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🔗 Video games 🔗 Computer science 🔗 Mathematics

Fast inverse square root, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates ​¹⁄_√x, the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number x in IEEE 754 floating-point format. This operation is used in digital signal processing to normalize a vector, i.e., scale it to length 1. For example, computer graphics programs use inverse square roots to compute angles of incidence and reflection for lighting and shading. The algorithm is best known for its implementation in 1999 in the source code of Quake III Arena, a first-person shooter video game that made heavy use of 3D graphics. The algorithm only started appearing on public forums such as Usenet in 2002 or 2003. At the time, it was generally computationally expensive to compute the reciprocal of a floating-point number, especially on a large scale; the fast inverse square root bypassed this step.

The algorithm accepts a 32-bit floating-point number as the input and stores a halved value for later use. Then, treating the bits representing the floating-point number as a 32-bit integer, a logical shift right by one bit is performed and the result subtracted from the number 0x5F3759DF, which is a floating point representation of an approximation of √2¹²⁷. This results in the first approximation of the inverse square root of the input. Treating the bits again as a floating-point number, it runs one iteration of Newton's method, yielding a more precise approximation.

The algorithm was originally attributed to John Carmack, but an investigation showed that the code had deeper roots in both the hardware and software side of computer graphics. Adjustments and alterations passed through both Silicon Graphics and 3dfx Interactive, with Gary Tarolli's implementation for the SGI Indigo as the earliest known use. It is not known how the constant was originally derived, though investigation has shed some light on possible methods.

With subsequent hardware advancements, especially the x86 SSE instruction rsqrtss, this method is not generally applicable to modern computing, though it remains an interesting example both historically and for more limited machines.

🔗 Computing

Malbolge () is a public domain esoteric programming language invented by Ben Olmstead in 1998, named after the eighth circle of hell in Dante's Inferno, the Malebolge.

Malbolge was specifically designed to be almost impossible to use, via a counter-intuitive 'crazy operation', base-three arithmetic, and self-altering code. It builds on the difficulty of earlier, challenging esoteric languages (such as Brainfuck and Befunge), but takes this aspect to the extreme, playing on the entangled histories of computer science and encryption. Despite this design, it is possible (though very difficult) to write useful Malbolge programs.

🔗 Human rights 🔗 Military history 🔗 Military history/North American military history 🔗 Military history/United States military history 🔗 Military history/Military science, technology, and theory 🔗 Military history/Weaponry 🔗 Medicine 🔗 Biology 🔗 Military history/World War II 🔗 Military history/Cold War 🔗 United States History 🔗 Medicine/Society and Medicine

Unethical human experimentation in the United States describes numerous experiments performed on human test subjects in the United States that have been considered unethical, and were often performed illegally, without the knowledge, consent, or informed consent of the test subjects. Such tests have occurred throughout American history, but particularly in the 20th century. The experiments include: the exposure of humans to many chemical and biological weapons (including infection with deadly or debilitating diseases), human radiation experiments, injection of toxic and radioactive chemicals, surgical experiments, interrogation and torture experiments, tests involving mind-altering substances, and a wide variety of others. Many of these tests were performed on children, the sick, and mentally disabled individuals, often under the guise of "medical treatment". In many of the studies, a large portion of the subjects were poor, racial minorities, or prisoners.

Funding for many of the experiments was provided by the United States government, especially the United States military, the Central Intelligence Agency, or private corporations involved with military activities. The human research programs were usually highly secretive, and in many cases information about them was not released until many years after the studies had been performed.

The ethical, professional, and legal implications of this in the United States medical and scientific community were quite significant, and led to many institutions and policies that attempted to ensure that future human subject research in the United States would be ethical and legal. Public outrage in the late 20th century over the discovery of government experiments on human subjects led to numerous congressional investigations and hearings, including the Church Committee and Rockefeller Commission, both of 1975, and the 1994 Advisory Committee on Human Radiation Experiments, among others.

🔗 Computing 🔗 Computing/Software

Rule of three ("Three strikes and you refactor") is a code refactoring rule of thumb to decide when similar pieces of code should be refactored to avoid duplication. It states that two instances of similar code don't require refactoring, but when similar code is used three times, it should be extracted into a new procedure. The rule was popularised by Martin Fowler in Refactoring and attributed to Don Roberts.

Duplication is considered a bad practice in programming because it makes the code harder to maintain. When the rule encoded in a replicated piece of code changes, whoever maintains the code will have to change it in all places correctly.

However, choosing an appropriate design to avoid duplication might benefit from more examples to see patterns in. Attempting premature refactoring risks selecting a wrong abstraction, which can result in worse code as new requirements emerge and will eventually need to be refactored again.

The rule implies that the cost of maintenance certainly outweighs the cost of refactoring and potential bad design when there are three copies, and may or may not if there are only two copies.

🔗 United States 🔗 Mathematics 🔗 Law 🔗 History of Science 🔗 United States/Indiana

The Indiana Pi Bill is the popular name for bill #246 of the 1897 sitting of the Indiana General Assembly, one of the most notorious attempts to establish mathematical truth by legislative fiat. Despite its name, the main result claimed by the bill is a method to square the circle, rather than to establish a certain value for the mathematical constant π, the ratio of the circumference of a circle to its diameter. The bill, written by the crank Edward J. Goodwin, does imply various incorrect values of π, such as 3.2. The bill never became law, due to the intervention of Professor C. A. Waldo of Purdue University, who happened to be present in the legislature on the day it went up for a vote.

The impossibility of squaring the circle using only compass and straightedge constructions, suspected since ancient times, was rigorously proven in 1882 by Ferdinand von Lindemann. Better approximations of π than those implied by the bill have been known since ancient times.

🔗 Mathematics

Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator D

${\displaystyle Df(x)={\frac {d}{dx}}f(x)\,,}$

and of the integration operator J

${\displaystyle Jf(x)=\int _{0}^{x}f(s)\,ds\,,}$

and developing a calculus for such operators generalizing the classical one.

In this context, the term powers refers to iterative application of a linear operator D to a function f, that is, repeatedly composing D with itself, as in ${\displaystyle D^{2}(f)=(D\circ D)(f)=D(D(f))}$.

For example, one may ask for a meaningful interpretation of:

${\displaystyle {\sqrt {D}}=D^{\frac {1}{2}}}$

as an analogue of the functional square root for the differentiation operator, that is, an expression for some linear operator that when applied twice to any function will have the same effect as differentiation. More generally, one can look at the question of defining a linear functional

${\displaystyle D^{a}}$

for every real-number a in such a way that, when a takes an integer value n ∈ ℤ, it coincides with the usual n-fold differentiation D if n > 0, and with the −nth power of J when n < 0.

One of the motivations behind the introduction and study of these sorts of extensions of the differentiation operator D is that the sets of operator powers { D^a |a ∈ ℝ } defined in this way are continuous semigroups with parameter a, of which the original discrete semigroup of { Dⁿ | n ∈ ℤ } for integer n is a denumerable subgroup: since continuous semigroups have a well developed mathematical theory, they can be applied to other branches of mathematics.

Fractional differential equations, also known as extraordinary differential equations, are a generalization of differential equations through the application of fractional calculus.

🔗 Biography 🔗 Russia 🔗 Mathematics 🔗 Biography/science and academia 🔗 Russia/science and education in Russia

Grigori Yakovlevich Perelman (Russian: Григорий Яковлевич Перельман, IPA: [ɡrʲɪˈɡorʲɪj ˈjakəvlʲɪvʲɪtɕ pʲɪrʲɪlʲˈman] (listen); born 13 June 1966) is a Russian mathematician who is known for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology.

In the 1990s, partly in collaboration with Yuri Burago, Mikhael Gromov, and Anton Petrunin, he made influential contributions to the study of Alexandrov spaces. In 1994, he proved the soul conjecture in Riemannian geometry, which had been an open problem for the previous 20 years. In 2002 and 2003, he developed new techniques in the analysis of Ricci flow, thereby providing a detailed sketch of a proof of the Poincaré conjecture and Thurston's geometrization conjecture, the former of which had been a famous open problem in mathematics for the past century. The full details of Perelman's work were filled in and explained by various authors over the following several years.

In August 2006, Perelman was offered the Fields Medal for "his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow", but he declined the award, stating: "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo." On 22 December 2006, the scientific journal Science recognized Perelman's proof of the Poincaré conjecture as the scientific "Breakthrough of the Year", the first such recognition in the area of mathematics.

On 18 March 2010, it was announced that he had met the criteria to receive the first Clay Millennium Prize for resolution of the Poincaré conjecture. On 1 July 2010, he rejected the prize of one million dollars, saying that he considered the decision of the board of the Clay Institute to be unfair, in that his contribution to solving the Poincaré conjecture was no greater than that of Richard S. Hamilton, the mathematician who pioneered the Ricci flow partly with the aim of attacking the conjecture. He had previously rejected the prestigious prize of the European Mathematical Society, in 1996.

🔗 Internet culture 🔗 Environment 🔗 Skepticism 🔗 Chemicals 🔗 Sociology

The dihydrogen monoxide parody involves calling water by an unfamiliar chemical name, most often "dihydrogen monoxide" (DHMO), and listing some of water's well-known effects in a particularly alarming manner, such as accelerating corrosion and causing suffocation. The parody often calls for dihydrogen monoxide to be banned, regulated, or labeled as dangerous. It demonstrates how a lack of scientific literacy and an exaggerated analysis can lead to misplaced fears.

The parody has been used with other chemical names, including "dihydrogen oxide", "hydroxyl acid", and "hydroxylic acid".

🔗 United States 🔗 Military history 🔗 Military history/Military science, technology, and theory 🔗 Military history/Weaponry 🔗 Korea

A graphite bomb is intended to be a non-lethal weapon used to disable an electrical grid. The bomb works by spreading a dense cloud of extremely fine, chemically treated carbon filaments over air-insulated high voltage installations like transformers and power lines, causing short-circuits and subsequent disruption of the electricity supply in an area, a region or even an entire small country. The weapon is sometimes referred to as blackout bomb or as soft bomb because its direct effects are largely confined to the targeted electrical power facility, with minimal risk of immediate collateral damage. However, since water supply systems and sewage treatment systems depend on electricity, widespread outbreaks of cholera and other waterborne diseases, causing large numbers of civilian deaths, have in the past been the direct consequence of this bomb's use.

🔗 International relations 🔗 Espionage 🔗 Soviet Union 🔗 Russia 🔗 Russia/history of Russia 🔗 English Language

In political jargon, a useful idiot is a derogatory term for a person perceived as propagandizing for a cause without fully comprehending the cause's goals, and who is cynically used by the cause's leaders. The term was originally used during the Cold War to describe non-communists regarded as susceptible to communist propaganda and manipulation. The term has often been attributed to Vladimir Lenin, but this attribution is unsubstantiated.