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Publication: Islam Watch

Date: 0October 5, 2009

URL: http://www.islam-watch.org/iw-new/index.php?option=com_content&view=article&id=203:zero-and-modern-numerals-islamic-or-indian&catid=57:fjordman&Itemid=58

I heard the claim from one European reader
that "The Arab world invented the zero, and it's been downhill ever since."
This is false, but unfortunately not an uncommon mistake. Our numeral system
dates back to India during the post-Roman era, but it came to Europe via the
medieval Middle East which is why these numbers are called Arabic numerals
in many European languages.

Even Muslims admit that they imported these
numerals from India. Calling them "Arabic" numerals is this therefore
deeply misleading. "Hindu-Arabic" number system could be accepted,
but the preferred term should be "Indian numerals."

The Maya in Mesoamerica developed a place-value
number system with a zero before the Indians, but this great innovation sadly
did not influence peoples elsewhere. According to Michael P. Closs in Mathematics
Across Cultures: The History of Non-Western Mathematics, "There is reason
to credit the Maya with the first invention of a zero symbol. It is absent
in the surviving epi-Olmec texts but is very common in the Maya inscriptions.
Zeros are found in many chronological counts in the Dresden Codex where they
occur in positional contexts just as other numerals. Most Maya glyphs come
in several variants and the same is true of the zero sign. The zeros in the
codices are identifiable as shells and are always painted red. In most cases,
the zero shells are stylized and simplified. In the inscriptions, the most
common form of the zero is shaped somewhat like a three quarter portion of
a Maltese cross."

The Aztecs who were politically dominant in
Central Mexico from the 1300s used hand, heart and arrow symbols to represent
fractional distances when calculating areas of land. Mesoamerican and especially
Mayan mathematics is the one pre-Columbian scientific achievement which compares
most favorably to developments in the Old World, but the mainstream development
of mathematics happened in the major Eurasian civilizations and the Maya seem
to have concentrated their efforts largely in the field of planetary astronomy.

The zero can be used as an empty place indicator,
to show that 2106 is different from 216. The ancient Babylonians had a place-value
number system with this feature, but base 60. The second use of zero is as
a number itself in the form we use it. Some historians of mathematics believe
that the Indian use of zero evolved from innovations by Greek astronomers.
Symbols for the first nine numbers of our number system have their origins
in the Brahmi system of writing in India, which dates back to at least the
mid-third century BC. More important than the form of the symbols is the notion
of place value, and here the evidence is weaker.

The Chinese had a multiplicative system with
the base 10, probably derived from the Chinese counting board. By the fourth
century BC the counting board, a checker board with rows and columns, had
come into use there. Numbers were represented by little rods made from bamboo
or ivory. The abacus was introduced in China around the fourteenth century
AD. Somewhere around or before the year 600 AD (the exact place and date remains
uncertain) Indians dropped symbols for numbers higher than 9 and began to
use symbols for 1 through 9 in our familiar place-value arrangement. Authors
James E. McClellan and Harold Dorn speculate whether "The appearance
of zero within the context of Indian mathematics may possibly be due to specifically
Indian religio-philosophical notions of 'nothingness.'" This is controversial
but worth considering. Ideas have practical consequences, and it sounds plausible
that the concept of "nothingness" would have greater cultural resonance
in a country influenced by Hinduism and Buddhism than in Christian-dominated
Europe, for example.

The question nevertheless remains why Indians
dropped their own multiplicative system and introduced the place-value system,
including a symbol for zero. We currently don't know for sure. Victor J. Katz
elaborates in his fine A History of Mathematic, Second Edition:

"It has been suggested, however, that
the true origins of the system in India may be found in the Chinese counting
board. Counting boards were portable. Certainly, Chinese traders who visited
India brought them along. In fact, since southeast Asia is the border between
Hindu culture and Chinese influence, it may well have been the area in which
the interchange took place. Perhaps what happened was that the Indians were
impressed with the idea of using only nine symbols, but they took for their
symbols the ones they had already been using. They then improved the Chinese
system of counting rods by using exactly the same symbols for each place value
rather than alternating two types of symbols in the various places. And because
they needed to be able to write numbers in some form, rather than just have
them on the counting board, they were forced to use a symbol, the dot and
later the circle, to represent the blank column of the counting board. If
this theory is correct, it is somewhat ironic that Indian scientists then
returned the favor and brought this new system back to China early in the
eighth century."

A decimal place-value system for integers
definitely existed in India by the eighth century AD, possibly earlier. Although
decimal fractions were used in China, in India there is no early evidence
of their use. It was the Muslims who "completed the Indian written decimal
place-value system by introducing these decimal fractions."

There is evidence of the transmission of pre-Ptolemaic
Greek astronomical knowledge to India, possibly along the Roman trade routes.
The earliest known Indian work containing trigonometry dates from the fifth
century AD. The Gupta period from the fourth to seventh centuries was a golden
age for Indian civilization, with a flourishing of art and literature. Astronomers
produced a series of textbooks (siddhanta or "solutions") covering
the basics of astronomy and planetary movements using Greek planetary theory.
The Aryabhatiya of the prominent Indian mathematical astronomer Aryabhata
(476-550) from 499 was an important work which summarized Hindu mathematics
up to that point in time, covering arithmetic, algebra, plane trigonometry
and spherical trigonometry. Next to Aryabhata, Brahmagupta (598-ca. 665) was
the most accomplished Indian astronomer and mathematician of this age, making
advances in algorithms for square roots and the solution of quadratic equations.

As Victor J. Katz writes, "in 773 an
Indian scholar visited the court of al-Mansur in Baghdad, bringing with him
a copy of an Indian astronomical text, quite possibly Brahmagupta's Brahmasphutasiddhanta.
The caliph ordered this work translated into Arabic… The earliest available
arithmetic text that deals with Hindu numbers is the Kitab al-jam'wal tafriq
bi hisab al-Hind (Book on Addition and Subtraction after the Method of the
Indians) by Muhammad ibn-Musa al-Khwarizmi (ca. 780-850), an early member
of the House of Wisdom. Unfortunately, there is no extant Arabic manuscript
of this work, only several different Latin versions made in Europe in the
twelfth century. In his text al-Khwarizmi introduced nine characters to designate
the first nine numbers and, as the Latin version tells us, a circle to designate
zero. He demonstrated how to write any number using these characters in our
familiar place-value notation. He then described the algorithms of addition,
subtraction, multiplication, division, halving, doubling, and determining
square roots, and gave examples of their use."

Some Sanskrit works were introduced to Europe
via Arabic translations. One Latin manuscript begins with the words "Dixit
Algorismi," or "al-Khwarizmi says." The word "algorismi,"
through some misunderstandings became a term referring to various arithmetic
operations and the source of the word algorithm. "Zero" derives
from sifr, Latinized into "zephirum." The word sifr itself was an
Arabic translation of Sanskrit sunya, meaning "empty." The English
word "sine" comes from a series of mistranslations of the Sanskrit
jya-ardha (chord-half). Aryabhata frequently abbreviated this term to jya
or jiva. When some Hindu works were translated into Arabic, this word was
transcribed phonetically into jiba. But since Arabic is a consonantal alphabet
usually written without added short vowels, later writers interpreted the
consonants jb as jaib, which means bosom or breast. When an Arabic work of
trigonometry was translated into Latin, the translator used the equivalent
Latin word sinus, which also meant bosom. This Latin word has become our modern
English "sine."

Rabbi Abraham ben Meir ibn Ezra, or Abenezra
(ca. 1090-1167), a Spanish-Jewish philosopher, poet and Biblical commentator,
left Spain before 1140 to escape persecution of the Jews by the regime of
the Muslim Almohads. He wrote three treatises which helped to bring the Indian
symbols to the attention of some of the learned people in Europe, but it took
several centuries for Indian numerals to become fully adopted in Europe.

Leonardo of Pisa (ca. 1170-1240), often known
as Fibonacci (son of Bonaccio), was an Italian and the first great Western
mathematician after the decline of ancient Greek science. The son of a merchant
from the city of Pisa with contacts in North Africa, Leonardo himself travelled
much in the region. He is most famous for his masterpiece the Liber abbaci
or Book of Calculation. The word abbaci (from abacus) does not refer to a
computing device but to calculation in general. The first edition appeared
in 1202, and a revised one was published in 1228. This work enjoyed a wide
European readership and contained rules for computing with the new Indian
numerals. The examples were often inspired by examples from Arabic-language
treatises, but filtered through Leonardo's creative and original genius. Indian
numerals faced powerful opposition for generations but were gradually adopted
during the Renaissance period, especially by Italian merchants. Their practical
advantages compared to the more cumbersome Roman numerals were simply too
great to ignore, although Roman numerals are still used for certain limited
purposes in the West in the twenty-first century.