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Unschooling is an informal learning that advocates learner-chosen activities as a primary means for learning. Unschooling students learn through their natural life experiences including play, household responsibilities, personal interests and curiosity, internships and work experience, travel, books, elective classes, family, mentors, and social interaction. Unschooling encourages exploration of activities initiated by the children themselves, believing that the more personal learning is, the more meaningful, well-understood and therefore useful it is to the child. While courses may occasionally be taken, unschooling questions the usefulness of standard curricula, conventional grading methods, and other features of traditional schooling in the education of each unique child.

The term "unschooling" was coined in the 1970s and used by educator John Holt, widely regarded as the father of unschooling. While unschooling is often considered a subset of homeschooling and homeschooling has been subject to widespread public debate, little media attention has been given to unschooling in particular.

Critics of unschooling see it as an extreme educational philosophy, with concerns that unschooled children will lack the social skills, structure, and motivation of their schooled peers, while proponents of unschooling say exactly the opposite is true: that self-directed education in a natural environment better equips a child to handle the "real world."

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.

A collective action problem or social dilemma is a situation in which all individuals would be better off cooperating but fail to do so because of conflicting interests between individuals that discourage joint action. The collective action problem has been addressed in political philosophy for centuries, but was most clearly established in 1965 in Mancur Olson's The Logic of Collective Action.

Problems arise when too many group members choose to pursue individual profit and immediate satisfaction rather than behave in the group's best long-term interests. Social dilemmas can take many forms and are studied across disciplines such as psychology, economics, and political science. Examples of phenomena that can be explained using social dilemmas include resource depletion and low voter turnout. The collective action problem can be understood through the analysis of game theory and the free-rider problem, which results from the provision of public goods. Additionally, the collective problem can be applied to numerous public policy concerns that countries across the world currently face.

The technology depicted in Terry Pratchett's Discworld novels takes two forms: magical and mechanical. Nearly all technology early in the series is at least partially magical, but in more recent books, a form of industrial revolution takes place, with numerous purely mechanical inventions being introduced. In Thud! ancient 'devices' of undisclosed origin and great power were introduced; it is not clear whether these are magical, mechanical, both or neither. Time-travel technology, the exact nature of which is usually unclear, is used by the History Monks. Most Discworld technologies have real-world equivalents, in function if not form.

The Great Vowel Shift was a series of changes in the pronunciation of the English language that took place primarily between 1400 and 1700, beginning in southern England and today having influenced effectively all dialects of English. Through this vowel shift, the pronunciation of all Middle English long vowels was changed. Some consonant sounds changed as well, particularly those that became silent; the term Great Vowel Shift is sometimes used to include these consonant changes.

English spelling began to become standardized in the 15th and 16th centuries, and the Great Vowel Shift is the major reason English spellings now often considerably deviate from how they represent pronunciations. The Great Vowel Shift was first studied by Otto Jespersen (1860–1943), a Danish linguist and Anglicist, who coined the term.

The High Arctic relocation (French: La délocalisation du Haut-Arctique, Inuktitut syllabics: ᖁᑦᑎᒃᑐᒥᐅᑦᑕ ᓅᑕᐅᓂᖏᑦ Inuktitut: Quttiktumut nuutauningit) took place during the Cold War in the 1950s, when 92 Inuit were moved by the Government of Canada to the High Arctic.

The relocation has been a source of controversy: on one hand being described as a humanitarian gesture to save the lives of starving indigenous people and enable them to continue a subsistence lifestyle; and on the other hand, said to be a forced migration instigated by the federal government to assert its sovereignty in the Far North by the use of "human flagpoles", in light of both the Cold War and the disputed territorial claims to the Canadian Arctic Archipelago. Both sides acknowledge that the relocated Inuit were not given sufficient support to prevent extreme privation during their first years after the move. The story was the subject of a book called The Long Exile, published by Melanie McGrath in 2006.

The Gotthard Base Tunnel (GBT; German: Gotthard-Basistunnel, Italian: Galleria di base del San Gottardo, Romansh: Tunnel da basa dal Son Gottard) is a railway tunnel through the Alps in Switzerland. It opened on 1 June 2016, and full service began on 11 December 2016. With a route length of 57.09 km (35.5 mi), it is the world's longest railway and deepest traffic tunnel and the first flat, low-level route through the Alps. It lies at the heart of the Gotthard axis and constitutes the third tunnel connecting the cantons of Uri and Ticino, after the Gotthard Tunnel and the Gotthard Road Tunnel.

The link consists of two single-track tunnels connecting Erstfeld (Uri) with Bodio (Ticino) and passing below Sedrun (Graubünden). It is part of the New Railway Link through the Alps (NRLA) project, which also includes the Ceneri Base Tunnel further south (scheduled to open late 2020) and the Lötschberg Base Tunnel on the other main north–south axis. It is referred to as a "base tunnel" since it bypasses most of the existing Gotthard railway line, a winding mountain route opened in 1882 across the Saint-Gotthard Massif, which was operating at its capacity before the opening of the GBT. The new base tunnel establishes a direct route usable by high-speed rail and heavy freight trains.

The main purpose of the Gotthard Base Tunnel is to increase local transport capacity through the Alpine barrier, especially for freight, notably on the Rotterdam–Basel–Genoa corridor, and more specifically to shift freight volumes from trucks to freight trains. This both significantly reduces the danger of fatal road crashes involving trucks, and reduces the environmental damage caused by heavy trucks. The tunnel provides a faster connection between the canton of Ticino and the rest of Switzerland, as well as between northern and southern Europe, cutting the Basel/Zürich–Lugano–Milan journey time for passenger trains by one hour (and from Lucerne to Bellinzona by 45 minutes).

After 64 percent of Swiss voters accepted the NRLA project in a 1992 referendum, first preparatory and exploratory work began in 1996. The official start of construction began on 4 November 1999 at Amsteg. Drilling operations in the eastern tunnel were completed on 15 October 2010 in a breakthrough ceremony broadcast live on Swiss TV, and in the western tunnel on 23 March 2011. The tunnel's constructor, AlpTransit Gotthard AG, originally planned to hand over the tunnel to Swiss Federal Railways (SBB CFF FFS) in operating condition in December 2016 but, on 4 February 2014, the handover date was changed to 5 June 2016 with the start of an 850-day opening countdown calendar on the AlpTransit homepage. As of 1998, the total projected cost of the project was CHF 6.323 billion; as of December 2015, the final cost is projected as CHF 9.560 billion. Nine people died during construction.

Amir Emad Mirmirani (Persian: امیرعماد میرمیرانی) known by the nickname Jadi, is a programmer, blogger and internet activist in the field of Free and open-source software and Linux in Iran. He was arrested in October 2022 during the Iranian protests following the death of Mahsa Amini.

This is a list of vegetables which are grown or harvested primarily for the consumption of their leafy parts, either raw or cooked. Many plants with leaves that are consumed in small quantities as a spice such as oregano, for medicinal purposes such as lime, or used in infusions such as tea, are not included in this list.

The Crookes radiometer (also known as a light mill) consists of an airtight glass bulb containing a partial vacuum, with a set of vanes which are mounted on a spindle inside. The vanes rotate when exposed to light, with faster rotation for more intense light, providing a quantitative measurement of electromagnetic radiation intensity.

The reason for the rotation was a cause of much scientific debate in the ten years following the invention of the device, but in 1879 the currently accepted explanation for the rotation was published. Today the device is mainly used in physics education as a demonstration of a heat engine run by light energy.

It was invented in 1873 by the chemist Sir William Crookes as the by-product of some chemical research. In the course of very accurate quantitative chemical work, he was weighing samples in a partially evacuated chamber to reduce the effect of air currents, and noticed the weighings were disturbed when sunlight shone on the balance. Investigating this effect, he created the device named after him.

It is still manufactured and sold as an educational aid or for curiosity.