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Anhedonia

Anhedonia is a diverse array of deficits in hedonic function, including reduced motivation or ability to experience pleasure. While earlier definitions emphasized the inability to experience pleasure, anhedonia is currently used by researchers to refer to reduced motivation, reduced anticipatory pleasure (wanting), reduced consummatory pleasure (liking), and deficits in reinforcement learning. In the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5), anhedonia is a component of depressive disorders, substance-related disorders, psychotic disorders, and personality disorders, where it is defined by either a reduced ability to experience pleasure, or a diminished interest in engaging in previously pleasurable activities. While the International Statistical Classification of Diseases and Related Health Problems, Tenth Revision (ICD-10) does not explicitly mention anhedonia, the depressive symptom analogous to anhedonia as described in the DSM-5 is a loss of interest or pleasure.

Definition
While anhedonia was originally defined in 1896 by Théodule-Armand Ribot as the reduced ability to experience pleasure, it has been used to refer to deficits in multiple facets of reward. Re-conceptualizations of anhedonia highlight the independence of "wanting" and "liking". "Wanting" is a component of anticipatory positive affect, mediating both the motivation (i.e. incentive salience) to engage with reward, as well as the positive emotions associated with anticipating a reward. "Liking", on the other hand, is associated with the pleasure derived from consuming a reward. The consciousness of reward-related processes has also been used to categorize reward in the context of anhedonia, as studies comparing implicit behavior versus explicit self-reports demonstrate a dissociation of the two. Learning has also been proposed as an independent facet of reward that may be impaired in conditions associated with anhedonia, but empirical evidence dissociating learning from either "liking" or "wanting" is lacking.

Anhedonia has also been used to refer to "affective blunting", "restricted range of affect", "emotional numbing", and "flat affect", particularly in the context of post-traumatic stress disorders. In PTSD patients, scales measuring these symptoms correlate strongly with scales that measure more traditional aspects of anhedonia, supporting this association.

Causes
Studies in clinical populations, healthy populations, and animal models have implicated a number of neurobiological substrates in anhedonia. Regions implicated in anhedonia include the prefrontal cortex as a whole, particularly the orbitofrontal cortex (OFC), the striatum, amygdala, anterior cingulate cortex (ACC), hypothalamus, and ventral tegmental area (VTA). Neuroimaging studies in humans have reported that deficits in consummatory aspects of reward are associated with abnormalities in the ventral striatum and medial prefrontal cortex, while deficits in anticipatory aspects of reward are related to abnormalities in hippocampal, dorsal ACC and prefrontal regions. These abnormalities are generally consistent with animal models, except for inconsistent findings with regard to the OFC. This inconsistency may be related to the difficulty in imaging the OFC due to its anatomical location, or the small number of studies performed on anhedonia; a number of studies have reported reduced activity in the OFC in schizophrenia and major depression, as well as a direct relationship between reduced activity and anhedonia. Researchers theorize that anhedonia may result from the breakdown in the brain's reward system, involving the neurotransmitter dopamine. Anhedonia can be characterised as "impaired ability to pursue, experience and/or learn about pleasure, which is often, but not always accessible to conscious awareness".

The conditions of akinetic mutism and negative symptoms are closely related. In akinetic mutism, a stroke or other lesion to the anterior cingulate cortex causes reduction in movement (akinetic) and speech (mutism).

Major depressive disorder
Anhedonia occurs in roughly 70% of people with a major depressive disorder. Anhedonia is a core symptom of major depressive disorder; therefore, individuals experiencing this symptom can be diagnosed with depression, even in the absence of low/depressed mood. The Diagnostic and Statistical Manual of Mental Disorders (DSM) describes a "lack of interest or pleasure", but these can be difficult to discern given that people tend to become less interested in things which do not give them pleasure. The DSM criterion of weight loss is probably related, and many individuals with this symptom describe a lack of enjoyment of food. They can portray any of the non-psychotic symptoms and signs of depression.

Schizophrenia
Anhedonia is one of the negative symptoms of schizophrenia. Although five domains are usually used to classify negative symptoms, factor analysis of questionnaires yield two factors, with one including deficits in pleasure and motivation. People with schizophrenia retrospectively report experiencing fewer positive emotions than healthy individuals. However, "liking" or consummatory pleasure, is intact in people with schizophrenia, as they report experiencing the same degree of positive affect when presented with rewarding stimuli. Neuroimaging studies support this behavioral observation, as most studies report intact responses in the reward system (i.e. ventral striatum, VTA) to simple rewards. However, studies on monetary rewards sometimes report reduced responsiveness. More consistent reductions are observed with regard to emotional response during reward anticipation, which is reflected in a reduced responsiveness of both cortical and subcortical components of the reward system. Schizophrenia is associated with reduced positive prediction errors (a normal pattern of response to an unexpected reward), which a few studies have demonstrated to be correlated with negative symptoms. People with schizophrenia demonstrate impairment in reinforcement learnings tasks only when the task requires explicit learning, or is sufficiently complex. Implicit reinforcement learning, on the other hand, is relatively intact. These deficits may be related to dysfunction in the ACC, OFC and dlPFC leading to abnormal representation of reward and goals.

Substance-related disorders
Anhedonia is common in people who are dependent upon any one or more of a wide variety of drugs, including alcohol, opioids, cannabinoids, and nicotine. Although anhedonia becomes less severe over time, it is a significant predictor of relapse.

Post-traumatic stress disorder
While PTSD is associated with reduced motivation, part of the anticipatory "wanting", it is also associated with elevated sensation seeking, and no deficits in physiological arousal, or self reported pleasure to positive stimuli. PTSD is also associated with blunted affect, which may be due to the high comorbidity with depression.

Parkinson's disease
Anhedonia occurs frequently in Parkinson's disease, with rates between 7%–45% being reported. Whether or not anhedonia is related to the high rates of depression in Parkinson's disease is unknown.

Bipolar depression
Anhedonia is also reported to appear in people with bipolar depression.

Attention deficit hyperactivity disorder
Anhedonia may be associated with ADHD. Impairments of dopaminergic and serotonergic function in the brain of those with ADHD result in dysregulation of reward processing which can lead to anhedonia.

Sexual anhedonia
Sexual anhedonia in males is also known as 'ejaculatory anhedonia'. This condition means that a male will ejaculate with no accompanying sense of pleasure.

The condition is most frequently found in males, but females can experience lack of pleasure when the body goes through the orgasm process as well.

Sexual anhedonia may be caused by:
 * Hyperprolactinaemia
 * Hypoactive sexual desire disorder (HSDD), also called inhibited sexual desire
 * Low levels of the hormone testosterone
 * Spinal cord injury
 * Multiple sclerosis
 * Use of SSRI antidepressants or having used SSRI antidepressants in the past.
 * Use (or previous use) of antidopaminergic neuroleptics (anti-psychotics)
 * Fatigue
 * Physical illness

It is very uncommon that a neurological examination and blood tests can determine the cause of a specific case of sexual anhedonia.

Patients may be prescribed sustained-release bupropion to aid in treatment, which has been shown to relieve sexual dysfunction even in patients without depression.

Definition
Social anhedonia is defined as a disinterest in social contact and a lack of pleasure in social situations, and is characterized by social withdrawal. This characteristic typically manifests as an indifference to other people. In contrast to introversion, a nonpathological dimension of human personality, social anhedonia represents a deficit in the ability to experience pleasure. Additionally, social anhedonia differs from social anxiety in that social anhedonia is predominantly typified by diminished positive affect, while social anxiety is distinguished by both decreased positive affect and exaggerated negative affect.

This trait is currently seen as a central characteristic, as well as a predictor, of schizophrenia spectrum disorders. It is also widely linked to autism spectrum disorder.

Signs and symptoms

 * Decreased ability to experience interpersonal pleasure
 * Social withdrawal/isolation
 * Decreased capacity for social contact and interaction
 * Lack of close friends and intimate relationships, and decreased quality of those relationships
 * Poor social adjustment
 * Decreased positive affect
 * Flat affect
 * Depressed mood
 * State-related anxiety

Background and early clinical observation
The term anhedonia is derived from the Greek an-, "without" and hēdonē, "pleasure". Interest in the nature of pleasure and its absence dates back to ancient Greek philosophers such as Epicurus. The symptoms of anhedonia were introduced to the realm of psychopathology in 1809 by John Haslam, who characterized a patient with schizophrenia as indifferent to "those objects and pursuits which formerly proved sources of delight and instruction". The concept was formally coined by Théodule-Armand Ribot and later used by psychiatrists Paul Eugen Bleuler and Emil Kraepelin to describe a core symptom of schizophrenia. In particular, Sandor Rado postulated that schizotypes, or individuals with the schizophrenic phenotype, have two key genetic deficits, one related to the ability to feel pleasure (anhedonia) and one related to proprioception. In 1962, Meehl furthered Rado's theory through the introduction of the concept of schizotaxia, a genetically driven neural integrative defect thought to give rise to the personality type of schizotypy. Loren and Jean Chapman further distinguished between two types of anhedonia: physical anhedonia, or a deficit in the ability to experience physical pleasure, and social, or a deficit in the ability to experience interpersonal pleasure.

Recent research suggests that social anhedonia may represent a prodrome of psychotic disorders. First-degree relatives of individuals with schizophrenia show elevated levels of social anhedonia, higher baseline scores of social anhedonia are associated with later development of schizophrenia. These findings provide support for the conjecture that it represents a genetic risk marker for schizophrenia-spectrum disorders.

Additionally, elevated levels of social anhedonia in patients with schizophrenia have been linked to poorer social functioning. Socially anhedonic individuals perform worse on a number of neuropsychological tests than non-anhedonic participants, and show similar physiological abnormalities seen in patients with schizophrenia.

Comorbidity
Anhedonia is present in several forms of psychopathology as well as autism spectrum disorder.

Depression
Social anhedonia is observed in both depression and schizophrenia. However, social anhedonia is a state related to the depressive episode and the other is a trait related to the personality construct associated with schizophrenia. These individuals both tend to score highly on self-report measures of social anhedonia. Blanchard, Horan, and Brown demonstrated that, although both the depression and the schizophrenia patient groups can look very similar in terms of social anhedonia cross-sectionally, over time as individuals with depression experience symptom remission, they show fewer signs of social anhedonia, while individuals with schizophrenia do not. Blanchard and colleagues (2011) found individuals with social anhedonia also had elevated rates of lifetime mood disorders including depression and dysthymia compared to controls.

Social anxiety
As mentioned above, social anxiety and social anhedonia differ in important ways. However, social anhedonia and social anxiety are also often comorbid. People with social anhedonia may display increased social anxiety and be at increased risk for social phobias and generalized anxiety disorder. It has yet to be determined what the exact relationship between social anhedonia and social anxiety is, and if one potentiates the other. Individuals with social anhedonia may display increased stress reactivity, meaning that they feel more overwhelmed or helpless in response to a stressful event compared to control subjects who experience the same type of stressor. This dysfunctional stress reactivity may correlate with hedonic capacity, providing a potential explanation for the increased anxiety symptoms experienced in people with social anhedonia. In an attempt to separate out social anhedonia from social anxiety, the Revised Social Anhedonia Scale didn't include items that potentially targeted social anxiety. However, more research must be conducted on the underlying mechanisms through which social anhedonia overlaps and interacts with social anxiety. The efforts of the "social processes" RDoC initiative will be crucial in differentiating between these components of social behavior that may underlie mental illnesses such as schizophrenia.

Primary relevance in schizophrenia and schizophrenia spectrum disorders
Social anhedonia is a core characteristic of schizotypy, which is defined as a continuum of personality traits that can range from normal to disordered and contributes to risk for psychosis and schizophrenia. Social anhedonia is a dimension of both negative and positive schizotypy. It involves social and interpersonal deficits, but is also associated with cognitive slippage and disorganized speech, both of which fall into the category of positive schizotypy. Not all people with schizophrenia display social anhedonia and likewise, people who have social anhedonia may never be diagnosed with a schizophrenia-spectrum disorder if they do not have the positive and cognitive symptoms that are most frequently associated with most schizophrenia-spectrum disorders.

Social anhedonia may be a valid predictor of future schizophrenia-spectrum disorders; young adults with social anhedonia perform in a similar direction to schizophrenia patients in tests of cognition and social behavior, showing potential predictive validity. Social anhedonia usually manifests in adolescence, possibly because of a combination of the occurrence of critical neuronal development and synaptic pruning of brain regions important for social behavior and environmental changes, when adolescents are in the process of becoming individuals and gaining more independence.

Treatment
There is no validated treatment for social anhedonia. Future research should focus on genetic and environmental risk factors to home in on specific brain regions and neurotransmitters that may be implicated in social anhedonia's cause and could be targeted with medication or behavioral treatments. Social support may also play a valuable role in the treatment of social anhedonia. Blanchard et al. found that a greater number of social supports, as well as a greater perceived social support network, were related to fewer schizophrenia-spectrum symptoms and to better general functioning within the social anhedonia group. So far, no medicine has been developed to specifically target anhedonia.

Gender differences
In the general population, males score higher than females on measures of social anhedonia. This sex difference is stable throughout time (from adolescence into adulthood) and is also seen in people with schizophrenia-spectrum disorders. These results may reflect a more broad pattern of interpersonal and social deficits seen in schizophrenia-spectrum disorders. On average, males with schizophrenia are diagnosed at a younger age, have more severe symptoms, worse treatment prognosis, and a decrease in overall quality of life compared to females with the disorder. These results, coupled with the sex difference seen in social anhedonia, outline the necessity for research on genetic and hormonal characteristics that differ between males and females, and that may increase risk or resilience for mental illnesses such as schizophrenia.

Assessing social anhedonia
There are several self-report psychometric measures of schizotypy which each contain subscales related to social anhedonia:
 * Revised Social Anhedonia Scale – Chapman Psychosis Proneness Scales
 * No Close Friends Subscale – Schizotypal Personality Questionnaire
 * Introverted Anhedonia Subscale – Oxford–Liverpool Inventory of Feelings and Experiences

Genetic components
L.J. and J.P. Chapman were the first to discuss the possibility that social anhedonia may stem from a genetic vulnerability. The disrupted in schizophrenia 1 (DISC1) gene has been consistently associated with risk for, and cause of, schizophrenia-spectrum disorders and other mental illnesses. More recently, DISC1 has been associated with social anhedonia within the general population. Tomppo identified a specific DISC1 allele that is associated with an increase in characteristics of social anhedonia. They also identified a DISC1 allele associated with decreased characteristics of social anhedonia, that was found to be preferentially expressed in women. More research needs to be conducted, but social anhedonia may be an important intermediate phenotype (endophenotype) between genes associated with risk for schizophrenia and phenotype of the disorder.

Neurobiological correlates
Researchers studying the neurobiology of social anhedonia posit that this trait may be linked to dysfunction of reward-related systems in the brain. This circuitry is critical for the sensation of pleasure, the computation of reward benefits and costs, determination of the effort required to obtain a pleasant stimulus, deciding to obtain that stimulus, and increasing motivation to obtain the stimulus. In particular, the ventral striatum and areas of the prefrontal cortex (PFC), including the orbitofrontal cortex (OFC) and dorsolateral (dl) PFC, are critically involved in the experience of pleasure and the hedonic perception of rewards. With regards to neurotransmitter systems, opioid, gamma-Aminobutyric acid and endocannabinoid systems in the nucleus accumbens, ventral pallidum, and OFC mediate the hedonic perception of rewards. Activity in the PFC and ventral striatum have been found to be decreased in anhedonic individuals with major depressive disorder (MDD) and schizophrenia. However, schizophrenia may be less associated with decreased hedonic capacity and more with deficient reward appraisal.

Specific musical anhedonia
Recent studies have found people who do not have any issue processing musical tones or beat, yet receive no pleasure from listening to music. Specific musical anhedonia is distinct from melophobia, the fear of music.

title: Anhedonia


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Freiberg (district)

Freiberg is a former district in Saxony, Germany. It was bounded by (from the west and clockwise) the district of Mittlerer Erzgebirgskreis, the city of Chemnitz, the districts of Mittweida, Meißen and Weißeritzkreis, and by the Czech Republic.

History
The district was established in 1994 by merging the former districts of Freiberg, Brand-Erbisdorf and Flöha. In August 2008, as a part of the district reform in Saxony, the districts of Döbeln, Freiberg and Mittweida were merged into the new district Mittelsachsen.

Geography
The district was located on the northern slopes of the Ore Mountains. The largest river of the region is the Freiberger Mulde, which rises on Czech territory and from there runs northwards.

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

title: Freiberg (district)


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Instrumentalism

In philosophy of science and in epistemology, instrumentalism is a methodological view that ideas are useful instruments, and that the worth of an idea is based on how effective it is in explaining and predicting natural phenomena. According to instrumentalists, a successful scientific theory reveals nothing known either true or false about nature's unobservable objects, properties or processes. *Anjan Chakravartty,, §4 "Antirealism: Foils for scientific realism: §4.1: "Empiricism", in Edward N. Zalta, ed, The Stanford Encyclopedia of Philosophy, Summer 2013 edn: "Traditionally, instrumentalists maintain that terms for unobservables, by themselves, have no meaning; construed literally, statements involving them are not even candidates for truth or falsity. The most influential advocates of instrumentalism were the logical empiricists (or logical positivists), including Carnap and Hempel, famously associated with the Vienna Circle group of philosophers and scientists as well as important contributors elsewhere. In order to rationalize the ubiquitous use of terms which might otherwise be taken to refer to unobservables in scientific discourse, they adopted a non-literal semantics according to which these terms acquire meaning by being associated with terms for observables (for example, 'electron' might mean 'white streak in a cloud chamber'), or with demonstrable laboratory procedures (a view called 'operationalism'). Insuperable difficulties with this semantics led ultimately (in large measure) to the demise of logical empiricism and the growth of realism. The contrast here is not merely in semantics and epistemology: a number of logical empiricists also held the neo-Kantian view that ontological questions 'external' to the frameworks for knowledge represented by theories are also meaningless (the choice of a framework is made solely on pragmatic grounds), thereby rejecting the metaphysical dimension of realism (as in Carnap 1950)".

 * Samir Okasha, Philosophy of Science: A Very Short Introduction (New York: Oxford University Press, 2002), p. 62: "Strictly we should distinguish two sorts of anti-realism. According to the first sort, talk of unobservable entities is not to be understood literally at all.  So when a scientist pus forward a theory about electrons, for example, we should not take him to be asserting the existence of entities called 'electrons'.  Rather, his talk of electrons is metaphorical.  This form of anti-realism was popular in the first half of the 20th century, but few people advocate it today.  It was motivated largely by a doctrine in the philosophy of language, according to which it is not possible to make meaningful assertions about things that cannot in principle be observed, a doctrine that few contemporary philosophers accept.  The second sort of anti-realism accepts that talk of unobservable entities should be taken at face value: if a theory says that electrons are negatively charged, it is true if electrons do exist and are negatively charged, but false otherwise.  But we will never know which, says the anti-realist.  So the correct attitude towards the claims that scientists make about unobservable reality is one of total agnosticism.  They are either true or false, but we are incapable of finding out which.  Most modern anti-realism is of this second sort". Scientific theory is merely a tool whereby humans predict observations in a particular domain of nature by formulating laws, which state or summarize regularities, while theories themselves do not reveal supposedly hidden aspects of nature that somehow explain these laws.  Instrumentalism is a perspective originally introduced by Pierre Duhem in 1906.Roberto Torretti, The Philosophy of Physics (Cambridge: Cambridge University Press, 1999), pp. 242–43: "Like Whewell and Mach, Duhem was a practicing scientist who devoted an important part of his adult life to the history and philosophy of physics.  ...  His philosophy is contained in La théorie physique: son objet, sa structure [The Aim and Structure of Physical Theory] (1906), which may well be, to this day, the best overall book on the subject.  Its main theses, although quite novel when first put forward, have in the meantime become commonplace, so I shall review them summarily without detailed argument, just to associate them with his name.  But first I ought to say that neither in the first nor in the second (1914) edition of his book did Duhem take into account—or even so much as mention—the deep changes that were then taking place in physics.  Still, the subsequent success and current entrenchment of Duhem's ideas are due above all to their remarkable agreement with—and the light they throw on—the practice of mathematical physics in the twentieth century.  In the first part of La théorie physique, Duhem contrasts two opinions concerning the aim of physical theory.  For some authors, it ought to furnish 'the explanation of a set of experimentally established laws', while for others it is 'an abstract system whose aim is to summarize and logically classify a set of experimental laws, without pretending to explain these laws' (Duhem 1914, p. 3).  Duhem resolutely sides with the latter.  His rejection of the former rests on his understanding of 'explanation' ('explication' in French), which he expresses as follows: 'To explain, explicare, is to divest reality from the appearances which enfold it like veils, in order to see the reality face to face' (pp 3–4).  Authors in the first group expect from physics the true vision of things-in-themselves that religious myth and philosophical speculation have hitherto been unable to supply.  Their explanation makes no sense unless (i) there is, 'beneath the sense appearances revealed to us by our perceptions, [...] a reality different from these appearances' and (ii) we know 'the nature of the elements which constitute' that reality (p 7).  Thus, physical theory cannot explain—in the stated sense—the laws established by experiment unless it depends on metaphysics and thus remains subject to the interminable disputes of metaphysicians.  Worse still, the teachings of no metaphysical school are sufficiently detailed and precise to account for all of the elements of physical theory (p 18).  Duhem instead assigns to physical theories a more modest but autonomous and readily attainable aim: 'A physical theory is not an explanation.  It is a system of mathematical propositions, derived from a small number of principles, whose purpose is to represent a set of experimental laws as simply, as completely, and as exactly as possible (Duhem 1914, p. 24)".

Rejecting scientific realism's ambitions to uncover metaphysical truth about nature, instrumentalism is usually categorized as an antirealism, although its mere lack of commitment to scientific theory's realism can be termed nonrealism. Instrumentalism merely bypasses debate concerning whether, for example, a particle spoken about in particle physics is a discrete entity enjoying individual existence, or is an excitation mode of a region of a field, or is something else altogether. Instrumentalism holds that theoretical terms need only be useful to predict the phenomena, the observed outcomes.

There are multiple versions of instrumentalism.

British empiricism
Newton's theory of motion, whereby any object instantly interacts with all other objects across the universe, motivated the founder of British empiricism, John Locke, to speculate that matter is capable of thought. The next leading British empiricist, George Berkeley, argued that an object's putative primary qualities as recognized by scientists, such as shape, extension, and impenetrability, are inconceivable without the putative secondary qualities of color, hardness, warmth, and so on. He also posed the question how or why an object could be properly conceived to exist independently of any perception of it. Berkeley did not object to everyday talk about the reality of objects, but instead took issue with philosophers' talk, who spoke as if they knew something beyond sensory impressions that ordinary folk did not.

For Berkeley, a scientific theory does not state causes or explanations, but simply identifies perceived types of objects and traces their typical regularities. Berkeley thus anticipated the basis of what Auguste Comte in the 1830s called positivism, although Comtean positivism added other principles concerning the scope, method, and uses of science that Berkeley would have disavowed. Berkeley also noted the usefulness of a scientific theory having terms that merely serve to aid calculations without their having to refer to anything in particular, so long as they proved useful in practice. Berkeley thus predated the insight that logical positivists—who originated in the late 1920s, but who, by the 1950s, had softened into logical empiricists—would be compelled to accept: theoretical terms in science do not always translate into observational terms.

The last great British empiricist, David Hume, posed a number of challenges to Francis Bacon's inductivism, which had been the prevailing, or at least the professed view concerning the attainment of scientific knowledge. Regarding himself as having placed his own theory of knowledge on par with Newton's theory of motion, Hume supposed that he had championed inductivism over scientific realism. Upon reading Hume's work, Immanuel Kant was "awakened from dogmatic slumber", and thus sought to neutralise any threat to science posed by Humean empiricism. Kant would develop the first stark philosophy of physics.

Transcendental idealism
To save Newton's law of universal gravitation, Immanuel Kant reasoned that the mind is the precondition of experience and so, as the bridge from the noumena, which are how the world's things exist in themselves, to the phenomena, which are humans' recognized experiences. And so mind itself contains the structure that determines space, time, and substance, how mind's own categorization of noumena renders space Euclidean, time constant, and objects' motions exhibiting the very determinism predicted by Newtonian physics. Kant apparently presumed that the human mind, rather than a phenomenon itself that had evolved, had been predetermined and set forth upon the formation of humankind. In any event, the mind also was the veil of appearance that scientific methods could never lift. And yet the mind could ponder itself and discover such truths, although not on a theoretical level, but only by means of ethics. Kant's metaphysics, then, transcendental idealism, secured science from doubt—in that it was a case of "synthetic a priori" knowledge ("universal, necessary and informative")—and yet discarded hope of scientific realism.

Logical empiricism
Since the mind has virtually no power to know anything beyond direct sensory experience, Ernst Mach's early version of logical positivism (empirio-criticism) verged on idealism. It was alleged to even be a surreptitious solipsism, whereby all that exists is one's own mind. Mach's positivism also strongly asserted the ultimate unity of the empirical sciences. Mach's positivism asserted phenomenalism as to new basis of scientific theory, all scientific terms to refer to either actual or potential sensations, thus eliminating hypotheses while permitting such seemingly disparate scientific theories as physical and psychological to share terms and forms. Phenomenalism was insuperably difficult to implement, yet heavily influenced a new generation of philosophers of science, who emerged in the 1920s while terming themselves logical positivists while pursuing a program termed verificationism. Logical positivists aimed not to instruct or restrict scientists, but to enlighten and structure philosophical discourse to render scientific philosophy that would verify philosophical statements as well as scientific theories, and align all human knowledge into a scientific worldview, freeing humankind from so many of its problems due to confused or unclear language.

The verificationists expected a strict gap between theory versus observation, mirrored by a theory's theoretical terms versus observable terms. Believing a theory's posited unobservables to always correspond to observations, the verificationists viewed a scientific theory's theoretical terms, such as electron, as metaphorical or elliptical at observations, such as white streak in cloud chamber. They believed that scientific terms lacked meanings unto themselves, but acquired meanings from the logical structure that was the entire theory that in turn matched patterns of experience. So by translating theoretical terms into observational terms and then decoding the theory's mathematical/logical structure, one could check whether the statement indeed matched patterns of experience, and thereby verify the scientific theory false or true. Such verification would be possible, as never before in science, since translation of theoretical terms into observational terms would make the scientific theory purely empirical, none metaphysical. Yet the logical positivists ran into insuperable difficulties. Moritz Schlick debated with Otto Neurath over foundationalism—the traditional view traced to Descartes as founder of modern Western philosophy—whereupon only nonfoundationalism was found tenable. Science, then, could not find a secure foundation of indubitable truth.

And since science aims to reveal not private but public truths, verificationists switched from phenomenalism to physicalism, whereby scientific theory refers to objects observable in space and at least in principle already recognizable by physicists. Finding strict empiricism untenable, verificationism underwent "liberalization of empiricism". Rudolf Carnap even suggested that empiricism's basis was pragmatic. Recognizing that verification—proving a theory false or true—was unattainable, they discarded that demand and focused on confirmation theory. Carnap sought simply to quantify a universal law's degree of confirmation—its probable truth—but, despite his great mathematical and logical skill, discovered equations never operable to yield over zero degree of confirmation. Carl Hempel found the paradox of confirmation. By the 1950s, the verificationists had established philosophy of science as subdiscipline within academia's philosophy departments. By 1962, verificationists had asked and endeavored to answer seemingly all the great questions about scientific theory. Their discoveries showed that the idealized scientific worldview was naively mistaken. By then the leader of the legendary venture, Hempel raised the white flag that signaled verificationism's demise. Suddenly striking Western society, then, was Kuhn's landmark thesis, introduced by none other than Carnap, verificationism's greatest firebrand. Instrumentalism exhibited by scientists often does not even discern unobservable from observable entities.

Historical turn
From the 1930s until Thomas Kuhn's 1962 The Structure of Scientific Revolutions, there were roughly two prevailing views about the nature of science. The popular view was scientific realism, which usually involved a belief that science was progressively unveiling a truer view, and building a better understanding, of nature. The professional approach was logical empiricism, wherein a scientific theory was held to be a logical structure whose terms all ultimately refer to some form of observation, while an objective process neutrally arbitrates theory choice, compelling scientists to decide which scientific theory was superior. Physicists knew better, but, busy developing the Standard Model, were so steeped in developing quantum field theory, that their talk, largely metaphorical, perhaps even metaphysical, was unintelligible to the public, while the steep mathematics warded off philosophers of physics. By the 1980s, physicists regarded not particles, but fields as the more fundamental, and no longer even hoped to discover what entities and processes might be truly fundamental to nature, perhaps not even the field. Kuhn had not claimed to have developed a novel thesis, but instead hoped to synthesize more usefully recent developments in the philosophy and history of science.

Scientific realism
One scientific realist, Karl Popper, rejected all variants of positivism via its focus on sensations rather than realism, and developed critical rationalism instead. Popper alleged that instrumentalism reduces basic science to what is merely applied science. The British physicist David Deutsch, in his much later 1997 book The Fabric of Reality, followed Popper's critique of instrumentalism and argued that a scientific theory stripped of its explanatory content would be of strictly limited utility.

Constructive empiricism as a form of instrumentalism
Bas van Fraassen's (1980) project of constructive empiricism focuses on belief in the domain of the observable, so for this reason it is described as a form of instrumentalism.

In the philosophy of mind
In the philosophy of mind, instrumentalism is the view that propositional attitudes like beliefs are not actually concepts on which we can base scientific investigations of mind and brain, but that acting as if other beings have beliefs is a successful strategy.

Relation to pragmatism
Instrumentalism is closely related to pragmatism, the position that practical consequences are an essential basis for determining meaning, truth or value.

Notable proponents

 * John Dewey (American pragmatist)
 * Richard Rorty

authors: Гармонический Мир

title: Instrumentalism


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Scientific realism

Scientific realism is the view that the universe described by science is real regardless of how it may be interpreted. A believer of scientific realism takes the universe as described by science to be true (or approximately true), because of their assertion that science can be used to find the truth (or approximate truth) about both the physical and metaphysical in the Universe.

Within philosophy of science, this view is often an answer to the question "how is the success of science to be explained?" The discussion on the success of science in this context centers primarily on the status of unobservable entities apparently talked about by scientific theories. Generally, those who are scientific realists assert that one can make valid claims about unobservables (viz., that they have the same ontological status) as observables, as opposed to instrumentalism.

Main features
Scientific realism involves two basic positions:

 * First, it is a set of claims about the features of an ideal scientific theory; an ideal theory is the sort of theory science aims to produce.

 * Second, it is the commitment that science will eventually produce theories very much like an ideal theory and that science has done pretty well thus far in some domains. One might be a scientific realist regarding some sciences while not being a realist regarding others.

According to scientific realism, an ideal scientific theory has the following features:
 * The claims the theory makes are either true or false, depending on whether the entities talked about by the theory exist and are correctly described by the theory. This is the semantic commitment of scientific realism.
 * The entities described by the scientific theory exist objectively and mind-independently. This is the metaphysical commitment of scientific realism.
 * There are reasons to believe some significant portion of what the theory says. This is the epistemological commitment.

Combining the first and the second claim entails that an ideal scientific theory says definite things about genuinely existing entities. The third claim says that we have reasons to believe that many scientific claims about these entities are true, but not all.

Scientific realism usually holds that science makes progress, i.e. scientific theories usually get successively better, or, rather, answer more and more questions. For this reason, scientific realists or otherwise, hold that realism should make sense of the progress of science in terms of theories being successively more like the ideal theory that scientific realists describe.

Characteristic claims
The following claims are typical of those held by scientific realists. Due to the wide disagreements over the nature of science's success and the role of realism in its success, a scientific realist would agree with some but not all of the following positions.
 * The best scientific theories are at least partially true.
 * The best theories do not employ central terms that are non referring expressions.
 * To say that a theory is approximately true is sufficient explanation of the degree of its predictive success.
 * The approximate truth of a theory is the only explanation of its predictive success.
 * Even if a theory employs expressions that do not have a reference, a scientific theory may be approximately true.
 * Scientific theories are in a historical process of progress towards a true account of the physical world.
 * Scientific theories make genuine, existential claims.
 * Theoretical claims of scientific theories should be read literally and are definitively either true or false.
 * The degree of the predictive success of a theory is evidence of the referential success of its central terms.
 * The goal of science is an account of the physical world that is literally true. Science has been successful because this is the goal that it has been making progress towards.

History
Scientific realism is related to much older philosophical positions including rationalism and metaphysical realism. However, it is a thesis about science developed in the twentieth century. Portraying scientific realism in terms of its ancient, medieval, and early modern cousins is at best misleading.

Scientific realism is developed largely as a reaction to logical positivism. Logical positivism was the first philosophy of science in the twentieth century and the forerunner of scientific realism, holding that a sharp distinction can be drawn between theoretical terms and observational terms, the latter capable of semantic analysis in observational and logical terms.

Logical positivism encountered difficulties with:
 * The verificationist theory of meaning—see Hempel (1950).
 * Troubles with the analytic-synthetic distinction—see Quine (1950).
 * The theory-ladenness of observation—see Hanson (1958) Kuhn (1970) and Quine (1960).
 * Difficulties moving from the observationality of terms to observationality of sentences—see Putnam (1962).
 * The vagueness of the observational-theoretical distinction—see G. Maxwell (1962).

These difficulties for logical positivism suggest, but do not entail, scientific realism, and led to the development of realism as a philosophy of science.

Realism became the dominant philosophy of science after positivism. Bas van Fraassen in his book The Scientific Image (1980) developed constructive empiricism as an alternative to realism. He argues against scientific realism that scientific theories do not aim for truth about unobservable entities. Responses to van Fraassen have sharpened realist positions and led to some revisions of scientific realism.

No miracles argument
One of the main arguments for scientific realism centers on the notion that scientific knowledge is progressive in nature, and that it is able to predict phenomena successfully. Many scientific realists (e.g., Ernan McMullin, Richard Boyd) think the operational success of a theory lends credence to the idea that its more unobservable aspects exist, because they were how the theory reasoned its predictions. For example, a scientific realist would argue that science must derive some ontological support for atoms from the outstanding phenomenological success of all the theories using them.

Arguments for scientific realism often appeal to abductive reasoning or "inference to the best explanation" (Lipton, 2004). For instance, one argument commonly used—the "miracle argument" or "no miracles argument"—starts out by observing that scientific theories are highly successful in predicting and explaining a variety of phenomena, often with great accuracy. Thus, it is argued that the best explanation—the only explanation that renders the success of science to not be what Hilary Putnam calls "a miracle"—is the view that our scientific theories (or at least the best ones) provide true descriptions of the world, or approximately so.

Bas van Fraassen replies with an evolutionary analogy: "I claim that the success of current scientific theories is no miracle. It is not even surprising to the scientific (Darwinist) mind. For any scientific theory is born into a life of fierce competition, a jungle red in tooth and claw. Only the successful theories survive—the ones which in fact latched on to actual regularities in nature." (The Scientific Image, 1980)

Some philosophers (e.g. Colin Howson) have argued that the no miracles argument commits the base rate fallacy.

Pessimistic induction
Pessimistic induction, one of the main arguments against realism, argues that the history of science contains many theories once regarded as empirically successful but which are now believed to be false. Additionally, the history of science contains many empirically successful theories whose unobservable terms are not believed to genuinely refer. For example, the effluvium theory of static electricity (a theory of the 16th Century physicist William Gilbert) is an empirically successful theory whose central unobservable terms have been replaced by later theories.

Realists reply that replacement of particular realist theories with better ones is to be expected due to the progressive nature of scientific knowledge, and when such replacements occur only superfluous unobservables are dropped. For example, Albert Einstein's theory of special relativity showed that the concept of the luminiferous ether could be dropped because it had contributed nothing to the success of the theories of mechanics and electromagnetism. On the other hand, when theory replacement occurs, a well-supported concept, such as the concept of atoms, is not dropped but is incorporated into the new theory in some form. These replies can lead scientific realists to structural realism.

Constructivist epistemology
Social constructivists might argue that scientific realism is unable to account for the rapid change that occurs in scientific knowledge during periods of scientific revolution. Constructivists may also argue that the success of theories is only a part of the construction.

However, these arguments ignore the fact that many scientists are not realists. During the development of quantum mechanics in the 1920s, the dominant philosophy of science was logical positivism. The alternative realist Bohm interpretation and many-worlds interpretation of quantum mechanics do not make such a revolutionary break with the concepts of classical physics.

Underdetermination problem
Another argument against scientific realism, deriving from the underdetermination problem, is not so historically motivated as these others. It claims that observational data can in principle be explained by multiple theories that are mutually incompatible. Realists might counter by saying that there have been few actual cases of underdetermination in the history of science. Usually the requirement of explaining the data is so exacting that scientists are lucky to find even one theory that fulfills it. Furthermore, if we take the underdetermination argument seriously, it implies that we can know about only what we have directly observed. For example, we could not theorize that dinosaurs once lived based on the fossil evidence because other theories (e.g., that the fossils are clever hoaxes) can account for the same data.

Incompatible models argument
According to the incompatible models argument, in certain cases the existence of diverse models for a single phenomenon can be taken as evidence of anti-realism. One example is due to Margaret Morrison, who worked to show that the shell model and the liquid-drop model give contradictory descriptions of the atomic nucleus, even though both models are predictive.

title: Scientific realism


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Surgical stainless steel

Surgical stainless steel is a grade of stainless steel used in biomedical applications. The most common "surgical steels" are austenitic SAE 316 stainless and martensitic SAE 440, SAE 420, and 17-4 stainless steels. There is no formal definition on what constitutes a "surgical stainless steel", so product manufacturers and distributors often apply the term to refer to any grade of corrosion resistant steel.

Medical grade stainless
SAE 316 and SAE 316L stainless steel, also referred to as marine grade stainless, is a chromium, nickel, molybdenum alloy of steel that exhibits relatively good strength and corrosion resistance. 316L is the low carbon version of 316 stainless steel.

316L in particular is biocompatible when produced to ASTM F138 / F139. It is a common choice for biomedical implants, as well as body piercings and body modification implants. Immune system reaction to nickel is a potential complication of stainless steel usage within the human body. There are nickel-free nitrogen-strengthened austenitic stainless steel alloys available which address this concern.

316 surgical steel is also used in the manufacture and handling of food and pharmaceutical products where it is often required in order to minimize metallic contamination.

The corrosion resistance properties of all stainless steels is greatly enhanced by the passivation process. ASTM A967 details this process.

Cutlery grade stainless
SAE 440 and SAE 420 stainless steels, known also by the name "Cutlery Stainless Steel", are high carbon steels alloyed with chromium. They have very good corrosion resistance compared to other cutlery steels, but their corrosion resistance is inferior to 316 stainless. Surgical cutting instruments are often made from 440 or 420 stainless due to its high hardness coupled with acceptable corrosion resistance. This type of stainless steel may be slightly magnetic.

General surgical tools are made from other chromium-bearing stainless steels, such as 17-4. ASTM F899 contains a list of commonly used metals for surgical instruments.

title: Surgical stainless steel


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Lowest temperature recorded on Earth

The lowest natural temperature ever directly recorded at ground level on Earth is −89.2 C at the then-Soviet Vostok Station in Antarctica on 21 July 1983 by ground measurements.

On 10 August 2010, satellite observations showed a surface temperature of −92 C at -81.8°N, 59.3°W, along a ridge between Dome Argus and Dome Fuji, at 3900 m elevation. The result was reported at the 46th annual meeting of the American Geophysical Union in San Francisco in December 2013; it is a provisional figure, and may be subject to revision. The value is not listed as the record lowest temperature as it was measured by remote sensing from satellite and not by ground-based thermometers, unlike the 1983 record. The temperature announced reflects that of the ice surface, while the Vostok readings measured the air above the ice, and so the two are not directly comparable. More recent work shows many locations in the high Antarctic where surface temperatures drop to approximately −98 C. Due to the very strong temperature gradient near the surface, these imply near-surface air temperature minima of approximately −94 C.

Historical progression
On 21 January 1838, a Russian merchant named Neverov recorded a temperature of −60 C in Yakutsk. On 15 January 1885, H. Wild reported that a temperature of −68 C was measured in Verkhoyansk. A later measurement at the same place in February 1892 was reported as −69.8 C. Soviet researchers later announced a recording of −67.7 C in February 1933 at Oymyakon, about 650 km to the south-east of Verkhoyansk; this measurement was reported by Soviet texts through the 1940s as a record low, with the previous measurement from Verkhoyansk retroactively adjusted to −67.6 C.

The next reliable measurement was made during the 1957 season at the Amundsen–Scott South Pole Station in Antarctica, yielding −73.6 C on 11 May and −74.5 C on 17 September. The next world record low temperature was a reading of −88.3 C, measured at the Soviet Vostok Station in 1968, on the Antarctic Plateau. Vostok again broke its own record with a reading of −89.2 C on 21 July 1983. This remains the record for a directly recorded temperature.

Early experiments
In 1904 Dutch scientist Heike Kamerlingh Onnes created a special lab in Leiden in the Netherlands with the aim of producing liquid helium. In 1908 he managed to lower the temperature to less than −269 °C (−452.2 F, 4 K), which is four degrees above absolute zero. Only in this exceptionally cold state will helium liquefy, the boiling point of helium being at −268.94 °C (−452.092 F). Kamerlingh Onnes received a Nobel Prize for his achievement.

Onnes' method relied upon depressurising the subject gases, causing them to cool by adiabatic cooling. This follows from the first law of thermodynamics;

$$\Delta U = \Delta Q - \Delta W$$

where U = internal energy, Q = heat added to the system, W = work done by the system.

Consider a gas in a box of set volume. If the pressure in the box is higher than atmospheric pressure, then upon opening the gas will do work on the surrounding atmosphere to expand. As this expansion is adiabatic and the gas has done work

$$\Delta Q = 0$$

$$\Delta W > 0$$

$$\Rightarrow \Delta U < 0$$

Now as the internal energy has decreased, so has the temperature.

Modern experiments
As of November 2000, nuclear spin temperatures below 100 pK were reported for an experiment at the Helsinki University of Technology Low Temperature Lab. However, this was the temperature of one particular type of motion—a quantum property called nuclear spin—not the overall average thermodynamic temperature for all possible degrees of freedom. At such low temperatures, the concept of "temperature" becomes multifaceted since molecular motion cannot be assumed to average out across degrees of freedom. The corresponding peak emission will be in radio waves, rather than in the familiar infrared, so it is very inefficiently absorbed by neighboring atoms, making it difficult to reach thermal equilibrium.

The Low Temperature Laboratory recorded a record low temperature of 100 pK, or 1.0 × 10−10 K in 1999.

The current apparatus for achieving low temperatures has two stages. The first utilizes a helium dilution refrigerator to get to temperatures of millikelvins, then the next stage uses adiabatic nuclear demagnetisation to reach picokelvins.

Extremely low temperatures are useful for observation of quantum mechanical phases of matter such as superfluids and Bose–Einstein condensates, which would be disrupted by thermal motion.

title: Lowest temperature recorded on Earth


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Talk:Observational techniques

Rename proposal
May I suggest that Observational techniques be renamed Observational techniques in marketing or Observational techniques (Marketing)? The term is used in other social sciences as well as the physical sciences. The same goes for the title of the article Experimental techniques. Most of the article is specific to marketing, and if the same amount were added concerning each the other fields that use the term, the article would end up very, very long indeed. GUllman 20:56 17 Jul 2003 (UTC)

 * You can rename it if you want. Actually, the way I wrote the article was to make the first two thirds very general. It applies to all the social sciences. In fact that part is more applicable to psychology, sociology, social anthropology, and ethnology, than it is to marketing. Only the last third, entitled "In Marketing research" is marketing specific. If you change the title, don't forget to change links on the pages that link to it.
 * The reason I didn't call it observational techniques (in the social sciences and marketing) is from what I can see about the way Wiki works, general titles are used on a first come, first serve basis. For example, when I did the article on Product, I had to call it product (business) because the general product category was already used by mathematics. I have found similar situations with positioning, distribution, and several other articles I have written. mydogategodshat 02:51 18 Jul 2003 (UTC)
 * I often do specify an article's discipline, but only when I have writen the article only with that discipline in mind : For example, logit analysis (in marketing) and multi dimensional scaling (in marketing). In cases like these, they would be of little value to anyone other than marketers. Mathematicians would find them lacking in pure theory, and social scienticts would find some of the procedures quite different from what they are familiar with. mydogategodshat 01:03 19 Jul 2003 (UTC)

= observing license plates in store parking lots = Really?! How is that research? --195.122.7.51 12:25, 11 October 2007 (UTC)

title: Talk:Observational techniques


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Gumbel distribution

In probability theory and statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions.

This distribution might be used to represent the distribution of the maximum level of a river in a particular year if there was a list of maximum values for the past ten years. It is useful in predicting the chance that an extreme earthquake, flood or other natural disaster will occur. The potential applicability of the Gumbel distribution to represent the distribution of maxima relates to extreme value theory, which indicates that it is likely to be useful if the distribution of the underlying sample data is of the normal or exponential type.

The Gumbel distribution is a particular case of the generalized extreme value distribution (also known as the Fisher–Tippett distribution). It is also known as the log-Weibull distribution and the double exponential distribution (a term that is alternatively sometimes used to refer to the Laplace distribution). It is related to the Gompertz distribution: when its density is first reflected about the origin and then restricted to the positive half line, a Gompertz function is obtained.

In the latent variable formulation of the multinomial logit model — common in discrete choice theory — the errors of the latent variables follow a Gumbel distribution. This is useful because the difference of two Gumbel-distributed random variables has a logistic distribution.

The Gumbel distribution is named after Emil Julius Gumbel (1891–1966), based on his original papers describing the distribution.

Definitions
The cumulative distribution function of the Gumbel distribution is

 * $$F(x;\mu,\beta) = e^{-e^{-(x-\mu)/\beta}}\,$$

Standard Gumbel distribution
The standard Gumbel distribution is the case where $$\mu = 0$$ and $$\beta = 1$$ with cumulative distribution function
 * $$F(x) = e^{-e^{(-x)}}\,$$

and probability density function
 * $$f(x) = e^{-(x+e^{-x})}.$$

In this case the mode is 0, the median is $$-\ln(\ln(2)) \approx 0.3665$$, the mean is $$\gamma\approx 0.5772$$ (the Euler–Mascheroni constant), and the standard deviation is $$\pi/\sqrt{6} \approx 1.2825.$$

The cumulants, for n > 1, are given by
 * $$\kappa_n = (n-1)! \zeta(n).$$

Properties
The mode is μ, while the median is $$\mu-\beta \ln\left(\ln 2\right),$$ and the mean is given by
 * $$\operatorname{E}(X)=\mu+\gamma\beta$$,

where $$ \gamma $$ is the Euler–Mascheroni constant.

The standard deviation $$ \sigma $$ is $$\beta \pi/\sqrt{6}$$ hence $$\beta = \sigma \sqrt{6} / \pi \approx 0.78 \sigma. $$

At the mode, where $$ x = \mu $$, the value of $$F(x;\mu,\beta)$$ becomes $$ e^{-1} \approx 0.37 $$, irrespective of the value of $$ \beta. $$

If $$G_1,...,G_k$$ are iid Gumbel random variables with parameters $$(\mu,\beta)$$ then $$\max\{G_1,...,G_k\}$$ is also a Gumbel random variable with parameters $$(\mu+\beta\ln k, \beta)$$.

If $$G_1, G_2,...$$ are iid random variables such that $$\max\{G_1,...,G_k\}-\beta\ln k $$ has the same distribution as $$G_1$$ for all natural numbers $$ k $$, then $$G_1$$ is necessarily Gumbel distributed with scale parameter $$\beta$$ (actually it suffices to consider just two distinct values of k>1 which are coprime).

Related distributions
Theory related to the generalized multivariate log-gamma distribution provides a multivariate version of the Gumbel distribution.
 * If $$X $$ has a Gumbel distribution, then the conditional distribution of Y = −X given that Y is positive, or equivalently given that X is negative, has a Gompertz distribution. The cdf G of Y is related to F, the cdf of X, by the formula $$G(y) = P(Y \le y) = P(X \ge -y \mid X \le 0) = (F(0)-F(-y))/F(0)$$ for y > 0. Consequently, the densities are related by $$g(y) = f(-y)/F(0)$$: the Gompertz density is proportional to a reflected Gumbel density, restricted to the positive half-line.
 * If X is an exponentially distributed variable with mean 1, then −log(X) has a standard Gumbel distribution.
 * If $$X \sim \mathrm{Gumbel}(\alpha_X, \beta) $$ and $$ Y \sim \mathrm{Gumbel}(\alpha_Y, \beta) $$ are independent, then $$ X-Y \sim \mathrm{Logistic}(\alpha_X-\alpha_Y,\beta) \,$$ (see Logistic distribution).
 * If $$X, Y \sim \mathrm{Gumbel}(\alpha, \beta) $$ are independent, then $$X+Y \nsim \mathrm{Logistic}(2 \alpha,\beta)$$. Note that $$ E(X+Y) = 2\alpha+2\beta\gamma \neq 2\alpha = E\left(\mathrm{Logistic}(2 \alpha,\beta) \right) $$. More generally, the distribution of linear combinations of independent Gumbel random variables can be approximated by GNIG and GIG distributions.

Occurrence and applications

Gumbel has shown that the maximum value (or last order statistic) in a sample of random variables following an exponential distribution minus the natural logarithm of the sample size approaches the Gumbel distribution as the sample size increases.

Concretely, let $$ \rho(x)=e^{-x} $$ be the probability distribution of $$ x $$ and $$ Q(x)=1- e^{-x} $$ its cumulative distribution. Then the maximum value out of $$ N $$ realizations of $$ x $$ is smaller than $$ X $$ if and only if all realizations are smaller than $$ X $$. So the cumulative distribution of the maximum value $$ \tilde{x} $$ satisfies
 * $$P(\tilde{x}-\log(N)\le X)=P(\tilde{x}\le X+\log(N))=[Q(X+\log(N))]^N=\left(1- \frac{e^{-X}}{N}\right)^N, $$

and, for large $$ N $$, the right-hand-side converges to $$ e^{-e^{(-X)}}. $$

In hydrology, therefore, the Gumbel distribution is used to analyze such variables as monthly and annual maximum values of daily rainfall and river discharge volumes, and also to describe droughts. Gumbel has also shown that the estimator $r/(n+1)$ for the probability of an event — where r is the rank number of the observed value in the data series and n is the total number of observations — is an unbiased estimator of the cumulative probability around the mode of the distribution. Therefore, this estimator is often used as a plotting position.

In number theory, the Gumbel distribution approximates the number of terms in a random partition of an integer as well as the trend-adjusted sizes of maximal prime gaps and maximal gaps between prime constellations.

It appears in the coupon collector's problem.

Gumbel reparametrization tricks
In machine learning, the Gumbel distribution is sometimes employed to generate samples from the categorical distribution. This technique is called "Gumbel-max trick" and is a special example of "reparametrization tricks".

In detail, let $$(\pi_1, \ldots, \pi_n)$$ be nonnegative, and not all zero, and let $$g_1,\ldots, g_n$$ be independent samples of Gumbel(0, 1), then by routine integration,$$Pr(j = \arg\max_i (g_i + \log\pi_i)) = \frac{\pi_j}{\sum_i \pi_i}$$That is, $$\arg\max_i (g_i + \log\pi_i) \sim \text{Categorical}\left(\frac{\pi_j}{\sum_i \pi_i}\right)_j$$

Equivalently, given any $$x_1, ..., x_n\in \R$$, we can sample from its Boltzmann distribution by

$$Pr(j = \arg\max_i (g_i + x_i)) = \frac{e^{x_j}}{\sum_i e^{x_i}}$$Related equations include:
 * If $$x\sim \operatorname{Exp}(\lambda)$$, then $$(-\ln x - \gamma)\sim \text{Gumbel}(-\gamma + \ln\lambda, 1)$$.
 * $$\arg\max_i (g_i + \log\pi_i) \sim \text{Categorical}\left(\frac{\pi_j}{\sum_i \pi_i}\right)_j$$.
 * $$\max_i (g_i + \log\pi_i) \sim \text{Gumbel}\left(\log\left(\sum_i \pi_i \right), 1\right)$$. That is, the Gumbel distribution is a max-stable distribution family.
 * $$\mathbb E[\max_i (g_i + \beta x_i)] = \log \left(\sum_i e^{\beta x_i}\right) + \gamma.$$

Random variate generation
Since the quantile function (inverse cumulative distribution function), $$Q(p)$$, of a Gumbel distribution is given by

 * $$Q(p)=\mu-\beta\ln(-\ln(p)),$$

the variate $$Q(U)$$ has a Gumbel distribution with parameters $$\mu$$ and $$\beta$$ when the random variate $$U$$ is drawn from the uniform distribution on the interval $$(0,1)$$.

Probability paper

In pre-software times probability paper was used to picture the Gumbel distribution (see illustration). The paper is based on linearization of the cumulative distribution function $$F$$ :
 * $$ -\ln[-\ln(F)] = \frac{x-\mu}\beta $$

In the paper the horizontal axis is constructed at a double log scale. The vertical axis is linear. By plotting $$F$$ on the horizontal axis of the paper and the $$x$$-variable on the vertical axis, the distribution is represented by a straight line with a slope 1$$/\beta$$. When distribution fitting software like CumFreq became available, the task of plotting the distribution was made easier.

title: Gumbel distribution


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Jurassic Coast

The Jurassic Coast (also Dorset and East Devon Coast) is a World Heritage Site on the English Channel coast of southern England. It stretches from Exmouth in East Devon to Studland Bay in Dorset, a distance of about 96 mi, and was inscribed on the World Heritage List in mid-December 2001.

The site spans 185 million years of geological history, coastal erosion having exposed an almost continuous sequence of rock formation covering the Triassic, Jurassic and Cretaceous periods. At different times, this area has been desert, shallow tropical sea and marsh, and the fossilised remains of the various creatures that lived there have been preserved in the rocks.

Natural features seen on this stretch of coast include arches, pinnacles and stack rocks. In some places the sea has broken through resistant rocks to produce coves with restricted entrances and, in one place, the Isle of Portland is connected to the land by a barrier beach. In some parts of the coast, landslides are common. These have exposed a wide range of fossils, the different rock types each having its own typical fauna and flora, thus providing evidence of how animals and plants evolved in this region.

The area around Lulworth Cove contains a fossil forest, and 71 different rock strata have been identified at Lyme Regis, each with its own species of ammonite. The fossil collector Mary Anning lived here and her major discoveries of marine reptiles and other fossils were made at a time when the study of palaeontology was just starting to develop. The Charmouth Heritage Coast Centre provides information on the heritage coast, and the whole length of the site can be visited via the South West Coast Path.

World Heritage Site
The Jurassic Coast stretches from Orcombe Point near Exmouth in East Devon to Old Harry Rocks near Swanage in East Dorset, a distance of 96 mi. Inscribed on the World Heritage List in 2001, the Jurassic Coast was the first wholly natural World Heritage Site to be designated in the United Kingdom. At Orcombe Point, the "Geoneedle" (2002), an acute pyramidal sculpture, marks the western end of the heritage site; this is built out of fragments of the different types of rocks to be seen along the coast.

The UNESCO World Heritage Committee nomination document lists eight segments of coast included in the site. The segments are:

 * from Orcombe Rocks to Chit Rocks, Sidmouth
 * from River Sid, Sidmouth to Seaton Hole
 * the Axmouth to Lyme Regis Undercliff, from the mouth of the River Axe to The Cobb in Lyme Regis
 * from Lyme Regis to West Bay
 * Chesil Beach, the Fleet Lagoon and the Isle of Portland Coast
 * Portland Harbour Shore
 * from Bowleaze Cove to Peveril Point
 * from New Swanage to Studland Bay

The cliffs on this part of the coast are being eroded as sections crumble away and landslides occur. These processes reveal successive layers of sedimentary rock, uncovering the geological history at the modern coastline over a period of 185 million years, and disclosing an almost continuous sequence of rock formations covering the Triassic, Jurassic and Cretaceous periods. The fossils found in the area and the coastal geomorphologic features of this dynamic coast, have advanced the study of earth sciences for more than two hundred years. The area covered by the designation comprises the land between the mean low water mark and the top of the cliffs or the back of the beach.

The fossils found in abundance along this coastline provide evidence of how animals and plants evolved in this region. During the Triassic this area was a desert, while in the Jurassic it was part of a tropical sea, and in the Cretaceous it was covered by swamps. The fossilised remains of the animals and plants that lived in those periods are very well preserved, providing a wealth of information on their body shapes, the way they died and even the fossilised remains of their last meals. Fossil groups found here include crustaceans, insects, molluscs, echinoderms, fish, amphibians, reptiles and a few mammals. At Lulworth Cove there is a fossil forest of conifers, tree-ferns and cycads.

Geography

The Jurassic Coast consists of Triassic, Jurassic and Cretaceous cliffs, spanning the Mesozoic, documenting 185 million years of geological history. The site can be best viewed from the sea, when the dipping nature of the rock strata becomes apparent.

In East Devon, the coastal cliffs consist of steep cliffs of red sandstone from the Triassic, and at Budleigh Salterton, the gravel cliffs contain red quartzite pebbles which accumulate on the beach below as Budleigh pebbles, locally protected. Further east at Ladram Bay, more sandstone cliffs give rise to spectacular red sandstone stacks.

Around Lyme Regis and Charmouth the cliffs are of Jurassic clays and shale, and landslips are common. Chesil Beach is a good example of a barrier beach and stretches for 18 mi from Burton Bradstock to the Isle of Portland. The beach encloses an intertidal lagoon which is an internationally important Ramsar Convention site known for its biodiversity.

At Lulworth Cove, the waves have cut their way through the resistant Portland stone and created a horseshoe-shaped cove by eroding the softer sands and clays behind. Another feature of this part of the coast is Durdle Door, a natural arch. Sea stacks and pinnacles, such as Old Harry Rocks at Handfast Point, have been formed by erosion of the chalk cliffs.

The highest point on the Jurassic Coast, and on the entire south coast of Britain, is Golden Cap at 627 ft between Bridport and Charmouth.

This coast shows excellent examples of landforms, including the natural arch at Durdle Door, the cove and limestone folding at Lulworth Cove and a tied island, the Isle of Portland. Chesil Beach is a fine example of both a tombolo (a deposition landform in which an island is attached to the mainland by a narrow piece of land such as a spit or bar) and a storm beach (a beach affected by particularly fierce waves). The site has stretches of both concordant and discordant coastlines. Due to the quality of the varied geology, the site is the subject of international field studies.

The many sedimentary layers on this coastline are rich with fossils, the remains of the animals and plants present in the area whose tissues became immersed in deposits of mud which later hardened into rock. At Lyme Regis, for example, geologists have identified 71 layers of rock, each one containing fossils of a different species of ammonite.

History
At the end of the 18th century Georges Cuvier showed that some fossil animals resembled no living ones, thus demonstrating that animals could become extinct; this led to the emergence of palaeontology, the study of fossils. The coasts of eastern Devon and western Dorset were rich in fossil beds, but before this time the fossils had merely been gathered as a pastime or collected by local residents and sold to visitors as curios.

Mary Anning (1799–1847) lived in Lyme Regis and followed in her father's footsteps as a collector. She became an expert on the fossils to be found in the Blue Lias around the town and discovered the first complete Ichthyosaur skeleton at The Spittles. Other important discoveries of ichthyosaurs, plesiosaurs and a pterosaur followed, as well as invertebrates such as cephalopods and their ink sacs.

During World War II several sections of the Jurassic Coast became the property of the Ministry of War. One of the Royal Navy's largest bases was at Portland Harbour, though it has since closed. A major army base at Bovington remains in use today. Large areas of land, including the coast between Lulworth Cove and Kimmeridge, are still only partially accessible; this includes the ghost village of Tyneham which was evacuated after being requisitioned by the army in 1943.

Areas of the coast near Exmouth, The Fleet Lagoon at Weymouth and the beaches at Studland have also been used for military training but have since been returned to civilian use.

Parts of the coast, especially around Portland, can be dangerous, and shipwrecks have been a feature of the coast. In January 2007 the coast experienced its most environmentally damaging wreck when the MSC Napoli, a 2,400 capacity container ship, was beached at Branscombe near Sidmouth, losing oil and cargo.

Management and access
The Jurassic Coast is subject to severe weather conditions at times. Violent storms occurred in 1824 and 1974, and these and various lesser storms have battered the cliffs and caused flooding and structural damage in coastal towns. The coast is largely an eroding landscape and management of the site aims to allow the natural processes of erosion to continue while protecting people and property. Coastal defences have been put in place in Charmouth and Weymouth, where houses are at risk, but in other places, where the coastline remains in a natural state, the management policy is to take no action and allow erosion to take its course.

The Charmouth Heritage Coast Centre is an independent educational charity situated near the beach in Charmouth; it provides information and displays on the geology of the area and the wildlife, including a large collection of fossils and a rockpool aquarium. Family fossil-hunting trips are organised from here as well as other events and activities related to the geology and natural history of the area.

The entire length of the coast can be walked on the South West Coast Path. Landslips and rockfalls are a continuing feature of the evolution of this coast. On 6 May 2008, a 1300 ft section of the coast was dramatically re-shaped after a landslip that was described as the worst in 100 years. There was a fatality in 2012 when 400 tonne of rock fell onto the beach at Burton Bradstock and another cliff fall took place in 2016 at West Bay, near Bridport. There was a further cliff collapse at Hive Beach near the village of Burton Bradstock shortly before dawn on 29 August 2020 after prolonged rain fall. The public were warned to stay clear of the unstable rocks. On 15 April 2021, a further collapse occurred. The collapse was described as being the biggest UK rockfall in 60 years.

title: Jurassic Coast