The Invention of Zero and the Bakshali Manuscript
Bakshali Numericals
( Source: Wikipedia)
The greatest mathematical discovery of all time was
undoubtedly the invention of Zero. This allowed mathematicians and common
people to make calculations easily and conveniently, calculations that were otherwise
so complex that even very intelligent people floundered in making them. As
Bailey and Borwein put it in a major article published in 2011, it was a
discovery that eluded the greatest minds of the Western civilizations,
mathematicians of the caliber of Archimedes, and unsurprisingly was resisted fiercely
by Western mathematicians when they were first introduced to it by the Arabs
and even today is often ascribed to sources other than the right one. As the
French historian Georges Ifrah describes it ““Now that we can stand back from
the story, the birth of our modern number-system seems a colossal event in the
history of humanity, as momentous as the mastery of fire, the development of
agriculture, or the invention of writing, of the wheel, or of the steam engine.”
This discovery took place in India in the early years of the
Christian era. I like to think that it was in the days of the Gupta empire when
a mathematician working in Taxila discovered that inventing a “sunya “ ( zero)
would make it easy to calculate in tens. But the fact is that we simply do not
know. What we do know is that the first accurately dated manuscript that used this
system of decimal notation and zero was the Indian astronomical work
Lokavibhaga (Parts of the Universe"). This manuscript uses the decimal
system as a matter of course, assuming that the reader is aware of the system
thus proving that it originated much earlier than the 458 CE to which this
manuscript can be accurately dated.
That brings up to an even older manuscript which is to date
the earliest manuscript which mentions the word Zero (sunya).
In undivided India, the North West Frontier province has
always been a romantic name. The romance has been created in the nineteenth
century by the writings of English writers who found the feudal structure of
the area very much to their liking and portrayed the endless feuds and never ending
wars as a sort of knightly activity. However this geographical area was a wonderland long before this when it was the
home of the world’s oldest universities and a vibrant civilization that lasted
thousands of years and gave the name Gandhara to Indian history. It was during
this time in history that this land was the source of much that was great in
Indian history.
However in 1881, Bakshali was a nondescript village about 50
miles away from the provincial capital Peshawar. This was in the Mardan tehsil
and Bakshali was a village like any other, peopled by poor peasants and
grazers. One such man whose name unfortunately I could not unearth, was digging
at a mound at the outskirts of the village and he found, concealed between two
slabs of ancient stone a manuscript, the so called Bakshali Manuscript. This
man was the tenant in the land of the local Inspector of Police Mian An –Wan Uddin
and when he was informed of the matter he took it to the Assistant Commissioner
of Mardan . The AC now forwarded the manuscript to the then Lieutenant governor
of Punjab who was advised by the then Director General of Archeology in India,
General Sir Alexander Cunningham to send it to Dr Rudolf Hoernle who was
heading the Calcutta Madrassah .
Hoernle was the first antiquarian who examined the manuscript
and he presented a brief report before the Asiatic Society of Bengal and this was reprinted in their journal “ The Indian
Antiquary” in 1883. He gave a more detailed report at an international
conference in Vienna in 1886. This study was also published in the same journal
in 1888. Subsequently he presented to the manuscript to the Bodleian Library at
Oxford where it still lies.
Hoernle worked on the manuscript for almost 20 years, he was
the person who put lot of effort into making it possible to read the manuscript.
When it was found,, the birch bark manuscript consisted of an indeterminate number
of strips , many of which were stuck together and well-nigh impossible to
separate. The leaves were brittle and it
took much effort to separate them and he managed to get 70 leaves; many of them
had large parts missing. Hoernle and subsequent researchers who have worked on
this manuscript were of the opinion that the manuscript is only the middle part
of a much larger manuscript. Later researchers who added much to the knowledge
gained form this treasure included Bibhutibhusan Dutta , Dutta was one of the earliest
doctorates in mathematics form Calcutta University and retired as the
Rashbehari Professor of Applied mathematics and in later life became a
sanyasi, dying in Puskar as Swami Vidyaranya in 1958.
BibhutiBhushan Dutta
( Source: Wikipedia)
Another infamous person, who published the official Archeological
Society of India version of the document, was G R Kaye.He did signal work in
that he published the manuscript in facsimile form and this is the version that
most subsequent workers used. However his wholly untenable conclusions that
that the manuscript dates to the twelfth century and his contention that the
manuscript was based on Greek sources, made him a laughing stock.
It was in this manuscript, which contains many
trigonometric, arithmetical and other exercises that the Zero was first symbolized
as dot or a sunya. This makes it the earliest
reference to zero in the world.
What then is the date of the manuscript? There are two
clues: The language and script used and the contents. The manuscript was
written a series of shlokas which immediately dates it to before 500 CE as the
Arya style was had largely replaced the shloka style by that date. It was also
written in the Gatha dialect which was a precursor to Sanskrit which largely
replaced in by 300 CE. The contents of the manuscript also suggests that it
predates the classical period of Indian Mathematics, the period of Aryabhatta
whose famous Aryabhatia has been dated to c 500CE. All this suggests that the
actual work on which this manuscript is an obvious copy was written in the 1st
to 3rd centuries of the CE. This particular manuscript has not been accurately
dated yet, but recently there is a move to do radiocarbon dating to accurately
date this particular copy.
The concept of zero rapidly spread to China where there is evidence
that it was available during the Sui dynasty (581-616CE). Later it was carried
by Persian and Arab scholars to the European continent where as we have seen it
received a cool reception. That was the time when European scholarship believed
that all knowledge came from the Greeks!
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