Number

The number is a conceptual scheme, an abstraction of the second level from specific numbers: 1, 2, 3, ... etc. The abstraction procedure to recognize specific numbers is counting.

Counting is based on the ability to divide the surrounding world up into distinct objects. This ability emerged quite far back in the course of evolution; the vertebrates appear to have it in the same degree as humans do. The use of specific numbers is a natural integrated description complementary to the differential description by recognizing distinct objects. This ability would certainly be advantageous for higher animals in the struggle for existence. And cybernetic apparatus for counting could be very simple -- incomparably simpler than for recognition of separate objects in pictures.

Yet nature, for some reason, did not give our brain this ability. The numbers we can directly recognize are ridiculously small, up to five or six at best (though it can be somewhat extended by training). Thus the number 2 is a neuronal concept, but 20 and 200 are not. We can use them only through counting, creating artificial representqations in the material external to the brain. The material may be, and was historically, fingers and toes, then pebbles, notches etc., and finally sophisticated signes on paper and electronic states of computer circuitry. For theoretical purposes the best is still the ancient-style representation where a chosen symbol, say '1' stands for one object. Thus 2 is '11', and 5 is '11111'.