Number representations in the human cortex

arithmetic skills the association between symbolic and non-symbolic number processing becomes less strong.

For the remainder of this chapter, we will discuss our findings regarding these de-bates, methodological considerations, and future research directions.

9.1 Conclusions and considerations

9.1.1 Number representations in the human cortex

The first study (chapter 4) applied MVPA fMRI to look into the neural representations of dots and digits and questioned if these neural representation of digits and dots are overlapping on three different spatial scales (entire lobules, smaller regions of interest and a searchlight analysis with 2-voxel radius). Results showed that numbers in both formats were decodable in occipital, frontal, temporal and parietal regions.

However, there were no overlapping representations between dots and digits on any of the spatial scales. These data suggest that the human brain does not contain an abstract representation of numerical magnitude.

In chapter 5, we further investigated the nature of the association between digits and dots at a neural level. In line with studies on object cognition, which reported that the IPS processes the number of objects presented (Song & Jiang, 2006; Todd & Marois, 2005; Vogel & Machizawa, 2004; Y. Xu, 2008; Y. Xu & Chun, 2007b), our data suggest that Arabic digits are more related to one dot than to dot patterns with corresponding numerical magnitude. This significant finding contradicts again the hypothesis that numbers are processed in a format-independent manner in the human parietal cortex.

Taken together, our first two studies strongly contradict the previously published neuroimaging evidence in favor of the presence of an abstract number coding mech-anism in the human cortex (see chapter 1, for a meta-analysis and review see Ansari (2008); Nieder & Dehaene (2009)). However, several considerations regarding the studies discussed in chapter 4 and chapter 5 need to be addressed.

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Considerations

The possible influence of low-level stimuli properties Although our studies con-trolled the non-symbolic stimuli for low-level stimuli properties (e.g., overall number of pixels), we only controlled for one visual variable at the time, leaving open the possiblity that visual properties of the stimuli changed accordingly with the number (Gebuis & Reynvoet, 2012b). This might influence our results, as Gebuis & Reynvoet (2012b) demonstrated that people cannot extract number from a visual scene inde-pendent of its visual cues. Instead, number judgments are based on the integration of information from multiple visual cues. Gebuis and colleagues concluded (p642):

“The existence of an approximate number system that can extract number independ-ent of the visual cues appears unlikely. We therefore propose that number judgmindepend-ent is the result of the weighing of several distinct visual cues.” As we found significant decoding accuracies in the occipital cortex, one might wonder whether this has to do with only visual properties and not with number itself. However, a recent EEG study by Park et al. (2015) demonstrated a stronger modulation of visual responses for changes in numerosity than for visual properties of the number. These findings provide evidence, that it might be the case that the visual system is not relying expli-citly on visual properties to encode the numerosity.

The use of a direct number comparison task We failed to replicate the earlier findings of Eger et al. (2009) demonstrating cross-format generalization in the pari-etal cortex. Recently, two possible explanations were given by Piazza & Eger (2016) to account for the differences between the study of Eger et al. (2009) and our study.

First, the paradigm differed between the two studies. While we applied a direct num-ber comparison task, Eger et al. (2009) applied a delayed numnum-ber comparison task (first the sample was shown, a couple of seconds later the second number) separat-ing the number representation from the comparison process. However, it is important to remark that our failure to detect any overlapping representations by multivariate analyses was also found in two other studies, using other paradigms. Damarla & Just (2012) used a passive-viewing task and did not demonstrate significant cross-format

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generalization. Furthermore, Lyons et al. (2015) applied, as Eger et al. (2009), a paradigm where a temporal separation between the to-be-compared stimuli and found no overlapping neural representations by applying representational similarity analysis.

A second difference between our studies and the one of Eger and colleagues (2009), Eger et al. (2009) used a higher spatial resolution in their study compared to our studies. However, Piazza & Eger (2016) concluded that “these slight differences in imaging parameters across studies might not be critical.”

Failure to generalize, a null result as well Another important consideration, is that the absence of evidence may not be confused with evidence for absence. The failure to find cross-format generalization (chapter 4) (format-dependent hypothesis) is as much a null-result as the similar brain activity between digits and dots in the IPS (format-independent hypothesis).

However, in chapter 5, we directly addressed this issue by investigating the classi-fication rates during the generalization classiclassi-fication between digits and dots. Two scenarios were considered in this chapter: (a) if a significant generalization accuracy would be observed between digits and dots, this would confirm with significant res-ults the notion of format-independent neural number representations; or (b) if the generalization between digits and dots failed, but the digits would be significantly more classified as one dot instead of the dot condition with which the digit shares the numerical magnitude, this would confirm with significant results the format-dependent hypothesis of number representations.

We observed the latter scenario in chapter 5, namely digits were significantly more classified as one dot and not as the dot condition with the same numerical magnitude symbolized by the digit. These results were consistently obtained for different digits in IPS, its subregions, and many other brain regions. This means that the nature of the neural association between digits and dots is defined b the number of objects