title: Friction

text: John Leslie (1766–1832) noted a weakness in the views of Amontons and Coulomb: If friction arises from a weight being drawn up the inclined plane of successive asperities, why then isn't it balanced through descending the opposite slope? Leslie was equally skeptical about the role of adhesion proposed by Desaguliers, which should on the whole have the same tendency to accelerate as to retard the motion. In Leslie's view, friction should be seen as a time-dependent process of flattening, pressing down asperities, which creates new obstacles in what were cavities before.


title: Friction

text: Arthur Jules Morin (1833) developed the concept of sliding versus rolling friction. Osborne Reynolds (1866) derived the equation of viscous flow. This completed the classic empirical model of friction (static, kinetic, and fluid) commonly used today in engineering. In 1877, Fleeming Jenkin and J. A. Ewing investigated the continuity between static and kinetic friction.


title: Friction

text: The focus of research during the 20th century has been to understand the physical mechanisms behind friction. Frank Philip Bowden and David Tabor (1950) showed that, at a microscopic level, the actual area of contact between surfaces is a very small fraction of the apparent area. This actual area of contact, caused by asperities increases with pressure. The development of the atomic force microscope (ca. 1986) enabled scientists to study friction at the atomic scale, showing that, on that scale, dry friction is the product of the inter-surface shear stress and the contact area. These two discoveries explain Amonton's first law "(below)"; the macroscopic proportionality between normal force and static frictional force between dry surfaces.


title: Friction

text: The elementary property of sliding (kinetic) friction were discovered by experiment in the 15th to 18th centuries and were expressed as three empirical laws:


title: Friction

text: Dry friction resists relative lateral motion of two solid surfaces in contact. The two regimes of dry friction are 'static friction' ("stiction") between non-moving surfaces, and "kinetic friction" (sometimes called sliding friction or dynamic friction) between moving surfaces.


title: Friction

text: Coulomb friction, named after Charles-Augustin de Coulomb, is an approximate model used to calculate the force of dry friction. It is governed by the model:


title: Friction

text: The Coulomb friction formula_2 may take any value from zero up to formula_6, and the direction of the frictional force against a surface is opposite to the motion that surface would experience in the absence of friction. Thus, in the static case, the frictional force is exactly what it must be in order to prevent motion between the surfaces; it balances the net force tending to cause such motion. In this case, rather than providing an estimate of the actual frictional force, the Coulomb approximation provides a threshold value for this force, above which motion would commence. This maximum force is known as traction.


title: Friction

text: The force of friction is always exerted in a direction that opposes movement (for kinetic friction) or potential movement (for static friction) between the two surfaces. For example, a curling stone sliding along the ice experiences a kinetic force slowing it down. For an example of potential movement, the drive wheels of an accelerating car experience a frictional force pointing forward; if they did not, the wheels would spin, and the rubber would slide backwards along the pavement. Note that it is not the direction of movement of the vehicle they oppose, it is the direction of (potential) sliding between tire and road.


title: Friction

text: The normal force is defined as the net force compressing two parallel surfaces together, and its direction is perpendicular to the surfaces. In the simple case of a mass resting on a horizontal surface, the only component of the normal force is the force due to gravity, where formula_7. In this case, conditions of equilibrium tell us that the magnitude of the friction force is "zero", formula_8. In fact, the friction force always satisfies formula_9, with equality reached only at a critical ramp angle (given by formula_10) that is steep enough to initiate sliding.


title: Friction

text: The friction coefficient is an empirical (experimentally measured) structural property that depends only on various aspects of the contacting materials, such as surface roughness. The coefficient of friction is not a function of mass or volume. For instance, a large aluminum block has the same coefficient of friction as a small aluminum block. However, the magnitude of the friction force itself depends on the normal force, and hence on the mass of the block.


title: Friction

text: Depending on the situation, the calculation of the normal force formula_11 might include forces other than gravity. If an object is on a level surface and subjected to an external force formula_12 tending to cause it to slide, then the normal force between the object and the surface is just formula_13, where formula_14 is the block's weight and formula_15 is the downward component of the external force. Prior to sliding, this friction force is formula_16, where formula_17 is the horizontal component of the external force. Thus, formula_18 in general. Sliding commences only after this frictional force reaches the value formula_19. Until then, friction is whatever it needs to be to provide equilibrium, so it can be treated as simply a reaction.


title: Friction

text: If the object is on a tilted surface such as an inclined plane, the normal force from gravity is smaller than formula_14, because less of the force of gravity is perpendicular to the face of the plane. The normal force and the frictional force are ultimately determined using vector analysis, usually via a free body diagram.


title: Friction

text: In general, process for solving any statics problem with friction is to treat contacting surfaces "tentatively" as immovable so that the corresponding tangential reaction force between them can be calculated. If this frictional reaction force satisfies formula_18, then the tentative assumption was correct, and it is the actual frictional force. Otherwise, the friction force must be set equal to formula_19, and then the resulting force imbalance would then determine the acceleration associated with slipping.


title: Friction

text: The coefficient of friction (COF), often symbolized by the Greek letter µ, is a dimensionless scalar value which equals the ratio of the force of friction between two bodies and the force pressing them together, either during or at the onset of slipping. The coefficient of friction depends on the materials used; for example, ice on steel has a low coefficient of friction, while rubber on pavement has a high coefficient of friction. Coefficients of friction range from near zero to greater than one. The coefficient of friction between two surfaces of similar metals is greater than that between two surfaces of different metals; for example, brass has a higher coefficient of friction when moved against brass, but less if moved against steel or aluminum.


title: Friction

text: For surfaces at rest relative to each other, formula_23, where formula_24 is the "coefficient of static friction". This is usually larger than its kinetic counterpart. The coefficient of static friction exhibited by a pair of contacting surfaces depends upon the combined effects of material deformation characteristics and surface roughness, both of which have their origins in the chemical bonding between atoms in each of the bulk materials and between the material surfaces and any adsorbed material. The fractality of surfaces, a parameter describing the scaling behavior of surface asperities, is known to play an important role in determining the magnitude of the static friction.


title: Friction

text: For surfaces in relative motion formula_25, where formula_26 is the "coefficient of kinetic friction". The Coulomb friction is equal to formula_2, and the frictional force on each surface is exerted in the direction opposite to its motion relative to the other surface.


title: Friction

text: Arthur Morin introduced the term and demonstrated the utility of the coefficient of friction. The coefficient of friction is an empirical measurementit has to be measured experimentally, and cannot be found through calculations. Rougher surfaces tend to have higher effective values. Both static and kinetic coefficients of friction depend on the pair of surfaces in contact; for a given pair of surfaces, the coefficient of static friction is "usually" larger than that of kinetic friction; in some sets the two coefficients are equal, such as teflon-on-teflon.


title: Friction

text: Most dry materials in combination have friction coefficient values between 0.3 and 0.6. Values outside this range are rarer, but teflon, for example, can have a coefficient as low as 0.04. A value of zero would mean no friction at all, an elusive property. Rubber in contact with other surfaces can yield friction coefficients from 1 to 2. Occasionally it is maintained that "μ" is always < 1, but this is not true. While in most relevant applications "μ" < 1, a value above 1 merely implies that the force required to slide an object along the surface is greater than the normal force of the surface on the object. For example, silicone rubber or acrylic rubber-coated surfaces have a coefficient of friction that can be substantially larger than 1.


title: Friction

text: While it is often stated that the COF is a "material property," it is better categorized as a "system property." Unlike true material properties (such as conductivity, dielectric constant, yield strength), the COF for any two materials depends on system variables like temperature, velocity, atmosphere and also what are now popularly described as aging and deaging times; as well as on geometric properties of the interface between the materials, namely surface structure. For example, a copper pin sliding against a thick copper plate can have a COF that varies from 0.6 at low speeds (metal sliding against metal) to below 0.2 at high speeds when the copper surface begins to melt due to frictional heating. The latter speed, of course, does not determine the COF uniquely; if the pin diameter is increased so that the frictional heating is removed rapidly, the temperature drops, the pin remains solid and the COF rises to that of a 'low speed' test.


title: Friction

text: Under certain conditions some materials have very low friction coefficients. An example is (highly ordered pyrolytic) graphite which can have a friction coefficient below 0.01.


title: Friction

text: Static friction is friction between two or more solid objects that are not moving relative to each other. For example, static friction can prevent an object from sliding down a sloped surface. The coefficient of static friction, typically denoted as "μ", is usually higher than the coefficient of kinetic friction. Static friction is considered to arise as the result of surface roughness features across multiple length scales at solid surfaces. These features, known as asperities are present down to nano-scale dimensions and result in true solid to solid contact existing only at a limited number of points accounting for only a fraction of the apparent or nominal contact area. The linearity between applied load and true contact area, arising from asperity deformation, gives rise to the linearity between static frictional force and normal force, found for typical Amonton–Coulomb type friction.


title: Friction

text: The static friction force must be overcome by an applied force before an object can move. The maximum possible friction force between two surfaces before sliding begins is the product of the coefficient of static friction and the normal force: formula_28. When there is no sliding occurring, the friction force can have any value from zero up to formula_29. Any force smaller than formula_29 attempting to slide one surface over the other is opposed by a frictional force of equal magnitude and opposite direction. Any force larger than formula_29 overcomes the force of static friction and causes sliding to occur. The instant sliding occurs, static friction is no longer applicable—the friction between the two surfaces is then called kinetic friction. However, an apparent static friction can be observed even in the case when the true static friction is zero.


title: Friction

text: An example of static friction is the force that prevents a car wheel from slipping as it rolls on the ground. Even though the wheel is in motion, the patch of the tire in contact with the ground is stationary relative to the ground, so it is static rather than kinetic friction. Upon slipping, the wheel friction changes to kinetic friction. An anti-lock braking system operates on the principle of allowing a locked wheel to resume rotating so that the car maintains static friction.


title: Friction

text: The maximum value of static friction, when motion is impending, is sometimes referred to as limiting friction,


title: Friction

text: Kinetic friction, also known as dynamic friction or sliding friction, occurs when two objects are moving relative to each other and rub together (like a sled on the ground). The coefficient of kinetic friction is typically denoted as "μ", and is usually less than the coefficient of static friction for the same materials. However, Richard Feynman comments that "with dry metals it is very hard to show any difference."


title: Friction

text: The friction force between two surfaces after sliding begins is the product of the coefficient of kinetic friction and the normal force: formula_32. This is responsible for the Coulomb damping of an oscillating or vibrating system.


title: Friction

text: New models are beginning to show how kinetic friction can be greater than static friction. Kinetic friction is now understood, in many cases, to be primarily caused by chemical bonding between the surfaces, rather than interlocking asperities; however, in many other cases roughness effects are dominant, for example in rubber to road friction. Surface roughness and contact area affect kinetic friction for micro- and nano-scale objects where surface area forces dominate inertial forces.


title: Friction

text: The origin of kinetic friction at nanoscale can be explained by thermodynamics. Upon sliding, new surface forms at the back of a sliding true contact, and existing surface disappears at the front of it. Since all surfaces involve the thermodynamic surface energy, work must be spent in creating the new surface, and energy is released as heat in removing the surface. Thus, a force is required to move the back of the contact, and frictional heat is released at the front.


title: Friction

text: For certain applications, it is more useful to define static friction in terms of the maximum angle before which one of the items will begin sliding. This is called the "angle of friction" or "friction angle". It is defined as:


title: Friction

text: where formula_35 is the angle from horizontal and "μ" is the static coefficient of friction between the objects. This formula can also be used to calculate "μ" from empirical measurements of the friction angle.


title: Friction

text: Determining the forces required to move atoms past each other is a challenge in designing nanomachines. In 2008 scientists for the first time were able to move a single atom across a surface, and measure the forces required. Using ultrahigh vacuum and nearly zero temperature (5 K), a modified atomic force microscope was used to drag a cobalt atom, and a carbon monoxide molecule, across surfaces of copper and platinum.


title: Friction

text: The Coulomb approximation follows from the assumptions that: surfaces are in atomically close contact only over a small fraction of their overall area; that this contact area is proportional to the normal force (until saturation, which takes place when all area is in atomic contact); and that the frictional force is proportional to the applied normal force, independently of the contact area. The Coulomb approximation is fundamentally an empirical construct. It is a rule-of-thumb describing the approximate outcome of an extremely complicated physical interaction. The strength of the approximation is its simplicity and versatility. Though the relationship between normal force and frictional force is not exactly linear (and so the frictional force is not entirely independent of the contact area of the surfaces), the Coulomb approximation is an adequate representation of friction for the analysis of many physical systems.


title: Friction

text: When the surfaces are conjoined, Coulomb friction becomes a very poor approximation (for example, adhesive tape resists sliding even when there is no normal force, or a negative normal force). In this case, the frictional force may depend strongly on the area of contact. Some drag racing tires are adhesive for this reason. However, despite the complexity of the fundamental physics behind friction, the relationships are accurate enough to be useful in many applications.


title: Friction

text: , a single study has demonstrated the potential for an "effectively negative coefficient of friction in the low-load regime", meaning that a decrease in normal force leads to an increase in friction. This contradicts everyday experience in which an increase in normal force leads to an increase in friction. This was reported in the journal "Nature" in October 2012 and involved the friction encountered by an atomic force microscope stylus when dragged across a graphene sheet in the presence of graphene-adsorbed oxygen.


title: Friction

text: Despite being a simplified model of friction, the Coulomb model is useful in many numerical simulation applications such as multibody systems and granular material. Even its most simple expression encapsulates the fundamental effects of sticking and sliding which are required in many applied cases, although specific algorithms have to be designed in order to efficiently numerically integrate mechanical systems with Coulomb friction and bilateral or unilateral contact. Some quite nonlinear effects, such as the so-called Painlevé paradoxes, may be encountered with Coulomb friction.


title: Friction

text: Dry friction can induce several types of instabilities in mechanical systems which display a stable behaviour in the absence of friction.


title: Friction

text: These instabilities may be caused by the decrease of the friction force with an increasing velocity of sliding, by material expansion due to heat generation during friction (the thermo-elastic instabilities), or by pure dynamic effects of sliding of two elastic materials (the Adams–Martins instabilities). The latter were originally discovered in 1995 by George G. Adams and João Arménio Correia Martins for smooth surfaces and were later found in periodic rough surfaces. In particular, friction-related dynamical instabilities are thought to be responsible for brake squeal and the 'song' of a glass harp, phenomena which involve stick and slip, modelled as a drop of friction coefficient with velocity.


title: Friction

text: A practically important case is the self-oscillation of the strings of bowed instruments such as the violin, cello, hurdy-gurdy, erhu, etc.


title: Friction

text: A connection between dry friction and flutter instability in a simple mechanical system has been discovered, watch the movie for more details.


title: Friction

text: Frictional instabilities can lead to the formation of new self-organized patterns (or "secondary structures") at the sliding interface, such as in-situ formed tribofilms which are utilized for the reduction of friction and wear in so-called self-lubricating materials.


title: Friction

text: Fluid friction occurs between fluid layers that are moving relative to each other. This internal resistance to flow is named "viscosity". In everyday terms, the viscosity of a fluid is described as its "thickness". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. The less viscous the fluid, the greater its ease of deformation or movement.


title: Friction

text: All real fluids (except superfluids) offer some resistance to shearing and therefore are viscous. For teaching and explanatory purposes it is helpful to use the concept of an inviscid fluid or an ideal fluid which offers no resistance to shearing and so is not viscous.


title: Friction

text: Lubricated friction is a case of fluid friction where a fluid separates two solid surfaces. Lubrication is a technique employed to reduce wear of one or both surfaces in close proximity moving relative to each another by interposing a substance called a lubricant between the surfaces.


title: Friction

text: In most cases the applied load is carried by pressure generated within the fluid due to the frictional viscous resistance to motion of the lubricating fluid between the surfaces. Adequate lubrication allows smooth continuous operation of equipment, with only mild wear, and without excessive stresses or seizures at bearings. When lubrication breaks down, metal or other components can rub destructively over each other, causing heat and possibly damage or failure.


title: Friction

text: Skin friction arises from the interaction between the fluid and the skin of the body, and is directly related to the area of the surface of the body that is in contact with the fluid. Skin friction follows the drag equation and rises with the square of the velocity.


title: Friction

text: Skin friction is caused by viscous drag in the boundary layer around the object. There are two ways to decrease skin friction: the first is to shape the moving body so that smooth flow is possible, like an airfoil. The second method is to decrease the length and cross-section of the moving object as much as is practicable.


title: Friction

text: Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation.


title: Friction

text: Plastic deformation in solids is an irreversible change in the internal molecular structure of an object. This change may be due to either (or both) an applied force or a change in temperature. The change of an object's shape is called strain. The force causing it is called stress.


title: Friction

text: Elastic deformation in solids is reversible change in the internal molecular structure of an object. Stress does not necessarily cause permanent change. As deformation occurs, internal forces oppose the applied force. If the applied stress is not too large these opposing forces may completely resist the applied force, allowing the object to assume a new equilibrium state and to return to its original shape when the force is removed. This is known as elastic deformation or elasticity.


title: Friction

text: As a consequence of light pressure, Einstein in 1909 predicted the existence of "radiation friction" which would oppose the movement of matter. He wrote, "radiation will exert pressure on both sides of the plate. The forces of pressure exerted on the two sides are equal if the plate is at rest. However, if it is in motion, more radiation will be reflected on the surface that is ahead during the motion (front surface) than on the back surface. The backward-acting force of pressure exerted on the front surface is thus larger than the force of pressure acting on the back. Hence, as the resultant of the two forces, there remains a force that counteracts the motion of the plate and that increases with the velocity of the plate. We will call this resultant 'radiation friction' in brief."


title: Friction

text: Rolling resistance is the force that resists the rolling of a wheel or other circular object along a surface caused by deformations in the object or surface. Generally the force of rolling resistance is less than that associated with kinetic friction. Typical values for the coefficient of rolling resistance are 0.001.


title: Friction

text: One of the most common examples of rolling resistance is the movement of motor vehicle tires on a road, a process which generates heat and sound as by-products.


title: Friction

text: Any wheel equipped with a brake is capable of generating a large retarding force, usually for the purpose of slowing and stopping a vehicle or piece of rotating machinery. Braking friction differs from rolling friction because the coefficient of friction for rolling friction is small whereas the coefficient of friction for braking friction is designed to be large by choice of materials for brake pads.


title: Friction

text: Rubbing dissimilar materials against one another can cause a build-up of electrostatic charge, which can be hazardous if flammable gases or vapours are present. When the static build-up discharges, explosions can be caused by ignition of the flammable mixture.


title: Friction

text: Belt friction is a physical property observed from the forces acting on a belt wrapped around a pulley, when one end is being pulled. The resulting tension, which acts on both ends of the belt, can be modeled by the belt friction equation.


title: Friction

text: In practice, the theoretical tension acting on the belt or rope calculated by the belt friction equation can be compared to the maximum tension the belt can support. This helps a designer of such a rig to know how many times the belt or rope must be wrapped around the pulley to prevent it from slipping. Mountain climbers and sailing crews demonstrate a standard knowledge of belt friction when accomplishing basic tasks.


title: Friction

text: Devices such as wheels, ball bearings, roller bearings, and air cushion or other types of fluid bearings can change sliding friction into a much smaller type of rolling friction.


title: Friction

text: Many thermoplastic materials such as nylon, HDPE and PTFE are commonly used in low friction bearings. They are especially useful because the coefficient of friction falls with increasing imposed load. For improved wear resistance, very high molecular weight grades are usually specified for heavy duty or critical bearings.


title: Friction

text: A common way to reduce friction is by using a lubricant, such as oil, water, or grease, which is placed between the two surfaces, often dramatically lessening the coefficient of friction. The science of friction and lubrication is called tribology. Lubricant technology is when lubricants are mixed with the application of science, especially to industrial or commercial objectives.


title: Friction

text: Superlubricity, a recently discovered effect, has been observed in graphite: it is the substantial decrease of friction between two sliding objects, approaching zero levels. A very small amount of frictional energy would still be dissipated.


title: Friction

text: Lubricants to overcome friction need not always be thin, turbulent fluids or powdery solids such as graphite and talc; acoustic lubrication actually uses sound as a lubricant.


title: Friction

text: Another way to reduce friction between two parts is to superimpose micro-scale vibration to one of the parts. This can be sinusoidal vibration as used in ultrasound-assisted cutting or vibration noise, known as dither.


title: Friction

text: According to the law of conservation of energy, no energy is destroyed due to friction, though it may be lost to the system of concern. Energy is transformed from other forms into thermal energy. A sliding hockey puck comes to rest because friction converts its kinetic energy into heat which raises the thermal energy of the puck and the ice surface. Since heat quickly dissipates, many early philosophers, including Aristotle, wrongly concluded that moving objects lose energy without a driving force.


title: Friction

text: When an object is pushed along a surface along a path C, the energy converted to heat is given by a line integral, in accordance with the definition of work


title: Friction

text: Energy lost to a system as a result of friction is a classic example of thermodynamic irreversibility.


title: Friction

text: In the reference frame of the interface between two surfaces, static friction does "no" work, because there is never displacement between the surfaces. In the same reference frame, kinetic friction is always in the direction opposite the motion, and does "negative" work. However, friction can do "positive" work in certain frames of reference. One can see this by placing a heavy box on a rug, then pulling on the rug quickly. In this case, the box slides backwards relative to the rug, but moves forward relative to the frame of reference in which the floor is stationary. Thus, the kinetic friction between the box and rug accelerates the box in the same direction that the box moves, doing "positive" work.


title: Friction

text: The work done by friction can translate into deformation, wear, and heat that can affect the contact surface properties (even the coefficient of friction between the surfaces). This can be beneficial as in polishing. The work of friction is used to mix and join materials such as in the process of friction welding. Excessive erosion or wear of mating sliding surfaces occurs when work due to frictional forces rise to unacceptable levels. Harder corrosion particles caught between mating surfaces in relative motion (fretting) exacerbates wear of frictional forces. As surfaces are worn by work due to friction, fit and surface finish of an object may degrade until it no longer functions properly. For example, bearing seizure or failure may result from excessive wear due to work of friction.


title: Flag

text: A flag is a piece of fabric (most often rectangular or quadrilateral) with a distinctive design and colours. It is used as a symbol, a signalling device, or for decoration. The term "flag" is also used to refer to the graphic design employed, and flags have evolved into a general tool for rudimentary signalling and identification, especially in environments where communication is challenging (such as the maritime environment, where semaphore is used). Many flags fall into groups of similar designs called flag families. The study of flags is known as "vexillology" from the Latin , meaning "flag" or "banner".


title: Flag

text: National flags are patriotic symbols with widely varied interpretations that often include strong military associations because of their original and ongoing use for that purpose. Flags are also used in messaging, advertising, or for decorative purposes.


title: Flag

text: Some military units are called "flags" after their use of flags. A "flag" (Arabic: ) is equivalent to a brigade in Arab countries. In Spain, a "flag" (Spanish: "") is a battalion-equivalent in the Spanish Legion.


title: Flag

text: Ships with vexilloids were represented on predynastic Egyptian pottery . In antiquity, field signs or standards that can be categorised as vexilloid or "flag-like" were used in warfare, which originated in ancient Egypt or Assyria. Examples include the Sassanid battle standard Derafsh Kaviani, and the standards of the Roman legions such as the eagle of Augustus Caesar's Xth legion and the dragon standard of the Sarmatians; the latter was allowed to fly freely in the wind, carried by a horseman, but depictions suggest that it bore more similarity to an elongated dragon kite than to a simple flag.


title: Flag

text: While the origin of the flag remains a mystery, the oldest flag discovered is actually made of bronze and is called a Derafsh or 'flag-like' Shahdad, which was found in Shahdad, Iran, and dates back to c. 2400 BCE. It features a seated man and a kneeling woman facing each other, with a star in between. This iconography can be found in other Bronze Age pieces of art in the area as well.


title: Flag

text: Flags as recognized today, made of a piece of cloth representing a particular entity, were almost certainly the invention of the ancient peoples of the Indian subcontinent or the Zhou dynasty of Ancient China. Chinese flags had devices such as a red bird, a white tiger, or a blue dragon, and royal flags were to be treated with a level of respect similar to that given to the ruler. Indian flags were often triangular and decorated with attachments such as a yak's tail and the state umbrella. Silk flags spread to the Near East from China or it was simply the silk which made the journey to be fashioned by people who had independently arrived at the idea of rectangle clothed attached to a pole. Flags were probably transmitted to Europe via the Muslim world, where plainly coloured flags were being used due to Islamic proscriptions. They are often mentioned in the early history of Islam and may have been copied from India.


title: Flag

text: In Europe, during the High Middle Ages, flags came to be used primarily as a heraldic device in battle, allowing more easily to identify a knight than only from the heraldic device painted on the shield. Already during the high medieval period, and increasingly during the Late Middle Ages, city states and communes such as those of the Old Swiss Confederacy also began to use flags as field signs. Regimental flags for individual units became commonplace during the Early Modern period.


title: Flag

text: During the peak of the age of sail, beginning in the early 17th century, it was customary (and later a legal requirement) for ships to fly flags designating their nationality; these flags eventually evolved into the national flags and maritime flags of today. Flags also became the preferred means of communications at sea, resulting in various systems of flag signals; "see, International maritime signal flags".


title: Flag

text: Use of flags outside of military or naval context begins only with the rise of nationalist sentiment by the end of the 18th century, although some flags date back earlier. The flags of countries such as Austria, Denmark or Turkey emerged from the midst of legend while many others, including those of Poland and Switzerland, grew out of the heraldic emblems of the Middle Ages. The 17th century saw the birth of several national flags through revolutionary struggle. One of these was the flag of the Netherlands, which appeared during the 80-year Dutch rebellion which began in 1568 against Spanish domination.


title: Flag

text: Political change and social reform, allied to a growing sense of nationhood among ordinary people, led to the birth of new nations and flags all over the world in the 19th and 20th centuries.


title: Flag

text: One of the most popular uses of a flag is to symbolise a nation or country. Some national flags have been particularly inspirational to other nations, countries, or subnational entities in the design of their own flags. Some prominent examples include:


title: Flag

text: A "civil" flag is a version of the national flag that is flown by civilians on non-government installations or craft. The use of civil flags was more common in the past, in order to denote buildings or ships that were not crewed by the military. In some countries the civil flag is the same as the war flag or state flag, but without the coat of arms, such as in the case of Spain, and in others it's an alteration of the war flag.


title: Flag

text: Several countries, including the British Army and the Royal Navy (White Ensign) of the United Kingdom (Great Britain) and the Soviet Union have had unique flags flown by their armed forces separately, rather than the national flag.


title: Flag

text: Other countries' armed forces (such as those of the United States or Switzerland) use their standard national flag, in addition, the U.S. has alongside flags and seals designed from long tradition for each of its six uniformed military services/military sub-departments in the U.S. Department of Defense and the U.S. Department of Homeland Security. The Philippines' armed forces may use their standard national flag, but during times of war the flag is turned upside down. Bulgaria's flag is also turned upside down during times of war. These are also considered war flags, though the terminology only applies to the flag's military usage.


title: Flag

text: Large versions of the war flag flown on the warships of countries' navies are known as battle ensigns. In addition besides flying the national standard or a military services' emblem flag at a military fort, base, station or post and at sea at the stern (rear) or main top mast of a warship, a Naval Jack flag and other Maritime flags, pennants and emblems are flown at the bow (front). In times of war waving a white flag is a banner of truce, talks/negotiations or surrender.


title: Flag

text: Four distinctive African flags currently in the collection of the National Maritime Museum in Britain were flown in action by Itsekiri ships under the control of Nana Olomu during the conflict in the late 19th century. One is the flag generally known as the Benin Empire flag and one is referred to as Nana Olomu's flag.


title: Flag

text: Among international flags are the Flag of the United Nations, the Olympic flag, flag of NATO and the Paralympic flag.


title: Flag

text: Flags are particularly important at sea, where they can mean the difference between life and death, and consequently where the rules and regulations for the flying of flags are strictly enforced. A national flag flown at sea is known as an ensign. A courteous, peaceable merchant ship or yacht customarily flies its ensign (in the usual ensign position), together with the flag of whatever nation it is currently visiting at the mast (known as a courtesy flag). To fly one's ensign alone in foreign waters, a foreign port or in the face of a foreign warship traditionally indicates a willingness to fight, with cannon, for the right to do so. As of 2009, this custom is still taken seriously by many naval and port authorities and is readily enforced in many parts of the world by boarding, confiscation and other civil penalties. In some countries yacht ensigns are different from merchant ensigns in order to signal that the yacht is not carrying cargo that requires a customs declaration. Carrying commercial cargo on a boat with a yacht ensign is deemed to be smuggling in many jurisdictions. Traditionally, a vessel flying under the courtesy flag of a specific nation, regardless of the vessel's country of registry, is considered to be operating under the law of her 'host' nation.


title: Flag

text: There is a system of international maritime signal flags for numerals and letters of the alphabet. Each flag or pennant has a specific meaning when flown individually. As well, semaphore flags can be used to communicate on an "ad hoc" basis from ship to ship over short distances.


title: Flag

text: Another category of maritime flag flown by some United States Government ships is the distinctive mark. Although the United States Coast Guard has its own service ensign, all other U.S. Government ships fly the national ensign their service ensign, following United States Navy practice. To distinguish themselves from ships of the Navy, such ships historically have flown their parent organisation's flag from a forward mast as a distinctive mark. Today, for example, commissioned ships of the National Oceanic and Atmospheric Administration (NOAA) fly the NOAA flag as a distinctive mark.


title: Flag

text: Flags are usually rectangular in shape (often in the ratio 2:3, 1:2, or 3:5), but may be of any shape or size that is practical for flying, including square, triangular, or swallow tailed. A more unusual flag shape is that of the flag of Nepal, which is in the shape of two stacked triangles. Other unusually shaped flags include the civil flags of Ohio (a swallowtail); Tampa, Florida; and Pike County, Ohio.


title: Flag

text: Many flags are dyed through and through to be inexpensive to manufacture, such that the reverse side is the mirror image of the obverse (front) side, generally the side displayed when, from the observer's point of view, the flag flies from pole-side left to right. This presents two possibilities:


title: Flag

text: Some complex flag designs are not intended to be shown on both sides, requiring separate obverse and reverse sides if made correctly. In these cases there is a design element (usually text) which is not symmetric and should be read in the same direction, regardless of whether the hoist is to the viewer's left or right. These cases can be divided into two types:


title: Flag

text: Common designs on flags include crosses, stripes, and divisions of the surface, or "field", into bands or quarters—patterns and principles mainly derived from heraldry. A heraldic coat of arms may also be flown as a banner of arms, as is done on both the state flag of Maryland and the flag of Kiribati.


title: Flag

text: The "de jure" flag of Libya under Muammar Gaddafi, which consisted of a rectangular field of green, was for a long period the only national flag using a single colour and no design or insignia. However, other historical states have also used flags without designs or insignia, such as the short-lived Soviet Republic of Hungary and the more recent Sultanate of Muscat and Oman, whose flags were both a plain field of red.


title: Flag

text: Colours are normally described with common names, such as "red", but may be further specified using colourimetry.


title: Flag

text: The largest flag flown from a flagpole worldwide, according to Guinness World Records, is the flag of the United Arab Emirates flown in Sharjah. This flag was . The largest flag ever made was the flag of Qatar; the flag, which measures at , was completed in December 2013 in Doha.


title: Flag

text: The general parts of a flag are: canton (the upper inner section of the flag), field or ground (the entire flag except the canton), the hoist (the edge used to attach the flag to the hoist), and the fly (the furthest edge from the hoist end).


title: Flag

text: Vertical flags are sometimes used in lieu of the standard horizontal flag in central and eastern Europe, particularly in the German-speaking countries. This practice came about because the relatively brisk wind needed to display horizontal flags is not common in these countries.


title: Flag

text: The standard horizontal flag (no. 1 in the preceding illustration) is nonetheless the form most often used even in these countries.


title: Flag

text: The vertical flag (German: "Hochformatflagge" or "Knatterflagge"; no. 2) is a vertical form of the standard flag. The flag's design may remain unchanged (No. 2a) or it may change, e.g. by changing horizontal stripes to vertical ones (no. 2b). If the flag carries an emblem, it may remain centred or may be shifted slightly upwards.


title: Flag

text: The vertical flag for hoisting from a beam (German: "Auslegerflagge" or "Galgenflagge"; no. 3) is additionally attached to a horizontal beam, ensuring that it is fully displayed even if there is no wind.


title: Flag

text: The vertical flag for hoisting from a horizontal pole (German: "Hängeflagge"; no. 4) is hoisted from a horizontal pole, normally attached to a building. The topmost stripe on the horizontal version of the flag faces away from the building.


title: Flag

text: The vertical flag for hoisting from a crossbar or banner (German: "Bannerflagge"; no. 5) is firmly attached to a horizontal crossbar from which it is hoisted, either by a vertical pole (no. 5a) or a horizontal one (no. 5b). The topmost stripe on the horizontal version of the flag normally faces to the left.


title: Flag

text: Flags can play many different roles in religion. In Buddhism, prayer flags are used, usually in sets of five differently coloured flags. Several flags and banners including the Black Standard are associated with Islam. Many national flags and other flags include religious symbols such as the cross, the crescent, or a reference to a patron saint. Flags are also adopted by religious groups and flags such as the Jain flag, Nishan Sahib (Sikhism), the Saffron flag (Hindu) and the Christian flag are used to represent a whole religion.


title: Flag

text: Some countries use diplomatic flags, such as the United Kingdom (see ) and the Kingdom of Thailand (see ).


title: Flag

text: The socialist movement uses red flags to represent their cause. The anarchist movement has a variety of different flags, but the primary flag associated with them is the black flag. In the Spanish civil war, the anarchists used the red-and-black bisected flag. In the 20th century, the rainbow flag was adopted as a symbol of the LGBT social movements. Its derivatives include the Bisexual pride and Transgender pride flags.


title: Flag

text: Some of these political flags have become national flags, such as the red flag of the Soviet Union and national socialist banners for Nazi Germany. The present Flag of Portugal is based on what had been the political flag of the Portuguese Republican Party previous to the 5 October 1910 revolution which brought this party to power.


title: Flag

text: Throughout history, monarchs have often had personal flags (including royal standards), representing the royal person, including in personal union of national monarchies.


title: Flag

text: Flags are often representative of an individual's affinity or allegiance to a country, team or business and can be presented in various ways. A popular trend that has surfaced revolves around the idea of the 'mobile' flag in which an individual displays their particular flag of choice on their vehicle. These items are commonly referred to as car flags and are usually manufactured from high strength polyester material and are attached to a vehicle via a polypropylene pole and clip window attachment.


title: Flag

text: In Australia, Canada, New Zealand, the Philippines, Ireland and the United Kingdom, a pair of red-yellow flags is used to mark the limits of the bathing area on a beach, usually guarded by surf lifesavers. If the beach is closed, the poles of the flags are crossed. The flags are coloured with a red triangle and a yellow triangle making a rectangular flag, or a red rectangle over a yellow rectangle. On many Australian beaches there is a slight variation with beach condition signalling. A red flag signifies a closed beach (in the UK also other dangers), yellow signifies strong current or difficult swimming conditions, and green represents a beach safe for general swimming. In Ireland, a red and yellow flag indicates that it is safe to swim; a red flag that it is unsafe; and no flag indicates that there are no lifeguards on duty. Blue flags may also be used away from the yellow-red lifesaver area to designate a zone for surfboarding and other small, non-motorised watercraft.


title: Flag

text: A surf flag exists, divided into four quadrants. The top left and bottom right quadrants are black, and the remaining area is white.


title: Flag

text: Signal flag "India" (a black circle on a yellow square) is frequently used to denote a "blackball" zone where surfboards cannot be used but other water activities are permitted.


title: Flag

text: Railways use a number of coloured flags. When used as wayside signals they usually use the following meanings (exact meanings are set by the individual railroad company):


title: Flag

text: Flags displayed on the front of a moving locomotive are an acceptable replacement for classification lights and usually have the following meanings (exact meanings are set by the individual railroad company):


title: Flag

text: Additionally, a railroad brakeman will typically carry a red flag to make his or her hand signals more visible to the engineer. Railway signals are a development of railway flags.


title: Flag

text: A flagpole, flagmast, flagstaff, or staff can be a simple support made of wood or metal. If it is taller than can be easily reached to raise the flag, a cord is used, looping around a pulley at the top of the pole with the ends tied at the bottom. The flag is fixed to one lower end of the cord, and is then raised by pulling on the other end. The cord is then tightened and tied to the pole at the bottom. The pole is usually topped by a flat plate or ball called a "truck" (originally meant to keep a wooden pole from splitting) or a finial in a more complex shape. Very high flagpoles may require more complex support structures than a simple pole, such as a guyed mast.


title: Flag

text: Since 26 December 2021, the tallest free-standing flagpole in the world is the Cairo Flagpole, located in the New Administrative Capital under construction in Egypt at a height of , exceeding the former record holders, the Jeddah Flagpole in Saudi Arabia (height: ), the Dushanbe Flagpole in Tajikistan (height: ) and the National Flagpole in Azerbaijan (height: ). The flagpole in North Korea is the fourth tallest flagpole in the world, however, it is not free-standing. It is a radio tower supported flagpole. Many of these were built by American company Trident Support: the Dushanbe Flagpole, the National Flagpole in Azerbaijan, the Ashgabat flagpole in Turkmenistan at ; the Aqaba Flagpole in Jordan at ; the Raghadan Flagpole in Jordan at ; and the Abu Dhabi Flagpole in the United Arab Emirates at .


title: Flag

text: The current tallest flagpole in India (and the tallest flying the tricolour) is the flagpole in Belgaum, Karnataka which was first hoisted on 12 March 2018. The tallest flagpole in the United Kingdom from 1959 until 2013 stood in Kew Gardens. It was made from a Canadian Douglas-fir tree and was in height.


title: Flag

text: The current tallest flagpole in the United States (and the tallest flying an American flag) is the pole completed before Memorial Day 2014 and custom-made with an base in concrete by wind turbine manufacturer Broadwind Energy. It is situated on the north side of the Acuity Insurance headquarters campus along Interstate 43 in Sheboygan, Wisconsin, and is visible from Cedar Grove. The pole can fly a 220-pound flag for in light wind conditions and a heavier 350-pound flag in higher wind conditions.


title: Flag

text: Flagpoles can be designed in one piece with a taper (typically a steel taper or a Greek entasis taper), or be made from multiple pieces to make them able to expand. In the United States, ANSI/NAAMM guide specification FP-1001-97 covers the engineering design of metal flagpoles to ensure safety.


title: Flag

text: Hoisting the flag is the act of raising the flag on the flagpole. Raising or lowering flags, especially national flags, usually involves ceremonies and certain sets of rules, depending on the country, and usually involve the performance of a national anthem.


title: Flag

text: A flag-raising squad is a group of people, usually troops, cadets, or students, that march in and bring the flags for the flag-hoisting ceremony. Flag-hoisting ceremonies involving flag-raising squads can be simple or elaborate, involving large numbers of squads. Elaborate flag-hoisting ceremonies are usually performed on national holidays.


title: Flag

text: The cord or rope that ties a flag to its pole is called a halyard. Flags may have a strip of fabric along the hoist side called a "heading" for the halyard to pass through, or a pair of grommets for the halyard to be threaded through. Flags may also be held in position using Inglefield clips.


title: Flag

text: Semaphore is a form of communication that utilises flags. The signalling is performed by an individual using two flags (or lighted wands), the positions of the flags indicating a symbol. The person who holds the flags is known as the signalman. This form of communication is primarily used by naval signallers. This technique of signalling was adopted in the early 19th century and is still used in various forms today.


title: Flag

text: The colours of the flags can also be used to communicate. For example; a white flag means, among other things, surrender or peace, a red flag can be used as a warning signal, and a black flag can mean war, or determination to defeat enemies.


title: Flag

text: Orientation of a flag is also used for communication, though the practice is rarely used given modern communication systems. Raising a flag upside-down was indicative that the raising force controlled that particular area, but that it was in severe distress.


title: Alcubierre drive

text: The Alcubierre drive () is a speculative warp drive idea according to which a spacecraft could achieve apparent faster-than-light travel by contracting space in front of it and expanding space behind it, under the assumption that a configurable energy-density field lower than that of vacuum (that is, negative mass) could be created. Proposed by theoretical physicist Miguel Alcubierre in 1994, the Alcubierre drive is based on a solution of Einstein's field equations. Since those solutions are metric tensors, the Alcubierre drive is also referred to as Alcubierre metric.


title: Alcubierre drive

text: Objects cannot accelerate to the speed of light within normal spacetime; instead, the Alcubierre drive shifts space around an object so that the object would arrive at its destination more quickly than light would in normal space without breaking any physical laws.


title: Alcubierre drive

text: Although the metric proposed by Alcubierre is consistent with the Einstein field equations, construction of such a drive is not necessarily possible. The proposed mechanism of the Alcubierre drive implies a negative energy density and therefore requires exotic matter or manipulation of dark energy. If exotic matter with the correct properties cannot exist, then the drive cannot be constructed. At the close of his original article, however, Alcubierre argued (following an argument developed by physicists analyzing traversable wormholes) that the Casimir vacuum between parallel plates could fulfill the negative-energy requirement for the Alcubierre drive.


title: Alcubierre drive

text: Some research has claimed that such a concept is possible with purely positive energy using 'soliton' waves.


title: Alcubierre drive

text: Another possible issue is that, although the Alcubierre metric is consistent with Einstein's equations, general relativity does not incorporate quantum mechanics. Some physicists have presented arguments to suggest that a theory of quantum gravity (which would incorporate both theories) would eliminate those solutions in general relativity that allow for backward time travel ("see" the chronology protection conjecture) and thus make the Alcubierre drive invalid.


title: Alcubierre drive

text: In 1994, Miguel Alcubierre proposed a method for changing the geometry of space by creating a wave that would cause the fabric of space ahead of a spacecraft to contract and the space behind it to expand. The ship would then ride this wave inside a region of flat space, known as a "warp bubble", and would not move within this bubble but instead be carried along as the region itself moves due to the actions of the drive. The local velocity relative to the deformed space-time would be subluminal, but the speed at which a spacecraft could move would be superluminal, thereby rendering possible interstellar flight, such as a visit to "Proxima Centauri" within a few days.


title: Alcubierre drive

text: The Alcubierre metric defines the warp-drive spacetime. It is a Lorentzian manifold that, if interpreted in the context of general relativity, allows a warp bubble to appear in previously flat spacetime and move away at effectively faster-than-light speed. The interior of the bubble is an inertial reference frame and inhabitants experience no proper acceleration. This method of transport does not involve objects in motion at faster-than-light speeds with respect to the contents of the warp bubble; that is, a light beam within the warp bubble would still always move more quickly than the ship. Because objects within the bubble are not moving (locally) more quickly than light, the mathematical formulation of the Alcubierre metric is consistent with the conventional claims of the laws of relativity (namely, that an object with mass cannot attain or exceed the speed of light) and conventional relativistic effects such as time dilation would not apply as they would with conventional motion at near-light speeds.


title: Alcubierre drive

text: An extension of the Alcubierre metric that eliminates the expansion of the volume elements and instead relies on the change in distances along the direction of travel is that of mathematician José Natário. In his metric, spacetime contracts towards the prow of the ship and expands in the direction perpendicular to the motion, meaning that the bubble actually "slides" through space, roughly speaking by "pushing space aside".


title: Alcubierre drive

text: The Alcubierre drive remains a hypothetical concept with seemingly difficult problems, though the amount of energy required is no longer thought to be unobtainably large. Furthermore, Alexey Bobrick and Gianni Martire claim that, in principle, a class of subluminal, spherically symmetric warp drive spacetimes can be constructed based on physical principles presently known to humanity, such as positive energy.


title: Alcubierre drive

text: Using the ADM formalism of general relativity, the spacetime is described by a foliation of space-like hypersurfaces of constant coordinate time , with the metric taking the following general form:


title: Alcubierre drive

text: With this particular form of the metric, it can be shown that the energy density measured by observers whose 4-velocity is normal to the hypersurfaces is given by:


title: Alcubierre drive

text: Thus, because the energy density is negative, one needs exotic matter to travel more quickly than the speed of light. The existence of exotic matter is not theoretically ruled out; however, generating and sustaining enough exotic matter to perform feats such as faster-than-light travel (and to keep open the "throat" of a wormhole) is thought to be impractical. According to writer Robert Low, within the context of general relativity it is impossible to construct a warp drive in the absence of exotic matter.


title: Alcubierre drive

text: Astrophysicist Jamie Farnes from the University of Oxford has proposed a theory, published in the peer-reviewed scientific journal "Astronomy & Astrophysics", that unifies dark energy and dark matter into a single dark fluid, and which is expected to be testable by new scientific instruments capable of being constructed by circa 2030. Farnes found that Albert Einstein had explored the idea of gravitationally repulsive negative masses while developing the equations of general relativity, an idea which leads to a "beautiful" hypothesis where the cosmos has equal amounts of positive and negative qualities. Farnes' theory relies on negative masses that behave identically to the physics of the Alcubierre drive, providing a natural solution for the current "crisis in cosmology" due to a time-variable Hubble parameter.


title: Alcubierre drive

text: As Farnes' theory allows a positive mass (i.e. a ship) to reach a speed equal to the speed of light, it has been dubbed "controversial". If the theory is correct, which has been highly debated in the scientific literature, it would explain dark energy, dark matter, allow closed timelike curves (see time travel), and suggest that an Alcubierre drive is physically possible with exotic matter.


title: Alcubierre drive

text: With regard to certain specific effects of special relativity, such as Lorentz contraction and time dilation, the Alcubierre metric has some apparently peculiar aspects. In particular, Alcubierre has shown that a ship using an Alcubierre drive travels on a free-fall geodesic even while the warp bubble is accelerating: its crew would be in free fall while accelerating without experiencing accelerational g-forces. Enormous tidal forces, however, would be present near the edges of the flat-space volume because of the large space curvature there, but a suitable specification of the metric would keep the tidal forces very small within the volume occupied by the ship.


title: Alcubierre drive

text: The original warp-drive metric and simple variants of it happen to have the ADM form, which is often used in discussing the initial-value formulation of general relativity. This might explain the widespread misconception that this spacetime is a "solution" of the field equation of general relativity. Metrics in ADM form are "adapted" to a certain family of inertial observers, but these observers are not really physically distinguished from other such families. Alcubierre interpreted his "warp bubble" in terms of a contraction of space ahead of the bubble and an expansion behind, but this interpretation could be misleading, since the contraction and expansion actually refer to the relative motion of nearby members of the family of ADM observers.


title: Alcubierre drive

text: In general relativity, one often first specifies a plausible distribution of matter and energy, and then finds the geometry of the spacetime associated with it; but it is also possible to run the Einstein field equations in the other direction, first specifying a metric and then finding the energy–momentum tensor associated with it, and this is what Alcubierre did in building his metric. This practice means that the solution can violate various energy conditions and require exotic matter. The need for exotic matter raises questions about whether one can distribute the matter in an initial spacetime that lacks a warp bubble in such a way that the bubble is created at a later time, although some physicists have proposed models of dynamical warp-drive spacetimes in which a warp bubble is formed in a previously flat space. Moreover, according to Serguei Krasnikov, generating a bubble in a previously flat space for a "one-way" FTL trip requires forcing the exotic matter to move at local faster-than-light speeds, something that would require the existence of tachyons, although Krasnikov also notes that when the spacetime is not flat from the outset, a similar result could be achieved without tachyons by placing in advance some devices along the travel path and programming them to come into operation at preassigned moments and to operate in a preassigned manner. Some suggested methods avoid the problem of tachyonic motion, but would probably generate a naked singularity at the front of the bubble. Allen Everett and Thomas Roman comment on Krasnikov's finding (Krasnikov tube):


title: Alcubierre drive

text: [The finding] does not mean that Alcubierre bubbles, if it were possible to create them, could not be used as a means of superluminal travel. It only means that the actions required to change the metric and create the bubble must be taken beforehand by some observer whose forward light cone contains the entire trajectory of the bubble.


title: Alcubierre drive

text: For example, if one wanted to travel to Deneb (2,600 light-years away) and arrive less than 2,600 years in the future according to external clocks, it would be required that someone had already begun work on warping the space from Earth to Deneb at least 2,600 years ago:


title: Alcubierre drive

text: A spaceship appropriately located with respect to the bubble trajectory could then choose to enter the bubble, rather like a passenger catching a passing trolley car, and thus make the superluminal journey ... as Krasnikov points out, causality considerations do not prevent the crew of a spaceship from arranging, by their own actions, to complete a "round trip" from Earth to a distant star and back in an arbitrarily short time, as measured by clocks on Earth, by altering the metric along the path of their outbound trip.


title: Alcubierre drive

text: The metric of this form has significant difficulties because all known warp-drive spacetime theories violate various energy conditions. Nevertheless, an Alcubierre-type warp drive might be realized by exploiting certain experimentally verified quantum phenomena, such as the Casimir effect, that lead to stress–energy tensors that also violate the energy conditions, such as negative mass–energy, when described in the context of the quantum field theories.


title: Alcubierre drive

text: If certain quantum inequalities conjectured by Ford and Roman hold, the energy requirements for some warp drives may be unfeasibly large as well as negative. For example, the energy equivalent of −10 kg might be required to transport a small spaceship across the Milky Way—an amount orders of magnitude greater than the estimated mass of the observable universe. Counterarguments to these apparent problems have also been offered, although the energy requirements still generally require a Type III civilization on the Kardashev scale.


title: Alcubierre drive

text: Chris Van Den Broeck of the Katholieke Universiteit Leuven in Belgium, in 1999, tried to address the potential issues. By contracting the 3+1-dimensional surface area of the bubble being transported by the drive, while at the same time expanding the three-dimensional volume contained inside, Van Den Broeck was able to reduce the total energy needed to transport small atoms to less than three solar masses. Later in 2003, by slightly modifying the Van den Broeck metric, Serguei Krasnikov reduced the necessary total amount of negative mass to a few milligrams. Van Den Broeck detailed this by saying that the total energy can be reduced dramatically by keeping the surface area of the warp bubble itself microscopically small, while at the same time expanding the spatial volume inside the bubble. However, Van Den Broeck concludes that the energy densities required are still unachievable, as are the small size (a few orders of magnitude above the Planck scale) of the spacetime structures needed.


title: Alcubierre drive

text: In 2012, physicist Harold White and collaborators announced that modifying the geometry of exotic matter could reduce the mass–energy requirements for a macroscopic space ship from the equivalent of the planet Jupiter to that of the Voyager 1 spacecraft (c. 700 kg) or less, and stated their intent to perform small-scale experiments in constructing warp fields. White proposed to thicken the extremely thin wall of the warp bubble, so the energy is focused in a larger volume, but the overall peak energy density is actually smaller. In a flat 2D representation, the ring of positive and negative energy, initially very thin, becomes a larger, fuzzy torus (donut shape). However, as this less energetic warp bubble also thickens toward the interior region, it leaves less flat space to house the spacecraft, which has to be smaller. Furthermore, if the intensity of the space warp can be oscillated over time, the energy required is reduced even more. According to White, a modified Michelson–Morley interferometer could test the idea: one of the legs of the interferometer would appear to have a slightly different length when the test devices were energised. Alcubierre has expressed skepticism about the experiment, saying: "from my understanding there is no way it can be done, probably not for centuries if at all".


title: Alcubierre drive

text: In 2021, physicist Erik Lentz described a way warp drives sourced from known and familiar purely positive energy could exist – warp bubbles based on superluminal self-reinforcing "soliton" waves. He also claimed that he will work on reducing the (positive) energy requirement.


title: Alcubierre drive

text: Krasnikov proposed that if tachyonic matter cannot be found or used, then a solution might be to arrange for masses along the path of the vessel to be set in motion in such a way that the required field was produced. But in this case, the Alcubierre drive vessel can only travel routes that, like a railroad, have first been equipped with the necessary infrastructure. The pilot inside the bubble is causally disconnected from its walls and cannot carry out any action outside the bubble: the bubble cannot be used for the first trip to a distant star because the pilot cannot place infrastructure ahead of the bubble while "in transit". For example, traveling to Vega (which is 25 light-years from Earth) requires arranging everything so that the bubble moving toward Vega with a superluminal velocity would appear; such arrangements will always take more than 25 years.


title: Alcubierre drive

text: Coule has argued that schemes, such as the one proposed by Alcubierre, are infeasible because matter placed "en route" of the intended path of a craft must be placed at superluminal speed—that constructing an Alcubierre drive requires an Alcubierre drive even if the metric that allows it is physically meaningful. Coule further argues that an analogous objection will apply to "any" proposed method of constructing an Alcubierre drive.


title: Alcubierre drive

text: An article by José Natário (2002) argues that crew members could not control, steer or stop the ship in its warp bubble because the ship could not send signals to the front of the bubble.


title: Alcubierre drive

text: A 2009 article by Carlos Barceló, Stefano Finazzi, and Stefano Liberati uses quantum theory to argue that the Alcubierre drive at faster-than-light velocities is impossible mostly because extremely high temperatures caused by Hawking radiation would destroy anything inside the bubble at superluminal velocities and destabilize the bubble itself; the article also argues that these problems are absent if the bubble velocity is subluminal, although the drive still requires exotic matter.


title: Alcubierre drive

text: Brendan McMonigal, Geraint F. Lewis, and Philip O'Byrne have argued that were an Alcubierre-driven ship to decelerate from superluminal speed, the particles that its bubble had gathered in transit would be released in energetic outbursts akin to the infinitely-blueshifted radiation hypothesized to occur at the inner event horizon of a Kerr black hole; forward-facing particles would thereby be energetic enough to destroy anything at the destination directly in front of the ship.


title: Alcubierre drive

text: The amount of negative energy required for such a propulsion is not yet known. Pfenning and Allen Everett of Tufts hold that a warp bubble traveling at 10-times the speed of light must have a wall thickness of no more than 10 meters—close to the limiting Planck length, 1.6 × 10 meters. In Alcubierre's original calculations, a bubble macroscopically large enough to enclose a ship of 200 meters would require a total amount of exotic matter greater than the mass of the observable universe, and straining the exotic matter to an extremely thin band of 10 meters is considered impractical. Similar constraints apply to Krasnikov's superluminal subway. Chris Van den Broeck constructed a modification of Alcubierre's model that requires much less exotic matter but places the ship in a curved space-time "bottle" whose neck is about 10 meters.


title: Alcubierre drive

text: Calculations by physicist Allen Everett show that warp bubbles could be used to create closed timelike curves in general relativity, meaning that the theory predicts that they could be used for backwards time travel. While it is possible that the fundamental laws of physics might allow closed timelike curves, the chronology protection conjecture hypothesizes that in all cases where the classical theory of general relativity allows them, quantum effects would intervene to eliminate the possibility, making these spacetimes impossible to realize. A possible type of effect that would accomplish this is a buildup of vacuum fluctuations on the border of the region of spacetime where time travel would first become possible, causing the energy density to become high enough to destroy the system that would otherwise become a time machine. Some results in semiclassical gravity appear to support the conjecture, including a calculation dealing specifically with quantum effects in warp-drive spacetimes that suggested that warp bubbles would be semiclassically unstable, but ultimately the conjecture can only be decided by a full theory of quantum gravity.


title: Alcubierre drive

text: Alcubierre briefly discusses some of these issues in a series of lecture slides posted online, where he writes: "beware: in relativity, any method to travel faster than light can in principle be used to travel back in time (a time machine)". In the next slide, he brings up the chronology protection conjecture and writes: "The conjecture has not been proven (it wouldn't be a conjecture if it had), but there are good arguments in its favor based on quantum field theory. The conjecture does not prohibit faster-than-light travel. It just states that if a method to travel faster than light exists, and one tries to use it to build a time machine, something will go wrong: the energy accumulated will explode, or it will create a black hole."


title: Alcubierre drive

text: The "Star Trek" television series and films use the term "warp drive" to describe their method of faster-than-light travel. Neither the Alcubierre theory, nor anything similar, existed when the series was conceived—the term "warp drive" and general concept originated with John W. Campbell's 1931 science fiction novel "Islands of Space". Alcubierre stated in an email to William Shatner that his theory was directly inspired by the term used in the show and cites the "'warp drive' of science fiction" in his 1994 article. A "USS Alcubierre" appears in the "Star Trek" tabletop RPG "Star Trek Adventures".


title: BASIC

text: BASIC (Beginners' All-purpose Symbolic Instruction Code) is a family of general-purpose, high-level programming languages designed for ease of use. The original version was created by John G. Kemeny and Thomas E. Kurtz at Dartmouth College in 1964. They wanted to enable students in non-scientific fields to use computers. At the time, nearly all computers required writing custom software, which only scientists and mathematicians tended to learn.


title: BASIC

text: In addition to the program language, Kemeny and Kurtz developed the Dartmouth Time Sharing System (DTSS), which allowed multiple users to edit and run BASIC programs simultaneously on remote terminals. This general model became very popular on minicomputer systems like the PDP-11 and Data General Nova in the late 1960s and early 1970s. Hewlett-Packard produced an entire computer line for this method of operation, introducing the HP2000 series in the late 1960s and continuing sales into the 1980s. Many early video games trace their history to one of these versions of BASIC.


title: BASIC

text: The emergence of microcomputers in the mid-1970s led to the development of multiple BASIC dialects, including Microsoft BASIC in 1975. Due to the tiny main memory available on these machines, often 4 KB, a variety of Tiny BASIC dialects were also created. BASIC was available for almost any system of the era, and became the "de facto" programming language for home computer systems that emerged in the late 1970s. These PCs almost always had a BASIC interpreter installed by default, often in the machine's firmware or sometimes on a ROM cartridge.


title: BASIC

text: BASIC declined in popularity in the 1990s, as more powerful microcomputers came to market and programming languages with advanced features (such as Pascal and C) became tenable on such computers. In 1991, Microsoft released Visual Basic, combining an updated version of BASIC with a visual forms builder. This reignited use of the language and "VB" remains a major programming language in the forms of VBA and VB.NET.


title: BASIC

text: John G. Kemeny was the math department chairman at Dartmouth College. Based largely on his reputation as an innovator in math teaching, in 1959 the school won an Alfred P. Sloan Foundation award for $500,000 to build a new department building. Thomas E. Kurtz had joined the department in 1956, and from the 1960s Kemeny and Kurtz agreed on the need for programming literacy among students outside the traditional STEM fields. Kemeny later noted that "Our vision was that every student on campus should have access to a computer, and any faculty member should be able to use a computer in the classroom whenever appropriate. It was as simple as that."


title: BASIC

text: Kemeny and Kurtz had made two previous experiments with simplified languages, DARSIMCO (Dartmouth Simplified Code) and DOPE (Dartmouth Oversimplified Programming Experiment). These did not progress past a single freshman class. New experiments using Fortran and ALGOL followed, but Kurtz concluded these languages were too tricky for what they desired. As Kurtz noted, Fortran had numerous oddly-formed commands, notably an "almost impossible-to-memorize convention for specifying a loop: . Is it '1, 10, 2' or '1, 2, 10', and is the comma after the line number required or not?"


title: BASIC

text: Moreover, the lack of any sort of immediate feedback was a key problem; the machines of the era used batch processing and took a long time to complete a run of a program. While Kurtz was visiting MIT, John McCarthy suggested that time-sharing offered a solution; a single machine could divide up its processing time among many users, giving them the illusion of having a (slow) computer to themselves. Small programs would return results in a few seconds. This led to increasing interest in a system using time-sharing and a new language specifically for use by non-STEM students.


title: BASIC

text: Kemeny wrote the first version of BASIC. The acronym "BASIC" comes from the name of an unpublished paper by Thomas Kurtz. The new language was heavily patterned on FORTRAN II; statements were one-to-a-line, numbers were used to indicate the target of loops and branches, and many of the commands were similar or identical to Fortran. However, the syntax was changed wherever it could be improved. For instance, the difficult to remember codice_1 loop was replaced by the much easier to remember , and the line number used in the DO was instead indicated by the codice_2. Likewise, the cryptic codice_3 statement of Fortran, whose syntax matched a particular instruction of the machine on which it was originally written, became the simpler . These changes made the language much less idiosyncratic while still having an overall structure and feel similar to the original FORTRAN.


title: BASIC

text: The project received a $300,000 grant from the National Science Foundation, which was used to purchase a GE-225 computer for processing, and a Datanet-30 realtime processor to handle the Teletype Model 33 teleprinters used for input and output. A team of a dozen undergraduates worked on the project for about a year, writing both the DTSS system and the BASIC compiler. The first version BASIC language was released on 1 May 1964.


title: BASIC

text: Initially, BASIC concentrated on supporting straightforward mathematical work, with matrix arithmetic support from its initial implementation as a batch language, and character string functionality being added by 1965. Usage in the university rapidly expanded, requiring the main CPU to be replaced by a GE-235, and still later by a GE-635. By the early 1970s there were hundreds of terminals connected to the machines at Dartmouth, some of them remotely.


title: BASIC

text: Wanting use of the language to become widespread, its designers made the compiler available free of charge. In the 1960s, software became a chargeable commodity; until then, it was provided without charge as a service with the very expensive computers, usually available only to lease. They also made it available to high schools in the Hanover, New Hampshire area and regionally throughout New England on Teletype Model 33 and Model 35 teleprinter terminals connected to Dartmouth via dial-up phone lines, and they put considerable effort into promoting the language. In the following years, as other dialects of BASIC appeared, Kemeny and Kurtz's original BASIC dialect became known as "Dartmouth BASIC".


title: BASIC

text: New Hampshire recognized the accomplishment in 2019 when it erected a highway historical marker in Hanover describing the creation of "the first user-friendly programming language".


title: BASIC

text: The emergence of BASIC took place as part of a wider movement towards time-sharing systems. First conceptualized during the late 1950s, the idea became so dominant in the computer industry by the early 1960s that its proponents were speaking of a future in which users would "buy time on the computer much the same way that the average household buys power and water from utility companies".


title: BASIC

text: General Electric, having worked on the Dartmouth project, wrote their own underlying operating system and launched an online time-sharing system known as Mark I. It featured BASIC as one of its primary selling points. Other companies in the emerging field quickly followed suit; Tymshare introduced SUPER BASIC in 1968, CompuServe had a version on the DEC-10 at their launch in 1969, and by the early 1970s BASIC was largely universal on general-purpose mainframe computers. Even IBM eventually joined the club with the introduction of VS-BASIC in 1973.


title: BASIC

text: Although time-sharing services with BASIC were successful for a time, the widespread success predicted earlier was not to be. The emergence of minicomputers during the same period, and especially low-cost microcomputers in the mid-1970s, allowed anyone to purchase and run their own systems rather than buy online time which was typically billed at dollars per minute.


title: BASIC

text: BASIC, by its very nature of being small, was naturally suited to porting to the minicomputer market, which was emerging at the same time as the time-sharing services. These machines had very small main memory, perhaps as little as 4 KB in modern terminology, and lacked high-performance storage like hard drives that make compilers practical. On these systems, BASIC was normally implemented as an interpreter rather than a compiler due to the reduced need for working memory.


title: BASIC

text: A particularly important example was HP Time-Shared BASIC, which, like the original Dartmouth system, used two computers working together to implement a time-sharing system. The first, a low-end machine in the HP 2100 series, was used to control user input and save and load their programs to tape or disk. The other, a high-end version of the same underlying machine, ran the programs and generated output. For a cost of about $100,000, one could own a machine capable of running between 16 and 32 users at the same time. The system, bundled as the HP 2000, was the first mini platform to offer time-sharing and was an immediate runaway success, catapulting HP to become the third-largest vendor in the minicomputer space, behind DEC and Data General (DG).


title: BASIC

text: DEC, the leader in the minicomputer space since the mid-1960s, had initially ignored BASIC. This was due to their work with RAND Corporation, who had purchased a PDP-6 to run their JOSS language, which was conceptually very similar to BASIC. This led DEC to introduce a smaller, cleaned up version of JOSS known as FOCAL, which they heavily promoted in the late 1960s. However, with timesharing systems widely offering BASIC, and all of their competition in the minicomputer space doing the same, DEC's customers were clamoring for BASIC. After management repeatedly ignored their pleas, David H. Ahl took it upon himself to buy a BASIC for the PDP-8, which was a major success in the education market. By the early 1970s, FOCAL and JOSS had been forgotten and BASIC had become almost universal in the minicomputer market. DEC would go on to introduce their updated version, BASIC-PLUS, for use on the RSTS/E time-sharing operating system.


title: BASIC

text: During this period a number of simple text-based games were written in BASIC, most notably Mike Mayfield's "Star Trek". David Ahl collected these, some ported from FOCAL, and published them in an educational newsletter he compiled. He later collected a number of these into book form, "101 BASIC Computer Games", published in 1973. During the same period, Ahl was involved in the creation of a small computer for education use, an early personal computer. When management refused to support the concept, Ahl left DEC in 1974 to found the seminal computer magazine, "Creative Computing". The book remained popular, and was re-published on several occasions.


title: BASIC

text: The introduction of the first microcomputers in the mid-1970s was the start of explosive growth for BASIC. It had the advantage that it was fairly well known to the young designers and computer hobbyists who took an interest in microcomputers, many of whom had seen BASIC on minis or mainframes. Despite Dijkstra's famous judgement in 1975, "It is practically impossible to teach good programming to students that have had a prior exposure to BASIC: as potential programmers they are mentally mutilated beyond hope of regeneration", BASIC was one of the few languages that was both high-level enough to be usable by those without training and small enough to fit into the microcomputers of the day, making it the "de facto" standard programming language on early microcomputers.


title: BASIC

text: The first microcomputer version of BASIC was co-written by Bill Gates, Paul Allen and Monte Davidoff for their newly formed company, Micro-Soft. This was released by MITS in punch tape format for the Altair 8800 shortly after the machine itself, immediately cementing BASIC as the primary language of early microcomputers. Members of the Homebrew Computer Club began circulating copies of the program, causing Gates to write his Open Letter to Hobbyists, complaining about this early example of software piracy.


title: BASIC

text: Partially in response to Gates's letter, and partially to make an even smaller BASIC that would run usefully on 4 KB machines, Bob Albrecht urged Dennis Allison to write their own variation of the language. How to design and implement a stripped-down version of an interpreter for the BASIC language was covered in articles by Allison in the first three quarterly issues of the "People's Computer Company" newsletter published in 1975 and implementations with source code published in "". This led to a wide variety of Tiny BASICs with added features or other improvements, with versions from Tom Pittman and Li-Chen Wang becoming particularly well known.


title: BASIC

text: Micro-Soft, by this time Microsoft, ported their interpreter for the MOS 6502, which quickly become one of the most popular microprocessors of the 8-bit era. When new microcomputers began to appear, notably the "1977 trinity" of the TRS-80, Commodore PET and Apple II, they either included a version of the MS code, or quickly introduced new models with it. By 1978, MS BASIC was a "de facto" standard and practically every home computer of the 1980s included it in ROM. Upon boot, a BASIC interpreter in direct mode was presented.


title: BASIC

text: Commodore Business Machines included Commodore BASIC, based on Microsoft BASIC. The Apple II and TRS-80 each had two versions of BASIC, a smaller introductory version introduced with the initial releases of the machines and an MS-based version introduced as interest in the platforms increased. As new companies entered the field, additional versions were added that subtly changed the BASIC family. The Atari 8-bit family had its own Atari BASIC that was modified in order to fit on an 8 KB ROM cartridge. Sinclair BASIC was introduced in 1980 with the Sinclair ZX80, and was later extended for the Sinclair ZX81 and the Sinclair ZX Spectrum. The BBC published BBC BASIC, developed by Acorn Computers Ltd, incorporating many extra structured programming keywords and advanced floating-point operation features.


title: BASIC

text: As the popularity of BASIC grew in this period, computer magazines published complete source code in BASIC for video games, utilities, and other programs. Given BASIC's straightforward nature, it was a simple matter to type in the code from the magazine and execute the program. Different magazines were published featuring programs for specific computers, though some BASIC programs were considered universal and could be used in machines running any variant of BASIC (sometimes with minor adaptations). Many books of type-in programs were also available, and in particular, Ahl published versions of the original 101 BASIC games converted into the Microsoft dialect and published it from "Creative Computing" as "BASIC Computer Games". This book, and its sequels, provided hundreds of ready-to-go programs that could be easily converted to practically any BASIC-running platform. The book reached the stores in 1978, just as the home computer market was starting off, and it became the first million-selling computer book. Later packages, such as Learn to Program BASIC would also have gaming as an introductory focus. On the business-focused CP/M computers which soon became widespread in small business environments, Microsoft BASIC (MBASIC) was one of the leading applications.


title: BASIC

text: In 1978, David Lien published the first edition of "The BASIC Handbook: An Encyclopedia of the BASIC Computer Language", documenting keywords across over 78 different computers. By 1981, the second edition documented keywords from over 250 different computers, showcasing the explosive growth of the microcomputer era.


title: BASIC

text: When IBM was designing the IBM PC, they followed the paradigm of existing home computers in wanting to have a built-in BASIC. They sourced this from Microsoft – IBM Cassette BASIC – but Microsoft also produced several other versions of BASIC for MS-DOS/PC DOS including IBM Disk BASIC (BASIC D), IBM BASICA (BASIC A), GW-BASIC (a BASICA-compatible version that did not need IBM's ROM) and QBasic, all typically bundled with the machine. In addition they produced the Microsoft BASIC Compiler aimed at professional programmers. Turbo Pascal-publisher Borland published Turbo Basic 1.0 in 1985 (successor versions are still being marketed by the original author under the name PowerBASIC). Microsoft wrote the windowed AmigaBASIC that was supplied with version 1.1 of the pre-emptive multitasking GUI Amiga computers (late 1985 / early 1986), although the product unusually did not bear any Microsoft marks.


title: BASIC

text: These later variations introduced many extensions, such as improved string manipulation and graphics support, access to the file system and additional data types. More important were the facilities for structured programming, including additional control structures and proper subroutines supporting local variables. However, by the latter half of the 1980s, users were increasingly using pre-made applications written by others rather than learning programming themselves; while professional programmers now had a wide range of more advanced languages available on small computers. C and later C++ became the languages of choice for professional "shrink wrap" application development.


title: BASIC

text: In 1991, Microsoft introduced Visual Basic, an evolutionary development of QuickBASIC. It included constructs from that language such as block-structured control statements, parameterized subroutines and optional static typing as well as object-oriented constructs from other languages such as "With" and "For Each". The language retained some compatibility with its predecessors, such as the Dim keyword for declarations, "Gosub"/Return statements and optional line numbers which could be used to locate errors. An important driver for the development of Visual Basic was as the new macro language for Microsoft Excel, a spreadsheet program. To the surprise of many at Microsoft who still initially marketed it as a language for hobbyists, the language came into widespread use for small custom business applications shortly after the release of VB version 3.0, which is widely considered the first relatively stable version.


title: BASIC

text: While many advanced programmers still scoffed at its use, VB met the needs of small businesses efficiently as by that time, computers running Windows 3.1 had become fast enough that many business-related processes could be completed "in the blink of an eye" even using a "slow" language, as long as large amounts of data were not involved. Many small business owners found they could create their own small, yet useful applications in a few evenings to meet their own specialized needs. Eventually, during the lengthy lifetime of VB3, knowledge of Visual Basic had become a marketable job skill. Microsoft also produced VBScript in 1996 and Visual Basic .NET in 2001. The latter has essentially the same power as C# and Java but with syntax that reflects the original Basic language. The IDE, with its event-driven GUI builder, was also influential on other tools, most notably Borland Software's Delphi for Object Pascal and its own descendants such as Lazarus.


title: BASIC

text: Mainstream support for the final version 6.0 of the original Visual Basic ended on March 31, 2005, followed by extended support in March 2008. On March 11, 2020, Microsoft announced that evolution of the VB.NET language had also concluded, although it was still supported. Meanwhile, competitors exist such as Xojo and Gambas.


title: BASIC

text: Many other BASIC dialects have also sprung up since 1990, including the open source QB64 and FreeBASIC, inspired by QBasic, and the Visual Basic-styled RapidQ, Basic For Qt and Gambas. Modern commercial incarnations include PureBasic, PowerBASIC, Xojo, Monkey X and True BASIC (the direct successor to Dartmouth BASIC from a company controlled by Kurtz).


title: BASIC

text: Several web-based simple BASIC interpreters also now exist, including Microsoft's Small Basic. Many versions of BASIC are also now available for smartphones and tablets via the Apple App Store, or Google Play store for Android. On game consoles, an application for the Nintendo 3DS and Nintendo DSi called "Petit Computer" allows for programming in a slightly modified version of BASIC with DS button support. A version has also been released for Nintendo Switch.


title: BASIC

text: Variants of BASIC are available on graphing and otherwise programmable calculators made by Texas Instruments, HP, Casio, and others.


title: BASIC

text: QBasic, a version of Microsoft QuickBASIC without the linker to make EXE files, is present in the Windows NT and DOS-Windows 95 streams of operating systems and can be obtained for more recent releases like Windows 7 which do not have them. Prior to DOS 5, the Basic interpreter was GW-Basic. QuickBasic is part of a series of three languages issued by Microsoft for the home and office power user and small-scale professional development; QuickC and QuickPascal are the other two. For Windows 95 and 98, which do not have QBasic installed by default, they can be copied from the installation disc, which will have a set of directories for old and optional software; other missing commands like Exe2Bin and others are in these same directories.


title: BASIC

text: The various Microsoft, Lotus, and Corel office suites and related products are programmable with Visual Basic in one form or another, including LotusScript, which is very similar to VBA 6. The Host Explorer terminal emulator uses WWB as a macro language; or more recently the programme and the suite in which it is contained is programmable in an in-house Basic variant known as Hummingbird Basic. The VBScript variant is used for programming web content, Outlook 97, Internet Explorer, and the Windows Script Host. WSH also has a Visual Basic for Applications (VBA) engine installed as the third of the default engines along with VBScript, JScript, and the numerous proprietary or open source engines which can be installed like PerlScript, a couple of Rexx-based engines, Python, Ruby, Tcl, Delphi, XLNT, PHP, and others; meaning that the two versions of Basic can be used along with the other mentioned languages, as well as LotusScript, in a WSF file, through the component object model, and other WSH and VBA constructions. VBScript is one of the languages that can be accessed by the 4Dos, 4NT, and Take Command enhanced shells. SaxBasic and WWB are also very similar to the Visual Basic line of Basic implementations. The pre-Office 97 macro language for Microsoft Word is known as WordBASIC. Excel 4 and 5 use Visual Basic itself as a macro language. Chipmunk Basic, an old-school interpreter similar to BASICs of the 1970s, is available for Linux, Microsoft Windows and macOS.


title: BASIC

text: The ubiquity of BASIC interpreters on personal computers was such that textbooks once included simple "Try It In BASIC" exercises that encouraged students to experiment with mathematical and computational concepts on classroom or home computers. Popular computer magazines of the day typically included type-in programs.


title: BASIC

text: Futurist and sci-fi writer David Brin mourned the loss of ubiquitous BASIC in a 2006 "Salon" article as have others who first used computers during this era. In turn, the article prompted Microsoft to develop and release Small Basic; it also inspired similar projects like Basic-256. Dartmouth held a 50th anniversary celebration for BASIC on 1 May 2014, as did other organisations; at least one organisation of VBA programmers organised a 35th anniversary observance in 1999.


title: BASIC

text: Dartmouth College celebrated the 50th anniversary of the BASIC language with a day of events on April 30, 2014. A short documentary film was produced for the event.


title: BASIC

text: Minimal versions of BASIC had only integer variables and one- or two-letter variable names, which minimized requirements of limited and expensive memory (RAM). More powerful versions had floating-point arithmetic, and variables could be labelled with names six or more characters long. There were some problems and restrictions in early implementations; for example, Applesoft BASIC allowed variable names to be several characters long, but only the first two were significant, thus it was possible to inadvertently write a program with variables "LOSS" and "LOAN", which would be treated as being the same; assigning a value to "LOAN" would silently overwrite the value intended as "LOSS". Keywords could not be used in variables in many early BASICs; "SCORE" would be interpreted as "SC" OR "E", where OR was a keyword. String variables are usually distinguished in many microcomputer dialects by having $ suffixed to their name as a sigil, and values are often identified as strings by being delimited by "double quotation marks". Arrays in BASIC could contain integers, floating point or string variables.