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Empirical Relationship
In science, an empirical relationship or phenomenological relationship is a relationship or correlation that is supported by experiment and observation but not necessarily supported by theory. Analytical solutions without a theory An empirical relationship is supported by confirmatory data irrespective of theoretical basis such as first principles. Sometimes theoretical explanations for what were initially empirical relationships are found, in which case the relationships are no longer considered empirical. An example was the Rydberg formula to predict the wavelengths of hydrogen spectral lines. Proposed in 1876, it perfectly predicted the wavelengths of the Lyman series, but lacked a theoretical basis until Niels Bohr produced his Bohr model of the atom in 1925.McMullin, Ernan (1968), “What Do Physical Models Tell Us?”, in B. van Rootselaar and J. F. Staal (eds.), Logic, Methodology and Science III. Amsterdam: North Holland, 385–396. On occasion, what was thought to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science
Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for scientific reasoning is tens of thousands of years old. The earliest written records in the history of science come from Ancient Egypt and Mesopotamia in around 3000 to 1200 Common Era, BCE. Their contributions to mathematics, astronomy, and medicine entered and shaped Greek natural philosophy of classical antiquity, whereby formal attempts were made to provide explanations of events in the Universe, physical world based on natural causes. After the fall of the Western Roman Empire, knowledge of History of science in classical antiquity, Greek conceptions of the world deteriorated in Western Europe during the early centuries (400 to 1000 CE) of the Middle Ages, but was preserved in the Muslim world during the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bohr Model
In atomic physics, the Bohr model or Rutherford–Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar System, but with attraction provided by electrostatic forces in place of gravity. It came after the solar system Joseph Larmor model (1897), the solar system Jean Perrin model (1901), the cubical model (1902), the Hantaro Nagaoka Saturnian model (1904), the plum pudding model (1904), the quantum Arthur Haas model (1910), the Rutherford model (1911), and the nuclear quantum John William Nicholson model (1912). The improvement over the 1911 Rutherford model mainly concerned the new quantum physical interpretation introduced by Haas and Nicholson, but forsaking any attempt to align with classical physics radiation. The model's key success lay in explaining the Rydberg formula for the spectral emission lines of atomic hydrogen. While the Ry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Law
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four. Empirical examples The distributions of a wide variety of physical, biological, and man-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, the foraging pattern of various species, the sizes of activity patterns of neuronal populations, the frequencies of words in most languages, frequencies of family names, the species richness in clades of organisms, the sizes of power outages, volcanic eruptions, human judgments of stimulus intensity and many other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heuristic Argument
A heuristic argument is an argument that reasons from the value of a method or principle that has been shown experimentally (especially through trial-and-error) to be useful or convincing in learning, discovery and problem-solving, but whose line of reasoning involves key oversimplifications that make it not entirely rigorous. A widely used and important example of a heuristic argument is Occam's Razor. It is a speculative, non-rigorous argument that relies on analogy or intuition, and that allows one to achieve a result or an approximation that is to be checked later with more rigor. Otherwise, the results are generally to be doubted. It is used as a hypothesis or a conjecture in an investigation, though it can also be used as a mnemonic as well. See also * Empirical relationship *Heuristic *Probabilistic method The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empiricism
In philosophy, empiricism is an epistemological theory that holds that knowledge or justification comes only or primarily from sensory experience. It is one of several views within epistemology, along with rationalism and skepticism. Empiricism emphasizes the central role of empirical evidence in the formation of ideas, rather than innate ideas or traditions. However, empiricists may argue that traditions (or customs) arise due to relations of previous sensory experiences. Historically, empiricism was associated with the "blank slate" concept (''tabula rasa''), according to which the human mind is "blank" at birth and develops its thoughts only through experience. Empiricism in the philosophy of science emphasizes evidence, especially as discovered in experiments. It is a fundamental part of the scientific method that all hypotheses and theories must be tested against observations of the natural world rather than resting solely on ''a priori'' reasoning, intuition, or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phenomenological Model
A phenomenological model is a scientific model that describes the empirical relationship of phenomena to each other, in a way which is consistent with fundamental theory, but is not directly derived from theory. In other words, a phenomenological model is not derived from first principles. A phenomenological model forgoes any attempt to explain why the variables interact the way they do, and simply attempts to describe the relationship, with the assumption that the relationship extends past the measured values. Regression analysis In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ... is sometimes used to create statistical models that serve as phenomenological models. Examples of use Phenomenological models have been characterized as being completely independent of theories, though m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series, when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensionless Physical Constant
In physics, a dimensionless physical constant is a physical constant that is dimensionless, i.e. a pure number having no units attached and having a numerical value that is independent of whatever system of units may be used. For example, if one considers one particular airfoil, the Reynolds number value of the laminar–turbulent transition is one relevant dimensionless physical constant of the problem. However, it is strictly related to the particular problem: for example, it is related to the airfoil being considered and also to the type of fluid in which it moves. On the other hand, the term fundamental physical constant is used to refer to some ''universal'' dimensionless constants. Perhaps the best-known example is the fine-structure constant, ''α'', which has an approximate value of . The correct use of the term ''fundamental physical constant'' should be restricted to the dimensionless universal physical constants that currently cannot be derived from any other source. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Niels Bohr
Niels Henrik David Bohr (; 7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922. Bohr was also a philosopher and a promoter of scientific research. Bohr developed the Bohr model of the atom, in which he proposed that energy levels of electrons are discrete and that the electrons revolve in stable orbits around the atomic nucleus but can jump from one energy level (or orbit) to another. Although the Bohr model has been supplanted by other models, its underlying principles remain valid. He conceived the principle of complementarity: that items could be separately analysed in terms of contradictory properties, like behaving as a wave or a stream of particles. The notion of complementarity dominated Bohr's thinking in both science and philosophy. Bohr founded the Institute of Theoretical Physics at the University of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correlation
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are ''linearly'' related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. Howev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lyman Series
In physics and chemistry, the Lyman series is a hydrogen spectral series of transitions and resulting ultraviolet emission lines of the hydrogen atom as an electron goes from ''n'' ≥ 2 to ''n'' = 1 (where ''n'' is the principal quantum number), the lowest energy level of the electron. The transitions are named sequentially by Greek letters: from ''n'' = 2 to ''n'' = 1 is called Lyman-alpha, 3 to 1 is Lyman-beta, 4 to 1 is Lyman-gamma, and so on. The series is named after its discoverer, Theodore Lyman. The greater the difference in the principal quantum numbers, the higher the energy of the electromagnetic emission. History The first line in the spectrum of the Lyman series was discovered in 1906 by Harvard physicist Theodore Lyman, who was studying the ultraviolet spectrum of electrically excited hydrogen gas. The rest of the lines of the spectrum (all in the ultraviolet) were discovered by Lyman from 1906-1914. The spectrum of radiati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to identify atoms and molecules. These "fingerprints" can be compared to the previously collected ones of atoms and molecules, and are thus used to identify the atomic and molecular components of stars and planets, which would otherwise be impossible. Types of line spectra Spectral lines are the result of interaction between a quantum system (usually atoms, but sometimes molecules or atomic nuclei) and a single photon. When a photon has about the right amount of energy (which is connected to its frequency) to allow a change in the energy state of the system (in the case of an atom this is usually an electron changing orbitals), the photon is absorbed. Then the energy will be spontaneously re-emitted, either as one photon at the same frequ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
