We Are Mathematical Beings

In this mathematical-poetical text, the author posits mathematical thought as fundamental to concepts of self and world. Mathematics is not something exterior to be learned, but basic to daily life. For example, object permanence is an abstract concept of multiple perspectives compiled in to the idea of one stable object. Such abstraction is mathematics. These concepts exist both socially and materially. A wooden cube is both a social concept and a material object. We exist in a mathematically determined world. We use mathematics to enact new reals. This is so common that often we are unaware of it.

Developmental Trajectories of Picture-Based Object Representations during the First Year of Life

Experience with an object’s photo changes 9-month-olds’ preference for the referent object, confirming they can form picture-based object representations (Shinskey & Jachens, 2014). However, infants’ picture-based representations often appear weaker than object-based ones. The current study’s first objective was to investigate age differences in infants’ recognition memory for a real object after familiarization with its picture. The second objective was to test whether age differences in object permanence sensitivity with picture-based representations conceptually replicate those found with object-based representations, whereby 7-month-olds search more for familiar hidden objects but 11-month-olds search more for novel ones (Shinskey & Munakata, 2005; 2010). Twenty 6-month-olds and 20 11-month-olds were familiarized with an object’s photo and tested on their representation of the real referent object by comparing their preferential reaching for it versus a novel distractor object. The objects were visible in one condition testing recognition memory and hidden in another condition testing object permanence. Like 9-month-olds, 6- and 11-month-olds had a novelty preference with visible objects. This finding shows robust early recognition memory for an object after familiarization with its photo as well as developmental continuity. Unlike 9-month-olds, who switched to a familiarity preference with hidden objects, 6- and 11-month-olds switched to null preference. This U-shaped pattern fails to conceptually replicate 7- and 11-month-olds’ preferences with hidden objects after familiarization with a real object. It reveals discontinuity in sensitivity to an object’s permanence after familiarization with its picture, and suggests that such picture-based representations are weaker than object-based ones.

Comparative cognition in three understudied ungulate species: European bison, forest buffalos and giraffes

Background Comparative cognition has historically focused on a few taxa such as primates, birds or rodents. However, a broader perspective is essential to understand how different selective pressures affect cognition in different taxa, as more recently shown in several studies. Here we present the same battery of cognitive tasks to two understudied ungulate species with different socio-ecological characteristics, European bison (Bison bonasus) and forest buffalos (Syncerus caffer nanus), and we compare their performance to previous findings in giraffes (Giraffa camelopardalis). We presented subjects with an Object permanence task, Memory tasks with 30 and 60 s delays, two inference tasks based on acoustic cues (i.e. Acoustic inference tasks) and a control task to check for the use of olfactory cues (i.e. Olfactory task). Results Overall, giraffes outperformed bison and buffalos, and bison outperformed buffalos (that performed at chance level). All species performed better in the Object permanence task than in the Memory tasks and one of the Acoustic inference tasks (which they likely solved by relying on stimulus enhancement). Giraffes performed better than buffalos in the Shake full Acoustic inference task, but worse than bison and buffalos in the Shake empty Acoustic inference task. Conclusions In sum, our results are in line with the hypothesis that specific socio-ecological characteristics played a crucial role in the evolution of cognition, and that higher fission-fusion levels and larger dietary breadth are linked to higher cognitive skills. This study shows that ungulates may be an excellent model to test evolutionary hypotheses on the emergence of cognition.