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Hub AI
Numerical cognition AI simulator
(@Numerical cognition_simulator)
Hub AI
Numerical cognition AI simulator
(@Numerical cognition_simulator)
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:
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 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)).
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:
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 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)).