What We Mean When We Say "What's the Dollar of Mexico?": Prototypes and Mapping in Concept Space

We assume that the brain is some kind of a computer and look at operations implied by the figurative use of language. Figurative language is pervasive, bypasses the literal meaning of what is said and is interpreted metaphorically or by analogy. Such an interpretation calls for a mapping in concept space, leading us to speculate about the nature of concept space in terms of readily computable mappings. We find that mappings of the appropriate kind are possible in high-dimensional spaces and demonstrate them with the simplest such space, namely, where the dimensions are binary. Two operations on binary vectors, one akin to addition and the other akin to multiplication, allow new representations to be composed from existing ones, and the ``multiplication'' operation is also suited for the mapping. The properties of high-dimensional spaces have been shown elsewhere to correspond to cognitive phenomena such as memory recall. The present ideas further suggest the suitability of high-dimensional representation for cognitive modeling.