archive: The Universal History or numbers (Book review)
The Universal History or numbers (Book review)
Georges Ifrah
Rupa Book News
June 1999
Title: The Universal History or numbers (Book review)
Author: Georges Ifrah
Publication: Rupa Book News
Date: June 1999
The Universal History Or Numbers - from prehistory to the invention of
the computer by Georges Ifrah
The Harvill Press * Cove Price £19.99 * Special Price £12.95
Distributed by Rupa & Co.
Indian zero and numbers
Created the modern world!
By Dilip Salwi
" We owe the discovery of modern numeration and the elaboration of the
very foundations of written calculations to India alone," admits
Georges Ifrah explicitly in the book review. He is one of those few
western scholars who has made this admission openly in this voluminous
book which deals with, perhaps for the first time, the entire history
of numbers from the dawn of civilization. A Moroccon by birth, Jewish
by cultural heritage and a French by nationality, he could make such a
bold statement because he doesn't have the hang-ups of the West
academicians. The research for this book originally published in
French was moreover not sponsored by some academic European body. The
author had to work as a part-time hotel clerk, night watchman,
taxi-driver, waiter, etc. to meet the needs of his body and soul
during his travels to different parts of the world to trace the
origins of numbers which we take for granted but which have today
changed the entire world due to developments in science and technology
based upon them.
Primarily a school teacher of mathematics with humble origins, the
author was provoked into taking up research into the subject by some
simple questions raised by his students. When he began to look for
answers, he could not find them in the standard books and so began his
adventure. For collecting first hand information, he travelled from
America to Egypt, Mexico to India and Peru to China. The result is a
marvellous attempt at tracing the origins of numerals in all great
civilizations of the world. It is supported with beautiful diagrams,
drawings, tables and charts that speak volumes about the remarkable
counting skills of the ancient peoples, some known and some not at all
known.
Surprisingly, despite distances separating them, different languages,
cultures, climatic conditions, etc, ancient peoples, whether they
belonged to Babylonia, Sumer, Inca, Mayan, or Indus valley, they had
more or less adopted a single vertical bar for 1, a V for 5, and a
cross (x) for ten. In fact, the need for numerals arose when these
people had to keep a count of warriors during a war or hunting trip,
or when they had to count their sheep or food stock. The first
effective machine used for counting numbers was the hand. Fingers as
well as spaces between knuckles were commonly used (and sometimes even
used today) for counting purposes. It sounds unbelievable yet it is
true that one can count upto 99,999 with one hand, and upto
9,999,999,999 with both the hands! Remarkable human ingenuity!
Subsequently, a wide variety of number-recording devices such as
counting sticks (notch-based) in Europe, quipus (knot-based) in Peru,
calculi (pellet-based clay purses) in Egypt, etc, were invented to
keep a record of huge numbers because it became difficult for humans
to remember them. Counting tools such as abacus and checker-boards
were also invented in due course for counting huge numbers and
performing simple calculations. In the meanwhile, the notations for
numbers were developed, each civilization boasting of its own number
system, their bases diggering from 5, 10, 12, 20 to 60 but most
commonly adopted base was 10 wich is the total number of human fingers
(including thumbs) of a human being.
Numbers became increasingly unwieldy to handle as they grew big
because there was no effective system of mathematics to ease counting
and perform various types of calculations. The growth of mathematics
was therefore arrested despite the best contributions of Greek
mathematicians like Archimedes, Pythagorus, Apollonius and
Diophantes. It was only when zero was invented during the Gupta
Dynasty (240-535 A. D.) in India and used along with the age-old
Indian place value notation system of mathematics (the place of a
number in a notation decides its value) that the real rigour of
mathematics was revealed. Counting numbers and recording them on
paper became thereafter very easy and quick.
Indian mathematics reached its pinnacle in the 6th to 10th century and
its fame spread especially to the Arab world. Several Arab scholars
visited India and translated Indian treatises on mathematics into
Arabic. Despite stiff initial resistance, Indian zero and numerals
won the hearts of Arab Scholars like lbn Sina, al-Biruni, and finally
al-Khowarizmi. In due course, rumours about their versatility and
ease of counting and recording reached the ears of European
accountants, who were fed up of the cumbersome counting boards.
Indian zero and numerals, soon reached Europe under the guise of
'Arabic' numerals, a misconception that continues to prevail even
today in Europe. Several historical factors, including the Crusades
and the French Revolution, wereresponsible for the widespread adoption
of Indian numerals and zero all over Europe and then the entire
world. The subsequent developments in science and technology based on
these numerals, including the invention of the computer, clearly shows
that the Indian zero and numbers are as momentous a discovery as the
mastery of fire, development of agriculture, invention of writing, and
invention of wheel and engine!
The author gives credit to the discovery of place value system of
mathematics of Indians, to the precise and highly scientific Sanskrit
language. He claims that zero as a number was discovered
independently in other civilizations like Sumer and Maya also but it
did not gain acceptance due to the lack of an appropriate number
system. He also emphasises that throughout the history and evolution
of numerals neither logic nor mathematicians were the guiding light in
their invention; they evolved in response to the concerns of the
accountants! He interlaces some of the tedious and scholarly
mathematical findings and interesting yet indepth hypotheses about
numerals and zero with some fascinating and entertaining stories,
legends, and even myths and supernatural ideas about numerals
collected from the various civilizations of the world. Often, he
resorts to illustrated examples taken from the daily, simple lives of
those ancient and medieval people to explain or prove a mathematical
point or to provide a glimpse into their mathematical acumen.
No doubt, the author's main purpose of providing to the common man
having no prior knowledge of mathematics, the universal history of
numbers, is more than fulfilled through this book but h will be its
massive size and prohibitive price -- rather than its language or
mathematics--which will dissuade many from buying and reading this
otherwise well illustrated book. But, certainly, this book which
gives a special place to Indian mathematics, including a dictionary of
Sanskrit terms, should find a place in all our libraries. It should
be a matter of pride for all of us!
(Dilip M. Salwi is a Delhi-based science writer and author of several
popular science books)
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