## Monday, May 30, 2011

### Mathematics

• Contrary to a widespread perception, the real number 0.999...—where the decimal point is followed by an infinite sequence of nines—is exactly equal to 1.[193] They are two different ways of writing the same real number.[194] A 2009 study by Weller et al.[195] states that "Tall and Schwarzenberger (1978) asked first year university mathematics students whether 0.999... is equal to 1. The majority of the students thought that 0.999... is less than 1." Weller et al. go on to describe their own controlled experiment, performed "during the 2005 fall semester at a major research university in the southern United States. Pre-service elementary and middle school teachers from all five sections of a sophomore-level mathematics content course on number and operation participated in the study." The results are striking: "On the question of whether .999...=1, 72% of the control group and 83% of the experimental group expressed their view that .999... is not equal to 1."
• When a sequence of independent trials of a random process is observed to contain a remarkably long run in which some possible outcome did not occur (for example, when a rouletteball ended up on black 26 times in a row, and not even once on red, as reportedly happened on August 18, 1913 in the Monte Carlo Casino[196]), the underrepresented outcome is often believed then to be more likely for the next trial: it is thought to be "due".[197][198][199] This misconception is known as the gambler's fallacy; in reality, by the definition of statistical independence, that outcome is just as likely or unlikely on the next trial as always—a property sometimes informally described by the phrase, "the system has no memory".
• In a game show, there are three closed doors, one hiding a car, and each of the others concealing a goat. The player wishing to win a car selects a door, which remains closed. The host, knowing where the car is hidden, proceeds to reveal a goat behind one of the remaining doors, and offers the player a chance to switch his choice of door to the remaining door. Should the player switch? The correct answer, contrary to a common misconception, is that he should. Indeed, doing so doubles his chances of winning.[200][201][202][203]

### Physics

• The Coriolis effect does not determine the direction that water rotates in a bathtub drain or a flushing toilet.[204] The Coriolis effect induced by the Earth's daily rotation is too small to affect the direction of water in a typical bathtub drain. The effect becomes significant and noticeable only at large scales, such as in weather systems or oceanic currents. Other forces dominate the dynamics of water in drains.[205] In addition, most toilets in the United States inject water into the bowl at an angle, causing a spin too fast to be significantly affected by the Coriolis effect.[206]
• Gyroscopic forces are not required for a rider to balance a bicycle.[207][208][209][210] Although gyroscopic forces are a factor, the stability of a bicycle is determined primarily by inertia,[210] steering geometry, and the rider's ability to counteract tilting by steering.
• It is not true that air takes the same time to travel above and below an aircraft's wing.[211] This misconception is widespread among textbooks and non-technical reference books, and even appears in pilot training materials. In fact the air moving over the top of an airfoil generating lift is always moving much faster than the equal transit theory would imply,[211] as described in the incorrect and correct explanations of lift force.
• The idea that lightning never strikes the same place twice is one of the oldest and most well-known superstitions about lightning. There is no reason that lightning would not be able to strike the same place twice; if there is a thunderstorm in a given area, then objects and places which are more prominent or conductive (and therefore minimize distance) are more likely to be struck. For instance, lightning strikes the Empire State Building in New York City about 100 times per year.[212][213]
• A penny dropped from the Empire State Building will not kill a person or crack the sidewalk.[214] The terminal velocity of a falling penny is about 30–50 miles per hour, and the penny will not exceed that speed regardless of the height from which it is dropped. At that speed, its energy is not enough to penetrate a human skull or crack concrete, as demonstrated onan episode of Mythbusters.
• It is a common misconception that in large bodies, such as the oceans, that the color of water is blue due to the reflections from the sky on its surface. Reflection of light off the surface of water only contributes significantly when the water surface is extremely still, i.e., mirror-like, and the angle of incidence is high, as water's reflectivity rapidly approaches near total reflection under these circumstances, as governed by the Fresnel equations. While relatively small quantities of water are observed by humans to be colorless, pure water has a slight blue color that becomes a deeper blue as the thickness of the observed sample increases. The blue tint of water is an intrinsic property and is caused by selectiveabsorption and scattering of white light. Impurities dissolved or suspended in water may give water different colored appearances.[215][216]

### Psychology

• Photographic or eidetic memory refers to the ability to remember images with extremely high precision—so high as to mimic a camera. However, it is highly unlikely that photographic memory exists, as to date there is no hard scientific evidence that anyone has ever had it.[217] Many people have claimed to have a photographic memory, but those people have been shown to have good memories as a result of mnemonic devices rather than a natural capacity for detailed memory encoding.[218] There are rare cases of individuals with exceptional memory, but none of them has a memory that mimics a camera.
• Schizophrenia is not the same thing as Dissociative identity disorder, namely split or multiple personalities.[219][220][221][222][223][224][225] Etymologically, the term "schizophrenia" comes from the Greek roots skhizein (σχίζειν, "to split") and phrēn, phren- (φρήν, φρεν-; "mind") and is a juxtaposition proposed by the Swiss psychiatrist Eugen Bleuler, which may have given rise to this common misconception.