ABSTRACT
How do people represent and use abstract mathematical notions that have few or no real-world counterparts? For example, how are we able to think of imaginary numbers, surreal numbers, or even negative numbers? One proposal is that abstract knowledge domains (such as number, time, ideas, ect.) are represented through analogical extensions from more concrete or more experience based domains (e.g., Lakoff & Johnson, 1980, Boroditsky 2000). Lakoff and Nunez (2001) have suggested that the same kinds of experience based may be used for all manner of mathematical concepts. This paper focuses on the domain of negative numbers.
