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🔗 Numismatics 🔗 Numismatics/Cryptocurrency 🔗 Cryptocurrency

A proof-of-work (PoW) system (or protocol, or function) is a consensus mechanism. It deters denial-of-service attacks and other service abuses such as spam on a network by requiring some work from the service requester, usually meaning processing time by a computer. The concept was invented by Cynthia Dwork and Moni Naor as presented in a 1993 journal article. The term "proof of work" was first coined and formalized in a 1999 paper by Markus Jakobsson and Ari Juels.

A key feature of these schemes is their asymmetry: the work must be moderately hard (yet feasible) on the requester side but easy to check for the service provider. This idea is also known as a CPU cost function, client puzzle, computational puzzle, or CPU pricing function. It is distinct from a CAPTCHA, which is intended for a human to solve quickly, while being difficult to solve for a computer.

🔗 Philosophy 🔗 Skepticism 🔗 Philosophy/Logic 🔗 Psychology

Magical thinking is a term used in anthropology, philosophy and psychology, denoting the causal relationships between thoughts, actions and events. There are subtle differences in meaning between individual theorists as well as amongst fields of study.

In anthropology, it denotes the attribution of causality between entities grouped with one another (coincidence) or similar to one another.

In psychology, the entities between which a causal relation has to be posited are more strictly delineated; here it denotes the belief that one's thoughts by themselves can bring about effects in the world or that thinking something corresponds with doing it. In both cases, the belief can cause a person to experience fear, seemingly not rationally justifiable to an observer outside the belief system, of performing certain acts or having certain thoughts because of an assumed correlation between doing so and threatening calamities.

In psychiatry, magical thinking is a disorder of thought content; here it denotes the false belief that one's thoughts, actions, or words will cause or prevent a specific consequence in some way that defies commonly understood laws of causality.

🔗 Economics

In finance, the rule of 72, the rule of 70 and the rule of 69.3 are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (usually years) to obtain the approximate number of periods required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and when only a basic calculator is available.

These rules apply to exponential growth and are therefore used for compound interest as opposed to simple interest calculations. They can also be used for decay to obtain a halving time. The choice of number is mostly a matter of preference: 69 is more accurate for continuous compounding, while 72 works well in common interest situations and is more easily divisible. There is a number of variations to the rules that improve accuracy. For periodic compounding, the exact doubling time for an interest rate of r percent per period is

${\displaystyle t={\frac {\ln(2)}{\ln(1+r/100)}}\approx {\frac {72}{r}}}$,

where t is the number of periods required. The formula above can be used for more than calculating the doubling time. If one wants to know the tripling time, for example, replace the constant 2 in the numerator with 3. As another example, if one wants to know the number of periods it takes for the initial value to rise by 50%, replace the constant 2 with 1.5.

🔗 United States/U.S. Government 🔗 United States 🔗 Mass surveillance 🔗 Espionage 🔗 Military history 🔗 Military history/North American military history 🔗 Military history/United States military history 🔗 United States/Military history - U.S. military history 🔗 Military history/Military science, technology, and theory 🔗 Military history/Intelligence 🔗 United Kingdom 🔗 Military history/Australia, New Zealand and South Pacific military history 🔗 Military history/Canadian military history 🔗 Military history/European military history 🔗 Military history/British military history

ECHELON, originally a secret government code name, is a surveillance program (signals intelligence/SIGINT collection and analysis network) operated by the United States with the aid of four other signatory states to the UKUSA Security Agreement: Australia, Canada, New Zealand, and the United Kingdom, also known as the Five Eyes.

Created in the late 1960s to monitor the military and diplomatic communications of the Soviet Union and its Eastern Bloc allies during the Cold War, the ECHELON project became formally established in 1971.

By the end of the 20th century, the system referred to as "ECHELON" had evolved beyond its military and diplomatic origins into "a global system for the interception of private and commercial communications" (mass surveillance and industrial espionage).

🔗 Physics

In stellar physics, the Jeans instability causes the collapse of interstellar gas clouds and subsequent star formation, named after James Jeans. It occurs when the internal gas pressure is not strong enough to prevent gravitational collapse of a region filled with matter. For stability, the cloud must be in hydrostatic equilibrium, which in case of a spherical cloud translates to:

${\displaystyle {\frac {dp}{dr}}=-{\frac {G\rho (r)M_{enc}(r)}{r^{2}}}}$,

where ${\displaystyle M_{enc}(r)}$ is the enclosed mass, ${\displaystyle p}$ is the pressure, ${\displaystyle \rho (r)}$ is the density of the gas (at radius ${\displaystyle r}$), ${\displaystyle G}$ is the gravitational constant, and ${\displaystyle r}$ is the radius. The equilibrium is stable if small perturbations are damped and unstable if they are amplified. In general, the cloud is unstable if it is either very massive at a given temperature or very cool at a given mass; under these circumstances, the gas pressure cannot overcome gravity, and the cloud will collapse.

🔗 Internet 🔗 Computing 🔗 Computing/Computer hardware 🔗 Finance & Investment 🔗 Economics 🔗 Law 🔗 Computing/Software 🔗 Computing/Free and open-source software 🔗 Computing/Computer science 🔗 Cryptography 🔗 Cryptography/Computer science 🔗 Numismatics 🔗 Guild of Copy Editors 🔗 Numismatics/Cryptocurrency 🔗 Cryptocurrency 🔗 Open 🔗 Computing/Computer Security

Bitcoin (₿) is a cryptocurrency. It is a decentralized digital currency without a central bank or single administrator that can be sent from user to user on the peer-to-peer bitcoin network without the need for intermediaries.

Transactions are verified by network nodes through cryptography and recorded in a public distributed ledger called a blockchain. Bitcoin was invented in 2008 by an unknown person or group of people using the name Satoshi Nakamoto and started in 2009 when its source code was released as open-source software. Bitcoins are created as a reward for a process known as mining. They can be exchanged for other currencies, products, and services. Research produced by University of Cambridge estimates that in 2017, there were 2.9 to 5.8 million unique users using a cryptocurrency wallet, most of them using bitcoin.

Bitcoin has been criticized for its use in illegal transactions, its high electricity consumption, price volatility, and thefts from exchanges. Some economists, including several Nobel laureates, have characterized it as a speculative bubble. Bitcoin has also been used as an investment, although several regulatory agencies have issued investor alerts about bitcoin.

🔗 Switzerland

🔗 Spaceflight 🔗 Physics 🔗 Astronomy 🔗 Solar System

The Pioneer anomaly or Pioneer effect was the observed deviation from predicted accelerations of the Pioneer 10 and Pioneer 11 spacecraft after they passed about 20 astronomical units (3×10⁹ km; 2×10⁹ mi) on their trajectories out of the Solar System. The apparent anomaly was a matter of much interest for many years but has been subsequently explained by an anisotropic radiation pressure caused by the spacecraft's heat loss.

Both Pioneer spacecraft are escaping the Solar System but are slowing under the influence of the Sun's gravity. Upon very close examination of navigational data, the spacecraft were found to be slowing slightly more than expected. The effect is an extremely small acceleration towards the Sun, of (8.74±1.33)×10⁻¹⁰ m/s², which is equivalent to a reduction of the outbound velocity by 1 km/h over a period of ten years. The two spacecraft were launched in 1972 and 1973. The anomalous acceleration was first noticed as early as 1980 but not seriously investigated until 1994. The last communication with either spacecraft was in 2003, but analysis of recorded data continues.

Various explanations, both of spacecraft behavior and of gravitation itself, were proposed to explain the anomaly. Over the period from 1998 to 2012, one particular explanation became accepted. The spacecraft, which are surrounded by an ultra-high vacuum and are each powered by a radioisotope thermoelectric generator (RTG), can shed heat only via thermal radiation. If, due to the design of the spacecraft, more heat is emitted in a particular direction by what is known as a radiative anisotropy, then the spacecraft would accelerate slightly in the direction opposite of the excess emitted radiation due to the recoil of thermal photons. If the excess radiation and attendant radiation pressure were pointed in a general direction opposite the Sun, the spacecraft's velocity away from the Sun would be decreasing at a rate greater than could be explained by previously recognized forces, such as gravity and trace friction due to the interplanetary medium (imperfect vacuum).

By 2012 several papers by different groups, all reanalyzing the thermal radiation pressure forces inherent in the spacecraft, showed that a careful accounting of this explains the entire anomaly; thus the cause is mundane and does not point to any new phenomenon or need for a different physical paradigm. The most detailed analysis to date, by some of the original investigators, explicitly looks at two methods of estimating thermal forces, concluding that there is "no statistically significant difference between the two estimates and [...] that once the thermal recoil force is properly accounted for, no anomalous acceleration remains."

🔗 Chemistry

Aqua regia (; from Latin, lit. "regal water" or "king's water") is a mixture of nitric acid and hydrochloric acid, optimally in a molar ratio of 1:3. Aqua regia is a yellow-orange (sometimes red) fuming liquid, so named by alchemists because it can dissolve the noble metals, gold and platinum, though not all metals.

🔗 Mathematics

In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix that generalizes the eigendecomposition of a square normal matrix to any ${\displaystyle m\times n}$ matrix via an extension of the polar decomposition.

Specifically, the singular value decomposition of an ${\displaystyle m\times n}$ real or complex matrix ${\displaystyle \mathbf {M} }$ is a factorization of the form ${\displaystyle \mathbf {U\Sigma V^{*}} }$, where ${\displaystyle \mathbf {U} }$ is an ${\displaystyle m\times m}$ real or complex unitary matrix, ${\displaystyle \mathbf {\Sigma } }$ is an ${\displaystyle m\times n}$ rectangular diagonal matrix with non-negative real numbers on the diagonal, and ${\displaystyle \mathbf {V} }$ is an ${\displaystyle n\times n}$ real or complex unitary matrix. If ${\displaystyle \mathbf {M} }$ is real, ${\displaystyle \mathbf {U} }$ and ${\displaystyle \mathbf {V} =\mathbf {V^{*}} }$ are real orthonormal matrices.

The diagonal entries ${\displaystyle \sigma _{i}=\Sigma _{ii}}$ of ${\displaystyle \mathbf {\Sigma } }$ are known as the singular values of ${\displaystyle \mathbf {M} }$. The number of non-zero singular values is equal to the rank of ${\displaystyle \mathbf {M} }$. The columns of ${\displaystyle \mathbf {U} }$ and the columns of ${\displaystyle \mathbf {V} }$ are called the left-singular vectors and right-singular vectors of ${\displaystyle \mathbf {M} }$, respectively.

The SVD is not unique. It is always possible to choose the decomposition so that the singular values ${\displaystyle \Sigma _{ii}}$are in descending order. In this case, Σ (but not always U and V) is uniquely determined by M.

The term sometimes refers to the compact SVD, a similar decomposition ${\displaystyle \mathbf {M} =\mathbf {U\Sigma V^{*}} }$ in which Σ is square diagonal of size ${\displaystyle r\times r}$, where ${\displaystyle r\leq \min\{m,n\}}$ is the rank of M, and has only the non-zero singular values. In this variant, ${\displaystyle \mathbf {U} }$ is an ${\displaystyle m\times r}$ matrix and ${\displaystyle \mathbf {V} }$ is an ${\displaystyle n\times r}$ matrix, such that ${\displaystyle \mathbf {U^{*}U} =\mathbf {V^{*}V} =\mathbf {I} _{r\times r}}$.

Mathematical applications of the SVD include computing the pseudoinverse, matrix approximation, and determining the rank, range, and null space of a matrix. The SVD is also extremely useful in all areas of science, engineering, and statistics, such as signal processing, least squares fitting of data, and process control.