The effects of depression on number perception and its implications for theories of numerical cognition

Most theories of numerical cognition assume that the perception of a quantity is independent of that which the quantity describes (termed an abstract quantity representation). Beck’s cognitive theory of depression, in contrast, assumes that depressed individuals maintain negative perceptual biases and that depressed individuals’ perception of quantity will be dependent on that which the quantity describes. Here, we explore the nature of quantity representations by assessing whether level of depression and valence of events influences individuals’ perceptions of numerical quantities. In a number bisection task, we presented participants with three quantities: one associated with the time until a positive event, one associated with the time until a negative event, and a target number. The participant was asked to judge whether the quantity denoted by the target number was closer to the time until the positive or negative event. Results indicated that event valence influenced the perception of quantity and this perceptual bias interacted with the level of depression. Thus, these findings indicate that quantity representations are malleable and are represented non-abstractly in the brain.

Mapping the Brain for Math

Brain stimulation techniques allow for the search of crucial areas for a given function. Not always convergent with neuroimaging, TMS studies have targeted parietal areas critical for quantity representation, spatio-numerical links, numerical and non-numerical quantity, finger gnosis and calculation. TMS data indicate the intraparietal sulcus and surrounding areas in the left and right hemisphere as crucial for quantity processing, although left hemisphere might be dominant. Bilateral parietal loci are essential for calculation and bilateral parietal areas are behind the spatio-numerical link, which extends to frontal and posterior parietal sites. DCE studies to date have focused on the dominant hemisphere, have used calculation tasks and have found both dissociation and overlap between operations. An integrative view of positive findings and a focus on convergence and possible improvement is proposed. Although regularities are found between these techniques, more research is needed before arriving at conclusions that will have basic and clinical importance.

The Event Search Engine

In a remote or local environment in which a sensor network always collects data produced by sensors attached to physical objects, the engine presented here saves the data sent through the Internet and searches for data segments that correspond to real-world events by using natural language (NL) words in a query that are input in an web browser. The engine translates each query into a physical quantity representation searches for a sensor data segment that satisfies the representation, and sends back the event occurrence time, place, or related objects as a reply to the query to the remote or local environment in which the web browser displays them. The engine, which we expect to be one of the upcoming Internet services, exemplifies the concept of symbiosis that bridges the gaps between the real space and the digital space.

Numerical Values Leave a Semantic Imprint on Associated Signs in Monkeys

Animals and humans share an evolutionary ancient quantity representation which is characterized by analog magnitude features: Discriminating magnitudes becomes more difficult with increasing set sizes (size effect) and with decreasing distance between two numerosities (distance effect). Humans show these effects even with number symbols. We wondered whether monkeys would show the same psychophysical effects with numerical signs and addressed this issue by training three monkeys to associate visual shapes with numerosities. We then confronted the monkeys with trials in which they had to match these visual signs with each other. The monkeys' performance in this shape versus shape protocol was positively correlated with the numerical distance and the magnitudes associated with the signs. Additionally, the monkeys responded significantly slower for signs with higher assigned numerical values. These findings suggest that the numerical values imprint their analog magnitudes characteristics onto the associated visual sign in monkeys, an effect that we also found reflected in the discharges of prefrontal neurons. This provides evidence for a precursor of the human number symbol knowledge.