<s> [INST] <<SYS>> You are a responsible assistant committed to providing accurate and helpful responses. Avoid sharing harmful or biased content. Clarify any unclear or incorrect questions rather than providing false or misleading information. <</SYS>> What is Pressure and can you explain it in depth? [/INST] Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.: 445  Gauge pressure (also spelled gage pressure) is the pressure relative to the ambient pressure.
Pressure is a standard mechanical quantity. Various units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre (N/m2); similarly, the pound-force per square inch (psi) is the traditional unit of pressure in the imperial and U.S. customary systems. Pressure may also be expressed in terms of standard atmospheric pressure; the atmosphere (atm) is equal to this pressure, and the torr is defined as 1⁄760 of this. Manometric units such as the centimetre of water, millimetre of mercury, and inch of mercury are used to express pressures in terms of the height of column of a particular fluid in a manometer.

Definition
Pressure is the amount of force applied perpendicular to the surface of an object per unit area. The symbol for it is "p" or P.
The IUPAC recommendation for pressure is a lower-case p.
However, upper-case P is widely used. The usage of P vs p depends upon the field in which one is working, on the nearby presence of other symbols for quantities such as power and momentum, and on writing style.

Formula
Mathematically:

        p
        =

            F
            A

        ,

    {\displaystyle p={\frac {F}{A}},}
  where:

        p

    {\displaystyle p}
   is the pressure,

        F

    {\displaystyle F}
   is the magnitude of the normal force,

        A

    {\displaystyle A}
   is the area of the surface on contact.Pressure is a scalar quantity. It relates the vector area element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates the two normal vectors:

        d

            F

            n

        =
        −
        p

        d

          A

        =
        −
        p

          n

        d
        A
        .

    {\displaystyle d\mathbf {F} _{n}=-p\,d\mathbf {A} =-p\,\mathbf {n} \,dA.}
  The minus sign comes from the convention  that the force is considered towards the surface element, while the normal vector points outward. The equation has meaning in that, for any surface S in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation.
It is incorrect (although rather usual) to say "the pressure is directed in such or such direction". The pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same.Pressure is distributed to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics, and it is conjugate to volume.

Units
The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N/m2, or kg·m−1·s−2). This name for the unit was added in 1971; before that, pressure in SI was expressed simply in newtons per square metre.
Other units of pressure, such as pounds per square inch (lbf/in2) and bar, are also in common use. The CGS unit of pressure is the barye (Ba), equal to 1 dyn·cm−2, or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre (g/cm2 or kg/cm2) and the like without properly identifying the force units. But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as units of force is expressly forbidden in SI. The technical atmosphere (symbol: at) is 1 kgf/cm2 (98.0665 kPa, or 14.223 psi).
Since a system under pressure has the potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume. It is therefore related to energy density and may be expressed in units such as joules per cubic metre (J/m3, which is equal to Pa).
Mathematically:

        p
        =

              F
              ⋅

                distance

              A
              ⋅

                distance

        =

            Work
            Volume

        =

            Energy (J)

                Volume

              (

                  m

                  3

              )

        .

    {\displaystyle p={\frac {F\cdot {\text{distance}}}{A\cdot {\text{distance}}}}={\frac {\text{Work}}{\text{Volume}}}={\frac {\text{Energy (J)}}{{\text{Volume }}({\text{m}}^{3})}}.}
  Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilopascals (kPa) in most other fields, except aviation where the hecto- prefix is commonly used. The inch of mercury is still used in the United States. Oceanographers usually measure underwater pressure in decibars (dbar) because pressure in the ocean increases by approximately one decibar per metre depth.
The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressure at Earth mean sea level and is defined as 101325 Pa.
Because pressure is commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid (e.g., centimetres of water, millimetres of mercury or inches of mercury). The most common choices are mercury (Hg) and water; water is nontoxic and readily available, while mercurys high density allows a shorter column (and so a smaller manometer) to be used to measure a given pressure. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh, where g is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely. When millimetres of mercury (or inches of mercury) are quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units. One millimetre of mercury is approximately equal to one torr. The water-based units still depend on the density of water, a measured, rather than defined, quantity. These manometric units are still encountered in many fields. Blood pressure is measured in millimetres of mercury in most of the world, and lung pressures in centimetres of water are still common.Underwater divers use the metre sea water (msw or MSW) and foot sea water (fsw or FSW) units of pressure, and these are the standard units for pressure gauges used to measure pressure exposure in diving chambers and personal decompression computers. A msw is defined as 0.1 bar (= 100000 Pa = 10000 Pa), is not the same as a linear metre of depth. 33.066 fsw = 1 atm (1 atm = 101325 Pa / 33.066 = 3064.326 Pa).  Note that the pressure conversion from msw to fsw is different from the length conversion: 10 msw = 32.6336 fsw, while 10 m = 32.8083 ft.Gauge pressure is often given in units with "g" appended, e.g. "kPag", "barg" or "psig", and units for measurements of absolute pressure are sometimes given a suffix of "a", to avoid confusion, for example "kPaa", "psia". However, the US National Institute of Standards and Technology recommends that, to avoid confusion, any modifiers be instead applied to the quantity being measured rather than the unit of measure. For example, "pg = 100 psi" rather than "p = 100 psig".
Differential pressure is expressed in units with "d" appended; this type of measurement is useful when considering sealing performance or whether a valve will open or close.
Presently or formerly popular pressure units include the following:

atmosphere (atm)
manometric units:
centimetre, inch, millimetre (torr) and micrometre (mTorr, micron) of mercury,
height of equivalent column of water, including millimetre (mm H2O), centimetre (cm H2O), metre, inch, and foot of water;
imperial and customary units:
kip, short ton-force, long ton-force, pound-force, ounce-force, and poundal per square inch,
short ton-force and long ton-force per square inch,
fsw (feet sea water) used in underwater diving, particularly in connection with diving pressure exposure and decompression;
non-SI metric units:
bar, decibar, millibar,
msw (metres sea water), used in underwater diving, particularly in connection with diving pressure exposure and decompression,
kilogram-force, or kilopond, per square centimetre (technical atmosphere),
gram-force and tonne-force (metric ton-force) per square centimetre,
barye (dyne per square centimetre),
kilogram-force and tonne-force per square metre,
sthene per square metre (pieze).

Examples
As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall. Although the force applied to the surface is the same, the thumbtack applies more pressure because the point concentrates that force into a smaller area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. Unlike stress, pressure is defined as a scalar quantity. The negative gradient of pressure is called the force density.Another example is a knife. If we try to cut with the flat edge, force is distributed over a larger surface area resulting in less pressure, and it will not cut. Whereas using the sharp edge, which has less surface area, results in greater pressure, and so the knife cuts smoothly. This is one example of a practical application of pressureFor gases, pressure is sometimes measured not as an absolute pressure, but relative to atmospheric pressure; such measurements are called gauge pressure. An example of this is the air pressure in an automobile tire, which might be said to be "220 kPa (32 psi)", but is actually 220 kPa (32 psi) above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa (14.7 psi), the absolute pressure in the tire is therefore about 320 kPa (46 psi). In technical work, this is written "a gauge pressure of 220 kPa (32 psi)". Where space is limited, such as on pressure gauges, name plates, graph labels, and table headings, the use of a modifier in parentheses, such as "kPa (gauge)" or "kPa (absolute)", is permitted. In non-SI technical work, a gauge pressure of 32 psi (220 kPa) is sometimes written as "32 psig", and an absolute pressure as "32 psia", though the other methods explained above that avoid attaching characters to the unit of pressure are preferred.Gauge pressure is the relevant measure of pressure wherever one is interested in the stress on storage vessels and the plumbing components of fluidics systems. However, whenever equation-of-state properties, such as densities or changes in densities, must be calculated, pressures must be expressed in terms of their absolute values. For instance, if the atmospheric pressure is 100 kPa (15 psi), a gas (such as helium) at 200 kPa (29 psi) (gauge) (300 kPa or 44 psi [absolute]) is 50% denser than the same gas at 100 kPa (15 psi) (gauge) (200 kPa or 29 psi [absolute]). Focusing on gauge values, one might erroneously conclude the first sample had twice the density of the second one.

Scalar nature
In a static gas, the gas as a whole does not appear to move. The individual molecules of the gas, however, are in constant random motion. Because we are dealing with an extremely large number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. If we enclose the gas within a container, we detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas, and the force per unit area (the pressure) is the same. We can shrink the size of our "container" down to a very small point (becoming less true as we approach the atomic scale), and the pressure will still have a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has magnitude but no direction sense associated with it. Pressure force acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular (at right angle) to the surface.A closely related quantity is the stress tensor σ, which relates the vector force

          F

    {\displaystyle \mathbf {F} }
   to the
vector area

          A

    {\displaystyle \mathbf {A} }
   via the linear relation

          F

        =
        σ

          A

    {\displaystyle \mathbf {F} =\sigma \mathbf {A} }
  .
This tensor may be expressed as the sum of the viscous stress tensor minus the hydrostatic pressure. The negative of the stress tensor is sometimes called the pressure tensor, but in the following, the term "pressure" will refer only to the scalar pressure.According to the theory of general relativity, pressure increases the strength of a gravitational field (see stress–energy tensor) and so adds to the mass-energy cause of gravity. This effect is unnoticeable at everyday pressures but is significant in neutron stars, although it has not been experimentally tested.

Types
Fluid pressure
Fluid pressure is most often the compressive stress at some point within a fluid.  (The term fluid refers to both liquids and gases – for more information specifically about liquid pressure, see section below.)

Fluid pressure occurs in one of two situations:

An open condition, called "open channel flow", e.g. the ocean, a swimming pool, or the atmosphere.
A closed condition, called "closed conduit", e.g. a water line or gas line.Pressure in open conditions usually can be approximated as the pressure in "static" or non-moving conditions (even in the ocean where there are waves and currents), because the motions create only negligible changes in the pressure. Such conditions conform with principles of fluid statics. The pressure at any given point of a non-moving (static) fluid is called the hydrostatic pressure.
Closed bodies of fluid are either "static", when the fluid is not moving, or "dynamic", when the fluid can move as in either a pipe or by compressing an air gap in a closed container. The pressure in closed conditions conforms with the principles of fluid dynamics.
The concepts of fluid pressure are predominantly attributed to the discoveries of Blaise Pascal and Daniel Bernoulli. Bernoullis equation can be used in almost any situation to determine the pressure at any point in a fluid. The equation makes some assumptions about the fluid, such as the fluid being ideal and incompressible. An ideal fluid is a fluid in which there is no friction, it is inviscid (zero viscosity). The equation for all points of a system filled with a constant-density fluid is

            p
            γ

        +

              v

                2

              2
              g

        +
        z
        =

          c
          o
          n
          s
          t

        ,

    {\displaystyle {\frac {p}{\gamma }}+{\frac {v^{2}}{2g}}+z=\mathrm {const} ,}
  where:

p, pressure of the fluid,

          γ

    {\displaystyle {\gamma }}
   = ρg, density × acceleration of gravity is the (volume-) specific weight of the fluid,
v, velocity of the fluid,
g, acceleration of gravity,
z, elevation,

            p
            γ

    {\displaystyle {\frac {p}{\gamma }}}
  , pressure head,

              v

                2

              2
              g

    {\displaystyle {\frac {v^{2}}{2g}}}
  , velocity head.

Applications
Hydraulic brakes
Artesian well
Blood pressure
Hydraulic head
Plant cell turgidity
Pythagorean cup
Pressure washing

Explosion or deflagration pressures
Explosion or deflagration pressures are the result of the ignition of explosive gases, mists, dust/air suspensions, in unconfined and confined spaces.

Negative pressures
While pressures are, in general, positive, there are several situations in which negative pressures may be encountered:

When dealing in relative (gauge) pressures. For instance, an absolute pressure of 80 kPa may be described as a gauge pressure of −21 kPa (i.e., 21 kPa below an atmospheric pressure of 101 kPa). For example, abdominal decompression is an obstetric procedure during which negative gauge pressure is applied intermittently to a pregnant womans abdomen.
Negative absolute pressures are possible. They are effectively tension, and both bulk solids and bulk liquids can be put under negative absolute pressure by pulling on them. Microscopically, the molecules in solids and liquids have attractive interactions that overpower the thermal kinetic energy, so some tension can be sustained. Thermodynamically, however, a bulk material under negative pressure is in a metastable state, and it is especially fragile in the case of liquids where the negative pressure state is similar to superheating and is easily susceptible to cavitation. In certain situations, the cavitation can be avoided and negative pressures sustained indefinitely, for example, liquid mercury has been observed to sustain up to −425 atm in clean glass containers. Negative liquid pressures are thought to be involved in the ascent of sap in plants taller than 10 m (the atmospheric pressure head of water).
The Casimir effect can create a small attractive force due to interactions with vacuum energy; this force is sometimes termed "vacuum pressure" (not to be confused with the negative gauge pressure of a vacuum).
For non-isotropic stresses in rigid bodies, depending on how the orientation of a surface is chosen, the same distribution of forces may have a component of positive pressure along one surface normal, with a component of negative pressure acting along another surface normal.
The stresses in an electromagnetic field are generally non-isotropic, with the pressure normal to one surface element (the normal stress) being negative, and positive for surface elements perpendicular to this.
In cosmology, dark energy creates a very small yet cosmically significant amount of negative pressure, which accelerates the expansion of the universe.

Stagnation pressure
Stagnation pressure is the pressure a fluid exerts when it is forced to stop moving. Consequently, although a fluid moving at higher speed will have a lower static pressure, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by:

          p

            0

        =

            1
            2

        ρ

          v

            2

        +
        p

    {\displaystyle p_{0}={\frac {1}{2}}\rho v^{2}+p}
  where

          p

            0

    {\displaystyle p_{0}}
   is the stagnation pressure,

        ρ

    {\displaystyle \rho }
   is the density,

        v

    {\displaystyle v}
   is the flow velocity,

        p

    {\displaystyle p}
   is the static pressure.The pressure of a moving fluid can be measured using a Pitot tube, or one of its variations such as a Kiel probe or Cobra probe, connected to a manometer. Depending on where the inlet holes are located on the probe, it can measure static pressures or stagnation pressures.

Surface pressure and surface tension
There is a two-dimensional analog of pressure – the lateral force per unit length applied on a line perpendicular to the force.
Surface pressure is denoted by π:

        π
        =

            F
            l

    {\displaystyle \pi ={\frac {F}{l}}}
  and shares many similar properties with three-dimensional pressure. Properties of surface chemicals can be investigated by measuring pressure/area isotherms, as the two-dimensional analog of Boyles law, πA = k, at constant temperature.
Surface tension is another example of surface pressure, but with a reversed sign, because "tension" is the opposite to "pressure".

Pressure of an ideal gas
In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with temperature and quantity, and inversely with volume:

        p
        =

              n
              R
              T

            V

        ,

    {\displaystyle p={\frac {nRT}{V}},}
  where:

p is the absolute pressure of the gas,
n is the amount of substance,
T is the absolute temperature,
V is the volume,
R is the ideal gas constant.Real gases exhibit a more complex dependence on the variables of state.

Vapour pressure
Vapour pressure is the pressure of a vapour in thermodynamic equilibrium with its condensed phases in a closed system. All liquids and solids have a tendency to evaporate into a gaseous form, and all gases have a tendency to condense back to their liquid or solid form.
The atmospheric pressure boiling point of a liquid (also known as the normal boiling point) is the temperature at which the vapor pressure equals the ambient atmospheric pressure. With any incremental increase in that temperature, the vapor pressure becomes sufficient to overcome atmospheric pressure and lift the liquid to form vapour bubbles inside the bulk of the substance. Bubble formation deeper in the liquid requires a higher pressure, and therefore higher temperature, because the fluid pressure increases above the atmospheric pressure as the depth increases.
The vapor pressure that a single component in a mixture contributes to the total pressure in the system is called partial vapor pressure.

Liquid pressure
When a person swims under the water, water pressure is felt acting on the persons eardrums. The deeper that person swims, the greater the pressure. The pressure felt is due to the weight of the water above the person. As someone swims deeper, there is more water above the person and therefore greater pressure. The pressure a liquid exerts depends on its depth.
Liquid pressure also depends on the density of the liquid. If someone was submerged in a liquid more dense than water, the pressure would be correspondingly greater. Thus, we can say that the depth, density and liquid pressure are directly proportionate. The pressure due to a liquid in liquid columns of constant density or at a depth within a substance is represented by the following formula:

        p
        =
        ρ
        g
        h
        ,

    {\displaystyle p=\rho gh,}
  where:

p is liquid pressure,
g is gravity at the surface of overlaying material,
ρ is density of liquid,
h is height of liquid column or depth within a substance.Another way of saying the same formula is the following:

        p
        =

          weight density

        ×

          depth

        .

    {\displaystyle p={\text{weight density}}\times {\text{depth}}.}
  The pressure a liquid exerts against the sides and bottom of a container depends on the density and the depth of the liquid. If atmospheric pressure is neglected, liquid pressure against the bottom is twice as great at twice the depth; at three times the depth, the liquid pressure is threefold; etc. Or, if the liquid is two or three times as dense, the liquid pressure is correspondingly two or three times as great for any given depth. Liquids are practically incompressible – that is, their volume can hardly be changed by pressure (water volume decreases by only 50 millionths of its original volume for each atmospheric increase in pressure). Thus, except for small changes produced by temperature, the density of a particular liquid is practically the same at all depths.
Atmospheric pressure pressing on the surface of a liquid must be taken into account when trying to discover the total pressure acting on a liquid. The total pressure of a liquid, then, is ρgh plus the pressure of the atmosphere. When this distinction is important, the term total pressure is used. Otherwise, discussions of liquid pressure refer to pressure without regard to the normally ever-present atmospheric pressure.
The pressure does not depend on the amount of liquid present. Volume is not the important factor – depth is. The average water pressure acting against a dam depends on the average depth of the water and not on the volume of water held back. For example, a wide but shallow lake with a depth of 3 m (10 ft) exerts only half the average pressure that a small 6 m (20 ft) deep pond does. (The total force applied to the longer dam will be greater, due to the greater total surface area for the pressure to act upon. But for a given 5-foot (1.5 m)-wide section of each dam, the 10 ft (3.0 m) deep water will apply one quarter the force of 20 ft (6.1 m) deep water). A person will feel the same pressure whether their head is dunked a metre beneath the surface of the water in a small pool or to the same depth in the middle of a large lake. If four vases contain different amounts of water but are all filled to equal depths, then a fish with its head dunked a few centimetres under the surface will be acted on by water pressure that is the same in any of the vases. If the fish swims a few centimetres deeper, the pressure on the fish will increase with depth and be the same no matter which vase the fish is in. If the fish swims to the bottom, the pressure will be greater, but it makes no difference what vase it is in. All vases are filled to equal depths, so the water pressure is the same at the bottom of each vase, regardless of its shape or volume. If water pressure at the bottom of a vase were greater than water pressure at the bottom of a neighboring vase, the greater pressure would force water sideways and then up the narrower vase to a higher level until the pressures at the bottom were equalized. Pressure is depth dependent, not volume dependent, so there is a reason that water seeks its own level.
Restating this as energy equation, the energy per unit volume in an ideal, incompressible liquid is constant throughout its vessel. At the surface, gravitational potential energy is large but liquid pressure energy is low. At the bottom of the vessel, all the gravitational potential energy is converted to pressure energy. The sum of pressure energy and gravitational potential energy per unit volume is constant throughout the volume of the fluid and the two energy components change linearly with the depth.  Mathematically, it is described by Bernoullis equation, where velocity head is zero and comparisons per unit volume in the vessel are

            p
            γ

        +
        z
        =

          c
          o
          n
          s
          t

        .

    {\displaystyle {\frac {p}{\gamma }}+z=\mathrm {const} .}
  Terms have the same meaning as in section Fluid pressure.

Direction of liquid pressure
An experimentally determined fact about liquid pressure is that it is exerted equally in all directions. If someone is submerged in water, no matter which way that person tilts their head, the person will feel the same amount of water pressure on their ears. Because a liquid can flow, this pressure isnt only downward. Pressure is seen acting sideways when water spurts sideways from a leak in the side of an upright can. Pressure also acts upward, as demonstrated when someone tries to push a beach ball beneath the surface of the water. The bottom of a boat is pushed upward by water pressure (buoyancy).
When a liquid presses against a surface, there is a net force that is perpendicular to the surface </s>


<s> [INST] <<SYS>> You are a responsible assistant committed to providing accurate and helpful responses. Avoid sharing harmful or biased content. Clarify any unclear or incorrect questions rather than providing false or misleading information. <</SYS>> What is Hypertensive crisis and can you explain it in depth? [/INST] Severely elevated blood pressure (equal to or greater than a systolic 180 or diastolic of 120—sometimes termed malignant or accelerated hypertension) is referred to as a hypertensive crisis, as blood pressure at this level confers a high risk of complications. People with blood pressures in this range may have no symptoms, but are more likely to report headaches (22% of cases) and dizziness than the general population. Other symptoms accompanying a hypertensive crisis may include visual deterioration due to retinopathy, breathlessness due to heart failure, or a general feeling of malaise due to kidney failure </s>


<s> [INST] <<SYS>> You are a responsible assistant committed to providing accurate and helpful responses. Avoid sharing harmful or biased content. Clarify any unclear or incorrect questions rather than providing false or misleading information. <</SYS>> What is Aphagia and can you explain it in depth? [/INST] Aphagia is the inability or refusal to swallow. The word is derived from the Ancient Greek prefix α, meaning "not" or "without," and the suffix φαγία, derived from the verb φαγεῖν, meaning "to eat." It is related to dysphagia which is difficulty swallowing (Greek prefix δυσ, dys, meaning difficult, or defective), and odynophagia, painful swallowing (from ὀδύνη, odyn(o), meaning "pain"). Aphagia may be temporary or long term, depending on the affected organ. It is an extreme, life-threatening case of dysphagia.  Depending on the cause, untreated dysphagia may develop into aphagia.

Behavioural classification
The following behavioural classifications result from studies performed on rats, in which lesions were made on the lateral hypothalamus region in the brain.

Passive aphagia: An animal with passive aphagia will not respond to food if it is presented. However, if food is inserted into the mouth, the animal will chew.
Active aphagia: Active aphagia is a complete rejection of food. The animal will physically push food away or move its head from it. One might first sample the food by smelling or tasting, then spit out anything in the mouth. Afterwards the animal will show a complete repulsion to the food. The animal reacts to food as if it is bitter or foul.
Mixed aphagia: When presented with food, the animal initially does not react positively or negatively. However, when food is placed in the mouth, the animal demonstrates active aphagia, spitting out the food and refusing to eat thereafter.These studies point to the function of the hypothalamus in regulating food intake. Animals in this study also demonstrated several other types of eating behaviour: "weak eating," in which the animal slowly approaches, chews, and swallows small observable amounts of food for a brief period; "good eating," in which the animal reaches normally for the food and eats reliably; and "vigorous eating," in which the animal gluttonously reaches for and devours the food. In these cases, there was either minor or no damage to the lateral hypothalamus.Aphagia not classified under behavioral aphagia typically has a structural cause, see causes.

Causes
Aphagia is usually the result of many different diseases as well as different medical treatments. The most common causes of aphagia are:

Aesophageal cancer – there are two types of aesophageal cancer. The squamous cell cancer from the squamous cells of the tongue or the adenocarcinoma from glandular cells present at the junction of the esophagus and stomach. This leads to a local tumour growth with spreading later. This spreading may lead to larger tumors that would result in the inability to swallow.
Aesophageal webs – thin membranes located in the esophagus. Abnormalities can cause constrictions within the esophagus.
Globus pharyngis – commonly referred to as lumps in ones throat
Myasthenia gravis – the thymus gland is thought to be necessary for the deletion of auto-reactive T cells, and seems to have an important role in the pathogenesis of myasthenia gravis. In patients the thymus is typically enlarged, and contains many germinal centres with T and B cell areas very similar to those seen in lymph nodes. The tumour in thymoma associated disease is typically epithelial in nature.
Facioscapulohumeral muscular dystrophy – even though there is not a clear correlation between the facioscapulohumeral muscular dystrophy and the pharyngeal and upper aesophageal striated muscle. Minor, and nonspecific, primary aesophageal dysmotility was present as seen in the 2008 study by Joerg-patrick Stübgen.
Multiple sclerosis – may lead to aesophageal dysmotility Chemotherapy – radiation from cancer therapy may cause a stricture of the throat leading to the inability to swallow.
Stroke – swallowing problems can cause stroke victims to aspirate food or liquid into the lungs and cause pneumonia mostly in elderly people.
Parkinsons disease – the mechanism of swallowing disorders in Parkinsons disease may be related to extrapyramidal and autonomic system disorders. The cardinal symptoms of Parkinsons disease: tremor, bradykinesia, and rigidity are initially responsible for swallowing, which is mainly observed in the advanced stages of the disease
Damage to the lateral hypothalamus can also lead to aphagia, as seen in the 1978 study by Timothy Schallert and Ian Whishaw.
Other causes might be due to depression, cervical spine disease and conversion disorders.It is important to note that all these causes (except due to the damage of the lateral hypothalamus) are indirect.

Diagnosis
Modified barium swallow – videofluoroscopic swallow (fluoroscopy) </s>


<s> [INST] <<SYS>> You are a responsible assistant committed to providing accurate and helpful responses. Avoid sharing harmful or biased content. Clarify any unclear or incorrect questions rather than providing false or misleading information. <</SYS>> What is Sealpox and can you explain it in depth? [/INST]  </s>


<s> [INST] <<SYS>> You are a responsible assistant committed to providing accurate and helpful responses. Avoid sharing harmful or biased content. Clarify any unclear or incorrect questions rather than providing false or misleading information. <</SYS>> What is Tachypnea and can you explain it in depth? [/INST]  </s>


<s> [INST] <<SYS>> You are a responsible assistant committed to providing accurate and helpful responses. Avoid sharing harmful or biased content. Clarify any unclear or incorrect questions rather than providing false or misleading information. <</SYS>> What is Bloating and can you explain it in depth? [/INST] Abdominal bloating (or simply bloating) is a short-term disease that affects the gastrointestinal tract. Bloating is generally characterized by an excess buildup of gas, air or fluids in the stomach. A person may have feelings of tightness, pressure or fullness in the stomach; it may or may not be accompanied by a visibly distended abdomen. Bloating can affect anyone of any age range and is usually self-diagnosed, in most cases does not require serious medical attention or treatment. Although this term is usually used interchangeably with abdominal distension, these symptoms probably have different pathophysiological processes, which are not fully understood.The first step for the management is to find a treatment for the underlying causes that produce it through a detailed medical history and a physical examination. The discomfort can be alleviated by the use of certain drugs and dietary modifications.Bloating can also be caused by chronic conditions and in rare cases can be a reoccurring life-threatening problem.

Symptoms and signs
The most common symptom associated with bloating is a sensation that the abdomen is full or distended. Rarely, bloating may be painful or cause shortness of breath.Pains that are due to bloating will feel sharp and cause the stomach to cramp. These pains may occur anywhere in the body and can change locations quickly. They are so painful that they are sometimes mistaken for heart pains when they develop on the upper left side of the chest. Pains on the right side are often confused with problems in the appendix or the gallbladder.
One symptom of gas that is not normally associated with it is the hiccup. Hiccups are harmless and will diminish on their own; they also help to release gas that is in the digestive tract before it moves down to the intestines and causes bloating. Important but uncommon causes of abdominal bloating include ascites and tumors.

Causes
There are many causes of bloating, including: diet, irritable bowel syndrome, lactose intolerance, reflux, and constipation.
Specific medical conditions like Crohns disease or bowel obstruction can also contribute to the amount of stomach bloating experienced.
Common causes of abdominal bloating are:

Overeating
Gastric distension
Lactose intolerance, fructose intolerance and other food intolerances
Premenstrual syndrome
Food allergy
Aerophagia (air swallowing, a nervous habit)
Irritable bowel syndrome
Celiac disease
Non-celiac gluten sensitivity
Partial bowel obstruction
Gastric dumping syndrome or rapid gastric emptying
Gas-producing foods
Constipation
Visceral fat
Splenic-flexure syndrome
Menstruation, dysmenorrhea
Polycystic ovary syndrome and ovarian cysts
Alvarez syndrome, bloating of unknown or psychogenic origin without excess gas in the digestive tract
Massive infestation with intestinal parasites (e.g., Ascaris lumbricoides)
Diverticulosis
Certain medications, such as phentermine
Occurs in some due to salivary hypersecretion and dehydration.
Ovarian cancerImportant but uncommon causes of abdominal bloating include:

Large cancerous intra-abdominal tumors of the ovary, liver, uterus and stomach
Megacolon, an abnormal dilation of the colon caused by some diseases, such as Chagas disease, a parasitic infection
Cardiopulmonary resuscitation procedures, due to the artificial mouth-to-mouth insufflation of air.In animals, causes of abdominal bloating include:

Gastric dilatation volvulus, a condition of dogs which occurs when gas is trapped inside the stomach and gastric torsion prevents it from escaping
Ruminal tympany, a condition of ruminant animals which occurs when gas cannot escape from the rumen.All the factors mentioned contribute to bloated stomach abdominal pain.
Every person produces gases in their body during the digestion of food, such as methane, hydrogen, carbon dioxide, and nitrogen. And some of them are released outside the body, sometimes in small quantities that one does not notice and sometimes in larger quantities that may affect the normal course of life.

Fiber
Most cases of stomach bloating are due to improper diet. Gas occurs because of the bacteria in the colon and is a by-product of soluble fiber digestion. Inadequate or irregular intake of fiber and water will cause a person to experience bloating or constipation. The most common natural sources of fiber include fruits and vegetables as well as wheat or oat bran. These fibers are most likely to cause flatulence. Fiber is made by plants and is not easily digested by the human gastrointestinal tract. There are two main types of dietary fiber: soluble and insoluble fiber. Soluble fiber is prebiotic and readily fermented in the colon into gases, while insoluble fiber is metabolically inert and absorbs water as it moves through the digestive system, aiding in defecation. Most types of fiber (insoluble) are attached to body water in the intestine and increase the volume of stools.

Bowel gas
Gas in the gastrointestinal tract has only two sources. It is either swallowed air or is produced by bacteria that normally inhabit the intestines, primarily the colon.Belching or burping is a universal ability that works by removing gas from the stomach through the mouth. The stomach can become bloated when too much air is swallowed during eating and drinking too quickly. As the stomach swells, belching removes the gas and alleviates the pain associated with it. Burping can also be used as a form of relief from abdominal discomfort other than too much gas in the stomach.Flatulence, or farting, provides relief of much the same kind as burping, but involves the passage of gas from the body via the anus, not the mouth. Bacteria present in the intestinal tract cause gas that is expelled from the anus. They produce the gas as food is digested and moved from the small intestine. This gas builds up and causes swelling or bloating in the abdominal area before it is released.

Constipation
A common gastrointestinal problem is constipation—infrequent bowel movements, hard stools, or strain during the movements—which causes serious cases of bloating. Since most cases of constipation are temporary, simple lifestyle changes, such as getting more exercise and increasing ones intake of fiber, can contribute to alleviating constipation. Some cases of constipation will continue to worsen and require unconventional methods to release the feces and reduce the amount of stomach bloating. Blood in the stool, intense pain in the abdomen, rectal pain, unexplained weight loss, and continued bloating and constipation not relieved by the above lifestyle changes should be reported to a doctor. Bloating consistently accompanies constipation, and they will not develop without an underlying cause.

Heartburn and acid reflux
Painful burning sensations in the chest that are caused by gastroesophageal reflux is known as heartburn. Reflux is the backflow of gastric acid juices from the stomach into the oesophagus.  Heartburn has different triggers, including certain foods, medications, obesity, and stress. These triggers are different for each individual. Gastroesophageal reflux disease or GERD is a chronic condition that can lead to more serious complications like esophageal cancer. Treatment options are available to treat the symptoms and the condition, but there is no cure for the disease. Symptoms include burping, abdominal and stomach bloating, along with pain and discomfort. Heavy meals, lying down or bending over after eating should be avoided to help prevent reflux from occurring. The stomach bloating experienced with reflux is intense and will remain until the food is digested all the way.
Postmortem bloating occurs in cadavers, due to the formation of gases by bacterial action and putrefaction of the internal tissues of the abdomen and the inside of the intestines.

Related conditions
Conditions that are related to bloating include constipation, lactose intolerance, and acid reflux disease. All of these conditions share the same symptoms and can share the same causative agents. These causes include unhealthy diet, smoking, alcohol consumption, low amount of exercise, and overall health. Each of these conditions can be experienced as a symptom of the others and is also a cause for each of them. In most cases where one of the conditions is present, there is at least one if not two of the others. Treatment for each condition is performed using the same medications and recommended dietary changes like increased fiber intake and reduced fat intake. If the conditions develop into diseases such as gastroesophageal reflux disease or chronic constipation, additional medications will be required. Bloating and flatulence are sometimes related to constipation, and treating the underlying condition may be helpful.

Treatment
Diets
Promising evidence on the potential efficacy of the low-FODMAP diet in functional abdominal bloating is provided by the reduction of the bloating which has been observed in some studies on patients with irritable bowel syndrome. Regarding the gluten-free diet, there is insufficient scientific evidence to recommend it to reduce bloating and abdominal distension.
As regards the FODMAP diet, this should be provided by experts in nutrition to reduce the risks associated with elimination diets.

Medications
There are many over-the-counter (OTC) medications that can be used to treat bloating.
Food enzymes can be found in some products that will help break down the sugars found in grains, vegetables and dairy products. They can be taken before food is consumed or added to the food that causes the gas and bloating. The most common treatment is antacids. These medications have no effect on the gas that is present in the intestines but enable gas build-up to be belched away more easily, reducing the amount of bloating that develops.  Another treatment is simethicone, an oral anti-foaming agent that helps the body to expel the gas more quickly.
Combinations of prokinetics, such as domperidone + metoclopramide + diphenhydramine (the latter for the prevention of extrapyramidal reactions, especially acute dystonic reactions) + proton pump inhibitors (PPIs), have dramatic effects on bloaters and belchers especially.

See also
Tympany

References
Notes

Bibliography

Partly based on Abdominal bloating. MedlinePlus (US public domain Medical Encyclopedia) </s>


<s> [INST] <<SYS>> You are a responsible assistant committed to providing accurate and helpful responses. Avoid sharing harmful or biased content. Clarify any unclear or incorrect questions rather than providing false or misleading information. <</SYS>> What is Ultralight aviation and can you explain it in depth? [/INST] Ultralight aviation (called microlight aviation in some countries) is the flying of lightweight, 1- or 2-seat fixed-wing aircraft. Some countries differentiate between weight-shift control and conventional three-axis control aircraft with ailerons, elevator and rudder, calling the former "microlight" and the latter "ultralight".
During the late 1970s and early 1980s, mostly stimulated by the hang gliding movement, many people sought affordable powered flight. As a result, many aviation authorities set up definitions of lightweight, slow-flying aeroplanes that could be subject to minimum regulations. The resulting aeroplanes are commonly called "ultralight aircraft" or "microlights", although the weight and speed limits differ from country to country. In Europe, the sporting (FAI) definition limits the maximum stalling speed to 65 km/h (40 mph) and the maximum take-off weight to 450 kg (992 lb), or 472.5 kg (1,042 lb) if a ballistic parachute is installed. The definition means that the aircraft has a slow landing speed and short landing roll in the event of an engine failure.In most affluent countries, microlights or ultralight aircraft now account for a significant percentage of the global civilian-owned aircraft. For instance in Canada in February 2018, the ultralight aircraft fleet made up to 20.4% of the total civilian aircraft registered. In other countries that do not register ultralight aircraft, like the United States, it is unknown what proportion of the total fleet they make up. In countries where there is no specific extra regulation, ultralights are considered regular aircraft and subject to certification requirements for both aircraft and pilot.

Definitions
Australia
In Australia, ultralight aircraft and their pilots can either be registered with the Hang Gliding Federation of Australia (HGFA) or Recreational Aviation Australia (RA Aus). In all cases, except for privately built single seat ultralight aeroplanes, microlight aircraft or trikes are regulated by the Civil Aviation Regulations.

Canada
United Kingdom
Pilots of a powered, fixed wing aircraft or paramotors do not need a licence, provided its weight with a full fuel tank is not more than 75 kg (165 lb), but they must obey the rules of the air.For heavier microlights the current UK regulations are similar to the European ones, but helicopters and gyroplanes are not included.Other than the very earliest aircraft, all two-seat UK microlights (and until 2007 all single-seaters) have been required to meet an airworthiness standard; BCAR Section S.
In 2007, Single Seat DeRegulated (SSDR), a sub-category of single seat aircraft was introduced, allowing owners more freedom for modification and experiments. By 2017 the airworthiness of all single seat microlights became solely the responsibility of the user, but pilots must hold a microlight licence; currently NPPL(M) (National Private Pilots Licence).

New Zealand
Ultralights in New Zealand are subject to NZCAA General Aviation regulations with microlight specific variations as described in Part 103 and AC103-1.

United States
The United States FAAs definition of an ultralight is significantly different from that in most other countries and can lead to some confusion when discussing the topic. The governing regulation in the United States is FAR 103 Ultralight Vehicles. In 2004, the FAA introduced the "Light-sport aircraft" category, which resembles some other countries microlight categories </s>


<s> [INST] <<SYS>> You are a responsible assistant committed to providing accurate and helpful responses. Avoid sharing harmful or biased content. Clarify any unclear or incorrect questions rather than providing false or misleading information. <</SYS>> What is Apraxia and can you explain it in depth? [/INST] Apraxia is a motor disorder caused by damage to the brain (specifically the posterior parietal cortex or corpus callosum), which causes difficulty with motor planning to perform tasks or movements. The nature of the damage determines the disorders severity, and the absence of sensory loss or paralysis helps to explain the level of difficulty. Children may be born with apraxia; its cause is unknown, and symptoms are usually noticed in the early stages of development. Apraxia occurring later in life, known as acquired apraxia, is typically caused by traumatic brain injury, stroke, dementia, Alzheimers disease, brain tumor, or other neurodegenerative disorders. The multiple types of apraxia are categorized by the specific ability and/or body part affected.
The term "apraxia" comes from the Greek ἀ- a- ("without") and πρᾶξις praxis ("action").

Types
The several types of apraxia include:

Apraxia of speech (AOS) is having difficulty planning and coordinating the movements necessary for speech (e.g. potato=totapo, topato). AOS can independently occur without issues in areas such as verbal comprehension, reading comprehension, writing, articulation, or prosody.
Buccofacial or orofacial apraxia, the most common type of apraxia, is the inability to carry out facial movements on demand. For example, an inability to lick ones lips, wink, or whistle when requested to do so. This suggests an inability to carry out volitional movements of the tongue, cheeks, lips, pharynx, or larynx on command.
Constructional apraxia is the inability to draw, construct, or copy simple configurations, such as intersecting shapes. These patients have difficulty copying a simple diagram or drawing basic shapes.
Gait apraxia is the loss of ability to have normal function of the lower limbs such as walking. This is not due to loss of motor or sensory functions.
Ideational/conceptual apraxia is having an inability to conceptualize a task and impaired ability to complete multistep actions. This form of apraxia consists of an inability to select and carry out an appropriate motor program.  For example, the patient may complete actions in incorrect orders, such as buttering bread before putting it in the toaster, or putting on shoes before putting on socks. Also, a loss occurs in the ability to voluntarily perform a learned task when given the necessary objects or tools. For instance, if given a screwdriver, these patients may try to write with it as if it were a pen, or try to comb their hair with a toothbrush.
Ideomotor apraxia is having deficits in the ability to plan or complete motor actions that rely on semantic memory.  These patients are able to explain how to perform an action, but unable to "imagine" or act out a movement such as "pretend to brush your teeth" or "pucker as though you bit into a sour lemon." When the ability to perform an action automatically when cued remains intact, though, this is known as automatic-voluntary dissociation. For example, they may not be able to pick up a phone when asked to do so, but can perform the action without thinking when the phone rings.
Limb-kinetic apraxia is having the inability to perform precise, voluntary movements of extremities. For example, a person affected by limb apraxia may have difficulty waving hello, tying shoes, or typing on a computer. This type is common in patients who have experienced a stroke, some type of brain trauma, or have Alzheimers disease.
Oculomotor apraxia is having difficulty moving the eye on command, especially with saccade movements that direct the gaze to targets. This is one of the three major components of Balints syndrome.

Causes
Apraxia is most often due to a lesion located in the dominant (usually left) hemisphere of the brain, typically in the frontal and parietal lobes. Lesions may be due to stroke, acquired brain injuries, or neurodegenerative diseases such as Alzheimers disease or other dementias, Parkinsons disease, or Huntingtons disease. Also, apraxia possibly may be caused by lesions in other areas of the brain.Ideomotor apraxia is typically due to a decrease in blood flow to the dominant hemisphere of the brain and particularly the parietal and premotor areas. It is frequently seen in patients with corticobasal degeneration.Ideational apraxia has been observed in patients with lesions in the dominant hemisphere near areas associated with aphasia, but more research is needed on ideational apraxia due to brain lesions. The localization of lesions in areas of the frontal and temporal lobes would provide explanation for the difficulty in motor planning seen in ideational apraxia, as well as its difficulty to distinguish it from certain aphasias.Constructional apraxia is often caused by lesions of the inferior nondominant parietal lobe, and can be caused by brain injury, illness, tumor, or other condition that can result in a brain lesion.

Diagnosis
Although qualitative and quantitative studies exist, little consensus exists on the proper method to assess for apraxia. The criticisms of past methods include failure to meet standard psychometric properties and research-specific designs that translate poorly to nonresearch use.The Test to Measure Upper Limb Apraxia (TULIA) is one method of determining upper limb apraxia through the qualitative and quantitative assessment of gesture production. In contrast to previous publications on apraxic assessment, the reliability and validity of TULIA was thoroughly investigated. The TULIA consists of subtests for the imitation and pantomime of nonsymbolic ("put your index finger on top of your nose"), intransitive ("wave goodbye"), and transitive ("show me how to use a hammer") gestures. Discrimination (differentiating between well- and poorly performed tasks) and recognition (indicating which object corresponds to a pantomimed gesture) tasks are also often tested for a full apraxia evaluation.However, a strong correlation may not be seen between formal test results and actual performance in everyday functioning or activities of daily living (ADLs). A comprehensive assessment of apraxia should include formal testing, standardized measurements of ADLs, observation of daily routines, self-report questionnaires, and targeted interviews with the patients and their relatives.As stated above, apraxia should not be confused with aphasia (the inability to understand language); however, they frequently occur together. Apraxia is so often accompanied by aphasia that many believe that if a person displays AOS, then the patient also having some level of aphasia should be assumed.

Treatment
Treatment for individuals with apraxia includes speech therapy, occupational therapy, and physical therapy. Currently, no medications are indicated for the treatment of apraxia, only therapy treatments. Generally, treatments for apraxia have received little attention for several reasons, including the tendency for the condition to resolve spontaneously in acute cases. Additionally, the very nature of the automatic-voluntary dissociation of motor abilities that defines apraxia means that patients may still be able to automatically perform activities if cued to do so in daily life. Nevertheless,  patients experiencing apraxia have less functional independence in their daily lives, and that evidence for the treatment of apraxia is scarce. However, a literature review of apraxia treatment to date reveals that although the field is in its early stages of treatment design, certain aspects can be included to treat apraxia.One method is through rehabilitative treatment, which has been found to positively impact apraxia, as well as ADLs. In this review, rehabilitative treatment consisted of 12 different contextual cues, which were used to teach patients how to produce the same gesture under different contextual situations. Additional studies have also recommended varying forms of gesture therapy, whereby the patient is instructed to make gestures (either using objects or symbolically meaningful and nonmeaningful gestures) with progressively less cuing from the therapist. Patients with apraxia may need to use a form of alternative and augmentative communication depending on the severity of the disorder. In addition to using gestures as mentioned, patients can also use communication boards or more sophisticated electronic devices if needed.No single type of therapy or approach has been proven as the best way to treat a patient with apraxia, since each patients case varies </s>


<s> [INST] <<SYS>> You are a responsible assistant committed to providing accurate and helpful responses. Avoid sharing harmful or biased content. Clarify any unclear or incorrect questions rather than providing false or misleading information. <</SYS>> What is 4 and can you explain it in depth? [/INST] 4 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures.

In mathematics
Four is the smallest composite number, its proper divisors being 1 and 2. Four is the sum and product of two with itself:

        2

    {\displaystyle 2}
   +

        2

    {\displaystyle 2}
   =

        4

    {\displaystyle 4}
   =

        2

    {\displaystyle 2}
   x

        2

    {\displaystyle 2}
  , the only number

        b

    {\displaystyle b}
   such that

        a

    {\displaystyle a}
   +

        a

    {\displaystyle a}
   =

        b

    {\displaystyle b}
   =

        a

    {\displaystyle a}
   x

        a

    {\displaystyle a}
  , which also makes four the smallest squared prime number

          p

            2

    {\displaystyle p^{2}}
  . In Knuths up-arrow notation, 2 ↑↑ 2 = 2 ↑↑↑ 2 = 4, and so forth, for any number of up arrows. By consequence, four is the only square one more than a prime number, specifically three. The sum of the first four prime numbers two + three + five + seven is the only sum of four consecutive prime numbers that yields an odd prime number, seventeen, which is the fourth super-prime. Four lies between the first proper pair of twin primes, three and five, which are the first two Fermat primes, like seventeen, which is the third. On the other hand, the square of four 42, equivalently the fourth power of two 24, is sixteen; the only number that has

          a

            b

    {\displaystyle a^{b}}
   =

          b

            a

    {\displaystyle b^{a}}
   as a form of factorization. Holistically, there are four elementary arithmetic operations in mathematics: addition (+), subtraction (−), multiplication (×), and division (÷); and four basic number systems, the real numbers

          R

    {\displaystyle \mathbb {R} }
  , rational numbers

          Q

    {\displaystyle \mathbb {Q} }
  , integers

          Z

    {\displaystyle \mathbb {Z} }
  , and natural numbers

          N

    {\displaystyle \mathbb {N} }
  .
Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e.

        4
        x

    {\displaystyle 4x}
   =

          y

            2

    {\displaystyle y^{2}}
   −

          z

            2

    {\displaystyle z^{2}}
  . A number is a multiple of 4 if its last two digits are a multiple of 4. For example, 1092 is a multiple of 4 because 92 = 4 × 23.
Lagranges four-square theorem states that every positive integer can be written as the sum of at most four square numbers. Three are not always sufficient; 7 for instance cannot be written as the sum of three squares.There are four all-Harshad numbers: 1, 2, 4, and 6. 12, which is divisible by four thrice over, is a Harshad number in all bases except octal.
A four-sided plane figure is a quadrilateral or quadrangle, sometimes also called a tetragon. It can be further classified as a rectangle or oblong, kite, rhombus, and square.
Four is the highest degree general polynomial equation for which there is a solution in radicals.The four-color theorem states that a planar graph (or, equivalently, a flat map of two-dimensional regions such as countries) can be colored using four colors, so that adjacent vertices (or regions) are always different colors. Three colors are not, in general, sufficient to guarantee this. The largest planar complete graph has four vertices.A solid figure with four faces as well as four vertices is a tetrahedron, which is the smallest possible number of faces and vertices a polyhedron can have. The regular tetrahedron, also called a 3-simplex, is the simplest Platonic solid. It has four regular triangles as faces that are themselves at dual positions with the vertices of another tetrahedron. Tetrahedra can be inscribed inside all other four Platonic solids, and tessellate space alongside the regular octahedron in the alternated cubic honeycomb.
Four-dimensional space is the highest-dimensional space featuring more than three regular convex figures:

Two-dimensional: infinitely many regular polygons.
Three-dimensional: five regular polyhedra; the five Platonic solids which are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
Four-dimensional: six regular polychora; the 5-cell, 8-cell or tesseract, 16-cell, 24-cell, 120-cell, and 600-cell. The 24-cell, made of regular octahedra, has no analogue in any other dimension; it is self-dual, with its 24-cell honeycomb dual to the 16-cell honeycomb.
Five-dimensional and every higher dimension: three regular convex

        n

    {\displaystyle n}
  -polytopes, all within the infinite family of regular

        n

    {\displaystyle n}
  -simplexes,

        n

    {\displaystyle n}
  -hypercubes, and

        n

    {\displaystyle n}
  -orthoplexes.The fourth dimension is also the highest dimension where regular self-intersecting figures exist:

Two-dimensional: infinitaly many regular star polygons.
Three-dimensional: four regular star polyhedra, the regular Kepler-Poinsot star polyhedra.
Four-dimensional: ten regular star polychora, the Schläfli–Hess star polychora. They contain cells of Kepler-Poinsot polyhedra alongside regular tetrahedra, icosahedra and dodecahedra.
Five-dimensional and every higher dimension: zero regular star-polytopes; uniform star polytopes in dimensions

        n

    {\displaystyle n}
   >

        4

    {\displaystyle 4}
   are the most symmetric, which mainly originate from stellations of regular

        n

    {\displaystyle n}
  -polytopes.Altogether, sixteen (or 16 = 42) regular convex and star polychora are generated from symmetries of four (4) Coxeter Weyl groups and point groups in the fourth dimension: the

            A

            4

    {\displaystyle \mathrm {A} _{4}}
   simplex,

            B

            4

    {\displaystyle \mathrm {B} _{4}}
   hypercube,

            F

            4

    {\displaystyle \mathrm {F} _{4}}
   icositetrachoric, and

            H

            4

    {\displaystyle \mathrm {H} _{4}}
   hexacosichoric groups; with the

            D

            4

    {\displaystyle \mathrm {D} _{4}}
   demihypercube group generating two alternative constructions.
There are also sixty-four (or 64 = 43) four-dimensional Bravais lattices, and sixty-four uniform polychora in the fourth dimension based on the same

            A

            4

    {\displaystyle \mathrm {A} _{4}}
  ,

            B

            4

    {\displaystyle \mathrm {B} _{4}}
  ,

            F

            4

    {\displaystyle \mathrm {F} _{4}}
   and

            H

            4

    {\displaystyle \mathrm {H} _{4}}
   Coxeter groups, and extending to prismatic groups of uniform polyhedra, including one special non-Wythoffian form, the grand antiprism. There are also two infinite families of duoprisms and antiprismatic prisms in the fourth dimension.
Four-dimensional differential manifolds have some unique properties. There is only one differential structure on

            R

            n

    {\displaystyle \mathbb {R} ^{n}}
   except when

        n

    {\displaystyle n}
   =

        4

    {\displaystyle 4}
  , in which case there are uncountably many.
The smallest non-cyclic group has four elements; it is the Klein four-group. An alternating groups are not simple for values

        n

    {\displaystyle n}
   ≤

        4

    {\displaystyle 4}
  .
Further extensions of the real numbers under Hurwitzs theorem states that there are four normed division algebras: the real numbers

          R

    {\displaystyle \mathbb {R} }
  , the complex numbers

          C

    {\displaystyle \mathbb {C} }
  , the quaternions

          H

    {\displaystyle \mathbb {H} }
  , and the octonions

          O

    {\displaystyle \mathbb {O} }
  . Under Cayley–Dickson constructions, the sedenions

          S

    {\displaystyle \mathbb {S} }
   constitute a further fourth extension over

          R

    {\displaystyle \mathbb {R} }
  . The real numbers are ordered, commutative and associative algebras, as well as alternative algebras with power-associativity. The complex numbers

          C

    {\displaystyle \mathbb {C} }
   share all four multiplicative algebraic properties of the reals

          R

    {\displaystyle \mathbb {R} }
  , without being ordered. The quaternions loose a further commutative algebraic property, while holding associative, alternative, and power-associative properties. The octonions are alternative and power-associative, while the sedenions are only power-associative. The sedenions and all further extensions of these four normed division algebras are solely power-associative with non-trivial zero divisors, which makes them non-division algebras.

          R

    {\displaystyle \mathbb {R} }
   has a vector space of dimension 1, while

          C

    {\displaystyle \mathbb {C} }
  ,

          H

    {\displaystyle \mathbb {H} }
  ,

          O

    {\displaystyle \mathbb {O} }
   and

          S

    {\displaystyle \mathbb {S} }
   work in algebraic number fields of dimensions 2, 4, 8, and 16, respectively.

List of basic calculations
Evolution of the Hindu-Arabic digit
Brahmic numerals represented 1, 2, and 3 with as many lines. 4 was simplified by joining its four lines into a cross that looks like the modern plus sign. The Shunga would add a horizontal line on top of the digit, and the Kshatrapa and Pallava evolved the digit to a point where the speed of writing was a secondary concern. The Arabs 4 still had the early concept of the cross, but for the sake of efficiency, was made in one stroke by connecting the "western" end to the "northern" end; the "eastern" end was finished off with a curve. The Europeans dropped the finishing curve and gradually made the digit less cursive, ending up with a digit very close to the original Brahmin cross.While the shape of the character for the digit 4 has an ascender in most modern typefaces, in typefaces with text figures the glyph usually has a descender, as, for example, in .

On the seven-segment displays of pocket calculators and digital watches, as well as certain optical character recognition fonts, 4 is seen with an open top.Television stations that operate on channel 4 have occasionally made use of another variation of the "open 4", with the open portion being on the side, rather than the top. This version resembles the Canadian Aboriginal syllabics letter ᔦ. The magnetic ink character recognition "CMC-7" font also uses this variety of "4".

In religion
Buddhism
Four Noble Truths – Dukkha, Samudaya, Nirodha, Magga
Four sights – observations which affected Prince Siddhartha deeply and made him realize the sufferings of all beings, and compelled him to begin his spiritual journey—an old man, a sick man, a dead man, and an ascetic
Four Great Elements – earth, water, fire, and wind
Four Heavenly Kings
Four Foundations of Mindfulness – contemplation of the body, contemplation of feelings, contemplation of mind, contemplation of mental objects
Four Right Exertions
Four Bases of Power
Four jhānas
Four arūpajhānas
Four Divine Abidings – loving-kindness, compassion, sympathetic joy, and equanimity
Four stages of enlightenment – stream-enterer, once-returner, non-returner, and arahant
Four main pilgrimage sites – Lumbini, Bodh Gaya, Sarnath, and Kusinara

Judeo-Christian symbolism
The Tetragrammaton is the four-letter name of God.
Ezekiel has a vision of four living creatures: a man, a lion, an ox, and an eagle.
The four Matriarchs (foremothers) of Judaism are Sarah, Rebekah, Leah, and Rachel.
The Four Species (lulav, hadass, aravah and etrog) are taken as one of the mitzvot on the Jewish holiday of Sukkot. (Judaism)
The Four Cups of Wine to drink on the Jewish holiday of Passover. (Judaism)
The Four Questions to be asked on the Jewish holiday of Passover. (Judaism)
The Four Sons to be dealt with on the Jewish holiday of Passover. (Judaism)
The Four Expressions of Redemption to be said on the Jewish holiday of Passover. (Judaism)
The four Gospels: Matthew, Mark, Luke, and John. (Christianity)
The Four Horsemen of the Apocalypse ride in the Book of Revelation. (Christianity)
The four holy cities of Judaism: Jerusalem, Hebron, Safed, and Tiberius

Hinduism
There are four Vedas: Rigveda, Samaveda, Yajurveda and Atharvaveda.
In Puruṣārtha, there are four aims of human life: Dharma, Artha, Kāma, Moksha.
The four stages of life Brahmacharya (student life), Grihastha (household life), Vanaprastha (retired life) and Sannyasa (renunciation).
The four primary castes or strata of society: Brahmana (priest/teacher), Kshatriya (warrior/politician), Vaishya (landowner/entrepreneur) and Shudra (servant/manual laborer).
The swastika symbol is traditionally used in Hindu religions as a sign of good luck and signifies good from all four directions.
The god Brahma has four faces.
There are four yugas: Satya, Dvapara, Treta and Kali

Islam
Eid al-Adha lasts for four days, from the 10th to the 14th of Dhul Hijja.
The four holy cities of Islam: Mecca, Medina, Jerusalem and Damascus.
The four tombs in the Green Dome: Muhammad, Abu Bakr, Umar ibn Khattab and Isa ibn Maryam (Jesus).
There are four Rashidun or Rightly Guided Caliphs: Abu Bakr, Umar ibn al-Khattab, Uthman ibn Affan and Ali ibn Abi Talib.
The Four Arch Angels in Islam are: Jibraeel (Gabriel), Mikaeel (Michael), Izraeel (Azrael), and Israfil (Raphael)
There are four months in which war is not permitted: Muharram, Rajab, Dhu al-Qidah and Dhu al-Hijjah.
There are four Sunni schools of fiqh: Hanafi, Shafi`i, Maliki and Hanbali.
There are four major Sunni Imams: Abū Ḥanīfa, Muhammad ibn Idris ash-Shafi`i, Malik ibn Anas and Ahmad ibn Hanbal.
There are four books in Islam: Taurait, Zaboor, Injeel, Quran.
Waiting for four months is ordained for those who take an oath for abstention from their wives.
The waiting period of the woman whose husband dies is four months and ten days.
When Abraham said: "My Lord, show me how You give life to the dead," Allah said: "Why! Do you have no faith?" Abraham replied: "Yes, but in order that my heart be at rest." He said: "Then take four birds, and tame them to yourself, then put a part of them on every hill, and summon them; they will come to you flying. [Al-Baqara 2:260]
The respite of four months was granted to give time to the mushriks in Surah At-Tawba so that they should consider their position carefully and decide whether to make preparation for war or to emigrate from the country or to accept Islam.
Those who accuse honorable women (of unchastity) but do not produce four witnesses, flog them with eighty lashes, and do not admit their testimony ever after. They are indeed transgressors. [An-Noor 24:4]

Taoism
Four Symbols of I Ching

Other
In a more general sense, numerous mythological and cosmogonical systems consider Four corners of the world as essentially corresponding to the four points of the compass.
Four is the sacred number of the Zia, an indigenous tribe located in the U.S. state of New Mexico.
The Chinese, the Koreans, and the Japanese are superstitious about the number four because it is a homonym for "death" in their languages.
In Slavic mythology, the god Svetovid has four heads.

In politics
Four Freedoms: four fundamental freedoms that Franklin D. Roosevelt declared ought to be enjoyed by everyone in the world: Freedom of Speech, Freedom of Religion, Freedom from Want, Freedom from Fear.
Gang of Four: Popular name for four Chinese Communist Party leaders who rose to prominence during Chinas Cultural Revolution, but were ousted in 1976 following the death of Chairman Mao Zedong. Among the four was Maos widow, Jiang Qing. Since then, many other political factions headed by four people have been called "Gangs of Four".

In computing
Four bits (half a byte) are sometimes called a nibble.

In science
A tetramer is an oligomer formed out of four sub-units.

In astronomy
Four terrestrial (or rocky) planets in the Solar System: Mercury, Venus, Earth, and Mars.
Four giant gas/ice planets in the Solar System: Jupiter, Saturn, Uranus, and Neptune.
Four of Jupiters moons (the Galilean moons) are readily visible from Earth with a hobby telescope.
Messier object M4, a magnitude 7.5 globular cluster in the constellation Scorpius.
The Roman numeral IV stands for subgiant in the Yerkes spectral classification scheme.

In biology
Four is the number of nucleobase types in DNA and RNA – adenine, guanine, cytosine, thymine (uracil in RNA).
Many chordates have four feet, legs or leglike appendages (tetrapods).
The mammalian heart consists of four chambers.
Many mammals (Carnivora, Ungulata) use four fingers for movement.
All insects with wings except flies and some others have four wings.
Insects of the superorder Endopterygota, also known as Holometabola, such as butterflies, ants, bees, beetles, fleas, flies, moths, and wasps, undergo holometabolism—complete metamorphism in four stages—from (1) embryo (ovum, egg), to (2) larva (such as grub, caterpillar), then (3) pupa (such as the chrysalis), and finally (4) the imago.
In the common ABO blood group system, there are four blood types (A, B, O, AB).
Humans have four canines and four wisdom teeth.
The cows stomach is divided in four digestive compartments: reticulum, rumen, omasum and abomasum.

In chemistry
Valency of carbon (that is basis of life on the Earth) is four. Also because of its tetrahedral crystal bond structure, diamond (one of the natural allotropes of carbon) is the hardest known naturally occurring material. It is also the valence of silicon, whose compounds form the majority of the mass of the Earths crust.
The atomic number of beryllium
There are four basic states of matter: solid, liquid, gas, and plasma.

In physics
Special relativity and general relativity treat nature as four-dimensional: 3D regular space and one-dimensional time are treated together and called spacetime. Also, any event E has a light cone composed of four zones of possible communication and cause and effect (outside the light cone is strictly incommunicado).
There are four fundamental forces (electromagnetism, gravitation, the weak nuclear force, and the strong nuclear force).
In statistical mechanics, the four functions inequality is an inequality for four functions on a finite distributive lattice.

In logic and philosophy
The symbolic meanings of the number four are linked to those of the cross and the square. "Almost from prehistoric times, the number four was employed to signify what was solid, what could be touched and felt. Its relationship to the cross (four points) made it an outstanding symbol of wholeness and universality, a symbol which drew all to itself". Where lines of latitude and longitude intersect, they divide the earth into four proportions. Throughout the world kings and chieftains have been called "lord of the four suns" or "lord of the four quarters of the earth", which is understood to refer to the extent of their powers both territorially and in terms of total control of their subjects doings.
The Square of Opposition, in both its Aristotelian version and its Boolean version, consists of four forms: A ("All S is R"), I ("Some S is R"), E ("No S is R"), and O ("Some S is not R").
In regard to whether two given propositions can have the same truth value, there are four separate logical possibilities: the propositions are subalterns (possibly both are true, and possibly both are false); subcontraries (both may be true, but not that both are false); contraries (both may be false, but not that both are true); or contradictories (it is not possible that both are true, and it is not possible that both are false).
Aristotle held that there are basically four causes in nature: the material, the formal, the efficient, and the final.
The Stoics held with four basic categories, all viewed as bodies (substantial and insubstantial): (1) substance in the sense of substrate, primary formless matter; (2) quality, matters organization to differentiate and individualize something, and coming down to a physical ingredient such as pneuma, breath; (3) somehow holding (or disposed), as in a posture, state, shape, size, action, and (4) somehow holding (or disposed) toward something, as in relative location, familial relation, and so forth.
Immanuel Kant expounded a table of judgments involving four three-way alternatives, in regard to (1) Quantity, (2) Quality, (3) Relation, (4) Modality, and, based thereupon, a table of four categories, named by the terms just listed, and each with three subcategories.
Arthur Schopenhauers doctoral thesis was On the Fourfold Root of the Principle of Sufficient Reason.
Franz Brentano held that any major philosophical period has four phases: (1) Creative and rapidly progressing with scientific interest and results; then declining through the remaining phases, (2) practical, (3) increasingly skeptical, and (4) literary, mystical, and scientifically worthless—until philosophy is renewed through a new periods first phase. (See Brentanos essay "The Four Phases of Philosophy and Its Current State" 1895, tr. by Mezei and Smith 1998.)
C. S. Peirce, usually a trichotomist, discussed four methods for overcoming troublesome uncertainties and achieving secure beliefs: (1) the method of tenacity (policy of sticking to initial belief), (2) the method of authority, (3) the method of congruity (following a fashionable paradigm), and (4) the fallibilistic, self-correcting method of science (see "The Fixation of Belief", 1877); and four barriers to inquiry, barriers refused by the fallibilist: (1) assertion of absolute certainty; (2) maintaining that something is unknowable; (3) maintaining that something is inexplicable because absolutely basic or ultimate; (4) holding that perfect exactitude is possible, especially such as to quite preclude unusual and anomalous phenomena (see "F.R.L." [First Rule of Logic], 1899).
Paul Weiss built a system involving four modes of being: Actualities (substances in the sense of substantial, spatiotemporally finite beings), Ideality or Possibility (pure normative form), Existence (the dynamic field), and God (unity). (See Weisss Modes of Being, 1958).
Karl Popper outlined a tetradic schema to describe the growth of theories and, via generalization, also the emergence of new behaviors and living organisms: (1) problem, (2) tentative theory, (3) (attempted) error-elimination (especially by way of critical discussion), and (4) new problem(s). (See Poppers Objective Knowledge, 1972, revised 1979.)
John Boyd (military strategist) made his key concept the decision cycle or OODA loop, consisting of four stages: (1) observation (data intake through the senses), (2) orientation (analysis and synthesis of data), (3) decision, and (4) action. Boyd held that his decision cycle has philosophical generality, though for strategists the point remains that, through swift decisions, one can disrupt an opponents decision cycle.
Richard McKeon outlined four classes (each with four subclasses) of modes of philosophical inquiry: (1) Modes of Being (Being); (2) Modes of Thought (That which is); (3) Modes of Fact (Existence); (4) Modes of Simplicity (Experience)—and, corresponding to them, four classes (each with four subclasses) of philosophical semantics: Principles, Methods, Interpretations, and Selections. (See McKeons "Philosophic Semantics and Philosophic Inquiry" in Freedom and History and Other Essays, 1989.)
Jonathan Lowe (E.J. Lowe) argues in The Four-Category Ontology, 2006, for four categories: kinds (substantial universals), attributes (relational universals and property-universals), objects (substantial particulars), and modes (relational particulars and property-particulars, also known as "tropes"). (See Lowes "Recent Advances in Metaphysics," 2001, Eprint)
Four opposed camps of the morality and nature of evil: moral absolutism, amoralism, moral relativism, and moral universalism.

In technology
The resin identification code used in recycling to identify low-density polyethylene.
Most furniture has four legs – tables, chairs, etc.
The four color process (CMYK) is used for printing.
Wide use of rectangles (with four angles and four sides) because they have effective form and capability for close adjacency to each other (houses, rooms, tables, bricks, sheets of paper, screens, film frames).
In the Rich Text Format specification, language code 4 is for the Chinese language. Codes for regional variants of Chinese are congruent to 4 mod 256.
Credit card machines have four-twelve function keys.
On most phones, the 4 key is associated with the letters G, H, and I, but on the BlackBerry Pearl, it is the key for D and F.
On many computer keyboards, the "4" key may also be used to type the dollar sign ($) if the shift key is held down.
It is the number of bits in a nibble, equivalent to half a byte
In internet slang, "4" can replace the word "for" (as "four" and "for" are pronounced similarly). For example, typing "4u" instead of "for you".
In Leetspeak, "4" may be used to replace the letter "A".
The TCP/IP stack consists of four layers.

In transport
Many internal combustion engines are called four-stroke engines because they complete one thermodynamic cycle in four distinct steps: Intake, compression, power, and exhaust.
Most vehicles, including motor vehicles, and particularly cars/automobiles and light commercial vehicles have four road wheels.
"Quattro", meaning four in the Italian language, is used by Audi as a trademark to indicate that all-wheel drive (AWD) technologies are used on Audi-branded cars. The word "Quattro" was initially used by Audi in 1980 in its original 4WD coupé, the Audi Quattro. Audi also has a privately held subsidiary company called quattro GmbH.
List of highways numbered 4

In sports
In the Australian Football League, the top level of Australian rules football, each team is allowed 4 "interchanges" (substitute players), who can be freely substituted at any time, subject to a limit on the total number of substitutions.
In baseball:
There are four bases in the game: first base, second base, third base, and home plate; to score a run, an offensive player must complete, in the sequence shown, a circuit of those four bases.
When a batter receives four pitches that the umpire declares to be "balls" in a single at-bat, a base on balls, informally known as a "walk", is awarded, with the batter sent to first base.
For scoring, number 4 is assigned to the second baseman.
Four is the most runs that can be scored on any single at bat, whereby all three baserunners and the batter score (the most common being via a grand slam).
The fourth batter in the batting lineup is called the cleanup hitter.
In basketball, the number four is used to designate the power forward position, often referred to as "the four spot" or "the four".
In cricket, a four is a specific type of scoring event, whereby the ball crosses the boundary after touching the ground at least one time, scoring four runs. Taking four wickets in four consecutive balls is typically referred to as a double hat trick (two consecutive, overlapping hat tricks).
In American Football teams get four downs to reach the line of gain.
In rowing, a four refers to a boat for four rowers, with or without coxswain. In rowing nomenclature, 4− represents a coxless four and 4+ represents a coxed four.
In rugby league:
A try is worth 4 points.
One of the two starting centres wears the jersey number 4. (An exception to this rule is the Super League, which uses static squad numbering.)
In rugby union:
One of the two starting locks wears the jersey number 4.
In the standard bonus points system, a point is awarded in the league standings to a team that scores at least 4 tries in a match, regardless of the match result.

In other fields
The phrase "four-letter word" is used to describe many swear words in the English language.
Four is the only number whose name in English has the same number of letters as its value.
Four (四, formal writing: 肆, pinyin sì) is considered an unlucky number in Chinese, Korean, Vietnamese and Japanese cultures mostly in Eastern Asia because it sounds like the word "death" (死, pinyin sǐ). To avoid complaints from people with tetraphobia, many numbered product lines skip the "four": e.g. Nokia cell phones (there was no series beginning with a 4 until the Nokia 4.2), Palm PDAs, etc </s>


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