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Tuesday, November 1, 2022

Quark–gluon plasma

From Wikipedia, the free encyclopedia
 
QCD phase diagram. Adapted from original made by R.S. Bhalerao.

Quark–gluon plasma (QGP) or quark soup is an interacting localized assembly of quarks and gluons at thermal (local kinetic) and (close to) chemical (abundance) equilibrium. The word plasma signals that free color charges are allowed. In a 1987 summary, Léon van Hove pointed out the equivalence of the three terms: quark gluon plasma, quark matter and a new state of matter. Since the temperature is above the Hagedorn temperature—and thus above the scale of light u,d-quark mass—the pressure exhibits the relativistic Stefan-Boltzmann format governed by temperature to the fourth power () and many practically massless quark and gluon constituents. It can be said that QGP emerges to be the new phase of strongly interacting matter which manifests its physical properties in terms of nearly free dynamics of practically massless gluons and quarks. Both quarks and gluons must be present in conditions near chemical (yield) equilibrium with their colour charge open for a new state of matter to be referred to as QGP.

In the Big Bang theory, quark–gluon plasma filled the entire Universe before matter as we know it was created. Theories predicting the existence of quark–gluon plasma were developed in the late 1970s and early 1980s. Discussions around heavy ion experimentation followed suit and the first experiment proposals were put forward at CERN and BNL in the following years. Quark–gluon plasma was detected for the first time in the laboratory at CERN in the year 2000.

Timeline of the CERN-SPS relativistic heavy ion program before QGP discovery.

General introduction

Quark–gluon plasma is a state of matter in which the elementary particles that make up the hadrons of baryonic matter are freed of their strong attraction for one another under extremely high energy densities. These particles are the quarks and gluons that compose baryonic matter. In normal matter quarks are confined; in the QGP quarks are deconfined. In classical quantum chromodynamics (QCD), quarks are the fermionic components of hadrons (mesons and baryons) while the gluons are considered the bosonic components of such particles. The gluons are the force carriers, or bosons, of the QCD color force, while the quarks by themselves are their fermionic matter counterparts.

Quark–gluon plasma is studied to recreate and understand the high energy density conditions prevailing in the Universe when matter formed from elementary degrees of freedom (quarks, gluons) at about 20μs after the Big Bang. Experimental groups are probing over a ‘large’ distance the (de)confining quantum vacuum structure, the present day relativistic æther, which determines prevailing form of matter and laws of nature. The experiments give insight to the origin of matter and mass: the matter and antimatter is created when the quark–gluon plasma ‘hadronizes’ and the mass of matter originates in the confining vacuum structure.

How the quark–gluon plasma fits into the general scheme of physics

QCD is one part of the modern theory of particle physics called the Standard Model. Other parts of this theory deal with electroweak interactions and neutrinos. The theory of electrodynamics has been tested and found correct to a few parts in a billion. The theory of weak interactions has been tested and found correct to a few parts in a thousand. Perturbative forms of QCD have been tested to a few percent. Perturbative models assume relatively small changes from the ground state, i.e. relatively low temperatures and densities, which simplifies calculations at the cost of generality. In contrast, non-perturbative forms of QCD have barely been tested. The study of the QGP, which has both a high temperature and density, is part of this effort to consolidate the grand theory of particle physics.

The study of the QGP is also a testing ground for finite temperature field theory, a branch of theoretical physics which seeks to understand particle physics under conditions of high temperature. Such studies are important to understand the early evolution of our universe: the first hundred microseconds or so. It is crucial to the physics goals of a new generation of observations of the universe (WMAP and its successors). It is also of relevance to Grand Unification Theories which seek to unify the three fundamental forces of nature (excluding gravity).

Five reasons to study quark–gluon plasma. The background of the slide is based on the Sistine Chapel ceiling fresco "The Creation of Adam" by Michelangelo. This picture ornamented the poster  of the first quark–gluon plasma summer school "Particle Production in Highly Excited Matter".

Reasons for studying the formation of quark–gluon plasma

The generally accepted model of the formation of the Universe states that it happened as the result of the Big Bang. In this model, in the time interval of 10−10–10−6 s after the Big Bang, matter existed in the form of a quark–gluon plasma. It is possible to reproduce the density and temperature of matter existing of that time in laboratory conditions to study the characteristics of the very early Universe. So far, the only possibility is the collision of two heavy atomic nuclei accelerated to energies of more than a hundred GeV. Using the result of a head-on collision in the volume approximately equal to the volume of the atomic nucleus, it is possible to model the density and temperature that existed in the first instants of the life of the Universe.

Relation to normal plasma

A plasma is matter in which charges are screened due to the presence of other mobile charges. For example: Coulomb's Law is suppressed by the screening to yield a distance-dependent charge, , i.e., the charge Q is reduced exponentially with the distance divided by a screening length α. In a QGP, the color charge of the quarks and gluons is screened. The QGP has other analogies with a normal plasma. There are also dissimilarities because the color charge is non-abelian, whereas the electric charge is abelian. Outside a finite volume of QGP the color-electric field is not screened, so that a volume of QGP must still be color-neutral. It will therefore, like a nucleus, have integer electric charge.

Because of the extremely high energies involved, quark-antiquark pairs are produced by pair production and thus QGP is a roughly equal mixture of quarks and antiquarks of various flavors, with only a slight excess of quarks. This property is not a general feature of conventional plasmas, which may be too cool for pair production (see however pair instability supernova).

Theory

One consequence of this difference is that the color charge is too large for perturbative computations which are the mainstay of QED. As a result, the main theoretical tools to explore the theory of the QGP is lattice gauge theory. The transition temperature (approximately 175 MeV) was first predicted by lattice gauge theory. Since then lattice gauge theory has been used to predict many other properties of this kind of matter. The AdS/CFT correspondence conjecture may provide insights in QGP, moreover the ultimate goal of the fluid/gravity correspondence is to understand QGP. The QGP is believed to be a phase of QCD which is completely locally thermalized and thus suitable for an effective fluid dynamic description.

Production

Production of QGP in the laboratory is achieved by colliding heavy atomic nuclei (called heavy ions as in an accelerator atoms are ionized) at relativistic energy in which matter is heated well above the Hagedorn temperature TH= 150 MeV per particle, which amounts to a temperature exceeding 1.66×1012 K. This can be accomplished by colliding two large nuclei at high energy (note that 175 MeV is not the energy of the colliding beam). Lead and gold nuclei have been used for such collisions at CERN SPS and BNL RHIC, respectively. The nuclei are accelerated to ultrarelativistic speeds (contracting their length) and directed towards each other, creating a "fireball", in the rare event of a collision. Hydrodynamic simulation predicts this fireball will expand under its own pressure, and cool while expanding. By carefully studying the spherical and elliptic flow, experimentalists put the theory to test.

Diagnostic tools

There is an overwhelming evidence for production of quark–gluon plasma in relativistic heavy ion collisions.

The important classes of experimental observations are

Expected properties

Thermodynamics

The cross-over temperature from the normal hadronic to the QGP phase is about 156 MeV. This "crossover" may actually not be only a qualitative feature, but instead one may have to do with a true (second order) phase transition, e.g. of the universality class of the three-dimensional Ising model. The phenomena involved correspond to an energy density of a little less than GeV/fm3. For relativistic matter, pressure and temperature are not independent variables, so the equation of state is a relation between the energy density and the pressure. This has been found through lattice computations, and compared to both perturbation theory and string theory. This is still a matter of active research. Response functions such as the specific heat and various quark number susceptibilities are currently being computed.

Flow

The discovery of the perfect liquid was a turning point in physics. Experiments at RHIC have revealed a wealth of information about this remarkable substance, which we now know to be a QGP. Nuclear matter at "room temperature" is known to behave like a superfluid. When heated the nuclear fluid evaporates and turns into a dilute gas of nucleons and, upon further heating, a gas of baryons and mesons (hadrons). At the critical temperature, TH, the hadrons melt and the gas turns back into a liquid. RHIC experiments have shown that this is the most perfect liquid ever observed in any laboratory experiment at any scale. The new phase of matter, consisting of dissolved hadrons, exhibits less resistance to flow than any other known substance. The experiments at RHIC have, already in 2005, shown that the Universe at its beginning was uniformly filled with this type of material—a super-liquid—which once the Universe cooled below TH evaporated into a gas of hadrons. Detailed measurements show that this liquid is a quark–gluon plasma where quarks, antiquarks and gluons flow independently.

Schematic representation of the interaction region formed in the first moments after the collision of heavy ions with high energies in the accelerator.

In short, a quark–gluon plasma flows like a splat of liquid, and because it's not "transparent" with respect to quarks, it can attenuate jets emitted by collisions. Furthermore, once formed, a ball of quark–gluon plasma, like any hot object, transfers heat internally by radiation. However, unlike in everyday objects, there is enough energy available so that gluons (particles mediating the strong force) collide and produce an excess of the heavy (i.e. high-energy) strange quarks. Whereas, if the QGP didn't exist and there was a pure collision, the same energy would be converted into a non-equilibrium mixture containing even heavier quarks such as charm quarks or bottom quarks.

The equation of state is an important input into the flow equations. The speed of sound (speed of QGP-density oscillations) is currently under investigation in lattice computations. The mean free path of quarks and gluons has been computed using perturbation theory as well as string theory. Lattice computations have been slower here, although the first computations of transport coefficients have been concluded. These indicate that the mean free time of quarks and gluons in the QGP may be comparable to the average interparticle spacing: hence the QGP is a liquid as far as its flow properties go. This is very much an active field of research, and these conclusions may evolve rapidly. The incorporation of dissipative phenomena into hydrodynamics is another active research area.

Jet quenching effect

Detailed predictions were made in the late 1970s for the production of jets at the CERN Super Proton–Antiproton Synchrotron. UA2 observed the first evidence for jet production in hadron collisions in 1981, which shortly after was confirmed by UA1.

The subject was later revived at RHIC. One of the most striking physical effects obtained at RHIC energies is the effect of quenching jets. At the first stage of interaction of colliding relativistic nuclei, partons of the colliding nuclei give rise to the secondary partons with a large transverse impulse ≥ 3–6 GeV / s. Passing through a highly heated compressed plasma, partons lose energy. The magnitude of the energy loss by the parton depends on the properties of the quark–gluon plasma (temperature, density). In addition, it is also necessary to take into account the fact that colored quarks and gluons are the elementary objects of the plasma, which differs from the energy loss by a parton in a medium consisting of colorless hadrons. Under the conditions of a quark–gluon plasma, the energy losses resulting from the RHIC energies by partons are estimated as dE / dx = 1 GeV / fm. This conclusion is confirmed by comparing the relative yield of hadrons with a large transverse impulse in nucleon-nucleon and nucleus-nucleus collisions at the same collision energy. The energy loss by partons with a large transverse impulse in nucleon-nucleon collisions is much smaller than in nucleus-nucleus collisions, which leads to a decrease in the yield of high-energy hadrons in nucleus-nucleus collisions. This result suggests that nuclear collisions cannot be regarded as a simple superposition of nucleon-nucleon collisions. For a short time, ~ 1 μs and in the final volume, quarks and gluons form some ideal liquid. The collective properties of this fluid are manifested during its movement as a whole. Therefore, when moving partons in this medium, it is necessary to take into account some collective properties of this quark–gluon liquid. Energy losses depend on the properties of the quark–gluon medium, on the parton density in the resulting fireball, and on the dynamics of its expansion. Losses of energy by light and heavy quarks during the passage of a fireball turn out to be approximately the same.

In November 2010 CERN announced the first direct observation of jet quenching, based on experiments with heavy-ion collisions.

Direct photons and dileptons

Direct photons and dileptons are arguably most penetrating tools to study relativistic heavy ion collisions. They are produced, by various mechanisms spanning the space-time evolution of the strongly interacting fireball.  They provide in principle a snapshot on the initial stage as well. They are hard to decipher and interpret as most of the signal is originating from hadron decays long after the QGP fireball has disintegrated.

Glasma hypothesis

Since 2008, there is a discussion about a hypothetical precursor state of the quark–gluon plasma, the so-called "Glasma", where the dressed particles are condensed into some kind of glassy (or amorphous) state, below the genuine transition between the confined state and the plasma liquid. This would be analogous to the formation of metallic glasses, or amorphous alloys of them, below the genuine onset of the liquid metallic state.

Although the experimental high temperatures and densities predicted as producing a quark–gluon plasma have been realized in the laboratory, the resulting matter does not behave as a quasi-ideal state of free quarks and gluons, but, rather, as an almost perfect dense fluid. Actually, the fact that the quark–gluon plasma will not yet be "free" at temperatures realized at present accelerators was predicted in 1984 as a consequence of the remnant effects of confinement.

In-laboratory formation of deconfined matter

A quark–gluon plasma (QGP) or quark soup is a state of matter in quantum chromodynamics (QCD) which exists at extremely high temperature and/or density. This state is thought to consist of asymptotically free strong-interacting quarks and gluons, which are ordinarily confined by color confinement inside atomic nuclei or other hadrons. This is in analogy with the conventional plasma where nuclei and electrons, confined inside atoms by electrostatic forces at ambient conditions, can move freely. Experiments to create artificial quark matter started at CERN in 1986/7, resulting in first claims that were published in 1991. It took several years before the idea became accepted in the community of particle and nuclear physicists. Formation of a new state of matter in Pb-Pb collisions was officially announced at CERN in view of the convincing experimental results presented by the CERN SPS WA97 experiment in 1999, and later elaborated by Brookhaven National Laboratory's Relativistic Heavy Ion Collider. Quark matter can only be produced in minute quantities and is unstable and impossible to contain, and will radioactively decay within a fraction of a second into stable particles through hadronization; the produced hadrons or their decay products and gamma rays can then be detected. In the quark matter phase diagram, QGP is placed in the high-temperature, high-density regime, whereas ordinary matter is a cold and rarefied mixture of nuclei and vacuum, and the hypothetical quark stars would consist of relatively cold, but dense quark matter. It is believed that up to a few microseconds (10−12 to 10−6 seconds) after the Big Bang, known as the quark epoch, the Universe was in a quark–gluon plasma state.

The strength of the color force means that unlike the gas-like plasma, quark–gluon plasma behaves as a near-ideal Fermi liquid, although research on flow characteristics is ongoing. Liquid or even near-perfect liquid flow with almost no frictional resistance or viscosity was claimed by research teams at RHIC and LHC's Compact Muon Solenoid detector. QGP differs from a "free" collision event by several features; for example, its particle content is indicative of a temporary chemical equilibrium producing an excess of middle-energy strange quarks vs. a nonequilibrium distribution mixing light and heavy quarks ("strangeness production"), and it does not allow particle jets to pass through ("jet quenching").

Experiments at CERN's Super Proton Synchrotron (SPS) begun experiments to create QGP in the 1980s and 1990s: the results led CERN to announce evidence for a "new state of matter" in 2000. Scientists at Brookhaven National Laboratory's Relativistic Heavy Ion Collider announced they had created quark–gluon plasma by colliding gold ions at nearly the speed of light, reaching temperatures of 4 trillion degrees Celsius. Current experiments (2017) at the Brookhaven National Laboratory's Relativistic Heavy Ion Collider (RHIC) on Long Island (NY, USA) and at CERN's recent Large Hadron Collider near Geneva (Switzerland) are continuing this effort, by colliding relativistically accelerated gold and other ion species (at RHIC) or lead (at LHC) with each other or with protons. Three experiments running on CERN's Large Hadron Collider (LHC), on the spectrometers ALICE, ATLAS and CMS, have continued studying the properties of QGP. CERN temporarily ceased colliding protons, and began colliding lead ions for the ALICE experiment in 2011, in order to create a QGP. A new record breaking temperature was set by ALICE: A Large Ion Collider Experiment at CERN in August 2012 in the ranges of 5.5 trillion (5.5×1012) kelvin as claimed in their Nature PR.

The formation of a quark–gluon plasma occurs as a result of a strong interaction between the partons (quarks, gluons) that make up the nucleons of the colliding heavy nuclei called heavy ions. Therefore experiments are referred to as relativistic heavy ion collision experiments. Theoretical and experimental works show that the formation of a quark–gluon plasma occurs at the temperature of T ≈ 150–160 MeV, the Hagedorn temperature, and an energy density of ≈ 0.4–1 GeV / fm3. While at first a phase transition was expected, present day theoretical interpretations propose a phase transformation similar to the process of ionisation of normal matter into ionic and electron plasma.

Quark–gluon plasma and the onset of deconfinement

The central issue of the formation of a quark–gluon plasma is the research for the onset of deconfinement. From the beginning of the research on formation of QGP, the issue was whether energy density can be achieved in nucleus-nucleus collisions. This depends on how much energy each nucleon loses. A influential reaction picture was the scaling solution presented by Bjorken. This model applies to ultra-high energy collisions. In experiments carried out at CERN SPS and BNL RHIC more complex situation arose, usually divided into three stages:

  • Primary parton collisions and baryon stopping at the time of complete overlapping of the colliding nuclei.
  • Redistribution of particle energy and new particles born in the QGP fireball.
  • The fireball of QGP matter equilibrates and expands before hadronizing.

More and more experimental evidence points to the strength of QGP formation mechanisms—operating even in LHC-energy scale proton-proton collisions.

Anti-union violence in the United States

Massachusetts militiamen with fixed bayonets surround a group of strikers during the Lawrence, Massachusetts Textile Strike of 1912

Anti-union violence in the United States is physical force intended to harm union officials, union organizers, union members, union sympathizers, or their families. It has most commonly been used either during union organizing efforts, or during strikes. The aim most often is to prevent a union from forming, to destroy an existing union, or to reduce the effectiveness of a union or a particular strike action. If strikers prevent people or goods to enter or leave a workplace, violence may be used to allow people and goods to pass the picket line.

Violence against unions may be isolated, or may occur as part of a campaign that includes spying, intimidation, impersonation, disinformation, and sabotage. Violence in labor disputes may be the result of unreasonable polarization, or miscalculation. It may be willful and provoked, or senseless and tragic. On some occasions, violence in labor disputes may be purposeful and calculated, for example the hiring and deployment of goon squads to intimidate, threaten or even assault strikers.

According to labor historians and other scholars, the US has had the bloodiest and most violent labor history of any industrialized nation.

History

Union organizer Frank Little was pulled from his bed and lynched in 1917 because of his union activities.

Historically, violence against unions has included attacks by detective and guard agencies, such as the Pinkertons, Baldwin Felts, Burns, or Thiel detective agencies; citizens groups, such as the Citizens' Alliance; company guards; police; national guard; or even the military. In particular, there are few curbs on what detective agencies are able to get away with. In the book From Blackjacks To Briefcases, Robert Michael Smith states that during the late nineteenth and early twentieth centuries, anti-union agencies spawned violence and wreaked havoc on the labor movement. One investigator who participated in a congressional inquiry into industrial violence in 1916 concluded that,

Espionage is closely related to violence. Sometimes it is the direct cause of violence, and, where that cannot be charged, it is often the indirect cause. If the secret agents of employers, working as members of the labor unions, do not always investigate acts of violence, they frequently encourage them. If they did not, they would not be performing the duties for which they are paid, for they are hired on the theory that labor organizations are criminal in character.

In U.S. Senate testimony in 1936 about an employer who wanted to contract with the Pinkerton agency, known personally to the author of the book The Pinkerton Story, this employer was characterized as a "sincerely upright and Godly man." Yet Pinkerton files record that the employer wanted the agency "to send in some thugs who could beat up the strikers." In 1936, the Pinkerton agency changed its focus from strike-breaking to undercover services. Pinkerton declined the request from this employer.

According to Morris Friedman, detective agencies were themselves for-profit companies, and a "bitter struggle" between capital and labor could be counted upon to create "satisfaction and immense profit" for agencies such as the Pinkerton company. Such agencies were in the perfect position to fan suspicion and mistrust "into flames of blind and furious hatred" on the part of the companies.

Agencies sell tactics including violence

Harry Wellington Laidler wrote a book in 1913 detailing how one of the largest union busters in the United States, Corporations Auxiliary Company, had a sales pitch offering the use of provocation and violence. The agency would routinely tell employers—prospective clients—of the methods used by their undercover operatives,

Once the union is in the field its members can keep it from growing if they know how, and our man knows how. Meetings can be set far apart. A contract can at once be entered into with the employer, covering a long period, and made very easy in its terms. However, these tactics may not be good, and the union spirit may be so strong that a big organization cannot be prevented. In this case our man turns extremely radical. He asks for unreasonable things and keeps the union embroiled in trouble. If a strike comes, he will be the loudest man in the bunch, and will counsel violence and get somebody in trouble. The result will be that the union will be broken up.

Different types of violence

Striking Pennsylvania mine workers began their protest march near Harwood. Many would soon be killed by the Luzerne County sheriff.

Some anti-union violence appears to be random, such as an incident during the 1912 textile strike in Lawrence, Massachusetts, in which a police officer fired into a crowd of strikers, killing Anna LoPizzo.

Anti-union violence may be used as a means to intimidate others, as in the hanging of union organizer Frank Little from a railroad trestle in Butte, Montana. A note was pinned to his body which said, "Others Take Notice! First And Last Warning!". The initial of the last names of seven well-known union activists in the Butte area were on the note, with the "L" for Frank Little circled.

Anti-union violence may be abrupt and unanticipated. Three years after Frank Little was lynched, a strike by Butte miners was suppressed with gunfire when deputized mine guards suddenly fired upon unarmed picketers in the Anaconda Road Massacre. Seventeen were shot in the back as they tried to flee, and one man died.

Machine gun equipped armored car built with steel from CF&I's Pueblo steel works, known to the striking miners as the Death Special. "The machine gun was turned on striking miners and used to riddle the Forbes tent colony."

The unprovoked attack was similar to another event, which had occurred twenty-three years earlier in Pennsylvania. During the Lattimer massacre, nineteen unarmed immigrant coal miners were suddenly gunned down at the Lattimer mine near Hazleton, Pennsylvania, on September 10, 1897. The miners, mostly of Polish, Slovak, Lithuanian and German ethnicity, were shot and killed by a Luzerne County sheriff's posse. In this group as well, all of the miners had been shot in the back. The shooting followed a brief tussle over the American flag carried by the miners. Their only crime was asserting their right to march in the face of demands that they disperse.

In 1927, during a coal strike in Colorado, state police and mine guards fired pistols, rifles and a machine gun into a group of five hundred striking miners and their wives in what came to be called the Columbine Mine Massacre. In this incident as well, many of the miners were immigrants, and there had been a disagreement over the question of trespassing onto company property in the town of Serene, with the miners asserting it was public property because of the post office. There was, once again, a tussle over American flags carried by the strikers.

While the Columbine mine shooting was a surprise, newspapers played a deadly role in conjuring the atmosphere of hate in which the violence occurred. Lurid editorials attacked the ethnicity of the strikers. Newspapers began calling for the governor to no longer withhold the "mailed fist", to strike hard and strike swiftly, and for "Machine Guns Manned By Willing Shooters" at more of the state's coal mines. Within days of these editorials, state police and mine guards fired on the miners and their wives, injuring dozens and killing six.

In all of the above incidents, the perpetrators were never caught, or went unpunished. An exception resulted from a shooting of strikers at the Williams & Clark Fertilizing Company near the Liebig Fertilizer Works at Carteret, New Jersey, in 1915. One striker was killed outright, and more than twenty were injured in an unprovoked attack when deputies fired on strikers who had stopped a train to check for strikebreakers. The strikers found no strikebreakers and were cheering as they exited the train. Forty deputies approached and suddenly fired on them with revolvers, rifles, and shotguns. As the strikers ran, "the deputies ... pursued, firing again and again." According to attending physicians, all the strikers' wounds were on the backs or legs, indicating the guards were pursuing them. A local government official who witnessed the shooting called it entirely unprovoked. Four more of the strikers, all critically injured, would die. Twenty-two of the guards were arrested and the crime was investigated by a Grand Jury; nine deputies were subsequently convicted of manslaughter.

Other anti-union violence may seem orchestrated, as in 1914 when mine guards and the state militia fired into a tent colony of striking miners in Colorado, an incident that came to be known as the Ludlow Massacre. During that strike, the company hired the Baldwin Felts agency, which built an armored car so their agents could approach the strikers' tent colonies with impunity. The strikers called it the "Death Special". At the Forbes tent colony,

[The Death Special] opened fire, a protracted spurt that sent some six hundred bullets tearing through the thin tents. One of the shots struck miner Luka Vahernik, fifty, in the head, killing him instantly. Another striker, Marco Zamboni, eighteen ... suffered nine bullet wounds to his legs... One tent was later found to have about 150 bullet holes...

After deaths of women and children at Ludlow,

[T]he backlash was vicious and bloody. Over the next ten days striking miners poured out their rage in attacks across the coalfields...

The U.S. Army was called upon to put an end to the violence, and the strike sputtered to an end that December.

As a result of Operative Smith's "clever and intelligent" work, a number of union organizers received severe beatings at the hands of unknown masked men, presumably in the employ of the company.

Morris Friedman offers examples of these incidents:

About February 13, 1904, William Farley, of Alabama, a member of the [UMWA] National Executive Board ... and the personal representative of [UMWA] President Mitchell ... addressed coal miners' meetings ... [on their return trip] eight masked men held them up with revolvers, dragged them from their wagon, threw them to the ground, beat them, kicked them, and almost knocked them into insensibility.

And,

On Saturday, April 30, 1904, W.M. Wardjon, a national organizer of the United Mine Workers, while on board a train en route to Pueblo, was assaulted by three men at Sargents, about thirty miles west of Salida. Mr. Wardjon was beaten into unconsciousness.

Friedman accused the Colorado Fuel and Iron Company (CF&I), operated by John D. Rockefeller and his lieutenant in Colorado, Jesse Welborn, of responsibility for the beatings during the 1903–04 strike.

Sometimes, there is simultaneous violence on both sides. In an auto workers strike organised by Victor Reuther and others in 1937, "[u]nionists assembled rocks, steel hinges, and other objects to throw at the cops, and police organized tear gas attacks and mounted charges."

Colorado labor war, 1903–1904

General Sherman Bell. Photo from The Pinkerton Labor Spy, published in 1907.
 
Karl Linderfelt, center. Original photo caption: "OFFICERS OF THE COLORADO NATIONAL GUARD From left to right: Captain R. J. Linderfelt, Lieut. T. C. Linderfelt, Lieut. K. E. Linderfelt, (who faced the charge of assault upon Louis Tikas, the dead strike leader), Lieut. G.S. Lawrence and Major Patrick Hamrock. The last three were in the Ludlow battle of April 20, 1914."

A study of industrial violence in 1969 concluded, "There is no episode in American labor history in which violence was as systematically used by employers as in the Colorado labor war of 1903 and 1904."

About the middle of February 1904, leadership of the Colorado National Guard became concerned that the Mine Owners were failing to cover the payroll of the soldiers. General Reardon ordered Major Ellison to take another soldier he could trust to "hold up or shoot the men coming off shift at the Vindicator mine" in order to convince the mine owners to pay. The implication of the secrecy was that the incident would then be blamed on the union.

However, Major Ellison reported that the miners took a route out of the mine that would not make ambush possible. Reardon ordered Ellison to pursue an alternative plan, which was shooting up one of the mines. Major Ellison and Sergeant Gordon Walter fired sixty shots into two mine buildings. The plan worked, and the mine owners paid up. Ellison would later testify (in October 1904) that General Reardon informed him Adjutant General Sherman Bell and Colorado Governor James Peabody knew about the plan. Major Ellison's testimony about the shooting plot, and about the staged attacks on striking miners, was corroborated by two other soldiers.

Ludlow massacre, 1914

Professor James H. Brewster, a faculty attorney with the University of Colorado who was investigating the strike for Governor Ammons, was aware that militia Lieutenant Karl Linderfelt was guilty of abuse and beatings of innocent citizens, including a small Greek boy "whose head was split open". Professor Brewster sent a telegram to Governor Ammons requesting Linderfelt's removal. No action was taken. In a subsequent face to face meeting with the governor, three months prior to the Ludlow Massacre, Brewster again insisted that Linderfelt be removed, but again, Ammons declined. In later testimony, Professor Brewster stated that Linderfelt was the reason for the massacre. On the day that the Ludlow Massacre occurred, Lieutenant Karl Linderfelt, commander of one of two companies of the Colorado National Guard, had Louis Tikas, leader of the Ludlow tent colony of striking miners, at gunpoint. Tikas was unarmed, and the miners would later explain that he approached the militia to ask them to stop shooting. While two militiamen held Tikas, Linderfelt broke a rifle butt over his head. Tikas and two other captured miners were later found shot dead. Tikas had been shot in the back. Their bodies lay along the Colorado and Southern railroad tracks for three days in full view of passing trains. The militia officers refused to allow them to be moved until a local of a railway union demanded the bodies be taken away for burial. A court martial found Lieutenant Linderfelt guilty of assaulting Tikas with a Springfield rifle, "but attaches no criminality thereto. And the court does therefor acquit him."

1916 Congressional investigation

In 1916, the Commission on Industrial Relations, created by the U.S. Congress, issued a final report on its investigation of industrial unrest. On the question of violence in industrial disputes, the Commission stated, in part,

Many instances of the use of physical force by the agents of employers have ... come before the Commission, indicating a relatively wide use, particularly in isolated communities.

Late 20th century anti-union violence

By the early 1900s, public tolerance for violence during labor disputes began to decrease. Yet violence involving strikebreaking troops and armed guards continued into the 1930s. The level of violence that anti-union agencies engaged in eventually resulted in their tactics becoming increasingly public, for there were a very great number of newspaper and muckraking articles written about such incidents. Resources that once were allocated to overt control over workforces began to be assigned to other methods of control, such as industrial espionage. After the Great Depression in 1929, the public no longer considered companies unassailable. Yet legislation related to employer strategies such as violent strike breaking would have to wait until after World War II. Beginning in the 1950s, employers began to embrace new methods of managing workers and unions which were still effective, but much more subtle.

A 1969 study of labor conflict violence in the United States examined the era following the 1947 passage of the Taft–Hartley Act and noted that attacks on strikers by company guards had all but disappeared. Violence still occurs in labor disputes, for example, when one side miscalculates. Bringing in outside security forces, as one example, can lead to violence in modern labor disputes.

The use of cameras and camcorders may affect levels of violence in labor disputes today.

Examples since 1940

Threats

Sometimes, threats of violence cause damage to union members or supporters. Other times, threats against unions or their members may backfire. For example, Indiana Deputy Attorney General Jeffrey Cox was fired after suggesting that Wisconsin Governor Scott Walker should use live ammunition against pro-union protesters involved in the 2011 Wisconsin protests. More recently, a Deputy Prosecutor in Indiana's Johnson County, Carlos Lam, suggested that Governor Walker should mount a "false flag" operation which would make it appear as if the union was committing violence. After initially claiming that his email account was hacked, Lam admitted to sending the suggestion and resigned.

Cullen Werwie, press secretary for Governor Walker, states that Walker's office was unaware of Lam's email. According to CBS News, Werwie also commented, "Certainly we do not support the actions suggested in (the) email. Governor Walker has said time and again that the protesters have every right to have their voice heard, and for the most part the protests have been peaceful. We are hopeful that the tradition will continue."

Dysfunctional family

From Wikipedia, the free encyclopedia
 
A dysfunctional family affects familial ties and creates conflicts in the same family space.

A dysfunctional family is a family in which conflict, misbehavior, and often child neglect or abuse on the part of individual parents occur continuously and regularly, leading other members to accommodate such actions. Children sometimes grow up in such families with the understanding that such a situation is normal. Dysfunctional families are primarily a result of two adults, one typically overtly abusive and the other codependent, and may also be affected by substance abuse or other forms of addiction, or sometimes by an untreated mental illness. Parents having grown up in a dysfunctional family may over-correct or emulate their own parents. In some cases, the dominant parent will abuse or neglect their children and the other parent will not object, misleading a child to assume blame.

Perceptions and historical context

A common misperception of dysfunctional families is the mistaken belief that the parents are on the verge of separation and divorce. While this is true in a few cases, often the marital satisfaction is very strong as the parents' faults actually complement each other. In short, they have nowhere else to go. However, this does not necessarily mean the family's situation is stable. Any major stressor, such as relocation, unemployment/underemployment, physical or mental illness, natural disaster, etc., can cause existing difficulties affecting the children to become much worse.

Dysfunctional families pervade all strata of society regardless of social, financial or intellectual status. Nevertheless, until recent decades, professionals (therapists, social workers, teachers, counselors, clergy, etc.) did not take the concept of a dysfunctional family seriously, especially not with reference to the middle and upper classes. Any intervention would have been seen as violating the sanctity of marriage and increasing the probability of divorce, which was socially unacceptable at the time. Historically, society expected the children of dysfunctional families to obey their parents (ultimately the father), and to cope with the situation alone.

Examples

Dysfunctional family members have common features and behavior patterns as a result of their experiences within the family structure. This tends to reinforce the dysfunctional behavior, either through enabling or perpetuation. The family unit can be affected by a variety of factors.

Common features

Nearly universal

Some features are common to most dysfunctional families:

  • Lack of empathy, understanding, and sensitivity towards certain family members, while expressing extreme empathy or appeasement towards one or more members who have real or perceived "special needs". In other words, one family member continuously receives far more than they deserve, while another is marginalized.
  • Denial (refusal to acknowledge abusive behavior, possibly believing that the situation is normal or even beneficial; also known as the "elephant in the room".)
  • Inadequate or missing boundaries for self (e.g. tolerating inappropriate treatment from others, failing to express what is acceptable and unacceptable treatment, tolerance of physical, emotional or sexual abuse.)
  • Disrespect of others' boundaries (e.g. physical contact that other person dislikes; breaking important promises without just cause; purposefully violating a boundary another person has expressed.)
  • Extremes in conflict (either too much fighting or insufficient peaceful arguing between family members.)
  • Unequal or unfair treatment of one or more family members due to their birth order, gender, age, family role (mother, etc.), abilities, race, caste, etc. (may include frequent appeasement of one member at the expense of others, or an uneven/inconsistent enforcement of rules.)

Not universal

Though not universal among dysfunctional families, and by no means exclusive to them, the following features are typical of dysfunctional families:

  • Abnormally high levels of jealousy or other controlling behaviors.
  • Conflict influenced by marital status:
    • Between separated or divorced parents, usually related to, or arising from their breakup.
    • Conflict between parents who remain married, often for the perceived "sake" of the children, but whose separation or divorce would in fact remove a detrimental influence on those children (must be evaluated on a case-by-case basis, as a breakup may harm children.)
    • Parents who wish to divorce, but cannot due to financial, societal (including religious), or legal reasons.
  • Children afraid to talk (within or outside the family) about what is happening at home, or are otherwise fearful of their parents.
  • Abnormal sexual behavior such as adultery, promiscuity, or incest.
  • Lack of time spent together, especially in recreational activities and social events ("We never do anything as a family.")
  • Parents insist that they treat their children fairly and equitably when that is not the case.
  • Family members (including children) who disown each other, or refuse to be seen together in public (either unilaterally or bilaterally.)

Specific examples

There are certain times where families can become dysfunctional due to specific situational examples. Some of these include difficulty integrating into a new culture, strain in the relationship between nuclear and extended family members, children in a rebellion phase, and ideological differences in belief systems.

Laundry List

The program "Adult Children of Alcoholics" includes something labeled as a "Laundry List". The Laundry List is core literature of the program Adult Children of Alcoholics. This list has 14 different statements that relate to being an adult child of a parent with an alcohol addiction. These statements provide commentary on how children have been affected by the trauma of having alcoholic parents. Some highlights of the statements include, "confusing love and pity", "having low self-esteem", and having a "loss of identity". The Laundry list is a helpful tool in group therapy in order to show families that they are not alone in their struggles.

Parenting

Unhealthy signs

Unhealthy parenting signs, which could lead to a family becoming dysfunctional include:

  • Unrealistic expectations
  • Ridicule
  • Conditional love
  • Disrespect; especially contempt
  • Emotional intolerance (family members not allowed to express the "wrong" emotions.)
  • Social dysfunction or isolation (for example, parents unwilling to reach out to other families—especially those with children of the same gender and approximate age, or do nothing to help their "friendless" child.)
  • Stifled speech (children not allowed to dissent or question authority.)
  • Denial of an "inner life" (children are not allowed to develop their own value systems.)
  • Being under- or over-protective
  • Apathy ("I don't care!")
  • Belittling ("You can't do anything right!")
  • Shame ("Shame on you!")
  • Bitterness (regardless of what is said, using a bitter tone of voice.)
  • Hypocrisy ("Do as I say, not as I do.")
  • Lack of forgiveness for minor misdeeds or accidents
  • Judgmental statements or demonization ("You are a liar!")
  • Being overly critical and withholding proper praise. (experts say 80–90% praise, and 10–20% constructive criticism is the most healthy.)
  • Double standards or giving "mixed messages" by having a dual system of values (i.e. one set for the outside world, another when in private, or teaching divergent values to each child.)
  • The absentee parent (seldom available for their child due to work overload, alcohol/drug abuse, gambling, or other addictions.)
  • Unfulfilled projects, activities, and promises affecting children ("We'll do it later.")
  • Giving to one child what rightly belongs to another
  • Gender prejudice (treats one gender of children fairly; the other unfairly.)
  • Discussion and exposure to sexuality: either too much, too soon or too little, too late
  • Faulty discipline based more on emotions or family politics than on established rules (e.g., punishment by "surprise".)
  • Having an unpredictable emotional state due to substance abuse, personality disorder(s), or stress
  • Parents always (or never) take their children's side when others report acts of misbehavior, or teachers report problems at school
  • Scapegoating (knowingly or recklessly blaming one child for the misdeeds of another)
  • "Tunnel vision" diagnosis of children's problems (for example, a parent may think their child is either lazy or has learning disabilities after he falls behind in school despite recent absence due to illness.)
  • Older siblings given either no or excessive authority over younger siblings with respect to their age difference and level of maturity.
  • Frequent withholding of consent ("blessing") for culturally common, lawful, and age-appropriate activities a child wants to take part in
  • The "know-it-all" (has no need to obtain child's side of the story when accusing, or listen to child's opinions on matters which greatly impact them.)
  • Regularly forcing children to attend activities for which they are extremely over- or under-qualified (e.g. using a preschool to babysit a typical nine-year-old boy, taking a young child to poker games, etc.)
  • Either being a miser ("scrooge") in totality or selectively allowing children's needs to go unmet (e.g. a father will not buy a bicycle for his son because he wants to save money for retirement or "something important".)
  • Disagreements about nature and nurture (parents, often non-biological, blame common problems on child's heredity, when faulty parenting may be the actual cause.)

Dysfunctional styles

"Children as pawns"

One common dysfunctional parental behavior is a parent's manipulation of a child in order to achieve some outcome adverse to the other parent's rights or interests. Examples include verbal manipulation such as spreading gossip about the other parent, communicating with the parent through the child (and in the process exposing the child to the risks of the other parent's displeasure with that communication) rather than doing so directly, trying to obtain information through the child (spying), or causing the child to dislike the other parent, with insufficient or no concern for the damaging effects of the parent's behavior on the child. While many instances of such manipulation occur in shared custody situations that have resulted from separation or divorce, it can also take place in intact families, where it is known as triangulation.

List of other dysfunctional styles

  • "Using" (destructively narcissistic parents who rule by fear and conditional love.)
  • Abusing (parents who use physical violence, or emotionally, or sexually abuse their children.)
  • Perfectionist (fixating on order, prestige, power, or perfect appearances, while preventing their child from failing at anything.)
  • Dogmatic or cult-like (harsh and inflexible discipline, with children not allowed, within reason, to dissent, question authority, or develop their own value system.)
  • Inequitable parenting (going to extremes for one child while continually ignoring the needs of another.)
  • Deprivation (control or neglect by withholding love, support, necessities, sympathy, praise, attention, encouragement, supervision, or otherwise putting their children's well-being at risk.)
  • Abuse among siblings (parents fail to intervene when a sibling physically or sexually abuses another sibling.)
  • Abandonment (a parent who willfully separates from their children, not wishing any further contact, and in some cases without locating alternative, long-term parenting arrangements, leaving them as orphans.)
  • Appeasement (parents who reward bad behavior—even by their own standards—and inevitably punish another child's good behavior in order to maintain the peace and avoid temper tantrums. "Peace at any price.")
  • Loyalty manipulation (giving unearned rewards and lavish attention trying to ensure a favored, yet rebellious child will be the one most loyal and well-behaved, while subtly ignoring the wants and needs of their most loyal child currently.)
  • "Helicopter parenting" (parents who micro-manage their children's lives or relationships among siblings—especially minor conflicts.)
  • "The deceivers" (well-regarded parents in the community, likely to be involved in some charitable/non-profit works, who abuse or mistreat one or more of their children.)
  • "Public image manager" (sometimes related to above, children warned to not disclose what fights, abuse, or damage happens at home, or face severe punishment "Don't tell anyone what goes on in this family".)
  • "The paranoid parent" (a parent having persistent and irrational fear accompanied by anger and false accusations that their child is up to no good or others are plotting harm.)
  • "No friends allowed" (parents discourage, prohibit, or interfere with their child from making friends of the same age and gender.)
  • Role reversal (parents who expect their minor children to take care of them instead.)
  • "Not your business" (children continuously told that a particular brother or sister who is often causing problems is none of their concern.)
  • Ultra-egalitarianism (either a much younger child is permitted to do whatever an older child may, or an older child must wait years until a younger child is mature enough.)
  • "The guard dog" (a parent who blindly attacks family members perceived as causing the slightest upset to their esteemed spouse, partner, or child.)
  • "My baby forever" (a parent who will not allow one or more of their young children to grow up and begin taking care of themselves.)
  • "The cheerleader" (one parent "cheers on" the other parent who is simultaneously abusing their child.)
  • "Along for the ride" (a reluctant de facto, step, foster, or adoptive parent who does not truly care about their non-biological child, but must co-exist in the same home for the sake of their spouse or partner) (See also: Cinderella effect).
  • "The politician" (a parent who repeatedly makes or agrees to children's promises while having little to no intention of keeping them.)
  • "It's taboo" (parents rebuff any questions children may have about sexuality, pregnancy, romance, puberty, certain areas of human anatomy, nudity, etc.)
  • Identified patient (one child, usually selected by the mother, who is forced into going to therapy while the family's overall dysfunction is kept hidden.)
  • Münchausen syndrome by proxy (a much more extreme situation than above, where the child is intentionally made ill by a parent seeking attention from physicians and other professionals.)

Dynamical

Coalitions are subsystems within families with more rigid boundaries and are thought to be a sign of family dysfunction.

  • The isolated family member (either a parent or child up against the rest of the otherwise united family.)
  • Parent vs. parent (frequent fights amongst adults, whether married, divorced, or separated, conducted away from the children.)
  • The polarized family (a parent and one or more children on each side of the conflict.)
  • Parents vs. kids (intergenerational conflict, generation gap or culture shock dysfunction.)
  • The balkanized family (named after the three-way war in the Balkans where alliances shift back and forth.)
  • Free-for-all (a family that fights in a "free-for-all" style, though may become polarized when range of possible choices is limited.)

Children

Unlike divorce, and to a lesser extent, separation, there is often no record of an "intact" family being dysfunctional. As a result, friends, relatives, and teachers of such children may be completely unaware of the situation. In addition, a child may be unfairly blamed for the family's dysfunction, and placed under even greater stress than those whose parents separate.

The six basic roles

Children growing up in a dysfunctional family have been known to adopt or be assigned one or more of the following six basic roles:

  • The Golden Child (also known as the Hero or Superkid): a child who becomes a high achiever or overachiever outside the family (e.g., in academics or athletics) as a means of escaping the dysfunctional family environment, defining themselves independently of their role in the dysfunctional family, currying favor with parents, or shielding themselves from criticism by family members.
  • The Problem Child, Rebel, or Truth Teller: the child who a) causes most problems related to the family's dysfunction or b) "acts out" in response to preexisting family dysfunction, in the latter case often in an attempt to divert attention paid to another member who exhibits a pattern of similar misbehavior.
    • A variant of the "problem child" role is the Scapegoat, who is unjustifiably assigned the "problem child" role by others within the family or even wrongfully blamed by other family members for those members' own individual or collective dysfunction, often despite being the only emotionally stable member of the family.
  • The Caretaker: the one who takes responsibility for the emotional well-being of the family, often assuming a parental role; the intra-familial counterpart of the "Good Child"/"Superkid."
  • The Lost Child or Passive Kid: the inconspicuous, introverted, quiet one, whose needs are usually ignored or hidden.
  • The Mascot or Family Clown: uses comedy to divert attention away from the increasingly dysfunctional family system.
  • The Mastermind: the opportunist who capitalizes on the other family members' faults to get whatever they want; often the object of appeasement by grown-ups.

Effects on children

Children of dysfunctional families, either at the time, or as they grow older, may also:

  • Lack the ability to be playful, or childlike, and may "grow up too fast"; conversely they may grow up too slowly, or be in a mixed mode (e.g. well-behaved, but unable to care for themselves.)
  • Have moderate to severe mental health issues, including possible depression, anxiety, and suicidal thoughts.
  • Become addicted to drugs, including cigarettes or alcohol, especially if parents or friends have done the same.
  • Developing behavioral addictions to such things like gambling, excessive spending, video games, pornography, or food; the latter often resulting in obesity or/and other physical health issues.
  • Bully or harass others, or be an easy victim thereof (possibly taking a dual role in different settings.)
  • Be in denial regarding the severity of the family's situation.
  • Have mixed feelings of love–hate towards certain family members.
  • Become a sex offender, possibly including pedophilia.
  • Have difficulty forming healthy relationships within their peer group (usually due to shyness or a personality disorder.)
  • Spend an inordinate amount of time alone watching television, playing video games, surfing the Internet, listening to music, going out for late night drives alone, and engaging in other activities which lack in-person social interaction.
  • Feel angry, anxious, depressed, isolated from others, or unlovable.
  • Have a speech disorder (related to emotional abuse.)
  • Distrust others or even have paranoia.
  • Become a juvenile delinquent and turn to a life of crime (with or without dropping out of school), and possibly become a gang member as well.
  • Struggle academically at school or academic performance declines unexpectedly.
  • Have low self-esteem or a poor self image with difficulty expressing emotions.
  • Do not pay close attention to their own physical or mental health
  • May be at risk of self-harm or suicide.
  • Exhibits lack of organization in their day-to-day lives.
  • Rebel against parental authority, or conversely, uphold their family's values in the face of peer pressure, or even try to take an impossible "middle ground" that pleases no one.
  • Turning the tables by abusing their abusive elderly parents, upon the former reaching adulthood.
  • Think only of themselves to make up the difference of their childhoods (as they are still learning the balance of self-love.)
  • Have little self-discipline when parents are not around, such as compulsive spending, procrastinating too close to deadlines, etc. (unfamiliar, inchoate, and seemingly lax or avoidable real-world consequences vs. known, concrete, and rigidly imposed parental consequences.)
  • Find an (often abusive) spouse or partner at a young age, or run away from home.
  • Become pregnant or a parent of illegitimate children.
  • Be at risk of becoming poor or homeless, even if the family is already wealthy or middle-class.
  • Live a reclusive lifestyle without any spouse, partner, children, or friends.
  • Have auto-destructive or potentially self-damaging behaviors.
  • Join a cult to find the acceptance they never had at home, or at a minimum, have differing philosophical or religious beliefs from what they were previously taught.
  • Strive (as young adults) to live far away from particular family members or the family as a whole, possibly spending much more time with extended family.
  • Perpetuate dysfunctional behaviors in other relationships (especially their own children.)

Positive Outcomes

Although there are many negative outcomes that came come from growing up in a dysfunctional household, the brain can be able to produce positive ones as well. As discussed in the article, "Adult Children of Dysfunctional Families", resilience is something that can come out of these obstacles in children's lives and make for a brighter future. Resilience is defined as something positive that is able to be brought forth from negative experiences in childhood. (Resilience in Adult Children of Alcoholics: A Nonpathological Approach to Social Work Practice). This refers to the ability for children who go through many hardships with their parents growing up to be able to take those hardships and learn from them in order to develop better coping strategies and find meaning in their futures. For example, when children find themselves in a dysfunctional family life, they may take the route of either isolating themselves, or reaching out for help. When children reach out for help, they can develop resiliency over time by fostering positive relationships with guidance counselors, or other trusted adults that will continue to stay strong after they become adults themselves.

Resilience is also something that can be strengthened through community settings and positive interactions with others. A dysfunctional family can create a large amount of trauma for children that they may carry into their adult lives. Although different families may create different types of trauma for children, the way that trauma is processed is very similar. When children are able to bond and help each other through the process of dealing with trauma, they can find comfort, which in turn promotes resiliency. What trauma tends to do is make people feel like there is something wrong with them, and they should keep themselves away from the rest of society. This is why recognizing that one is not alone in their struggles is an extremely powerful thing.

Resources and Hope

The organization Adult Children of Alcoholics and Dysfunctional Families (ACA) serves as an extremely useful tool in providing support for people who come from a dysfunctional childhood where their caretakers suffered with alcoholism. What the ACA does that is hold a twelve step program that is designed to create emotional healing in adult children. By doing this, the program hopes to see the adult children equally as worthy as help and support as the people in their families who faced the alcoholism themselves. There are multiple kinds of meetings that the organization holds in order to bring resources to all different groups (women, men, LGBTQ+, teens, young adults). These meeting settings also have different formats, so that people can be met where they are in their individual healing journey. For example, one could view a guest speaker's presentation before they go into any formal counseling. This is an significant aspect to the resource of meeting's, because some people feel too overwhelmed by certain settings to even begin the process. It is better for a person to join the organization at all, than to be too nervous to go to a full-blown meeting and be turned away forever.

In popular culture

Equality (mathematics)

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Equality_...