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The number 6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is renowned for the following rule:

1. Take any four-digit number, using at least two different digits (leading zeros are allowed).
2. Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.
3. Subtract the smaller number from the bigger number.
4. Go back to step 2 and repeat.

The above process, known as Kaprekar's routine, will always reach its fixed point, 6174, in at most 7 iterations. Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174. For example, choose 1459:

The only four-digit numbers for which Kaprekar's routine does not reach 6174 are repdigits such as 1111, which give the result 0000 after a single iteration. All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4. For numbers with three identical numbers and a fourth number that is one number higher or lower (such as 2111), it is essential to treat 3-digit numbers with a leading zero; for example: 2111 – 1112 = 0999; 9990 – 999 = 8991; 9981 – 1899 = 8082; 8820 – 288 = 8532; 8532 – 2358 = 6174.

Baumol's cost disease (or the Baumol effect) is the rise of salaries in jobs that have experienced no or low increase of labor productivity, in response to rising salaries in other jobs that have experienced higher labor productivity growth. This pattern seemingly goes against the theory in classical economics in which real wage growth is closely tied to labor productivity changes. The phenomenon was described by William J. Baumol and William G. Bowen in the 1960s.

The rise of wages in jobs without productivity gains is from the requirement to compete for employees with jobs that have experienced gains and so can naturally pay higher salaries, just as classical economics predicts. For instance, if the retail sector pays its managers 19th-century-style salaries, the managers may decide to quit to get a job at an automobile factory, where salaries are higher because of high labor productivity. Thus, managers' salaries are increased not by labor productivity increases in the retail sector but by productivity and corresponding wage increases in other industries.

A whale fall occurs when the carcass of a whale has fallen onto the ocean floor at a depth greater than 1,000 m (3,300 ft), in the bathyal or abyssal zones. On the sea floor, these carcasses can create complex localized ecosystems that supply sustenance to deep-sea organisms for decades. This is unlike in shallower waters, where a whale carcass will be consumed by scavengers over a relatively short period of time. Whale falls were first observed in the late 1970s with the development of deep-sea robotic exploration. Since then, several natural and experimental whale falls have been monitored through the use of observations from submersibles and remotely operated underwater vehicles (ROVs) in order to understand patterns of ecological succession on the deep seafloor.

Deep sea whale falls are thought to be hotspots of adaptive radiation for specialized fauna. Organisms that have been observed at deep-sea whale fall sites include giant isopods, squat lobsters, bristleworms, prawns, shrimp, lobsters, hagfish, Osedax, crabs, sea cucumbers, and sleeper sharks. In the past three years whale fall sites have come under scrutiny, and new species have been discovered, including potential whale fall specialists. It has been postulated that whale falls generate biodiversity by providing evolutionary stepping stones for multiple lineages to move and adapt to new environmentally-challenging habitats. Researchers estimate that 690,000 carcasses/skeletons of the nine largest whale species are in one of the four stages of succession at any one time. This estimate implies an average spacing of 12 km (7.5 mi) and as little as 5 km (3.1 mi) along migration routes. They hypothesize that this distance is short enough to allow larvae to disperse/migrate from one to another.

Whale falls are able to occur in the deep open ocean due to cold temperatures and high hydrostatic pressures. In the coastal ocean, a higher incidence of predators as well as warmer waters hasten the decomposition of whale carcasses. Carcasses may also float due to decompositional gases, keeping the carcass at the surface. The bodies of most great whales (baleen and sperm whales) are slightly denser than the surrounding seawater, and only become positively buoyant when the lungs are filled with air. When the lungs deflate, the whale carcasses can reach the seafloor quickly and relatively intact due to a lack of significant whale fall scavengers in the water column. Once in the deep-sea, cold temperatures slow decomposition rates, and high hydrostatic pressures increase gas solubility, allowing whale falls to remain intact and sink to even greater depths.

Senet (or senat) is a board game from ancient Egypt, whose original rules are the subject of conjecture. The oldest hieroglyph resembling a senet game dates to around 3100 BC. The full name of the game in Egyptian is thought to have been zn.t n.t ḥˁb, meaning the "game of passing".

Arcosanti is a projected experimental town with a molten bronze bell casting business in Yavapai County, central Arizona, 70 mi (110 km) north of Phoenix, at an elevation of 3,732 feet (1,130 meters). Its arcology concept was posited by the Italian-American architect, Paolo Soleri (1919–2013). He began construction in 1970, to demonstrate how urban conditions could be improved while minimizing the destructive impact on the earth. He taught and influenced generations of architects and urban designers who studied and worked with him there to build the proposed "town".

The Magic Roundabout in Swindon, England, is a ring junction constructed in 1972 consisting of five mini-roundabouts arranged in a circle around a sixth, central circle. Located near the County Ground, home of Swindon Town F.C., its name comes from the popular children's television series The Magic Roundabout. In 2009 it was voted the fourth scariest junction in Britain.

A fossil natural nuclear fission reactor is a uranium deposit where self-sustaining nuclear chain reactions have occurred. This can be examined by analysis of isotope ratios. The conditions under which a natural nuclear reactor could exist had been predicted in 1956 by Paul Kazuo Kuroda. The phenomenon was discovered in 1972 in Oklo, Gabon by French physicist Francis Perrin under conditions very similar to what was predicted.

Oklo is the only known location for this in the world and consists of 16 sites at which self-sustaining nuclear fission reactions are thought to have taken place approximately 1.7 billion years ago, and ran for a few hundred thousand years, averaging probably less than 100 kW of thermal power during that time.

The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball. Indeed, the reassembly process involves only moving the pieces around and rotating them without changing their shape. However, the pieces themselves are not "solids" in the usual sense, but infinite scatterings of points. The reconstruction can work with as few as five pieces.

A stronger form of the theorem implies that given any two "reasonable" solid objects (such as a small ball and a huge ball), the cut pieces of either one can be reassembled into the other. This is often stated informally as "a pea can be chopped up and reassembled into the Sun" and called the "pea and the Sun paradox".

The reason the Banach–Tarski theorem is called a paradox is that it contradicts basic geometric intuition. "Doubling the ball" by dividing it into parts and moving them around by rotations and translations, without any stretching, bending, or adding new points, seems to be impossible, since all these operations ought, intuitively speaking, to preserve the volume. The intuition that such operations preserve volumes is not mathematically absurd and it is even included in the formal definition of volumes. However, this is not applicable here because in this case it is impossible to define the volumes of the considered subsets. Reassembling them reproduces a volume, which happens to be different from the volume at the start.

Unlike most theorems in geometry, the proof of this result depends in a critical way on the choice of axioms for set theory. It can be proven using the axiom of choice, which allows for the construction of non-measurable sets, i.e., collections of points that do not have a volume in the ordinary sense, and whose construction requires an uncountable number of choices.

It was shown in 2005 that the pieces in the decomposition can be chosen in such a way that they can be moved continuously into place without running into one another.

Eigengrau (German: "intrinsic gray", lit. "own gray"; pronounced [ˈʔaɪ̯gn̩ˌgʁaʊ̯]), also called Eigenlicht (Dutch and German: "own light"), dark light, or brain gray, is the uniform dark gray background that many people report seeing in the absence of light. The term Eigenlicht dates back to the nineteenth century, but has rarely been used in recent scientific publications. Common scientific terms for the phenomenon include "visual noise" or "background adaptation". These terms arise due to the perception of an ever-changing field of tiny black and white dots seen in the phenomenon.

Eigengrau is perceived as lighter than a black object in normal lighting conditions, because contrast is more important to the visual system than absolute brightness. For example, the night sky looks darker than Eigengrau because of the contrast provided by the stars.