Number Sense
Man, in even in the lower stages of development, possesses a faculty which, for want of a better can be christened as Number Sense. This faculty permits him to recognize that something has changed in a small collection when, without his direct knowledge, an object has been removed from or added to the collection.
Number sense should not be confused with counting, which is probably of a much later genre, and involves, as we shall see, a rather intricate mental process. Counting, so fast as we know, is an attribute exclusively human, whereas some brute species seems to possess a rudimentary number sense akin to our own. At least, such is the opinion of competent observers of animal behavior, and the theory is supported by a weighty mass of evidence.
Counting especially has become such an integral part of our mental equipment that psychological tests on our number perception are fraught with great difficulties. The genesis of number is hidden behind the impenetrable veil of countless prehistoric ages. Has the concept been born of experience, or has experience merely served to render explicit what was already latent in the primitive mind: Here is a fascinating subject for metaphysical speculation, but for this very reason beyond the scope of this study. It is counting that consolidated the concrete and therefore heterogeneous notion of plurality, so characteristic of primitive man, into the homogenous abstract number concept, which made mathematics possible.
We enter a hall. Before us are two collections: the seats of the auditorium, and the audience. Without counting we can ascertain whether the two collections are equal and, if not equal, which is the greater. For if every seat is taken and no man is standing, we know without counting that the two collections are equal. If every seat is taken and some in the audience are standing, we know without counting that there are more people than seats.
Whether we accept or not Mathematics is part of our DNA.
Number sense should not be confused with counting, which is probably of a much later genre, and involves, as we shall see, a rather intricate mental process. Counting, so fast as we know, is an attribute exclusively human, whereas some brute species seems to possess a rudimentary number sense akin to our own. At least, such is the opinion of competent observers of animal behavior, and the theory is supported by a weighty mass of evidence.
Counting especially has become such an integral part of our mental equipment that psychological tests on our number perception are fraught with great difficulties. The genesis of number is hidden behind the impenetrable veil of countless prehistoric ages. Has the concept been born of experience, or has experience merely served to render explicit what was already latent in the primitive mind: Here is a fascinating subject for metaphysical speculation, but for this very reason beyond the scope of this study. It is counting that consolidated the concrete and therefore heterogeneous notion of plurality, so characteristic of primitive man, into the homogenous abstract number concept, which made mathematics possible.
We enter a hall. Before us are two collections: the seats of the auditorium, and the audience. Without counting we can ascertain whether the two collections are equal and, if not equal, which is the greater. For if every seat is taken and no man is standing, we know without counting that the two collections are equal. If every seat is taken and some in the audience are standing, we know without counting that there are more people than seats.
Whether we accept or not Mathematics is part of our DNA.
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