Saturday, July 5, 2014

What do we know about precursors of the modern place-value systems for numerals?

A place-value system for writing numerals consists of a fixed set of symbols (digits), including a cipher for zero. Each symbol has a defined meaning and value depending on its position relative to other symbols within a composed number. In a number encoded by using the base-ten number system, for example, positions from right to left correspond to increasing positive powers of ten. More flexible, less systematic systems, such as the letter-based system of Hebrew numerals, apply a larger set of digits, but typically lack a symbol for zero. Yet, these less rigid concepts for number representation bear striking similarities with the rational, strictly positional, digit-minimized systems of today—including the dual, octal, decimal and hexadecimal number system.

How did place-value systems evolve? The history of the place-value idea can only be guessed at by relying on a few documents and some preserved specimens of counting boards. Joseph Mazur summarizes our fragmentary knowledge:
George Gheverghese Joseph tells us in his book The Crest of the Peacock that, aside from the Babylonians' clever sexagesimal (base 60) positional system, our modern place-value system is exclusively Indian. And yet Robert Kaplan, in his book The Nothing That Is: A Natural History of Zero, tells us that our system was Indian, but originated with the Greeks. Without solid written proof, there is no way of filling in the blanks of history. All we really know is that somehow, in some time and place, the clever place-value idea was transmitted from the Indians to the Arabs and later to the Europeans.
                                                                                              Joseph Mazur, 2014.
Joseph Mazur: Enlightening Symbols. Princeton University Press, Princeton and Oxford, 2014; page 38.

No comments:

Post a Comment