The beauty of numbers: From neurons to perception

Numbers appear everywhere in our daily life. Humans and animals share the ability to process non-symbolic number information (numerosity, i.e. the set size of a group of items), which helps to guide behavior and decision. Numerosity perception, resembling primary sensory perception, is considered a “number sense” across species and relates to the unique symbolic numerical cognition in humans. Converging evidence shows that single neurons tuned to specific numerosities (i.e. preferred numerosity), and that numerosity-selective neural populations organized systematically as topographic maps in human brain. Psychophysics studies have shown phenomena such as subitizing (< 4 items), attention and adaptation effects in numerosity perception (Chapter 1). However, it remains unclear the links between these perceptual consequences and the underlying neural mechanisms. In this thesis, we used population receptive field (pRF) modeling and ultra-high field (UHF) fMRI to explore the neural mechanism of numerosity, access the properties of the numerosity-tuned neural populations along the maps, and establish links between neural tuning and behavior perception of numerosity. In Chapter 2, we find neural populations tuned to small and large numerosities (up to 64) organized within the same topographic maps, suggesting a single neural mechanism. Furthermore, we find that tuning width increased with preferred numerosity increased and less cortical area devoted to larger numerosities, namely, a cortical magnification effect. These results suggest that differences in numerosity map properties might underlie distinct behavior performances on small (exact and accurate) and large numerosities (approximate and error-prone). In Chapter 3, we investigate effects of attention on numerosity-selective neuronal populations using stimuli consisting of two dot subsets in opposite colors. Participants attended to one of the subsets. We find that numerosity-selective neuronal populations respond to the attended subset while suppressing responses to the non-attended subsets. These results suggest that attention is necessary for numerosity-selective neuronal responses. Attentional selection on the numerosity of task-relevant objects while ignoring those of task-irrelevant objects is important to guarantee effective numerosity perception in natural scenes. It has been argued for decades that whether numbers are represented in an abstract way, that is, number representation is notation-independent. In Chapter 4, we ask whether numerosity maps are involved in symbolic number processing. We find that the numerosity map at the temporal-occipital cortex (NTO) also respond to symbolic numbers. Furthermore, only neural populations in the left NTO map are also tuned to symbolic numbers. These results suggest that the ventral temporal-occipital cortex plays important roles in linking non-symbolic numerosity and symbolic number processing. Since the discovery of numerosity maps was uncovered using 7T fMRI due to its higher signal-to-noise (SNR) and signal sensitivity, it has been inquired whether numerosity maps could be reconstructed at the standard field strength of 3T fMRI. In Chapter 5, we visit this question and quantify the extent to which 7T outperforms 3T in terms of the model predictive power as a function of scan runs. As the results, we were able to reconstruct numerosity maps at 3T. However, we find that much more functional runs are required at 3T than at 7T. On average, one 7T run has about 4 times the model predictive power of one 3T run. These results suggest that UHF MRI is beneficial to cognitive neuroscience to initially uncover functional maps, with higher SNR and signal sensitivity and thus reduce the number of runs required to achieve reliable activation compared to lower field strength. Chapter 6 summarizes the findings of the thesis, and discusses the strengths and weakness of the methodology used in this thesis. It also discusses new research questions evoked by the results of this dissertation.