Ensemble (mathematical physics)

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In physics, specifically statistical mechanics, an ensemble (also statistical ensemble) is an idealization consisting of a large number of virtual copies (sometimes infinitely many) of a system, considered all at once, each of which represents a possible state that the real system might be in. In other words, a statistical ensemble is a set of systems of particles used in statistical mechanics to describe a single system. The concept of an ensemble was introduced by J. Willard Gibbs in 1902.^[2]

A thermodynamic ensemble is a specific variety of statistical ensemble that, among other properties, is in statistical equilibrium (defined below), and is used to derive the properties of thermodynamic systems from the laws of classical or quantum mechanics.

Physical considerations

The ensemble formalises the notion that an experimenter repeating an experiment again and again under the same macroscopic conditions, but unable to control the microscopic details, may expect to observe a range of different outcomes.

The notional size of ensembles in thermodynamics, statistical mechanics and quantum statistical mechanics can be very large, including every possible microscopic state the system could be in, consistent with its observed macroscopic properties. For many important physical cases, it is possible to calculate averages directly over the whole of the thermodynamic ensemble, to obtain explicit formulas for many of the thermodynamic quantities of interest, often in terms of the appropriate partition function.

The concept of an equilibrium or stationary ensemble is crucial to many applications of statistical ensembles. Although a mechanical system certainly evolves over time, the ensemble does not necessarily have to evolve. In fact, the ensemble will not evolve if it contains all past and future phases of the system. Such a statistical ensemble, one that does not change over time, is called stationary and can be said to be in statistical equilibrium.

Terminology

• The word "ensemble" is also used for a smaller set of possibilities sampled from the full set of possible states. For example, a collection of walkers in a Markov chain Monte Carlo iteration is called an ensemble in some of the literature.
• The term "ensemble" is often used in physics and the physics-influenced literature. In probability theory, the term probability space is more prevalent.

Main types

Visual representation of five statistical ensembles (from left to right): microcanonical ensemble, canonical ensemble, grand canonical ensemble, isobaric-isothermal ensemble, isoenthalpic-isobaric ensemble

The study of thermodynamics is concerned with systems that appear to human perception to be "static" (despite the motion of their internal parts), and which can be described simply by a set of macroscopically observable variables. These systems can be described by statistical ensembles that depend on a few observable parameters, and which are in statistical equilibrium. Gibbs noted that different macroscopic constraints lead to different types of ensembles, with particular statistical characteristics.

"We may imagine a great number of systems of the same nature, but differing in the configurations and velocities which they have at a given instant, and differing in not merely infinitesimally, but it may be so as to embrace every conceivable combination of configuration and velocities..." J. W. Gibbs (1903)

Three important thermodynamic ensembles were defined by Gibbs:

• Microcanonical ensemble (or NVE ensemble) —a statistical ensemble where the total energy of the system and the number of particles in the system are each fixed to particular values; each of the members of the ensemble are required to have the same total energy and particle number. The system must remain totally isolated (unable to exchange energy or particles with its environment) in order to stay in statistical equilibrium.
• Canonical ensemble (or NVT ensemble)—a statistical ensemble where the energy is not known exactly but the number of particles is fixed. In place of the energy, the temperature is specified. The canonical ensemble is appropriate for describing a closed system which is in, or has been in, weak thermal contact with a heat bath. In order to be in statistical equilibrium, the system must remain totally closed (unable to exchange particles with its environment) and may come into weak thermal contact with other systems that are described by ensembles with the same temperature.
• Grand canonical ensemble (or μVT ensemble)—a statistical ensemble where neither the energy nor particle number are fixed. In their place, the temperature and chemical potential are specified. The grand canonical ensemble is appropriate for describing an open system: one which is in, or has been in, weak contact with a reservoir (thermal contact, chemical contact, radiative contact, electrical contact, etc.). The ensemble remains in statistical equilibrium if the system comes into weak contact with other systems that are described by ensembles with the same temperature and chemical potential.

The calculations that can be made using each of these ensembles are explored further in their respective articles. Other thermodynamic ensembles can be also defined, corresponding to different physical requirements, for which analogous formulae can often similarly be derived. For example, in the reaction ensemble, particle number fluctuations are only allowed to occur according to the stoichiometry of the chemical reactions which are present in the system.

Equivalence

In thermodynamic limit all ensembles should produce identical observables due to Legendre transforms, deviations to this rule occurs under conditions that state-variables are non-convex, such as small molecular measurements. 

Representations

The precise mathematical expression for a statistical ensemble has a distinct form depending on the type of mechanics under consideration (quantum or classical). In the classical case, the ensemble is a probability distribution over the microstates. In quantum mechanics, this notion, due to von Neumann, is a way of assigning a probability distribution over the results of each complete set of commuting observables. In classical mechanics, the ensemble is instead written as a probability distribution in phase space; the microstates are the result of partitioning phase space into equal-sized units, although the size of these units can be chosen somewhat arbitrarily.

Requirements for representations

Putting aside for the moment the question of how statistical ensembles are generated operationally, we should be able to perform the following two operations on ensembles A, B of the same system:

• Test whether A, B are statistically equivalent.
• If p is a real number such that 0 < p < 1, then produce a new ensemble by probabilistic sampling from A with probability p and from B with probability 1 − p.

Under certain conditions, therefore, equivalence classes of statistical ensembles have the structure of a convex set.

Quantum mechanical

Main article: Density matrix

A statistical ensemble in quantum mechanics (also known as a mixed state) is most often represented by a density matrix, denoted by ${\displaystyle \hat{\rho }}$. The density matrix provides a fully general tool that can incorporate both quantum uncertainties (present even if the state of the system were completely known) and classical uncertainties (due to a lack of knowledge) in a unified manner. Any physical observable X in quantum mechanics can be written as an operator, ${\displaystyle \hat{X}}$. The expectation value of this operator on the statistical ensemble ${\displaystyle \rho }$ is given by the following trace:

${\displaystyle ⟨X⟩=\mathrm{Tr}(\hat{X}\rho ).}$

This can be used to evaluate averages (operator ${\displaystyle \hat{X}}$), variances (using operator ${\displaystyle {\hat{X}}^2}$), covariances (using operator ${\displaystyle \hat{X}\hat{Y}}$), etc. The density matrix must always have a trace of 1: ${\displaystyle \mathrm{Tr}\hat{\rho }=1}$ (this essentially is the condition that the probabilities must add up to one).

In general, the ensemble evolves over time according to the von Neumann equation.

Equilibrium ensembles (those that do not evolve over time, ${\displaystyle d\hat{\rho }/dt=0}$) can be written solely as a function of conserved variables. For example, the microcanonical ensemble and canonical ensemble are strictly functions of the total energy, which is measured by the total energy operator ${\displaystyle \hat{H}}$ (Hamiltonian). The grand canonical ensemble is additionally a function of the particle number, measured by the total particle number operator ${\displaystyle \hat{N}}$. Such equilibrium ensembles are a diagonal matrix in the orthogonal basis of states that simultaneously diagonalize each conserved variable. In bra–ket notation, the density matrix is

${\displaystyle \hat{\rho }=\sum _i{P}_i|{\psi }_i⟩⟨{\psi }_i|,}$

where the |ψ_i⟩, indexed by i, are the elements of a complete and orthogonal basis. (Note that in other bases, the density matrix is not necessarily diagonal.)

Classical mechanical

Evolution of an ensemble of classical systems in phase space (top). Each system consists of one massive particle in a one-dimensional potential well (red curve, lower figure). The initially compact ensemble becomes swirled up over time.

In classical mechanics, an ensemble is represented by a probability density function defined over the system's phase space. While an individual system evolves according to Hamilton's equations, the density function (the ensemble) evolves over time according to Liouville's equation.

In a mechanical system with a defined number of parts, the phase space has n generalized coordinates called q₁, ... q_n, and n associated canonical momenta called p₁, ... p_n. The ensemble is then represented by a joint probability density function ρ(p₁, ... p_n, q₁, ... q_n).

If the number of parts in the system is allowed to vary among the systems in the ensemble (as in a grand ensemble where the number of particles is a random quantity), then it is a probability distribution over an extended phase space that includes further variables such as particle numbers N₁ (first kind of particle), N₂ (second kind of particle), and so on up to N_s (the last kind of particle; s is how many different kinds of particles there are). The ensemble is then represented by a joint probability density function ρ(N₁, ... N_s, p₁, ... p_n, q₁, ... q_n). The number of coordinates n varies with the numbers of particles.

Any mechanical quantity X can be written as a function of the system's phase. The expectation value of any such quantity is given by an integral over the entire phase space of this quantity weighted by ρ:

${\displaystyle ⟨X⟩=\sum _{N_1=0}^{\mathrm{\infty }}\dots \sum _{N_s=0}^{\mathrm{\infty }}\int \dots \int \rho Xd{p}_1\dots d{q}_n.}$

The condition of probability normalization applies, requiring

${\displaystyle \sum _{N_1=0}^{\mathrm{\infty }}\dots \sum _{N_s=0}^{\mathrm{\infty }}\int \dots \int \rho d{p}_1\dots d{q}_n=1.}$

Phase space is a continuous space containing an infinite number of distinct physical states within any small region. In order to connect the probability density in phase space to a probability distribution over microstates, it is necessary to somehow partition the phase space into blocks that are distributed representing the different states of the system in a fair way. It turns out that the correct way to do this simply results in equal-sized blocks of canonical phase space, and so a microstate in classical mechanics is an extended region in the phase space of canonical coordinates that has a particular volume. In particular, the probability density function in phase space, ρ, is related to the probability distribution over microstates, P by a factor

${\displaystyle \rho =\frac{1}{h^{n}C}P,}$

where

• h is an arbitrary but predetermined constant with the units of energy×time, setting the extent of the microstate and providing correct dimensions to ρ.
• C is an overcounting correction factor (see below), generally dependent on the number of particles and similar concerns.

Since h can be chosen arbitrarily, the notional size of a microstate is also arbitrary. Still, the value of h influences the offsets of quantities such as entropy and chemical potential, and so it is important to be consistent with the value of h when comparing different systems.

Correcting overcounting in phase space

Typically, the phase space contains duplicates of the same physical state in multiple distinct locations. This is a consequence of the way that a physical state is encoded into mathematical coordinates; the simplest choice of coordinate system often allows a state to be encoded in multiple ways. An example of this is a gas of identical particles whose state is written in terms of the particles' individual positions and momenta: when two particles are exchanged, the resulting point in phase space is different, and yet it corresponds to an identical physical state of the system. It is important in statistical mechanics (a theory about physical states) to recognize that the phase space is just a mathematical construction, and to not naively overcount actual physical states when integrating over phase space. Overcounting can cause serious problems:

• Dependence of derived quantities (such as entropy and chemical potential) on the choice of coordinate system, since one coordinate system might show more or less overcounting than another.
• Erroneous conclusions that are inconsistent with physical experience, as in the mixing paradox.
• Foundational issues in defining the chemical potential and the grand canonical ensemble.

It is in general difficult to find a coordinate system that uniquely encodes each physical state. As a result, it is usually necessary to use a coordinate system with multiple copies of each state, and then to recognize and remove the overcounting.

A crude way to remove the overcounting would be to manually define a subregion of phase space that includes each physical state only once and then exclude all other parts of phase space. In a gas, for example, one could include only those phases where the particles' x coordinates are sorted in ascending order. While this would solve the problem, the resulting integral over phase space would be tedious to perform due to its unusual boundary shape. (In this case, the factor C introduced above would be set to C = 1, and the integral would be restricted to the selected subregion of phase space.)

A simpler way to correct the overcounting is to integrate over all of phase space but to reduce the weight of each phase in order to exactly compensate the overcounting. This is accomplished by the factor C introduced above, which is a whole number that represents how many ways a physical state can be represented in phase space. Its value does not vary with the continuous canonical coordinates, so overcounting can be corrected simply by integrating over the full range of canonical coordinates, then dividing the result by the overcounting factor. However, C does vary strongly with discrete variables such as numbers of particles, and so it must be applied before summing over particle numbers.

As mentioned above, the classic example of this overcounting is for a fluid system containing various kinds of particles, where any two particles of the same kind are indistinguishable and exchangeable. When the state is written in terms of the particles' individual positions and momenta, then the overcounting related to the exchange of identical particles is corrected by using

${\displaystyle C=N_1!N_2!\dots N_s!.}$

This is known as "correct Boltzmann counting".

Ensembles in statistics

Main articles: Principle of maximum entropy and Markov random field

The formulation of statistical ensembles used in physics has now been widely adopted in other fields, in part because it has been recognized that the canonical ensemble or Gibbs measure serves to maximize the entropy of a system, subject to a set of constraints: this is the principle of maximum entropy. This principle has now been widely applied to problems in linguistics, robotics, and the like.

In addition, statistical ensembles in physics are often built on a principle of locality: that all interactions are only between neighboring atoms or nearby molecules. Thus, for example, lattice models, such as the Ising model, model ferromagnetic materials by means of nearest-neighbor interactions between spins. The statistical formulation of the principle of locality is now seen to be a form of the Markov property in the broad sense; nearest neighbors are now Markov blankets. Thus, the general notion of a statistical ensemble with nearest-neighbor interactions leads to Markov random fields, which again find broad applicability; for example in Hopfield networks.

Ensemble average

In statistical mechanics, the ensemble average is defined as the mean of a quantity that is a function of the microstate of a system, according to the distribution of the system on its micro-states in this ensemble.

Since the ensemble average is dependent on the ensemble chosen, its mathematical expression varies from ensemble to ensemble. However, the mean obtained for a given physical quantity does not depend on the ensemble chosen at the thermodynamic limit. The grand canonical ensemble is an example of an open system.

Classical statistical mechanics

For a classical system in thermal equilibrium with its environment, the ensemble average takes the form of an integral over the phase space of the system:

${\displaystyle \overline{A}=\frac{\int A{e}^{-\beta H(q_1,q_2,\dots ,q_M,p_1,p_2,\dots ,p_N)}d\tau }{\int e^{-\beta H(q_1,q_2,\dots ,q_M,p_1,p_2,\dots ,p_N)}d\tau },}$

where

${\displaystyle \overline{A}}$ is the ensemble average of the system property A,

${\displaystyle \beta }$ is ${\displaystyle \frac{1}{kT}}$, known as thermodynamic beta,

H is the Hamiltonian of the classical system in terms of the set of coordinates ${\displaystyle q_i}$ and their conjugate generalized momenta ${\displaystyle p_i}$,

${\displaystyle d\tau }$ is the volume element of the classical phase space of interest.

The denominator in this expression is known as the partition function and is denoted by the letter Z.

Quantum statistical mechanics

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In quantum statistical mechanics, for a quantum system in thermal equilibrium with its environment, the weighted average takes the form of a sum over quantum energy states, rather than a continuous integral:^{[clarification needed]}

${\displaystyle \overline{A}=\frac{\sum _i{A}_i{e}^{-\beta E_i}}{\sum _i{e}^{-\beta E_i}}.}$

Canonical ensemble average

The generalized version of the partition function provides the complete framework for working with ensemble averages in thermodynamics, information theory, statistical mechanics and quantum mechanics.

The microcanonical ensemble represents an isolated system in which energy (E), volume (V) and the number of particles (N) are all constant. The canonical ensemble represents a closed system which can exchange energy (E) with its surroundings (usually a heat bath), but the volume (V) and the number of particles (N) are all constant. The grand canonical ensemble represents an open system which can exchange energy (E) and particles (N) with its surroundings, but the volume (V) is kept constant.

Operational interpretation

In the discussion given so far, while rigorous, we have taken for granted that the notion of an ensemble is valid a priori, as is commonly done in physical context. What has not been shown is that the ensemble itself (not the consequent results) is a precisely defined object mathematically. For instance,

• It is not clear where this very large set of systems exists (for example, is it a gas of particles inside a container?)
• It is not clear how to physically generate an ensemble.

In this section, we attempt to partially answer this question.

Suppose we have a preparation procedure for a system in a physics lab: For example, the procedure might involve a physical apparatus and some protocols for manipulating the apparatus. As a result of this preparation procedure, some system is produced and maintained in isolation for some small period of time. By repeating this laboratory preparation procedure we obtain a sequence of systems X₁, X₂, ...,X_k, which in our mathematical idealization, we assume is an infinite sequence of systems. The systems are similar in that they were all produced in the same way. This infinite sequence is an ensemble.

In a laboratory setting, each one of these prepped systems might be used as input for one subsequent testing procedure. Again, the testing procedure involves a physical apparatus and some protocols; as a result of the testing procedure we obtain a yes or no answer. Given a testing procedure E applied to each prepared system, we obtain a sequence of values Meas (E, X₁), Meas (E, X₂), ..., Meas (E, X_k). Each one of these values is a 0 (or no) or a 1 (yes).

Assume the following time average exists:

${\displaystyle \sigma (E)=\underset{N\to \mathrm{\infty }}{lim}\frac{1}{N}\sum _{k=1}^N\mathrm{Meas}(E,X_k)}$

For quantum mechanical systems, an important assumption made in the quantum logic approach to quantum mechanics is the identification of yes–no questions to the lattice of closed subspaces of a Hilbert space. With some additional technical assumptions one can then infer that states are given by density operators S so that:

${\displaystyle \sigma (E)=\mathrm{Tr}(ES).}$

We see this reflects the definition of quantum states in general: A quantum state is a mapping from the observables to their expectation values.

Sterilization law in the United States

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

Sterilization law is the area of law, that concerns a person's purported right to choose or refuse reproductive sterilization and when a given government may limit it. In the United States, it is typically understood to touch on federal and state constitutional law, statutory law, administrative law, and common law. This article primarily focuses on laws concerning compulsory sterilization that have not been repealed or abrogated, i.e. are still good laws, in whole or in part, in each jurisdiction.

Federal law

U.S. Supreme Court

"We have seen more than once that the public welfare may call upon the best citizens for their lives. It would be strange if it could not call upon those who already sap the strength of the State for these lesser sacrifices, often not felt to be such by those concerned, in order to prevent our being swamped with incompetence. It is better for all the world if, instead of waiting to execute degenerate offspring for crime or to let them starve for their imbecility, society can prevent those who are manifestly unfit from continuing their kind. The principle that sustains compulsory vaccination is broad enough to cover cutting the Fallopian tubes. [...] Three generations of imbeciles are enough."

U.S. Supreme Court Justice Oliver Wendell Holmes, Jr. in his infamous 1927 court opinion.

In Buck v. Bell, the United States Supreme Court ruled in a majority opinion written by Justice Oliver Wendell Holmes Jr. that a state statute that authorized compulsory sterilization of the unfit, including the intellectually disabled, "for the protection and health of the state" did not violate the Due Process clause of the Fourteenth Amendment to the United States Constitution.

In Skinner v. State of Oklahoma, the United States Supreme Court ruled that an Oklahoma compulsory sterilization law that applied to "habitual criminals" but exempted those convicted of white-collar crimes violated the Equal Protection Clause of the 14th Amendment.

Stump v. Sparkman (1978) is the leading United States Supreme Court decision on judicial immunity. It involved an Indiana judge who was sued by a young woman who had been sterilized without her knowledge as a minor in accordance with the judge's order. The Supreme Court held that the judge was immune from being sued for issuing the order because it was issued as a judicial function. The case has been called one of the most controversial in recent Supreme Court history.

U.S. District and Appellate Courts

In 2007 the United States Court of Appeals for the District of Columbia Circuit heard Doe ex. rel. Tarlow v. District of Columbia. The Court upheld a 2003 District of Columbia statute that stated the conditions for authorizing a non-emergency surgical procedure on a mentally incompetent person. Under the Appellate Court's interpretation of the statute, a court located in the District of Columbia, must apply the "best interest of the patient" standard to a person who was never competent, and the court must apply the "known wishes of the patient" standard to a person who was once competent.

In the 2001 case of Vaughn v. Ruoff, a husband and wife sued three social workers for coercing his wife, "diagnosed as mildly retarded", into getting a sterilization as a condition for getting their children back from state custody. The United States Court of Appeals for the Eighth Circuit held that the social workers did not have sovereign immunity and could be sued for violating the couple's Fourteenth Amendment right because the procedural due process requirements for performing a sterilization are clearly established by Buck v. Bell and were not met in this case.

In 1975, in Cox v. Stanton, the United States Court of Appeals for the Fourth Circuit decided the statute of limitations for a lawsuit challenging the legality of a sterilization begins to accrue when the plaintiff discovers the sterilization.

Poe v. Lynchburg Training School & Hospital concerned whether or not patients who had been involuntarily sterilized in Lynchburg Training School and Hospital, a state mental institution in Virginia, as part of a program of eugenics in the early and mid-20th century had their constitutional rights violated.

United States Code

Under 22 United States Code section 2151b, foreign aid used for population planning and the combat of HIV, tuberculosis, and malaria may not be used to fund "a program of coercive abortion or involuntary sterilization.

Federal programs

Department of Veterans Affairs

The Veterans Health Administration or V.A. permits the sterilization of a patient, who is unable to give informed consent, if the guardian of the patient gives consent to the procedure; a witness, not associated with the V.A., witnesses the guardian signing the consent form; a healthcare committee completes a finding on the need for the procedure; and the Director of the facility approves of the procedure.

Federally Assisted Family Planning Projects

The Office of the Assistant Secretary for Health, Health Resources and Services Administration, National Institutes of Health, Centers for Disease Control, Alcohol, Drug Abuse and Mental Health Administration and all of their constituent agencies are only authorized to perform a sterilization on a patient if the individual is at least 21 years old, mentally competent, gave informed consent to the procedure, and at least 30 days but not more than 180 days passed since the individual gave consent to the procedure. "Programs or projects to which this subpart applies shall not perform or arrange for the performance of a sterilization of any mentally incompetent individual or institutionalized individual."

Indian Health Service

See also: Sterilization of Native American women

Indian Health Service (IHS) is an operating division within the United States Department of Health and Human Services. The IHS offers sterilization as a method of family planning. Tubal ligation and vasectomy are the only procedures which may be performed for the primary purpose of sterilization. The IHS requires for the patient to give informed consent to the operation, be at least 21 years of age, and not be institutionalized in a correctional or mental health facility.

Medicaid Services

A state plan must provide that a Medicaid agency will pay for the sterilization procedure if the individual is at least 21 years old, mentally competent, voluntarily gave informed consent to the procedure, and must be done for a purpose other than for "rendering the individual permanently incapable of reproducing." Medicaid will not pay "for the sterilization of a mentally incompetent or institutionalized individual."

State law

State sterilization laws are required to be in compliance with the United States Constitution.

Alabama

In 1935 Dr W. D. Partlow proposed a bill to sterilize those with hereditary "mental disease".

Alaska

In 1981 the Alaska Supreme Court held that an Alaskan Superior Court has the authority to order the sterilization of a "mental incompetent" person upon petition by their legal guardian if it is proven with clear and convincing evidence that sterilization is in the intellectually disabled person's best interest.

Arkansas

Arkansas Code section 20-49-101 to -207 provides the guidelines for sterilizing an incompetent patient.

In 1991, the Arkansas Supreme Court held the part of the Arkansas sterilization statute that allowed sterilization of an incompetent through direct medical channels, rather than approval from a court, to be unconstitutional because it denied the patient procedural due process. 

California

See also: Eugenics in California

See also: Madrigal v. Quilligan

In 2013, the 4th District Court of Appeal held that a developmentally disabled adult with "mild mental retardation" may be reproductively sterilized if the court determines there is clear and convincing evidence that the procedure is medically necessary for the patient. The court held that Probate Code section 2357 regulated the patients court order for medical treatment because the sterilization was incidental to acquiring medical care and not the purpose of the medical treatment; alternatively, Probate Code section 1950 et seq. applies when the objective is to prevent the patient from bearing children.

In 1978, a federal class action lawsuit was brought from Los Angeles County, California, involving the sterilization of Mexican American women. Most of the women were monolingual Spanish speakers and testified that they did not understand that the procedures they were undergoing would affect their ability to become pregnant or sustain a pregnancy.

In 1985, the Supreme Court of California held that a California statute that completely prohibits the sterilization of the developmentally disabled is overbroad and unconstitutional because a mentally incompetent person has a constitutional right to sterilization if a less intrusive method of birth control is not available.

The California Penal Code prohibits inmates from being sterilized unless the procedure is required to protect the life of the inmate or the procedure is necessary for treating a diagnosed condition and the patient gave consent to the procedure.

Colorado

Colorado Revised Statutes section 25.5-10-233 governs court-ordered sterilizations.

In 1981, the Colorado Supreme Court held that a district court may authorize the sterilization of a "mentally retarded person" if the court finds with clear and convincing evidence the procedure is medically essential. The Court defined "medically essential" as a procedure that is "clearly necessary, in the opinion of experts, to preserve the life or physical or mental health of the mentally retarded person.

In 1990, the Colorado Supreme Court held that a person "mentally incompetent to make some decisions is not necessarily incompetent . . . to grant or withhold consent to sterilization." Three members of the Court dissented from the majority opinion and stated that the "individual’s capacity to understand the risks of pregnancy and childbirth [should also be part of] the test for determining one’s competence to make a decision regarding sterilization."

Connecticut

A person unable to give informed consent may only be sterilized if a Connecticut Probate Court determines it is in the patient's best interest.

Delaware

Throughout its history, Delaware forcibly sterilized over 1,500 people. In October 2023, Delaware fully banned any form of forced sterilization. The repeal did not include an apology to the past victims.

Florida

A person unable to give informed consent may only be sterilized or given an abortion with specific authority from the court. The court must find clear and convincing evidence the person is unable to give consent and the procedure is in the best interest of the individual. The statute expressly states that these requirements "are procedural and do not establish any new or independent right to or authority" over the individual regarding abortion or sterilization.

A court may authorize for a surrogate to provide consent to the sterilization or abortion of another person, after the surrogate petitions the court, provides supporting documents on the intent of the patient, gives notice to all relevant parties, and a hearing is conducted to review the matter.

Under Florida statute § 985.18, delinquent children ordered by the court to undergo psychological or physical health exams may not be given a "permanent sterilization" unless the procedure is medically necessary "to protect or preserve the life of the child."

Georgia

Under Georgia Code, an incompetent person may be sterilized after a petition requesting sterilization is brought by the parents or guardians, two physicians examine the patient, the hospital in which the sterilization is to be performed approves of the sterilization, and after a hearing the judge finds by clear and convincing evidence the patient is a person subject to this code.

In 1983, the Supreme Court of Georgia held the Georgia sterilization code unconstitutional because it used the “preponderance of the evidence” standard, and a court order that permanently deprives a person of a fundamental right requires a judicial finding of “clear and convincing” evidence. Since this case, the Georgia legislature changed the code to require “clear and convincing” evidence in order to comply with the requirements of the Constitution.

Hawaii

The beginning of the Eugenics movement in the islands of Hawaii have been traced back to the early 1900s when a plan to sterilize all persons that were deemed “unfit” for procreation was uncovered. The group of unfit peoples included those of low income, Native Americans, deadly criminals, and those diagnosed as criminally insane. In 1950, sterilization of women after they give birth, if considered unfit to procreate, was happening. This kind of sterilization was found to have been happening on plantations. Doctors would say it was necessary for the mothers to stay healthy. As of 2010 there was a movement to pay “former and current drug users” approximately $200 to voluntarily be sterilized. This movement was named “Project Prevention.” This was created in order to prevent “medical disabilities” from being passed down from generation to generation. Project Prevention was very controversial with people claiming was, “promoting stereotypes and prejudices against pregnant women.”

Illinois

In 2008 the Illinois Appellate Court held that in determining a petition for the sterilization of an incompetent ward, a court should apply the substituted consent standard if there is clear and convincing evidence regarding how the ward would decide if the ward were competent; however, the court should apply the best interest of the patient standard if the ward's substituted judgment cannot be proven by clear and convincing evidence.

Indiana

In 1907, Indiana enacted the first sterilization law.

In 1983, the Indiana Supreme Court authorized for the sterilization of a mentally ill twelve-year-old girl who engaged in self-destructive behavior such as pulling her hair, biting herself, banging her head, ripping her skin with her fingernails, and resisting the "restraints in order to hurt her own body." The patient's parents and her doctors were both in agreement that a hysterectomy was necessary in order to prevent "hemorrhaging and infection, and possibly death" because the patient's excitement with her own blood may cause her "to induce bleeding by poking into her vagina or abdomen in an attempt to keep the blood flowing" once she develops her menstruation cycle. The Court held that a specific Indiana statute authorizing sterilization was not necessary in order to authorize the sterilization, the juvenile court had the authority to authorize sterilizations if there was clear and convincing evidence that the medical procedure was necessary, and in this case there was overwhelming evidence that the sterilization was medically necessary.

In 1990, the Indiana Court of Appeals held that an appointed guardian may consent to health care for an adult incapable of consenting if there is "clear and convincing evidence that the judicially appointed guardian brought the petition for sterilization in good faith and the sterilization is in the best interest of the incompetent adult." Judge Sullivan wrote a concurring opinion stating that he was not convinced that in this present case the sterilization was done for healthcare, and consequentially, the consent of the guardian is not a factor in considering the legality of the sterilization. According to Sullivan a sterilization of an incompetent requires "an evidentiary hearing, following which the court finds clear and convincing evidence that sterilization is in the best interests of the individual concerned.

In 2003, the Supreme Court of Indiana recognized the medical malpractice tort of "wrongful pregnancy" when a woman became pregnant after a failed sterilization procedure. The court decided that the damages may include the cost of the pregnancy but may not include the ordinary cost of raising the child.

Iowa

In 1988, the Iowa Supreme Court held that a district court has jurisdiction to authorize the sterilization of an incompetent person, even in the absence of an Iowa statute regulating sterilization.

In 2014, the Iowa Supreme Court held that court approval is required for the sterilization of an incompetent person.

Maine

Under Title 34 B Chapter 7 of the Maine Revised Statutes, also known as the "Due Process in Sterilization Act of 1982," a hearing and a District Court order authorizing the sterilization is required if the sterilization is sought for "A. Persons under age 18 years and not married or otherwise emancipated; B. Persons presently under public or private guardianship or conservatorship; C. Persons residing in a state institution providing care, treatment or security, or otherwise in state custody; or D. Persons from whom a physician could not obtain informed consent." The hearing to determine the patient's ability to give informed consent requires at least two disinterested experts in developmental disabilities or mental health, including at least one psychologist or psychiatrist to examine the person to determine competency. If the court determines the person is not competent to give informed consent the court will appoint at least three disinterested experts to examine the person for the beneficial or detrimental effects of sterilization. The sterilization may be authorized if the court determines with clear and convincing evidence that the sterilization is in the best interests of the patient and other methods of contraception are inappropriate or unworkable for the person.

In 1985, the Maine Supreme Judicial Court heard a petition from a mother requesting for the court to authorize the sterilization of her mentally incompetent daughter. The court held that it did have the authority to grant a petition for sterilization if it is proven with clear and convincing evidence the sterilization is in the best interest of the patient; however, in this case, the court did not grant the petition because the physicians did not state the patient was capable of reproducing.

Maryland

In 1982 the Maryland Court of Appeals held that circuit courts have the jurisdiction to hear a petition for the sterilization on an incompetent minor. The court may only approve of the petition for sterilization if it is proven with clear and convincing evidence that the "procedure is medically necessary to preserve the life or physical or mental health of the incompetent minor."

In Maryland, a minor has the same capacity as an adult to consent to the use of contraception other than sterilization.

Massachusetts

In 1982 the Appeals Court of Massachusetts held that a court of general jurisdiction has the authority to hear a petition to sterilize a mentally retarded person. The court stated that the court must use substituted consent to determine if the sterilization should be authorized, and "no sterilization is to be compelled on the basis of any State or parental interest."

In 1991 the Appeals Court affirmed the substituted consent standard and wrote that "the guardian's petition" to authorize an abortion for their borderline retarded daughter "should have been allowed."

In 2012 the Appeals Court overturned a decision by a lower court requiring a sterilization and abortion on a woman with "schizophrenia and/or schizoaffective disorder and bipolar mood disorder." The appellate court wrote that the lower court did not follow the due process requirements for a sterilization and the decision to require the abortion was not made using the substituted consent standard. The lower court judge later stated that she required the abortion because she believed that if the patient were healthy she "would elect to abort the pregnancy to protect her own well-being." Rima Kundnani wrote that this case shows how "proper standards must therefore be established to avoid judicial abuse and to protect the reproductive rights of mentally ill women."

Michigan

In 1998 the Michigan Supreme Court held that a probate court has jurisdiction to hear a petition by a guardian for authorization to consent to an extraordinary procedure, including sterilization, if the procedure is in the ward's best interest.

In 2022, Michigan voters passed Proposal 3, which amended the Constitution of Michigan to establish an individual right to reproductive freedom. Proposal 3 defines the right to reproductive freedom to include the right to make decisions about sterilization.

Minnesota

See also: Eugenics in Minnesota

The sterilization law passed in Minnesota in 1925 stated that anyone of any age that was determined to be “feeble minded” was legally able to be sterilized, with or without permission. Around 1930, Minnesota began to be known as “the most feeble minded-conscious” state because of the way they care for the mentally disabled. Out of the population, around 2,350 people were victimized by this sterilization. 519 of these victims were men and 1,831 were women. Throughout the 1930s, sterilization rates were high, but as the war broke out, it became less of a priority and rates dropped tremendously. 

Mississippi

As the 26th state to pass any kind of sterilization law, Mississippi began the first sterilization on an inmate. The people affected by this law were “persons who are afflicted with hereditary forms of insanity that are recurrent, idiocy, imbecility, feeble-mindedness or epilepsy.” Approximately three people every year from the year 1938 to the year 1941 were involuntarily sterilized. Mississippi is rated number eighteen for most sterilizations of all states in the United States.

Missouri

Laws considering sterilization in Missouri began by targeting criminals and slowly began to include people with any incurable disease, epilepsy, and eventually all with mental disabilities. Currently, one must be at least 21 years of age in order to be sterilized.

Montana

In total, 256 people were affected by sterilization in Montana. Around 74% of those people were women and 28% were men. These laws began in the early 1920s and peaked around the mid 1930s. They targeted the “idiots, feeble-minded, insane, and epileptics, who are inmates of state institutions.”

Nebraska

More than half of all people who were sterilized were deemed to be "mentally deficient." This sterilization was ended in 1963. 

Nevada

In the early 1900s, it was mandatory to sterilize all men by “means of vasectomy (but not castration)” if they were found to be guilty of child molestation. This law was not repealed until around 50 years later. 

New Hampshire

In 1980 the New Hampshire Supreme Court held that a probate court may approve a petition for the sterilization of an incompetent minor if a guardian ad litem is appointed to represent the minor and the court finds with clear and convincing evidence that the sterilization is in the best interest of the patient.

New Jersey

In 1980, the New Jersey Supreme Court held that a mentally disabled woman has the right to be sterilized under the privacy rights of both the New Jersey and Federal Constitutions; however, the incompetent must be represented by counsel and the court may only authorize the sterilization if there is clear and convincing evidence the sterilization is in the person's best interest.

In 2011, the New Jersey Division of Mental Health and Guardianship Advocacy brought an appeal to challenge the procedures the court followed to authorize the sterilization of a severely mentally disabled girl for reasons of medical necessity. The Division recommended more stringent procedures; however, the Superior Court dismissed the issue as moot because the girl was already sterilized.

New York

In 1983, the New York Supreme Court authorized the sterilization of an incompetent person. In 2002, a New York County Court authorized the sterilization of a woman with an intellectual disability who gave informed consent to the procedure.

North Carolina

Under North Carolina General Statutes § 35A-1245, a mentally ill or mentally retarded patient who is unable to give informed consent may be sterilized with an order of the clerk or court after the clerk appoints an attorney to represent the patient and the clerk determines the sterilization is "medically necessary and is not solely for the purpose of sterilization or for hygiene or convenience."

In 1985, the North Carolina Supreme Court held that a court has authority to authorize the sterilization of an incompetent person if the sterilization is in the best interest of the patient.

In 2013, the General Assembly of North Carolina passed an appropriations bill to give compensation, up to $50,000 per person, to individuals sterilized under the authority of the Eugenics Board of North Carolina. However, in 2016, a claimant was denied compensation for her involuntary sterilization because the sterilization did not occur under the authority of the Eugenics Board, so the Court was unable to allow compensation for the claimant.

North Dakota

In the early 1900s a law was passed allowing the sterilization of inmates and “so-called defectives, though it rarely happened with only thirty-nine known cases. Around ten years later, the law was deemed “invalid” because the basic human rights of each individual were not being accounted for. In a ten-year span, around 580 people were reported being sterilized. 

Ohio

Under Ohio statutory law, "no resident shall be subjected to sterilization without the resident's informed consent" except as provided in the statute.

In 2004 the Supreme Court of Ohio vacated part of a decision from a lower court that required for the defendant to make “all reasonable efforts to avoid conceiving another child” during his five-year probationary period.^[75]

Oregon

Under the Oregon Revised Statutes section 436.305, a court has the authority to order a sterilization on a patient who is unable to give informed consent if a hearing proves with clear and convincing evidence that the "sterilization is in the best interest of the individual. Under the statute, "Best interest” means that: (a) The individual is physically capable of procreating; (b) The individual is likely to engage in sexual activity at the present or in the near future under circumstances likely to result in pregnancy; (c) All less drastic alternative contraceptive methods, including supervision, education and training, have proved unworkable or inapplicable, or are medically contraindicated; (d) The proposed method of sterilization conforms with standard medical practice, is the least intrusive method available and appropriate, and can be carried out without unreasonable risk to the life and health of the individual; and (e) The nature and extent of the individual's disability, as determined by empirical evidence and not solely on the basis of standardized tests, renders the individual permanently incapable of caring for and raising a child, even with reasonable assistance."

In 1972, the Oregon Court of Appeals upheld the sterilization of a seventeen-year-old mentally ill girl with a history of sexual and physical abuse by her family. The Court based its decision on the recommendation of the State Board of Social Protection and the testimony of a psychiatrist who stated that the patient would never be able to provide parental guidance and judgment, saying, "she would never be able to provide the parental guidance and judgment which a child requires even though she might be able to master the skills necessary to take physical care of herself and a child." The psychiatrist "based this conclusion on the girl's lack of emotional control, her consistent low scores in areas of judgment on psychological tests, and the likelihood that she would abuse a child."

Pennsylvania

In 1993, the Superior Court of Pennsylvania held that a mentally incompetent patient may be sterilized without her informed consent if there is clear and convincing evidence the sterilization is in her best interest.

Rhode Island

It was not until the late 1900s that it became legal for “patients and doctors” to be sterilized by choice. Information regarding Rhode Island is difficult to find because proper records were never kept and most documentation was lost. Due to Rhode Island being a predominantly Catholic state, birth control such as sterilization was never made mandatory for any reason.

Tennessee

No sterilization laws were ever passed in Tennessee, though bills have been created. In the mid 1960s a bill was created to pass sterilization for mentally ill patients. Tennessee was a part of a series of surveys regarding mental stability in the southern states. An institution was then created for the “feeble-minded” as a result. Tennessee eventually supported said institution.

Texas

In 2012, Katie Barnhill wrote that minimal laws exists in Texas for courts and guardians to know what to do if a non-medically necessary sterilization is in the best interest of the mentally incompetent person. It was stated in the mid 1800s that those with “undesirable traits” such as those who come from low income or who are mentally ill should be sterilized. 

Vermont

Vermont does not have any kind of documentation regarding their sterilization laws open to the public. “Our understanding” of any laws that were created in regards to sterilization in this state is that all types of sterilization was completely voluntary. 

Virginia

See also: Virginia Sterilization Act of 1924

An act, passed by the General Assembly of Virginia in 1988 and amended in 2013, provides the procedural requirements necessary for a physician to lawfully sterilize a patient capable of giving informed consent and incapable of giving informed consent.

A physician may perform a sterilization procedure on a patient if the patient is capable of giving informed consent, the patient consents to the procedure in writing, and the physician explains the consequences of the procedure and alternative methods of contraception.

A court may authorize a physician to perform a sterilization on a mentally incompetent adult or child after the procedural requirements are met and the court finds with clear and convincing evidence the patient is or is likely to engage sexual activity, no other contraceptive is reasonably available, the patient's mental disability renders the patient permanently unable to care for a child, and the procedure conforms with medical standards.

Washington

In 1980, the mother of a mentally incompetent minor petitioned the court for an order authorizing the sterilization of the minor. The Washington Supreme Court held that the Washington Superior courts have authority under the Washington constitution to grant the sterilization; however, the mother failed to show with clear and convincing evidence the sterilization was in the best interest of the minor.

In 1991, the Washington Court of Appeals heard a petition for sterilization brought by the parents of an incompetent child named K.M. The Court held that the sterilization of a mentally incompetent patient can be constitutional; however, the incompetent must be represented by independent counsel and the attorney must take an adversarial role in defense of the incompetent’s reproductive rights. Two physicians testified in support of K.M.’s psychological need for sterilization, however; the Court held that K.M.'s attorney did not take an adversarial role because the physicians and witnesses should have been cross examined, and every argument in defense of K.M. should have made. The Appeals Court “remanded for a new hearing, with counsel appointed to represent K.M.”

The Ashley Treatment occurred in Washington state.

West Virginia

West Virginia allows sterilizations on competent non-minors who give informed consent to the procedure.

Wisconsin

Under section 54.25 of the Wisconsin Statutes, a court may determine that a person who was found incompetent has incapacity to consent to a sterilization procedure. The guardian may not provide substituted consent for the incompetent person, unless the court determines the "individual is competent to exercise the right under some but not all circumstances."

In 2001, the Wisconsin Supreme Court, in State v. Oakley, upheld a lower court's decision to impose a probation requirement that prohibited a man from having more children "unless he shows that he can support that child and his current children." The Court held that the condition was reasonably related to Oakley's rehabilitation and not overly broad because Oakley already had nine children and intentionally refused to pay child support, and Oakley was eligible for prison so the condition was less restrictive than prison. Additionally, the Court held that the restriction satisfies strict scrutiny since the restriction was narrowly tailored because Oakley could have not intentionally refused to pay child support, and the restriction met the State's compelling interest of having parents support their children.

Reproducibility

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Reproducibility

Reproducibility, closely related to replicability and repeatability, is a major principle underpinning the scientific method. For the findings of a study to be reproducible means that results obtained by an experiment or an observational study or in a statistical analysis of a data set should be achieved again with a high degree of reliability when the study is replicated. There are different kinds of replication but typically replication studies involve different researchers using the same methodology. Only after one or several such successful replications should a result be recognized as scientific knowledge.

Types of Reproducibility

There are different kinds of replication studies, each serving a unique role in scientific validation:

Direct Replication – The exact experiment or study is repeated under the same conditions to verify the original findings.

Conceptual Replication – A study tests the same hypothesis but uses a different methodology, materials, or population to see if the results hold in different contexts.

Computational Reproducibility – In data science and computational research, reproducibility requires making all datasets, code, and algorithms openly available so others can replicate the analysis and obtain the same results.

Importance of Reproducibility

Reproducibility serves several critical purposes in science:

Verification of Results – Confirms that findings are not due to random chance or errors.

Building Trust in Research – Scientists, policymakers, and the public rely on reproducible studies to make informed decisions. Advancing Knowledge – Establishes a strong foundation for future research by validating existing theories.

Avoiding Bias and Fraud – Helps detect false positives, publication bias, and data manipulation that could mislead the scientific community. Challenges in Achieving Reproducibility

Despite its importance, many studies fail reproducibility tests, leading to what is known as the replication crisis in fields like psychology, medicine, and social sciences. Some key challenges include:

Insufficient Data Sharing – Many researchers do not make raw data, code, or methodology openly available, making replication difficult. Small Sample Sizes – Studies with limited sample sizes may show results that do not generalize to larger populations.

Publication Bias – Journals tend to publish positive findings rather than null or negative results, leading to an incomplete scientific record. Complex Experimental Conditions – In some cases, small variations in laboratory settings, equipment, or researcher expertise can affect outcomes, making exact replication difficult.

Real-World Applications of Reproducibility

Medical Research – Reproducibility ensures that clinical trials and drug effectiveness studies produce reliable results before treatments reach the public.

AI and Machine Learning – Scientists emphasize reproducibility in AI by requiring open-source models and datasets to validate algorithm performance.

Climate Science – Climate models must be reproducible across different datasets and simulations to ensure accurate predictions of global warming.

Pharmaceutical Development – Drug discovery relies on reproducing experiments across multiple labs to ensure safety and efficacy.

Improving Reproducibility in Science

To enhance reproducibility, researchers and institutions can adopt several best practices:

Open Data and Code – Making datasets and computational methods publicly available ensures that others can verify results.

Registered Reports – Some scientific journals now accept studies based on pre-registered research plans, reducing bias.

Standardized Methods – Using well-documented, standardized experimental protocols helps ensure consistent results.

Independent Replication Studies – Funding agencies and journals should prioritize replication studies to strengthen scientific integrity.

With a narrower scope, reproducibility has been defined in computational sciences as having the following quality: the results should be documented by making all data and code available in such a way that the computations can be executed again with identical results.

In recent decades, there has been a rising concern that many published scientific results fail the test of reproducibility, evoking a reproducibility or replication crisis.

History

Boyle's air pump was, in terms of the 17th century, a complicated and expensive scientific apparatus, making reproducibility of results difficult.

The first to stress the importance of reproducibility in science was the Anglo-Irish chemist Robert Boyle, in England in the 17th century. Boyle's air pump was designed to generate and study vacuum, which at the time was a very controversial concept. Indeed, distinguished philosophers such as René Descartes and Thomas Hobbes denied the very possibility of vacuum existence. Historians of science Steven Shapin and Simon Schaffer, in their 1985 book Leviathan and the Air-Pump, describe the debate between Boyle and Hobbes, ostensibly over the nature of vacuum, as fundamentally an argument about how useful knowledge should be gained. Boyle, a pioneer of the experimental method, maintained that the foundations of knowledge should be constituted by experimentally produced facts, which can be made believable to a scientific community by their reproducibility. By repeating the same experiment over and over again, Boyle argued, the certainty of fact will emerge.

The air pump, which in the 17th century was a complicated and expensive apparatus to build, also led to one of the first documented disputes over the reproducibility of a particular scientific phenomenon. In the 1660s, the Dutch scientist Christiaan Huygens built his own air pump in Amsterdam, the first one outside the direct management of Boyle and his assistant at the time Robert Hooke. Huygens reported an effect he termed "anomalous suspension", in which water appeared to levitate in a glass jar inside his air pump (in fact suspended over an air bubble), but Boyle and Hooke could not replicate this phenomenon in their own pumps. As Shapin and Schaffer describe, "it became clear that unless the phenomenon could be produced in England with one of the two pumps available, then no one in England would accept the claims Huygens had made, or his competence in working the pump". Huygens was finally invited to England in 1663, and under his personal guidance Hooke was able to replicate anomalous suspension of water. Following this Huygens was elected a Foreign Member of the Royal Society. However, Shapin and Schaffer also note that "the accomplishment of replication was dependent on contingent acts of judgment. One cannot write down a formula saying when replication was or was not achieved".

The philosopher of science Karl Popper noted briefly in his famous 1934 book The Logic of Scientific Discovery that "non-reproducible single occurrences are of no significance to science". The statistician Ronald Fisher wrote in his 1935 book The Design of Experiments, which set the foundations for the modern scientific practice of hypothesis testing and statistical significance, that "we may say that a phenomenon is experimentally demonstrable when we know how to conduct an experiment which will rarely fail to give us statistically significant results". Such assertions express a common dogma in modern science that reproducibility is a necessary condition (although not necessarily sufficient) for establishing a scientific fact, and in practice for establishing scientific authority in any field of knowledge. However, as noted above by Shapin and Schaffer, this dogma is not well-formulated quantitatively, such as statistical significance for instance, and therefore it is not explicitly established how many times must a fact be replicated to be considered reproducible.

Terminology

Replicability and repeatability are related terms broadly or loosely synonymous with reproducibility (for example, among the general public), but they are often usefully differentiated in more precise senses, as follows.

Two major steps are naturally distinguished in connection with reproducibility of experimental or observational studies: When new data is obtained in the attempt to achieve it, the term replicability is often used, and the new study is a replication or replicate of the original one. Obtaining the same results when analyzing the data set of the original study again with the same procedures, many authors use the term reproducibility in a narrow, technical sense coming from its use in computational research. Repeatability is related to the repetition of the experiment within the same study by the same researchers. Reproducibility in the original, wide sense is only acknowledged if a replication performed by an independent researcher team is successful.

The terms reproducibility and replicability sometimes appear even in the scientific literature with reversed meaning, as different research fields settled on their own definitions for the same terms.

Measures of reproducibility and repeatability

In chemistry, the terms reproducibility and repeatability are used with a specific quantitative meaning. In inter-laboratory experiments, a concentration or other quantity of a chemical substance is measured repeatedly in different laboratories to assess the variability of the measurements. Then, the standard deviation of the difference between two values obtained within the same laboratory is called repeatability. The standard deviation for the difference between two measurement from different laboratories is called reproducibility. These measures are related to the more general concept of variance components in metrology.

Reproducible research

Reproducible research method

The term reproducible research refers to the idea that scientific results should be documented in such a way that their deduction is fully transparent. This requires a detailed description of the methods used to obtain the data and making the full dataset and the code to calculate the results easily accessible. This is the essential part of open science.

To make any research project computationally reproducible, general practice involves all data and files being clearly separated, labelled, and documented. All operations should be fully documented and automated as much as practicable, avoiding manual intervention where feasible. The workflow should be designed as a sequence of smaller steps that are combined so that the intermediate outputs from one step directly feed as inputs into the next step. Version control should be used as it lets the history of the project be easily reviewed and allows for the documenting and tracking of changes in a transparent manner.

A basic workflow for reproducible research involves data acquisition, data processing and data analysis. Data acquisition primarily consists of obtaining primary data from a primary source such as surveys, field observations, experimental research, or obtaining data from an existing source. Data processing involves the processing and review of the raw data collected in the first stage, and includes data entry, data manipulation and filtering and may be done using software. The data should be digitized and prepared for data analysis. Data may be analysed with the use of software to interpret or visualise statistics or data to produce the desired results of the research such as quantitative results including figures and tables. The use of software and automation enhances the reproducibility of research methods.

There are systems that facilitate such documentation, like the R Markdown language or the Jupyter notebook. The Open Science Framework provides a platform and useful tools to support reproducible research.

Reproducible research in practice

Psychology has seen a renewal of internal concerns about irreproducible results (see the entry on replicability crisis for empirical results on success rates of replications). Researchers showed in a 2006 study that, of 141 authors of a publication from the American Psychological Association (APA) empirical articles, 103 (73%) did not respond with their data over a six-month period. In a follow-up study published in 2015, it was found that 246 out of 394 contacted authors of papers in APA journals did not share their data upon request (62%). In a 2012 paper, it was suggested that researchers should publish data along with their works, and a dataset was released alongside as a demonstration. In 2017, an article published in Scientific Data suggested that this may not be sufficient and that the whole analysis context should be disclosed.

In economics, concerns have been raised in relation to the credibility and reliability of published research. In other sciences, reproducibility is regarded as fundamental and is often a prerequisite to research being published, however in economic sciences it is not seen as a priority of the greatest importance. Most peer-reviewed economic journals do not take any substantive measures to ensure that published results are reproducible, however, the top economics journals have been moving to adopt mandatory data and code archives. There is low or no incentives for researchers to share their data, and authors would have to bear the costs of compiling data into reusable forms. Economic research is often not reproducible as only a portion of journals have adequate disclosure policies for datasets and program code, and even if they do, authors frequently do not comply with them or they are not enforced by the publisher. A Study of 599 articles published in 37 peer-reviewed journals revealed that while some journals have achieved significant compliance rates, significant portion have only partially complied, or not complied at all. On an article level, the average compliance rate was 47.5%; and on a journal level, the average compliance rate was 38%, ranging from 13% to 99%.

A 2018 study published in the journal PLOS ONE found that 14.4% of a sample of public health statistics researchers had shared their data or code or both.

There have been initiatives to improve reporting and hence reproducibility in the medical literature for many years, beginning with the CONSORT initiative, which is now part of a wider initiative, the EQUATOR Network. This group has recently turned its attention to how better reporting might reduce waste in research, especially biomedical research.

Reproducible research is key to new discoveries in pharmacology. A Phase I discovery will be followed by Phase II reproductions as a drug develops towards commercial production. In recent decades Phase II success has fallen from 28% to 18%. A 2011 study found that 65% of medical studies were inconsistent when re-tested, and only 6% were completely reproducible.

Noteworthy irreproducible results

Hideyo Noguchi became famous for correctly identifying the bacterial agent of syphilis, but also claimed that he could culture this agent in his laboratory. Nobody else has been able to produce this latter result.

In March 1989, University of Utah chemists Stanley Pons and Martin Fleischmann reported the production of excess heat that could only be explained by a nuclear process ("cold fusion"). The report was astounding given the simplicity of the equipment: it was essentially an electrolysis cell containing heavy water and a palladium cathode which rapidly absorbed the deuterium produced during electrolysis. The news media reported on the experiments widely, and it was a front-page item on many newspapers around the world (see science by press conference). Over the next several months others tried to replicate the experiment, but were unsuccessful.

Nikola Tesla claimed as early as 1899 to have used a high frequency current to light gas-filled lamps from over 25 miles (40 km) away without using wires. In 1904 he built Wardenclyffe Tower on Long Island to demonstrate means to send and receive power without connecting wires. The facility was never fully operational and was not completed due to economic problems, so no attempt to reproduce his first result was ever carried out.

Other examples which contrary evidence has refuted the original claim:

• N-rays, a hypothesized form of radiation subsequently found to be illusory
• Polywater, a hypothesized polymerized form of water found to be just water with common contaminations
• Stimulus-triggered acquisition of pluripotency, revealed to be the result of fraud
• GFAJ-1, a bacterium that could purportedly incorporate arsenic into its DNA in place of phosphorus
• MMR vaccine controversy — a study in The Lancet claiming the MMR vaccine caused autism was revealed to be fraudulent
• Schön scandal — semiconductor "breakthroughs" revealed to be fraudulent
• Power posing — a social psychology phenomenon that went viral after being the subject of a very popular TED talk, but was unable to be replicated in dozens of studies

Pre-existence

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Pre-existence

God resting after creation – Christ depicted as the creator of the world prior to his incarnation as Jesus, Byzantine mosaic in Monreale, Sicily.

Pre-existence, premortal existence, beforelife, or life before birth, is the belief that each individual human soul existed before mortal conception, and at some point before birth enters or is placed into the body. Concepts of pre-existence can encompass either the belief that the soul came into existence at some time prior to conception or the belief that the soul is eternal. Alternative positions are traducianism and creationism, which both hold that the individual human soul does not come into existence until conception or later. It is to be distinguished from preformation, which is about physical existence and applies to all living things.

Ancient Greek thought

Further information: Metempsychosis

Plato believed in the pre-existence of the soul, which tied in with his innatism. He thought that we are born with knowledge from a previous life that is subdued at birth and must be relearned. He saw all attainment of knowledge not as acquiring new information, but as remembering previously known information.

Baha'i Faith

Baháʼí literature refers in a number of places to at least four key dimensions of pre-existence. Firstly, that the individual soul of a human being comes into being at the time of conception and only thereafter is eternal; in other words, it is not pre-existent. Secondly, in distinction to the above, that the souls of the world's greatest spiritual teachers, the founders of world religions, are pre-existent. Thirdly, that God, a reality which human consciousness can not comprehend, is pre-existent, that is he exists prior to time and to his creation. Fourthly, that the relationship between God and the phenomenal or contingent world is one of emanation, as the rays of the sun are to the earth. In other words, the pre-existent world of God remains separate from and does not descend into his creation.

Buddhism

In Buddhist cosmology, saṃsāra is the cycle of life and death. When a person dies in earth its human soul is born into the Naraka (underworld or the "purgatories" of the souls) and afterwards it is reborn on earth. Yama, a dharmapala (wrathful god), is said to judge the dead and preside over the Narakas and the cycle.

A being is born into a Naraka as a direct result of its accumulated actions (karma) and resides there for a finite period of time (it varies from hundreds of millions to sextillions of years, but these periods are equivalent to hours or even years in earth time) until that karma has achieved its full result. After its karma is used up, it will be reborn in one of the higher worlds as the result of karma that had not yet ripened. The cycle is completed or finished when the soul reach the Nirvana.

Chinese mythology

In Chinese mythology, the Naihe Bridge (奈何桥), also called the Bridge of Forgetfulness, connects earth with the Diyu ("earth prison"), that is the realm of the dead or purgatory. It is typically depicted as a subterranean maze with various levels and chambers, to which souls are taken after death to atone for the sins they committed when they were alive. The number of levels in Diyu it is said to be three, four, ten or even Eighteen "courts", each of which is ruled by a judge, collectively known as the Yama Kings. The god of the dead is King Yan, it oversees the kings of the courts. Ox-Head and Horse-Face are the guardians of Diyu, and their role is the capture of human souls who have died and bring them before the courts of Hell, where they are rewarded or punished based on the actions performed in their lifetime. Legend has it that the dead who have committed serious sins in life cannot cross the Naihe Bridge and will be pushed into the "Blood River Pool" by Ox-Head and Horse-Face to suffer the torture of insects, ants and snakes, while the dead who have done good deeds will be able to cross the bridge very easily.

The goddess of forgetfulness, Meng Po, serves Meng Po Soup (孟婆汤) on the Naihe Bridge. This soup wipes the memory of the persons before they cross the bridge so they can reincarnate into their next life without the burdens of the previous life. She awaits the dead souls at the entrance of the 9th round (Fengdu). In some variations she is referred as Lady Meng Jiang

Christianity

See also: Pre-existence of Christ

A concept of pre-existence was advanced by Origen, a second and third-century church father. Origen believed that each human soul was created by God at some time prior to conception. He wrote that already "one of [his] predecessors" had interpreted the Scripture to teach pre-existence, which seems to be a reference to the Jewish philosopher Philo.

Some scholars, including John Behr and Marguerite Harl, argue that this idea, condemned by the church, may have been taught by some later Origenists, but that Origen himself was orthodox in this regard and "never used the terms 'pre-existence of souls' or 'pre-existent intellects', and that Origen was talking about realities outside of time and not about any concept of temporality before our time. Such orthodox understandings of Origen also show up in Maximus the Confessor and in the idea of an atemporal fall as taught by Christian theologians Sergei Bulgakov and David Bentley Hart.

Church Fathers Tertullian and Jerome held to traducianism and creationism, respectively, and pre-existence was condemned as heresy in the Second Council of Constantinople in AD 553.

Origen referenced Romans 9:11-14 as evidence for his position:

For the children being not yet born, neither having done any good or evil, that the purpose of God according to election might stand, not of works, but of him that calleth; It was said unto her, The elder shall serve the younger. As it is written, Jacob have I loved, but Esau have I hated. What shall we say then? Is there unrighteousness with God? God forbid.

— "Romans 9: 11-14".

Origen argued that God could not love Jacob and hate Esau until Jacob had done something worthy of love and Esau had done something worthy of hatred and so the passage means only that Jacob and Esau had not yet done good or evil in this life and their conduct before this life was the reason why Esau would serve Jacob.

Origen also referenced Jeremiah 1:5:

Before I formed thee in the belly, I knew thee; and before thou camest forth out of the womb, I sanctified thee, and I ordained thee a prophet unto the nations.

He brought forth a question:

How could his soul and its images be formed along with his body, who, before he was created in the womb, is said to be known to God, and was sanctified by Him before his birth?

Those who reject pre-existence, which would be every Christian denomination that accepts the conclusions of the Second Council of Constantinople (i.e., all Catholics and Eastern Orthodox Christians and many Protestants), simply see Jeremiah 1:5 as another passage about God's foreknowledge. This ecumenical Council explicitly stated "If anyone asserts the fabulous pre-existence of souls, and shall assert the monstrous restoration which follows from it: let him be anathema."

Latter-day Saints

Main article: Premortal life (Latter Day Saints)

See also: Mormon cosmology § Pre-mortality, and Plan of salvation (Latter Day Saints) § Premortal life

The concept of premortal life is an early and fundamental doctrine of Mormonism. In the faith's eponymous text, the Book of Mormon, published on March 26, 1830, the premortal spirit of Christ appears in human form and explains that individuals were created in the beginning in the image of Christ. In 1833, early in the Latter Day Saint movement, its founder Joseph Smith taught that human souls are co-eternal with God the Father just as Jesus is co-eternal with God the Father, "Man was also in the beginning with God. Intelligence, or the light of truth, was not created or made, neither indeed can be."

After Smith's death, the doctrine of premortal life was elaborated by some other leaders within the Church of Jesus Christ of Latter-day Saints (LDS Church). Although the mind and intelligence of humanity were still considered to be co-eternal with God, and not created, Brigham Young taught that the spirit was different from the mind or intelligence, resolving the seeming conflict between Book of Mormon verses indicating God was creator and Smith's later teaching that all individuals were co-eternal with God. Young postulated that we each had a pre-spirit intelligence that later became part of a spirit body, which then eventually entered a physical body and was born on earth.

The LDS Church teaches that during the premortal life, there was a learning process which eventually led to the next necessary step in the premortal spirits' opportunity to progress. This next step included the need to gain a physical body that could experience pain, sorrow and joy and "walk by faith". According to this belief, these purposes were explained and discussed in councils in heaven, followed by the War in Heaven where Satan rebelled against the plan of Heavenly Father.

Hinduism

In the Bhagavad Gita, considered by Hindus to be a most holy scripture, Krishna tells Arjuna; "Never was there a time when I did not exist, nor you, nor all these kings; nor in the future shall any of us cease to be." Hinduism teaches reincarnation. Consequently, everyone has pre-existed in another form.

Islam

In Islam, all souls are believed to have been created in adult form before earthly life at the same time the God created the father of mankind, Adam. The Qur'an recounts the story of when the descendants of Adam were brought forth before God to testify that God alone is the Lord of creation and so only God is worthy of worship and so on the Day of Judgement, people cannot use the excuse that they worshipped others only because they were following the ways of their ancestors. Humans do not remember, as they are born with an undeveloped mind (leaving only an innate awareness that God exists and is one, known as the Fitra), and God decreed when every human would be born into the physical world.