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🔗 Time 🔗 Writing

Kairos (Ancient Greek: καιρός) is an Ancient Greek word meaning the right, critical, or opportune moment. The ancient Greeks had two words for time: chronos (χρόνος) and kairos. The former refers to chronological or sequential time, while the latter signifies a proper or opportune time for action. While chronos is quantitative, kairos has a qualitative, permanent nature. Kairos also means weather in Modern Greek. The plural, καιροί (kairoi (Ancient and Modern Greek)) means the times. Kairos is a term, idea, and practice that has been applied in several fields including classical rhetoric, modern rhetoric, digital media, Christian theology, and science.

🔗 United States 🔗 Numismatics 🔗 Numismatics/American currency 🔗 United States/Massachusetts

BerkShares is a local currency that circulates in The Berkshires region of Massachusetts. It was launched on September 29, 2006 by BerkShares Inc., with research and development assistance from the Schumacher Center for a New Economics. The BerkShares website lists around 400 businesses in Berkshire County that accept the currency. Since launch, over 10 million BerkShares have been issued from participating branch offices of local banks (as of February 2020, 9 branches of 3 different banks). The bills were designed by John Isaacs and were printed by Excelsior Printing on special paper with incorporated security features from Crane & Co.. BerkShares are pegged with an exchange rate to the US dollar, but the Schumacher Center has discussed the possibility of pegging its value to a basket of local goods in order to insulate the local economy against volatility in the US economy.

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Some of the many ways to read Wikipedia while offline:

• Kiwix: (§ Kiwix) – index of images (2024)
• XOWA: (§ XOWA) – index of images (2015)
• WikiTaxi: § WikiTaxi (for Windows)
• aarddict: § Aard Dictionary / Aard 2
• BzReader: § BzReader and MzReader (for Windows)
• WikiFilter: § WikiFilter
• Wikipedia on rockbox: § Wikiviewer for Rockbox
• Selected Wikipedia articles as a printed document: Help:Printing

Some of them are mobile applications – see "List of Wikipedia mobile applications".

🔗 Mathematics

The Trachtenberg system is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. It was developed by the Russian Jewish engineer Jakow Trachtenberg in order to keep his mind occupied while being in a Nazi concentration camp.

The rest of this article presents some methods devised by Trachtenberg. Some of the algorithms Trachtenberg developed are ones for general multiplication, division and addition. Also, the Trachtenberg system includes some specialised methods for multiplying small numbers between 5 and 13.

The section on addition demonstrates an effective method of checking calculations that can also be applied to multiplication.

🔗 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.