Mathematical Logic Depended on Numbers
January 30, 2023
The earliest form of mathematics that is known to us is counting. A concept that was developed by our prehistoric ancestors as a method of tracking how many of various items they possessed. Evidence for this can be seen in the form of tally marks found on prehistoric cave walls and found objects. Tallies often appeared in groups of five suggesting our early ancestors likely had a grasp of the concept of five, which could then have been used to account for larger numbers.
Discovery of the Lebombo Bone
The Lebombo Bone is a remarkable artifact that provides evidence of the earliest known form of mathematics in the human species. It is a small fragment of a baboon fibula bone that was excavated from Border Cave in the Lebombo Mountains between South Africa and Swaziland by archeologists.
On the bone are 29 distinct notches incised into the surface, with an additional notch bringing the total to 30. These notches show that a form of counting and arithmetic was being practiced as early as 35,000 B.C.E. The Lebombo Bone is important evidence for how people were using numbers in their daily lives at least 37,000 years ago.
Another archeological find was the Ishango Bone, which was also a baboon leg bone with carving lines, provided proof of prehistoric people still using tally marks to keep count some 20,000 years later. Both African bones stand as testaments to the earliest power of applied mathematics and serve as an enduring testimony to the power of numbers and their long history of use in advancing human civilization.
Evolution of Tally Marks to Numbers
Common sense and ancient evidence points to the idea that numbers and counting began with the number "one". Tally marks were combined to form systems that allowed counting to be more efficient like the fifth mark being angled through the first four. From these basic beginnings, mathematics was born and different cultures used numbers in creative new ways, such as to better understand the universe by tracking a lunar phase on an ancient calendar.
It is clear that numbers are the foundation on which mathematics is built, and without them it would not be possible to create or break down the complex equations used every day. The power of numbers allowed individuals to explore and define many things in their world. From counting to arithmetic operations like addition and subtraction, from fractions and algebra to geometry, math has always been and remains an essential tool for our global humanity.
Numeral Systems and Positional Notation
Strange as it seems, there was a time when the numbers we use today did not exist. In fact, Egyptian and Ancient Greek cultures essentially used numbers that were similar to prehistoric tally marks and someone had to repeatedly inscribe a symbol and add them together. These early numeral systems made it very cumbersome to write large numbers. Independently, the Babylonian, Chinese and Aztec civilizations developed positional notation to reuse the same symbols.
The earliest known numeral system with place value was the Mesopotamian base sixty system that predated the Egyptian base ten system by 300 years. Today, it is difficult for us to imagine math without the number zero but the Ancient Greeks neither had a name for such a number nor did mathematicians use it as a placeholder. However, the Mayans and Sumerian scribes independently developed a symbol for zero but with no assigned value of its own.
Seventh century mathematicians in India were the first to use small dots (sunya) under numbers to graphically represent a zero. It had a null value and served as a placeholder for metrology. Most importantly, without the discovery of zero, there would be no advanced mathematics like calculus and we wouldn’t have modern day physics, engineering, computing, finance, or economics. Although not all cultures use the Hindu-Arabic base ten numbering system, it is considered the best numeral system invented to date and is universally well understood.
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Math is fundamental to our world and understanding how it works is an important part of living in the modern age. Fortunately, math is a universal language, as the symbols and organization to form equations are the same in every country of the world. Even in societies where words are read right-to-left, numbers are read left-to-right, just as they are in English.
The language professionals at ProLingo understand the role number systems played in the development of unique languages worldwide. If you are expanding your consumer base to include new markets, it is important to work with interpreters and translators that have the "knowledge of" and "appreciation for" both the functional and cultural values native speakers assign to numbers.
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