by Aparna Ramachandran
Imagine a shepherd from prehistoric times. He needs to make sure he has the right number of sheep each night as he heads to his tent. He looks around and matches a pebble for each sheep. He sleeps soundly each night knowing he hasn’t lost any of them.
With time, his sheep have doubled in number. It is getting cumbersome to keep using pebbles. He develops the tally system. A notched baboon bone dating back 35,000 years was found in Africa and was apparently used for counting. A wolf bone found in Czechoslovakia in the 1930s had 57 notches at regular intervals. It was found to be 30,000 years old and assumed to be a hunter’s record of his kills.
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The idea of a numeration system makes sense if it is based on tangible reference points in human experience. For instance, the base 10 or decimal systems that are common today are based on the fingers of both hands. The base 2 or binary system used in computer programming is based on the two arms. Other bases of numeration systems include the fingers of one hand – the base 5 system and the base 20 system which is the total of all a person’s fingers and toes.
Early civilizations did not have any use for large numbers and had no need to count beyond small numbers. However, with the rise of permanent settlements, the requirement for a slightly more comprehensive and sophisticated numbering system came into being.
5000 BC – Sumerians and Egyptians – using large numbers in their government and business records
2000 B.C. – Hindu-Arabic system
1800 B.C. – The decimal or base 10 numbering system was in use
1000 B.C. – Decimal systems were common in European and Indian cultures
876 A.D. – Appearance of ‘zero’ as the placeholder
945-1003 A.D – Reign of Gerbert of Aurillac
The Hindu-Arabic system was brought into Europe and began to replace Roman numerals (I, II, III, IV…) in Europe, especially in business transactions and mathematics.
16th Century – Europe was well versed in the Hindu-Arabic system, though Roman numerals were still used
Ancient Egyptian Numeration – Simple Grouping
The Ancient Egyptian system evolved from simple tallying to basic grouping with 10 as the base. This served as the foundation for less repetition of symbols and making it easier to interpret numerals. Based on the evidence of several papyri found, Egyptian numerations systems were geared towards practical purposes such as tallying the count of a grain harvest.
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Ancient Greek Numeration – Ciphered System
The Greeks used letters of their alphabet to represent numerical symbols. This kind of numeration system was known as a ciphered system and was very useful for small numbers. Theirs was a decimal (base 10) system. The first 9 alphabets symbolized the numerals from 1 to 9. However, multiples of 10 [through 90] were assigned 9 more alphabets. Similarly more letters were assigned to multiples of 100 [through 900].
In the case of larger numbers (multiples of 1000) a small stroke would be used alongside the symbol for the numbers 1 to 9.
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Ancient Chinese Numeration – Multiplicative Grouping
Relative to the Egyptian system where the symbol for 10 would be written nine times to denote 90, the Chinese system evolved in a different direction. All repetitions were handled by simply using a separate multiplier symbol for each counting number less than the base. This system was later adopted by the Japanese.
Chinese numerals are read from top to bottom rather than left to right. So, using multiplicative grouping would involve using a pair of symbols. The multiplier on top and the unit below.
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The Hindu-Arabic Positional System
A simple grouping system relies on the repetition of symbols while a multiplicative grouping system relies on using specific multipliers rather than repetition.
However, optimum efficiency is achieved with placeholders wherein only the multipliers are used. The different powers of the base don’t require a separate symbol as it is self-evident in the position occupied by the numeral.
In a positional numeration system, a digit conveys two meanings – face value and place value. The former indicates the inherent value of the symbol, but the latter indicates the power of the base associated with the position occupied by the digit.
The Ancient Tamil Numeration System
Closer to home numbers and alphabets were referred to as ‘ennum ezhuthum’. Zero was referred to as suzhiyam which was later coined as suzhi [present day]. The texts had representations for both singular and plural based on important, tangible objects present in nature – such as celestial bodies, vegetation, parts of the human body, and more.
For instance, the sun and moon were used to denote the number 1. Eyes, ears present as they were in pairs referred to two. Mukanni (Three fruits) – for three – came about to refer to the three main fruits consumed and present in the region (mango, jackfruit, and banana)
The Tamil system had separate symbols for each of the numerals and also made use of a grouping system for larger numbers. An interesting aspect of this numeration system was the terminology used in business transactions and daily life to refer to uncountable nouns based on how much would be bartered. For instance, a handful, a cupful was widely used and standardized measures.
Fast forward to 2015 and you are watching Bahubali lead his soldiers against the Kalakeya invaders. The language spoken was a dialect made of clicks.
The numbering system within Kiliki introduced recently, has 10 numerals, making counting extremely easy. Each numeral except zero is represented by a symbol composed of lines. The number of lines used in each symbol represents the number itself.
Number | How I remember |
1 | One line running diagonally |
2 | Two lines coming to make a V |
3 | Three lines making an inverted triangle |
4 | A square with 4 lines |
5 | The above symbol with a diagonal |
6 | Two triangles forming a star |
7 | A sun with 7 rays of light |
8 | Two small rectangles aligned on top of each other |
9 | The above with a diagonal |
0 | A circle |
References
htttp://socrates.bmcc.cuny.edu/jsamuels/text/mhh-discrete-04.1.pdf
https://science.jrank.org/pages/4778/Numeration-Systems-History.html
https://science.jrank.org/pages/4779/Numeration-Systems-bases-numeration-systems.html