The History of Numbers

[Dr. Jai Maharaj]

Vedic Science

The History of Numbers

By David Osborn
vedicsciences.net

Numbers and counting have become an integral part of our
everyday life, especially when we take into account the
modern computer.These words you are reading have been
recorded on a computer using a code of ones and zeros. It
is an interesting story how these digits have come to
dominate our world.

Numbers Around the World

Presently, the earliest known archaeological evidence of
any form of writing or counting are scratch marks on a
bone from 150,000 years ago. But the first really solid
evidence of counting,in the form of the number one, is
from a mere twenty-thousand years ago. An ishango bone
was found in the Congo with two identical markings of
sixty scratches each and equally numbered groups on the
back.These markings are a certain indication of counting
and they mark a defining moment in western civilization.1

Zoologists tell us that mammals other than humans are
only able to count up to three or four, while our early
ancestors were able to count further.They believed that
the necessity for numbers became more apparent when
humans started to build their own houses, as opposed to
living in caves and the like.

Anthropologists tell us that in Suma, in about 4,000 BCE,
Sumerians used tokens to represent numbers, an
improvement over notches in a stick or bone. A very
important development from using tokens to represent
numbers was that in addition to adding tokens you can
also take away, giving birth to arithmetic, an event of
major significance.The Sumerian's tokens made possible
the arithmetic required for them to assess wealth,
calculate profit and loss and even more importantly, to
collect taxes, as well as keep permanent records. The
standard belief is that in this way numbers became the
world's first writings and thus accounting was born.

More primitive societies, such as the Wiligree of Central
Australia, never used numbers, nor felt the need for
them.We may ask, why then did the Sumerians on the other
side of the world feel the need for simple mathematics?
The answer of course, was because they lived in cities
which required organizing. For example, grain needed to
be stored and determining how much each citizen received
required arithmetic.

Egyptians loved all big things, such as big buildings,
big statues and big armies. They developed numbers of
drudgery for everyday labor and large numbers for
aristocrats, such as a thousand, ten thousand and even a
million.The Egyptians transformation of using "one" from
counting things to measuring things was of great
significance.

Their enthusiasm for building required accurate
measurements so they defined their own version of "one."
A cubit was defined as the length of a mans arm from
elbow to finger tips plus the width of his palm. Using
this standardized measure of "one" the Egyptians
completed vast construction projects, such as their great
pyramids, with astonishing accuracy.

Two and a half thousand years ago, in 520 BCE, Pythagorus
founded his vegetarian school of math in Greece.
Pythagorus was intrigued by whole numbers,noticing that
pleasing harmonies are combinations of whole numbers.
Convinced that the number one was the basis of the
universe, he tried to make all three sides of a triangle
an exact number of units, a feat which he was not able to
accomplish. He was thus defeated by his own favorite
geometrical shape, one for which he would be forever
famous.

His Pythagorean theorem has been credited to him, even
though ancient Indian texts, the Sulva Sutras (800 BCE)
and the Shatapatha Brahmana (8th to 6th centuries BCE)
prove that this theorem was known in India some two
thousand years before his birth.

Later in the third century BCE, Archimedes, the renowned
Greek scientist, who loved to play games with numbers,
entered the realm of the unimaginable, trying to
calculate such things as how many grains of sand would
fill the entire universe. Some of these intellectual
exercises proved to be useful, such as turning a sphere
into a cylinder. His formula was later used to take a
globe and turn it into a flat map.

Romans invading Greece were interested in power, not
abstract mathematics. They killed Archimedes in 212 BCE
and thereby impeded the development of mathematics. Their
system of Roman numerals was too complicated for
calculating, so actual counting had to be done on a
counting board, an early form of the abacus.

Although the usage of the Roman numeral system spread all
over Europe and remained the dominant numeral system for
more than five hundred years, not a single Roman
mathematician is celebrated today. The Romans were more
interested in using numbers to record their conquests and
count dead bodies.

Numbers in Early India

In India, emphasis was not on military organization but
in finding enlightenment. Indians, as early as 500 BCE,
devised a system of different symbols for every number
from one to nine, a system that came to be called Arabic
numerals, because they spread first to Islamic countries
before reaching Europe centuries later.

What is historically known goes back to the days of the
Harappan civilization (2,600-3,000 BCE). Since this
Indian civilization delved into commerce and cultural
activities, it was only natural that they devise systems
of weights and measurements. For example a bronze rod
marked in units of 0.367 inches was discovered and points
to the degree of accuracy they demanded. Evidently,such
accuracy was required for town planning and construction
projects.Weights corresponding to units of 0.05, 0.1,
0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200 and 500 have been
discovered and they obviously played important parts in
the development of trade and commerce.

It seems clear from the early Sanskrit works on
mathematics that the insistent demand of the times was
there, for these books are full of problems of trade and
social relationships involving complicated calculations.
There are problems dealing with taxation, debt and
interest, problems of partnership, barter and exchange,
and the calculation of the fineness of gold. The
complexities of society, government operations and
extensive trade required simpler methods of calculation.

Earliest Indian Literary and Archaeological References

When we discuss the numerals of today's decimal number
system we usually refer to them as "Arabian numbers."
Their origin, however, is in India, where they were first
published in the Lokavibhaga on the 28th of August 458
AD.This Jain astronomical work, Lokavibhaga or "Parts of
the Universe," is the earliest document clearly
exhibiting familiarity with the decimal system. One
section of this same work gives detailed astronomical
observations that confirm to modern scholars that this
was written on the date it claimed to be written: 25
August 458 CE (Julian calendar). As Ifrah2 points out,
this information not only allows us to date the document
with precision, but also proves its authenticity. Should
anyone doubt this astronomical information, it should be
pointed out that to falsify such data requires a much
greater understanding and skill than it does to make the
original calculations.

The origin of the modern decimal-based place value system
is ascribed to the Indian mathematician Aryabhata I, 498
CE. Using Sanskrit numeral words for the digits,
Aryabhata stated "Sthanam sthanam dasa gunam" or "place
to place is ten times in value."The oldest record of this
value place assignment is in a document recorded in 594
CE, a donation charter of Dadda III of Sankheda in the
Bharukachcha region.

The earliest recorded inscription of decimal digits to
include the symbol for the digit zero, a small circle,
was found at the Chaturbhuja Temple at Gwalior, India,
dated 876 CE.This Sanskrit inscription states that a
garden was planted to produce flowers for temple worship
and calculations were needed to assure they had enough
flowers. Fifty garlands are mentioned (line 20), here 50
and 270 are written with zero. It is accepted as the
undisputed proof of the first use of zero.

The usage of zero along with the other nine digits opened
up a whole new world of science for the Indians. Indeed
Indian astronomers were centuries ahead of the Christian
world.The Indian scientists discovered that the earth
spins on its axis and moves around the sun, a fact that
Copernicus in Europe didn't understand until a thousand
years later -- a discovery that he would have been
persecuted for, had he lived longer.

From these and other sources there can be no doubt that
our modern system of arithmetic -- differing only in
variations on the symbols used for the digits and minor
details of computational schemes -- originated in India
at least by 510 CE and quite possibly by 458 CE.

The first sign that the Indian numerals were moving west
comes from a source which predates the rise of the Arab
nations. In 662 AD Severus Sebokht, a Nestorian bishop
who lived in Keneshra on the Euphrates river, wrote
regarding the Indian system of calculation with decimal
numerals:

"... more ingenious than those of the Greeks and the
Babylonians, and of their valuable methods of calculation
which surpass description..." 3

This passage clearly indicates that knowledge of the
Indian number system was known in lands soon to become
part of the Arab world as early as the seventh century.
The passage itself, of course, would certainly suggest
that few people in that part of the world knew anything
of the system. Severus Sebokht as a Christian bishop
would have been interested in calculating the date of
Easter (a problem to Christian churches for many hundreds
of years). This may have encouraged him to find out about
the astronomy works of the Indians and in these, of
course, he would find the arithmetic of the nine symbols.

The Decimal Number System

The Indian numerals are elements of Sanskrit and existed
in several variants well before their formal publication
during the late Gupta Period (c. 320-540 CE). In contrast
to all earlier number systems, the Indian numerals did
not relate to fingers, pebbles, sticks or other physical
objects.

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Jai Maharaj, Jyotishi
Om Shanti

http://bit.do/jaimaharaj