the-french-artist/wikipedia_20220301.simple_sentence_embeddings huggingface dataset:
Soil 
 Soils are usually thicker in places where ice sheets covered the ground during the Pleistocene ice ages.
Soil 
 The sand will make one layer, the silt will make another layer and the clay will make another layer.
Organic 
 Organic farming, agriculture conducted according to certain standards, especially the use of only naturally produced fertilizers and non-chemical means of pest control.
3D 
 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.
3D 
 Other 3D coordinate systems such as spherical coordinates include both linear and angular measurements.
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.
Humidity 
 Higher humidity reduces the effectiveness of sweating in cooling the body by reducing the rate of evaporation of moisture from the skin.
Calabi-Yau manifold 
 The Calabi–Yau manifold's properties, such as Ricci flatness, have applications in theoretical physics.
Calabi-Yau manifold 
 Particularly in superstring theory, the extra dimensions of spacetime might take the form of a 6-dimensional Calabi–Yau manifold.
Quantum mechanics 
 Mechanics is the part of physics that explains how things move and quantum is the Latin word for 'how much'.
Quantum mechanics 
 A quantum of energy is the least amount possible (or the least extra amount), and quantum mechanics describes how that energy moves or interacts.
Quantum mechanics 
 Atoms used to be considered the smallest building blocks of matter, but modern science has shown that there are even smaller particles, like protons, neutrons and electrons.
Quantum mechanics 
 Much of modern physics and chemistry can be described and understood using the mathematical rules of quantum mechanics.
Quantum mechanics 
 The mathematics used to study subatomic particles and electromagnetic waves is very complex because they act in very strange ways.
Quantum mechanics 
 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.
Quantum mechanics 
 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).
Quantum mechanics 
 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.
Quantum mechanics 
 If the color of the light is infrared (lower in frequency than red light), each photon can heat up what it hits.
Quantum mechanics 
 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.
Quantum mechanics 
 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 
 The mathematical equations of quantum mechanics are abstract, which means it is impossible to know the exact physical properties of a particle (like its position or momentum) for sure.
Quantum mechanics 
 Instead, a mathematical function called the wavefunction provides information about the probability with which a particle has a given property.
Quantum mechanics 
 For example, the wavefunction can tell you what the probability is that a particle can be found in a certain location, but it can't tell you where it is for sure.
Quantum mechanics 
 Because of this uncertainty and other factors, you cannot use classical mechanics (the physics that describe how large objects move) to predict the motion of quantum particles.
Quantum mechanics 
 Ultraviolet light is higher in frequency than violet light, such that it is not even in the visible light range.
Quantum mechanics 
 Each photon in the ultraviolet range has a lot of energy, enough to hurt skin cells and cause a sunburn.
Quantum mechanics 
 In fact, most forms of sunburn are not caused by heat; they are caused by the high energy of the sun's UV rays damaging your skin cells.
Quantum mechanics 
 Even higher frequencies of light (or electromagnetic radiation) can penetrate deeper into the body and cause even more damage.
Quantum mechanics 
 Areas where it is important to kill germs often use ultraviolet lamps to destroy bacteria, fungi, etc.
Quantum mechanics 
 Quantum mechanics started when it was discovered that if a particle has a certain frequency, it must also have a certain amount of energy.
Quantum mechanics 
 Quantum mechanics also explains the way that a photon can interfere with itself, and many other things never imagined in classical physics.
Quantum mechanics 
 Nobody before had ever guessed that frequency is directly proportional to energy (this means that as one of them doubles, the other does, too).
Quantum mechanics 
 Under what are called natural units, then the number representing the frequency of a photon would also represent its energy.
Quantum mechanics 
 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).
Quantum mechanics 
 Quantum mechanics is based on the knowledge that a photon of a certain frequency means a photon of a certain amount of energy.
Quantum mechanics 
 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.
Quantum mechanics 
 Isaac Newton thought that light was made of very small things that we would now call particles (he referred to them as "Corpuscles").
Quantum mechanics 
 The Photoelectric effect discovered by Albert Einstein proved that light had to act like particles that carried specific amounts of energy, and that the energies were linked to their frequencies.
Quantum mechanics 
 Later, physicists found out that everything behaves both like a wave and like a particle, not just light.
Quantum mechanics 
 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.
Quantum mechanics 
 Quantum mechanics formulae and ideas were made to explain the light that comes from glowing hydrogen.
Quantum mechanics 
 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.
Quantum mechanics 
 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. (
Quantum mechanics 
 This is because electrons and other charged particles were known to emit light and lose energy when they changed speed or turned.)
Quantum mechanics 
 Hydrogen lamps work like neon lights, but neon lights have their own unique group of colors (and frequencies) of light.
Quantum mechanics 
 Then, a Swiss mathematician named Johann Balmer figured out an equation that told what λ (lambda, for wave length) would be:
Quantum mechanics 
 Putting in different numbers for m and n, it is easy to predict frequencies for many types of light (ultraviolet, visible, and infared).
Quantum mechanics 
 In 1908, Walter Ritz made the Ritz combination principle that shows how certain gaps between frequencies keep repeating themselves.
Quantum mechanics 
 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.
Quantum mechanics 
 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. (
Quantum mechanics 
 This led to a theory about subatomic particles and electromagnetic waves called wave-particle duality.
Quantum mechanics 
 This is where particles and waves were neither one nor the other, but had certain properties of both.
Quantum mechanics 
 In 1913, Niels Bohr came up with the idea that electrons could only take up certain orbits around the nucleus of an atom.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 It has to predict spaced-out frequencies when the electrons involved are moving between orbits close to the nucleus (center) of the atom, but it also has to predict that the frequencies will get closer and closer together as we look at what the electron does in moving between orbits farther and farther out.
Quantum mechanics 
 It will also predict that the intensity differences between frequencies get closer and closer together as we go out.
Quantum mechanics 
 Where classical physics already gives the right answers by one set of equations the new physics has to give the same answers but by different equations.
Quantum mechanics 
 Classical physics uses the methods of the French mathematician Fourier to make a math picture of the physical world, and 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.
Quantum mechanics 
 The numbers that he calculated would put dots on a graph, but there would be no line drawn between the dots.
Quantum mechanics 
 And making one "graph" just of dots for every set of calculations would have wasted lots of paper and not have gotten anything done.
Quantum mechanics 
 Heisenberg found a way to efficiently predict the intensities for different frequencies and to organize that information in a helpful way.
Quantum mechanics 
 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:
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 It is confusing that they used negative numbers when the electrons were actually gaining energy, but that is just the way it is.
Quantum mechanics 
 Since the Rydberg rule gives us frequencies, we can use that rule to put in numbers depending on where the electron goes.
Quantum mechanics 
 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.
Quantum mechanics 
 If the electron starts at n-a and ends up at n, then it has fallen from a higher orbit to a lower orbit.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 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.):
Quantum mechanics 
 But to do that he had to multiply two amplitudes (how high a wave measures) to work out the intensity. (
Quantum mechanics 
 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.
Quantum mechanics 
 He was used to calling the grid or table that we could write by doing, for instance, all the math for frequencies, a matrix.
Quantum mechanics 
 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.
Quantum mechanics 
 Even though he did not know about matrix math, Heisenberg already saw this "different answers" problem and it had bothered him.
Quantum mechanics 
 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."
Quantum mechanics 
 By "indeterminate" Heisenberg meant that something like an electron is just not pinned down until it gets pinned down.
Quantum mechanics 
 It is a little like a jellyfish that is always squishing around and cannot be "in one place" unless you kill it.
Quantum mechanics 
 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.
Quantum mechanics 
 Having trouble measuring something is a problem, but it is not the problem Heisenberg was talking about.
Quantum mechanics 
 First, we will start calling these grids "matrices," because we will soon need to talk about matrix multiplication.
Quantum mechanics 
 He did not know it, but this equation gives a blueprint for writing out two matrices (grids) and for multiplying them.
Quantum mechanics 
 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:
Quantum mechanics 
 The matrix for the product of the above two matrices as specified by the relevant equation in Heisenberg's 1925 paper is:
Quantum mechanics 
 Note how changing the order of multiplication changes the numbers, step by step, that are actually multiplied.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 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."
Quantum mechanics 
 It turned out that quantum mechanics was right, and that what Einstein had used as a reason to reject quantum mechanics actually happened.
Quantum mechanics 
 This kind of "spooky connection" between certain quantum events is now called "quantum entanglement".
Quantum mechanics 
 In the diagram, one characteristic (e.g., "up" spin) is drawn in red, and its mate (e.g., "down" spin) is drawn in blue.
Quantum mechanics 
 The purple band means that when, e.g., two electrons are put together the pair shares both characteristics.
Quantum mechanics 
 When they are later separated, one remaining on Earth and one going to some planet of the star Alpha Centauri, they still each have both spins.
Quantum mechanics 
 In other words, each one of them can "decide" to show itself as a spin-up electron or a spin-down electron.
Quantum mechanics 
 But if later on someone measures the other one, it must "decide" to show itself as having the opposite spin.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 In other words, the more we know about the speed and direction of something small, the less we can know about its position.
Quantum mechanics 
 The reason behind Heisenberg's uncertainty principle says that we can never know both the location and the momentum of a particle.
Quantum mechanics 
 If a high energy, or high frequency, light beam is used, we can tell precisely where it is, but cannot tell how fast it was going.
Quantum mechanics 
 This is because the high energy photon transfers energy to the particle and changes the particle's speed.
Quantum mechanics 
 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.
Quantum mechanics 
 Even Albert Einstein had trouble accepting such a bizarre concept, and in a well-known debate said, "God does not play dice".
Quantum mechanics 
 Quantum mechanics can also help us understand big things, such as stars and even the whole universe.
Quantum mechanics 
 Quantum mechanics is a very important part of the theory of how the universe began called the Big Bang.
Quantum mechanics 
 Everything made of matter is attracted to other matter because of a fundamental force called gravity.
Quantum mechanics 
 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 
 Quantum mechanics is the part of physics that can explain why all electronic technology works as it does.
Quantum mechanics 
 But the designers of the early computer hardware of around 1950 or 1960 did not need to think about quantum mechanics.
Quantum mechanics 
 However, the design of the more powerful integrated circuits and computer memory technologies of recent years does require quantum mechanics.
Quantum mechanics 
 Quantum mechanics explains things in very different ways from what we learn about the world when we are children.
Quantum mechanics 
 It also requires matrix algebra, complex numbers, probability theory, and partial differential equations.
Quantum mechanics 
 Physicists are not sure what some of the equations of quantum mechanics tell us about the real world.
Quantum mechanics 
 Quantum mechanics suggests that atoms and subatomic particles behave in strange ways, completely unlike anything we see in our everyday lives.
Quantum mechanics 
 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.
Quantum mechanics 
 Quantum mechanics describes nature in a way that is different from how we usually think about science.
Quantum mechanics 
 It tells us how likely to happen some things are, rather than telling us that they certainly will happen.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 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.
Quantum mechanics 
 So we know for sure that the bands will be brightest at the center and get dimmer and dimmer farther away.
Quantum mechanics 
 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).
Quantum mechanics 
 Before the measurement, the particle is in a "superposition of states," in which its properties have many values at the same time.
Quantum mechanics 
 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.
Quantum mechanics 
 In the time before the state of the quantum event is looked at, perhaps "the living and dead cat (pardon
Quantum mechanics 
 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.
Quantum mechanics 
 The particle in a 1-dimensional well is the most simple example showing that the energy of a particle can only have specific values.
Quantum mechanics 
 The well has zero potential energy inside a range and has infinite potential energy everywhere outside that range.
Quantum mechanics 
 For the 1-dimensional case in the  direction, the time-independent Schrödinger equation can be written as:
Quantum mechanics 
 This means that the particle can only have special energy values and cannot have the energy values in between.
Duisburg 
 Duisburg (; Westphalian: Duisborg, Ripuarian: Duisburch, Low Franconian: Duusbörg) is a German city in the state of North Rhine-Westphalia.
Kuopio 
 Two important schools are the University of Eastern Finland and the Savonia University of Applied Sciences.