Number
Of all the terrifying things humans have created, perhaps maths are a fairly tame, although remarkable, invention. While we clearly created maths, did we create numbers?
Primary Readings
Everyone should read these and be prepared to discuss.
| Feigenson, L., Dehaene, S., & Spelke, E. (2004) | Core systems of number. Trends in cognitive sciences, 8(7), 307-314. |
Secondary Readings
The presenter should read and incorporate at least two of these.
| Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004) | Exact and approximate arithmetic in an Amazonian indigene group. Science, 306(5695), 499-503.The study investigated numerical cognition in Munduruku speakers, who have a limited lexicon of number words. The Munduruku can compare and add approximate numbers but struggle with exact arithmetic. The study contributes to understanding the relationship between language and arithmetic and the role of language in numerical cognition. It highlights that while the Munduruku lack number words beyond 5, they still possess a nonverbal system for approximate number. This suggests that exact arithmetic may require language for a precise representation and manipulation of numbers. The study also emphasizes the potential impact of language on numerical cognition and how cultural and linguistic factors can influence numeric representation and processes. |
| Frank, M. C., Everett, D. L., Fedorenko, E., & Gibson, E. (2008) | Number as a cognitive technology: Evidence from Pirahã language and cognition. Cognition, 108(3), 819-824.This article explores the relationship between language and our understanding of numbers, focusing on the Pirahã tribe’s language and numerical abilities. Previous research has shown that the Pirahã language lacks words for exact numbers, but the tribe can perform exact matching tasks with large quantities of objects accurately. This suggests that language for exact numbers is a cultural invention, not a universal linguistic feature. Number words serve as a cognitive technology for representing and keeping track of large sets accurately. The article discusses the role of language in understanding numbers and the theories proposing that language plays a causal role in the acquisition of exact numerical competence. The article provides evidence that language for exact numbers is not a linguistic universal but a cultural invention, with implications for understanding the relationship between language and cognition in numerical competence |
| Jara‐Ettinger, J., Piantadosi, S., Spelke, E. S., Levy, R., & Gibson, E. (2017) | Mastery of the logic of natural numbers is not the result of mastery of counting: Evidence from late counters. Developmental Science, 20(6), e12459.TODO |
| Piantadosi, ST., Tenenbaum, JB and Goodman, ND (2012) | Bootstrapping in a language of thought: A formal model of numerical concept learning. Cognition 123.2: 199-217.TODO |
Questions under discussion
- How do we represent numbers?
- Are numbers universal to animals?
