakṣita and kamalaśīla).


title: Madhyamaka

text: The svātantrika states that conventional phenomena are understood to have a conventional essential existence, but without an ultimately existing essence. In this way they believe they are able to make positive or "autonomous" assertions using syllogistic logic because they are able to share a subject that is established as appearing in common - the proponent and opponent use the same kind of valid cognition to establish it. The name comes from this quality of being able to use autonomous arguments in debate.


title: Madhyamaka

text: In contrast, the central technique avowed by the is to show by "" (or reductio ad absurdum) that any positive assertion (such as "asti" or "nāsti", "it is", or "it is not") or view regarding phenomena must be regarded as merely conventional ( or "lokavyavahāra"). The "prāsaṅgika" holds that it is not necessary for the proponent and opponent to use the same kind of valid cognition ("pramana") to establish a common subject; indeed it is possible to change the view of an opponent through a reductio argument.


title: Madhyamaka

text: Although presented as a divide in doctrine, the major difference between svātantrika and prasangika may be between two style of reasoning and arguing, while the division itself is exclusively Tibetan. Tibetan scholars were aware of alternative madhyamaka sub-classifications, but later Tibetan doxography emphasizes the nomenclature of prāsaṅgika versus svātantrika. No conclusive evidence can show the existence of an Indian antecedent, and it is not certain to what degree individual writers in Indian and Tibetan discussion held each of these views and if they held a view generally or only in particular instances. Both Prāsaṅgikas and Svātantrikas cited material in the āgamas in support of their arguments.


title: Madhyamaka

text: Longchen Rabjam noted in the 14th century that Candrakirti favored the approach when specifically discussing the analysis for ultimacy, but otherwise he made positive assertions such as when describing the paths of Buddhist practice in his "Madhyamakavatāra". Therefore, even make positive assertions when discussing conventional practice, they simply stick to using reductios specifically when analyzing for ultimate truth.


title: Madhyamaka

text: Further Tibetan philosophical developments began in response to the works of the scholar Dölpopa Shérap Gyeltsen (1292–1361) and led to two distinctly opposed Tibetan madhyamaka views on the nature of ultimate reality. An important Tibetan treatise on Emptiness and Buddha Nature is found in Dolpopa's voluminous study, "Mountain Doctrine".


title: Madhyamaka

text: Dolpopa, the founder of the Jonang school, viewed the Buddha and Buddha Nature as "not" intrinsically empty, but as truly real, unconditioned, and replete with eternal, changeless virtues. In the Jonang school, ultimate reality, i.e. Buddha Nature ("tathagatagarbha") is only empty of what is impermanent and conditioned (conventional reality), not of its own self which is ultimate Buddhahood and the luminous nature of mind. In Jonang, this ultimate reality is a "ground or substratum" which is "uncreated and indestructible, noncomposite and beyond the chain of dependent origination."


title: Madhyamaka

text: Basing himself on the Indian Tathāgatagarbha sūtras as his main sources, Dolpopa described the Buddha Nature as: [N]on-material emptiness, emptiness that is far from an annihilatory emptiness, great emptiness that is the ultimate pristine wisdom of superiors ...Buddha earlier than all Buddhas, ... causeless original Buddha.


title: Madhyamaka

text: This "great emptiness" i.e. the "tathāgatagarbha" is said to be filled with eternal powers and virtues:


title: Madhyamaka

text: The Jonang position came to be known as "emptiness of other" (")," because it held that the ultimate truth was positive reality that was not empty of its own nature, only empty of what it was other than itself. Dolpopa considered his view a form of madhyamaka, and called his system "Great Madhyamaka". Dolpopa opposed what he called "rangtong" (self-empty), the view that ultimate reality is that which is empty of self nature in a relative and absolute sense, that is to say that it is empty of everything, including itself. It is thus not a transcendental ground or metaphysical absolute which includes all the eternal Buddha qualities. This "rangtong - shentong" distinction became a central issue of contention among Tibetan Buddhist philosophers.


title: Madhyamaka

text: Alternative interpretations of the shentong view is also taught outside of Jonang. Some Kagyu figures, like Jamgon Kongtrul (1813–1899) as well as the unorthodox Sakya philosopher Sakya Chokden (1428–1507), supported their own forms of shentong.


title: Madhyamaka

text: The Gelug school was founded in the beginning of the 15th century by Je Tsongkhapa (1357–1419). Tsongkhapa's conception of emptiness draws mainly from the works of "prāsaṅgika" Indian thinkers like Buddhapalita, Candrakirti, and Shantideva and he argued that only their interpretation of Nagarjuna was ultimately correct. According to José I. Cabezón, Tsongkhapa also argued that the ultimate truth or emptiness was "an absolute negation ("med dgag")—the negation of inherent existence—and that nothing was exempt from being empty, including emptiness itself."


title: Madhyamaka

text: Tsongkhapa also maintained that the ultimate truth could be understood conceptually, an understanding which could later be transformed into a non-conceptual one. This conceptual understanding could only be done through the use of madhyamika reasoning, which he also sought to unify with the logical theories of Dharmakirti. Because of Tsongkhapa's view of emptiness as an absolute negation, he strongly attacked the other empty views of Dolpopa in his works. Tsongkhapa major work on madhyamaka is his commentary on the MMK called "Ocean of Reasoning".


title: Madhyamaka

text: According to Thupten Jinpa, Tsongkhapa's "doctrine of the object of negation" is one of his most innovative but also controversial ideas. Tsongkhapa pointed out that if one wants to steer a middle course between the extremes of "over-negation" (straying into nihilism) and "under-negation" (and thus reification), it is important to have a clear concept of exactly what is being negated in Madhyamaka analysis (termed "the object of negation").


title: Madhyamaka

text: According to Jay Garfield and Sonam Thakchoe, for Tsongkhapa, there are two aspects of the object of negation: “erroneous apprehension” ( "phyin ci log gi ‘dzin pa") and “the existence of intrinsic nature thereby apprehended” ("des bzung ba’i rang bzhin yod pa"). The second aspect is an erroneously reified fiction which does not exist even conventionally. This is the fundamental object of negation for Tsongkhapa "since the reified object must first be negated in order to eliminate the erroneous subjective state."


title: Madhyamaka

text: Tsongkhapa's understanding of the object of negation (Tib. "dgag bya") is subtle, and he describes one aspect of it as an "innate apprehension of self-existence." Thupten Jinpa glosses this as a belief that we have that leads us to "perceive things and events as possessing some kind of intrinsic existence and identity." Tsongkhapa's madhyamaka therefore, does not deny the conventional existence of things "per se", but merely rejects our way of experiencing things as existing in an essentialist way, which are false projections or imputations. This is the root of ignorance, which for Tsongkhapa is an "active defiling agency" (Sk. "kleśāvaraṇa") which projects a false sense of reality onto objects.