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L'ontogenesi e la filogenesi delle abilità numeriche
Get PDFIn the last decades several studies have demonstrated that some numerical abilities are not strictly related to symbolic language and they are not a human prerogative. Recently the ability to discriminate between two quantities has been demonstrated also in fish. The aim of this project was to study the mechanisms underlying the non verbal numerical abilities in vertebrates. I investigated whether fish possess two independent numerical systems for the representation of small (4) number or they possess a unique system that operates on the whole numerical scale. Both spontaneous choice and training experiments demonstrated that the ability to discriminate between large quantities was approximate and strongly dependent on the ratio between the numerosities, while discrimination in the small quantity range was not dependent on ratio and discriminating 3 from 4 was as easy as discriminating 1 from 4. The second part of the project regards the ontogeny of the ability to discriminate quantities. These experiments showed that the ability of fish to discriminate small numbers is innate and it is displayed immediately at birth while discrimination of large numbers emerges later as a result of both maturation and social experience. The third part concerns the role of non numerical variables in the discrimination of quantities. These experiments showed that fish are able to discriminate quantities even after the access to non numerical cues was made difficult and that learning a discrimination by using only numerical information is not more difficult than learning it by using only the non numerical variables. Finally, to investigate whether fish and humans share the same non verbal numerical systems, I carried out some experiments in which I compared fish and university students for their ability to discriminate the same numerical contrasts.
Taken together these findings support the suggestion that discrete and continuous quantities are processed in humans and nonhuman animals by systems that evolved from a common ancestor more than 450 million years ago.Negli ultimi anni è stato ampiamente dimostrato che le capacità numeriche non sono una prerogativa esclusivamente umana, infatti alcune abilità numeriche sono presenti anche in molte specie animali. Recentemente è stato dimostrato che anche i pesci sono in grado di compiere delle discriminazioni numeriche, e per questo sono stati utilizzati come modello sperimentale nel presente lavoro, allo scopo di approfondire lo studio dei meccanismi alla base delle abilità numeriche non verbali nei vertebrati. Una prima serie di esperimenti ha indagato se vi siano uno o due sistemi numerici non verbali nei pesci. I risultati, provenienti sia dagli esperimenti condotti con la procedura della scelta spontanea che da quelli condotti con la procedura di addestramento, hanno evidenziato come la capacità di discriminare grandi quantità (>4) sia fortemente influenzata dal rapporto numerico, mentre le discriminazioni tra piccole quantità (<4) non lo siano, in quanto discriminare 1 vs. 4 sarebbe facile quanto discriminare 3 vs. 4. Un secondo aspetto analizzato riguarda l’ontogenesi delle abilità numeriche. Questi esperimenti hanno evidenziato che nei pesci la capacità di discriminare piccole quantità è innata e presente fin dalla nascita, mentre quella di discriminare grandi quantità emerge più tardi come risultato della maturazione e dell’esperienza sociale. In seguito sono stati condotti una serie di esperimenti allo scopo di valutare il ruolo delle variabili non numeriche nelle discriminazioni di quantità: è emerso che i pesci sono in grado di discriminare diverse quantità anche quando l’accesso alle variabili non numeriche viene limitato; inoltre è stato dimostrato come per i pesci non sia più difficile apprendere una discriminazione sulla base della sola informazione numerica piuttosto che affidandosi alle sole variabili non numeriche, suggerendo che anche per i pesci il numero potrebbe essere una caratteristica primaria così come lo sono altre dimensioni degli stimoli. Infine in una serie di esperimenti le prestazioni dei pesci sono state confrontate con quelle degli esseri umani adulti in compiti paragonabili, allo scopo di verificare se i meccanismi alla base della discriminazione non verbale di quantità siano gli stessi in tutti i vertebrati.
Nel loro insieme questi dati supportano l’ipotesi che sia nell’uomo che nei pesci le quantità siano elaborate attraverso dei sistemi che potrebbero essere evoluti da un comune antenato più di 450 milioni di anni fa
Musicians outperform nonmusicians in magnitude estimation: Evidence of a common processing mechanism for time, space and numbers
No full textIt has been proposed that time, space, and numbers may be computed by a common magnitude system. Even though several behavioural and neuroanatomical studies have focused on this topic, the debate is still open. To date, nobody has used the individual differences for one of these domains to investigate the existence of a shared cognitive system. Musicians are known to outperform nonmusicians in temporal discrimination tasks. We therefore observed professional musicians and nonmusicians undertaking three different tasks: temporal (participants were required to estimate which of two tones lasted longer), spatial (which line was longer), and numerical discrimination (which group of dots was more numerous). If time, space, and numbers are processed by the same mechanism, it is expected that musicians will have a greater ability, even in nontemporal dimensions. As expected, musicians were more accurate with regard to temporal discrimination. They also gave better performances in both the spatial and the numerical tasks, but only outside the subitizing range. Our data are in accordance with the existence of a common magnitude system. We suggest, however, that this mechanism may not involve the whole numerical range
Small and large number discrimination in guppies
No full textNon-verbal numerical behavior in human infants, human adults, and non-human primates appears to be rooted in two distinct mechanisms: a precise system for tracking and comparing small numbers of items simultaneously (up to 3 or 4 items) and an approximate system for estimating numerical magnitude of a group of objects. The most striking evidence that these two mechanisms are distinct comes from the apparent inability of young human infants and non-human primates to compare quantites across the small (4) number boundary. We ask whether this distinction is present in lower animal species more distantly related to humans, guppies (Poecilia reticulata). We found that, like human infants and non-human primates, fish succeed at comparisons between large numbers only (5 vs. 10), succeed at comparisons between small numbers only (3 vs. 4), but systematically fail at comparisons that closely span the small/large boundary (3 vs. 5). Furthermore, increasing the distance between the small and large number resulted in successful discriminations (3 vs. 6, 3 vs. 7, and 3 vs. 9). This pattern of successes and failures is similar to those observed in human infants and non-human primates to suggest that the two systems are present and functionally distinct across a wide variety of animal species
Individual differences in non-symbolic numerical abilities predict mathematical achievements but contradict ATOM
Get PDFA significant debate surrounds the nature of the cognitive mechanisms involved in non-symbolic number estimation. Several studies have suggested the existence of the same cognitive system for estimation of time, space, and number, called " a theory of magnitude" (ATOM). In addition, researchers have proposed the theory that non-symbolic number abilities might support our mathematical skills. Despite the large number of studies carried out, no firm conclusions can be drawn on either topic.Methods: In the present study, we correlated the performance of adults on non-symbolic magnitude estimations and symbolic numerical tasks. Non-symbolic magnitude abilities were assessed by asking participants to estimate which auditory tone lasted longer (time), which line was longer (space), and which group of dots was more numerous (number). To assess symbolic numerical abilities, participants were required to perform mental calculations and mathematical reasoning.Results: We found a positive correlation between non-symbolic and symbolic numerical abilities. On the other hand, no correlation was found among non-symbolic estimations of time, space, and number.Conclusions: Our study supports the idea that mathematical abilities rely on rudimentary numerical skills that predate verbal language. By contrast, the lack of correlation among non-symbolic estimations of time, space, and number is incompatible with the idea that these magnitudes are entirely processed by the same cognitive system
Spontaneous number representation in mosquitofish
No full textWhile there is convincing evidence that preverbal human infants and non-human primates can spontaneously represent number, considerable debate surrounds the possibility that such capacity is also present in other animals. Fish show a remarkable ability to discriminate between different numbers of social companions. Previous work has demonstrated that in fish the same set of signature limits that characterize non-verbal numerical systems in primates is present but yet to provide any demonstration that fish can really represent number rather than basing their discrimination on continuous attributes that co-vary with number. In the present work, using the method of 'item by item' presentation, we provide the first evidence that fish are capable of selecting the larger group of social companions relying exclusively on numerical information. In our tests subjects could choose between one large and one small group of companions when permitted to see only one fish at a time. Fish were successful when both small (3 vs. 2) and large numbers (8 vs. 4) were involved and their performance was not affected by the density of the fish or by the overall space occupied by the group
Large Number Discrimination by Mosquitofish
Get PDFBackground: Recent studies have demonstrated that fish display rudimentary numerical abilities similar to those observed in mammals and birds. The mechanisms underlying the discrimination of small quantities (, 4) were recently investigated while, to date, no study has examined the discrimination of large numerosities in fish.
Methodology/Principal Findings: Subjects were trained to discriminate between two sets of small geometric figures using social reinforcement. In the first experiment mosquitofish were required to discriminate 4 from 8 objects with or without experimental control of the continuous variables that co-vary with number (area, space, density, total luminance). Results showed that fish can use the sole numerical information to compare quantities but that they preferentially use cumulative surface area as a proxy of the number when this information is available. A second experiment investigated the influence of the total number of elements to discriminate large quantities. Fish proved to be able to discriminate up to 100 vs. 200 objects, without showing any significant decrease in accuracy compared with the 4 vs. 8 discrimination. The third experiment investigated the influence of the ratio between the numerosities. Performance was found to decrease when decreasing the numerical distance. Fish were able to discriminate numbers when ratios were 1: 2 or 2: 3 but not when the ratio was 3: 4. The performance of a sample of undergraduate students, tested non-verbally using the same sets of stimuli, largely overlapped that of fish.
Conclusions/Significance: Fish are able to use pure numerical information when discriminating between quantities larger than 4 units. As observed in human and non-human primates, the numerical system of fish appears to have virtually no upper limit while the numerical ratio has a clear effect on performance. These similarities further reinforce the view of a common origin of non-verbal numerical systems in all vertebrates
Number versus continuous quantity in numerosity judgments by fish
No full textAbstract: In quantity discrimination tasks, adults, infants and animals have been sometimes observed to process number only after all continuous variables, such as area or density, have been controlled for. This has been taken as evidence that processing number may be more cognitively demanding than processing continuous variables. We tested this hypothesis by training mosquitofish to discriminate two items from three in three different conditions. In one condition, continuous variables were controlled while numerical information was available; in another, the number was kept constant and information relating to continuous variables was available; in the third condition, stimuli differed for both number and continuous quantities. Fish learned to discriminate more quickly when both number and continuous information were available compared to when they could use continuous information only or number only; there was no difference in the learning rate between the two latter conditions. Our results do not support the hypothesis that processing numbers imposes a higher cognitive load than processing continuous variables. Rather, they suggest that availability of multiple information sources may facilitate discrimination learning
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