text:
Erewhon

Erewhon: or, Over the Range is a novel by English writer Samuel Butler, first published anonymously in 1872, set in a fictional country discovered and explored by the protagonist. The book is a satire on Victorian society.

The first few chapters of the novel dealing with the discovery of Erewhon are in fact based on Butler's own experiences in New Zealand, where, as a young man, he worked as a sheep farmer on Mesopotamia Station for about four years (1860–64), and explored parts of the interior of the South Island and wrote about in his A First Year in Canterbury Settlement (1863).

The novel is one of the first to explore ideas of artificial intelligence, as influenced by Darwin's recently published On the Origin of Species (1859) and the machines developed out of the Industrial Revolution (late 18th to early 19th centuries). Specifically, it concerns itself, in the three-chapter "Book of the Machines", with the potentially dangerous ideas of machine consciousness and self-replicating machines.

Content
The greater part of the book consists of a description of Erewhon. The nature of this nation is intended to be ambiguous. At first glance, Erewhon appears to be a Utopia, yet it soon becomes clear that this is far from the case. Yet for all the failings of Erewhon, it is also clearly not a dystopia, such as that depicted in George Orwell's Nineteen Eighty-Four (1949).

As a satirical utopia, Erewhon has sometimes been compared to Gulliver's Travels (1726), by Jonathan Swift; the image of Utopia in this latter case also bears strong parallels with the self-view of the British Empire at the time. It can also be compared to the William Morris novel, News from Nowhere (1890) and Thomas More's Utopia (1516).

Erewhon satirises various aspects of Victorian society, including criminal punishment, religion, and anthropocentrism. For example, according to Erewhonian law, offenders are treated as if they were ill, whereas ill people are looked upon as criminals. Another feature of Erewhon is the absence of machines; this is due to the widely shared perception by the Erewhonians that machines are potentially dangerous.

The Book of the Machines
Butler developed the three chapters of Erewhon that make up "The Book of the Machines" from a number of articles he had contributed to The Press, which had just begun publication in Christchurch, New Zealand, beginning with "Darwin among the Machines" (1863). Butler was the first to write about the possibility that machines might develop consciousness by natural selection.

Many dismissed this as a joke, but, in his preface to the second edition, Butler wrote, "I regret that reviewers have in some cases been inclined to treat the chapters on Machines as an attempt to reduce Mr Darwin's theory to an absurdity. Nothing could be further from my intention, and few things would be more distasteful to me than any attempt to laugh at Mr Darwin."

Characters

 * Higgs—The narrator who informs the reader of the nature of Erewhonian society.
 * Chowbok (Kahabuka)—Higgs' guide into the mountains; he is a native who greatly fears the Erewhonians. He eventually abandons Higgs.
 * Yram—The daughter of Higgs' jailer who takes care of him when he first enters Erewhon. Her name is Mary spelled backwards.
 * Senoj Nosnibor—Higgs' host after he is released from prison; he hopes that Higgs will marry his elder daughter. His name is Robinson Jones backwards.
 * Zulora—Senoj Nosnibor's elder daughter—Higgs finds her unpleasant, but her father hopes Higgs will marry her. Her name is Aroluz backwards.
 * Arowhena—Senoj Nosnibor's younger daughter; she falls in love with Higgs and runs away with him.
 * Mahaina—A woman who claims to suffer from alcoholism but is believed to have a weak temperament.
 * Ydgrun—The incomprehensible goddess of the Erewhonians. Her name is an anagram of Grundy (from Mrs. Grundy, a character in Thomas Morton's play Speed the Plough).

Reception
In a 1945 broadcast, George Orwell praised the book and said that when Butler wrote Erewhon it needed "imagination of a very high order to see that machinery could be dangerous as well as useful". He recommended the novel, though not its sequel, Erewhon Revisited.

Deleuze and Guattari
The French philosopher Gilles Deleuze used ideas from Butler's book at various points in the development of his philosophy of difference. In Difference and Repetition (1968), Deleuze refers to what he calls "Ideas" as "Erewhon". "Ideas are not concepts", he argues, but rather "a form of eternally positive differential multiplicity, distinguished from the identity of concepts." "Erewhon" refers to the "nomadic distributions" that pertain to simulacra, which "are not universals like the categories, nor are they the hic et nunc or nowhere, the diversity to which categories apply in representation." "Erewhon", in this reading, is "not only a disguised no-where but a rearranged now-here."

In his collaboration with Félix Guattari, Anti-Oedipus (1972), Deleuze draws on Butler's "The Book of the Machines" to "go beyond" the "usual polemic between vitalism and mechanism" as it relates to their concept of "desiring-machines": "For one thing, Butler is not content to say that machines extend the organism, but asserts that they are really limbs and organs lying on the body without organs of a society, which men will appropriate according to their power and their wealth, and whose poverty deprives them as if they were mutilated organisms. For another, he is not content to say that organisms are machines, but asserts that they contain such an abundance of parts that they must be compared to very different parts of distinct machines, each relating to the others, engendered in combination with the others ... He shatters the vitalist argument by calling in question the specific or personal unity of the organism, and the mechanist argument even more decisively, by calling in question the structural unity of the machine."

Other uses
C. S. Lewis alludes to the book in his essay, The Humanitarian Theory of Punishment in the posthumously published collection, God in the Dock (1970).

Alan M. Turing references the book in his posthumously published paper, "Intelligent Machinery, A Heretical Theory". He writes, "At some stage therefore we should have to expect the machines to take control, in the way that is mentioned in Samuel Butler's Erewhon."

Aldous Huxley alludes to the book in his novels Island (1962) and The Doors of Perception (1954), as does Agatha Christie in Death on the Nile (1937). A copy of the book figures in Elizabeth Bowen's short story 'The Cat Jumps' (1934).

In 1994, a group of ex-Yugoslavian writers in Amsterdam, who had established the PEN centre of Yugoslav Writers in Exile, published a single issue of a literary journal Erewhon.

The 1973 movie The Day of the Dolphin features a boat named Erewhon.

In Bye Bye, Earth, Belle's sword is called "Erewhon", and the story makes reference to the book.

New Zealand sound art organisation, the Audio Foundation, published in 2012 an anthology edited by Bruce Russell named Erewhon Calling after Butler's book.

In 2014, New Zealand artist Gavin Hipkins released his first feature film, titled Erewhon and based on Butler's book. It premiered at the New Zealand International Film Festival and the Edinburgh Art Festival.

In "Smile", the second episode of the 2017 season of Doctor Who, the Doctor and Bill explore a spaceship named Erehwon. Despite the slightly different spelling, the episode writer Frank Cottrell-Boyce confirmed that this was a reference to Butler's novel.

The book The Open Society and Its Enemies, by Karl Popper, reproduces on its first page the following citation of Butler: "It will be seen ... that the Erewhonians are a meek and long-suffering people easily led by the nose, and quick to offer up common sense at the shrine of logic, when a philosopher arises among them who carries them away ... by convincing them that their existing institutions are not based on the strictest principles of morality".

"Erewhon" is the unofficial name US astronauts gave Regan Station, a military space station in David Brin's 1990 novel Earth.

The 'Butlerian Jihad' is the name of the crusade to wipe out 'thinking machines' in the novel, Dune, by Frank Herbert.

Erewhon is the name of an upscale Los Angeles-based natural foods grocery chain originally founded in Boston in 1966.

Erewhon is also the name of an independent speculative fiction publishing company founded in 2018 by Liz Gorinsky.

A copy of Erewhon figures prominently in the video for "A Barely Lit Path," the lead single from Oneohtrix Point Never's 2023 album Again.

title: Erewhon


text:
Ectopia (medicine)

An ectopia is a displacement or malposition of an organ or other body part, which is then referred to as ectopic.

Examples

 * Ectopic ACTH syndrome, also known as small-cell carcinoma.
 * Ectopic calcification, a pathologic deposition of calcium salts in tissues or bone growth in soft tissues
 * Cerebellar tonsillar ectopia, aka Chiari malformation, a herniation of the brain through the foramen magnum, which may be congenital or caused by trauma.
 * Ectopic cilia, a hair growing where it isn't supposed to be, commonly an eyelash on an abnormal spot on the eyelid, distichia
 * Ectopia cordis, the displacement of the heart outside the body during fetal development
 * Ectopic enamel, a tooth abnormality, where enamel is found in an unusual location, such as at the root of a tooth
 * Ectopic expression, the expression of a gene in an abnormal place in an organism
 * Ectopic hormone, a hormone produced by a tumor, such as small-cell carcinoma, can cause Cushing's syndrome
 * Ectopia lentis, the displacement of the crystalline lens of the eye
 * Neuronal ectopia
 * Ectopic pancreas, displacement of pancreatic tissue in the body with no connection, anatomical or vascular, to the pancreas
 * Ectopic recombination, the recombination between sequences (like leu2 sequences) present at different genomic locations
 * Renal ectopia occurs when both kidneys are on the same side of the body
 * Ectopic testis, a testis that has moved to an unusual location
 * Ectopic thymus, where thymus tissue is found in an abnormal location
 * Ectopic thyroid, where an entire or parts of the thyroid are located elsewhere in the body
 * Ectopic tooth, a tooth that erupted outside the dental arch
 * Ectopic ureter, where the ureter terminates somewhere other than the urinary bladder
 * Ectopia vesicae, a congenital anomaly in which part of the urinary bladder is present outside the body

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

title: Ectopia (medicine)


text:
Entorhinal cortex

The entorhinal cortex (EC) is an area of the brain's allocortex, located in the medial temporal lobe, whose functions include being a widespread network hub for memory, navigation, and the perception of time. The EC is the main interface between the hippocampus and neocortex. The EC-hippocampus system plays an important role in declarative (autobiographical/episodic/semantic) memories and in particular spatial memories including memory formation, memory consolidation, and memory optimization in sleep. The EC is also responsible for the pre-processing (familiarity) of the input signals in the reflex nictitating membrane response of classical trace conditioning; the association of impulses from the eye and the ear occurs in the entorhinal cortex.

Anatomy
The entorhinal cortex is a portion of the rostral parahippocampal gyrus.

Structure
It is usually divided into medial and lateral regions with three bands with distinct properties and connectivity running perpendicular across the whole area. A distinguishing characteristic of the EC is the lack of cell bodies where layer IV should be; this layer is called the Lamina dissecans.

Connections
The superficial layers – layers II and III – of EC project to the dentate gyrus and hippocampus: Layer II projects primarily to dentate gyrus and hippocampal region CA3; layer III projects primarily to hippocampal region CA1 and the subiculum. These layers receive input from other cortical areas, especially associational, perirhinal, and parahippocampal cortices, as well as prefrontal cortex. EC as a whole, therefore, receives highly processed input from every sensory modality, as well as input relating to ongoing cognitive processes, though it should be stressed that, within EC, this information remains at least partially segregated.

The deep layers, especially layer V, receive one of the three main outputs of the hippocampus and, in turn, reciprocate connections from other cortical areas that project to superficial EC.

Brodmann's areas

 * Brodmann area 28 is known as the "area entorhinalis"
 * Brodmann area 34 is known as the "area entorhinalis dorsalis"

Neuron information processing
In 2005, it was discovered that entorhinal cortex contains a neural map of the spatial environment in rats. In 2014, John O'Keefe, May-Britt Moser and Edvard Moser received the Nobel Prize in Physiology or Medicine, partly because of this discovery.

In rodents, neurons in the lateral entorhinal cortex exhibit little spatial selectivity, whereas neurons of the medial entorhinal cortex (MEC), exhibit multiple "place fields" that are arranged in a hexagonal pattern, and are, therefore, called "grid cells". These fields and spacing between fields increase from the dorso-lateral MEA to the ventro-medial MEA.

The same group of researchers has found speed cells in the medial entorhinal cortex of rats. The speed of movement is translated from proprioceptive information and is represented as firing rates in these cells. The cells are known to fire in correlation to future speed of the rodent.

Recently, a general theory has been proposed to elucidate the function of the reelin positive cells in the layer II of the entorhinal cortex. According to this concept, these cells would be generally organized into 1-dimensional ring attractors, and in the medial (in humans: posteromedial) portion, would function as grid cells (anatomically: stellate cells) while in lateral (in humans: anterolateral) portion, where they appear as fan cells, would enable the encoding of new episodic memories. This concept is underscored by the fact that fan cells of the entorhinal cortex are indispensable for the formation of episodic-like memories in rodents.

Single-unit recording of neurons in humans playing video games find path cells in the EC, the activity of which indicates whether a person is taking a clockwise or counterclockwise path. Such EC "direction" path cells show this directional activity irrespective of the location of where a person experiences themselves, which contrasts them to place cells in the hippocampus, which are activated by specific locations.

EC neurons process general information such as directional activity in the environment, which contrasts to that of the hippocampal neurons, which usually encode information about specific places. This suggests that EC encodes general properties about current contexts that are then used by hippocampus to create unique representations from combinations of these properties.

Research generally highlights a useful distinction in which the medial entorhinal cortex (MEC) mainly supports processing of space, whereas the lateral entorhinal cortex (LEC) mainly supports the processing of time.

The MEC exhibits a strong ~8 Hz rhythmic neural activity known as theta. Alterations in the neural activity across the brain region results in an observed "traveling wave" phenomena across the MEC long-axis, similar to that of the hippocampus, due to asymmetric theta oscillations. The underlying cause of these phase shifts and their waveform changes is unknown.

Individual variation in the volume of EC is linked to taste perception. People with a larger EC in the left hemisphere found quinine, the source of bitterness in tonic water, less bitter.

Alzheimer's disease
The entorhinal cortex is the first area of the brain to be affected in Alzheimer's disease; in year 2013, a functional magnetic resonance imaging study has localised the area to the lateral entorhinal cortex. Lopez et al. have shown, in a multimodal study, that there are differences in the volume of the left entorhinal cortex between progressing (to Alzheimer's disease) and stable mild cognitive impairment patients. These authors also found that the volume of the left entorhinal cortex inversely correlates with the level of alpha band phase synchronization between the right anterior cingulate and temporo-occipital regions.

In 2012, neuroscientists at UCLA conducted an experiment using a virtual taxi video game connected to seven epilepsy patients with electrodes already implanted in their brains, allowing the researchers to monitor neuronal activity whenever memories were being formed. As the researchers stimulated the nerve fibers of each of the patients' entorhinal cortex as they were learning, they were then able to better navigate themselves through various routes and recognize landmarks more quickly. This signified an improvement in the patients' spatial memory.

Research
Effect of aerobic exercise

A study on young subjects found aerobic fitness to be positively correlated with entorhinal cortex volume, indicating that aerobic exercise may have a positive effect on the medial temporal lobe memory system (which includes the entorhinal cortex).

In other animals
In rodents, the EC is located at the caudal end of the temporal lobe. The rodent entorhinal cortex shows a modular organization, with different properties and connections in different areas.

In primates it is located at the rostral end of the temporal lobe and stretches dorsolaterally.

title: Entorhinal cortex


text:
Ernst Haeckel

Ernst Heinrich Philipp August Haeckel (16 February 1834 – 9 August 1919) was a German zoologist, naturalist, eugenicist, philosopher, physician, professor, marine biologist and artist. He discovered, described and named thousands of new species, mapped a genealogical tree relating all life forms and coined many terms in biology, including ecology, phylum, phylogeny, and Protista. Haeckel promoted and popularised Charles Darwin's work in Germany and developed the influential but no longer widely held recapitulation theory ("ontogeny recapitulates phylogeny") claiming that an individual organism's biological development, or ontogeny, parallels and summarises its species' evolutionary development, or phylogeny.

The published artwork of Haeckel includes over 100 detailed, multi-colour illustrations of animals and sea creatures, collected in his Kunstformen der Natur ("Art Forms of Nature"), a book which would go on to influence the Art Nouveau artistic movement. As a philosopher, Ernst Haeckel wrote Die Welträthsel (1895–1899; in English: The Riddle of the Universe, 1900), the genesis for the term "world riddle" (Welträtsel); and Freedom in Science and Teaching to support teaching evolution.

Haeckel was also a promoter of scientific racism and embraced the idea of Social Darwinism. He was the first person to characterize the Great War the "first" World War, which he did as early as 1914.

Early life and education

Ernst Haeckel was born on 16 February 1834, in Potsdam (then part of the Kingdom of Prussia). In 1852 Haeckel completed studies at the Domgymnasium, the cathedral high-school of Merseburg. He then studied medicine in Berlin and Würzburg, particularly with Albert von Kölliker, Franz Leydig, Rudolf Virchow (with whom he later worked briefly as assistant), and with the anatomist-physiologist Johannes Peter Müller (1801–1858). Together with Hermann Steudner he attended botany lectures in Würzburg. In 1857 Haeckel attained a doctorate in medicine, and afterwards he received the license to practice medicine. The occupation of physician appeared less worthwhile to Haeckel after contact with suffering patients.

Career
Haeckel studied under Carl Gegenbaur at the University of Jena for three years. In 1861 he earned a habilitation in comparative anatomy and became a professor of zoology at the University at Jena, where he remained for 47 years, from 1862 to 1909. Between 1859 and 1866 Haeckel worked on many phyla, such as radiolarians, poriferans (sponges) and annelids (segmented worms). During a trip to the Mediterranean, Haeckel named nearly 150 new species of radiolarians.

From 1866 to 1867 Haeckel made an extended journey to the Canary Islands with Hermann Fol. On 17 October 1866 he arrived in London. Over the next few days he met Charles Lyell, and visited Thomas Huxley and family at their home. On 21 October he visited Charles Darwin at Down House in Kent. In 1867 he married Agnes Huschke. Their son Walter was born in 1868, their daughters Elizabeth in 1871 and Emma in 1873. In 1869 he traveled as a researcher to Norway, in 1871 to Croatia (where he lived on the island of Hvar in a monastery), and in 1873 to Egypt, Turkey, and Greece. In 1907 he had a museum built in Jena to teach the public about evolution. Haeckel retired from teaching in 1909, and in 1910 he withdrew from the Evangelical Church of Prussia.

On the occasion of his 80th birthday celebration he was presented with a two-volume work entitled Was wir Ernst Haeckel verdanken (What We Owe to Ernst Haeckel), edited at the request of the German Monistenbund by Heinrich Schmidt of Jena.

Personal life and death
In 1864, his first wife, Anna Sethe, died. Haeckel dedicated some species of jellyfish that he found beautiful (such as Desmonema annasethe) to her.

Haeckel's second wife, Agnes, died in 1915, and he became substantially frailer, breaking his leg and arm. He sold his "Villa Medusa" in Jena in 1918 to the Carl Zeiss foundation, which preserved his library. Haeckel died on 9 August 1919.

Religious views
In Monism as Connecting Religion and Science (1892), he argued in favor of monism as the view most compatible with the current scientific understanding of the natural world. His perspective of monism was pantheistic and impersonal. "The monistic idea of God, which alone is compatible with our present knowledge of nature, recognizes the divine spirit in all things. It can never recognise in God a 'personal being,' or, in other words, an individual of limited extension in space, or even of human form. God is everywhere." Haeckel became the most famous proponent of Monism in Germany. In 1906 Haeckel belonged to the founders of the Monist League (Deutscher Monistenbund), which took a stance against philosophical materialism and promote a "natural Weltanschauung". This organization lasted until 1933 and included such notable members as Wilhelm Ostwald, Georg von Arco (1869–1940), Helene Stöcker and Walter Arthur Berendsohn.

Politics
Haeckel's affinity for the German Romantic movement, coupled with his acceptance of a form of Lamarckism, influenced his political beliefs. Rather than being a strict Darwinian, Haeckel believed that the characteristics of an organism were acquired through interactions with the environment and that ontogeny reflected phylogeny. He saw the social sciences as instances of "applied biology", and that phrase was picked up and used for Nazi propaganda.

He was the first person to use the term "first world war" about World War I.

However, Haeckel's books were banned by the Nazi Party, which refused Monism and Haeckel's freedom of thought. Moreover, it is worth mentioning that Haeckel had often overtly recognized the great contribution of educated Jews to the German culture.

Research

Haeckel was a zoologist, an accomplished artist and illustrator, and later a professor of comparative anatomy. Although Haeckel's ideas are important to the history of evolutionary theory, and although he was a competent invertebrate anatomist most famous for his work on radiolaria, many speculative concepts that he championed are now considered incorrect. For example, Haeckel described and named hypothetical ancestral microorganisms that have never been found.

He was one of the first to consider psychology as a branch of physiology. He also proposed the kingdom Protista in 1866. His chief interests lay in evolution and life development processes in general, including development of nonrandom form, which culminated in the beautifully illustrated Kunstformen der Natur (Art forms of nature). Haeckel did not support natural selection, rather believing in Lamarckism.

Haeckel advanced a version of the earlier recapitulation theory previously set out by Étienne Serres in the 1820s and supported by followers of Étienne Geoffroy Saint-Hilaire including Robert Edmond Grant. It proposed a link between ontogeny (development of form) and phylogeny (evolutionary descent), summed up by Haeckel in the phrase "ontogeny recapitulates phylogeny". His concept of recapitulation has been refuted in the form he gave it (now called "strong recapitulation"), in favour of the ideas first advanced by Karl Ernst von Baer. The strong recapitulation hypothesis views ontogeny as repeating forms of adult ancestors, while weak recapitulation means that what is repeated (and built upon) is the ancestral embryonic development process. Haeckel supported the theory with embryo drawings that have since been shown to be oversimplified and in part inaccurate, and the theory is now considered an oversimplification of quite complicated relationships, however comparison of embryos remains a powerful way to demonstrate that all animals are related. Haeckel introduced the concept of heterochrony, the change in timing of embryonic development over the course of evolution.

Haeckel was a flamboyant figure, who sometimes took great, non-scientific leaps from available evidence. For example, at the time when Darwin published On the Origin of Species by Means of Natural Selection (1859), Haeckel postulated that evidence of human evolution would be found in the Dutch East Indies (now Indonesia). At that time, no remains of human ancestors had yet been identified. He described these theoretical remains in great detail and even named the as-yet unfound species, Pithecanthropus alalus, and instructed his students such as Richard and Oskar Hertwig to go and find it.

One student did find some remains: a Dutchman named Eugène Dubois searched the East Indies from 1887 to 1895, discovering the remains of Java Man in 1891, consisting of a skullcap, thighbone, and a few teeth. These remains are among the oldest hominid remains ever found. Dubois classified Java Man with Haeckel's Pithecanthropus label, though they were later reclassified as Homo erectus. Some scientists of the day suggested Dubois' Java Man as a potential intermediate form between modern humans and the common ancestor we share with the other great apes. The current consensus of anthropologists is that the direct ancestors of modern humans were African populations of Homo erectus (possibly Homo ergaster), rather than the Asian populations exemplified by Java Man and Peking Man. (Ironically, a new human species, Homo floresiensis, a dwarf human type, has recently been discovered in the island of Flores).

Polygenism and racial theory
The creationist polygenism of Samuel George Morton and Louis Agassiz, which presented human races as separately created species, was rejected by Charles Darwin, who argued for the monogenesis of the human species and the African origin of modern humans. In contrast to most of Darwin's supporters, Haeckel put forward a doctrine of evolutionary polygenism based on the ideas of the linguist August Schleicher, in which several different language groups had arisen separately from speechless prehuman Urmenschen (proto-humans), which themselves had evolved from simian ancestors. These separate languages had completed the transition from animals to man, and under the influence of each main branch of languages, humans had evolved – in a kind of Lamarckian use-inheritance – as separate species, which could be subdivided into races. From this, Haeckel drew the implication that languages with the most potential yield the human races with the most potential, led by the Semitic and Indo-Germanic groups, with Berber, Jewish, Greco-Roman and Germanic varieties to the fore. As Haeckel stated:

"We must mention here one of the most important results of the comparative study of languages, which for the Stammbaum of the species of men is of the highest significance, namely that human languages probably had a multiple or polyphyletic origin. Human language as such probably developed only after the species of speechless Urmenschen or Affenmenschen (ape-men) had split into several species or kinds. With each of these human species, language developed on its own and independently of the others. At least this is the view of Schleicher, one of the foremost authorities on this subject. ... If one views the origin of the branches of language as the special and principal act of becoming human, and the species of humankind as distinguished according to their language stem, then one can say that the different species of men arose independently of one another."

Haeckel's view can be seen as a forerunner of the views of Carleton Coon, who also believed that human races evolved independently and in parallel with each other. These ideas eventually fell from favour.

Haeckel also applied the hypothesis of polygenism to the modern diversity of human groups. He became a key figure in social darwinism and leading proponent of scientific racism, stating for instance:

"The Caucasian, or Mediterranean man (Homo Mediterraneus), has from time immemorial been placed at the head of all the races of men, as the most highly developed and perfect. It is generally called the Caucasian race, but as, among all the varieties of the species, the Caucasian branch is the least important, we prefer the much more suitable appellation proposed by Friedrich Müller, namely, that of Mediterranese. For the most important varieties of this species, which are moreover the most eminent actors in what is called 'Universal History', first rose to a flourishing condition on the shores of the Mediterranean. ... This species alone (with the exception of the Mongolian) has had an actual history; it alone has attained to that degree of civilisation which seems to raise men above the rest of nature."

Haeckel divided human beings into ten races, of which the Caucasian was the highest and the primitives were doomed to extinction. In his view, 'Negroes' were savages and Whites were the most civilised: for instance, he claimed that '[t]he Negro' had stronger and more freely movable toes than any other race, which, he argued, was evidence of their being less evolved, and which led him to compare them to four-handed" Apes'.

In his Ontogeny and Phylogeny Harvard paleontologist Stephen Jay Gould wrote: "[Haeckel's] evolutionary racism; his call to the German people for racial purity and unflinching devotion to a 'just' state; his belief that harsh, inexorable laws of evolution ruled human civilization and nature alike, conferring upon favored races the right to dominate others ... all contributed to the rise of Nazism."

In his introduction to the Nazi party ideologue Alfred Rosenberg's 1930 book, [The Myth of the Twentieth Century], Peter Peel affirms that Rosenberg had indeed read Haeckel.

In the same line of thought, historian Daniel Gasman states that Haeckel's ideology stimulated the birth of Fascist ideology in Italy and France.

However, in 2009 Robert J. Richards noted: "Haeckel, on his travels to Ceylon and Indonesia, often formed closer and more intimate relations with natives, even members of the untouchable classes, than with the European colonials." and says the Nazis rejected Haeckel, since he opposed antisemitism, while supporting ideas they disliked (for instance atheism, feminism, internationalism, pacifism etc.).

The Jena Declaration, published by the German Zoological Society, rejects the idea of human "races" and distances itself from the racial theories of Ernst Haeckel and other 20th century scientists. It claims that genetic variation between human populations is smaller than within them, demonstrating that the biological concept of "races" is invalid. The statement highlights that there are no specific genes or genetic markers that match with conventional racial categorizations. It also indicates that the idea of "races" is based on racism rather than any scientific factuality.

Asia hypothesis
Haeckel claimed the origin of humanity was to be found in Asia: he believed that Hindustan (Indian subcontinent) was the actual location where the first humans had evolved. Haeckel argued that humans were closely related to the primates of Southeast Asia and rejected Darwin's hypothesis of Africa.

Haeckel later claimed that the missing link was to be found on the lost continent of Lemuria located in the Indian Ocean. He believed that Lemuria was the home of the first humans and that Asia was the home of many of the earliest primates; he thus supported that Asia was the cradle of hominid evolution. Haeckel also claimed that Lemuria connected Asia and Africa, which allowed the migration of humans to the rest of the world.

In Haeckel's book The History of Creation (1884) he included migration routes which he thought the first humans had used outside of Lemuria.

Embryology and recapitulation theory

When Haeckel was a student in the 1850s he showed great interest in embryology, attending the rather unpopular lectures twice and in his notes sketched the visual aids: textbooks had few illustrations, and large format plates were used to show students how to see the tiny forms under a reflecting microscope, with the translucent tissues seen against a black background. Developmental series were used to show stages within a species, but inconsistent views and stages made it even more difficult to compare different species. It was agreed by all European evolutionists that all vertebrates looked very similar at an early stage, in what was thought of as a common ideal type, but there was a continuing debate from the 1820s between the Romantic recapitulation theory that human embryos developed through stages of the forms of all the major groups of adult animals, literally manifesting a sequence of organisms on a linear chain of being, and Karl Ernst von Baer's opposing view, stated in von Baer's laws of embryology, that the early general forms diverged into four major groups of specialised forms without ever resembling the adult of another species, showing affinity to an archetype but no relation to other types or any transmutation of species. By the time Haeckel was teaching he was able to use a textbook with woodcut illustrations written by his own teacher Albert von Kölliker, which purported to explain human development while also using other mammalian embryos to claim a coherent sequence. Despite the significance to ideas of transformism, this was not really polite enough for the new popular science writing, and was a matter for medical institutions and for experts who could make their own comparisons.

Darwin, Naturphilosophie and Lamarck
Darwin's On the Origin of Species, which made a powerful impression on Haeckel when he read it in 1864, was very cautious about the possibility of ever reconstructing the history of life, but did include a section reinterpreting von Baer's embryology and revolutionising the field of study, concluding that "Embryology rises greatly in interest, when we thus look at the embryo as a picture, more or less obscured, of the common parent-form of each great class of animals." It mentioned von Baer's 1828 anecdote (misattributing it to Louis Agassiz) that at an early stage embryos were so similar that it could be impossible to tell whether an unlabelled specimen was of a mammal, a bird, or of a reptile, and Darwin's own research using embryonic stages of barnacles to show that they are crustaceans, while cautioning against the idea that one organism or embryonic stage is "higher" or "lower", or more or less evolved. Haeckel disregarded such caution, and in a year wrote his massive and ambitious Generelle Morphologie, published in 1866, presenting a revolutionary new synthesis of Darwin's ideas with the German tradition of Naturphilosophie going back to Goethe and with the progressive evolutionism of Lamarck in what he called Darwinismus. He used morphology to reconstruct the evolutionary history of life, in the absence of fossil evidence using embryology as evidence of ancestral relationships. He invented new terms, including ontogeny and phylogeny, to present his evolutionised recapitulation theory that "ontogeny recapitulated phylogeny". The two massive volumes sold poorly, and were heavy going: with his limited understanding of German, Darwin found them impossible to read. Haeckel's publisher turned down a proposal for a "strictly scholarly and objective" second edition.

Embryological drawings

Haeckel's aim was a reformed morphology with evolution as the organising principle of a cosmic synthesis unifying science, religion, and art. He was giving successful "popular lectures" on his ideas to students and townspeople in Jena, in an approach pioneered by his teacher Rudolf Virchow. To meet his publisher's need for a popular work he used a student's transcript of his lectures as the basis of his Natürliche Schöpfungsgeschichte of 1868, presenting a comprehensive presentation of evolution. In the Spring of that year he drew figures for the book, synthesising his views of specimens in Jena and published pictures to represent types. After publication he told a colleague that the images "are completely exact, partly copied from nature, partly assembled from all illustrations of these early stages that have hitherto become known". There were various styles of embryological drawings at that time, ranging from more schematic representations to "naturalistic" illustrations of specific specimens. Haeckel believed privately that his figures were both exact and synthetic, and in public asserted that they were schematic like most figures used in teaching. The images were reworked to match in size and orientation, and though displaying Haeckel's own views of essential features, they support von Baer's concept that vertebrate embryos begin similarly and then diverge. Relating different images on a grid conveyed a powerful evolutionary message. As a book for the general public, it followed the common practice of not citing sources.

The book sold very well, and while some anatomical experts hostile to Haeckel's evolutionary views expressed some private concerns that certain figures had been drawn rather freely, the figures showed what they already knew about similarities in embryos. The first published concerns came from Ludwig Rütimeyer, a professor of zoology and comparative anatomy at the University of Basel who had placed fossil mammals in an evolutionary lineage early in the 1860s and had been sent a complimentary copy. At the end of 1868 his review in the Archiv für Anthropologie wondered about the claim that the work was "popular and scholarly", doubting whether the second was true, and expressed horror about such public discussion of man's place in nature with illustrations such as the evolutionary trees being shown to non-experts. Though he made no suggestion that embryo illustrations should be directly based on specimens, to him the subject demanded the utmost "scrupulosity and conscientiousness" and an artist must "not arbitrarily model or generalise his originals for speculative purposes" which he considered proved by comparison with works by other authors. In particular, "one and the same, moreover incorrectly interpreted woodcut, is presented to the reader three times in a row and with three different captions as [the] embryo of the dog, the chick, [and] the turtle". He accused Haeckel of "playing fast and loose with the public and with science", and failing to live up to the obligation to the truth of every serious researcher. Haeckel responded with angry accusations of bowing to religious prejudice, but in the second (1870) edition changed the duplicated embryo images to a single image captioned "embryo of a mammal or bird". Duplication using galvanoplastic stereotypes (clichés) was a common technique in textbooks, but not on the same page to represent different eggs or embryos. In 1891 Haeckel made the excuse that this "extremely rash foolishness" had occurred in undue haste but was "bona fide", and since repetition of incidental details was obvious on close inspection, it is unlikely to have been intentional deception.

The revised 1870 second edition of 1,500 copies attracted more attention, being quickly followed by further revised editions with larger print runs as the book became a prominent part of the optimistic, nationalist, anticlerical "culture of progress" in Otto von Bismarck's new German Empire. The similarity of early vertebrate embryos became common knowledge, and the illustrations were praised by experts such as Michael Foster of the University of Cambridge. In the introduction to his 1871 The Descent of Man, and Selection in Relation to Sex, Darwin gave particular praise to Haeckel, writing that if Natürliche Schöpfungsgeschichte "had appeared before my essay had been written, I should probably never have completed it". The first chapter included an illustration: "As some of my readers may never have seen a drawing of an embryo, I have given one of man and another of a dog, at about the same early stage of development, carefully copied from two works of undoubted accuracy" with a footnote citing the sources and noting that "Häckel has also given analogous drawings in his Schöpfungsgeschichte." The fifth edition of Haeckel's book appeared in 1874, with its frontispiece a heroic portrait of Haeckel himself, replacing the previous controversial image of the heads of apes and humans.

Controversy
Later in 1874, Haeckel's simplified embryology textbook Anthropogenie made the subject into a battleground over Darwinism aligned with Bismarck's Kulturkampf ("culture struggle") against the Catholic Church. Haeckel took particular care over the illustrations, changing to the leading zoological publisher Wilhelm Engelmann of Leipzig and obtaining from them use of illustrations from their other textbooks as well as preparing his own drawings including a dramatic double page illustration showing "early", "somewhat later" and "still later" stages of 8 different vertebrates. Though Haeckel's views had attracted continuing controversy, there had been little dispute about the embryos and he had many expert supporters, but Wilhelm His revived the earlier criticisms and introduced new attacks on the 1874 illustrations. Others joined in: both expert anatomists and Catholic priests and supporters were politically opposed to Haeckel's views.

While it has been widely claimed that Haeckel was charged with fraud by five professors and convicted by a university court at Jena, there does not appear to be an independently verifiable source for this claim. Recent analyses (Richardson 1998, Richardson and Keuck 2002) have found that some of the criticisms of Haeckel's embryo drawings were legitimate, but others were unfounded. There were multiple versions of the embryo drawings, and Haeckel rejected the claims of fraud. It was later said that "there is evidence of sleight of hand" on both sides of the feud between Haeckel and Wilhelm His. Robert J. Richards, in a paper published in 2008, defends the case for Haeckel, shedding doubt against the fraud accusations based on the material used for comparison with what Haeckel could access at the time.

Awards and honors
Haeckel was elected as a member to the American Philosophical Society in 1885. He was awarded the title of Excellency by Kaiser Wilhelm II in 1907 and the Linnean Society of London's prestigious Darwin-Wallace Medal in 1908. In the United States, Mount Haeckel, a 13418 ft summit in the Eastern Sierra Nevada, overlooking the Evolution Basin, is named in his honour, as is another Mount Haeckel, a 2941 m summit in New Zealand; and the asteroid 12323 Haeckel.

In Jena he is remembered with a monument at Herrenberg (erected in 1969), an exhibition at Ernst-Haeckel-Haus, and at the Jena Phyletic Museum, which continues to teach about evolution and share his work to this day.

The ratfish, Harriotta haeckeli is named in his honor.

The research vessel Ernst Haeckel is named in his honor.

In 1981, a botanical journal called Ernstia was started being published in the city of Maracay, Venezuela.

In 2013, Ernstia, a genus of calcareous sponges in the family Clathrinidae. The genus was erected to contain five species previously assigned to Clathrina. The genus name honors Ernst Haeckel for his contributions towards sponge taxonomy and phylogeny.

Publications

Darwin's 1859 book On the Origin of Species had immense popular influence, but although its sales exceeded its publisher's hopes it was a technical book rather than a work of popular science: long, difficult and with few illustrations. One of Haeckel's books did a great deal to explain his version of "Darwinism" to the world. It was a bestselling, provocatively illustrated book in German, titled Natürliche Schöpfungsgeschichte, published in Berlin in 1868, and translated into English as The History of Creation in 1876. Until 1909, eleven editions had appeared, as well as 25 translations into other languages. The Natürliche Schöpfungsgeschichte cemented Haeckel's reputation as one of Germany's most forceful popularizers of science. His Welträthsel were reprinted ten times after the book's first publication in 1899; ultimately, over 400,000 copies were sold.

Haeckel argued that human evolution consisted of precisely 22 phases, the 21st – the "missing link" – being a halfway step between apes and humans. He even formally named this missing link Pithecanthropus alalus, translated as "ape man without speech".

Haeckel's literary output was extensive, including many books, scientific papers, and illustrations.

Monographs

 * Radiolaria (1862)
 * Siphonophora (1869)
 * Monera (1870)
 * Calcareous Sponges (1872)

Challenger reports

 * Deep-Sea Medusae (1881)
 * Siphonophora (1888)
 * Deep-Sea Keratosa (1889)
 * Radiolaria (1887)

Books on biology and its philosophy

 * Generelle Morphologie der Organismen: allgemeine Grundzüge der organischen Formen-Wissenschaft, mechanisch begründet durch die von Charles Darwin reformirte Descendenz-Theorie. (1866) Berlin (General morphology of organisms: general foundations of form-science, mechanically grounded by the descendance theory reformed by Charles Darwin)
 * Natürliche Schöpfungsgeschichte (1868); in English The History of Creation (1876; 6th ed.: New York, D. Appleton and Co., 1914, 2 volumes)
 * Freie Wissenschaft und freie Lehre (1877), in English, Free Science and Free Teaching
 * Die systematische Phylogenie (1894) – Systematic Phylogeny
 * Die Welträthsel (1895–1899), also spelled Die Welträtsel – in English The Riddle of the Universe: At the Close of the Nineteenth Century, Translated by Joseph McCabe, New York and London: Harper & Brothers Publishers, 1900.
 * Über unsere gegenwärtige Kenntnis vom Ursprung des Menschen (1898) (On our current understanding of the origin of man) – in English The Last Link, 1898
 * Der Kampf um den Entwickelungsgedanken (1905) (The struggle over thought on evolution) – in English Last Words on Evolution: A Popular Retrospect and Summary, Translated from the Second Edition by Joseph McCabe, New York: Peter Eckler, Publisher; London: A. Owen & Co., 1906.
 * Die Lebenswunder (1904) – in English The Wonders of Life
 * Kristallseelen : Studien über das anorganische Leben (1917) (Crystal souls: studies on inorganic life)
 * Kristallseelen : Studien über das anorganische Leben (1917) (Crystal souls: studies on inorganic life)

Travel books

 * Indische Reisebriefe (1882) – Travel notes of India
 * Aus Insulinde: Malayische Reisebriefe (1901) – Travel notes of Malaysia
 * Kunstformen der Natur (1904) – Art forms of Nature, Digital Edition (1924)
 * Wanderbilder (1905) – "Travel Images"
 * A visit to Ceylon

For a fuller list of works of and about Haeckel, see his entry in the German Wikisource.

Assessments of potential influence on Nazism
Some historians have seen Haeckel's social Darwinism as a forerunner to Nazi ideology. Others have denied the relationship altogether.

The evidence is in some respects ambiguous. On one hand, Haeckel was an advocate of scientific racism. He held that evolutionary biology had definitively proven that races were unequal in intelligence and ability, and that their lives were also of unequal value, e.g., "These lower races (such as the Veddahs or Australian negroes) are psychologically nearer to the mammals (apes or dogs) than to civilised Europeans; we must therefore, assign a totally different value to their lives." As a result of the "struggle for existence", it followed that the "lower" races would eventually be exterminated. He was also a social Darwinist who believed that "survival of the fittest" was a natural law, and that struggle led to improvement of the race. As an advocate of eugenics, he also believed that about 200,000 mentally and congenitally ill should be killed by a medical control board. This idea was later put into practice by Nazi Germany, as part of the Aktion T4 program. Alfred Ploetz, founder of the German Society for Racial Hygiene, praised Haeckel repeatedly, and invited him to become an honorary member. Haeckel accepted the invitation. Haeckel also believed that Germany should be governed by an authoritarian political system, and that inequalities both within and between societies were an inevitable product of evolutionary law. Haeckel was also an extreme German nationalist who believed strongly in the superiority of German culture.

On the other hand, Haeckel was not an anti-Semite. In the racial hierarchies he constructed Jews tended to appear closer to the top, rather than closer to the bottom as in Nazi racial thought. He was also a pacifist until the First World War, when he wrote propaganda in favor of the war. The principal arguments of historians who deny a meaningful connection between Haeckel and Nazism are that Haeckel's ideas were very common at the time, that Nazis were much more strongly influenced by other thinkers, and that Haeckel is properly classified as a 19th-century German liberal, rather than a forerunner to Nazism. They also point to incompatibilities between evolutionary biology and Nazi ideology.

Nazis themselves divided on the question of whether Haeckel should be counted as a pioneer of their ideology. SS captain and biologist Heinz Brücher wrote a biography of Haeckel in 1936, in which he praised Haeckel as a "pioneer in biological state thinking". This opinion was also shared by the scholarly journal, Der Biologe, which celebrated Haeckel's 100th birthday, in 1934, with several essays acclaiming him as a pioneering thinker of Nazism. Other Nazis kept their distance from Haeckel. Nazi propaganda guidelines issued in 1935 listed books which popularized Darwin and evolution on an "expunged list". Haeckel was included by name as a forbidden author. Gunther Hecht, a member of the Nazi Department of Race Politics, also issued a memorandum rejecting Haeckel as a forerunner of Nazism. Kurt Hildebrandt, a Nazi political philosopher, also rejected Haeckel. Eventually Haeckel was rejected by Nazi bureaucrats.

title: Ernst Haeckel


text:
Talk:Electronics

Avionics
Should avionics be considered a principle branch of electronics, or simply the application of electronics to one particular field? Just as we don't list Automotive electronics, Marine electronics, Consumer electronics or Audio electronics as principle branches, I don't believe avionics should be considered a principle branch either. Meters (talk) 22:18, 17 May 2022 (UTC)

Tle
What is electronic particles 131.226.103.53 (talk) 07:52, 30 August 2023 (UTC)

 * Does this help? ~Kvng (talk) 14:30, 6 September 2023 (UTC)

title: Talk:Electronics


text:
Evolutionism

Evolutionism is a term used (usually derogatorily) to denote the theory of evolution. Its exact meaning has changed over time as the study of evolution has progressed. In the 19th century, it was used to describe the belief that organisms deliberately improved themselves through progressive inherited change (orthogenesis). The teleological belief went on to include cultural evolution and social evolution. In the 1970s, the term "Neo-Evolutionism" was used to describe the idea that "human beings sought to preserve a familiar style of life unless change was forced on them by factors that were beyond their control."

The term is most often used by creationists to describe adherence to the scientific consensus on evolution as equivalent to a secular religion. The term is very seldom used within the scientific community, since the scientific position on evolution is accepted by the overwhelming majority of scientists. Because evolutionary biology is the default scientific position, it is assumed that "scientists" or "biologists" are "evolutionists" unless specifically noted otherwise. In the creation–evolution controversy, creationists often call those who accept the validity of the modern evolutionary synthesis "evolutionists" and the theory itself "evolutionism".

19th-century teleological use
Before its use to describe biological evolution, the term "evolution" was originally used to refer to any orderly sequence of events with the outcome somehow contained at the start. The first five editions of Darwin's in Origin of Species used the word "evolved", but the word "evolution" was only used in its sixth edition in 1872. By then, Herbert Spencer had developed the concept theory that organisms strive to evolve due to an internal "driving force" (orthogenesis) in 1862. Edward B. Tylor and Lewis H Morgan brought the term "evolution" to anthropology though they tended toward the older pre-Spencerian definition helping to form the concept of unilineal (social) evolution used during the later part of what Trigger calls the Antiquarianism-Imperial Synthesis period (c1770-c1900). The term evolutionism subsequently came to be used for the now discredited theory that evolution contained a deliberate component, rather than the selection of beneficial traits from random variation by differential survival.

Modern use by creationists
The term evolution is widely used, but the term evolutionism is not used in the scientific community to refer to evolutionary biology as it is redundant and anachronistic.

However, the term has been used by creationists in discussing the creation–evolution controversy. For example, the Institute for Creation Research, in order to imply placement of evolution in the category of 'religions', including atheism, fascism, humanism and occultism, commonly uses the words evolutionism and evolutionist to describe the consensus of mainstream science and the scientists subscribing to it, thus implying through language that the issue is a matter of religious belief. The BioLogos Foundation, an organization that promotes the idea of theistic evolution, uses the term "evolutionism" to describe "the atheistic worldview that so often accompanies the acceptance of biological evolution in public discourse." It views this as a subset of scientism.

title: Evolutionism


text:
Entscheidungsproblem

In mathematics and computer science, the ; ) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. The problem asks for an algorithm that considers, as input, a statement and answers "yes" or "no" according to whether the statement is universally valid, i.e., valid in every structure.

Completeness theorem
By the completeness theorem of first-order logic, a statement is universally valid if and only if it can be deduced using logical rules and axioms, so the Entscheidungsproblem can also be viewed as asking for an algorithm to decide whether a given statement is provable using the rules of logic.

In 1936, Alonzo Church and Alan Turing published independent papers showing that a general solution to the Entscheidungsproblem is impossible, assuming that the intuitive notion of "effectively calculable" is captured by the functions computable by a Turing machine (or equivalently, by those expressible in the lambda calculus). This assumption is now known as the Church–Turing thesis.

History of the problem
The origin of the Entscheidungsproblem goes back to Gottfried Leibniz, who in the seventeenth century, after having constructed a successful mechanical calculating machine, dreamt of building a machine that could manipulate symbols in order to determine the truth values of mathematical statements. He realized that the first step would have to be a clean formal language, and much of his subsequent work was directed toward that goal. In 1928, David Hilbert and Wilhelm Ackermann posed the question in the form outlined above.

In continuation of his "program", Hilbert posed three questions at an international conference in 1928, the third of which became known as "Hilbert's Entscheidungsproblem". In 1929, Moses Schönfinkel published one paper on special cases of the decision problem, that was prepared by Paul Bernays.

As late as 1930, Hilbert believed that there would be no such thing as an unsolvable problem.

Negative answer
Before the question could be answered, the notion of "algorithm" had to be formally defined. This was done by Alonzo Church in 1935 with the concept of "effective calculability" based on his λ-calculus, and by Alan Turing the next year with his concept of Turing machines. Turing immediately recognized that these are equivalent models of computation.

A negative answer to the Entscheidungsproblem was then given by Alonzo Church in 1935–36 (Church's theorem) and independently shortly thereafter by Alan Turing in 1936 (Turing's proof). Church proved that there is no computable function which decides, for two given λ-calculus expressions, whether they are equivalent or not. He relied heavily on earlier work by Stephen Kleene. Turing reduced the question of the existence of an 'algorithm' or 'general method' able to solve the Entscheidungsproblem to the question of the existence of a 'general method' which decides whether any given Turing machine halts or not (the halting problem). If 'algorithm' is understood as meaning a method that can be represented as a Turing machine, and with the answer to the latter question negative (in general), the question about the existence of an algorithm for the Entscheidungsproblem also must be negative (in general). In his 1936 paper, Turing says: "Corresponding to each computing machine 'it' we construct a formula 'Un(it)' and we show that, if there is a general method for determining whether 'Un(it)' is provable, then there is a general method for determining whether 'it' ever prints 0".

The work of both Church and Turing was heavily influenced by Kurt Gödel's earlier work on his incompleteness theorem, especially by the method of assigning numbers (a Gödel numbering) to logical formulas in order to reduce logic to arithmetic.

The Entscheidungsproblem is related to Hilbert's tenth problem, which asks for an algorithm to decide whether Diophantine equations have a solution. The non-existence of such an algorithm, established by the work of Yuri Matiyasevich, Julia Robinson, Martin Davis, and Hilary Putnam, with the final piece of the proof in 1970, also implies a negative answer to the Entscheidungsproblem.

Generalizations
Using the deduction theorem, the Entscheidungsproblem encompasses the more general problem of deciding whether a given first-order sentence is entailed by a given finite set of sentences, but validity in first-order theories with infinitely many axioms cannot be directly reduced to the Entscheidungsproblem. Such more general decision problems are, however, of practical interest. Some first-order theories are algorithmically decidable; examples of this include Presburger arithmetic, real closed fields, and static type systems of many programming languages. On the other hand, the first-order theory of the natural numbers with addition and multiplication expressed by Peano's axioms cannot be decided with an algorithm.

Fragments
By default, the citations in the section are from Pratt-Hartmann (2023).

The classical Entscheidungsproblem asks that, given a first-order formula, whether it is true in all models. The finitary problem asks whether it is true in all finite models. Trakhtenbrot's theorem shows that this is also undecidable.

Some notations: $$\rm{Sat} (\Phi) $$ means the problem of deciding whether there exists a model for a set of logical formulas $$\Phi $$. $$\rm{FinSat} (\Phi) $$ is the same problem, but for finite models. The $$\rm{Sat} $$-problem for a logical fragment is called decidable if there exists a program that can decide, for each $$\Phi  $$ finite set of logical formulas in the fragment, whether $$\rm{Sat} (\Phi) $$ or not.

There is a hierarchy of decidabilities. On the top are the undecidable problems. Below it are the decidable problems. Furthermore, the decidable problems can be divided into a complexity hierarchy.

Aristotelean and relational
Aristotelean logic considers 4 kinds of sentences: "All p are q", "All p are not q", "Some p is q", "Some p is not q". We can formalize these kinds of sentences as a fragment of first-order logic:$$\forall x, p(x) \to \pm q(x), \quad \exists x, p(x) \wedge \pm  q(x) $$where $$p, q $$ are atomic predicates, and $$+q := q, \; -q := \neg q $$. Given a finite set of Aristotelean logic formulas, it is NLOGSPACE-complete to decide its $$\rm{Sat} $$. It is also NLOGSPACE-complete to decide $$\rm{Sat} $$ for a slight extension (Theorem 2.7):$$\forall x, \pm p(x) \to \pm  q(x), \quad \exists x, \pm p(x) \wedge \pm  q(x) $$Relational logic extends Aristotelean logic by allowing a relational predicate. For example, "Everybody loves somebody" can be written as $\forall x, \rm{body}(x), \exists y, \rm{body}(y) \wedge \rm{love}(x, y) $. Generally, we have 8 kinds of sentences:$$\begin{aligned} \forall x, p(x) \to (\forall y, q(x) \to \pm r(x, y)), &\quad \forall x, p(x) \to (\exists y, q(x) \wedge \pm r(x, y)) \\ \exists x, p(x) \wedge (\forall y, q(x) \to \pm r(x, y)), &\quad \exists x, p(x) \wedge (\exists y, q(x) \wedge \pm r(x, y)) \end{aligned} $$It is NLOGSPACE-complete to decide its $$\rm{Sat} $$ (Theorem 2.15). Relational logic can be extended to 32 kinds of sentences by allowing $$\pm p, \pm q $$, but this extension is EXPTIME-complete (Theorem 2.24).

Arity
The first-order logic fragment where the only variable names are $$x, y $$ is NEXPTIME-complete (Theorem 3.18). With $$x, y, z $$, it is RE-complete to decide its $$\rm{Sat} $$, and co-RE-complete to decide $$\rm{FinSat}  $$ (Theorem 3.15), thus undecidable.

The monadic predicate calculus is the fragment where each formula contains only 1-ary predicates and no function symbols. Its $$\rm{Sat}  $$ is NEXPTIME-complete (Theorem 3.22).

Quantifier prefix
Any first-order formula has a prenex normal form. For each possible quantifier prefix to the prenex normal form, we have a fragment of first-order logic. For example, the Bernays–Schönfinkel class, $$[\exists^*\forall^*]_= $$, is the class of first-order formulas with quantifier prefix $$\exists\cdots\exists\forall\cdots \forall     $$, equality symbols, and no function symbols.

For example, Turing's 1936 paper (p. 263) observed that since the halting problem for each Turing machine is equivalent to a first-order logical formula of form $$\forall \exists \forall \exists^6 $$, the problem $$\rm{Sat}(\forall \exists \forall \exists^6)    $$ is undecidable.

The precise boundaries are known, sharply:

 * $$\rm{Sat}(\forall \exists \forall) $$ and $$\rm{Sat}([\forall \exists \forall]_{=} ) $$are co-RE-complete, and the $$\rm{FinSat}  $$ problems are RE-complete (Theorem 5.2).
 * Same for $$\forall^3 \exists $$ (Theorem 5.3).
 * $$\exists^* \forall^2 \exists^* $$ is decidable, proved independently by Gödel, Schütte, and Kalmár.
 * $$[\forall^2 \exists]_= $$ is undecidable.
 * For any $$n \geq 0 $$, both $$\rm{Sat}(\exists^n \forall^*) $$ and $$\rm{Sat}([\exists^n \forall^*]_=)  $$ are NEXPTIME-complete (Theorem 5.1).
 * This implies that $$\rm{Sat}( [\exists^*\forall^*]_= ) $$ is decidable, a result first published by Bernays and Schönfinkel.
 * For any $$n \geq 0, m \geq 2  $$, $$\rm{Sat}(\exists^n \forall \exists^m )  $$ is EXPTIME-complete (Section 5.4.1).
 * For any $$n \geq 0 $$, $$\rm{Sat}([\exists^n \forall \exists^*]_=)  $$ is NEXPTIME-complete (Section 5.4.2).
 * This implies that $$\rm{Sat}(\exists^*\forall^*\exists^*) $$ is decidable, a result first published by Ackermann.
 * For any $$n \geq 0 $$, $$\rm{Sat}(\exists^n \forall \exists)  $$ and $$\rm{Sat}([\exists^n \forall \exists]_=)   $$ are PSPACE-complete (Section 5.4.3).

Börger et al. (2001) describes the level of computational complexity for every possible fragment with every possible combination of quantifier prefix, functional arity, predicate arity, and equality/no-equality.

Practical decision procedures
Having practical decision procedures for classes of logical formulas is of considerable interest for program verification and circuit verification. Pure Boolean logical formulas are usually decided using SAT-solving techniques based on the DPLL algorithm.

For more general decision problems of first-order theories, conjunctive formulas over linear real or rational arithmetic can be decided using the simplex algorithm, formulas in linear integer arithmetic (Presburger arithmetic) can be decided using Cooper's algorithm or William Pugh's Omega test. Formulas with negations, conjunctions and disjunctions combine the difficulties of satisfiability testing with that of decision of conjunctions; they are generally decided nowadays using SMT-solving techniques, which combine SAT-solving with decision procedures for conjunctions and propagation techniques. Real polynomial arithmetic, also known as the theory of real closed fields, is decidable; this is the Tarski–Seidenberg theorem, which has been implemented in computers by using the cylindrical algebraic decomposition.

title: Entscheidungsproblem


text:
Einhard

Einhard (also Eginhard or Einhart; E(g)inhardus; c. 775 – 14 March 840) was a Frankish scholar and courtier. Einhard was a dedicated servant of Charlemagne and his son Louis the Pious; his main work is a biography of Charlemagne, the Vita Karoli Magni, "one of the most precious literary bequests of the early Middle Ages".

Public life
Einhard was from the eastern German-speaking part of the Frankish Kingdom. Born into a family of landowners of some importance, his parents sent him to be educated by the monks of Fulda, one of the most impressive centers of learning in the Frank lands. Perhaps due to his small stature, which restricted his riding and sword-fighting ability, Einhard concentrated his energies on scholarship, especially the mastering of Latin. He was accepted into the hugely wealthy court of Charlemagne around 791 or 792. Charlemagne actively sought to amass scholarly men around him and established a royal school led by the Northumbrian scholar Alcuin. Einhard was evidently a talented builder and construction manager, because Charlemagne put him in charge of the completion of several palace complexes including Aachen and Ingelheim. Despite the fact that Einhard was on intimate terms with Charlemagne, he never achieved office in his reign. In 814, on Charlemagne's death, his son Louis the Pious made Einhard his private secretary. Einhard retired from court during the time of the disputes between Louis and his sons in the spring of 830.

He died at Seligenstadt in 840.

Private life
Einhard was married to Emma, of whom little is known. There is a possibility that their marriage bore a son, Vussin. Their marriage also appears to have been exceptionally liberal for the period, with Emma being as active as Einhard, if not more so, in the handling of their property. It is said that in the later years of their marriage Emma and Einhard abstained from sexual relations, choosing instead to focus their attentions on their many religious commitments. Though he was undoubtedly devoted to her, Einhard wrote nothing of his wife until after her death on 13 December 835, when he wrote to a friend that he was reminded of her loss in ‘every day, in every action, in every undertaking, in all the administration of the house and household, in everything needing to be decided upon and sorted out in my religious and earthly responsibilities’.

Religious beliefs
Einhard made numerous references to himself as a "sinner" according to his strong Christian faith. He erected churches at both of his estates in Michelstadt and Mulinheim. In Michelstadt, he also saw fit to build a basilica completed in 827 and then sent a servant, Ratleic, to Rome with an end to find relics for the new building. Once in Rome, Ratleic robbed a catacomb of the bones of the Martyrs Marcellinus and Peter and had them translated to Michelstadt. Once there, the relics made it known they were unhappy with their new tomb and thus had to be moved again to Mulinheim. Once established there, they proved to be miracle workers. Although unsure as to why these saints should choose such a "sinner" as their patron, Einhard nonetheless set about ensuring they continued to receive a resting place fitting of their honour. Between 831 and 834 he founded a Benedictine Monastery and, after the death of his wife, served as its Abbot until his own death in 840.

Local lore
Local lore from Seligenstadt portrays Einhard as the lover of Emma, one of Charlemagne's daughters, and has the couple elope from court. Charlemagne found them at Seligenstadt (then called Obermühlheim) and forgave them. This account is used to explain the name "Seligenstadt" by folk etymology. Einhard and his wife were originally buried in one sarcophagus in the choir of the church in Seligenstadt, but in 1810 the sarcophagus was presented by the Grand Duke of Hesse to the count of Erbach, who claims descent from Einhard as the husband of Imma, the reputed daughter of Charlemagne. The count put it in the famous chapel of his castle at Erbach in the Odenwald.

Works
The most famous of Einhard's works is his biography of Charlemagne, the Vita Karoli Magni, "The Life of Charlemagne" (c. 817–836), which provides much direct information about Charlemagne's life and character, written sometime between 817 and 830. In composing this he relied heavily upon the Royal Frankish Annals. Einhard's literary model was the classical work of the Roman historian Suetonius, the Lives of the Caesars, though it is important to stress that the work is very much Einhard's own, that is to say he adapts the models and sources for his own purposes. His work was written as a praise of Charlemagne, whom he regarded as a foster-father (nutritor) and to whom he was a debtor "in life and death". The work thus contains an understandable degree of bias, Einhard taking care to exculpate Charlemagne in some matters, not mention others, and to gloss over certain issues which would be of embarrassment to Charlemagne, such as the morality of his daughters; by contrast, other issues are curiously not glossed over, like his concubines.

Einhard is also responsible for three other extant works: a collection of letters, On the Translations and the Miracles of SS. Marcellinus and Petrus, and On the Adoration of the Cross. The latter dates from ca. 830 and was not rediscovered until 1885, when Ernst Dümmler identified a text in a manuscript in Vienna as the missing Libellus de adoranda cruce, which Einhard had dedicated to his pupil Lupus Servatus.

The Arch of Einhard was a reliquary made by Einhard, which reproduced on a small scale a Roman triumphal arch that represented the victory of Christianity. It has not survived.

title: Einhard


text:
Ester

In chemistry, an ester is a functional group derived from an acid (organic or inorganic) in which the hydrogen atom (H) of at least one acidic hydroxyl group (\sOH) of that acid is replaced by an organyl group (\sR). Analogues derived from oxygen replaced by other chalcogens belong to the ester category as well. According to some authors, organyl derivatives of acidic hydrogen of other acids are esters as well (e.g. amides), but not according to the IUPAC.

Glycerides are fatty acid esters of glycerol; they are important in biology, being one of the main classes of lipids and comprising the bulk of animal fats and vegetable oils. Lactones are cyclic carboxylic esters; naturally occurring lactones are mainly 5- and 6-membered ring lactones. Lactones contribute to the aroma of fruits, butter, cheese, vegetables like celery and other foods.

Esters can be formed from oxoacids (e.g. esters of acetic acid, carbonic acid, sulfuric acid, phosphoric acid, nitric acid, xanthic acid), but also from acids that do not contain oxygen (e.g. esters of thiocyanic acid and trithiocarbonic acid). An example of an ester formation is the substitution reaction between a carboxylic acid (R\sC(\dO)\sOH) and an alcohol (R'\sOH), forming an ester (R\sC(\dO)\sO\sR'), where R stands for any group (typically hydrogen or organyl) and R stands for organyl group.

Organyl esters of carboxylic acids typically have a pleasant smell; those of low molecular weight are commonly used as fragrances and are found in essential oils and pheromones. They perform as high-grade solvents for a broad array of plastics, plasticizers, resins, and lacquers, and are one of the largest classes of synthetic lubricants on the commercial market. Polyesters are important plastics, with monomers linked by ester moieties. Esters of phosphoric acid form the backbone of DNA molecules. Esters of nitric acid, such as nitroglycerin, are known for their explosive properties.

There are compounds in which an acidic hydrogen of acids mentioned in this article are not replaced by an organyl, but by some other group. According to some authors, those compounds are esters as well, especially when the first carbon atom of the organyl group replacing acidic hydrogen, is replaced by another atom from the group 14 elements (Si, Ge, Sn, Pb); for example, according to them, trimethylstannyl acetate (or trimethyltin acetate) CH3COOSn(CH3)3 is a trimethylstannyl ester of acetic acid, and dibutyltin dilaurate (CH3(CH2)10COO)2Sn((CH2)3CH3)2 is a dibutylstannylene ester of lauric acid, and the Phillips catalyst CrO2(OSi(OCH3)3)2 is a trimethoxysilyl ester of chromic acid (H2CrO4).

Etymology
The word ester was coined in 1848 by a German chemist Leopold Gmelin, probably as a contraction of the German Essigäther, "acetic ether".

IUPAC nomenclature
The names of esters that are formed from an alcohol and an acid, are derived from the parent alcohol and the parent acid, where the latter may be organic or inorganic. Esters derived from the simplest carboxylic acids are commonly named according to the more traditional, so-called "trivial names" e.g. as formate, acetate, propionate, and butyrate, as opposed to the IUPAC nomenclature methanoate, ethanoate, propanoate, and butanoate. Esters derived from more complex carboxylic acids are, on the other hand, more frequently named using the systematic IUPAC name, based on the name for the acid followed by the suffix -oate. For example, the ester hexyl octanoate, also known under the trivial name hexyl caprylate, has the formula CH3(CH2)6CO2(CH2)5CH3.

The chemical formulas of organic esters formed from carboxylic acids and alcohols usually take the form RCO2R' or RCOOR', where R and R' are the organyl parts of the carboxylic acid and the alcohol, respectively, and R can be a hydrogen in the case of esters of formic acid. For example, butyl acetate (systematically butyl ethanoate), derived from butanol and acetic acid (systematically ethanoic acid) would be written CH3CO2(CH2)3CH3. Alternative presentations are common including BuOAc and CH3COO(CH2)3CH3.

Cyclic esters are called lactones, regardless of whether they are derived from an organic or inorganic acid. One example of an organic lactone is γ-valerolactone.

Orthoesters
An uncommon class of esters are the orthoesters. One of them are the esters of orthocarboxylic acids. Those esters have the formula RC(OR′)3, where R stands for any group (organic or inorganic) and R stands for organyl group. For example, triethyl orthoformate (HC(OCH2CH3)3) is derived, in terms of its name (but not its synthesis) from esterification of orthoformic acid (HC(OH)3) with ethanol.

Esters of inorganic acids
Esters can also be derived from inorganic acids.
 * Perchloric acid forms perchlorate esters, e.g., methyl perchlorate (CH3\sO\sCl(\dO)3)
 * Sulfuric acid forms sulfate esters, e.g., dimethyl sulfate ((CH3\sO\s)2S(\dO)2) and methyl bisulfate (CH3\sO\sS(\dO)2\sOH)
 * Nitric acid forms nitrate esters, e.g. methyl nitrate (CH3\sO\sNO2) and nitroglycerin (CH(\sO\sNO2)(\sCH2\sO\sNO2)2)
 * Phosphoric acid forms phosphate esters, e.g. triphenyl phosphate (O\dP(\sO\sC6H5)3) and methyl dihydrogen phosphate (O\dP(\sO\sCH3)(\sOH)2)
 * Pyrophosphoric (diphosphoric) acid forms pyrophosphate esters, e.g. tetraethyl pyrophosphate, ADP, dADP, ADPR, cADPR, CDP, dCDP, GDP, dGDP, UDP, dTDP, MEcPP, HMBPP, DMAPP, IPP, GPP, FPP, GGPP, ThDP, FAD, NAD, NADP.
 * Triphosphoric acid forms triphosphate esters, e.g. ATP, dATP, CTP, dCTP, GTP, dGTP, UTP, dTTP, ITP, XTP, ThTP, AThTP.
 * Carbonic acid forms carbonate esters, e.g. dimethyl carbonate ((CH3\sO\s)2C\dO) and 5-membered cyclic ethylene carbonate ((\sCH2\sO\s)2C\dO) (if one classifies carbonic acid as an inorganic compound)
 * Trithiocarbonic acid forms trithiocarbonate esters, e.g. dimethyl trithiocarbonate ((CH3\sS\s)2C\dS) (if one classifies trithiocarbonic acid as an inorganic compound)
 * Chloroformic acid forms chloroformate esters, e.g. methyl chloroformate (Cl\sC(\dO)\sO\sCH3) (if one classifies chloroformic acid as an inorganic compound)
 * Boric acid forms borate esters, e.g. trimethyl borate (B(\sO\sCH3)3)
 * Chromic acid forms di-tert-butyl chromate (((CH3)3C\sO\s)2Cr(\dO)2)

Inorganic acids that exist as tautomers form two or more types of esters.
 * Thiosulfuric acid forms two types of thiosulfate esters, e.g. O,O-dimethyl thiosulfate ((CH3\sO\s)2S(\dO)(\dS)) and O,S-dimethyl thiosulfate ((CH3\sO\s)(CH3\sS\s)S(\dO)2)
 * Thiocyanic acid forms thiocyanate esters, e.g. methyl thiocyanate (CH3\sS\sC\tN) (if one classifies thiocyanic acid as an inorganic compound), but forms isothiocyanate "esters" as well, e.g. methyl isothiocyanate (CH3\sN\dC\dS), although organyl isothiocyanates are not classified as esters by the IUPAC
 * Phosphorous acid forms two types of esters: phosphite esters, e.g. triethyl phosphite (P(\sO\sCH2CH3)3), and phosphonate esters, e.g. diethyl phosphonate (H\sP(\dO)(\sO\sCH2CH3)2)

Some inorganic acids that are unstable or elusive form stable esters.
 * Sulfurous acid, which is unstable, forms stable dimethyl sulfite ((CH3\sO\s)2S\dO)
 * Dicarbonic acid, which is unstable, forms stable dimethyl dicarbonate (CH3\sO\sC(\dO)\sO\sC(\dO)\sO\sCH3)

In principle, a part of metal and metalloid alkoxides, of which many hundreds are known, could be classified as esters of the corresponding acids (e.g. aluminium triethoxide (Al(OCH2CH3)3) could be classified as an ester of aluminic acid which is aluminium hydroxide, tetraethyl orthosilicate (Si(OCH2CH3)4) could be classified as an ester of orthosilicic acid, and titanium ethoxide (Ti(OCH2CH3)4) could be classified as an ester of orthotitanic acid).

Structure and bonding
Esters derived from carboxylic acids and alcohols contain a carbonyl group C=O, which is a divalent group at C atom, which gives rise to 120° C–C–O and O–C–O angles. Unlike amides, carboxylic acid esters are structurally flexible functional groups because rotation about the C–O–C bonds has a low barrier. Their flexibility and low polarity is manifested in their physical properties; they tend to be less rigid (lower melting point) and more volatile (lower boiling point) than the corresponding amides. The pKa of the alpha-hydrogens on esters of carboxylic acids is around 25 (alpha-hydrogen is a hydrogen bound to the carbon adjacent to the carbonyl group (C=O) of carboxylate esters).

Many carboxylic acid esters have the potential for conformational isomerism, but they tend to adopt an S-cis (or Z) conformation rather than the S-trans (or E) alternative, due to a combination of hyperconjugation and dipole minimization effects. The preference for the Z conformation is influenced by the nature of the substituents and solvent, if present. Lactones with small rings are restricted to the s-trans (i.e. E) conformation due to their cyclic structure.

Physical properties and characterization
Esters derived from carboxylic acids and alcohols are more polar than ethers but less polar than alcohols. They participate in hydrogen bonds as hydrogen-bond acceptors, but cannot act as hydrogen-bond donors, unlike their parent alcohols. This ability to participate in hydrogen bonding confers some water-solubility. Because of their lack of hydrogen-bond-donating ability, esters do not self-associate. Consequently, esters are more volatile than carboxylic acids of similar molecular weight.

Characterization and analysis
Esters are generally identified by gas chromatography, taking advantage of their volatility. IR spectra for esters feature an intense sharp band in the range 1730–1750 cm−1 assigned to νundefined. This peak changes depending on the functional groups attached to the carbonyl. For example, a benzene ring or double bond in conjugation with the carbonyl will bring the wavenumber down about 30 cm−1.

Applications and occurrence
Esters are widespread in nature and are widely used in industry. In nature, fats are, in general, triesters derived from glycerol and fatty acids. Esters are responsible for the aroma of many fruits, including apples, durians, pears, bananas, pineapples, and strawberries. Several billion kilograms of polyesters are produced industrially annually, important products being polyethylene terephthalate, acrylate esters, and cellulose acetate.
 * Triglyceride unsaturated Structural Formulae V2.svg found in a linseed oil, a triester of glycerol  (center, black) derived of  linoleic acid  (bottom right, green),  alpha-linolenic acid  (left, red), and  oleic acid  (top right, blue).]]

Preparation
Esterification is the general name for a chemical reaction in which two reactants (typically an alcohol and an acid) form an ester as the reaction product. Esters are common in organic chemistry and biological materials, and often have a pleasant characteristic, fruity odor. This leads to their extensive use in the fragrance and flavor industry. Ester bonds are also found in many polymers.

Esterification of carboxylic acids with alcohols
The classic synthesis is the Fischer esterification, which involves treating a carboxylic acid with an alcohol in the presence of a dehydrating agent:
 * RCO2H + R'OH ⇌ RCO2R' + H2O

The equilibrium constant for such reactions is about 5 for typical esters, e.g., ethyl acetate. The reaction is slow in the absence of a catalyst. Sulfuric acid is a typical catalyst for this reaction. Many other acids are also used such as polymeric sulfonic acids. Since esterification is highly reversible, the yield of the ester can be improved using Le Chatelier's principle:
 * Using the alcohol in large excess (i.e., as a solvent).
 * Using a dehydrating agent: sulfuric acid not only catalyzes the reaction but sequesters water (a reaction product). Other drying agents such as molecular sieves are also effective.
 * Removal of water by physical means such as distillation as a low-boiling azeotrope with toluene, in conjunction with a Dean-Stark apparatus.

Reagents are known that drive the dehydration of mixtures of alcohols and carboxylic acids. One example is the Steglich esterification, which is a method of forming esters under mild conditions. The method is popular in peptide synthesis, where the substrates are sensitive to harsh conditions like high heat. DCC (dicyclohexylcarbodiimide) is used to activate the carboxylic acid to further reaction. 4-Dimethylaminopyridine (DMAP) is used as an acyl-transfer catalyst.
 * Steglich-1.svg

Another method for the dehydration of mixtures of alcohols and carboxylic acids is the Mitsunobu reaction:
 * RCO2H + R'OH + P(C6H5)3 + R2N2 → RCO2R' + OP(C6H5)3 + R2N2H2

Carboxylic acids can be esterified using diazomethane:
 * RCO2H + CH2N2 → RCO2CH3 + N2

Using this diazomethane, mixtures of carboxylic acids can be converted to their methyl esters in near quantitative yields, e.g., for analysis by gas chromatography. The method is useful in specialized organic synthetic operations but is considered too hazardous and expensive for large-scale applications.

Esterification of carboxylic acids with epoxides
Carboxylic acids are esterified by treatment with epoxides, giving β-hydroxyesters:
 * RCO2H + RCHCH2O → RCO2CH2CH(OH)R

This reaction is employed in the production of vinyl ester resin from acrylic acid.

Alcoholysis of acyl chlorides and acid anhydrides
Alcohols react with acyl chlorides and acid anhydrides to give esters:
 * RCOCl + R'OH → RCO2R' + HCl
 * (RCO)2O + R'OH → RCO2R' + RCO2H

The reactions are irreversible simplifying work-up. Since acyl chlorides and acid anhydrides also react with water, anhydrous conditions are preferred. The analogous acylations of amines to give amides are less sensitive because amines are stronger nucleophiles and react more rapidly than does water. This method is employed only for laboratory-scale procedures, as it is expensive.

Alkylation of carboxylic acids and their salts
Trimethyloxonium tetrafluoroborate can be used for esterification of carboxylic acids under conditions where acid-catalyzed reactions are infeasible:
 * RCO2H + (CH3)3OBF4 -> RCO2CH3 + (CH3)2O + HBF4

Although rarely employed for esterifications, carboxylate salts (often generated in situ) react with electrophilic alkylating agents, such as alkyl halides, to give esters. Anion availability can inhibit this reaction, which correspondingly benefits from phase transfer catalysts or such highly polar aprotic solvents as DMF. An additional iodide salt may, via the Finkelstein reaction, catalyze the reaction of a recalcitrant alkyl halide. Alternatively, salts of a coordinating metal, such as silver, may improve the reaction rate by easing halide elimination.

Transesterification
Transesterification, which involves changing one ester into another one, is widely practiced:
 * RCO2R' + CH3OH → RCO2CH3 + R'OH

Like the hydrolysation, transesterification is catalysed by acids and bases. The reaction is widely used for degrading triglycerides, e.g. in the production of fatty acid esters and alcohols. Poly(ethylene terephthalate) is produced by the transesterification of dimethyl terephthalate and ethylene glycol:
 * n (C6H4)(CO2CH3)2 + 2n C2H4(OH)2 → [(C6H4)(CO2)2(C2H4)]_{n} + 2n CH3OH

A subset of transesterification is the alcoholysis of diketene. This reaction affords 2-ketoesters.
 * (CH2CO)2 + ROH → CH3C(O)CH2CO2R

Carbonylation
Alkenes undergo "hydroesterification" in the presence of metal carbonyl catalysts. Esters of propanoic acid are produced commercially by this method:
 * H2C\dCH2 + ROH + CO → CH3CH2CO2R

A preparation of methyl propionate is one illustrative example.
 * H2C\dCH2 + CO + CH3OH → CH3CH2CO2CH3

The carbonylation of methanol yields methyl formate, which is the main commercial source of formic acid. The reaction is catalyzed by sodium methoxide:
 * CH3OH + CO → HCO2CH3

Addition of carboxylic acids to alkenes and alkynes
In hydroesterification, alkenes and alkynes insert into the O\sH bond of carboxylic acids. Vinyl acetate is produced industrially by the addition of acetic acid to acetylene in the presence of zinc acetate catalysts:
 * HC\tCH + CH3CO2H → CH3CO2CH\dCH2

Vinyl acetate can also be produced by palladium-catalyzed reaction of ethylene, acetic acid, and oxygen:
 * 2 H2C\dCH2 + 2 CH3CO2H + O2 → 2 CH3CO2CH\dCH2 + 2 H2O

Silicotungstic acid is used to manufacture ethyl acetate by the alkylation of acetic acid by ethylene:
 * H2C\dCH2 + CH3CO2H → CH3CO2CH2CH3

From aldehydes
The Tishchenko reaction involves disproportionation of an aldehyde in the presence of an anhydrous base to give an ester. Catalysts are aluminium alkoxides or sodium alkoxides. Benzaldehyde reacts with sodium benzyloxide (generated from sodium and benzyl alcohol) to generate benzyl benzoate. The method is used in the production of ethyl acetate from acetaldehyde.

Other methods

 * Favorskii rearrangement of α-haloketones in presence of base
 * Baeyer–Villiger oxidation of ketones with peroxides
 * Pinner reaction of nitriles with an alcohol
 * Nucleophilic abstraction of a metal–acyl complex
 * Hydrolysis of orthoesters in aqueous acid
 * Cellulolysis via esterification
 * Ozonolysis of alkenes using a work up in the presence of hydrochloric acid and various alcohols.
 * Anodic oxidation of methyl ketones leading to methyl esters.
 * Interesterification exchanges the fatty acid groups of different esters.

Reactions
Esters react with nucleophiles at the carbonyl carbon. The carbonyl is weakly electrophilic but is attacked by strong nucleophiles (amines, alkoxides, hydride sources, organolithium compounds, etc.). The C–H bonds adjacent to the carbonyl are weakly acidic but undergo deprotonation with strong bases. This process is the one that usually initiates condensation reactions. The carbonyl oxygen in esters is weakly basic, less so than the carbonyl oxygen in amides due to resonance donation of an electron pair from nitrogen in amides, but forms adducts.

Hydrolysis and saponification
Esterification is a reversible reaction. Esters undergo hydrolysis under acidic and basic conditions. Under acidic conditions, the reaction is the reverse reaction of the Fischer esterification. Under basic conditions, hydroxide acts as a nucleophile, while an alkoxide is the leaving group. This reaction, saponification, is the basis of soap making.
 * [[Image:Ester hydrolysis.svg|750px|Ester saponification (basic hydrolysis)]]

The alkoxide group may also be displaced by stronger nucleophiles such as ammonia or primary or secondary amines to give amides (ammonolysis reaction):
 * RCO2R' + NH2R → RCONHR + R'OH

This reaction is not usually reversible. Hydrazines and hydroxylamine can be used in place of amines. Esters can be converted to isocyanates through intermediate hydroxamic acids in the Lossen rearrangement.

Sources of carbon nucleophiles, e.g., Grignard reagents and organolithium compounds, add readily to the carbonyl.

Reduction
Compared to ketones and aldehydes, esters are relatively resistant to reduction. The introduction of catalytic hydrogenation in the early part of the 20th century was a breakthrough; esters of fatty acids are hydrogenated to fatty alcohols.
 * RCO2R' + 2 H2 → RCH2OH + R'OH

A typical catalyst is copper chromite. Prior to the development of catalytic hydrogenation, esters were reduced on a large scale using the Bouveault–Blanc reduction. This method, which is largely obsolete, uses sodium in the presence of proton sources.

Especially for fine chemical syntheses, lithium aluminium hydride is used to reduce esters to two primary alcohols. The related reagent sodium borohydride is slow in this reaction. DIBAH reduces esters to aldehydes.

Direct reduction to give the corresponding ether is difficult as the intermediate hemiacetal tends to decompose to give an alcohol and an aldehyde (which is rapidly reduced to give a second alcohol). The reaction can be achieved using triethylsilane with a variety of Lewis acids.

Claisen condensation and related reactions
As for aldehydes, the hydrogen atoms on the carbon adjacent ("α to") the carboxyl group in esters are sufficiently acidic to undergo deprotonation, which in turn leads to a variety of useful reactions. Deprotonation requires relatively strong bases, such as alkoxides. Deprotonation gives a nucleophilic enolate, which can further react, e.g., the Claisen condensation and its intramolecular equivalent, the Dieckmann condensation. This conversion is exploited in the malonic ester synthesis, wherein the diester of malonic acid reacts with an electrophile (e.g., alkyl halide), and is subsequently decarboxylated. Another variation is the Fráter–Seebach alkylation.

Other reactions

 * Methyl esters are often susceptible to decarboxylation in the Krapcho decarboxylation.
 * Phenyl esters react to hydroxyarylketones in the Fries rearrangement.
 * Specific esters are functionalized with an α-hydroxyl group in the Chan rearrangement.
 * Esters with β-hydrogen atoms can be converted to alkenes in ester pyrolysis.
 * A direct conversion of esters to nitriles.
 * Pairs of esters are coupled to give α-hydroxyketones in the acyloin condensation

Protecting groups
As a class, esters serve as protecting groups for carboxylic acids. Protecting a carboxylic acid is useful in peptide synthesis, to prevent self-reactions of the bifunctional amino acids. Methyl and ethyl esters are commonly available for many amino acids; the t-butyl ester tends to be more expensive. However, t-butyl esters are particularly useful because, under strongly acidic conditions, the t-butyl esters undergo elimination to give the carboxylic acid and isobutylene, simplifying work-up.

Hazards
Esters react with strong oxidizing acids, which may cause a violent reaction that is sufficiently exothermic to ignite the esters and the reaction products. Heat is also generated by the interaction of esters with alkali solutions. Very flammable hydrogen gas is generated by mixing esters with alkali metals and ionic hydrides.

List of ester odorants
Many esters have distinctive fruit-like odors, and many occur naturally in the essential oils of plants. This has also led to their common use in artificial flavorings and fragrances which aim to mimic those odors.

title: Ester