History of numerals

This is not about the history of numbers, but rather about the history of numerals, i.e. symbols for representing numbers. See also History of the Hindu–Arabic numeral system.

The first method of counting by humans was counting on fingers.[1] This evolved into sign language for the hand-to-eye communication of numbers which, while not writing, gave way to written numbers. Later developed new forms of counting.

Bones and other artifacts have been discovered with marks cut into them that many believe are tally marks.[2] These tally marks may have been used for counting elapsed time, such as numbers of days, lunar cycles or keeping records of quantities, such as of animals.

A tallying system has no concept of place value (as in modern decimal notation), which limits its representation of large numbers. Nonetheless tallying systems are considered the first kind of abstract numeral system.

Tallies made by carving notches in wood, bone, and stone were used for at least forty thousand years. Stone age cultures, including ancient Native American groups, used tallies for gambling with horses, slaves, personal services and trade-goods.

Lebombo bone is a baboon fibula with incised markings discovered in the Lebombo Mountains located between South Africa and Swaziland. The bone is between 44,200 and 43,000 years old, according to two dozen radiocarbon datings. According to The Universal Book of Mathematics the Lebombo bone's 29 notches suggest "it may have been used as a lunar phase counter, in which case African women may have been the first mathematicians, because keeping track of menstrual cycles requires a lunar calendar." But the bone is clearly broken at one end, so the 29 notches can only be a minimum number. Furthermore, in the many more notched bones since found there is no consistent notch tally, many being in the 1–10 range.

Ishango bone is an artifact with a sharp piece of quartz affixed to one end, perhaps for engraving. It was first thought to be a tally stick, as it has a series of what has been interpreted as tally marks carved in three columns running the length of the tool. But some scientists have suggested that the groupings of notches indicate a mathematical understanding that goes beyond counting. It has also been suggested that the scratches might have been to create a better grip on the handle or for some other non-mathematical reason. Is believed that the bone has more than 20,000 years old.[3][4]

References

  1. ↑ The Earliest Calculating – The Hand, Ifrah (2000), pages 47–61.
  2. ↑ Marshak, A., The Roots of Civilisation; Cognitive Beginnings of Man’s First Art, Symbol and Notation, (Weidenfeld & Nicolson, London: 1972), 81ff.
  3. ↑ Marshack, Alexander (1991): The Roots of Civilization, Colonial Hill, Mount Kisco, NY.
  4. ↑ Brooks, A.S. and Smith, C.C. (1987): "Ishango revisited: new age determinations and cultural interpretations", The African Archaeological Review, 5 : 65–78.
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