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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'.