Aarushhh/wikipedia-simple-splitted huggingface dataset:
The MacBook uses a power efficient CPU, M1, and has a power-efficient Retina display, and is slimmer than previous models.
 The MacBook, MacBook Pro, and MacBook Air have highly recyclable aluminium and glass enclosures, mercury-free displays and arsenic-free display glass. The printed circuit boards, electrical components, mechanical parts, and internal cables are BFR-free and PVC-free.
 The MacBook, MacBook Air, MacBook Pro, and the LED Cinema Display contain energy-efficient LED display technology. The MacBook LED-backlit display uses 30% less power compared to conventional CCFL-backlit displays.
 Sleep-mode energy usage has decreased 93% between the first-generation and current-generation iMac. This is due to improvements in CPU power management and increased hardware efficiency.
 Between the fourth-generation iPod nano and the first-generation iPod nano, the packaging is 32% lighter and uses 54% less volume.
Apple products are compliant with the European Directive on the Restriction of the Use of Certain Hazardous Substances in Electrical and Electronic Equipment, also known as the RoHS directive. Examples of materials restricted by RoHS include lead, mercury, cadmium, hexavalent chromium, and PBB and PBDE flame retardants. Apple met many of the RoHS requirements long before the July 2006 deadline.
 Starting from the iPhone 12, iPhone 12 Pro and Apple Watch Series 6, Apple products stopped shipping with chargers and EarPods as an incentive for users to reuse previous accessories.
People

CEOs 
 1977–1981: Michael Scott
 1981–1983: Mike Markkula
 1983–1993: John Sculley
 1993–1996: Michael Spindler
 1996–1997: Gil Amelio
 1997–2011: Steve Jobs (Interim CEO 1997–2000)
 2004, 2009, 2011–present: Tim Cook (Acting CEO during Steve Jobs' health issues; replaced Steve Jobs after he resigned)

Directors 
 the following individuals sit on the board of Apple Inc.
 Arthur D. Levinson, chairman and CEO of Genentech
 Tim Cook
 James A. Bell, retired President of Boeing
 Al Gore, former Vice President of the United States
 Andrea Jung, chairman and CEO of Avon Products
 Ronald Sugar, former chairman and CEO of Northrop Grumman
 Susan Wagner, co-founder of BlackRock

Executives 
 Arthur D. Levinson, Chairman
 Tim Cook, CEO
 Jeff Williams, COO
Employees 
Since the formation of the Apple Computer Company in 1977, Apple has employed over 95,000 people worldwide. The majority of Apple's employees have been in the United States but Apple has substantial manufacturing, sales, marketing, and support organizations worldwide, with some engineering operations in Paris and Tokyo.

Apple employees include employees of companies Apple owns, and less important, but still relevant companies such as FileMaker Inc. and Braeburn Capital.

Controversy 
Apple Corps has sued Apple Inc. many times for trademark infringement. In the first case, Apple Inc. agreed not to go into the music industry. Apple Corps believes this agreement was broken when Apple Inc. launched the iTunes Store, Apple's online music store.
The two companies had trouble in the past, over the use of the Apple name. They made a deal that Apple Computer would not act as a music company. When Apple Computer Inc. began to sell their iPod, and set up their iTunes music store, Apple Corps believed they had broken their agreement, and took them to court. Apple Computer won the case, but the two companies later worked out a new deal. This deal now means that the Beatles music is now on the iTunes store, whereas it was not there before. Apple Computer Inc. was then renamed as Apple Inc. because of its mobile technology business. Steve Jobs, then CEO of Apple, Inc., has said in the past that he loves music from The Beatles, which can be considered to be very ironic.

Related pages
 Pixar, an animation studio founded by Steve Jobs, one of the founders of Apple

References
References 

 
 

1976 establishments in California
Apple Inc.
Steve Jobs
1976 establishments
American entertainment companies
American software companies
Companies based in San Francisco
Companies listed on NASDAQ
Companies listed on the London Stock Exchange
Companies listed on the Tokyo Stock Exchange
Electronics companies of the United States
Mobile phones
Soil is loose material which lies on top of the land. It has many things in it, like tiny grains of rock, minerals, water and air. Soil also has living things and dead things in it: "organic matter". Soil is important for life on Earth.

Because soil holds water and nutrients, it is a very good place for plants to grow. Soil holds the roots, and lets plants stand above the ground to collect the light they need to live. Almost as important are the fungi. There are fungi which grow into plant roots, a symbiosis known as mycorrhiza. This helps trees grow. There are many other fungi that live by breaking down dead organic material: the remains of other living things. The broken down material is a main source of plant nutrients.  The soil also has many microorganisms living in it. Many of them eat the organic material in the soil. They use oxygen and release carbon dioxide. They also release mineral nutrients into the soil.
Many animals dig into the soil and make the soil their home. The large animals use soil to make dens for sleeping and giving birth. The small animals live most of their life in the soil.  Earthworms are famous for improving soil. This is because the holes they make let air go into the soil. The holes also let water go through.

Soil is different in different places on Earth. This is because the climate and rocks in the Earth are different in different places on Earth.  Soils are usually thicker in places where ice sheets covered the land during the Pleistocene ice ages.  This is because the ice sheets ground the rock into powder as they slowly moved over the surface.

What is soil 
Soil is made of four things.
Rock pieces and the rocks are made of minerals,
dead and living things (organic matter, humus),
water (soil moisture),
air.
Soil has rock pieces made small by wind and rain and sun and snow.  The rocks are made of minerals and some of the minerals dissolve in water.  Some of the minerals dissolved in water can be used as food by plants. Soil also has dead and living things (organic matter) in it.  When a plant dies, it is eaten by animals including bacteria in the soil. When the bacteria are done eating, what is left behind is called humus. When the bacteria die the plant food (minerals) goes back into the soil.  A food for plants is called a "plant nutrient".  There are many kinds of plant nutrients.  

Water can enter the gaps in the soil.  Half of the soil is gaps filled with water and air.  Water in soil is called soil moisture.  Plants drink the water and the minerals in the water. Plant roots need air to live. If plant roots do not have air, the roots will die. If the plant roots die, the plant will die. A plant that dies is eaten by bacteria and becomes plant nutrients again.
Soil texture 
Every soil has different amounts of sand and silt and clay. The mix of sand and silt and clay is the "texture" of the soil. We can also say the mix has a "soil texture". A soil with a lot of sand is called a "sandy soil texture". A soil with a lot of silt is called a "silt soil texture". A soil with a lot of clay is called a "clay soil texture". Farmers like to grow food in the best soil. The best soil is half sand and some silt and a little clay. The organic matter found in the soil is not counted in the soil texture. Only the rocks are counted when we discover the soil texture. Soil texture is very important.
Soil horizons (layers) 

A soil has a "soil texture" (sand and silt and clay) and it has organic matter mixed in it. But weather changes the soil. It is cold on the Earth near the north and south poles. It is hot near the equator of the Earth. Some places on Earth get a lot of rain and some places get no rain. Hot and wet weather make one kind of soil. Cold and dry weather make another kind of soil. Rain water makes small things in the soil move down with the water. When the things in the water get stuck in the soil those things make a layer in the soil. If you dig down into the soil you may find many layers in the soil. The layers may have different colors. The layers may have different "soil textures". The top part of the soil may have a lot of humus and sand. Below that layer there may be a layer of silt. Below that layer there may be a layer of clay.
We call those layers "soil horizons". The top horizon may be an inch (25mm) thick. We call that layer the "O" horizon or sometimes "topsoil". The next layer (horizon) is the "B" horizon.  The next lower layer of soil is the "C" horizon. The bottom layer has many rocks and may be called the bedrock or "R" horizon for "rock".   Deep down, there is always bedrock.   But you may have to dig down a mile (a km) or more. When the soil dries, the soil may shrink and cracks will form in the soil. The soil in the top layer may fall down into the cracks. This causes the layers of soil to be changed because they are mixed. There may be many types soil where you live or only one type of soil. Different rocks make different soil textures. Different weather makes the different soil textures different. And so, there are different soils all over the world.

Soil carbon
Soil carbon 

People want to keep carbon in the soil, because when it is in the air (in carbon dioxide or methane) it makes the world hotter. If people dig or plow too much then carbon can escape from the soil into the air.

Related pages 
 Agronomy
 Soil fertility

References

Other websites

 Short video about soil from The Guardian newspaper

Soil
The word organic is used for different things:
 Something of, or relating to, an organism
 Organic chemistry, chemistry that is based on carbon, which is the basis for all living things.
 Organic matter in soil is material that is, or once was, a plant or animal.
 Organic farming, agriculture conducted according to certain standards, especially the use of only naturally produced fertilizers and non-chemical means of pest control.
3D (or 3-D) means three-dimensional, or having three dimensions. For example, a box is three-dimensional; it is solid, and not thin like a piece of paper. It has volume, a top and bottom, left and right (sides), as well as a front and back. You can turn the box around to view it from another side (called a face, surface or simply side).

A dimension can be measured in inches, microns, miles, kilometers, or any other unit of length.

The three dimensions are often called length (or depth), width (or breadth), and height. Some purposes use other words. 

3D graphics are used to make video games or animated movies.  Many calculations are needed to make pictures seem three-dimensional on a screen. Modern computers usually have a GPU (Graphics Processing Unit) to handle these calculations.

Binocular vision helps people to see the third dimension easily.

In mathematics
In mathematics 

In the Cartesian coordinate system, length, width, and height are given in letters (variables) to make them easier to write, or if a value is not known. Often X is width, Y is height, and Z is length. Other 3D coordinate systems such as spherical coordinates use both linear and angular measurements.

The mathematical study of 3D shapes and dimensions is called solid geometry.

Space-time theory 

Some people think of time as if it were a fourth dimension. This is called space-time theory. In this idea, there are three dimensions of space, along with the dimension of time.

Related pages 
 3D printing
 Holography
 Perspective (graphical)

Computing
Animation
Geometry
Humidity means water vapor in the air, but not to liquid droplets in fog, clouds, or rain.  Deserts usually have low humidity, and tropical regions have high humidity. The word "humid" often means that the humidity is high, which gives the feeling of being very damp (wet air), stuffy, or even sweltering when the temperature is also high. When the humidity is low, the air can be said to be "not humid" or "dry."

Higher humidity reduces the effectiveness of sweating in cooling the body by reducing the rate of evaporation of moisture from the skin.

The term "relative humidity" is used to note the amount of humidity as a percent, from 0-100%. Meteorologists use  hygrometers to measure the humidity in the air.

Humidity affects the rate of evaporation. With a higher humidity, the rate of evaporation is less.

Related pages
 Dew point
Relative humidity

Meteorology
Weather measurements
A Calabi–Yau manifold, or 'Calabi–Yau space', is a special type of manifold. It is described in certain branches of mathematics such as algebraic geometry.  

The Calabi–Yau manifold's properties, such as Ricci flatness, have applications in theoretical physics. Particularly in superstring theory, the extra dimensions of spacetime might take the form of a 6-dimensional Calabi–Yau manifold. This led to the idea of  string theory mirror symmetry.

Algebraic geometry
Quantum mechanics explains how the universe works at a scale smaller than atoms. It is also called  quantum physics or quantum theory. Mechanics is the part of physics that explains how things move and quantum is the Latin word for 'how much'. A quantum of energy is the least amount possible (or the least extra amount), and quantum mechanics describes how that energy moves or interacts.

Atoms were long considered the smallest pieces of matter, but modern science has shown that there are even smaller subatomic particles, like protons, neutrons and electrons.  Quantum mechanics describes how the particles that make up atoms work.

Quantum physics also tells us how electromagnetic waves (like light) work. Wave–particle duality means that particles behave like waves and waves behave like particles. (They are not two kinds of things, they are something like both: this is their duality.) Much of modern physics and chemistry can be described and understood using the mathematical rules of quantum mechanics.
The mathematics used to study subatomic particles and electromagnetic waves is very complex because they act in very strange ways.

Waves and photons 
Photons are particles that are point-sized, tinier than atoms. Photons are like "packets" or packages of energy. Light sources such as candles or lasers produce light in bits called photons. 

The more photons a lamp produces, the brighter the light. Light is a form of energy that behaves like the waves in water or radio waves. The distance between the top of one wave and the top of the next wave is called a 'wavelength'. Each photon carries a certain amount, or 'quantum', of energy depending on its wavelength.
A light's color depends on its wavelength. The color violet (the bottom or innermost color of the rainbow) has a wavelength of about 400 nm ("nanometers") which is 0.00004 centimeters or 0.000016 inches. Photons with wavelengths of 10-400 nm are called ultraviolet (or UV) light. Such light cannot be seen by the human eye. On the other end of the visual spectrum, red light is about 700 nm. Infrared light is about 700 nm to 300,000 nm. Human eyes are not sensitive to infrared light either.

Wavelengths are not always so small. Radio waves have longer wavelengths.  The wavelengths for an FM radio can be several meters in length (for example, stations transmitting on 99.5 FM are emitting radio energy with a wavelength of about 3 meters, which is about 10 feet). Each photon has a certain amount of energy related to its wavelength. The shorter the wavelength of a photon, the greater its energy. For example, an ultraviolet photon has more energy than an infrared photon.
Wavelength and frequency (the number of times the wave crests per second) are inversely proportional, which means a longer wavelength will have a lower frequency, and vice versa. If the color of the light is infrared (lower in frequency than red light), each photon can heat up what it hits. So, if a strong infrared lamp (a heat lamp) is pointed at a person, that person will feel warm, or even hot, because of the energy stored in the many photons. The surface of the infrared lamp may even get hot enough to burn someone who may touch it.
Humans cannot see infrared light, but we can feel the radiation in the form of heat.  For example, a person walking by a brick building that has been heated by the sun will feel heat from the building without having to touch it.
Quantum mechanics started when it was discovered that if a particle has a certain frequency, it must also have a certain amount of energy. Energy is proportional to frequency (E ∝ f). The higher the frequency, the more energy a photon has, and the more damage it can do. Quantum mechanics later grew to explain the internal structure of atoms. Quantum mechanics also explains the way that a photon can interfere with itself, and many other things never imagined in classical physics.

Quantization 
Max Planck discovered the relationship between frequency and energy. Nobody before had ever guessed that frequency is directly proportional to energy (this means that as one of them doubles, the other does, too). Under what are called natural units, then the number representing the frequency of a photon would also represent its energy. The equation would then be:

meaning energy equals frequency.
But the way physics grew, there was no natural connection between the units that were used to measure energy and the units commonly used to measure time (and therefore frequency). So the formula that Planck worked out to make the numbers all come out right was:

or, energy equals h times frequency. This h is a number called Planck's constant after its discoverer.

Quantum mechanics is based on the knowledge that a photon of a certain frequency means a photon of a certain amount of energy. Besides that relationship, a specific kind of atom can only give off certain frequencies of radiation, so it can also only give off photons that have certain amounts of energy.

History 

Isaac Newton thought that light was made of very small things that we would now call particles (he referred to them as "Corpuscles"). Christiaan Huygens thought that light was made of waves. Scientists thought that a thing cannot be a particle and a wave at the same time.
Here are some of the people who discovered the basic parts of quantum mechanics: Max Planck, Albert Einstein, Satyendra Nath Bose, Niels Bohr, Louis de Broglie, Max Born, Paul Dirac, Werner Heisenberg, Wolfgang Pauli, Erwin Schrödinger, John von Neumann, and Richard Feynman. They did their work in the first half of the 20th century.

Beyond Planck 

Quantum mechanics formulae and ideas were made to explain the light that comes from glowing hydrogen. The quantum theory of the atom also had to explain why the electron stays in its orbit, which other ideas were not able to explain. It followed from the older ideas that the electron would have to fall in to the center of the atom because it starts out being kept in orbit by its own energy, but it would quickly lose its energy as it revolves in its orbit. (This is because electrons and other charged particles were known to emit light and lose energy when they changed speed or turned.)
Hydrogen lamps work like neon lamps, but neon lamps have their own unique group of colors (and frequencies) of light. Scientists learned that they could identify all elements by the light colors they produce. They just could not figure out how the frequencies were determined.

Then, a Swiss mathematician named Johann Balmer figured out an equation that told what λ (lambda, for wave length) would be:

where B is a number that Balmer determined to be equal to 364.56 nm.

This equation only worked for the visible light from a hydrogen lamp. But later, the equation was made more general:

where R is the Rydberg constant, equal to 0.0110 nm−1, and n must be greater than m.

Putting in different numbers for m and n, it is easy to predict frequencies for many types of light (ultraviolet, visible, and infared). To see how this works, go to Hyperphysics and go down past the middle of the page. (Use H = 1 for hydrogen.)
In 1908, Walter Ritz made the Ritz combination principle that shows how certain gaps between frequencies keep repeating themselves. This turned out to be important to Werner Heisenberg several years later.

In 1905, Albert Einstein used Planck's idea to show that a beam of light is made up of a stream of particles called photons. The energy of each photon depends on its frequency. Einstein's idea is the beginning of the idea in quantum mechanics that all subatomic particles like electrons, protons, neutrons, and others are both waves and particles at the same time. (See picture of atom with the electron as waves at atom.) This led to a theory about subatomic particles and electromagnetic waves called wave-particle duality. This is where particles and waves were neither one nor the other, but had certain properties of both.
In 1913, Niels Bohr came up with the idea that electrons could only take up certain orbits around the nucleus of an atom. Under Bohr's theory, the numbers called m and n in the equation above could represent orbits. Bohr's theory said electrons could begin in some orbit m and end up in some orbit n, or an electron could begin in some orbit n and end up in some orbit m so if a photon hits an electron, its energy will be absorbed, and the electron will move to a higher orbit because of that extra energy. Under Bohr's theory, if an electron falls from a higher orbit to a lower orbit, then it will have to give up energy in the form of a photon. The energy of the photon will equal the energy difference between the two orbits, and the energy of a photon makes it have a certain frequency and color
. Bohr's theory provided a good explanation of many aspects of subatomic phenomena, but failed to answer why each of the colors of light produced by glowing hydrogen (and by glowing neon or any other element) has a brightness of its own, and the brightness differences are always the same for each element.
By the time Niels Bohr came out with his theory, most things about the light produced by a hydrogen lamp were known, but scientists still could not explain the brightness of each of the lines produced by glowing hydrogen.

Werner Heisenberg took on the job of explaining the brightness or "intensity" of each line. He could not use any simple rule like the one Balmer had come up with. He had to use the very difficult math of classical physics that figures everything out in terms of things like the mass (weight) of an electron, the charge (static electric strength) of an electron, and other tiny quantities. Classical physics already had answers for the brightness of the bands of color that a hydrogen lamp produces, but the classical theory said that there should be a continuous rainbow, and not four separate color bands. Heisenberg's explanation is:
Classical physics uses the mathematical methods of Joseph Fourier to make a math picture of the physical world,  It uses collections of smooth curves that go together to make one smooth curve that gives, in this case, intensities for light of all frequencies from some light. But it is not right because that smooth curve only appears at higher frequencies. At lower frequencies, there are always isolated points and nothing connects the dots. So, to make a map of the real world, Heisenberg had to make a big change. He had to do something to pick out only the numbers that would match what was seen in nature. Sometimes people say he "guessed" these equations, but he was not making blind guesses. He found what he needed. The numbers that he calculated would put dots on a graph, but there would be no line drawn between the dots. And making one "graph" just of dots for every set of calculations would have wasted lots of paper and not have gotten anything done
. Heisenberg found a way to efficiently predict the intensities for different frequencies and to organize that information in a helpful way.
Just using the empirical rule given above, the one that Balmer got started and Rydberg improved, we can see how to get one set of numbers that would help Heisenberg get the kind of picture that he wanted:

The rule says that when the electron moves from one orbit to another it either gains or loses energy, depending on whether it is getting farther from the center or nearer to it. So we can put these orbits or energy levels in as headings along the top and the side of a grid. For historical reasons the lowest orbit is called n, and the next orbit out is called n - a, then comes n - b, and so forth. It is confusing that they used negative numbers when the electrons were actually gaining energy, but that is just the way it is.
Since the Rydberg rule gives us frequencies, we can use that rule to put in numbers depending on where the electron goes. If the electron starts at n and ends up at n, then it has not really gone anywhere, so it did not gain energy and it did not lose energy. So the frequency is 0.  If the electron starts at n-a and ends up at n, then it has fallen from a higher orbit to a lower orbit. If it does so then it loses energy, and the energy it loses shows up as a photon. The photon has a certain amount of energy, e, and that is related to a certain frequency f by the equation e = h f. So we know that a certain change of orbit is going to produce a certain frequency of light, f.  If the electron starts at n and ends up at n - a, that means it has gone from a lower orbit to a higher orbit. That only happens when a photon of a certain frequency and energy comes in from the outside, is absorbed by the electron and gives it its energy, and that is what makes the electron go out to a higher orbit
. So, to keep everything making sense, we write that frequency as a negative number. There was a photon with a certain frequency and now it has been taken away.
So we can make a grid like this, where f(a←b) means the frequency involved when an electron goes from energy state (orbit) b to energy state a (Again, sequences look backwards, but that is the way they were originally written.):

Grid of f
Heisenberg did not make the grids like this. He just did the math that would let him get the intensities he was looking for. But to do that he had to multiply two amplitudes (how high a wave measures) to work out the intensity. (In classical physics, intensity equals amplitude squared.) He made an odd-looking equation to handle this problem, wrote out the rest of his paper, handed it to his boss, and went on vacation. Dr. Born looked at his funny equation and it seemed a little crazy. He must have wondered, "Why did Heisenberg give me this strange thing? Why does he have to do it this way?" Then he realized that he was looking at a blueprint for something he already knew very well. He was used to calling the grid or table that we could write by doing, for instance, all the math for frequencies, a matrix. And Heisenberg's weird equation was a rule for multiplying two of them together. Max Born was a very, very good mathematician
. He knew that since the two matrices (grids) being multiplied represented different things (like position (x,y,z) and momentum (mv), for instance), then when you multiply the first matrix by the second you get one answer and when you multiply the second matrix by the first matrix you get another answer. Even though he did not know about matrix math, Heisenberg already saw this "different answers" problem and it had bothered him. But Dr. Born was such a good mathematician that he saw that the difference between the first matrix multiplication and the second matrix multiplication was always going to involve Planck's constant, h, multiplied by the square root of negative one, i. So within a few days of Heisenberg's discovery they already had the basic math for what Heisenberg liked to call the "indeterminacy principle." By "indeterminate" Heisenberg meant that something like an electron is just not pinned down until it gets pinned down
. It is a little like a jellyfish that is always squishing around and cannot be "in one place" unless you kill it. Later, people got in the habit of calling it "Heisenberg's uncertainty principle," which made many people make the mistake of thinking that electrons and things like that are really "somewhere" but we are just uncertain about it in our own minds. That idea is wrong. It is not what Heisenberg was talking about. Having trouble measuring something is a problem, but it is not the problem Heisenberg was talking about.
Heisenberg's idea is very hard to grasp, but we can make it clearer with an example. First, we will start calling these grids "matrices," because we will soon need to talk about matrix multiplication.

Suppose that we start with two kinds of measurements, position (q) and momentum (p). In 1925, Heisenberg wrote an equation like this one:

 (Equation for the conjugate variables momentum and position)

He did not know it, but this equation gives a blueprint for writing out two matrices (grids) and for multiplying them. The rules for multiplying one matrix by another are a little messy, but here are the two matrices according to the blueprint, and then their product:

Matrix of p

Matrix of q

The matrix for the product of the above two matrices as specified by the relevant equation in Heisenberg's 1925 paper is:

Where:
 
A=p(n←n-a)*q(n-a←n-b)+p(n←n-b)*q(n-b←n-b)+p(n←n-c)*q(n-c←n-b)+.....

B=p(n-a←n-a)*q(n-a←n-c)+p(n-a←n-b)*q(n-b←n-c)+p(n-a←n-c)*q(n-c←n-c)+.....
C=p(n-b←n-a)*q(n-a←n-d)+p(n-b←n-b)*q(n-b←n-d)+p(n-b←n-c)*q(n-d←n-d)+.....

and so forth.

If the matrices were reversed, the following values would result:

A=q(n←n-a)*p(n-a←n-b)+q(n←n-b)*p(n-b←n-b)+q(n←n-c)*p(n-c←n-b)+.....
B=q(n-a←n-a)*p(n-a←n-c)+q(n-a←n-b)*p(n-b←n-c)+q(n-a←n-c)*p(n-c←n-c)+.....
C=q(n-b←n-a)*p(n-a←n-d)+q(n-b←n-b)*p(n-b←n-d)+q(n-b←n-c)*p(n-d←n-d)+.....

and so forth.

Note how changing the order of multiplication changes the numbers, step by step, that are actually multiplied.

Beyond Heisenberg 
The work of Werner Heisenberg seemed to break a log jam. Very soon, many different other ways of explaining things came from people such as Louis de Broglie, Max Born, Paul Dirac, Wolfgang Pauli, and Erwin Schrödinger. 
 
The math used by Heisenberg and earlier people is not very hard to understand, but the equations quickly grew very complicated as physicists looked more deeply into the atomic world.
Further mysteries 
In the early days of quantum mechanics, Albert Einstein suggested that if it were right then quantum mechanics would mean that there would be "spooky action at a distance." It turned out that quantum mechanics was right, and that what Einstein had used as a reason to reject quantum mechanics actually happened. This kind of "spooky connection" between certain quantum events is now called "quantum entanglement".
Einstein argued that over such a great distance it was crazy to think that forcing one electron to show its spin would then somehow make the other electron show an opposite characteristic. He said that the two electrons must have been spin-up or spin-down all along, but that quantum mechanics could not predict which characteristic each electron had. Being unable to predict, only being able to look at one of them with the right experiment, meant that quantum mechanics could not account for something important. Therefore, Einstein said, quantum mechanics had a big hole in it. Quantum mechanics was incomplete.

Later, it turned out that experiments showed that it was Einstein who was wrong.
Heisenberg uncertainty principle 
In 1925, Werner Heisenberg described the Uncertainty principle, which says that the more we know about where a particle is, the less we can know about how fast it is going and in which direction. In other words, the more we know about the speed and direction of something small, the less we can know about its position. Physicists usually talk about the momentum in such discussions instead of talking about speed. Momentum is just the speed of something in a certain direction times its mass.
The principle also says that there are many pairs of measurements for which we cannot know both of them about any particle (a very small thing), no matter how hard we try. The more we learn about one of such a pair, the less we can know about the other.

Even Albert Einstein had trouble accepting such a bizarre concept, and in a well-known debate said, "God does not play dice".
To this, Danish physicist Niels Bohr famously responded, "Einstein, don't tell God what to do".

Uses of quantum mechanics 
Electrons surround every atom's nucleus. Chemical bonds link atoms to form molecules. A chemical bond links two atoms when electrons are shared between those atoms. Thus quantum mechanics is the physics of the chemical bond and of chemistry. Quantum mechanics helps us understand how molecules are made, and what their properties are.
Quantum mechanics can also help us understand big things, such as stars and even the whole universe. Quantum mechanics is a very important part of the theory of how the universe began called the Big Bang.

Everything made of matter is attracted to other matter because of a fundamental force called gravity. Einstein's theory that explains gravity is called the theory of general relativity. A problem in modern physics is that some conclusions of quantum mechanics do not seem to agree with the theory of general relativity.
Quantum mechanics is the part of physics that can explain why all electronic technology works as it does. Thus quantum mechanics explains how computers work, because computers are electronic machines. But the designers of the early computer hardware of around 1950 or 1960 did not need to think about quantum mechanics. The designers of radios and televisions at that time did not think about quantum mechanics either. However, the design of the more powerful integrated circuits and computer memory technologies of recent years does require quantum mechanics.
 
Quantum mechanics has also made possible technologies such as:
 Spectroscopy
 Lasers
 MRIs
 CDs and DVDs
Why quantum mechanics is hard to learn 
Quantum mechanics is a challenging subject for several reasons:
 Quantum mechanics explains things in very different ways from what we learn about the world when we are children.
 Understanding quantum mechanics requires more mathematics than algebra and simple calculus. It also requires matrix algebra, complex numbers, probability theory, and partial differential equations.
 Physicists are not sure what some of the equations of quantum mechanics tell us about the real world.
 Quantum mechanics suggests that atoms and subatomic particles behave in strange ways, completely unlike anything we see in our everyday lives.
 Quantum mechanics describes things that are extremely  small, so we cannot see some of them without special equipment, and we cannot see many of them at all.
One example is Young's double-slit experiment. If we shoot single photons (single units of light) from a laser at a sheet of photographic film, we will see a single spot of light on the developed film. If we put a sheet of metal in between, and make two very narrow slits in the sheet, when we fire many photons at the metal sheet, and they have to go through the slits, then we will see something remarkable. All the way across the sheet of developed film we will see a series of bright and dark bands. We can use mathematics to tell exactly where the bright bands will be and how bright the light was that made them, that is, we can tell ahead of time how many photons will fall on each band. But if we slow the process down and see where each photon lands on the screen we can never tell ahead of time where the next one will show up
. We can know for sure that it is most likely that a photon will hit the center bright band, and that it gets less and less likely that a photon will show up at bands farther and farther from the center. So we know for sure that the bands will be brightest at the center and get dimmer and dimmer farther away. But we never know for sure which photon will go into which band.
One of the strange conclusions of quantum mechanics theory is the "Schrödinger's cat" effect. Certain properties of a particle, such as their position, speed of motion, direction of motion, and "spin", cannot be talked about until something measures them (a photon bouncing off of an electron would count as a measurement of its position, for example). Before the measurement, the particle is in a "superposition of states," in which its properties have many values at the same time. Schrödinger said that quantum mechanics seemed to say that if something (such as the life or death of a cat) was determined by a quantum event, then its state would be determined by the state that resulted from the quantum event, but only at the time that somebody looked at the state of the quantum event. In the time before the state of the quantum event is looked at, perhaps "the living and dead cat (pardon
the expression) [are] mixed or smeared out in equal parts."
Reduced Planck's constant
People often use the symbol , which is called "h-bar."  . H-bar is a unit of angular momentum. When this new unit is used to describe the orbits of electrons in atoms, the angular momentum of any electron in orbit is always a whole number.

Example 
The particle in a 1-dimensional well is the most simple example showing that the energy of a particle can only have specific values. The energy is said to be "quantized."
The well has zero potential energy inside a range and has infinite potential energy everywhere outside that range. For the 1-dimensional case in the  direction, the time-independent Schrödinger equation can be written as:

 

Using differential equations, we can figure out that  can be written as
 
or as
  (by Euler's formula).

The walls of the box mean that the wavefunction must have a special form. The wavefunction of the particle must be zero anytime the walls are infinitely tall.  At each wall:
Consider x = 0
 sin 0 = 0, cos 0 = 1. To satisfy  the cos term has to be removed. Hence D = 0

Now consider: 
 at , 
 If  then  for all x. This solution is not useful.
 therefore  must be true, giving us

We can see that  must be an integer.  This means that the particle can only have special energy values and cannot have the energy values in between.  This is an example of energy "quantization."

Related pages 
 Electromagnetic wave
 Electron
 Photon
 Quantum entanglement
 Quantum computer
 Quantum state
 Schrödinger equation

References 
 Feynman, Richard, 1985. The Strange Theory of Light and Matter . Princeton University Press.
 McEvoy, J.P. and Oscar Zarate, 1996. Introducing Quantum Theory.  Icon Books.

Notes

More reading

Other websites 

 A history of quantum mechanics
 Introduction to Quantum Theory at Quantiki 
 Quantum mechanics - Citizendium

Basic physics ideas
Nuclear physics
Quantum mechanics
Duisburg (; , Ripuarian: Duisburch, Low Franconian: Duusbörg) is a German city in the state of North Rhine-Westphalia. It is where the Rhine and the Ruhr rivers meet. About 500,000 people live in Duisburg.

References

Other websites

Imperial free cities
Urban districts in Regierungsbezirk Düsseldorf
Kuopio is a city in Northern Savonia, Finland. It is the biggest city and cultural center of Eastern Finland. In November 2015 the population was about 112.000. It is the 8th biggest city in Finland. 

The city is surrounded by lake Kallavesi. Many parts of the city are built on islands. Kuopio has always been a city of education. Two important schools are the University of Eastern Finland and the Savonia University of Applied Sciences.

History 
In 2011 the town of Karttula merged with Kuopio. In 2013 Nilsiä merged as well. In 2015, Maaninka merged with the city. In 2017 Juankoski merged with the city.

Twin towns — Sister cities

Kuopio is twinned with:

References

Cities in Finland
Municipalities of North Savo
A hammer is a tool for putting nails into objects such as wood. It has a long handle, and a tip with a flat end for hitting nails. The most common type of hammer (sometimes called a claw hammer) has a curved end (on the other side of the hitting end) for pulling nails out.

A sledgehammer is a hammer that has a longer shaft, and a more massive head. The user can swing it with two hands and apply more force.

History 
Hammers were used around 3.3 million years ago. The first hammers were made without handles. Stones attached to sticks with strips of leather or animal sinew were being used. Hammers with handles were made in 30,000 BCE during the middle of the Paleolithic Stone Age. The hammer was used for building, food and protection.

Classification of hammers 
Hammers can be classified into two. They are:

Hand-powered hammers 

Hand-powered hammers are hammers that are used with the hand. Examples include:
Ball-peen hammer
 Boiler scaling hammer
 Brass hammer
 Bricklayer's hammer
 Carpenter's hammer
 Cow hammer
 Cross-peen hammer
 Dead blow hammer
 Demolition hammer
 Drilling hammer
 Electrician's hammer
 Engineer's hammer
 Gavel
 Geologist's hammer
 Knife-edged hammer
 Lathe hammer
 Lump hammer
 Magnetic double-head hammer
 Magnetic tack hammer
 Mallet
 Railway track keying hammer
 Rock climbing hammer
 Rounding hammer
 Shingler's hammer
 Sledgehammer
 Soft-faced hammer
 Splitting maul
 Strike Tack hammer
 Stonemason's hammer
 Tinner
 Upholstery hammer
 Warrington hammer
 Welder's chipping hammer

Mechanically-powered hammer
Mechanically powered hammers are hammers that are used with a machine. Examples include:

 Hammer drill
 High Frequency Impact Treatment hammer
 Jackhammer
 Steam hammer
 Trip hammer

Hammers as weapons 
Big hammers were sometimes used as weapons. A tiny hammer is also used inside most small arms.

References 

Basic English 850 words
Tools
Faeces  (or faeces), also called poo or poop is the body's solid waste left over from eating food. Human feces leave the intestinal tract and are removed from the body through the anus. Feces are known for their unpleasant odor. The color, which can range from dark green through brown (the most common color) to bright yellow, depends on a lot of different things; for example, different foods can change the color of feces, so can some illnesses, like diarrhea. The consistency of feces changes too. In humans it is measured using the Bristol stool scale, a system for separating feces into 7 different types. It is used for medical diagnosis.

Although feces are generally thought to be waste, they actually have many uses. Feces are used by some scientists to follow animal populations. Feces from animals and humans can be used to create fertilizers for plant crops. Some feces are also used as a fuel for fires.
Animals can also poop. In informal language, there are many words for feces. These are often offensive or even vulgar. Examples include "shit", "poop", and "crap".

In popular culture, there are a few books about feces. Most of these books are for children. One is called Everyone Poops. It was written by Tarō Gomi, who is from Japan.

Smell of feces 
Poop smells like rotten eggs. It is known for its stinky smell.

References

Related pages 
 Diarrhea
 Constipation
 Coprophagia
 Urine
 Sanitation

Digestive system
Catholicism is the traditions and beliefs of Catholic Churches. It refers to their theology, liturgy, morals and spirituality. The term usually refers to churches, both western and eastern, that are in full communion with the Holy See.

In 2012, there were more than 1.1 billion Catholics worldwide. This makes up more than 17% of the world population.

The word "Catholicism" comes from the Greek word catholikismos (). This means "universal".

Characteristics

The word "Catholicism" refers to so many things, including its religious beliefs (called theologies and "doctrines"), and its form of religious worship (called liturgies).  The word also refers to Catholic religious beliefs about ethics (things that are right and wrong). It also refers to the ways that members of the Catholic religion live and practice their religion.
Many people use the word Catholicism to talk about religious beliefs of the Catholic Church, whose leader is called the "Bishop of Rome" and often called the "Pope". The Catholic Church is based in the Vatican City, a small independent country in the city of Rome, Italy. Sometimes the word also refers to beliefs of other Christian churches, including the Eastern Orthodox Churches, who have many beliefs similar to the Catholic Church, but do not believe the Bishop of Rome is their leader.

The word Catholicism is often used to tell the difference between the beliefs of Catholic Christians and the beliefs of others called Protestant Christians. Catholic and Orthodox churches use church leaders, called bishops, to determine beliefs. Protestants, however, often use each member's own understanding of the Bible to determine beliefs. Protestants use guidelines from the 16th-century Protestant Reformation to understand the Bible. It is the world's second largest religious denomination after Sunnism.
Where the word Catholic came from
The oldest document that uses the name "Catholic Church" is a letter written by a man named Ignatius. Ignatius lived in the ancient city of Antioch. In the year 107, Ignatius wrote a letter addressed to the Christian community in the ancient city of Smyrna. In this letter, Ignatius encouraged the Christian Community to be loyal to their leader, the Bishop. Ignatius wrote:

"Wherever the bishop shall appear, there let the multitude of the people also be; even as, wherever Jesus Christ is, there is the Catholic Church."

Groups who call themselves "Catholic" 
Many different denominations (groups) of Christians call themselves "catholic". Often these groups have special beliefs about their leaders, called bishops. They believe Jesus of Nazareth (whom Christians believe is the Son of God) appointed the first bishops, who appointed future bishops, who eventually appointed each community's current bishops. This appointing of leaders is called "Apostolic Succession".
The groups that use the term "Catholic" to talk about themselves are the:

 Catholic Church, which is also called the Roman Catholic Church.
 Eastern Orthodox and Oriental Orthodox
 Old Catholic, Anglican, and some Lutheran and other groups
 Communities that believe they lost their "Apostolic Succession", but asked a different community to "ordain" new leaders for them. ("Ordain" or consecrate" is a word for the ceremony that makes a bishop or new religious leader.)

Not all communities believe that other communities use the term "catholic" properly. Also, not all communities believe that the other communities have apostolic succession either. For example, the Catholic Church believes that the Eastern Orthodox have apostolic succession. However, the Catholic Church does not believe that the Anglicans or Lutherans have it.
Eastern Orthodox have similar beliefs about Anglicans and Lutherans. Not all Eastern Orthodox believe that the Catholic Church has apostolic succession. Different members of the Eastern Orthodox churches have different opinions.

However, the Anglicans and Lutherans generally believe that all Christians are part of the "catholic" church. These groups have a very different understanding of the term "Catholic".

History

How it was started 
Catholicism was started as a result of Jesus of Nazareth, a Jewish man whom Christians believe is the Son of God, a Christian belief known as the Trinity (Father, Son, and Holy Spirit). Catholics believe Jesus to be a descendant of David, a Jewish king from a long time ago. Jesus was crucified by the Romans in the year 33 AD. Catholics believe Jesus rose from the dead, and spoke to his followers, called the twelve Apostles. They also believe that Jesus rose into Heaven, and then sent the Holy Spirit to guide his followers at an event known as Pentecost.
One of his followers, the apostle named Saint Peter, was appointed leader by Jesus and later became recognized as the first Pope, or Bishop of Rome, soon after that he was captured and was martyred in Rome. Catholics believe that Saint Peter was given the "keys of the Kingdom of Heaven," meaning that Jesus made him and the apostles in charge of forgiving sins. Catholics believe that Saint Peter passed the Apostolic Power (the ability to ordain priests and consecrate the Eucharist), given to him by Christ, to the Popes, who continue to pass the power through the papacy to this day. At the current time, the pope is Pope Francis, who is the leader of the Catholic Church. The word pope comes from the Latin word for "father."