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Hilbert's paradox of the Grand Hotel (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and this process may be repeated infinitely often. The idea was introduced by David Hilbert in a 1924 lecture "Über das Unendliche", reprinted in (Hilbert 2013, p.730), and was popularized through George Gamow's 1947 book One Two Three... Infinity.

"The staff ate it later" (Japanese: この後、スタッフが美味しくいただきました, Hepburn: Kono ato, sutaffu ga oishiku itadakimashita; More fully translated as the staff ate and enjoyed it later) is a caption shown on screen in a Japanese TV program to indicate that the food presented during the program was not thrown away after filming. Some have questioned the authenticity of displaying the caption.

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.

In programming jargon, Yoda conditions (also called Yoda notation) is a programming style where the two parts of an expression are reversed from the typical order in a conditional statement. A Yoda condition places the constant portion of the expression on the left side of the conditional statement. The name for this programming style is derived from the Star Wars character named Yoda, who speaks English with a non-standard syntax.

Yoda conditions are part of the Symfony, and the WordPress coding standards.

The "PayPal Mafia" is a group of former PayPal employees and founders who have since founded and developed additional technology companies such as Tesla Motors, LinkedIn, Palantir Technologies, SpaceX, YouTube, Yelp, and Yammer. Most of the members attended Stanford University or University of Illinois at Urbana–Champaign at some point in their studies.

On April 16, 2013, a sophisticated assault was carried out on Pacific Gas and Electric Company's Metcalf Transmission Substation in Coyote, California, near the border of San Jose. The attack, in which gunmen fired on 17 electrical transformers, resulted in more than $15 million worth of equipment damage, but it had little impact on the station's electrical power supply.