Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article


Doctor of Philosophy




Ansari, Daniel


A striking way that humans differ from other species is our unique ability to represent and manipulate symbols. This ability to process numerical magnitudes symbolically (e.g., ‘three’, ‘3’) is widely thought to be supported by an ancient system that evolved to process nonsymbolic numerical magnitudes (i.e., quantities). In this thesis, I present four empirical studies to uncover whether symbolic representations are indeed supported by the system that evolved to process quantities, or if symbolic representations are sub-served by a similar but ultimately distinct system.

In experiments 1 and 2, I investigate how the adult brain processes symbols and quantities using quantitative neuroimaging meta-analytic techniques (Experiment 1), and a tightly controlled fMRI paradigm (experiment 2). Results from the meta-analysis indicate that symbols and quantities are sub-served by both common and distinct brain regions along the frontal-parietal lobes. However, using a tightly controlled adaptation paradigm to isolate brain regions that underpin symbols and quantities reveal that regions supporting symbols are quite distinct from those supporting quantities, spatially and representationally. Thus, symbols might not be processed using the system that evolved to process quantities.

In experiment 3, I examine whether the processing of symbols is similar to quantities under different attentional conditions. I discover that in addition to participants being more efficient at effortfully comparing symbols than quantities, embedding distracting symbols into stimuli during a quantity comparison task affected performance more than embedding quantities into a symbolic comparison task. This indicates that symbols and quantities are processed differently, under different attentional conditions, and therefore are likely sub-served by different representational systems.

In experiment 4, I investigate the origin of the difference between how humans process symbols and quantities by exploring whether children’s symbolic number knowledge relates to their spontaneous attending to quantities. I find that children are more likely to attend to quantity if they know the number word that corresponds to the quantity, suggesting that learning symbols may influence how children conceptualize quantities.

In summary, while there are some similarities in how humans process symbols and quantities, there are many important differences both behaviourally, and the neural level of organization. Consequently, these findings challenge the longstanding belief that the culturally acquired ability to conceptualize numbers symbolically is grounded in the ancient system that evolved to estimate quantities.

Summary for Lay Audience

The uniquely human ability to think about numbers as symbols sets us apart from other species that can only think about numbers nonsymbolically (i.e., quantities, such as collections of dots). How does the human brain support this exceptional ability to conceptualize numbers symbolically? Are the ancient systems that evolved to estimate quantities repurposed for symbolic thinking? I examine similarities and differences in how humans think about symbolic numbers compared to quantities.

I explore whether the parts of the adult human brain that are activated in response to symbolic numbers are also activated in response to quantities. Specifically, I 1) synthesize previous research that examines brain responses to symbols and quantities to identify consistencies across these studies and 2) collect measures of brain activation while participants passively view symbols, quantities, and physical sizes. I discover that brain regions that are associated with thinking about numbers symbolically are quite distinct from brain regions that evolved to understand quantities.

Subsequently, I examine whether the similarities and differences between thinking about symbols and quantities depend on what participants are instructed to pay attention to. I discover that participants are faster and more accurate, comparing two symbols than two quantities. Additionally, when participants compare quantities, they perform more poorly if there is a distracting symbol present. Interestingly, the presence of a quantity when comparing symbols is less distracting. Together, this work shows that how human adults think about symbols and quantities is quite different.

To understand the origin of this difference I explore the relationship between how humans think about symbols and quantities in children, while these systems are developing. I examine whether having knowledge of symbolic numbers influences the degree to which children notice quantities in their environment. I find that children are more likely to notice and use quantities to solve a problem if they have learned the verbal number word that corresponds to the quantity.

Discoveries from this thesis reveal that humans conceptualize symbolic numbers in a way that is quite distinct from nonsymbolic quantities. This indicates that humans possess a system used to process symbols that is distinct from the evolutionarily ancient system used to estimate quantities. Future investigations are needed to understand better how we learn numerical symbols over the course of our development.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.