Monkeys display classic signatures of human symbolic arithmetic.

Non-human primates compare quantities in a crude manner, by approximating their values. Less is known about the mental transformations that non-humans can perform over approximate quantities, such as arithmetic transformations. There is evidence that human symbolic arithmetic has a deep psychological connection with the primitive, approximate forms of quantification of non-human animals. Here, we ask whether the subtle performance signatures that humans exhibit during symbolic arithmetic also bear a connection to primitive arithmetic. Specifically, we examined the problem size effect, the tie effect, and the practice effect-effects which are commonly observed in children's math performance in school. We show that, like humans, monkeys exhibited the problem size and tie effects, indicating commonalities in arithmetic algorithms with humans. Unlike humans, however, monkeys did not exhibit a practice effect. Together, these findings provide new evidence for a cognitive relation between non-symbolic and symbolic arithmetic.

Empty sets as part of the numerical continuum: conceptual precursors to the zero concept in rhesus monkeys.

The goal of the current research was to explore whether monkeys possess conceptual precursors necessary for understanding zero. We trained rhesus monkeys on a nonsymbolic numerical matching-to-sample task, and on a numerical ordering task. We then introduced nondifferentially reinforced trials that contained empty sets to determine whether monkeys would treat empty sets as numerical values. All monkeys successfully matched and ordered the empty sets without any training. Accuracy showed distance effects, indicating that they treated empty sets as values on a numerical continuum.

Nothing to it: precursors to a zero concept in preschoolers.

Do young children understand the numerical value of empty sets prior to developing a concept of symbolic zero? Are empty sets represented as mental magnitudes? In order to investigate these questions, we tested 4-year old children and adults with a numerical ordering task in which the goal was to select two stimuli in ascending numerical order with occasional empty set stimuli. Both children and adults showed distance effects for empty sets. Children who were unable to order the symbol zero (e.g., 0<1), but who successfully ordered countable integers (e.g., 2<4) nevertheless showed distance effects with empty sets. These results suggest that empty sets are represented on the same numerical continuum as non-empty sets and that children represent empty sets numerically prior to understanding symbolic zero.

Mechanisms of inferential order judgments in humans (Homo sapiens) and rhesus monkeys (Macaca mulatta).

If A > B, and B > C, it follows logically that A > C. The process of reaching that conclusion is called transitive inference (TI). Several mechanisms have been offered to explain transitive performance. Scanning models claim that the list is scanned from the ends of the list inward until a match is found. Positional discrimination models claim that positional uncertainty accounts for accuracy and reaction time patterns. In Experiment 1, we trained rhesus monkeys (Macaca mulatta) and humans (Homo sapiens) on adjacent pairs (e.g., AB, BC, CD, DE, EF) and tested them with previously untrained nonadjacent pairs (e.g., BD). In Experiment 2, we trained a second list and tested with nonadjacent pairs selected between lists (e.g., B from List 1, D from List 2). We then introduced associative competition between adjacent items in Experiment 3 by training 2 items per position (e.g., B1C1, B2C2) before testing with untrained nonadjacent items. In all 3 experiments, humans and monkeys showed distance effects in which accuracy increased, and reaction time decreased, as the distance between items in each pair increased (e.g., BD vs. BE). In Experiment 4, we trained adjacent pairs with separate 9- and 5-item lists. We then tested with nonadjacent pairs selected between lists to determine whether list items were chosen according to their absolute position (e.g., D, 5-item list > E, 9-item list), or their relative position (e.g., D, 5-item list < E, 9-item list). Both monkeys' and humans' choices were most consistent with a relative positional organization.

Numerical rule-learning in ring-tailed lemurs (lemur catta).

We investigated numerical discrimination and numerical rule-learning in ring-tailed lemurs (Lemur catta). Two ring-tailed lemurs were trained to respond to two visual arrays, each of which contained between one and four elements, in numerically ascending order. In Experiment 1, lemurs were trained with 36 exemplars of each of the numerosities 1-4 and then showed positive transfer to trial-unique novel exemplars of the values 1-4. In Experiments 2A and 2B, lemurs were tested on their ability to transfer an ascending numerical rule from the values 1-4 to novel values 5-9. Both lemurs successfully ordered the novel values with above chance accuracy. Accuracy was modulated by the ratio between the two numerical values suggesting that lemurs accessed the approximate number system when performing the task.

Do monkeys think in metaphors? Representations of space and time in monkeys and humans.

Research on the relationship between the representation of space and time has produced two contrasting proposals. ATOM posits that space and time are represented via a common magnitude system, suggesting a symmetrical relationship between space and time. According to metaphor theory, however, representations of time depend on representations of space asymmetrically. Previous findings in humans have supported metaphor theory. Here, we investigate the relationship between time and space in a nonverbal species, by testing whether non-human primates show space-time interactions consistent with metaphor theory or with ATOM. We tested two rhesus monkeys and 16 adult humans in a nonverbal task that assessed the influence of an irrelevant dimension (time or space) on a relevant dimension (space or time). In humans, spatial extent had a large effect on time judgments whereas time had a small effect on spatial judgments. In monkeys, both spatial and temporal manipulations showed large bi-directional effects on judgments. In contrast to humans, spatial manipulations in monkeys did not produce a larger effect on temporal judgments than the reverse. Thus, consistent with previous findings, human adults showed asymmetrical space-time interactions that were predicted by metaphor theory. In contrast, monkeys showed patterns that were more consistent with ATOM.

Context affects the numerical semantic congruity effect in rhesus monkeys (Macaca mulatta).

Do monkeys anchor their numerical judgments based on the context in which their choices are presented? We addressed this question by varying the numerical range across sessions while macaque monkeys made ordinal judgments. Monkeys were trained to make a conditional discrimination whereby they were reinforced for ordering arrays of dots in ascending or descending numerical order, dependent on a color cue. Monkeys were tested using two ranges of numerosities that converged on a single pair. Similar to the findings of Cantlon and Brannon (2005), we found a semantic congruity effect whereby decision time was systematically influenced by the congruity between the cue (ascending or descending) and the relative Numerical Magnitude of the stimuli within each range. Furthermore, monkeys showed a context effect, such that decision time for a given pair was dependent on whether it was a relatively small or large set of values compared to the other values presented in that session. This finding suggests that, similar to humans, the semantic congruity effect observed in monkeys is anchored by the context. Thus our data provide further evidence for the existence of a shared numerical comparison process in monkeys and humans.

Social Complexity Predicts Transitive Reasoning in Prosimian Primates.

Transitive Inference is a form of deductive reasoning that has been suggested as one cognitive mechanism by which animals could learn the many relationships within their group's dominance hierarchy. This process thus bears relevance to the social intelligence hypothesis which posits evolutionary links between various forms of social and nonsocial cognition. Recent evidence corroborates the link between social complexity and transitive inference and indicates that highly social animals may show superior transitive reasoning even in nonsocial contexts. We examined the relationship between social complexity and transitive inference in two species of prosimians, a group of primates that diverged from the common ancestor of monkeys, apes, and humans over 50 million years ago. In Experiment 1, highly social ring-tailed lemurs, Lemur catta, outperformed the less social mongoose lemurs, Eulemur mongoz, in tests of transitive inference and showed more robust representations of the underlying ordinal relationships between the stimuli. In Experiment 2, after training under a correction procedure that emphasized the underlying linear dimension of the series, both species showed similar transitive inference. This finding suggests that the two lemur species differ not in their fundamental ability to make transitive inferences, but rather in their predisposition to mentally organize information along a common underlying dimension. Together, these results support the hypothesis that social complexity is an important selective pressure for the evolution of cognitive abilities relevant to transitive reasoning.