Humanity's primal (原始的) efforts to systematize the concepts of size, shapes, and number are usually regarded as the earliest mathematics. However, the concept of number and the counting process developed so long【C1】______ the time of recorded history (there is archaeological【C2】______ that counting was employed by humans as far back as 50,000 years ago) that the【C3】______ of this development is largely conjectural (好推测的). Imaging how it probably came【C4】______ is not difficult. The argument that humans, 【C5】______ in prehistoric times, had some number sense, at least【C6】______ the extent of recognizing the concepts of more and less when some objects were【C7】______ to or taken away from a small group, seems fair, for studies have shown that some animal possesses such a【C8】______ . With the【C9】______ evolution of society, simple counting became necessary. A tribe had to know how many members it had and how many enemies, and shepherd needed to know【C10】______ the flock of sheep was decreasing in size. Probably the earliest way of keeping a count was by some simple tally (计算, 记录) method,【C11】______ the principle of one-to-one corre-spondence. In【C12】______ a count of sheep, for example, one finger per sheep could be【C13】______ . Counts could also be【C14】______ by making scratches in the dirt or on a stone, by cutting notches in a piece of wood, or by tying knots in a string.【C15】______ , perhaps later, an assortment of vocal【C16】______ was developed as a word tally against the number of objects in, a small group. And【C17】______ later, with the development of writing, a set of【C18】______ was invented to stand for these numbers. Such an imagined development is【C19】______ by reports of anthropologists in their studies of present-day societies that are【C20】______ to be similar to those of early humans. 【C1】