A Neural Model of How The Brain Represents and Compares Numbers

Many psychophysical expeliments have shown that the representation of numbers and numerical quantities in humans and animals is related to number magnitude. i\ neural network model is proposed to quantitatively simulate error rates in 'lu'ultiriccttion 'tnd numerical comparison tasks, and reaction times for number priming and numerical assessment and comparison tasks. Transient responses to inputs arc integrated before they activate an ordered spatial map that selectively responds to the number of events in a sequence. The dynamics of numerical comparison are encoded in activity pattern changes within this spatial map. Such changes cause a "directional comparison wave" whose properties mimic data about numerical comparison. These model mechanisms are variants of neural mechanisms that have elsewhere been used to explain data about motion perception, attention shifts, and target tracking. Thus, the present model suggests how numerical representations may have emerged as specializations of more primitive mechanisms in the cortical Where processing stream. Introduction: Human and Animal Numerical Abilities The roots of modem number system can be traced to the ancient Egyptians and Chinese. The final design of the base-l 0 system is believed to have been developed by the Hindu-Arabic mathematicians in the 8'II 111 centuries AD. C:111 one say that this was the beginning of the formation or number sense on earth'? In fact, animals managed to survive in challenging environments for millions of years. Choosing a larger prey to hunt, a tree with more fruit, or a flower with more honey required some abilities to estimate and compare magnitudes and quantities in order to choose the one that would enhance survival. Obviously, people are much more numerically competent than animals, but they have a serious advantage: the symbolic notation. If unable to use either verbal or Arabic notation, humans may perform no better than animals in certain estimation and comparison tasks. Error rates and reaction times in animal data depend on stimulus properties in a manner similar to human data (Dehaene, 1998; Gallistel, 1989). In particular, the Number Size Effect indicates that processing is more difficult for larger quantities or numbers, as reflected in larger reaction times (Figure 1) and error 320