Cohen Kadosh & Walsh (CK&W) correctly point out that assessing technical limitations is critical in weighing the evidence favoring one or the other of the opposing views, abstract or non-abstract, about numerical representation in parietal cortex (PC). On at least three counts, they have overlooked relevant limitations.
CK&W state that: “Single-cell neurophysiology offers better temporal and spatial resolution than human neuroimaging” (sect. 8, para. 1). While strictly true, this seems to imply that the two techniques are measuring the same variable. This is of course untrue: The functional magnetic resonance imaging (fMRI) measures a haemodynamic response, not neuronal activity. Contrary to what has been conveniently assumed, the relationship between these two variables is far from resolved and depends upon the experimental conditions: while the link might be relatively direct in passive sensory stimulation, this is not the case when using task paradigms (Sirotin & Das Reference Sirotin and Das2009). The statement also ignores the whole issue of homology between the human and monkey brain, which we have only begun to resolve with the advent of monkey fMRI (Orban et al. Reference Orban, Van Essen and Vanduffel2004). Two facts are particularly relevant here. The surface area of the cortical sheet is ten times larger in humans than in the monkey (Van Essen Reference Van Essen, Chalupa and Werner2004), which implies that human cortex includes two to five times more functional areas than its monkey counterpart. On the other hand, the relationship of these areas with cortical sulci having identical labels can differ between the species, as the human MT/V5 complex illustrates. In human parietal cortex, the regions corresponding to the lateral bank of monkey intraparietal sulcus (IPS) are located in the medial bank of human IPS, especially on the posterior side (Grefkes & Fink Reference Grefkes and Fink2005). This implies that the homologue of monkey ventral intraparietal (VIP) area, where Nieder records his numerically selective neurons (Diester & Nieder Reference Diester and Nieder2007), is not actually located in the human IPS!
CK&W present the results of fMRI adaptation experiments as one of the main indications for a non-abstract representation in PC. They neglect the evidence that adaptation differs between time scales and between cortical areas (Krekelberg et al. Reference Krekelberg, Boynton and van Wezel2006; Verhoef et al. Reference Verhoef, Kayaert, Franko, Vangeneugden and Vogels2008). More seriously, they failed to see the implications of the Sawamura et al. (Reference Sawamura, Orban and Vogels2006) study, which they did quote in their review. Briefly, Sawamura et al. showed that infero-temporal (IT) neurons which respond equally well to two stimuli, say, images of a pig and of a hammer, will adapt when the two identical images follow one another, either two pigs or two hammers, but not, or much less, when the hammer follows the pig or the reverse. Thus, adaptation overestimates neuronal response selectivity and functional magnetic resonance adaptation (fMRA) cannot be used to derive neuronal tuning widths, as in Piazza et al. (Reference Piazza, Izard, Pinel, Le Bihan and Dehaene2004). The results also imply that at these high levels adaptation occurs not at the cell soma level, but somewhere earlier, either in the dendritic tree or in the inputs. The use of adaptation to prove a non-abstract representation actually implies adaptation at the soma. If this assumption does not hold, the predictions for the abstract and non-abstract case become identical. Exactly the same argument can be made for the combination of adaptation with transcranial magnetic stimulation (TMS), presented by CK&W as their second main argument for non-abstract representation. If adaptation does not involve the cell soma, both hypotheses predict that the parietal neurons will be equally active, and hence, that TMS will have the same effect, opposite to what has been assumed. This dramatic example shows that it is of utmost importance that assumptions made in interpreting fMRI data, be tested. This also holds for the multivoxel technique.
The final evidence for non-abstract representation are the Nieder single-cell data (Diester & Nieder Reference Diester and Nieder2007), but here CK&W neglect the limitations that the experimental model imposes upon these results. To be sure, the monkey is the best model that we have experimental access to, but it is not perfect, as there is ample evidence for differences in brain size (Van Essen Reference Van Essen, Chalupa and Werner2004) and cognitive competences (Penn et al. Reference Penn, Holyoak and Povinelli2008) between the two species. Hence, what applies to the monkey may not necessarily hold for the human. It is conceivable that the non-abstract representation in the monkey is supplemented in humans by abstract representations, say, in the evolutionarily new areas of the parietal cortex.
Does this mean, then, that the evidence for an abstract representation is solid? This is not the case either. As CK&W correctly pointed out, even it had been demonstrated that different numerical notations activated the same voxels in PC, this need not imply that the representation is carried by a single neuronal population. It is important to notice that even this demonstration is unconvincing thus far, given the extensive smoothing and averaging across subjects that is typical of most fMRI studies (Georgieva et al. Reference Georgieva, Peeters, Kolster, Todd and Orban2009).
Unfortunately, the authors in their discussions of future directions completely overlooked the studies that provide a solution to the problems outlined here: fMRI in the awake monkey (Vanduffel et al. Reference Vanduffel, Fize, Mandeville, Nelissen, Van, Rosen, Tootell and Orban2001). In fact, it replaces a direct comparison between human fMRI and single-cell studies in monkeys, which involves two unknowns, with two comparisons, each of which involves only a single unknown that can be resolved (Orban Reference Orban2002). The comparison between single-cells and MR signals in the monkey allows one not only to address the relationship between neuronal activity and MR signals (Logothetis et al. Reference Logothetis, Pauls, Augath, Trinath and Oeltermann2001; Sirotin & Das Reference Sirotin and Das2009), but equally important, to understand the relationship between MR procedure and neuronal selectivity. This procedure can take a variety of forms: it may be a slow adaptation procedure (Nelissen et al. Reference Nelissen, Vanduffel and Orban2006), or a test, based on a comparison of response levels under different conditions (Georgieva et al. Reference Georgieva, Peeters, Kolster, Todd and Orban2009). On the other hand, a comparison of fMRI in humans and monkeys allows the homology question to be addressed, when multiple properties of several neighboring regions are compared (Durand et al. Reference Durand, Peeters, Norman, Todd and Orban2009). The integration of single-cell studies and human functional imaging using awake monkey fMRI creates a brilliant future for cognitive neuroscience and lies at the heart of translational research in cognitive neurology.
