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🔗 Systems 🔗 Systems/Chaos theory

The Burning Ship fractal, first described and created by Michael Michelitsch and Otto E. Rössler in 1992, is generated by iterating the function:

${\displaystyle z_{n+1}=(|\operatorname {Re} \left(z_{n}\right)|+i|\operatorname {Im} \left(z_{n}\right)|)^{2}+c,\quad z_{0}=0}$

in the complex plane ${\displaystyle \mathbb {C} }$ which will either escape or remain bounded. The difference between this calculation and that for the Mandelbrot set is that the real and imaginary components are set to their respective absolute values before squaring at each iteration. The mapping is non-analytic because its real and imaginary parts do not obey the Cauchy–Riemann equations.

🔗 Energy

The gravitation water vortex power plant is a type of micro hydro vortex turbine system which is capable of converting energy in a moving fluid to rotational energy using a low hydraulic head of 0.7–3 metres (2 ft 4 in–9 ft 10 in). The technology is based on a round basin with a central drain. Above the drain the water forms a stable line vortex which drives a water turbine.

It was first patented by Greek-Australian Lawyer & Inventor Paul Kouris in 1996, who was searching for a way to harness the power inherent in a vortex.

Later, Austrian Inventor Franz Zotlöterer created a similar turbine while attempting to find a way to aerate water without an external power source.

🔗 Physics 🔗 Astronomy

Entropic gravity, also known as emergent gravity, is a theory in modern physics that describes gravity as an entropic force—a force with macro-scale homogeneity but which is subject to quantum-level disorder—and not a fundamental interaction. The theory, based on string theory, black hole physics, and quantum information theory, describes gravity as an emergent phenomenon that springs from the quantum entanglement of small bits of spacetime information. As such, entropic gravity is said to abide by the second law of thermodynamics under which the entropy of a physical system tends to increase over time.

At its simplest, the theory holds that when gravity becomes vanishingly weak—levels seen only at interstellar distances—it diverges from its classically understood nature and its strength begins to decay linearly with distance from a mass.

Entropic gravity provides the underlying framework to explain Modified Newtonian Dynamics, or MOND, which holds that at a gravitational acceleration threshold of approximately 1.2×10⁻¹⁰ m/s², gravitational strength begins to vary inversely (linearly) with distance from a mass rather than the normal inverse-square law of the distance. This is an exceedingly low threshold, measuring only 12 trillionths gravity's strength at earth's surface; an object dropped from a height of one meter would fall for 36 hours were earth's gravity this weak. It is also 3,000 times less than exists at the point where Voyager 1 crossed our solar system's heliopause and entered interstellar space.

The theory claims to be consistent with both the macro-level observations of Newtonian gravity as well as Einstein's theory of general relativity and its gravitational distortion of spacetime. Importantly, the theory also explains (without invoking the existence of dark matter and its accompanying math featuring new free parameters that are tweaked to obtain the desired outcome) why galactic rotation curves differ from the profile expected with visible matter.

The theory of entropic gravity posits that what has been interpreted as unobserved dark matter is the product of quantum effects that can be regarded as a form of positive dark energy that lifts the vacuum energy of space from its ground state value. A central tenet of the theory is that the positive dark energy leads to a thermal-volume law contribution to entropy that overtakes the area law of anti-de Sitter space precisely at the cosmological horizon.

The theory has been controversial within the physics community but has sparked research and experiments to test its validity.

🔗 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.