Considerable research in cognitive science, neuroscience, and developmental science has revealed that the temporal, spatial, and numerical features of a stimulus can interact with one another [], as when larger stimuli are perceived as lasting longer than smaller stimuli. These findings have inspired the prominent hypothesis that time, space, and number are processed by a ‘common magnitude system’, which represents these dimensions via the same unit of magnitude []. According to current theorizing, the parietal cortex mediates this system []. To test the species generality and neuroanatomical foundations of this hypothesis, we asked whether space–time interactions can be observed in birds. Unlike mammals, birds lack a cortex []; rather, they possess a neuron-dense pallium that is organized in clusters, in contrast to the laminar structure of the mammalian cortex []. Despite these striking neuroanatomical disparities, we observed reliable space–time interactions in pigeons. Our findings suggest that common magnitude systems are more widespread among animals than previously believed and need not be cortically dependent in all species.

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8 Merritt D.J.

Casasanto D.

Brannon E.M. Do monkeys think in metaphors? Representations of space and time in monkeys and humans. To explore this common magnitude hypothesis, we assessed whether pigeons would show cross-dimensional interactions using a task devised by Merritt et al. [], which produces space–time interactions in humans and nonhuman primates. Specifically, across intermixed training trials, we taught pigeons to judge the spatial-length or the temporal-duration of a horizontal line — spatial and temporal tasks, respectively. After presenting the line, pigeons were shown two choice stimuli. For the spatial task, if the line-length was short (6 cm), pigeons received food for pecking one choice stimulus; but if the line-length was long (24 cm), pigeons received food for pecking the other choice stimulus. Similarly, for the temporal task, pigeons received food for pecking one of two different choice stimuli depending on whether the duration of the line had been short (2 s) or long (8 s).

During testing, we introduced intermediate values for the length of the line in the spatial task and for the duration of the line in the temporal task. Critically, we also varied the values of the irrelevant dimension to see if this would affect how pigeons judged the relevant dimension. Specifically, in the spatial task, we presented the line for either a shorter or longer duration than in training; similarly, in the temporal task, we presented shorter or longer line-lengths than in training.

Figure 1 Proportion of ‘long’ responses during cross-dimensional testing. Show full caption The left panel corresponds to spatial trials in which pigeons had to judge the length of a line that had either a short, medium, or long temporal duration. The right panel corresponds to temporal trials in which pigeons had to judge the duration of a line of either short, medium, or long spatial length. Figure 1 depicts the proportion of ‘long’ responses as a function of the magnitude of the relevant dimension during the spatial and temporal tasks. As expected, these values increased as the magnitude of the stimulus being judged increased. More importantly, varying the irrelevant dimension systematically affected judgments of the relevant dimension.

We first quantified this effect by calculating the Point of Subjective Equality (PSE) for each trial type. The PSE is the relevant dimension value that was equally likely to be reported as short or long. Increases or decreases in this measure indicate an increased tendency for stimuli to be judged as short or long, respectively. For the spatial task, presenting the line for a short, medium, or long period of time yielded PSEs of 21.37, 18.95, and 15.14 cm, respectively. Similarly, for the temporal task, varying the spatial-length of the line to be short, medium, or long produced PSEs of 6.60, 5.90, and 4.42 s, respectively.

Next, we analysed the data using a mixed-effects logistic regression model (Supplemental Information). In the spatial task, short and long line-durations caused the overall proportion of long-length choices to decrease and increase, respectively (Short-duration line: B = –0.72, Z = –3.40, p < 0.001; Long-duration line: B = 0.43, Z = 2.86, p < 0.01). Importantly, these changes were not uniform across all line-length values. Specifically, short-duration lines exerted a greater effect on judgments of longer line-lengths (B = –0.33, Z = –8.92, p < 0.001), whereas long-duration lines exerted a greater effect on judgments of short line-lengths (B = –0.42, Z = –13.43, p < 0.001).

In the temporal task, short and long line-lengths prompted the overall proportion of long duration choices to decrease and increase, respectively, although these trends were not significant (Short-length line: B = –0.72, Z = –1.47, p > 0.05; Long-length line: B = 0.45, Z = 1.73, p > 0.05). More importantly, and as with the spatial task, these changes were not uniform across all line-durations. Specifically, shorter line-lengths had a greater effect on judgments of longer line-durations (B = –0.12, Z = –2.81, p < 0.01), whereas longer line-lengths had a greater effect on judgments of shorter line-durations (B = –0.61, Z = –20.78, p < 0.001).

8 Merritt D.J.

Casasanto D.

Brannon E.M. Do monkeys think in metaphors? Representations of space and time in monkeys and humans. Collectively, our results show that space–time interactions do indeed occur in birds and closely parallel those observed in monkeys []. They thus speak to the possible neural and adaptive foundations of common magnitude coding.

9 Mello G.B.M.

Soares S.

Paton J.J. A scalable population code for time in the striatum. 4 Walsh V. A theory of magnitude: common cortical metrics of time, space and quantity. One possibility is that this system may not be cortically dependent. The striatum is shared between birds and mammals, and integrates diverse information, such as time and goal-directed behavior []. Perhaps this structure also integrates time, space, and number. However, considerable causal evidence already shows that the parietal cortex mediates time, space, and number judgments [].

6 Shimizu T.

Shinozuka K.

Uysal A.K.

Kellogg S.L. The origins of the bird brain: multiple pulses of cerebral expansion in evolution. 7 Jarvis E.D.

Güntürkün O.

Bruce L.

Csillag A.

Karten H.

Kuenzel W.

Medina L.

Paxinos G.

Perkel D.J.

Shimizu T.

et al. Avian brains and a new understanding of vertebrate brain evolution. Another possibility is that there actually are areas in the avian pallium that are homologous to areas of mammalian parietal cortex. However, current evidence does not support this idea [].

10 Castro L.

Wasserman E.A. Executive control and task switching in pigeons. 5 Güntürkün O.

Ströckens F.

Scarf D.

Colombo M. Apes, feathered apes, and pigeons: differences and similarities. Finally, the common magnitude system may have emerged in birds and mammals via convergent evolution, in which common selection pressures cause similar traits to develop in different species. Consistent with this hypothesis, birds perform exceptionally well on tasks known to be cortically dependent in mammals, such as tests of executive functioning []. The avian pallium, although structurally distinct from the mammalian cortex, may have evolved to perform analogous cognitive processes [].

Notably, convergent evolution is regularly discussed with respect to adaptive functions. This might suggest that the common magnitude system serves an adaptive function, which could represent a fruitful line of future inquiry. Although substantial attention has been paid to establishing that time, space, and number can interact with one another, exactly why these interactions emerge remains unclear.