How
many types of number systems do you know?
Usual
answer is
1.
Roman numerals
2.
Arabic numerals (wrongly called so of course, as they originated in India)
Ancient
Indians are credited with invention of the decimal number system, place value
system and zero (with its properties). Indians were also familiar with negative
numbers and properties of infinity (seen in Yajur Veda and also Buddhist and
Jain literature). Indians were very adept at dealing with fractions and had a
very accurate calendar too. They needed the accurate calendar for the purposes
of navigation. Since the Mauryan times, India had 1000s of merchant ships
sailing in the Indian ocean.
Sanskrit language has words for very large numbers
(due to lot of work done in astronomy). Most Indians are familiar with lakh,
crore, …but the numbers are named up to 51st power of 10 and also in
some cases up to even larger numbers.
Such
large numbers were necessary because Indian astronomers counted time in terms
of astronomical events.
There are 3 types of number systems used in
Indian mathematics:
Bhutasamkhya system- earliest
Aryabhata’s
system
Katapayadi
system
In
Rigveda, numbers are referred in words.
Bhutasamkhya is a method of recording numbers using ordinary
words having connotations of numerical values. For example the Sanskrit word
for ‘eye’ or ‘hand’ or ‘ear’ would denote 2, that for ‘finger’ would denote 10.
Since Sanskrit is very rich in synonyms, mathematical formulae could be
expressed in a poetic fashion by using this system. So instead of having
separate names for the digits, ordinary words could be used.
The Āryabhaṭa numeration is a system of numerals based on Sanskrit phonemes. The digits are represented using consonants, place values are represented using
vowels. It was introduced in the early 6th century in India by Aryabhata, in the first
chapter titled Gītika Padam of his Aryabhatiya. It
attributes a numerical value to each syllable of the form consonant+vowel
possible in Sanskrit phomology, from ka = 1 up to hau = 1018. Aryabhata’s system
however made the numerals into words that were sometimes very difficult to
pronounce.
Katapayadi System: There is a many-to-one mapping between
consonants and a number. For example ka, ta, pa or ya…any of these can be used
to represent the number 1. Kh, tha, pa or ra represent 2 and so on. All stand-alone
vowels represent the number 0. The system has a few more complications and
details are covered in the attached lecture.
For anyone interested in Mathematics, the whole lecture series
is a must-watch.
Lastly…
The significance of the development of the positional number
system is probably best described by the French mathematician Pierre Simon Laplace (1749–1827) who wrote:
It is India that gave us the ingenious method of expressing all
numbers by the means of ten symbols, each symbol receiving a value of position,
as well as an absolute value; a profound and important idea which appears so
simple to us now that we ignore its true merit, but its very simplicity, the
great ease which it has lent to all computations, puts our arithmetic in the
first rank of useful inventions, and we shall appreciate the grandeur of this
achievement when we remember that it escaped the genius of Archimedes and
Apollonius, two of the greatest minds produced by antiquity.
