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Origin of the Arabic Numerals offers the
reader two stories the author believes they have
never been told in a book before. The history of
mathematics suffers from many shortcomings. Many
of its “established facts” are neither
established nor facts. Two centuries after its
manufacture essentially by two orientalists
hired by the East India Company two centuries
ago, it is simply extraordinary that the story
of the appropriation of the Arabic cipher system
and its numerals remains untold. Not a hint
about this brazen high jacking can be read in
any of the hundreds of books published since the
death in 1929 of G. R. Kaye, the last great
independent-minded expert on the Arabic numeric
system. The story of the appropriation is the
best-kept secret in the history of mathematics
and now, believes the author, is a good time to
reveal that unnecessarily-kept secret.
The other story in the book is much older,
simpler, and therefore potentially more
astonishing. If correct, it may be one of the
oldest stories told in a book about those little
“things” that are so essential to human
civilisation, the sudden disappearance of which
could cause it to grind to a halt. This is the
story of the unique digits we use today. Now,
symbols that can be recognised by a computer
must be special. Symbols that can be recognised
by monkeys must also be special, but symbols
that can be recognised by machines, monkeys and
humans must be the only universal script
invented by human beings in a time beyond the
horizon of our remotest past.
Also it appears that human beings needed to
identify and document ownership of property and
other important assets by means of numeric
symbols many centuries before they needed
letters to preserve thought and ideas. How old
the universal numeric system we use today is,
nobody knows. What can be said is that most of
our numerals have an ancient Arabian origin, and
they even exhibit close connections with ancient
Egyptian.
The Ciphering of Europe
There are two numeric alphabets in use
today with certain variations: The eastern
numerals used in the Arab world and many other
countries outside it, and the western numerals
used in some North African Arab states, Europe,
the USA and many other countries. The western
numerals are a relatively new introduction most
probably from Arab Al Andalus in the 12th
of 13th century, and in a very
limited scale. The eastern numerals are very
ancient; they are the master set from which the
western numerals were adapted.
Both sets of numerals are pictograms of
formations of hand and fingers. This means that
when we write numerals, we are drawing miniature
shapes of actual numeric hand and finger
formations. Long before paper was invented
traders and ordinary individuals used hand and
finger formations to calculate and convey
numbers in open markets.
The story of how Europe came to use the
Arabic cipher system and its numerals is told in
chapters 15 and 16 of the Origin of Arabic
Numerals. Ignoring the narrative that the
Arabic numeric system was brought from al-
Andalus in the 10th century by Gerbert
d'Aurillac (946-1003) leaves history with a
disappointing account of the wider spread
diffusion of the Arabic system in Europe some
400 hundred years later than claimed and 650
years after the publication of al-Khwarizmi’s
al-Jabr Wa Muqabalah. A realistic account of
the European history of mathematics, therefore,
would suggest that the Arabic numeral system was
used in isolated cases but “outside Italy most
merchants continued to keep their accounts in
Roman numerals till about 1550, and monasteries
and colleges till about 1650… Arabic numerals
are used in the pagination of some books printed
in Venice in 1471 and 1482. No instance of a
date or number being written in Arabic numerals
is known to occur in any English parish register
or the court roll of any English manor before
the sixteenth century; but in the rent-roll of
the St Andrews Chapter, Scotland, the Arabic
numerals were used in 1490.”*
Again, the student of history should be
careful not to confuse the occurrence of a few
exploratory Arabic numerals in a few records
with the ‘diffusion’ of the Arabic numeral
system. Some scholars described in some
histories as among the first to work with the
Arabic system do not appear to have succeeded in
explaining how the system works. It was
necessary, therefore, to prepare for the
introduction of the system with explanatory
notes of some of its most important functions.
This was done not by scholars, as often
claimed, but by professional publishers of
almanacs and calendars because they needed to
sell their products. Almanacs and calendars
enjoyed wide circulation in the 15th century.
Some were composed with special reference to
ecclesiastical events and contained dates for
different festivals and fasts of the church for
a period of some seven or eight years in
advance, as well as notes on church rituals. The
demand for such publications was significant, as
“nearly every monastery and church of any
pretensions possessed one of these. Others were
written especially for the use of astrologers
and physicians, and some of them contained notes
on various scientific subjects, especially
medicine and astronomy.”
Those almanacs and calendars needed to use
Arabic numerals intensively. Their contribution
to the diffusion of the Arabic system cannot be
overestimated. Another important category of
professionals who helped to diffuse the Arabic
system were the makers of instruments and
gadgets. The dramatic increase in the number of
ships needed to serve the New World and the
accelerated international trade created a huge
demand for navigational instruments. Likewise,
the prosperity brought by trade created a demand
for clocks and elaborate novelties that required
numbers. The choices faced by these artisans
were limited due to the lack of a standardised
European use of numeric systems and
measurements, and many had to experiment with
different systems until the marketplace forced
the use of the Arabic numeric system. Whether in
accounting, publishing, manufacturing and other
crafts, the marketplace in the late 15th century
spearheaded the diffusion of the Arabic numeric
system among the rest of society rather than
scholars and historians.
It may sound incredible but it does appear
that it took most Europeans more than 150 years
to accept the concept of the zero. The
controversy surrounding the zero persisted for
another three hundred years. “From the middle of
the fourteenth century down to the fifteenth,
when the Arabic system began to be generally
adopted in calendars (long before its
application to common accounts in bookkeeping),
explanations clearly pointing out the power of
place, which gives to the digit its decimal
value, were frequently attached to Latin texts.”
To the rescue rushed the Flemish Simon
Stevinus with a book written in his native
tongue and translated into French by Simon of
Bruges who adopted the word disme as the
devise or representation of the new system of
arithmetic. The English translation was done by
Richard Norton (1606). It took another book,
Clavis Mathematica, for the famous Dr.
Peacock to declare that from this date (1631)
onwards the Arabic numeral system became fully
established in Europe.
*Please refer
to the book for footnotes, as well as to a
substantial number of tables, charts and
illustrations supporting the topics discussed in
the book and especially a large number of hand
and finger numeral formations using both the
eastern and western numeral pictograms. A number
of PowerPoint and PDF presentations covering
various aspects of Arabic cipher system and its
numerals will soon be available. These can be
downloaded free of charge from
www.bishtawi.com and www.arabicnumerals.net
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