[nukkad] Indian numerals

[Zaveri Rohit <>]

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Hello all,
        Highly intellectual and given to abstract thinking as they were,
one would expect the ancient Indians to excel in mathetics. Europe got its
early arithmatic and algebra from the Arabs-hence the Arabic numerals-but
the Arabs themselves had previously taken them from India. The astonishing
progress that the Indians had made in mathematics is now well known and it
is recognized that the foundations of modern arithmatic and algebra were
laid long ago in India. The clumsy method of using a counting frame and the
use of Roman and such like numerals had long retarded progress when the ten
Indian numerals, including the zero sign, liberated the human mind from
these restrictions and threw a flood of light on the behaviour of numbers.
These number symbols were unique and entirely different from all other
symbols that had been in use in other countries. They are common enough
today and we take them for granted, yet they contained germs of
revolutionary progress in them. It took many centuries for them to travel
from India, via Baghdad, to the western world.
   Two hundred odd years ago, during Nepoleon's time, La Place wrote : ' It
is India that gave us the ingenious method of expressing all numbers by
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 arithmatic 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 men produced by antiquity.'
>The origins of geometry, arithmatic and algebra in India go back to remote
periods. Probably to begin with there was some kind of geometrical algebra
used for making figures for Vedic altars. Mention is made in most ancient
books of the geometrical method for the transformation of a square into a
rectangle having a given side : ax = c. Geometrical figures are even now
commonly used in Hindu ceremonies. Geometry made progress in India but in
this respect Greece and Alexandria (in Egypt) went ahead. It was in
arithmatic and algebra that India kept the lead. The inventor or inventors
of the decimal place value system and the zero mark are not known without
entering into controversy, although one name emerges is that of logician
Nagarjuna. The earliest use of the zero symbol, so far discovered, is in
one of the sriptural books dated about 200 BC. It is considered probable
that the place-value system was invented about the begining of the
Christian era. The zero, called shunya or nothing, was originally a dot and
later it became a small circle. It was considered a number like any other.
Prof. Halstead thus emphasizes the vital significance of this invention :
'The importance of creation of the zero mark can never be exaggerated. This
giving to airy nothing, not merely a local habitation and a name, a
picture, a symbol but helpful power, is the characteristic of the Hindu
race from whence it sprang. It is like coining Nirvana into dynamos. No
single mathematical creation has been more potent for the general on-go of
intelligence and power.'          Yet another modern mathematician has
grown eloquent over this historic event. Dantzig in his 'Number' writes
:"This long period of nearly 5000 years saw the rise and fall of many a
civilization, each leaving behind it a heritage of literature, arts,
philosophy and religion. But what was the net achievement in the field of
reckoning, the earliest art practised by man ? An inflexible numeration so
to crude as to make progress well nigh impossible, and a calcuting device
so limited in scope that even elementary calculations called for the
services of an expert....   Man used these devices for thousands of years
without making a single worthwhile improvement in the instrument, without
contributing a single important idea to the system....  Even when compared
with the slow growth of ideas during the dark ages, the history of
reckoning presents a peculiar picture of desolate stagnation. When viewed
in this light the achievements of the unknown Hindu, who sometimes in the
first centuries of our era discovered the principle of position, assumes
importance no less than a world event."                Rohit Zaveri.


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