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Uncovering the spatial nature of numbers: An investigation of its origins and neural basis

Final Report Summary - SPANUM (Uncovering the spatial nature of numbers: An investigation of its origins and neural basis)

The ability to think about continuous magnitudes including approximate number, spatial location, temporal duration, loudness, and brightness is foundational to human reasoning. We, and many species of non-human creatures, use this ability to forage for food, to find our way home, and to track oncoming stimuli. For hundreds or perhaps thousands of years, it has been noted that there are similarities in the ways we reason about these different magnitudes. Some of the connections are metaphorical (as when, in English, we talk about “counting down to the big event”—using number to talk about time, or “an expensive item setting us back”—using space to talk about number). Other connections seem to run deeper—as with the longstanding observation that computing number and computing spatial area often mutually interfere with one another. But only recently have psychologists been able to query the links between our representations of number, space, time, and other magnitudes in a rigorous empirical way. This kind of research, of which the project SPANUM has been a scientific leader, has great practical and theoretical potential implications. On the practical side, recent investigations have shown that individual differences in people’s ability to represent approximate number, to estimate spatial extent, and to map number onto extent, predict many aspects of their future mathematical performance. Even more recent work suggests that giving people training in magnitude approximation tasks may improve their subsequent math scores. Thus, from an applied perspective, understanding the developmental origins of our ability to think about number and space, characterizing their relationship to one another, and tracking the development of these, has potential future value for educational aims.

In addition, the project SPANUM has been poised to play a major role in advancing the field’s theoretical understanding of our ability to represent and reason about deeply abstract entities (as one cannot directly perceive a number, a point in space, or a temporal duration). A current hot- ebate in cognitive science concerns whether there are distinct representational systems that allow us to think about number, and to think about time, and to think about duration, etc.—where these systems share a similar format as well as anatomical interconnections but are fundamentally separate—or whether there is a single “generalized” magnitude system that produces an undifferentiated representation of ordered scales, whose representations are somehow transformed later in processing into distinct thoughts about number, space, and time. Hundreds of papers have been published on this topic. Yet, no matter whether the other inquiries find evidence for separate systems or a single unified system, the deep question remains unanswered. The problem is that adults (or even children) may have learned to parcel an undifferentiated representation into distinct dimensions, or may have learned to link representations that were initially separate—in either case, culture and experience could be source of the observed effects, leaving unanswered the question of how magnitudes are foundationally represented, prior to enculturation or conscious strategizing. The project SPANUM has addressed this question in a way that no other work has done in the past.

Testing adults or older children can never reveal to us whether humans have a deep foundational link between number, space, time, and other magnitude dimensions, or whether we learn to link these either through language and cultural metaphors, or through observation natural correlations between these dimensions. The best way to answer this question is by testing infants— preferably infants with very minimal experience in the world. Studying newborns is an extremely difficult undertaking. There are relatively few studies of newborn cognition—and most of the existing studies are of infants’ auditory and language processing abilities. With the project SPANUM we have studied relationships between newborn infants’ abstract concepts of number, space, and time.

In early 2014 we have published a scientific work in the journal ‘Proceedings of the National Academy of Sciences’ showing that from birth humans have an abstract sense of magnitude that is shared by the dimensions of number, spatial extent and temporal duration. In particular, we have shown that when newborns experience an increase in either number of temporal duration they expect the dimension of spatial extent to increase. Same results have been obtained when newborns experience a decrease in these dimensions. The implications of this work are important for the scientific community. First, it demonstrates access to a newborn population and the success of the cross-dimensional change detection methodology. This paper opens the door to many future studies that will further investigate newborns’ ability to link representations of number, space, and time with other magnitudes (like brightness).

The project SPANUM has also undertaken the challenge of understanding the neural basis of the number-space link in adult humans, by seeking direct anatomical evidence for the spatial format of number, asking in particular whether seeing a number automatically activates a corresponding (variable) spatial length. Using fMRI, in this study we have acquired high resolution brain images while participants passively viewed different instances of numerosities and of line lengths. Based on new techniques recently developed for the analysis of brain imaging data, we use an analysis based on the establishment of a similarity matrix within and between dimensions (this analysis is based on multidimensional scaling methods, but at the neural level). The description of the magnitude-related areas at an anatomical level will eventually have implications for the designing of rehabilitation programs.