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π Monty Hall Problem
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975 (Selvin 1975a), (Selvin 1975b). It became famous as a question from a reader's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990 (vos Savant 1990a):
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Vos Savant's response was that the contestant should switch to the other door (vos Savant 1990a). Under the standard assumptions, contestants who switch have a 2/3 chance of winning the car, while contestants who stick to their initial choice have only a 1/3 chance.
The given probabilities depend on specific assumptions about how the host and contestant choose their doors. A key insight is that, under these standard conditions, there is more information about doors 2 and 3 than was available at the beginning of the game when door 1 was chosen by the player: the host's deliberate action adds value to the door he did not choose to eliminate, but not to the one chosen by the contestant originally. Another insight is that switching doors is a different action than choosing between the two remaining doors at random, as the first action uses the previous information and the latter does not. Other possible behaviors than the one described can reveal different additional information, or none at all, and yield different probabilities. Yet another insight is that your chance of winning by switching doors is directly related to your chance of choosing the winning door in the first place: if you choose the correct door on your first try, then switching loses; if you choose a wrong door on your first try, then switching wins; your chance of choosing the correct door on your first try is 1/3, and the chance of choosing a wrong door is 2/3.
Many readers of vos Savant's column refused to believe switching is beneficial despite her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong (Tierney 1991). Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy (vos Savant 1991a). Paul ErdΕs, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating vos Savantβs predicted result (Vazsonyi 1999).
The problem is a paradox of the veridical type, because the correct choice (that one should switch doors) is so counterintuitive it can seem absurd, but is nevertheless demonstrably true. The Monty Hall problem is mathematically closely related to the earlier Three Prisoners problem and to the much older Bertrand's box paradox.
Discussed on
- "Monty Hall Problem" | 2022-06-09 | 24 Upvotes 116 Comments
- "Monty Hall Problem" | 2019-10-24 | 122 Upvotes 252 Comments
- "Monty Hall problem" | 2010-02-22 | 14 Upvotes 27 Comments
π Bloom's 2 sigma problem
Bloom's 2 sigma problem refers to an educational phenomenon observed by educational psychologist Benjamin Bloom and initially reported in 1984 in the journal Educational Researcher. Bloom found that the average student tutored one-to-one using mastery learning techniques performed two standard deviations better than students who learn via conventional instructional methods β that is, "the average tutored student was above 98% of the students in the control class". Additionally, the variation of the students' achievement changed: "about 90% of the tutored students ... attained the level of summative achievement reached by only the highest 20%" of the control class. Bloom's graduate students J. Anania and A. J. Burke conducted studies of this effect at different grade levels and in different schools, observing students with "great differences in cognitive achievement, attitudes, and academic self-concept".
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- "Bloom's 2 Sigma Problem" | 2023-02-25 | 266 Upvotes 130 Comments
- "Bloom's 2 Sigma Problem" | 2020-08-24 | 54 Upvotes 15 Comments
- "Bloom's 2 sigma problem" | 2018-10-01 | 57 Upvotes 18 Comments
π 1% rule
In Internet culture, the 1% rule is a rule of thumb pertaining to participation in an internet community, stating that only 1% of the users of a website add content, while the other 99% of the participants only lurk. Variants include the 1β9β90 rule (sometimes 90β9β1 principle or the 89:10:1 ratio), which states that in a collaborative website such as a wiki, 90% of the participants of a community only consume content, 9% of the participants change or update content, and 1% of the participants add content.
Similar rules are known in information science, such as the 80/20 rule known as the Pareto principle, that 20 percent of a group will produce 80 percent of the activity, however the activity may be defined.
Discussed on
- "1% rule" | 2020-03-18 | 465 Upvotes 151 Comments
- "1% rule (Internet culture)" | 2014-01-13 | 105 Upvotes 61 Comments
π Mpemba Effect
The Mpemba effect is a process in which hot water can freeze faster than cold water. The phenomenon is temperature-dependent. There is disagreement about the parameters required to produce the effect and about its theoretical basis.
The Mpemba effect is named after Tanzanian scientist Erasto Bartholomeo Mpemba (b.1950) who discovered it in 1963. There were preceding ancient accounts of similar phenomena, but these lacked sufficient detail to attempt verification.
Discussed on
- "Mpemba effect β Hot water freezes faster" | 2019-11-11 | 17 Upvotes 3 Comments
- "Mpemba effect: warmer water can freeze faster than colder water" | 2016-05-08 | 91 Upvotes 38 Comments
- "Mpemba effect: warmer water can freeze faster than colder water" | 2013-04-27 | 32 Upvotes 25 Comments
- "The Mpemba Effect" | 2009-12-13 | 36 Upvotes 15 Comments
π East Germany balloon escape
On 16 September 1979, eight people from two families escaped from East Germany by crossing the border into West Germany at night in a homemade hot air balloon. The unique feat was the result of over a year and a half of preparations involving three different balloons, various modifications, and a first, unsuccessful attempt. The failed attempt alerted the East German authorities to the plot, but the police were unable to identify the escapees before their second, successful flight two months later.
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- "East Germany balloon escape" | 2026-01-16 | 724 Upvotes 301 Comments
π Oblique Strategies
Oblique Strategies (subtitled Over One Hundred Worthwhile Dilemmas) is a card-based method for promoting creativity jointly created by Brian Eno and Peter Schmidt, first published in 1975. Physically, it takes the form of a deck of 7-by-9-centimetre (2.8Β in ΓΒ 3.5Β in) printed cards in a black box. Each card offers a challenging constraint intended to help artists (particularly musicians) break creative blocks by encouraging lateral thinking.
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- "Oblique Strategies" | 2022-05-22 | 48 Upvotes 20 Comments
- "Oblique Strategies" | 2020-09-14 | 203 Upvotes 54 Comments
- "Oblique Strategies" | 2015-09-03 | 10 Upvotes 2 Comments
π Qanat
A qanat or kariz is a gently sloping underground channel to transport water from an aquifer or water well to surface for irrigation and drinking, acting as an underground aqueduct. This is an old system of water supply from a deep well with a series of vertical access shafts. The qanats still create a reliable supply of water for human settlements and irrigation in hot, arid, and semi-arid climates, but the value of this system is directly related to the quality, volume, and regularity of the water flow. Traditionally qanats are built by a group of skilled laborers, muqannΔ«s, with hand labor. The profession historically paid well and was typically handed down from father to son. According to most sources, the qanat technology was developed in ancient Iran by the Persian people sometime in the early 1st millennium BCE, and spread from there slowly westward and eastward. However, some other sources suggest a Southeast Arabian origin.
π Great Vowel Shift
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 (1860β1943), a Danish linguist and Anglicist, who coined the term.
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- "Great Vowel Shift" | 2021-04-14 | 259 Upvotes 268 Comments
- "Great Vowel Shift" | 2018-04-06 | 129 Upvotes 117 Comments
π Wow signal
The Wow! signal was a strong narrowband radio signal received on August 15, 1977, by Ohio State University's Big Ear radio telescope in the United States, then used to support the search for extraterrestrial intelligence. The signal appeared to come from the direction of the constellation Sagittarius and bore the expected hallmarks of extraterrestrial origin.
Astronomer Jerry R. Ehman discovered the anomaly a few days later while reviewing the recorded data. He was so impressed by the result that he circled the reading on the computer printout, "6EQUJ5", and wrote the comment "Wow!" on its side, leading to the event's widely used name.
The entire signal sequence lasted for the full 72-second window during which Big Ear was able to observe it, but has not been detected since, despite several subsequent attempts by Ehman and others. Many hypotheses have been advanced on the origin of the emission, including natural and human-made sources, but none of them adequately explains the signal.
Although the Wow! signal had no detectable modulationβa technique used to transmit information over radio wavesβit remains the strongest candidate for an alien radio transmission ever detected.
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- "Wow Signal" | 2024-03-12 | 40 Upvotes 4 Comments
- "Wow signal" | 2015-07-05 | 43 Upvotes 31 Comments
- "Wow signal" | 2014-03-12 | 125 Upvotes 95 Comments
- "Wow signal" | 2010-03-15 | 27 Upvotes 13 Comments
π Poka-yoke
Poka-yoke (γγ«γ¨γ±, [poka yoke]) is a Japanese term that means "mistake-proofing" or "inadvertent error prevention". A poka-yoke is any mechanism in any process that helps an equipment operator avoid (yokeru) mistakes (poka). Its purpose is to eliminate product defects by preventing, correcting, or drawing attention to human errors as they occur. The concept was formalised, and the term adopted, by Shigeo Shingo as part of the Toyota Production System. It was originally described as baka-yoke, but as this means "fool-proofing" (or "idiot-proofing") the name was changed to the milder poka-yoke.
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- "Poka-Yoke" | 2025-01-09 | 69 Upvotes 46 Comments
- "Poka Yoke" | 2021-09-08 | 99 Upvotes 62 Comments
- "Poka-yoke" | 2018-09-23 | 160 Upvotes 60 Comments