Bohemianism

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

Pierre-Auguste Renoir, In Summer (or Lise the Bohemian), 1868, oil on canvas, Berlin, Germany: Alte Nationalgalerie

Bohemianism is a social and cultural movement that has, at its core, a way of life away from society's conventional norms and expectations. The term originates from the French bohème and spread to the English-speaking world. It was used to describe mid-19th-century non-traditional lifestyles, especially of artists, writers, journalists, musicians, and actors in major European cities.

Bohemian is a 19th-century historical and literary topos that places the milieu of young metropolitan artists and intellectuals—particularly those of the Latin Quarter in Paris—in a context of poverty, hunger, appreciation of friendship, idealization of art and contempt for money. Based on this topos, the most diverse real-world subcultures are often referred to as "bohemian" in a figurative sense, especially (but by no means exclusively) if they show traits of a precariat.

Bohemians were associated with unorthodox or anti-establishment political or social viewpoints expressed through free love, frugality, and—in some cases—simple living, van dwelling or voluntary poverty. A more economically privileged, wealthy, or even aristocratic bohemian circle is sometimes referred to as haute bohème (literally "Upper Bohemian").

The term bohemianism emerged in France in the early 19th century out of perceived similarities between the urban Bohemians and the Romani people; La bohème was a common term for the Romani people of France, who were thought to have reached France in the 15th century via Bohemia (the western part of modern Czech Republic). Bohemianism and its adjective bohemian in this specific context are not connected to the native inhabitants of the historical region of Bohemia (the Czechs).

Origins

European bohemianism

Literary and artistic bohemians were associated in the French imagination with the roving Roma people, often referred to as "gypsies". Romani were called bohémiens in French because they were believed to have come to France from Bohemia.

The title character in Carmen (1875), a French opera by Georges Bizet set in the Spanish city of Seville, is referred to as a bohémienne in Meilhac and Halévy's libretto. Her signature aria declares love itself to be a "gypsy child" (enfant de Bohême), going where it pleases and obeying no laws.

The term bohemian has come to be very commonly accepted in our day as the description of a certain kind of literary gypsy, no matter in what language he speaks, or what city he inhabits .... A Bohemian is simply an artist or "littérateur" who, consciously or unconsciously, secedes from conventionality in life and in art.

— Westminster Review, 1862

Henri Murger's 1845 collection of short stories, Scènes de la vie de bohème (Scenes of Bohemian Life), was written to glorify and legitimize the bohemian lifestyle.^[6] Murger's collection formed the basis of Giacomo Puccini's 1896 opera La bohème.

In England, bohemian in this sense initially was popularised in William Makepeace Thackeray's 1848 novel Vanity Fair. Public perceptions of the alternative lifestyles supposedly led by artists were further molded by George du Maurier's romanticized best-selling novel of Bohemian culture Trilby (1894). The novel outlines the fortunes of three expatriate English artists, their Irish model, and two colourful Central European musicians, in the artist quarter of Paris.

In Spanish literature, the Bohemian impulse can be seen in Ramón del Valle-Inclán's 1920 play Luces de Bohemia.

In his song "La Bohème", Charles Aznavour described the Bohemian lifestyle in Montmartre. The 2001 film Moulin Rouge! also imagines the Bohemian lifestyle of actors and artists in Montmartre at the turn of the 20th century.

American bohemianism

Bohemian Grove during the summer Hi-Jinks, circa 1911–1916

In the 1850s, Bohemian culture started to become established in the United States via immigration. In New York City in 1857, a group of 15 to 20 young, cultured journalists flourished as self-described bohemians until the American Civil War began in 1861. This group gathered at a German bar on Broadway called Pfaff's beer cellar. Members included their leader Henry Clapp Jr., Ada Clare, Walt Whitman, Fitz Hugh Ludlow, and actress Adah Isaacs Menken.

Similar groups in other cities were broken up as well by the Civil War and reporters spread out to report on the conflict. During the war, correspondents began to assume the title bohemian, and newspapermen in general took up the moniker. Bohemian became synonymous with newspaper writer. In 1866, war correspondent Junius Henri Browne, who wrote for the New York Tribune and Harper's Magazine, described bohemian journalists such as he was, as well as the few carefree women and lighthearted men he encountered during the war years.

San Francisco journalist Bret Harte first wrote as "The Bohemian" in The Golden Era in 1861, with this persona taking part in many satirical doings, the lot published in his book Bohemian Papers in 1867. Harte wrote, "Bohemia has never been located geographically, but any clear day when the sun is going down, if you mount Telegraph Hill, you shall see its pleasant valleys and cloud-capped hills glittering in the West ..."

Mark Twain included himself and Charles Warren Stoddard in the bohemian category in 1867. By 1872, when a group of journalists and artists who gathered regularly for cultural pursuits in San Francisco were casting about for a name, the term bohemian became the main choice, and the Bohemian Club was born. Club members who were established and successful, pillars of their community, respectable family men, redefined their own form of bohemianism to include people like them who were bons vivants, sportsmen, and appreciators of the fine arts. Club member and poet George Sterling responded to this redefinition:

Any good mixer of convivial habits considers he has a right to be called a bohemian. But that is not a valid claim. There are two elements, at least, that are essential to Bohemianism. The first is devotion or addiction to one or more of the Seven Arts; the other is poverty. Other factors suggest themselves: for instance, I like to think of my Bohemians as young, as radical in their outlook on art and life; as unconventional, and, though this is debatable, as dwellers in a city large enough to have the somewhat cruel atmosphere of all great cities.

— Parry, 2005)

Despite his views, Sterling associated with the Bohemian Club, and caroused with artist and industrialist alike at the Bohemian Grove.

Canadian composer Oscar Ferdinand Telgmann and poet George Frederick Cameron wrote the song "The Bohemian" in the 1889 opera Leo, the Royal Cadet.

The American writer and Bohemian Club member Gelett Burgess, who coined the word blurb, supplied this description of the amorphous place called Bohemia:

Gelett Burgess drew this fanciful "Map of Bohemia" for The Lark, March 1, 1896 (see also The Winter's Tale § The seacoast of Bohemia)

To take the world as one finds it, the bad with the good, making the best of the present moment—to laugh at Fortune alike whether she be generous or unkind—to spend freely when one has money, and to hope gaily when one has none—to fleet the time carelessly, living for love and art—this is the temper and spirit of the modern Bohemian in his outward and visible aspect. It is a light and graceful philosophy, but it is the Gospel of the Moment, this exoteric phase of the Bohemian religion; and if, in some noble natures, it rises to a bold simplicity and naturalness, it may also lend its butterfly precepts to some very pretty vices and lovable faults, for in Bohemia one may find almost every sin save that of Hypocrisy. ...

His faults are more commonly those of self-indulgence, thoughtlessness, vanity and procrastination, and these usually go hand-in-hand with generosity, love and charity; for it is not enough to be one's self in Bohemia, one must allow others to be themselves, as well. ...

What, then, is it that makes this mystical empire of Bohemia unique, and what is the charm of its mental fairyland? It is this: there are no roads in all Bohemia! One must choose and find one's own path, be one's own self, live one's own life.

— Ayloh, 1902)

In New York City, the pianist Rafael Joseffy formed an organization of musicians in 1907 with friends, such as Rubin Goldmark, called "The Bohemians (New York Musicians' Club)". Near Times Square, Joel Rinaldo presided over "Joel's Bohemian Refreshery", where the Bohemian crowd gathered from before the turn of the 20th century until Prohibition began to bite. Jonathan Larson's musical Rent, and specifically the song "La Vie Boheme", portrayed the postmodern Bohemian culture of New York in the late 20th century.

In May 2014, a story on NPR suggested, after a century and a half, some Bohemian ideal of living in poverty for the sake of art had fallen in popularity among the latest generation of American artists. In the feature, a recent graduate of the Rhode Island School of Design related "her classmates showed little interest in living in garrets and eating ramen noodles."

People

An illustration from Henri Murger's 1899 book Bohemian Life.

The term has become associated with various artistic or academic communities and is used as a generalized adjective describing such people, environs, or situations: bohemian (boho—informal) is defined in The American College Dictionary as "a person with artistic or intellectual tendencies, who lives and acts with no regard for conventional rules of behavior".

Many prominent European and American figures of the 19th and 20th centuries belonged to the bohemian subculture, and any comprehensive "list of bohemians" would be tediously long. Bohemianism has been approved of by some bourgeois writers such as Honoré de Balzac, but most conservative cultural critics do not condone bohemian lifestyles.

In Bohemian Manifesto: a Field Guide to Living on the Edge, author Laren Stover breaks down the bohemian into five distinct mind-sets or styles, as follows:

• Beat: also drifters, but non-materialist and art-focused
• Dandy: no money, but try to appear as if they have it by buying and displaying expensive or rare items – such as brands of alcohol
• Gypsy: the expatriate types, they create their own Gypsy ideal of nirvana wherever they go
• Nouveau: bohemians that are rich who attempt to join traditional bohemianism with contemporary culture
• Zen: "post-beat", focus on spirituality rather than art

Aimée Crocker, an American world traveler, adventuress, heiress, and mystic, was dubbed the "queen of Bohemia" in the 1910s by the world press for living an uninhibited, sexually liberated, and aggressively non-conformist life in San Francisco, New York, and Paris. She spent the bulk of her fortune inherited from her father Edwin B. Crocker, a railroad tycoon and art collector, on traveling all over the world (lingering the longest in Hawaii, India, Japan, and China) and partying with famous artists of her time such as Oscar Wilde, Robert Louis Stevenson, Mark Twain, the Barrymores, Enrico Caruso, Isadora Duncan, Henri Matisse, Auguste Rodin, and Rudolph Valentino. Crocker had countless affairs and married five times in five different decades of her life, each man being in his twenties. She was famous for her tattoos and pet snakes and was reported to have started the first Buddhist colony in Manhattan. Spiritually inquisitive, Crocker had a ten-year affair with occultist Aleister Crowley and was a devoted student of Hatha Yoga.

Maxwell Bodenheim, an American poet and novelist, was known as the king of Greenwich Village Bohemians during the 1920s and his writing brought him international fame during the Jazz Age.

Former brewery turned artist center in Prenzlauer Berg

In the 20th-century United States, the bohemian impulse was famously seen in the 1940s hipsters, the 1950s Beat generation (exemplified by writers such as William S. Burroughs, Allen Ginsberg, Jack Kerouac, and Lawrence Ferlinghetti), the much more widespread 1960s counterculture, and 1960s and 1970s hippies.

In 2001, political and cultural commentator David Brooks contended that much of the cultural ethos of well-to-do middle-class Americans is Bohemian-derived, coining the oxymoron "Bourgeois Bohemians" or "Bobos". A similar term in Germany is Bionade-Biedermeier, a 2007 German neologism combining Bionade (a trendy lemonade brand) and Biedermeier (an era of introspective Central European culture between 1815 and 1848). The coinage was introduced in 2007 by Henning Sußebach, a German journalist, in an article that appeared in Zeitmagazin concerning Berlin's Prenzlauer Berg lifestyle. The hyphenated term gained traction and has been quoted and referred to since. A German ARD TV broadcaster used the title Boheme and Biedermeier in a 2009 documentary about Berlin's Prenzlauer Berg. The main focus was on protagonists, that contributed to the image of a paradise for the (organic and child-raising) well-to-do, depicting cafés where "Bionade-Biedermeier sips from Fair-Trade".

Quantum mysticism

From Wikipedia, the free encyclopedia

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

Quantum mysticism, sometimes referred to pejoratively as quantum quackery or quantum woo, is a set of metaphysical beliefs and associated practices that seek to relate spirituality or mystical worldviews to the ideas of quantum mechanics and its interpretations. Quantum mysticism is considered pseudoscience and quackery by many quantum mechanics experts.

Before the 1970s the term was usually used in reference to the postulate that "consciousness causes collapse" but was later more closely associated with the purportedly pseudoscientific views espoused by New Age thinkers such as Fritjof Capra and other members of the Fundamental Fysiks Group, who were influential in popularizing the modern form of quantum mysticism.

History

Many early quantum physicists held some interest in traditionally Eastern metaphysics. Physicists Werner Heisenberg and Erwin Schrödinger, two of the main pioneers of quantum mechanics in the 1920s, were interested in Eastern mysticism, but are not known to have directly associated one with the other. In fact, both endorsed the Copenhagen interpretation of quantum mechanics.

The historian of religion Olav Hammer said that "Schrödinger’s studies of Hindu mysticism never compelled him to pursue the same course as quantum metaphysicists such as David Bohm or Fritjof Capra." Schrödinger biographer Walter J. Moore said that Schrödinger's two interests of quantum physics and Hindu mysticism were "strangely dissociated".

In his 1961 paper "Remarks on the mind–body question", Eugene Wigner suggested that a conscious observer played a fundamental role in quantum mechanics, a concept which is part of the consciousness causes collapse interpretation. While his paper served as inspiration for later mystical works by others, Wigner's ideas were primarily philosophical and were not considered overtly pseudoscientific like the mysticism that followed. By the late 1970s, Wigner had shifted his position and rejected the role of consciousness in quantum mechanics. Harvard historian Juan Miguel Marin suggests that "consciousness [was] introduced hypothetically at the birth of quantum physics, [and] the term 'mystical' was also used by its founders, to argue in favor of and against such an introduction."

Mysticism was argued against by Albert Einstein. Einstein's theories have often been falsely believed to support mystical interpretations of quantum theory. Einstein said, with regard to quantum mysticism, "No physicist believes that. Otherwise he wouldn't be a physicist." He debates several arguments about the approval of mysticism, even suggesting Bohr and Pauli to be in support of and to hold a positive belief in mysticism which he believes to be false.

Niels Bohr denied quantum mysticism and had rejected the hypothesis that quantum theory requires a conscious observer as early as 1927, despite having been "sympathetic towards the hypothesis that understanding consciousness might require an extension of quantum theory to accommodate laws other than those of physics".

In New Age thought

In the early 1970s, New Age culture began to incorporate ideas from quantum physics, beginning with books by Arthur Koestler, Lawrence LeShan and others which suggested that purported parapsychological phenomena could be explained by quantum mechanics.

In this decade, the Fundamental Fysiks Group emerged. This group of physicists embraced quantum mysticism, parapsychology, Transcendental Meditation, and various New Age and Eastern mystical practices.

Inspired in part by Wigner's exploration that consciousness causes collapse, Fritjof Capra, a member of the Fundamental Fysiks Group, wrote The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism (1975), which espoused New Age quantum physics; the book was popular among the non-scientific public. In 1979, Gary Zukav, a non-scientist and "the most successful of Capra's followers", published The Dancing Wu Li Masters. The Fundamental Fysiks Group and Capra's book are said to be major influences for the rise of quantum mysticism as a pseudoscientific interpretation of quantum mechanics.

Modern usage and examples

In contrast to the mysticism of the early 20th century, today quantum mysticism typically refers to New Age beliefs that combine ancient mysticism with the language of quantum mechanics. Called a pseudoscience and a "hijacking" of quantum physics, it draws upon "coincidental similarities of language rather than genuine connections" to quantum mechanics. Physicist Murray Gell-Mann coined the phrase "quantum flapdoodle" to refer to the misuse and misapplication of quantum physics to other topics.

An example of such use is New Age guru Deepak Chopra's "quantum theory" that aging is caused by the mind, expounded in his books Quantum Healing (1989) and Ageless Body, Timeless Mind (1993). In 1998, Chopra was awarded the parody Ig Nobel Prize in the physics category for "his unique interpretation of quantum physics as it applies to life, liberty, and the pursuit of economic happiness". In 2012, Stuart Hameroff and Chopra proposed that the "quantum soul" could exist "apart from the body" and "in space-time geometry, outside the brain, distributed nonlocally".

The 2004 film What the Bleep Do We Know!? dealt with a range of New Age ideas in relation to physics. It was produced by the Ramtha School of Enlightenment, founded by J.Z. Knight, a channeler who said that her teachings were based on a discourse with a 35,000-year-old disembodied entity named Ramtha. Featuring Fundamental Fysiks Group member Fred Alan Wolf, the film misused some aspects of quantum mechanics—including the Heisenberg uncertainty principle and the observer effect—as well as biology and medicine. Numerous critics dismissed the film for its use of pseudoscience.

Numerical cognition

From Wikipedia, the free encyclopedia

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

Numerical cognition is a subdiscipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics. As with many cognitive science endeavors, this is a highly interdisciplinary topic, and includes researchers in cognitive psychology, developmental psychology, neuroscience and cognitive linguistics. This discipline, although it may interact with questions in the philosophy of mathematics, is primarily concerned with empirical questions.

Topics included in the domain of numerical cognition include:

• How do non-human animals process numerosity?
• How do infants acquire an understanding of numbers (and how much is inborn)?
• How do humans associate linguistic symbols with numerical quantities?
• How do these capacities underlie our ability to perform complex calculations?
• What are the neural bases of these abilities, both in humans and in non-humans?
• What metaphorical capacities and processes allow us to extend our numerical understanding into complex domains such as the concept of infinity, the infinitesimal or the concept of the limit in calculus?
• Heuristics in numerical cognition

Comparative studies

A variety of research has demonstrated that non-human animals, including rats, lions and various species of primates have an approximate sense of number (referred to as "numerosity"). For example, when a rat is trained to press a bar 8 or 16 times to receive a food reward, the number of bar presses will approximate a Gaussian or Normal distribution with peak around 8 or 16 bar presses. When rats are more hungry, their bar-pressing behavior is more rapid, so by showing that the peak number of bar presses is the same for either well-fed or hungry rats, it is possible to disentangle time and number of bar presses. In addition, in a few species the parallel individuation system has been shown, for example in the case of guppies which successfully discriminated between 1 and 4 other individuals.

Similarly, researchers have set up hidden speakers in the African savannah to test natural (untrained) behavior in lions. These speakers can play a number of lion calls, from 1 to 5. If a single lioness hears, for example, three calls from unknown lions, she will leave, while if she is with four of her sisters, they will go and explore. This suggests that not only can lions tell when they are "outnumbered" but that they can do this on the basis of signals from different sensory modalities, suggesting that numerosity is a multisensory concept.

Developmental studies

Developmental psychology studies have shown that human infants, like non-human animals, have an approximate sense of number. For example, in one study, infants were repeatedly presented with arrays of (in one block) 16 dots. Careful controls were in place to eliminate information from "non-numerical" parameters such as total surface area, luminance, circumference, and so on. After the infants had been presented with many displays containing 16 items, they habituated, or stopped looking as long at the display. Infants were then presented with a display containing 8 items, and they looked longer at the novel display.

Because of the numerous controls that were in place to rule out non-numerical factors, the experimenters infer that six-month-old infants are sensitive to differences between 8 and 16. Subsequent experiments, using similar methodologies showed that 6-month-old infants can discriminate numbers differing by a 2:1 ratio (8 vs. 16 or 16 vs. 32) but not by a 3:2 ratio (8 vs. 12 or 16 vs. 24). However, 10-month-old infants succeed both at the 2:1 and the 3:2 ratio, suggesting an increased sensitivity to numerosity differences with age.

In another series of studies, Karen Wynn showed that infants as young as five months are able to do very simple additions (e.g., 1 + 1 = 2) and subtractions (3 - 1 = 2). To demonstrate this, Wynn used a "violation of expectation" paradigm, in which infants were shown (for example) one Mickey Mouse doll going behind a screen, followed by another. If, when the screen was lowered, infants were presented with only one Mickey (the "impossible event") they looked longer than if they were shown two Mickeys (the "possible" event). Further studies by Karen Wynn and Koleen McCrink found that although infants' ability to compute exact outcomes only holds over small numbers, infants can compute approximate outcomes of larger addition and subtraction events (e.g., "5+5" and "10-5" events).

There is debate about how much these infant systems actually contain in terms of number concepts, harkening to the classic nature versus nurture debate. Gelman & Gallistel (1978) suggested that a child innately has the concept of natural number, and only has to map this onto the words used in her language. Carey (2004, 2009) disagreed, saying that these systems can only encode large numbers in an approximate way, where language-based natural numbers can be exact. Without language, only numbers 1 to 4 are believed to have an exact representation, through the parallel individuation system. One promising approach is to see if cultures that lack number words can deal with natural numbers. The results so far are mixed (e.g., Pica et al. (2004)); Butterworth & Reeve (2008), Butterworth, Reeve, Reynolds & Lloyd (2008)).

Neuroimaging and neurophysiological studies

Human neuroimaging studies have demonstrated that regions of the parietal lobe, including the intraparietal sulcus (IPS) and the inferior parietal lobule (IPL) are activated when subjects are asked to perform calculation tasks. Based on both human neuroimaging and neuropsychology, Stanislas Dehaene and colleagues have suggested that these two parietal structures play complementary roles. The IPS is thought to house the circuitry that is fundamentally involved in numerical estimation, number comparison, and on-line calculation, or quantity processing (often tested with subtraction) while the IPL is thought to be involved in rote memorization, such as multiplication. Thus, a patient with a lesion to the IPL may be able to subtract, but not multiply, and vice versa for a patient with a lesion to the IPS. In addition to these parietal regions, regions of the frontal lobe are also active in calculation tasks. These activations overlap with regions involved in language processing such as Broca's area and regions involved in working memory and attention. Additionally, the inferotemporal cortex is implicated in processing the numerical shapes and symbols, necessary for calculations with Arabic digits. More current research has highlighted the networks involved with multiplication and subtraction tasks. Multiplication is often learned through rote memorization and verbal repetitions, and neuroimaging studies have shown that multiplication uses a left lateralized network of the inferior frontal cortex and the superior-middle temporal gyri in addition to the IPL and IPS. Subtraction is taught more with quantity manipulation and strategy use, more reliant upon the right IPS and the posterior parietal lobule.

Single-unit neurophysiology in monkeys has also found neurons in the frontal cortex and in the intraparietal sulcus that respond to numbers. Andreas Nieder trained monkeys to perform a "delayed match-to-sample" task. For example, a monkey might be presented with a field of four dots, and is required to keep that in memory after the display is taken away. Then, after a delay period of several seconds, a second display is presented. If the number on the second display match that from the first, the monkey has to release a lever. If it is different, the monkey has to hold the lever. Neural activity recorded during the delay period showed that neurons in the intraparietal sulcus and the frontal cortex had a "preferred numerosity", exactly as predicted by behavioral studies. That is, a certain number might fire strongly for four, but less strongly for three or five, and even less for two or six. Thus, we say that these neurons were "tuned" for specific quantities. Note that these neuronal responses followed Weber's law, as has been demonstrated for other sensory dimensions, and consistent with the ratio dependence observed for non-human animals' and infants' numerical behavior.

It is important to note that while primates have remarkably similar brains to humans, there are differences in function, ability, and sophistication. They make for good preliminary test subjects, but do not show small differences that are the result of different evolutionary tracks and environment. However, in the realm of number, they share many similarities. As identified in monkeys, neurons selectively tuned to number were identified in the bilateral intraparietal sulci and prefrontal cortex in humans. Piazza and colleagues investigated this using fMRI, presenting participants with sets of dots where they either had to make same-different judgments or larger-smaller judgments. The sets of dots consisted of base numbers 16 and 32 dots with ratios in 1.25, 1.5, and 2. Deviant numbers were included in some trials in larger or smaller amounts than the base numbers. Participants displayed similar activation patterns as Nieder found in the monkeys. The intraparietal sulcus and the prefrontal cortex, also implicated in number, communicate in approximating number and it was found in both species that the parietal neurons of the IPS had short firing latencies, whereas the frontal neurons had longer firing latencies. This supports the notion that number is first processed in the IPS and, if needed, is then transferred to the associated frontal neurons in the prefrontal cortex for further numerations and applications. Humans displayed Gaussian curves in the tuning curves of approximate magnitude. This aligned with monkeys, displaying a similarly structured mechanism in both species with classic Gaussian curves relative to the increasingly deviant numbers with 16 and 32 as well as habituation. The results followed Weber's Law, with accuracy decreasing as the ratio between numbers became smaller. This supports the findings made by Nieder in macaque monkeys and shows definitive evidence for an approximate number logarithmic scale in humans.

With an established mechanism for approximating non-symbolic number in both humans and primates, a necessary further investigation is needed to determine if this mechanism is innate and present in children, which would suggest an inborn ability to process numerical stimuli much like humans are born ready to process language. Cantlon, Brannon, Carter & Pelphrey (2006) set out to investigate this in 4 year old healthy, normally developing children in parallel with adults. A similar task to Piazza's was used in this experiment, without the judgment tasks. Dot arrays of varying size and number were used, with 16 and 32 as the base numerosities. in each block, 232 stimuli were presented with 20 deviant numerosities of a 2.0 ratio both larger and smaller. For example, out of the 232 trials, 16 dots were presented in varying size and distance but 10 of those trials had 8 dots, and 10 of those trials had 32 dots, making up the 20 deviant stimuli. The same applied to the blocks with 32 as the base numerosity. To ensure the adults and children were attending to the stimuli, they put 3 fixation points throughout the trial where the participant had to move a joystick to move forward. Their findings indicated that the adults in the experiment had significant activation of the IPS when viewing the deviant number stimuli, aligning with what was previously found in the aforementioned paragraph. In the 4 year olds, they found significant activation of the IPS to the deviant number stimuli, resembling the activation found in adults. There were some differences in the activations, with adults displaying more robust bilateral activation, where the 4 year olds primarily showed activation in their right IPS and activated 112 less voxels than the adults. This suggests that at age 4, children have an established mechanism of neurons in the IPS tuned for processing non-symbolic numerosities. Other studies have gone deeper into this mechanism in children and discovered that children do also represent approximate numbers on a logarithmic scale, aligning with the claims made by Piazza in adults.

Izard, Sann, Spelke & Streri (2009) investigated abstract number representations in infants using a different paradigm than the previous researchers because of the nature and developmental stage of the infants. For infants, they examined abstract number with both auditory and visual stimuli with a looking-time paradigm. The sets used were 4vs.12, 8vs.16, and 4vs.8. The auditory stimuli consisted of tones in different frequencies with a set number of tones, with some deviant trials where the tones were shorter but more numerous or longer and less numerous to account for duration and its potential confounds. After the auditory stimuli was presented with 2 minutes of familiarization, the visual stimuli was presented with a congruent or incongruent array of colorful dots with facial features. they remained on the screen until the infant looked away. They found that infants looked longer at the stimuli that matched the auditory tones, suggesting that the system for approximating non-symbolic number, even across modalities, is present in infancy. What is important to note across these three particular human studies on nonsymbolic numerosities is that it is present in infancy and develops over the lifetime. The honing of their approximation and number sense abilities as indicated by the improving Weber fractions across time, and usage of the left IPS to provide a wider berth for processing of computations and enumerations lend support for the claims that are made for a nonsymbolic number processing mechanism in human brains.

Relations between number and other cognitive processes

There is evidence that numerical cognition is intimately related to other aspects of thought – particularly spatial cognition. One line of evidence comes from studies performed on number-form synaesthetes. Such individuals report that numbers are mentally represented with a particular spatial layout; others experience numbers as perceivable objects that can be visually manipulated to facilitate calculation. Behavioral studies further reinforce the connection between numerical and spatial cognition. For instance, participants respond quicker to larger numbers if they are responding on the right side of space, and quicker to smaller numbers when on the left –the so-called "Spatial-Numerical Association of Response Codes", or SNARC effect. This effect varies across culture and context, however, and some research has even begun to question whether the SNARC reflects an inherent number-space association, instead invoking strategic problem solving or a more general cognitive mechanism like conceptual metaphor.^[23][24] Moreover, neuroimaging studies reveal that the association between number and space also shows up in brain activity. Regions of the parietal cortex, for instance, show shared activation for both spatial and numerical processing. These various lines of research suggest a strong, but flexible, connection between numerical and spatial cognition.

Modification of the usual decimal representation was advocated by John Colson. The sense of complementation, missing in the usual decimal system, is expressed by signed-digit representation.

Heuristics in numerical cognition

Several consumer psychologists have also studied the heuristics that people use in numerical cognition. For example, Thomas & Morwitz (2009) reviewed several studies showing that the three heuristics that manifest in many everyday judgments and decisions – anchoring, representativeness, and availability – also influence numerical cognition. They identify the manifestations of these heuristics in numerical cognition as: the left-digit anchoring effect, the precision effect, and the ease of computation effect respectively. The left-digit effect refers to the observation that people tend to incorrectly judge the difference between $4.00 and $2.99 to be larger than that between $4.01 and $3.00 because of anchoring on left-most digits. The precision effect reflects the influence of the representativeness of digit patterns on magnitude judgments. Larger magnitudes are usually rounded and therefore have many zeros, whereas smaller magnitudes are usually expressed as precise numbers; so relying on the representativeness of digit patterns can make people incorrectly judge a price of $391,534 to be more attractive than a price of $390,000. The ease of computation effect shows that magnitude judgments are based not only on the output of a mental computation, but also on its experienced ease or difficulty. Usually it is easier to compare two dissimilar magnitudes than two similar magnitudes; overuse of this heuristic can make people incorrectly judge the difference to be larger for pairs with easier computations, e.g. $5.00 minus $4.00, than for pairs with difficult computations, e.g. $4.97 minus $3.96.

Ethnolinguistic variance

The numeracy of indigenous peoples is studied to identify universal aspects of numerical cognition in humans. Notable examples include the Pirahã people who have no words for specific numbers and the Munduruku people who only have number words up to five. Pirahã adults are unable to mark an exact number of tallies for a pile of nuts containing fewer than ten items. Anthropologist Napoleon Chagnon spent several decades studying the Yanomami in the field. He concluded that they have no need for counting in their everyday lives. Their hunters keep track of individual arrows with the same mental faculties that they use to recognize their family members. There are no known hunter-gatherer cultures that have a counting system in their language. The mental and lingual capabilities for numeracy are tied to the development of agriculture and with it large numbers of indistinguishable items.

Research outlet

The Journal of Numerical Cognition is an open-access, free-to-publish, online-only journal outlet specifically for research in the domain of numerical cognition.