抄録
We presented two cases of acalculia with cerebral infarction. They showed specific impairment in Arabic system of notation. Writing and reading of each digit was intact. One of them complained feeling of alienation from number. We tried the representation form of natural numbers in human brain based on the topology and investigated the conception of numbers. The former is one of mathematical approach to the human brain function.
From the topological point of view, an arbitrary natural number could be considered as a Cartesian product composed by two kinds of sets. The one corresponds to the digits and the other to the locations (place value). Both sets are supposed to be totally ordered sets. Two kinds of projections could also be supposed. The one projects to the digits and the other to the locations. Thus an arbitrary natural number could be represented as a graph on a plane. The symptoms of our presented two cases suggest that the representation form of natural numbers as Cartesian product is realized in human brain, although precise neuronal network remains unknown.
From the symptoms of our presented two cases, conception of natural numbers and their representation form in human brain considered to be not equal. In fact, both cases partially preserved the conception of numbers. Although number is very abstract object in mathematics, it is always together with some unit in everyday life. Natural number could be one of the attributions of each concrete object. Many previous reports of acalculia suggest that the conception of natural number is supported by diffusely distributed neural network in human brain.
We hope that the mathematical approach and formulation to the symptoms of brain damaged patients would contribute to development of neuropsychology and cognitive science.
