Cohen Kadosh & Walsh (CK&W) present a comprehensive argument against the abstract representation of numbers in the parietal lobes. Their discussion focuses on behavioral and neuroimaging studies, which comprise the bulk of the numerosity literature. But, as CK&W point out, these techniques do not provide the sampling resolution necessary to definitively answer the question of abstract number representation. In contrast, single-neuron electrophysiology provides high spatial and temporal resolution, allowing researchers to monitor the activity of individual neurons in real time. This technique is therefore the most promising avenue for addressing the issue of abstract number representation. In this commentary, I present two single-neuron experimental manipulations that, to my knowledge, have not been used in studies of number-sensitive neurons. These manipulations could help move single-cell studies beyond simple correlation to a more causal understanding of the neuronal basis of number processing.

First, temporary pharmaceutical inactivation (Li et al. Reference Li, Mazzoni and Andersen1999; Wardak et al. Reference Wardak, Olivier and Duhamel2002) of number-sensitive patches of parietal cortex can be used to test the usefulness of reported number representations. Although it would be a challenge to demonstrate that all number neurons were inactivated in the parietal lobe, a large portion of neurons can be reliably “switched off” and re-activated over time. Accordingly, animals should show severely diminished performance on number-related tasks during inactivation if numerons truly support their ability to accurately process numerosity. Following the lead of the tasks reviewed in the target article, number-related task performance would have to be assessed across different number formats. The existence of abstract number representations predicts comparable decreases in performance regardless of number format when compared to pre-inactivation measurements. Temporary inactivation is therefore one way in which our understanding of number representations can progress beyond correlational evidence.

If abstract number neurons exist, then they presumably underlie our ability to perceive and process various numbers. Thus, to tease apart the influence of number neurons on perception, it would be useful to have a situation in which perceived numerosity can be manipulated independently of displayed numerosity. Fortunately, such a psychophysical “trick” has been recently discovered (Burr & Ross Reference Burr and Ross2008; see also Durgin Reference Durgin2008).

The second manipulation involves the “apparent numerosity adaptation” paradigm (Burr & Ross Reference Burr and Ross2008). In this task, subjects fixate a center target while two patches consisting of many stationary stimuli are presented, one to the left and one to the right of fixation. Immediately after an extended period of adaptation, test patches are then presented in the same two locations and subjects are asked to make a numerical judgment, usually in the form of a two-alternative forced choice task (e.g., “Which patch contains more items, left or right?”). Burr and Ross (Reference Burr and Ross2008) showed that adapting to a large number of stimuli decreases subsequent numerosity judgments, while adapting to a small number of stimuli produces artificially increased numerosity judgments. The numerical perception of the subjects can therefore be manipulated in a controlled manner based on the number of stimuli in the adapting patch.

For single-neuron recordings, this task could be passively presented to animal subjects. Better yet, animals could be trained to make “more” or “less” judgments when the two test patches are presented after adaptation. We can then ask how number neurons in parietal cortex respond over time in the adaptation task (i.e., during and after adaptation). For example, if a neuron with a preferred numerosity of 20 (Nieder & Merten Reference Nieder and Merten2007) is isolated and the animal is adapted with a patch of 100 stimuli, will the subsequent test presentation of 20 stimuli cause the neuron to fire maximally, consistent with the veridical presented number? Or, alternatively, will the neuron's response shift towards the adapted numerosity, in line with the subject's percept? Again, different formats of number stimuli can also be used for adaptation and testing (Diester & Nieder, in press). Following the labeled-line coding hypothesis (Nieder & Merten Reference Nieder and Merten2007), numeron selectivity should be predictably manipulated by low- and high-numerosity adaptation across formats. A series of systematic adaptation-and-test conditions on the same neuron would help elucidate the functional role of number neurons, and shed light on the issues of automaticity and intentionality raised by CK&W.

A combination of the two manipulations may prove to be the most fruitful. Changes in task performance during inactivation – both in the standard delayed-match-to-sample task (typically used by Nieder and colleagues) and the adaptation task proposed above – can be used to assess the function of number neurons in numerosity judgments. This investigation could be extended to putative number-sensitive neurons in prefrontal cortex (PFC). This extension would help disambiguate the role of parietal and prefrontal number neurons, as well as allow for the testing of CK&W's hypothesis that PFC plays a “post-representational” role in relation to number processing in the parietal lobes.

These two manipulations are, to be sure, not complete experiments. But they are based on established techniques in the field that are well within our current capabilities. The onus to carry out these experiments is on proponents of abstract number representation because, as CK&W highlight, there are currently too many issues of interpretation to conclude in favor of abstractness. Regardless, for both sides of the issue, a straightforward manipulation of the responses of single neurons seems to be the most definitive method for uncovering the abstractness of number representations in the parietal lobes.