Neuronal population coding of continuous and discrete quantity in the primate posterior parietal cortex

Abstract

Quantitative knowledge guides vital decisions in the life of animals and humans alike. The posterior parietal cortex in primates has been implicated in representing abstract quantity, both continuous (extent) and discrete (number of items), supporting the idea of a putative generalized magnitude system in this brain area. Whether or not single neurons encode different types of quantity, or how quantitative information is represented in the neuronal responses, however, is unknown. We show that length and numerosity are encoded by functionally overlapping groups of parietal neurons. Using a statistical classifier, we found that the activity of populations of quantityselective neurons contained accurate information about continuous and discrete quantity. Unexpectedly, even neurons that were nonselective according to classical spike-count measures conveyed robust categorical information that predicted the monkeys' quantity judgments. Thus, different information-carrying processes of partly intermingled neuronal networks in the parietal lobe seem to encode various forms of abstract quantity.monkey ͉ single-unit recording ͉ statistical classifier T he questions ''how many?'' and ''how much?'' refer to two different types of quantity. Abstract quantity may be discrete and enumerable, thus referring to the number of elements, as opposed to continuous and uncountable quantity such as spatial extent (1). Behavior based on abstract quantitative parameters is clearly adaptive; for instance, understanding how much drinking water is around (2, 3) or how many individuals belong to an opponent party (4, 5) guide vital decisions in the life of animals and humans alike.The conceptual similarity between discrete and continuous quantity is perceptually reflected by behavioral interference phenomena. In a number comparison task, for example, choosing the numerically larger number takes significantly longer if the numeral is smaller in size compared with the numerically smaller number (e.g., in the comparison 2 versus 7) (6, 7). This number-size interference implies interactions on the neuronal level when discrete and continuous quantities are processed. The parietal cortex has recently been implicated in the representation of different types of quantity information (8-10). Functional imaging studies in humans suggest that anatomical vicinity (7, 11-13) or even a common magnitude system (14) for the representation of numerical (discrete) and spatial (continuous) quantity in the parietal cortex might be responsible for behavioral interference phenomena between numerical and spatial quantity (15,16).How continuous quantity is encoded by single nerve cells, and how it relates to numerosity representations, however, remains unknown. We analyzed the response properties of individual neurons in the fundus of the intraparietal sulcus (IPS) of monkeys simultaneously engaged in numerosity and length discrimination tasks. Using a neural network classification technique, we investigated to what extent the responses of small populations of neuro...

Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation

“…Each of these neurons is tuned to a preferred numerosity value (e.g., 4), but also fires when close numerosities are presented (3 and 5, 6), and thus represent numbers only approximately, in a format which would be suitable to encode continuous quantities. Recently, Tuduscius and Nieder (2007) tested whether the numerositysensitive neurons in the IPS were also sensitive to line length (a continuous variable). They found that the populations encoding these two attributes overlapped partially: 11.5 and 10% of the neurons were activated for physical size and numerosity, respectively; whereas, 3.5% fired for both physical size and numerosity.…”

Math, monkeys, and the developing brain

“…Although some neurons responded only to numerosity and others only to line length, a subset of cells (∼20%) responded to both magnitudes of line length and numerical value. These and other studies, including functional MRI studies of adults, have led some researchers to argue for a "distributed but overlapping" representation of different magnitudes at the neural level (4,8,61). Simply put, different types of magnitude representation, including size, number, and time (and possibly others such as brightness), share some neural resources in parietal cortex but not others.…”

“…Moreover, some data even suggest that a single parietal neuron can represent more than one type of magnitude. In one study (61), monkeys were trained to perform a line-length matching task and a numerical matching task. During stimulus presentation as well as a subsequent delay, single neurons in the IPS responded selectively to visual stimuli according to their numerosity or length.…”

Zooming in and out from the mental number line: Evidence for a number range effect.

“…These representations are assumed to be automatic in the sense that they are not affected by task demands. At a later stage, abstract representations may emerge in accordance with the task requirements in the prefrontal cortex, which is associated with training effects, working memory and strategy application (see also Gilbert & Burgess 2008;Tudusciuc & Nieder, 2007).…”

“…These representations are assumed to be automatic in the sense that they are not affected by task demands. At a later stage, abstract representations may emerge in accordance with the task requirements in the prefrontal cortex, which is associated with training effects, working memory and strategy application (see also Gilbert & Burgess 2008;Tudusciuc & Nieder, 2007).The objective of the present study was to explore whether the granularity or resolution of the evoked mental number line can also be changed by context. Consider a numerical comparison task, in which participants are presented with pairs of numbers (one pair at a 5 NUMBER RANGE EFFECT time) and are asked to select the larger number in each pair.…”