Early Number Systems and Symbols

Numbers and Number Systems

Ancient Number Systems

1. Babylonian Number System

  • Recording of Numbers: The Babylonians used a base-60 (sexagesimal) system.
  • Operations on Numbers:
    • Example computations:
    • Multiply the given number by 10, expressing the result in Chinese numerals: 五千((十四) which translates to "five thousand fourteen."
  • Example of Calculation:


    • 2 imes 144,000 \
      0 imes 7200 \
      16 imes 360 \
      7 imes 20 \
      11 imes 1 \
      = 290,311

2. Mayan Number System

  • Developed a positional number system with base 20.
  • Utilized an additive grouping technique (based on 5).
  • Symbol Representation:
    • Each dot represents 1.
    • Each horizontal bar represents 5.
    • The numbers 1 to 19 were expressed through combinations of dots and bars.
  • Numerical Representation:
    • To express numbers like 1492, 1999, 1066, and others in Mayan numerals, one must combine the dots and bars as per the mentioned rules.
  • Conversion and Calendar System:
    • The Mayan year was structured into 18 months of 20 days, plus 5 extra holidays. This leads to:
    • Total days in a year: (18 imes 20) + 5 = 365 .
    • Larger convenience: The numerals were organized such as:
    • The third position held a value of 360 instead of 400. Thus followed by: 1, 20, 360, 7200, 144,000, etc.
  • Notation: Numbers were written vertically with larger units on top, and the absence of a number was depicted with a symbol resembling a small shell or half-closed eye.

Mathematical Operations in Mayan System

  • A section focused on different operations such as:
    • Addition
    • Subtraction
    • Multiplication
  • Particularly outlined tasks to multiply numbers by 20 or higher powers of 20, suggesting rules implied for multiplication in Mayan notation.

Comparison of Symbol Requirements Across Different Cultures

  • Comparative analysis of the number of symbols needed to represent 999,999 in various numeral systems:
    • Egyptian Hieroglyphics
    • Babylonian Cuneiform
    • Ionian Greek Numerals
    • Roman Numerals
    • Chinese Rod Numerals
    • Traditional Chinese Numerals
    • Mayan Numerals

Bibliographic References

  • An extensive bibliography lists foundational texts and studies related to numeration, ethnomathematics, cultural perspectives of mathematics, and historical developments. Some notable references include:
    • Ascher, Marcia. Ethnomathematics.
    • Boyer, Carl. Fundamental Steps in the Development of Numeration.
    • Ifrah, Georges. From One to Zero: A Universal History of Numbers.
    • Seidenberg, A. The Ritual Origin of Counting.
    • Zaslavsky, Claudia. Africa Counts: Number Patterns in African Culture.