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🔗 Mathematics

Langton's ant is a two-dimensional universal Turing machine with a very simple set of rules but complex emergent behavior. It was invented by Chris Langton in 1986 and runs on a square lattice of black and white cells. The universality of Langton's ant was proven in 2000. The idea has been generalized in several different ways, such as turmites which add more colors and more states.

🔗 Linguistics 🔗 New York (state) 🔗 New York (state)/Western New York

"Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo" is a grammatically correct sentence in American English, often presented as an example of how homonyms and homophones can be used to create complicated linguistic constructs through lexical ambiguity. It has been discussed in literature in various forms since 1967, when it appeared in Dmitri Borgmann's Beyond Language: Adventures in Word and Thought.

The sentence employs three distinct meanings of the word buffalo:

• as a proper noun to refer to a specific place named Buffalo, the city of Buffalo, New York, being the most notable;
• as a verb (uncommon in regular usage) to buffalo, meaning "to bully, harass, or intimidate" or "to baffle"; and
• as a noun to refer to the animal, bison (often called buffalo in North America). The plural is also buffalo.

An expanded form of the sentence which preserves the original word order is: "Buffalo bison, that other Buffalo bison bully, also bully Buffalo bison."

🔗 Mathematics 🔗 Statistics

Simpson's paradox, which goes by several names, is a phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined. This result is often encountered in social-science and medical-science statistics and is particularly problematic when frequency data is unduly given causal interpretations. The paradox can be resolved when causal relations are appropriately addressed in the statistical modeling.

Simpson's paradox has been used as an exemplar to illustrate to the non-specialist or public audience the kind of misleading results mis-applied statistics can generate. Martin Gardner wrote a popular account of Simpson's paradox in his March 1976 Mathematical Games column in Scientific American.

Edward H. Simpson first described this phenomenon in a technical paper in 1951, but the statisticians Karl Pearson et al., in 1899, and Udny Yule, in 1903, had mentioned similar effects earlier. The name Simpson's paradox was introduced by Colin R. Blyth in 1972.

It is also referred to as or Simpson's reversal, Yule–Simpson effect, amalgamation paradox, or reversal paradox.

🔗 Computer science 🔗 Philosophy 🔗 Philosophy/Logic 🔗 Philosophy/Philosophy of science 🔗 Philosophy/Philosophy of mind

Moravec's paradox is the observation by artificial intelligence and robotics researchers that, contrary to traditional assumptions, reasoning (which is high-level in humans) requires very little computation, but sensorimotor skills (comparatively low-level in humans) require enormous computational resources. The principle was articulated by Hans Moravec, Rodney Brooks, Marvin Minsky and others in the 1980s. As Moravec writes, "it is comparatively easy to make computers exhibit adult level performance on intelligence tests or playing checkers, and difficult or impossible to give them the skills of a one-year-old when it comes to perception and mobility".

Similarly, Minsky emphasized that the most difficult human skills to reverse engineer are those that are unconscious. "In general, we're least aware of what our minds do best", he wrote, and added "we're more aware of simple processes that don't work well than of complex ones that work flawlessly".

🔗 Physics 🔗 Philosophy 🔗 Philosophy/Metaphysics

The Boltzmann brain argument suggests that it is more likely for a single brain to spontaneously and briefly form in a void (complete with a false memory of having existed in our universe) than it is for our universe to have come about in the way modern science thinks it actually did. It was first proposed as a reductio ad absurdum response to Ludwig Boltzmann's early explanation for the low-entropy state of our universe.

In this physics thought experiment, a Boltzmann brain is a fully formed brain, complete with memories of a full human life in our universe, that arises due to extremely rare random fluctuations out of a state of thermodynamic equilibrium. Theoretically over a period of time on the order of hundreds of billions of years, by sheer chance atoms in a void could spontaneously come together in such a way as to assemble a functioning human brain. Like any brain in such circumstances, it would almost immediately stop functioning and begin to deteriorate.

The idea is ironically named after the Austrian physicist Ludwig Boltzmann (1844–1906), who in 1896 published a theory that tried to account for the fact that we find ourselves in a universe that is not as chaotic as the budding field of thermodynamics seemed to predict. He offered several explanations, one of them being that the universe, even one that is fully random (or at thermal equilibrium), would spontaneously fluctuate to a more ordered (or low-entropy) state. One criticism of this "Boltzmann universe" hypothesis is that the most common thermal fluctuations are as close to equilibrium overall as possible; thus, by any reasonable criterion, actual humans in the actual universe would be vastly less likely than "Boltzmann brains" existing alone in an empty universe.

Boltzmann brains gained new relevance around 2002, when some cosmologists started to become concerned that, in many existing theories about the Universe, human brains in the current Universe appear to be vastly outnumbered by Boltzmann brains in the future Universe who, by chance, have exactly the same perceptions that we do; this leads to the conclusion that statistically we ourselves are likely to be Boltzmann brains. Such a reductio ad absurdum argument is sometimes used to argue against certain theories of the Universe. When applied to more recent theories about the multiverse, Boltzmann brain arguments are part of the unsolved measure problem of cosmology. Boltzmann brains remain a thought experiment; physicists do not believe that we are actually Boltzmann brains, but rather use the thought experiment as a tool for evaluating competing scientific theories.

🔗 Mathematics

The potato paradox is a mathematical calculation that has a counter-intuitive result. The Universal Book of Mathematics states the problem as follows:

Fred brings home 100 kg of potatoes, which (being purely mathematical potatoes) consist of 99% water. He then leaves them outside overnight so that they consist of 98% water. What is their new weight? The surprising answer is 50 kg.

In Quine's classification of paradoxes, the potato paradox is a veridical paradox.

🔗 Environment 🔗 Economics

In economics, the Jevons paradox (; sometimes Jevons effect) occurs when technological progress or government policy increases the efficiency with which a resource is used (reducing the amount necessary for any one use), but the rate of consumption of that resource rises due to increasing demand. The Jevons paradox is perhaps the most widely known paradox in environmental economics. However, governments and environmentalists generally assume that efficiency gains will lower resource consumption, ignoring the possibility of the paradox arising.

In 1865, the English economist William Stanley Jevons observed that technological improvements that increased the efficiency of coal-use led to the increased consumption of coal in a wide range of industries. He argued that, contrary to common intuition, technological progress could not be relied upon to reduce fuel consumption.

The issue has been re-examined by modern economists studying consumption rebound effects from improved energy efficiency. In addition to reducing the amount needed for a given use, improved efficiency also lowers the relative cost of using a resource, which increases the quantity demanded. This counteracts (to some extent) the reduction in use from improved efficiency. Additionally, improved efficiency increases real incomes and accelerates economic growth, further increasing the demand for resources. The Jevons paradox occurs when the effect from increased demand predominates, and improved efficiency increases the speed at which resources are used.

Considerable debate exists about the size of the rebound in energy efficiency and the relevance of the Jevons paradox to energy conservation. Some dismiss the paradox, while others worry that it may be self-defeating to pursue sustainability by increasing energy efficiency. Some environmental economists have proposed that efficiency gains be coupled with conservation policies that keep the cost of use the same (or higher) to avoid the Jevons paradox. Conservation policies that increase cost of use (such as cap and trade or green taxes) can be used to control the rebound effect.

🔗 Military history/Early Muslim military history 🔗 Games

The two envelopes problem, also known as the exchange paradox, is a brain teaser, puzzle, or paradox in logic, probability, and recreational mathematics. It is of special interest in decision theory, and for the Bayesian interpretation of probability theory. Historically, it arose as a variant of the necktie paradox. The problem typically is introduced by formulating a hypothetical challenge of the following type:

It seems obvious that there is no point in switching envelopes as the situation is symmetric. However, because you stand to gain twice as much money if you switch while risking only a loss of half of what you currently have, it is possible to argue that it is more beneficial to switch. The problem is to show what is wrong with this argument.

🔗 Aviation 🔗 Disaster management 🔗 Aviation/Aviation accident project 🔗 Canada 🔗 Aviation/aircraft project 🔗 Aviation/gliding project 🔗 Canada/History of Canada 🔗 Canada/Manitoba

Air Canada Flight 143 was a Canadian scheduled domestic passenger flight between Montreal and Edmonton that ran out of fuel on July 23, 1983, at an altitude of 41,000 feet (12,000 m), midway through the flight. The crew was able to glide the Boeing 767 aircraft safely to an emergency landing at a former Royal Canadian Air Force base in Gimli, Manitoba, that had been turned into a motor racing track. This unusual aviation incident earned the aircraft the nickname "Gimli Glider".

The subsequent investigation revealed that a combination of company failures, human errors and confusion over unit measures had led to the aircraft being refuelled with insufficient fuel for the planned flight.

🔗 Environment 🔗 Occupational Safety and Health 🔗 Brazil 🔗 Brazil/History of Brazil 🔗 Science Policy

The Goiânia accident [ɡojˈjɐniɐ] was a radioactive contamination accident that occurred on September 13, 1987, in Goiânia, in the Brazilian state of Goiás, after a forgotten radiotherapy source was taken from an abandoned hospital site in the city. It was subsequently handled by many people, resulting in four deaths. About 112,000 people were examined for radioactive contamination and 249 of them were found to have been contaminated.

In the cleanup operation, topsoil had to be removed from several sites, and several hundred houses were demolished. All the objects from within those houses, including personal possessions, were seized and incinerated. Time magazine has identified the accident as one of the world's "worst nuclear disasters" and the International Atomic Energy Agency called it "one of the world's worst radiological incidents".