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Fermi Problem
A Fermi problem (or Fermi question, Fermi quiz), also known as an order-of-magnitude problem, is an estimation problem in physics or engineering education, designed to teach dimensional analysis or approximation of extreme scientific calculations. Fermi problems are usually back-of-the-envelope calculations. Fermi problems typically involve making justified guesses about quantities and their variance or lower and upper bounds. In some cases, order-of-magnitude estimates can also be derived using dimensional analysis. A Fermi estimate (or order-of-magnitude estimate, order estimation) is an estimate of an extreme scientific calculation. The estimation technique is named after physicist Enrico Fermi as he was known for his ability to make good approximate calculations with little or no actual data. Historical background An example is Enrico Fermi's estimate of the strength of the atomic bomb that detonated at the Trinity test, based on the distance traveled by pieces of paper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Estimation Theory
Estimation theory is a branch of statistics that deals with estimating the values of Statistical parameter, parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An ''estimator'' attempts to approximate the unknown parameters using the measurements. In estimation theory, two approaches are generally considered: * The probabilistic approach (described in this article) assumes that the measured data is random with probability distribution dependent on the parameters of interest * The set estimation, set-membership approach assumes that the measured data vector belongs to a set which depends on the parameter vector. Examples For example, it is desired to estimate the proportion of a population of voters who will vote for a particular candidate. That proportion is the parameter sought; the estimate is based on a small random sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Of Magnitude
In a ratio scale based on powers of ten, the order of magnitude is a measure of the nearness of two figures. Two numbers are "within an order of magnitude" of each other if their ratio is between 1/10 and 10. In other words, the two numbers are within about a factor of 10 of each other. For example, 1 and 1.02 are within an order of magnitude. So are 1 and 2, 1 and 9, or 1 and 0.2. However, 1 and 15 are not within an order of magnitude, since their ratio is 15/1 = 15 > 10. The reciprocal ratio, 1/15, is less than 0.1, so the same result is obtained. Differences in order of magnitude can be measured on a base-10 logarithmic scale in " decades" (i.e., factors of ten). For example, there is one order of magnitude between 2 and 20, and two orders of magnitude between 2 and 200. Each division or multiplication by 10 is called an order of magnitude. This phrasing helps quickly express the difference in scale between 2 and 2,000,000: they differ by 6 orders of magnitude. Examples o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Maryland, College Park
The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public university, public Land-grant university, land-grant research university in College Park, Maryland, United States. Founded in 1856, UMD is the Flagship university, flagship institution of the University System of Maryland. It is known as the biggest university in the state of Maryland. UMD is the largest university in Maryland and the Washington metropolitan area. Its eleven schools and colleges offer over 200 degree-granting programs, including 113 undergraduate majors, 107 Master's degree, master's programs, and 83 Doctorate, doctoral programs. UMD's athletic teams are known as the Maryland Terrapins and compete in NCAA Division I as a member of the Big Ten Conference. A member of the Association of American Universities, The University of Maryland's proximity to Washington, D.C. has resulted in many research partnerships with the Federal government of the United States, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Cow
file:SphericalCow2.gif, Comic of a spherical cow as illustrated by a 1996 meeting of the American Astronomical Association, in reference to astronomy modeling The spherical cow is a humour, humorous metaphor for highly idealization (philosophy of science), simplified scientific models of complex phenomena. Originating in theoretical physics, the metaphor refers to some scientific tendencies to develop toy models that reduce a problem to the simplest form imaginable, making calculations more feasible, even if the simplification hinders the model's application to reality. History The phrase comes from a joke that spoofs the simplifying assumptions sometimes used in theoretical physics. John Harte (scientist), John Harte, who received his Ph.D. from the University of Wisconsin in 1965, reported that he first heard the joke as a graduate student. One of the earliest published references is in a 1970 article by Arthur O. Williams Jr. of Brown University, who described it as "a prof ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stein's Example
In decision theory and estimation theory, Stein's example (also known as Stein's phenomenon or Stein's paradox) is the observation that when three or more parameters are estimated simultaneously, there exist combined estimators more accurate on average (that is, having lower expected mean squared error) than any method that handles the parameters separately. It is named after Charles Stein of Stanford University, who discovered the phenomenon in 1955. An intuitive explanation is that optimizing for the mean-squared error of a ''combined'' estimator is not the same as optimizing for the errors of separate estimators of the individual parameters. In practical terms, if the combined error is in fact of interest, then a combined estimator should be used, even if the underlying parameters are independent. If one is instead interested in estimating an individual parameter, then using a combined estimator does not help and is in fact worse. Formal statement The following is the simples ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Of Approximation
In science, engineering, and other quantitative disciplines, order of approximation refers to formal or informal expressions for how accurate an approximation is. Usage in science and engineering In formal expressions, the ordinal number used before the word order refers to the highest power in the series expansion used in the approximation. The expressions: a ''zeroth-order approximation'', a ''first-order approximation'', a ''second-order approximation'', and so forth are used as fixed phrases. The expression a ''zero-order approximation'' is also common. Cardinal numerals are occasionally used in expressions like an ''order-zero approximation'', an ''order-one approximation'', etc. The omission of the word ''order'' leads to phrases that have less formal meaning. Phrases like first approximation or to a first approximation may refer to ''a roughly approximate value of a quantity''. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heuristic
A heuristic or heuristic technique (''problem solving'', '' mental shortcut'', ''rule of thumb'') is any approach to problem solving that employs a pragmatic method that is not fully optimized, perfected, or rationalized, but is nevertheless "good enough" as an approximation or attribute substitution. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision. Context Gigerenzer & Gaissmaier (2011) state that sub-sets of ''strategy'' include heuristics, regression analysis, and Bayesian inference. Heuristics are strategies based on rules to generate optimal decisions, like the anchoring effect and utility maximization problem. These strategies depend on using readily accessible, though loosely applicable, information to control problem solving in human beings, machines and abstract i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Handwaving
Hand-waving (with various spellings) is a pejorative label for attempting to be seen as effective – in word, reasoning, or deed – while actually doing nothing effective or substantial. Cites the ''Random House Dictionary'' and ''The Dictionary of American Slang'' 4th ed. It is often applied to debating techniques that involve fallacies, misdirection and the glossing over of details. Online edition:Homepagementions a ver. 4.4.8, but the text of the work say It is also used academically to indicate unproven claims and skipped steps in proofs (sometimes intentionally, as in lectures and instructional materials), with some specific meanings in particular fields, including literary criticism, speculative fiction, mathematics, logic, science and engineering. The term can additionally be used in work situations, when attempts are made to display productivity or assure accountability without actually resulting in them. The term can also be used as a self-admission of, and suggestion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dead Reckoning
In navigation, dead reckoning is the process of calculating the current position of a moving object by using a previously determined position, or fix, and incorporating estimates of speed, heading (or direction or course), and elapsed time. The corresponding term in biology, to describe the processes by which animals update their estimates of position or heading, is path integration. Advances in navigational aids that give accurate information on position, in particular satellite navigation using the Global Positioning System, have made simple dead reckoning by humans obsolete for most purposes. However, inertial navigation systems, which provide very accurate directional information, use dead reckoning and are very widely applied. Etymology Contrary to myth, the term "dead reckoning" was not originally used to abbreviate "deduced reckoning", nor is it a misspelling of the term "ded reckoning". The use of "ded" or "deduced reckoning" is not known to have appeared earlier th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guesstimate
''Guesstimate'' is an informal English portmanteau of ''guess'' and '' estimate'', first used by American statisticians in 1934 or 1935.''guesstimate'' Dictionary.com Unabridged (v 1.1) It is defined as an estimate made without using adequate or complete information, or, more strongly, as an estimate arrived at by work or .''guesstimate'' American Heritage Dictionary Like the words estimate and guess, guesstimate may be used as a verb o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale (ratio)
The scale ratio of a model represents the proportional ratio of a linear dimension of the model to the same feature of the original. Examples include a 3-dimensional scale model of a building or the scale drawings of the elevations or plans of a building. In such cases the scale is dimensionless and exact throughout the model or drawing. The scale can be expressed in four ways: in words (a lexical scale), as a ratio, as a fraction and as a graphical (bar) scale. Thus on an architect's drawing one might read 'one centimeter to one meter', 1:100, 1/100, or . A bar scale would also normally appear on the drawing. Colon may also be substituted with a specific, slightly raised ratio symbol , ie. . General representation Generally, a representation may involve more than one scale at the same time. For example, a drawing showing a new road in elevation might use different horizontal and vertical scales. An elevation of a bridge might be annotated with arrows with a length proportion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Elasticity
Linear elasticity is a mathematical model of how solid objects deform and become internally stressed by prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics. The fundamental assumptions of linear elasticity are infinitesimal strains — meaning, "small" deformations — and linear relationships between the components of stress and strain — hence the "linear" in its name. Linear elasticity is valid only for stress states that do not produce yielding. Its assumptions are reasonable for many engineering materials and engineering design scenarios. Linear elasticity is therefore used extensively in structural analysis and engineering design, often with the aid of finite element analysis. Mathematical formulation Equations governing a linear elastic boundary value problem are based on three tensor partial differential equations for the balance of linear momentum and six in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
