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Hail

Hail is a form of solid precipitation. It is distinct from ice pellets (American English "sleet"), though the two are often confused. It consists of balls or irregular lumps of ice, each of which is called a hailstone. Ice pellets generally fall in cold weather, while hail growth is greatly inhibited during low surface temperatures.

Unlike other forms of water ice precipitation, such as graupel (which is made of rime ice), ice pellets (which are smaller and translucent), and snow (which consists of tiny, delicately crystalline flakes or needles), hailstones usually measure between 5 mm and 15 cm in diameter. The METAR reporting code for hail 5 mm or greater is GR, while smaller hailstones and graupel are coded GS.

Hail is possible within most thunderstorms (as it is produced by cumulonimbus), as well as within 2 nmi of the parent storm. Hail formation requires environments of strong, upward motion of air within the parent thunderstorm (similar to tornadoes) and lowered heights of the freezing level. In the mid-latitudes, hail forms near the interiors of continents, while, in the tropics, it tends to be confined to high elevations.

There are methods available to detect hail-producing thunderstorms using weather satellites and weather radar imagery. Hailstones generally fall at higher speeds as they grow in size, though complicating factors such as melting, friction with air, wind, and interaction with rain and other hailstones can slow their descent through Earth's atmosphere. Severe weather warnings are issued for hail when the stones reach a damaging size, as it can cause serious damage to human-made structures, and, most commonly, farmers' crops.

Definition
Any thunderstorm which produces hail that reaches the ground is known as a hailstorm. An ice crystal with a diameter of >5 mm is considered a hailstone. Hailstones can grow to 15 cm and weigh more than 0.5 kg.

Unlike ice pellets, hailstones are often layered and can be irregular and clumped together. Hail is composed of transparent ice or alternating layers of transparent and translucent ice at least 1 mm thick, which are deposited upon the hailstone as it travels through the cloud, suspended aloft by air with strong upward motion until its weight overcomes the updraft and falls to the ground. Although the diameter of hail is varied, in the United States, the average observation of damaging hail is between 1 in and golf-ball-sized 1.75 in.

Stones larger than 2 cm are usually considered large enough to cause damage. The Meteorological Service of Canada issues severe thunderstorm warnings when hail that size or above is expected. The US National Weather Service has a 1 in diameter threshold, effective January 2010, an increase over the previous threshold of 0.75 in hail. Other countries have different thresholds according to local sensitivity to hail; for instance, grape-growing areas could be adversely impacted by smaller hailstones. Hailstones can be very large or very small, depending on how strong the updraft is: weaker hailstorms produce smaller hailstones than stronger hailstorms (such as supercells), as the more powerful updrafts in a stronger storm can keep larger hailstones aloft.

Formation
Hail forms in strong thunderstorm clouds, particularly those with intense updrafts, high liquid-water content, great vertical extent, large water droplets, and where a good portion of the cloud layer is below freezing (0 C). These types of strong updrafts can also indicate the presence of a tornado. The growth rate of hailstones is impacted by factors such as higher elevation, lower freezing zones, and wind shear.

Layer nature of the hailstones
Like other precipitation in cumulonimbus clouds, hail begins as water droplets. As the droplets rise and the temperature goes below freezing, they become supercooled water and will freeze on contact with condensation nuclei. A cross-section through a large hailstone shows an onion-like structure. This means that the hailstone is made of thick and translucent layers, alternating with layers that are thin, white and opaque. Former theory suggested that hailstones were subjected to multiple descents and ascents, falling into a zone of humidity and refreezing as they were uplifted. This up and down motion was thought to be responsible for the successive layers of the hailstone. New research, based on theory as well as field study, has shown this is not necessarily true.

The storm's updraft, with upwardly directed wind speeds as high as 110 mph, blows the forming hailstones up the cloud. As the hailstone ascends, it passes into areas of the cloud where the concentration of humidity and supercooled water droplets varies. The hailstone's growth rate changes depending on the variation in humidity and supercooled water droplets that it encounters. The accretion rate of these water droplets is another factor in the hailstone's growth. When the hailstone moves into an area with a high concentration of water droplets, it captures the latter and acquires a translucent layer. Should the hailstone move into an area where mostly water vapor is available, it acquires a layer of opaque white ice. Furthermore, the hailstone's speed depends on its position in the cloud's updraft and its mass. This determines the varying thicknesses of the layers of the hailstone. The accretion rate of supercooled water droplets onto the hailstone depends on the relative velocities between these water droplets and the hailstone itself. This means that generally the larger hailstones will form some distance from the stronger updraft, where they can pass more time growing. As the hailstone grows, it releases latent heat, which keeps its exterior in a liquid phase. Because it undergoes "wet growth", the outer layer is sticky (i.e. more adhesive), so a single hailstone may grow by collision with other smaller hailstones, forming a larger entity with an irregular shape.

Hail can also undergo "dry growth", in which the latent heat release through freezing is not enough to keep the outer layer in a liquid state. Hail forming in this manner appears opaque due to small air bubbles that become trapped in the stone during rapid freezing. These bubbles coalesce and escape during the "wet growth" mode, and the hailstone is more clear. The mode of growth for a hailstone can change throughout its development, and this can result in distinct layers in a hailstone's cross-section.

The hailstone will keep rising in the thunderstorm until its mass can no longer be supported by the updraft. This may take at least 30 minutes, based on the force of the updrafts in the hail-producing thunderstorm, whose top is usually greater than 10 km high. It then falls toward the ground while continuing to grow, based on the same processes, until it leaves the cloud. It will later begin to melt as it passes into air above freezing temperature. Thus, a unique trajectory in the thunderstorm is sufficient to explain the layer-like structure of the hailstone. The only case in which multiple trajectories can be discussed is in a multicellular thunderstorm, where the hailstone may be ejected from the top of the "mother" cell and captured in the updraft of a more intense "daughter" cell. This, however, is an exceptional case.

Factors favoring hail
Hail is most common within continental interiors of the mid-latitudes, as hail formation is considerably more likely when the freezing level is below the altitude of 11000 ft. Movement of dry air into strong thunderstorms over continents can increase the frequency of hail by promoting evaporational cooling, which lowers the freezing level of thunderstorm clouds, giving hail a larger volume to grow in. Accordingly, hail is less common in the tropics despite a much higher frequency of thunderstorms than in the mid-latitudes because the atmosphere over the tropics tends to be warmer over a much greater altitude. Hail in the tropics occurs mainly at higher elevations.

Hail growth becomes vanishingly small when air temperatures fall below -30 C, as supercooled water droplets become rare at these temperatures. Around thunderstorms, hail is most likely within the cloud at elevations above 20000 ft. Between 10000 ft and 20000 ft, 60% of hail is still within the thunderstorm, though 40% now lies within the clear air under the anvil. Below 10000 ft, hail is equally distributed in and around a thunderstorm to a distance of 2 nmi.

Climatology
Hail occurs most frequently within continental interiors at mid-latitudes and is less common in the tropics, despite a much higher frequency of thunderstorms than in the mid-latitudes. Hail is also much more common along mountain ranges because mountains force horizontal winds upwards (known as orographic lifting), thereby intensifying the updrafts within thunderstorms and making hail more likely. The higher elevations also result in there being less time available for hail to melt before reaching the ground. One of the more common regions for large hail is across mountainous northern India, which reported one of the highest hail-related death tolls on record in 1888. China also experiences significant hailstorms. Central Europe and southern Australia also experience a lot of hailstorms. Regions where hailstorms frequently occur are southern and western Germany, northern and eastern France, southern and eastern Benelux, and northern Italy. In southeastern Europe, Croatia and Serbia experience frequent occurrences of hail. Some mediterranean countries register the maximum frequency of hail during the Fall season.

In North America, hail is most common in the area where Colorado, Nebraska, and Wyoming meet, known as "Hail Alley". Hail in this region occurs between the months of March and October during the afternoon and evening hours, with the bulk of the occurrences from May through September. Cheyenne, Wyoming is North America's most hail-prone city with an average of nine to ten hailstorms per season. To the north of this area and also just downwind of the Rocky Mountains is the Hailstorm Alley region of Alberta, which also experiences an increased incidence of significant hail events.

Hailstorms are also common in several regions of South America, particularly in the temperate latitudes. The central region of Argentina, extending from the Mendoza region eastward towards Córdoba, experiences some of the most frequent hailstorms in the world, with 10-30 storms per year on average. The Patagonia region of southern Argentina also sees frequent hailstorms, though this may be partially due to graupel (small hail) being counted as hail in this colder region. The triple border region between the Brazilian states of Paraná, Santa Catarina, and Argentina, in southern Brazil is another area known for damaging hailstorms. Hailstorms are also common in parts of Paraguay, Uruguay, and Bolivia that border the high-frequency hail regions of northern Argentina. The high frequency of hailstorms in these areas of South America is attributed to the region's orographic forcing of convection, combined with moisture transport from the Amazon and instability created by temperature contrasts between the surface and upper atmosphere. In Colombia, the cities of Bogotá and Medellín also see frequent hailstorms due to their high elevation. Southern Chile also sees persistent hail from mid april through october.

Short-term detection
Weather radar is a very useful tool to detect the presence of hail-producing thunderstorms. However, radar data has to be complemented by a knowledge of current atmospheric conditions which can allow one to determine if the current atmosphere is conducive to hail development.

Modern radar scans many angles around the site. Reflectivity values at multiple angles above ground level in a storm are proportional to the precipitation rate at those levels. Summing reflectivities in the Vertically Integrated Liquid or VIL, gives the liquid water content in the cloud. Research shows that hail development in the upper levels of the storm is related to the evolution of VIL. VIL divided by the vertical extent of the storm, called VIL density, has a relationship with hail size, although this varies with atmospheric conditions and therefore is not highly accurate. Traditionally, hail size and probability can be estimated from radar data by computer using algorithms based on this research. Some algorithms include the height of the freezing level to estimate the melting of the hailstone and what would be left on the ground.

Certain patterns of reflectivity are important clues for the meteorologist as well. The three body scatter spike is an example. This is the result of energy from the radar hitting hail and being deflected to the ground, where they deflect back to the hail and then to the radar. The energy took more time to go from the hail to the ground and back, as opposed to the energy that went directly from the hail to the radar, and the echo is further away from the radar than the actual location of the hail on the same radial path, forming a cone of weaker reflectivities.

More recently, the polarization properties of weather radar returns have been analyzed to differentiate between hail and heavy rain. The use of differential reflectivity ($$Z_{dr}$$), in combination with horizontal reflectivity ($$Z_{h}$$) has led to a variety of hail classification algorithms. Visible satellite imagery is beginning to be used to detect hail, but false alarm rates remain high using this method.

Size and terminal velocity

The size of hailstones is best determined by measuring their diameter with a ruler. In the absence of a ruler, hailstone size is often visually estimated by comparing its size to that of known objects, such as coins. Using the objects such as hen's eggs, peas, and marbles for comparing hailstone sizes is imprecise, due to their varied dimensions. The UK organisation, TORRO, also scales for both hailstones and hailstorms.

When observed at an airport, METAR code is used within a surface weather observation which relates to the size of the hailstone. Within METAR code, GR is used to indicate larger hail, of a diameter of at least 0.25 in. GR is derived from the French word grêle. Smaller-sized hail, as well as snow pellets, use the coding of GS, which is short for the French word grésil.

Terminal velocity of hail, or the speed at which hail is falling when it strikes the ground, varies. It is estimated that a hailstone of 1 cm in diameter falls at a rate of 9 m/s, while stones the size of 8 cm in diameter fall at a rate of 48 m/s. Hailstone velocity is dependent on the size of the stone, its drag coefficient, the motion of wind it is falling through, collisions with raindrops or other hailstones, and melting as the stones fall through a warmer atmosphere. As hailstones are not perfect spheres, it is difficult to accurately calculate their drag coefficient - and, thus, their speed.

Size comparisons to objects
In the United States, the National Weather Service reports hail size as a comparison to everyday objects. Hailstones larger than 1 inch in diameter are denoted as "severe."

Hail records
Megacryometeors, large rocks of ice that are not associated with thunderstorms, are not officially recognized by the World Meteorological Organization as "hail", which are aggregations of ice associated with thunderstorms, and therefore records of extreme characteristics of megacryometeors are not given as hail records.

 * Heaviest: 1.02 kg; Gopalganj District, Bangladesh, 14 April 1986.
 * Largest diameter officially measured: 7.9 in diameter, 18.622 in circumference; Vivian, South Dakota, 23 July 2010.
 * Largest circumference officially measured: 18.74 in circumference, 7.0 in diameter; Aurora, Nebraska, 22 June 2003.
 * Greatest average hail precipitation: Kericho, Kenya experiences hailstorms, on average, 50 days annually. Kericho is close to the equator and the elevation of 7,200 ft contributes to it being a hot spot for hail. Kericho reached the world record for 132 days of hail in one year.

Hazards
Hail can cause serious damage, notably to automobiles, aircraft, skylights, glass-roofed structures, livestock, and most commonly, crops. Hail damage to roofs often goes unnoticed until further structural damage is seen, such as leaks or cracks. It is hardest to recognize hail damage on shingled roofs and flat roofs, but all roofs have their own hail damage detection problems. Metal roofs are fairly resistant to hail damage, but may accumulate cosmetic damage in the form of dents and damaged coatings.

Hail is one of the most significant thunderstorm hazards to aircraft. When hailstones exceed 0.5 in in diameter, planes can be seriously damaged within seconds. The hailstones accumulating on the ground can also be hazardous to landing aircraft. Hail is a common nuisance to drivers of automobiles, severely denting the vehicle and cracking or even shattering windshields and windows unless parked in a garage or covered with a shielding material. Wheat, corn, soybeans, and tobacco are the most sensitive crops to hail damage. Hail is one of Canada's most expensive hazards.

Rarely, massive hailstones have been known to cause concussions or fatal head trauma. Hailstorms have been the cause of costly and deadly events throughout history. One of the earliest known incidents occurred around the 9th century in Roopkund, Uttarakhand, India, where 200 to 600 nomads seem to have died of injuries from hail the size of cricket balls.

Accumulations

Narrow zones where hail accumulates on the ground in association with thunderstorm activity are known as hail streaks or hail swaths, which can be detectable by satellite after the storms pass by. Hailstorms normally last from a few minutes up to 15 minutes in duration. Accumulating hail storms can blanket the ground with over 2 in of hail, cause thousands to lose power, and bring down many trees. Flash flooding and mudslides within areas of steep terrain can be a concern with accumulating hail.

Depths of up to 18 in have been reported. A landscape covered in accumulated hail generally resembles one covered in accumulated snow and any significant accumulation of hail has the same restrictive effects as snow accumulation, albeit over a smaller area, on transport and infrastructure. Accumulated hail can also cause flooding by blocking drains, and hail can be carried in the floodwater, turning into a snow-like slush which is deposited at lower elevations.

On somewhat rare occasions, a thunderstorm can become stationary or nearly so while prolifically producing hail and significant depths of accumulation do occur; this tends to happen in mountainous areas, such as the July 29, 2010 case of a foot of hail accumulation in Boulder County, Colorado. On June 5, 2015, hail up to four feet deep fell on one city block in Denver, Colorado. The hailstones, described as between the size of bumble bees and ping pong balls, were accompanied by rain and high winds. The hail fell in only the one area, leaving the surrounding area untouched. It fell for one and a half hours between 10:00 pm and 11:30 pm. A meteorologist for the National Weather Service in Boulder said, "It's a very interesting phenomenon. We saw the storm stall. It produced copious amounts of hail in one small area. It's a meteorological thing." Tractors used to clear the area filled more than 30 dump truck loads of hail.

Research focused on four individual days that accumulated more than 5.9 in of hail in 30 minutes on the Colorado front range has shown that these events share similar patterns in observed synoptic weather, radar, and lightning characteristics, suggesting the possibility of predicting these events prior to their occurrence. A fundamental problem in continuing research in this area is that, unlike hail diameter, hail depth is not commonly reported. The lack of data leaves researchers and forecasters in the dark when trying to verify operational methods. A cooperative effort between the University of Colorado and the National Weather Service is in progress. The joint project's goal is to enlist the help of the general public to develop a database of hail accumulation depths.

Suppression and prevention
During the Middle Ages, people in Europe used to ring church bells and fire cannons to try to prevent hail, and the subsequent damage to crops. Updated versions of this approach are available as modern hail cannons. Cloud seeding after World War II was done to eliminate the hail threat, particularly across the Soviet Union, where it was claimed a 70–98% reduction in crop damage from hail storms was achieved by deploying silver iodide in clouds using rockets and artillery shells. But these effects have not been replicated in randomized trials conducted in the West. Hail suppression programs have been undertaken by 15 countries between 1965 and 2005.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Hail


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Hypnotherapy

Hypnotherapy, also known as hypnotic medicine, is the use of hypnosis in psychotherapy. The efficacy of hypnotherapy is not well supported by scientific evidence, and, due to the lack of evidence indicating any level of efficacy, it is regarded as a type of alternative medicine by reputable medical organisations such as the National Health Service.

Definition
The United States Department of Labor's Dictionary of Occupational Titles (DOT) describes the job of the hypnotherapist:"'Induces hypnotic state in client to increase motivation or alter behavior patterns: Consults with client to determine nature of problem. Prepares client to enter hypnotic state by explaining how hypnosis works and what client will experience. Tests subject to determine degree of physical and emotional suggestibility. Induces hypnotic state in client, using individualized methods and techniques of hypnosis based on interpretation of test results and analysis of client's problem. May train client in self-hypnosis conditioning.'"

Traditional
The form of hypnotherapy practiced by most Victorian hypnotists, including James Braid and Hippolyte Bernheim, mainly employed direct suggestion of symptom removal, with some use of therapeutic relaxation and occasionally aversion to alcohol, drugs, etc.

Ericksonian
In the 1950s, Milton H. Erickson developed a radically different approach to hypnotism, which has subsequently become known as "Ericksonian hypnotherapy" or "Neo-Ericksonian hypnotherapy." Based on his belief that dysfunctional behaviors were defined by social tension, Erickson coopted the subject's behavior to establish rapport, a strategy he termed "utilization." Once rapport was established, he made use of an informal conversational approach to direct awareness. His methods included complex language patterns and client-specific therapeutic strategies (reflecting the nature of utilization). He claimed to have developed ways to suggest behavior changes during apparently ordinary conversation.

This divergence from tradition led some, including Andre Weitzenhoffer, to dispute whether Erickson was right to label his approach "hypnosis" at all. Erickson's foundational paper, however, considers hypnosis as a mental state in which specific types of "work" may be done, rather than a technique of induction.

The founders of neuro-linguistic programming (NLP), a method somewhat similar in some regards to some versions of hypnotherapy, claimed that they had modelled the work of Erickson extensively and assimilated it into their approach. Weitzenhoffer disputed whether NLP bears any genuine resemblance to Erickson's work.

Solution-focused
In the 2000s, hypnotherapists began to combine aspects of solution-focused brief therapy (SFBT) with Ericksonian hypnotherapy to produce therapy that was goal-focused (what the client wanted to achieve) rather than the more traditional problem-focused approach (spending time discussing the issues that brought the client to seek help). A solution-focused hypnotherapy session may include techniques from NLP.

Cognitive/behavioral
Cognitive behavioral hypnotherapy (CBH) is an integrated psychological therapy employing clinical hypnosis and cognitive behavioral therapy (CBT). The use of CBT in conjunction with hypnotherapy may result in greater treatment effectiveness. A meta-analysis of eight different researches revealed "a 70% greater improvement" for patients undergoing an integrated treatment to those using CBT only.

In 1974, Theodore X. Barber and his colleagues published a review of the research which argued, following the earlier social psychology of Theodore R. Sarbin, that hypnotism was better understood not as a "special state" but as the result of normal psychological variables, such as active imagination, expectation, appropriate attitudes, and motivation. Barber introduced the term "cognitive-behavioral" to describe the nonstate theory of hypnotism, and discussed its application to behavior therapy.

The growing application of cognitive and behavioral psychological theories and concepts to the explanation of hypnosis paved the way for a closer integration of hypnotherapy with various cognitive and behavioral therapies.

Many cognitive and behavioral therapies were themselves originally influenced by older hypnotherapy techniques, e.g., the systematic desensitisation of Joseph Wolpe, the cardinal technique of early behavior therapy, was originally called "hypnotic desensitisation" and derived from the Medical Hypnosis (1948) of Lewis Wolberg.

Curative
Peter Marshall, author of A Handbook of Hypnotherapy, devised the Trance Theory of Mental Illness, which asserts that people suffering from depression, or certain other kinds of neuroses, are already living in a trance. He asserts that this means the hypnotherapist does not need to induce trance, but instead to make them understand this and lead them out of it.

Mindful
Mindful hypnotherapy is therapy that incorporates mindfulness and hypnotherapy. A pilot study was made at Baylor University, Texas, and published in the International Journal of Clinical and Experimental Hypnosis. Gary Elkins, director of the Mind-Body Medicine Research Laboratory at Baylor University called it "a valuable option for treating anxiety and stress reduction” and "an innovative mind-body therapy". The study showed a decrease in stress and an increase in mindfulness.

Relationship to scientific medicine
Hypnotherapy practitioners occasionally attract the attention of mainstream medicine. Attempts to instill academic rigor have been frustrated by the complexity of client suggestibility, which has social and cultural aspects, including the reputation of the practitioner. Results achieved in one time and center of study have not been reliably transmitted to future generations.

In the 1700s Anton Mesmer offered pseudoscientific justification for his practices, but his rationalizations were debunked by a commission that included Benjamin Franklin.

Menopause
There is evidence supporting the use of hypnotherapy in the treatment of menopause related symptoms, including hot flashes. The North American Menopause Society recommends hypnotherapy for the nonhormonal management of menopause-associated vasomotor symptoms, giving it the highest level of evidence.

Irritable bowel syndrome
The use of hypnotherapy in treating the symptoms of irritable bowel syndrome is supported by research, including randomized controlled trials. Gut-directed hypnotherapy is recommended in the treatment of irritable bowel syndrome by the American College of Gastroenterology clinical guideline for the management of IBS.

Childbirth
Hypnotherapy is often applied in the birthing process and the post-natal period,  but there is insufficient evidence to determine if it alleviates pain during childbirth and no evidence that it is effective against post-natal depression.

Bulimia
Literature shows that a wide variety of hypnotic interventions have been investigated for the treatment of bulimia nervosa, with inconclusive effect. Similar studies have shown that groups suffering from bulimia nervosa, undergoing hypnotherapy, were more exceptional to no treatment, placebos, or other alternative treatments.

Anxiety
Hypnotherapy is shown to be comparable in effectiveness to other forms of therapy, such as cognitive-behavioral therapy, that utilize relaxation techniques and imagery. It has also shown to be successful when used to reduce anxiety in those with dental anxiety and phobias.

PTSD
Post Traumatic Stress Disorder (PTSD) and its symptoms have been shown to improve due to implementation of hypnotherapy, in both long and short term. As research continues, hypnotherapy is being more openly considered as an effective intervention for those with PTSD.

Depression
Hypnotherapy has been shown to be effective when used to treat long term depressive symptoms. It has been shown to be comparable to the efficacy of cognitive-behavioral therapy, and when used in tandem, efficacy seems to increase.

Other uses
Historically hypnotism was used therapeutically by some psychiatrists in the Victorian era, to treat the condition then known as hysteria.

Modern hypnotherapy has been used to treat certain habit disorders and control irrational fears, and addiction.

Efficacy

 * A 2003 meta-analysis on the efficacy of hypnotherapy concluded that "the efficacy of hypnosis is not verified for a considerable part of the spectrum of psychotherapeutic practice."
 * In 2007, a meta-analysis from the Cochrane Collaboration found that the therapeutic effect of hypnotherapy was "superior to that of a waiting list control or usual medical management, for abdominal pain and composite primary IBS symptoms, in the short term in patients who fail standard medical therapy", with no harmful side-effects. However the authors noted that the quality of data available was inadequate to draw any firm conclusions.
 * Two Cochrane reviews in 2012 concluded that there was insufficient evidence to support its efficacy in managing the pain of childbirth or post-natal depression.
 * A 2014 meta-analysis that focused on hypnotherapy's efficacy on irritable bowel syndrome found that it was beneficial for short term abdominal pain and other gastrointestinal issues.
 * In 2016, a literature review published in La Presse Médicale found that there is not sufficient evidence to "support the efficacy of hypnosis in chronic anxiety disorders".
 * In 2019, a Cochrane review was unable to find evidence of benefit of hypnosis in smoking cessation, and suggested if there is, it is small at best.
 * A 2019 meta-analysis of hypnosis as a treatment for anxiety found that "the average participant receiving hypnosis reduced anxiety more than about 79% of control participants," also noting that "hypnosis was more effective in reducing anxiety when combined with other psychological interventions than when used as a stand-alone treatment."
 * In a 2022 meta-analysis on hypnotherapy's efficacy on dental anxiety, it was found that "hypnosis can also be regarded as powerful and successful method for anxiety reduction," but also stated that further research is required.

United States
The laws regarding hypnosis and hypnotherapy vary by state and municipality. Some states, like Colorado, Connecticut and Washington, have mandatory licensing and registration requirements, while many other states have no specific regulations governing the practice of hypnotherapy.

UK National Occupational Standards
In 2002, the Department for Education and Skills developed National Occupational Standards for hypnotherapy linked to National Vocational Qualifications based on the then National Qualifications Framework under the Qualifications and Curriculum Authority. NCFE, a national awarding body, issues level four national vocational qualification diploma in hypnotherapy. Currently AIM Awards offers a Level 3 Certificate in Hypnotherapy and Counselling Skills at level 3 of the Regulated Qualifications Framework.

UK Confederation of Hypnotherapy Organisations (UKCHO)
The regulation of the hypnotherapy profession in the UK is at present the main focus of UKCHO, a non-profit umbrella body for hypnotherapy organisations. Founded in 1998 to provide a non-political arena to discuss and implement changes to the profession of hypnotherapy, UKCHO currently represents 9 of the UK's professional hypnotherapy organisations and has developed standards of training for hypnotherapists, along with codes of conduct and practice that all UKCHO registered hypnotherapists are governed by. As a step towards the regulation of the profession, UKCHO's website now includes a National Public Register of Hypnotherapists who have been registered by UKCHO's Member Organisations and are therefore subject to UKCHO's professional standards. Further steps to full regulation of the hypnotherapy profession will be taken in consultation with the Prince's Foundation for Integrated Health.

The National Council for Hypnotherapy (NCH)
The National Council for Hypnotherapy is a Professional Association, established in 1973 to create a National Membership Organisation for independent Hypnotherapy Practitioners.

The organisation is not for profit with a Board of 12-15 people composed of Executives and Directors, the latter usually ‘in practice’ Hypnotherapists and trainers of Hypnotherapy. The current Chair, Tracey Grist has been in position since 2016.

The NCH is a VO (Verifying organisation) for the CNHC, which means that NCH members meet the criteria to become Registrants of the CNHC.

The NCH membership meet the national hypnotherapy training standards via the externally verified Hypnotherapy practitioner Diploma (HPD) through the NCFE.

Members agree to follow the CECP; the NCH’s ethical code of practice, all members are expected to be insured to practice, meet supervision requirements and annual CPD expectations.

Australia
Professional hypnotherapy and use of the occupational titles hypnotherapist or clinical hypnotherapist are not government-regulated in Australia.

In 1996, as a result of a three-year research project led by Lindsay B. Yeates, the Australian Hypnotherapists Association (founded in 1949), the oldest hypnotism-oriented professional organization in Australia, instituted a peer-group accreditation system for full-time Australian professional hypnotherapists, the first of its kind in the world, which "accredit[ed] specific individuals on the basis of their actual demonstrated knowledge and clinical performance; instead of approving particular 'courses' or approving particular 'teaching institutions'" (Yeates, 1996, p.iv; 1999, p.xiv). The system was further revised in 1999.

Australian hypnotism/hypnotherapy organizations (including the Australian Hypnotherapists Association) are seeking government regulation similar to other mental health professions. However, currently hypnotherapy is not subject to government regulation through the Australian Health Practitioner Regulation Agency (AHPRA).

title: Hypnotherapy


text:
Talk:Hypnotherapy

Article needs a thorough review
I got behind reviewing this article. As I'm catching up, I'm noticing edits, often from WP:SPA accounts, that may have WP:PROMO, WP:OR, WP:MEDRS, or WP:FRINGE problems:
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 * did some cleanup, but I'm concerned this new editor may have removed properly referenced information
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I'm noting these here as it's going to take time to unravel it all. --Hipal (talk) 21:06, 21 April 2022 (UTC)

 * Hey! Go ahead and restore stuff if as far as you can tell it is properly referenced. You've got the revision logs, so it's all laid out!
 * I'll caution that on some of the articles where I removed content, the sources seemed to fail WP criteria. (ex, I seem to remember some citations pointing at academic-sounding organizations that were actually just two unaccredited people with a web page) Nyeogmi (talk) 23:46, 21 April 2022 (UTC)
 * Thanks. Yes, there's a lot of poorly sourced information being added that reviewers are catching, especially WP:MEDRS and WP:PROMO problems. I made the note because I've not found the time for a thorough review after noticing some of these problems months ago. --Hipal (talk) 16:52, 22 April 2022 (UTC)

Wiki Education assignment: Psychology Capstone
— Assignment last updated by Hkhan11 (talk) 00:19, 2 October 2022 (UTC)

Uses
There is some question as to whether the "uses" section is appropriately demarcating how hypnotherapy is actually used. Most hypnotherapy is used in the context of alternative medicine and the precise rationale is not well-defined in terms of condition or symptom. Thus, this section is entirely misleading. The best reviews we have on the subject is that people seek out hypnotherapy for such a wide range of reasons that to single them out as we do on this page is to do a disservice to the reader in actually describing how such activities are actually practiced. I don't even know how to begin to address this, but a complete overhaul seems like it is probably a good idea. Note also that this issue has been discussed on WP:FTN. jps (talk) 16:24, 4 December 2022 (UTC)

Wiki Education assignment: ANTH 193 - Behavioral Science in Practice
— Assignment last updated by Dkhora (talk) 19:37, 8 December 2023 (UTC)

Lead in
The lead for this article is ridiculously negative, given that hypnotherapy is widely accepted for certain conditions such as IBS. This clearly needs to be rephrased to something with a more neutral point of view to avoid misleading readers Publius Obsequium (talk) 00:38, 21 June 2024 (UTC)
 * The lead is based on the article, and the not well supported and lack of evidence indicating any level of efficacy are based especially on the Efficacy section. That section in turn is based on the best possible sources, Cochrane meta-analyses.
 * That beats "widely accepted" by a very long margin. --Hob Gadling (talk) 06:55, 21 June 2024 (UTC)

title: Talk:Hypnotherapy


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Hangman (game)

Hangman is a guessing game for two or more players. One player thinks of a word, phrase, or sentence and the other(s) tries to guess it by suggesting letters or numbers within a certain number of guesses. Originally a paper-and-pencil game, there are now electronic versions.

History
Though the origins of the game are unknown, a variant is mentioned in a book of children's games assembled by Alice Gomme in 1894 called Birds, Beasts, and Fishes. This version lacks the image of a hanged man, instead relying on keeping score as to the number of attempts it took each player to fill in the blanks.

A version which incorporated hanging imagery was described in a 1902 article in The Philadelphia Inquirer, which stated that it was popular at "White Cap" parties hosted by Vigilance Committees where guests would wear "white peaked caps with masks".

Overview
The word to guess is represented by a row of dashes representing each letter or number of the word. Rules may permit or forbid proper nouns, such as names, places, brands, or slang. If the guessing player suggests a letter which occurs in the word, the other player writes it in all its correct positions. If the suggested letter does not occur in the word, the other player adds (or alternatively, removes) one element of a hanged stick figure as a tally mark. Generally, the game ends once the word is guessed, or if the stick figure is complete — signifying that all guesses have been used.

The player guessing the word may, at any time, attempt to guess the whole word. If the word is correct, the game is over and the guesser wins. Otherwise, the other player may choose to penalize the guesser by adding an element to the diagram. If the guesser makes enough incorrect guesses to allow the other player to complete the diagram, the guesser loses. However, the guesser can also win by guessing all the letters that appear in the word, thereby completing the word, before the diagram is completed.

Variants
As the name of the game suggests, the diagram is designed to look like a hanging man. This has led to some controversy. In situations where drawing a public execution may not be advisable, alternative methods to keep track of the number of incorrect guesses can be used, such as crossing apples off of a tree.

Some modifications to game play (house rules) to increase the difficulty level are sometimes implemented, such as limiting guesses on high-frequency consonants and vowels. Another alternative is to give the definition of the word; this can be used to facilitate the learning of a foreign language.

How many incorrect guesses are allowed in the game can also be modified. This can be done by adding extra elements to the stick figure, like a face or shoes, or by first drawing elements of the gallows for every mistake before starting to draw the stick figure.

Strategy
The fact that the twelve most commonly occurring letters in the English language are e-t-a-o-i-n-s-h-r-d-l-u (from most to least), along with other letter-frequency lists, are used by the guessing player to increase the odds when it is their turn to guess. On the other hand, the same lists can be used by the puzzle setter to stump their opponent by choosing a word that deliberately avoids common letters (e.g. rhythm or zephyr) or one that contains rare letters (e.g. jazz).

Another common strategy is to guess vowels first, as English only has five vowels (a, e, i, o, and u, while y may sometimes, but rarely, be used as a vowel) and almost every word has at least one.

According to a 2010 study conducted by Jon McLoone for Wolfram Research, the most difficult words to guess include jazz, buzz, hajj, faff, fizz, fuzz and variations of these.

Derivations
The American game show Wheel of Fortune was inspired by hangman. Merv Griffin conceived of the show after recalling long car trips as a child, on which he and his sister played the game.

Brazil also had a show in the 1960s and again from 2012–2013 called 'Let's Play Hangman', hosted by Silvio Santos. Brazil would later get its own version of Wheel of Fortune, running from 1980 to 1993, again from 2003 to 2012 (during which the new Let's Play Hangman aired), and again since 2013 to the present. These shows were also hosted by Santos.

In July 2017, the BBC introduced a game show of its own called Letterbox, which is also based on hangman.

title: Hangman (game)


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Harmonic mean

In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired.

The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. As a simple example, the harmonic mean of 1, 4, and 4 is
 * $$\left(\frac{1^{-1} + 4^{-1} + 4^{-1}}{3}\right)^{-1} = \frac{3}{\frac{1}{1} + \frac{1}{4} + \frac{1}{4}} = \frac{3}{1.5} = 2\,.$$

Definition
The harmonic mean H of the positive real numbers $$x_1, x_2, \ldots, x_n$$ is defined to be

 * $$H(x_1, x_2, \ldots, x_n) = \frac{n}{\displaystyle \frac1{x_1} + \frac1{x_2} + \cdots + \frac1{x_n}} = \frac{n}{\displaystyle \sum_{i=1}^n \frac1{x_i}}.$$

It is the reciprocal of the arithmetic mean of the reciprocals, and vice versa:

 * $$\begin{align}

H(x_1, x_2, \ldots, x_n) &= \frac{1}{\displaystyle A\left(\frac1{x_1}, \frac1{x_2}, \ldots \frac1{x_n}\right)}, \\ A(x_1, x_2, \ldots, x_n) &= \frac{1}{\displaystyle H\left(\frac1{x_1}, \frac1{x_2}, \ldots \frac1{x_n}\right)}, \end{align}$$

where the arithmetic mean is defined as $A(x_1, x_2, \ldots, x_n) = \tfrac1n \sum_{i=1}^n x_i.$

The harmonic mean is a Schur-concave function, and dominated by the minimum of its arguments, in the sense that for any positive set of arguments, $$\min(x_1 \ldots x_n) \le H(x_1 \ldots x_n) \le n \min(x_1 \ldots x_n)$$. Thus, the harmonic mean cannot be made arbitrarily large by changing some values to bigger ones (while having at least one value unchanged).

The harmonic mean is also concave, which is an even stronger property than Schur-concavity. One has to take care to only use positive numbers though, since the mean fails to be concave if negative values are used.

Relationship with other means
The harmonic mean is one of the three Pythagorean means. For all positive data sets containing at least one pair of nonequal values, the harmonic mean is always the least of the three means, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between. (If all values in a nonempty data set are equal, the three means are always equal to one another; e.g., the harmonic, geometric, and arithmetic means of {2, 2, 2} are all 2.)

It is the special case M−1 of the power mean: $$H\left(x_1, x_2, \ldots, x_n\right) = M_{-1}\left(x_1, x_2, \ldots, x_n\right) = \frac{n}{x_1^{-1} + x_2^{-1} + \cdots + x_n^{-1}}$$

Since the harmonic mean of a list of numbers tends strongly toward the least elements of the list, it tends (compared to the arithmetic mean) to mitigate the impact of large outliers and aggravate the impact of small ones.

The arithmetic mean is often mistakenly used in places calling for the harmonic mean. In the speed example below for instance, the arithmetic mean of 40 is incorrect, and too big.

The harmonic mean is related to the other Pythagorean means, as seen in the equation below. This can be seen by interpreting the denominator to be the arithmetic mean of the product of numbers n times but each time omitting the j-th term. That is, for the first term, we multiply all n numbers except the first; for the second, we multiply all n numbers except the second; and so on. The numerator, excluding the n, which goes with the arithmetic mean, is the geometric mean to the power n. Thus the n-th harmonic mean is related to the n-th geometric and arithmetic means. The general formula is $$H\left(x_1, \ldots, x_n\right) = \frac{\left(G\left(x_1, \ldots, x_n\right)\right)^n} {A\left(x_2 x_3 \cdots x_n, x_1 x_3 \cdots x_n, \ldots, x_1 x_2 \cdots x_{n-1}\right)} = \frac{\left(G\left(x_1, \ldots, x_n\right)\right)^n} {A\left(        \frac{1}{x_1} {\prod\limits_{i=1}^n x_i},         \frac{1}{x_2} {\prod\limits_{i=1}^n x_i},         \ldots,         \frac{1}{x_n} {\prod\limits_{i=1}^n x_i}       \right)}. $$

If a set of non-identical numbers is subjected to a mean-preserving spread — that is, two or more elements of the set are "spread apart" from each other while leaving the arithmetic mean unchanged — then the harmonic mean always decreases.

Two numbers

For the special case of just two numbers, $$x_1$$ and $$x_2$$, the harmonic mean can be written
 * $$H = \frac{2x_1 x_2}{x_1 + x_2} \qquad $$   or    $$ \qquad \frac{1}{H} = \frac{(1/x_1) + (1/x_2)}{2}.$$

In this special case, the harmonic mean is related to the arithmetic mean $$A = \frac{x_1 + x_2}{2}$$ and the geometric mean $$G = \sqrt{x_1 x_2},$$ by
 * $$H = \frac{G^2}{A} = G\left(\frac{G}{A}\right).$$

Since $$\tfrac{G}{A} \le 1$$ by the inequality of arithmetic and geometric means, this shows for the n = 2 case that H ≤ G (a property that in fact holds for all n). It also follows that $$G = \sqrt{AH}$$, meaning the two numbers' geometric mean equals the geometric mean of their arithmetic and harmonic means.

Three numbers
For the special case of three numbers, $$x_1$$, $$x_2$$ and $$x_3$$, the harmonic mean can be written
 * $$H = \frac{3 x_1 x_2 x_3}{x_1 x_2 + x_1 x_3 + x_2 x_3}.$$

Three positive numbers H, G, and A are respectively the harmonic, geometric, and arithmetic means of three positive numbers if and only if the following inequality holds

 * $$\frac{A^3}{G^3} + \frac{G^3}{H^3} + 1 \le \frac3{4} \left(1 + \frac{A}{H}\right)^2.$$

Weighted harmonic mean
If a set of weights $$w_1$$, ..., $$w_n$$ is associated to the data set $$x_1$$, ..., $$x_n$$, the weighted harmonic mean is defined by

H = \frac{\sum\limits_{i=1}^n w_i}{\sum\limits_{i=1}^n \frac{w_i}{x_i}} = \left( \frac{\sum\limits_{i=1}^n w_i x_i^{-1}}{\sum\limits_{i=1}^n w_i} \right)^{-1}. $$

The unweighted harmonic mean can be regarded as the special case where all of the weights are equal.

Average speed
In many situations involving rates and ratios, the harmonic mean provides the correct average. For instance, if a vehicle travels a certain distance d outbound at a speed x (e.g. 60 km/h) and returns the same distance at a speed y (e.g. 20 km/h), then its average speed is the harmonic mean of x and y (30 km/h), not the arithmetic mean (40 km/h). The total travel time is the same as if it had traveled the whole distance at that average speed. This can be proven as follows:

Average speed for the entire journey = $Total distance traveled⁄Sum of time for each segment$ = $2d⁄d⁄x + d⁄y$ = $2⁄1⁄x+1⁄y$

However, if the vehicle travels for a certain amount of time at a speed x and then the same amount of time at a speed y, then its average speed is the arithmetic mean of x and y, which in the above example is 40 km/h.

Average speed for the entire journey = $Total distance traveled⁄Sum of time for each segment$ = $xt+yt⁄2t$ = $x+y⁄2$

The same principle applies to more than two segments: given a series of sub-trips at different speeds, if each sub-trip covers the same distance, then the average speed is the harmonic mean of all the sub-trip speeds; and if each sub-trip takes the same amount of time, then the average speed is the arithmetic mean of all the sub-trip speeds. (If neither is the case, then a weighted harmonic mean or weighted arithmetic mean is needed. For the arithmetic mean, the speed of each portion of the trip is weighted by the duration of that portion, while for the harmonic mean, the corresponding weight is the distance. In both cases, the resulting formula reduces to dividing the total distance by the total time.)

However, one may avoid the use of the harmonic mean for the case of "weighting by distance". Pose the problem as finding "slowness" of the trip where "slowness" (in hours per kilometre) is the inverse of speed. When trip slowness is found, invert it so as to find the "true" average trip speed. For each trip segment i, the slowness si = 1/speedi. Then take the weighted arithmetic mean of the si's weighted by their respective distances (optionally with the weights normalized so they sum to 1 by dividing them by trip length). This gives the true average slowness (in time per kilometre). It turns out that this procedure, which can be done with no knowledge of the harmonic mean, amounts to the same mathematical operations as one would use in solving this problem by using the harmonic mean. Thus it illustrates why the harmonic mean works in this case.

Density
Similarly, if one wishes to estimate the density of an alloy given the densities of its constituent elements and their mass fractions (or, equivalently, percentages by mass), then the predicted density of the alloy (exclusive of typically minor volume changes due to atom packing effects) is the weighted harmonic mean of the individual densities, weighted by mass, rather than the weighted arithmetic mean as one might at first expect. To use the weighted arithmetic mean, the densities would have to be weighted by volume. Applying dimensional analysis to the problem while labeling the mass units by element and making sure that only like element-masses cancel makes this clear.

Electricity
If one connects two electrical resistors in parallel, one having resistance x (e.g., 60 Ω) and one having resistance y (e.g., 40 Ω), then the effect is the same as if one had used two resistors with the same resistance, both equal to the harmonic mean of x and y (48 Ω): the equivalent resistance, in either case, is 24 Ω (one-half of the harmonic mean). This same principle applies to capacitors in series or to inductors in parallel.

However, if one connects the resistors in series, then the average resistance is the arithmetic mean of x and y (50 Ω), with total resistance equal to twice this, the sum of x and y (100 Ω). This principle applies to capacitors in parallel or to inductors in series.

As with the previous example, the same principle applies when more than two resistors, capacitors or inductors are connected, provided that all are in parallel or all are in series.

The "conductivity effective mass" of a semiconductor is also defined as the harmonic mean of the effective masses along the three crystallographic directions.

Optics
As for other optic equations, the thin lens equation $1⁄f$ = $1⁄u$ + $1⁄v$ can be rewritten such that the focal length f is one-half of the harmonic mean of the distances of the subject u and object v from the lens.

Two thin lenses of focal length f1 and f2 in series is equivalent to two thin lenses of focal length fhm, their harmonic mean, in series. Expressed as optical power, two thin lenses of optical powers P1 and P2 in series is equivalent to two thin lenses of optical power Pam, their arithmetic mean, in series.

In finance
The weighted harmonic mean is the preferable method for averaging multiples, such as the price–earnings ratio (P/E). If these ratios are averaged using a weighted arithmetic mean, high data points are given greater weights than low data points. The weighted harmonic mean, on the other hand, correctly weights each data point. The simple weighted arithmetic mean when applied to non-price normalized ratios such as the P/E is biased upwards and cannot be numerically justified, since it is based on equalized earnings; just as vehicles speeds cannot be averaged for a roundtrip journey (see above).

For example, consider two firms, one with a market capitalization of $150 billion and earnings of $5 billion (P/E of 30) and one with a market capitalization of $1 billion and earnings of $1 million (P/E of 1000). Consider an index made of the two stocks, with 30% invested in the first and 70% invested in the second. We want to calculate the P/E ratio of this index.

Using the weighted arithmetic mean (incorrect):
 * $$P/E = 0.3 \times 30 + 0.7 \times 1000 = 709$$

Using the weighted harmonic mean (correct):
 * $$P/E = \frac{0.3 + 0.7}{0.3/30 + 0.7/1000} \approx 93.46$$

Thus, the correct P/E of 93.46 of this index can only be found using the weighted harmonic mean, while the weighted arithmetic mean will significantly overestimate it.

In geometry
In any triangle, the radius of the incircle is one-third of the harmonic mean of the altitudes.

For any point P on the minor arc BC of the circumcircle of an equilateral triangle ABC, with distances q and t from B and C respectively, and with the intersection of PA and BC being at a distance y from point P, we have that y is half the harmonic mean of q and t.

In a right triangle with legs a and b and altitude h from the hypotenuse to the right angle, $h²$ is half the harmonic mean of $a²$ and $b²$.

Let t and s (t > s) be the sides of the two inscribed squares in a right triangle with hypotenuse c. Then $s²$ equals half the harmonic mean of $c²$ and $t²$.

Let a trapezoid have vertices A, B, C, and D in sequence and have parallel sides AB and CD. Let E be the intersection of the diagonals, and let F be on side DA and G be on side BC such that FEG is parallel to AB and CD. Then FG is the harmonic mean of AB and DC. (This is provable using similar triangles.)

One application of this trapezoid result is in the crossed ladders problem, where two ladders lie oppositely across an alley, each with feet at the base of one sidewall, with one leaning against a wall at height A and the other leaning against the opposite wall at height B, as shown. The ladders cross at a height of h above the alley floor. Then h is half the harmonic mean of A and B. This result still holds if the walls are slanted but still parallel and the "heights" A, B, and h are measured as distances from the floor along lines parallel to the walls. This can be proved easily using the area formula of a trapezoid and area addition formula.

In an ellipse, the semi-latus rectum (the distance from a focus to the ellipse along a line parallel to the minor axis) is the harmonic mean of the maximum and minimum distances of the ellipse from a focus.

In other sciences
In computer science, specifically information retrieval and machine learning, the harmonic mean of the precision (true positives per predicted positive) and the recall (true positives per real positive) is often used as an aggregated performance score for the evaluation of algorithms and systems: the F-score (or F-measure). This is used in information retrieval because only the positive class is of relevance, while number of negatives, in general, is large and unknown. It is thus a trade-off as to whether the correct positive predictions should be measured in relation to the number of predicted positives or the number of real positives, so it is measured versus a putative number of positives that is an arithmetic mean of the two possible denominators.

A consequence arises from basic algebra in problems where people or systems work together. As an example, if a gas-powered pump can drain a pool in 4 hours and a battery-powered pump can drain the same pool in 6 hours, then it will take both pumps $6·4⁄6 + 4$, which is equal to 2.4 hours, to drain the pool together. This is one-half of the harmonic mean of 6 and 4: $2·6·4⁄6 + 4 = 4.8$. That is, the appropriate average for the two types of pump is the harmonic mean, and with one pair of pumps (two pumps), it takes half this harmonic mean time, while with two pairs of pumps (four pumps) it would take a quarter of this harmonic mean time.

In hydrology, the harmonic mean is similarly used to average hydraulic conductivity values for a flow that is perpendicular to layers (e.g., geologic or soil) - flow parallel to layers uses the arithmetic mean. This apparent difference in averaging is explained by the fact that hydrology uses conductivity, which is the inverse of resistivity.

In sabermetrics, a baseball player's Power–speed number is the harmonic mean of their home run and stolen base totals.

In population genetics, the harmonic mean is used when calculating the effects of fluctuations in the census population size on the effective population size. The harmonic mean takes into account the fact that events such as population bottleneck increase the rate genetic drift and reduce the amount of genetic variation in the population. This is a result of the fact that following a bottleneck very few individuals contribute to the gene pool limiting the genetic variation present in the population for many generations to come.

When considering fuel economy in automobiles two measures are commonly used – miles per gallon (mpg), and litres per 100 km. As the dimensions of these quantities are the inverse of each other (one is distance per volume, the other volume per distance) when taking the mean value of the fuel economy of a range of cars one measure will produce the harmonic mean of the other – i.e., converting the mean value of fuel economy expressed in litres per 100 km to miles per gallon will produce the harmonic mean of the fuel economy expressed in miles per gallon. For calculating the average fuel consumption of a fleet of vehicles from the individual fuel consumptions, the harmonic mean should be used if the fleet uses miles per gallon, whereas the arithmetic mean should be used if the fleet uses litres per 100 km. In the USA the CAFE standards (the federal automobile fuel consumption standards) make use of the harmonic mean.

In chemistry and nuclear physics the average mass per particle of a mixture consisting of different species (e.g., molecules or isotopes) is given by the harmonic mean of the individual species' masses weighted by their respective mass fraction.

Beta distribution

The harmonic mean of a beta distribution with shape parameters α and β is:

 * $$H = \frac{\alpha - 1}{\alpha + \beta - 1} \text{ conditional on } \alpha > 1 \, \, \& \, \, \beta > 0 $$

The harmonic mean with α < 1 is undefined because its defining expression is not bounded in [0, 1].

Letting α = β

 * $$H = \frac{\alpha - 1}{2 \alpha - 1}$$

showing that for α = β the harmonic mean ranges from 0 for α = β = 1, to 1/2 for α = β → ∞.

The following are the limits with one parameter finite (non-zero) and the other parameter approaching these limits:

 * $$\begin{align}

\lim_{\alpha \to 0} H &= \text{ undefined } \\ \lim_{\alpha \to 1} H &= \lim_{\beta \to \infty} H = 0 \\ \lim_{\beta \to 0} H &= \lim_{\alpha \to \infty} H = 1 \end{align}$$

With the geometric mean the harmonic mean may be useful in maximum likelihood estimation in the four parameter case.

A second harmonic mean (H1 − X) also exists for this distribution

 * $$H_{1-X} = \frac{\beta - 1}{\alpha + \beta - 1} \text{ conditional on } \beta > 1 \, \, \& \, \, \alpha > 0$$

This harmonic mean with β < 1 is undefined because its defining expression is not bounded in [ 0, 1 ].

Letting α = β in the above expression

 * $$H_{1-X} = \frac{\beta - 1}{2 \beta - 1} $$

showing that for α = β the harmonic mean ranges from 0, for α = β = 1, to 1/2, for α = β → ∞.

The following are the limits with one parameter finite (non zero) and the other approaching these limits:

 * $$\begin{align}

\lim_{\beta \to 0} H_{1-X} &= \text{ undefined } \\ \lim_{\beta \to 1} H_{1-X} &= \lim_{\alpha \to \infty} H_{1-X} = 0 \\ \lim_{\alpha \to 0} H_{1-X} &= \lim_{\beta \to \infty} H_{1-X} = 1 \end{align}$$

Although both harmonic means are asymmetric, when α = β the two means are equal.

Lognormal distribution
The harmonic mean ( H ) of the lognormal distribution of a random variable X is

 * $$H = \exp \left( \mu - \frac{1}{2} \sigma^2 \right),$$

where μ and σ2 are the parameters of the distribution, i.e. the mean and variance of the distribution of the natural logarithm of X.

The harmonic and arithmetic means of the distribution are related by

 * $$\frac{\mu^*}{H} = 1 + C_v^2 \, ,$$

where Cv and μ* are the coefficient of variation and the mean of the distribution respectively..

The geometric (G), arithmetic and harmonic means of the distribution are related by

 * $$H \mu^* = G^2.$$

Pareto distribution
The harmonic mean of type 1 Pareto distribution is

 * $$H = k \left( 1 + \frac{1}{\alpha} \right)$$

where k is the scale parameter and α is the shape parameter.

Statistics
For a random sample, the harmonic mean is calculated as above. Both the mean and the variance may be infinite (if it includes at least one term of the form 1/0).

Sample distributions of mean and variance
The mean of the sample m is asymptotically distributed normally with variance s2.
 * $$s^2 = \frac{m \left[\operatorname{E}\left(\frac{1}{x} - 1\right)\right]}{m^2 n}$$

The variance of the mean itself is
 * $$\operatorname{Var}\left(\frac{1}{x}\right) = \frac{m \left[\operatorname{E}\left(\frac{1}{x} - 1\right)\right]}{n m^2}$$

where m is the arithmetic mean of the reciprocals, x are the variates, n is the population size and E is the expectation operator.

Delta method
Assuming that the variance is not infinite and that the central limit theorem applies to the sample then using the delta method, the variance is

 * $$\operatorname{Var}(H) = \frac{1}{n}\frac{s^2}{m^4}$$

where H is the harmonic mean, m is the arithmetic mean of the reciprocals

 * $$m = \frac{1}{n} \sum{ \frac{1}{x} }.$$

s2 is the variance of the reciprocals of the data

 * $$s^2 = \operatorname{Var}\left( \frac{1}{x} \right) $$

and n is the number of data points in the sample.

Jackknife method
A jackknife method of estimating the variance is possible if the mean is known. This method is the usual 'delete 1' rather than the 'delete m' version.

This method first requires the computation of the mean of the sample (m)
 * $$m = \frac{n}{ \sum{ \frac{1}{x} } }$$

where x are the sample values.

A series of value wi is then computed where
 * $$w_i = \frac{n - 1}{ \sum_{j \neq i} \frac{1}{x} }.$$

The mean (h) of the wi is then taken:
 * $$h = \frac{1}{n} \sum{w_i}$$

The variance of the mean is
 * $$\frac{n - 1}{n} \sum{(m - w_i)}^2.$$

Significance testing and confidence intervals for the mean can then be estimated with the t test.

Size biased sampling
Assume a random variate has a distribution f( x ). Assume also that the likelihood of a variate being chosen is proportional to its value. This is known as length based or size biased sampling.

Let μ be the mean of the population. Then the probability density function f*( x ) of the size biased population is
 * $$f^*(x) = \frac{x f(x)}{\mu}$$

The expectation of this length biased distribution E*( x ) is
 * $$\operatorname{E}^*(x) = \mu \left[ 1 + \frac{\sigma^2}{\mu^2} \right]$$

where σ2 is the variance.

The expectation of the harmonic mean is the same as the non-length biased version E( x )
 * $$ E^*( x^{ -1 } ) = E( x )^{ -1 } $$

The problem of length biased sampling arises in a number of areas including textile manufacture pedigree analysis and survival analysis

Akman et al. have developed a test for the detection of length based bias in samples.

Shifted variables
If X is a positive random variable and q > 0 then for all ε > 0
 * $$\operatorname{Var} \left[\frac{1}{(X + \epsilon)^q}\right] < \operatorname{Var} \left(\frac{1}{X^q}\right) .$$

Moments
Assuming that X and E(X) are > 0 then
 * $$\operatorname{E}\left[ \frac{1}{X} \right] \ge \frac{1}{ \operatorname{E}(X) }$$

This follows from Jensen's inequality.

Gurland has shown that for a distribution that takes only positive values, for any n > 0
 * $$\operatorname{E} \left(X^{-1}\right) \ge \frac{\operatorname{E} \left(X^{n-1}\right)}{\operatorname{E}\left(X^n\right)} .$$

Under some conditions
 * $$\operatorname{E}(a + X)^{-n} \sim \operatorname{E}\left(a + X^{-n}\right)$$

where ~ means approximately equal to.

Sampling properties
Assuming that the variates (x) are drawn from a lognormal distribution there are several possible estimators for H:

 * $$\begin{align}

H_1 &= \frac{n}{ \sum\left(\frac{1}{x}\right) } \\ H_2 &= \frac{\left( \exp\left[ \frac{1}{n} \sum \log_e(x) \right] \right)^2}{ \frac{1}{n} \sum(x) } \\ H_3 &= \exp \left(m - \frac{1}{2} s^2 \right) \end{align}$$

where
 * $$m = \frac{1}{n} \sum \log_e (x)$$
 * $$s^2 = \frac{1}{n} \sum \left(\log_e (x) - m\right)^2$$

Of these H3 is probably the best estimator for samples of 25 or more.

Bias and variance estimators
A first order approximation to the bias and variance of H1 are

 * $$\begin{align}

\operatorname{bias}\left[ H_1 \right] &= \frac{H C_v}{n} \\ \operatorname{Var}\left[ H_1 \right] &= \frac{H^2 C_v}{n} \end{align}$$

where Cv is the coefficient of variation.

Similarly a first order approximation to the bias and variance of H3 are

 * $$\begin{align}

\frac{H \log_e \left(1 + C_v\right)}{2n} \left[ 1 + \frac{1 + C_v^2}{2} \right] \\ \frac{H \log_e \left(1 + C_v\right)}{n} \left[ 1 + \frac{1 + C_v^2}{4} \right] \end{align}$$

In numerical experiments H3 is generally a superior estimator of the harmonic mean than H1. H2 produces estimates that are largely similar to H1.

title: Harmonic mean


text:
Hellbender

The hellbender (Cryptobranchus alleganiensis), also known as the hellbender salamander, is a species of aquatic giant salamander endemic to the eastern and central United States. It is the largest salamander in North America. A member of the family Cryptobranchidae, the hellbender is the only extant member of the genus Cryptobranchus. Other closely related salamanders in the same family are in the genus Andrias, which contains the Japanese and Chinese giant salamanders. The hellbender, which is much larger than all other salamanders in its geographic range, employs an unusual means of respiration (which involves cutaneous gas exchange through capillaries found in its lateral skin folds), and fills a particular niche—both as a predator and prey—in its ecosystem, which either it or its ancestors have occupied for around 65 million years. The species is listed as Vulnerable on the IUCN Red List of Threatened Species due to the impacts of disease and widespread habitat loss and degradation throughout much of its range.

Etymology
The origin of the name "hellbender" is unclear. The Missouri Department of Conservation says: "The name 'hellbender' probably comes from the animal's odd look. One theory claims the hellbender was named by settlers who thought 'it was a creature from hell where it's bent on returning.' Another rendition says the undulating skin of a hellbender reminded observers of 'horrible tortures of the infernal regions.' In reality, it's a harmless aquatic salamander."

In a study conducted in Indiana, informing the public about the rarity and locality of the hellbender resulted in more positive attitudes toward this species than were previously held. Other vernacular names include snot otter, lasagna lizard, devil dog, mud-devil, mud dog, water dog, grampus, Allegheny alligator, and leverian water newt.

The generic name, Cryptobranchus, is derived from the Ancient Greek (hidden) and  (gill). The subspecific name bishopi is in honor of American herpetologist Sherman C. Bishop.

Description
C. alleganiensis has a flat body and head, with beady dorsal eyes and slimy skin. Like most salamanders, it has short legs with four toes on the front legs and five on its back limbs, and its tail is keeled for propulsion. Its tail is shaped like a rudder, but it is rarely used for swimming; these salamanders use pads on their toes instead to grip rocks and walk up and down streams instead of swimming. The hellbender has working lungs, but gill slits are often retained, although only immature specimens have true gills; the hellbender absorbs oxygen from the water through capillaries of its side frills. The frills run from their neck down to the base of their tail on each side of their body. The frills’ function is to increase the surface area of the hellbender and to help the hellbender breathe. Only occasionally leaving the water, the hellbender makes little use of these lungs and the juveniles lose their external gills after around 18 months or about 125 mm in length. Hellbenders use their lungs for buoyancy more than breathing. It is blotchy brown or red-brown in color, with a paler underbelly. Hellbenders can also be described as having a gray, or yellowish-brown, to even black coloration.

Both males and females grow to an adult length of 24 to 40 cm from snout to vent, with a total length of 30 to 74 cm, making them the fourth-largest aquatic salamander species in the world (after the South China giant salamander, the Chinese giant salamander and the Japanese giant salamander, respectively) and the largest amphibian in North America, although this length is rivaled by the reticulated siren of the southeastern United States (although the siren is much leaner in build). While males and females grow at similar rates, the females tend to live longer and therefore grow larger. An adult weighs 1.5 to 2.5 kg, making them the fifth heaviest living amphibian in the world after their South China, Chinese and Japanese cousins and the goliath frog, while the largest cane toads may also weigh as much as a hellbender. Hellbenders reach sexual maturity at about five years of age, and may live 30 years in captivity.

The hellbender has a few characteristics that make it distinguishable from other native salamanders, including a gigantic, dorsoventrally flattened body with thick folds travelling down the sides, a single open gill slit on each side, and hind feet with five toes each. Easily distinguished from most other endemic salamander species simply by their size, hellbenders average up to 60 cm or about 2 ft in length; the only species requiring further distinction (due to an overlap in distribution and size range) is the common mudpuppy (Necturus maculosus). This demarcation can be made by noting the presence of external gills in the mudpuppy, which are lacking in the hellbender, as well as the presence of four toes on each hind foot of the mudpuppy (in contrast with the hellbender's five). Furthermore, the average size of C. a. alleganiensis has been reported to be 45–60 cm (with some reported as reaching up to 74 cm or 30 in), while N. m. maculosus has a reported average size of 28 to 40 cm in length, which means that hellbender adults will still generally be notably larger than even the biggest mudpuppies.

Taxonomy
The genus Cryptobranchus has historically been considered to contain only one species, C. alleganiensis, with two subspecies, C. a. alleganiensis and C. a. bishopi. A recent decline in population size of the Ozark subspecies C. a. bishopi has led to further research into populations of this subspecies, including genetic analysis to determine the best method for conservation. Crowhurst et al., for instance, found that the "Ozark subspecies" denomination is insufficient for describing genetic (and therefore evolutionary) divergence within the genus Cryptobranchus in the Ozark region. They found three equally divergent genetic units within the genus: C. a. alleganiensis, and two distinct eastern and western populations of C. a. bishopi. These three groups were shown to be isolated, and are considered to most likely be "diverging on different evolutionary paths".

Distribution
Hellbenders are present in a number of Eastern US states, from southern New York to northern Georgia, including parts of Ohio, Pennsylvania, Maryland, West Virginia, Virginia, Kentucky, Illinois, Indiana, Tennessee, North Carolina, South Carolina, Alabama, Mississippi, Arkansas, Missouri, and extending into Oklahoma and Kansas. The subspecies (or species, depending on the source) C. a. bishopi is confined to the Ozarks of northern Arkansas and southern Missouri, while C. a. alleganiensis is found in the rest of these states.

Some hellbender populations—namely a few in Missouri, Pennsylvania, and Tennessee—have historically been noted to be quite abundant, but several man-made threats have converged on the species such that it has seen a serious population decline throughout its range. In Missouri, it is estimated that the populations have declined by 77% since the 1980s. Hellbender populations were listed in 1981 as already extirpated or endangered in Illinois, Indiana, Iowa, and Maryland, decreasing in Arkansas and Kentucky, and generally threatened as a species throughout their range by various human activities and developments.

Ecology
Hellbenders are found in clear, clean water and their presence is an indicator that the water is good quality. The hellbender salamander, considered a "habitat specialist", has adapted to fill a specific niche within a very specific environment, and is labeled as such "because its success is dependent on a constancy of dissolved oxygen, temperature and flow found in swift water areas", which in turn limits it to a narrow spectrum of stream/river choices. As a result of this specialization, hellbenders are generally found in areas with large, irregularly shaped, and intermittent rocks and swiftly moving water, while they tend to avoid wider, slow-moving waters with muddy banks and/or slab rock bottoms. This specialization likely contributed to the decline in their populations, as collectors could easily identify their specific habitats. One collector noted, at one time, "one could find a specimen under almost every suitable rock", but after years of collecting, the population had declined significantly. The same collector noted, he "never found two specimens under the same rock", corroborating the account given by other researchers that hellbenders are generally solitary; they are thought to gather only during the mating season. If rocks are lacking, hellbenders have been known to use holes in stream banks as habitat. On average, their home range is estimated to be 198 square meters as of 2005. The ideal habitat for a hellbender has a large amount of gravel, low pH, cool water temperatures, and low specific conductivity. The large amounts of gravel enable the hellbender to hide, cool water temperatures allow for more efficient cutaneous gas exchange, and low specific conductivity may indicate an undisturbed stream. Hellbender communities may be more concentrated in undisturbed areas.

Both subspecies, C. a. alleganiensis and C. a. bishopi undergo a metamorphosis after around a year and a half of life. At this point, when they are roughly 13.5 cm long, they lose the gills present during their larval stage. Until then, they are easily confused with mudpuppies, and can be differentiated often only through toe number. After this metamorphosis, hellbenders must be able to absorb oxygen through the folds in their skin, which is largely behind the need for fast-moving, oxygenated water. If a hellbender ends up in an area of slow-moving water, not enough of it will pass over its skin in a given time, making it difficult to garner enough oxygen to support necessary respiratory functions. A below-favorable oxygen content can make life equally difficult.

Hellbenders are preyed upon by diverse predators, including various fish and reptiles (including both snakes and turtles). Particularly, largemouth bass is a predator that can consume a hellbender 1-3 years old. Cannibalism of eggs is also considered a common occurrence. One study found that in areas with increased deforestation, the likelihood of filial cannibalism increases.

In another study by Kenison & Wilson (2018), researchers found that young, captive hellbenders showed altered behavior in response to predatory fish nearby. Because of their altered behavior, it was observed and concluded that hellbenders are capable of detecting kairomones, which are chemical cues emitted by predatory species. This suggests that hellbenders can recognize kairomones as stressful stimuli and identify potential predators.

Behavior
Once a hellbender finds a favorable location, it generally does not stray too far from it—except occasionally for breeding and hunting—and will protect it from other hellbenders both in and out of the breeding season. While the range of two hellbenders may overlap, they are noted as rarely being present in the overlapping area when the other salamander is in the area. The species is at least somewhat nocturnal, with peak activity being reported by one source as occurring around "two hours after dark" and again at dawn (although the dawn peak was recorded in the lab and could be misleading as a result). Nocturnal activity has been found to be most prevalent in early summer, perhaps coinciding with highest water depths. Adult hellbenders can live up to 25-30 years.

Diet
C. alleganiensis feeds primarily on crayfish and small fish, but also insects, worms, molluscs, tadpoles and smaller salamanders. A study conducted in 2017 found that larval hellbenders eat mayfly and caddisfly nymphs. One report, written by a commercial collector in the 1940s, noted a trend of more crayfish predation in the summer during times of higher prey activity, whereas fish made up a larger part of the winter diet, when crayfish are less active. There seems to be a specific temperature range in which hellbenders feed, as well: between 45 and 80 F. Cannibalism—mainly on eggs—has been known to occur within hellbender populations. One researcher claimed perhaps density is maintained, and density dependence in turn created, in part by intraspecific predation. When feeding on large prey items relative to themselves, it has been found that they use suction feeding.

Reproduction
The hellbenders' breeding season begins in late August or early- to mid-September and can continue as late as the end of November, depending on region. They exhibit no sexual dimorphism, except during the fall mating season, when males have a bulging ring around their cloacal glands. Unlike most salamanders, the hellbender performs external fertilization. Before mating, each male excavates a brood site, a saucer-shaped depression under a rock or log, with its entrance positioned out of the direct current, usually pointing downstream. The male remains in the brood site awaiting a female. When a female approaches, the male guides or drives her into his burrow and prevents her from leaving until she oviposits.

Female hellbenders lay 150–200 eggs over a two- to three-day period; the eggs are 18-20 mm in diameter, connected by five to ten cords. As the female lays eggs, the male positions himself alongside or slightly above them, spraying the eggs with sperm while swaying his tail and moving his hind limbs, which disperses the sperm uniformly. The male often tempts other females to lay eggs in his nest, and as many as 1,946 eggs have been counted in a single nest. Males also exhibit mate and shelter guarding. Mortality rate is high for hellbender eggs. Studies have found that until the female successfully reproduces, the male hellbender will guard her in his territory until the reproduction is complete. Cannibalism, however, leads to a much lower number of eggs in hellbender nests than would be predicted by egg counts. Adult males are more likely to cannibalize their own offspring in degraded sites with limited food availability.

After oviposition, the male drives the female away from the nest and guards the eggs. Incubating males rock back and forth and undulate their lateral skin folds, which circulates the water, increasing oxygen supply to both eggs and adult. Incubation lasts from 45 to 75 days, depending on region. Males are known to show solitary parental care for the eggs and larvae for at least 7-8 months.

Hatchling hellbenders are 25-33 mm long, have a yolk sac as a source of energy for the first few months of life, and lack functional limbs.

Adaptations
Hellbenders are superbly adapted to the shallow, fast-flowing, rocky streams in which they live. Their flattened shape offers little resistance to the flowing water, allowing them to work their way upstream and also to crawl into narrow spaces under rocks. The wrinkles and folds along their skin are used to expand surface area for cutaneous respiration. Their skin also has a secretion that is important for innate immunity against chytrid activity. Although their eyesight is relatively poor, they have light-sensitive cells all over their bodies. Those on their tails are especially finely tuned and may help them position safely under rocks without their tails poking out to give themselves away. They have a good sense of smell and move upstream in search of food such as dead fish, following the trail of scent molecules. Smell is possibly their most important sense when hunting. They also have a lateral line similar to those of fish, with which they can detect vibrations in the water.

Conservation status
Research throughout the range of the hellbender has shown a dramatic decline in populations in the majority of locations. As of 2022, the species is classified as Vulnerable by the IUCN. Many different anthropogenic sources have contributed to this decline, including the siltation and sedimentation, blocking of dispersal/migration routes, and destruction of riverine habitats created by dams and other development, as well as pollution, disease and overharvesting for commercial and scientific purposes. As many of these detrimental effects have irreversibly damaged hellbender populations, it is important to conserve the remaining populations through protecting habitats and—perhaps in places where the species was once endemic and has been extirpated—by augmenting numbers through reintroduction.

Due to sharp decreases seen in the Ozark subspecies, researchers have been trying to differentiate C. a. alleganiensis and C. a. bishopi into two management units. Indeed, researchers found significant genetic divergence between the two groups, as well as between them and another isolated population of C. a. alleganiensis. This could be reason enough to ensure work is done on both subspecies, as preserving extant genetic diversity is of crucial ecological importance.

The Ozark hellbender has been listed as an endangered species under the Endangered Species Act by the US Fish and Wildlife Service since October 5, 2011. This hellbender subspecies inhabits the White River and Spring River systems in southern Missouri and northern Arkansas, and its population has declined an estimated 75% since the 1980s, with only about 590 individuals remaining in the wild. Degraded water quality, habitat loss resulting from impoundments, ore and gravel mining, sedimentation, and collection for the pet trade are thought to be the main factors resulting in the amphibian's decline. When chytridiomycosis killed 75% of the St. Louis Zoo's captive hellbender population between March 2006 and April 2007, tests began to be conducted on wild populations. The disease has been detected in all Missouri populations of the Ozark hellbender. NatureServe treats C. a. alleganiensis as an Imperiled Subspecies, C. a. bishopi as a Critically Imperiled Subspecies, and the species as a whole as Vulnerable.

The Ozark hellbender was successfully bred in captivity for the first time at the St. Louis Zoo, in a joint project with the Missouri Department of Conservation, hatching on November 15, 2011.

Apart from the Ozark efforts, head-starting programs, in which eggs are collected from the wild and raised in captivity for re-release at a less vulnerable stage, have been initiated in Indiana, New York, and Ohio.

Members of the Pennsylvania State Senate have voted to approve the eastern hellbender as the official state amphibian in an effort to raise awareness about its endangered status. The legislation has been mired in controversy due to a dispute by House members who argue that Wehrle's salamander should be given the honor. The legislation did not pass in 2018, but was reintroduced in 2019. On April 23, 2019, Pennsylvania Governor Tom Wolf signed legislation making the eastern hellbender Pennsylvania's official state amphibian. Youth members of the Chesapeake Bay Foundation's Pennsylvania Student Leadership Council were heavily involved writing and advocating on behalf of this legislation. They hope that the success of the hellbender bill in the Pennsylvania Senate will contribute to clean water efforts and raise awareness for the hellbender's struggling population.

Threats
The hellbender faces an array of challenges that jeopardize its habitat and overall well-being. These challenges include habitat degradation, habitat modifications, pollution, and the looming threat of emerging diseases. The conservation of this species is of paramount importance to ensure its continued existence in the wild.

The hellbender faces a significant threat due to habitat degradation, primarily caused by activities like dam construction, which disrupts water flow and submerges vital riffle habitats. Logging, mining, and road construction contribute to sedimentation, covering essential nesting and shelter sites. Chemical pollutants and misconceptions about the species have led to declines. Over-collection for sale and deliberate eradication efforts have also been detrimental.

The salamander's habitat is further jeopardized by habitat modifications stemming from industrialization and urbanization, including increased stream channelization and pollution from agricultural runoff, mining, and thermal pollution. Diseases, like Batrachochytrium dendrobatidis (Bd) and Ranavirus infections, have been detected in hellbender populations, contributing to population declines.

An emerging disease threat is the salamander chytrid fungus (Batrachochytrium salamandrivorans, or "Bsal"), which has caused severe declines in other salamander species. Although not confirmed in the Americas, Bsal's potential introduction poses a substantial risk. If introduced, the impacts on hellbender populations could be swift and severe, necessitating immediate mitigation measures.

title: Hellbender


text:
Doc Edgerton

Harold Eugene "Doc" Edgerton (April 6, 1903 – January 4, 1990), also known as Papa Flash, was an American scientist and researcher, a professor of electrical engineering at the Massachusetts Institute of Technology. He is largely credited with transforming the stroboscope from an obscure laboratory instrument into a common device. He also was deeply involved with the development of sonar and deep-sea photography, and his equipment was used in collaboration with Jacques Cousteau in searches for shipwrecks and even the Loch Ness Monster.

Early years
Edgerton was born in Fremont, Nebraska, on April 6, 1903, the son of Mary Nettie Coe and Frank Eugene Edgerton, a descendant of Samuel Edgerton, the son of Richard Edgerton, one of the founders of Norwich, Connecticut, and Alice Ripley, a great-granddaughter of Governor William Bradford (1590–1657) of the Plymouth Colony and a passenger on the Mayflower. His father was a lawyer, journalist, author and orator and served as the assistant attorney general of Nebraska from 1911 to 1915. Edgerton grew up in Aurora, Nebraska. He also spent some of his childhood years in Washington, DC, and Lincoln, Nebraska.

Education
In 1925 Edgerton received a bachelor's degree in electrical engineering from the University of Nebraska-Lincoln where he became a member of Acacia fraternity. He earned an SM in electrical engineering from MIT in 1927. Edgerton used stroboscopes to study synchronous motors for his ScD thesis in electrical engineering at MIT, awarded in 1931. He credited Charles Stark Draper with inspiring him to photograph everyday objects using electronic flash; the first was a stream of water from a faucet.

In 1936 Edgerton visited hummingbird expert May Rogers Webster. He was able to illustrate with her help that it was possible to take photographs of the birds beating their wings 60 times a second using an exposure of one hundred thousandth of a second. A picture of her with the birds flying around her appeared in National Geographic.

Career
In 1937 Edgerton began a lifelong association with photographer Gjon Mili, who used stroboscopic equipment, in particular, multiple studio electronic flash units, to produce strikingly beautiful photographs, many of which appeared in Life Magazine. When taking multiflash photographs this strobe light equipment could flash up to 120 times a second. Edgerton was a pioneer in using short duration electronic flash in photographing fast events photography, subsequently using the technique to capture images of balloons at different stages of their bursting, a bullet during its impact with an apple, or using multiflash to track the motion of a devil stick, for example.

He was awarded a bronze medal by the Royal Photographic Society in 1934, the Howard N. Potts Medal from the Franklin Institute in 1941, the Golden Plate Award of the American Academy of Achievement in 1966, the David Richardson Medal by the Optical Society of America in 1968, the Albert A. Michelson Medal from the same Franklin Institute in 1969, and the National Medal of Science in 1973.

Edgerton partnered with Kenneth J. Germeshausen to do consulting for industrial clients. Later Herbert Grier joined them. The company name "Edgerton, Germeshausen, and Grier" was changed to EG&G in 1947. EG&G became a prime contractor for the Atomic Energy Commission and had a major role in photographing and recording nuclear tests for the US through the fifties and sixties. For this role Edgerton and Charles Wykoff and others at EG&G developed and manufactured the Rapatronic camera.

His work was instrumental in the development of side-scan sonar technology, used to scan the sea floor for wrecks. Edgerton worked with undersea explorer Jacques Cousteau, by first providing him with custom-designed underwater photographic equipment featuring electronic flash, and then by developing sonar techniques used to discover the Britannic. Edgerton participated in the discovery of the American Civil War battleship USS Monitor. While working with Cousteau, he acquired the nickname in photographic circles: "Papa Flash". In 1988 Doc Edgerton worked with Paul Kronfield in Greece on a sonar search for the lost city of Helike, believed to be the basis for the legend of Atlantis.

Edgerton co-founded EG&G, Inc., which manufactured advanced electronic equipment including side-scan sonars and sub-bottom profiling equipment. EG&G also invented and manufactured the Krytron, the detonation trigger for the hydrogen bomb, and an EG&G division supervised many of America's nuclear tests.

In addition to having the scientific and engineering acumen to perfect strobe lighting commercially, Edgerton is equally recognized for his visual aesthetic: many of the striking images he created in illuminating phenomena that occurred too fast for the naked eye now adorn art museums worldwide. In 1940, his high speed stroboscopic short film Quicker'n a Wink won an Oscar.

Edgerton was appointed a professor of electrical engineering at the Massachusetts Institute of Technology (MIT) in 1934. At MIT Edgerton created a technology lab nicknamed Strobe Alley, considered by author Pagan Kennedy as a forerunner of the Hackerspace. This lab and its encouragement of tinkering and invention influenced the careers of MIT students such as Martin Klein, who contributed to the development of side scan sonar.

In 1956, Edgerton was elected a Fellow of the American Academy of Arts and Sciences. He became a member of the United States National Academy of Sciences in 1964 and a member of the American Philosophical Society in 1972. He was especially loved by MIT students for his willingness to teach and his kindness: "The trick to education", he said, "is to teach people in such a way that they don't realize they're learning until it's too late". His last undergraduate class, taught during fall semester 1977, was a freshman seminar titled "Bird and Insect Photography". One of the graduate student dormitories at MIT carries his name.

In 1962, Edgerton appeared on I've Got a Secret, where he demonstrated strobe flash photography by shooting a bullet into a playing card and photographing the result.

Edgerton's work was featured in an October 1987 National Geographic Magazine article entitled "Doc Edgerton: the man who made time stand still".

Family
After graduating from the University of Nebraska-Lincoln, Edgerton married Esther May Garrett in 1928. She was born in Aurora, Nebraska, on September 8, 1903, and died on March 9, 2002, in Charleston, South Carolina. She received a bachelor's degree in mathematics, music and education from the University of Nebraska-Lincoln. A skilled pianist and singer, she attended the New England Conservatory of Music and taught in public schools in Aurora, Nebraska and Boston. During their marriage they had three children: Mary Louise (April 21, 1931), William Eugene (8/9/1933), Robert Frank (5/10/1935). His sister, Mary Ellen Edgerton, was the wife of L. Welch Pogue (1899–2003) a pioneering aviation attorney and Chairman of the old Civil Aeronautics Board. The technology writer, journalist, and commentator David Pogue is his great nephew.

Death
Edgerton remained active throughout his later years, and was seen on the MIT campus many times after his official retirement. He died suddenly on January 4, 1990, at the MIT Faculty Club at the age of 86, and is buried in Mount Auburn Cemetery, Cambridge, Massachusetts.

Legacy
On July 3, 1990, in an effort to memorialize Edgerton's accomplishments, several community members in Aurora, Nebraska, decided to construct a "Hands-On" science center. It was designated as a "teaching museum," that would preserve Doc's work and artifacts, as well as feature the "Explorit Zone" where people of all ages could participate in hands-on exhibits and interact with live science demonstrations. After five years of private and community-wide fund-raising, as well as individual investments by Doc's surviving family members, the Edgerton Explorit Center was officially dedicated on September 9, 1995, in Aurora.

At MIT, the Edgerton Center, founded in 1992, is a hands-on laboratory resource for undergraduate and graduate students, and also conducts educational outreach programs for high school students and teachers.

Works

 * Flash! Seeing the Unseen by Ultra High-Speed Photography (1939, with James R. Killian Jr.). Boston: Hale, Cushman & Flint.
 * Electronic Flash, Strobe (1970). New York: McGraw-Hill.
 * Moments of Vision (1979, with Mr. Killian). Cambridge, Massachusetts: MIT. ISBN 0-262-05022-6
 * Sonar Images (1986, with Mr. Killian). Englewood Cliffs, NJ: Prentice-Hall. ISBN 0-13-822651-2
 * Stopping Time, a collection of his photographs, (1987). New York: H.N. Abrams. ISBN 0-8109-1514-6

Photographs
Some of Edgerton's noted photographs are :
 * Milk Drop Coronet (1935)
 * Hummingbirds (1936)
 * Football Kick (1938)
 * Gussie Moran's Tennis Swing (1949)
 * Diver (1955)
 * Cranberry Juice into Milk (1960)
 * Moscow Circus (1963)
 * Bullet Through Banana (1964)
 * .30 Bullet Piercing an Apple (1964)
 * Cutting the Card Quickly (1964)
 * Pigeon Release (1965)
 * Bullet Through Candle Flame (1973) (with Kim Vandiver)

Exhibitions

 * Flashes of Inspiration: The Work of Harold Edgerton, Massachusetts Institute of Technology, Cambridge, Massachusetts, 2009.
 * Seeing the Unseen: The High Speed Photography of Dr. Harold Edgerton, Ikon Gallery, Birmingham, January 1976; then toured to The Photographers' Gallery, London; Hatton Gallery, Newcastle University; Midland Group Gallery, Nottingham; Modern Art Oxford; and Arnolfini, Bristol. Curated by John Myers and Geoffrey Holt.
 * Seeing the Unseen: Photographs and films by Harold E. Edgerton, The Pallasades Shopping Centre, Birmingham. A repeat organised by Ikon Gallery of the previous exhibition.

Collections
Edgerton's work is held in the following public collection:
 * Museum of Modern Art, New York City: 29 prints (as of July 2018)
 * International Photography Hall of Fame, St. Louis, MO
 * Winnipeg Art Gallery | Qaumajuq - Winnipeg, MB: 60 prints

title: Doc Edgerton