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🔗 Mathematics

In number theory, Mills' constant is defined as the smallest positive real number A such that the floor function of the double exponential function

${\displaystyle \lfloor A^{3^{n}}\rfloor }$

is a prime number, for all natural numbers n. This constant is named after William H. Mills who proved in 1947 the existence of A based on results of Guido Hoheisel and Albert Ingham on the prime gaps. Its value is unknown, but if the Riemann hypothesis is true, it is approximately 1.3063778838630806904686144926... (sequence A051021 in the OEIS).

🔗 Psychology 🔗 Cognitive science

Functional fixedness is a cognitive bias that limits a person to use an object only in the way it is traditionally used. The concept of functional fixedness originated in Gestalt psychology, a movement in psychology that emphasizes holistic processing. Karl Duncker defined functional fixedness as being a "mental block against using an object in a new way that is required to solve a problem". This "block" limits the ability of an individual to use components given to them to complete a task, as they cannot move past the original purpose of those components. For example, if someone needs a paperweight, but they only have a hammer, they may not see how the hammer can be used as a paperweight. Functional fixedness is this inability to see a hammer's use as anything other than for pounding nails; the person couldn't think to use the hammer in a way other than in its conventional function.

When tested, 5-year-old children show no signs of functional fixedness. It has been argued that this is because at age 5, any goal to be achieved with an object is equivalent to any other goal. However, by age 7, children have acquired the tendency to treat the originally intended purpose of an object as special.

🔗 Computer science

TLA⁺ is a formal specification language developed by Leslie Lamport. It is used to design, model, document, and verify programs, especially concurrent systems and distributed systems. TLA⁺ has been described as exhaustively-testable pseudocode, and its use likened to drawing blueprints for software systems; TLA is an acronym for Temporal Logic of Actions.

For design and documentation, TLA⁺ fulfills the same purpose as informal technical specifications. However, TLA⁺ specifications are written in a formal language of logic and mathematics, and the precision of specifications written in this language is intended to uncover design flaws before system implementation is underway.

Since TLA⁺ specifications are written in a formal language, they are amenable to finite model checking. The model checker finds all possible system behaviours up to some number of execution steps, and examines them for violations of desired invariance properties such as safety and liveness. TLA⁺ specifications use basic set theory to define safety (bad things won't happen) and temporal logic to define liveness (good things eventually happen).

TLA⁺ is also used to write machine-checked proofs of correctness both for algorithms and mathematical theorems. The proofs are written in a declarative, hierarchical style independent of any single theorem prover backend. Both formal and informal structured mathematical proofs can be written in TLA⁺; the language is similar to LaTeX, and tools exist to translate TLA⁺ specifications to LaTeX documents.

TLA⁺ was introduced in 1999, following several decades of research into a verification method for concurrent systems. A toolchain has since developed, including an IDE and distributed model checker. The pseudocode-like language PlusCal was created in 2009; it transpiles to TLA⁺ and is useful for specifying sequential algorithms. TLA⁺² was announced in 2014, expanding language support for proof constructs. The current TLA⁺ reference is The TLA⁺ Hyperbook by Leslie Lamport.

🔗 Medicine 🔗 Chemicals 🔗 Medicine/Neurology 🔗 Pharmacology 🔗 Medicine/Psychiatry 🔗 Epilepsy

Benzodiazepines (BZD, BDZ, BZs), colloquially called "benzos", are a class of depressant drugs whose core chemical structure is the fusion of a benzene ring and a diazepine ring. They are prescribed to treat conditions such as anxiety disorders, insomnia, and seizures. The first benzodiazepine, chlordiazepoxide (Librium), was discovered accidentally by Leo Sternbach in 1955 and was made available in 1960 by Hoffmann–La Roche, who soon followed with diazepam (Valium) in 1963. By 1977, benzodiazepines were the most prescribed medications globally; the introduction of selective serotonin reuptake inhibitors (SSRIs), among other factors, decreased rates of prescription, but they remain frequently used worldwide.

Benzodiazepines are depressants that enhance the effect of the neurotransmitter gamma-aminobutyric acid (GABA) at the GABA_A receptor, resulting in sedative, hypnotic (sleep-inducing), anxiolytic (anti-anxiety), anticonvulsant, and muscle relaxant properties. High doses of many shorter-acting benzodiazepines may also cause anterograde amnesia and dissociation. These properties make benzodiazepines useful in treating anxiety, panic disorder, insomnia, agitation, seizures, muscle spasms, alcohol withdrawal and as a premedication for medical or dental procedures. Benzodiazepines are categorized as short, intermediate, or long-acting. Short- and intermediate-acting benzodiazepines are preferred for the treatment of insomnia; longer-acting benzodiazepines are recommended for the treatment of anxiety.

Benzodiazepines are generally viewed as safe and effective for short-term use—about two to four weeks—although cognitive impairment and paradoxical effects such as aggression or behavioral disinhibition can occur. A minority of people have paradoxical reactions after taking benzodiazepines such as worsened agitation or panic. Benzodiazepines are associated with an increased risk of suicide due to aggression, impulsivity, and negative withdrawal effects. Long-term use is controversial because of concerns about decreasing effectiveness, physical dependence, benzodiazepine withdrawal syndrome, and an increased risk of dementia and cancer. The elderly are at an increased risk of both short- and long-term adverse effects, and as a result, all benzodiazepines are listed in the Beers List of inappropriate medications for older adults. There is controversy concerning the safety of benzodiazepines in pregnancy. While they are not major teratogens, uncertainty remains as to whether they cause cleft palate in a small number of babies and whether neurobehavioural effects occur as a result of prenatal exposure; they are known to cause withdrawal symptoms in the newborn.

Taken in overdose, benzodiazepines can cause dangerous deep unconsciousness, but they are less toxic than their predecessors, the barbiturates, and death rarely results when a benzodiazepine is the only drug taken. Combined with other central nervous system (CNS) depressants such as alcohol and opioids, the potential for toxicity and fatal overdose increases significantly. Benzodiazepines are commonly used recreationally and also often taken in combination with other addictive substances, and are controlled in most countries.

🔗 Computing 🔗 Economics 🔗 Apps

A super-app (also written as super app or superapp) is a mobile or web application that can provide multiple services including payment and financial transaction processing, effectively becoming an all-encompassing self-contained commerce and communication online platform that embraces many aspects of personal and commercial life. Notable examples of super-apps include Tencent's WeChat in China, and Grab in Southeast Asia.

🔗 Computing

Modelica is an object-oriented, declarative, multi-domain modeling language for component-oriented modeling of complex systems, e.g., systems containing mechanical, electrical, electronic, hydraulic, thermal, control, electric power or process-oriented subcomponents. The free Modelica language is developed by the non-profit Modelica Association. The Modelica Association also develops the free Modelica Standard Library that contains about 1360 generic model components and 1280 functions in various domains, as of version 3.2.1.

🔗 Politics

Quadratic voting is a collective decision-making procedure where individuals allocate votes to express the degree of their preferences, rather than just the direction of their preferences. By doing so, quadratic voting helps enable users to address issues of voting paradox and majority-rule. Quadratic voting works by allowing users to 'pay' for additional votes on a given matter to express their preference for given issues more strongly, resulting in voting outcomes that are aligned with the highest willingness to pay outcome, rather than just the outcome preferred by the majority regardless of the intensity of individual preferences. The payment for votes may be through either artificial or real currencies (e.g. with tokens distributed equally among voting members or with real money). Under various sets of conditions, quadratic voting has been shown to be much more efficient than one-person-one-vote in aligning collective decisions with doing the most good for the most people. Quadratic voting (abbreviated as QV) is considered a promising alternative to existing democratic structures to solve some of the known failure modes of one-person-one-vote democracies. Quadratic voting is a variant of cumulative voting in the class of cardinal voting. It differs from Cumulative voting by altering "the cost" and "the vote" relation from linear to quadratic.

Quadratic voting is based upon market principles, where each voter is given a budget of vote credits that they have the personal decisions and delegation to spend in order to influence the outcome of a range of decisions. If a participant has a strong preference for or against a specific decision, additional votes could be allocated to proportionally demonstrate the voter's preferences. A vote pricing rule determines the cost of additional votes, with each vote becoming increasingly more expensive. By increasing voter credit costs, this demonstrates an individual's preferences and interests toward the particular decision. This money is eventually cycled back to the voters based upon per capita. Both Weyl and Lalley conducted research to demonstrate that this decision-making policy expedites efficiency as the number of voters increases. The simplified formula on how quadratic voting functions is:

cost to the voter = (number of votes)².

The quadratic nature of the voting suggests that a voter can use their votes more efficiently by spreading them across many issues. For example, a voter with a budget of 16 vote credits can apply 1 vote credit to each of the 16 issues. However, if the individual has a stronger passion or sentiment on an issue, they could allocate 4 votes, at the cost of 16 credits, to the singular issue, effectively using up their entire budget. This mechanism towards voting demonstrates that there is a large incentive to buy and sell votes, or to trade votes. Using this anonymous ballot system provides identity protection from vote buying or trading since these exchanges cannot be verified by the buyer or trader.

🔗 Skepticism 🔗 Psychology 🔗 Debating

The Gish gallop is a technique used during debating that focuses on overwhelming an opponent with as many arguments as possible, without regard for accuracy or strength of the arguments. The term was coined by Eugenie Scott and named after the creationist Duane Gish, who used the technique frequently against proponents of evolution.

🔗 Economics

The iron law of wages is a proposed law of economics that asserts that real wages always tend, in the long run, toward the minimum wage necessary to sustain the life of the worker. The theory was first named by Ferdinand Lassalle in the mid-nineteenth century. Karl Marx and Friedrich Engels attribute the doctrine to Lassalle (notably in Marx's 1875 Critique of the Gotha Program), the idea to Thomas Malthus's An Essay on the Principle of Population, and the terminology to Goethe's "great, eternal iron laws" in Das Göttliche.

It was coined in reference to the views of classical economists such as David Ricardo's Law of rent, and the competing population theory of Thomas Malthus. It held that the market price of labour would always, or almost always, tend toward the minimum required for the subsistence of the labourers, reducing as the working population increased and vice versa. Ricardo believed that happened only under particular conditions.