Numerical differences
Question: On a trip to Saudi Arabia I expected to find 鈥淎rabic鈥� numerals in
use (as we call them in the western hemisphere).
Arabian numerals are entirely different, so how did ours become known as
Arabic?
Answer: Both sets of numerals originally come from India. Although the
numerals used by Europeans, Americans, and much of the international community
are referred to as Arabic numerals they were not originally created by the
Arabs. This misnomer originated in the 9th century when a manuscript on
arithmetic which had been written in India was translated soon after into
Arabic. Merchants then carried this book to Europe where it was subsequently
translated into Latin.
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Because the source for the Latin translation was an Arabic text, the numerals
were falsely ascribed to the Arabs. This is where the confusion arose: the
numerals came from India and are not Arabic at all.
The present set of Arabic numerals evolved over the early centuries but has
changed little since the advent of printed books in around 1445. Curiously the
numerals 4, 5, 6 and 7 underwent the most changes from the original script. The
numerals used in Arabic countries (and Iran) have undergone minor changes from
the original Hindu manuscript.
Paul Marselian
San Diego, California
Answer: Indians made two crucial advances in number systems. They introduced
place numbers and they introduced a special symbol for zero.
The value of these innovations can readily be experienced by anyone trying to
do simple arithmetic with nonplace-value systems, like Roman numerals.
Place-value numeration allows the mathematician to arrange addition in columns
and to carry over numbers from the 鈥渙ne鈥檚鈥� to the 鈥渢ens鈥�, or from the tens to
the hundreds columns. This is very difficult to do with Roman numerals
It is interesting that all Indic scripts are written from left to right (like
English), and so are the numbers. Arabic, however writes words from right to
left. However, its numbers, being borrowed from those used in India, are written
from left to right. Many speakers of Arabic are unaware of the reason why their
numbers are written in an opposite way to their words even though they may use
them every day.
William Wolf
Chicago, Illinois
Answer: We did indeed get our numerals from the Arabs, who had adopted them
originally from India. In Arabic they are therefore called al-arq谩m
al-hind铆ya which translates as 鈥渢he Indian numerals鈥�.
Philip Stewart
Oxford
Answer: The numerals that we use today are called Arabic because Europeans
adopted them from the Arabs. However, they are Indian in origin.
According to popular tradition the Arabic numerals were invented soon after
the start of the 6th century by the Indian astronomer Aryabhata. They made up
the first fully positional numeral system, in which the numeral 1 could stand
for 鈥渙ne鈥�, 鈥渁 hundred鈥� or 鈥� a thousand鈥�, depending on its position in the
number.
It was not the first use of a symbol for zero, however. This occurs in late
Babylonian numerals. Aryabhata is said to have been inspired by the sand abacus,
a device for multiplying numbers by making marks in a grid drawn on sand, in
which the position of the marks is significant.
The Arabs brought Indian scholars to Baghdad in 771 to teach them how to use
the new numerals, which they originally called huruf alghubar, or sand
letters after the sand grid mentioned above.
Europeans started to use them widely after 1202, when Leonardo of Pisa
explained and detailed their use in his Book of the Abacus.
Ralph Hancock
London
Answer: In 1299, the city of Florence issued a decree prohibiting the
commercial use of Arabic numerals because they were easily falsified. For
example, a 鈥�0鈥� could easily be changed to a 鈥�6鈥�.
Ron Webb,
Macclesfield, Cheshire
Answer: The precise glyphs that are used for the digits have varied
considerably over the centuries. Those used in Europe were stabilised by the
selection William Caxton used for his printing press.
Prior to that there was considerable variation, particularly for the glyphs
that were used for four and five. For a long time the glyph we now use for four
would have been considered to represent five.
It is not surprising that the actual glyphs used in Arabic- speaking
countries are very different from those that we use now, and these differences
can be very confusing especially to the unwary.
The traffic speed limit on the bridge running between Khartoum and Omdurman
used to be posted in both English and Arabic. The limit was 10 miles per hour,
but apprehended drivers frequently defended themselves on the grounds that they
had never exceeded the 15 miles per hour that they had seen on the signpost.
This is because the glyph we use for zero is very similar to that used in Arabic
for five.
To add to the confusion, the Arabic glyph for zero is also very close to the
raised point that we traditionally use as a decimal point.
Francis Glassborow
Oxford
This week鈥檚 questions
On the road again: How is car tyre road noise generated? How can it be
minimised and are the methods compatible with other desirable environmental
effects? Are there comparative lists for cars or tyres that can be
consulted?
Mike Coon
Maidenhead, Berkshire
The blue room: Why is it that a room that is being illuminated by a
television appears blue to an outside viewer regardless of the colours that are
being displayed on the screen?
Dave Greenfield
Philadelphia, Pennsylvania
Neck ache: Do giraffes standing on the plains of Africa ever get struck by
lightning?
Cristiane Delamboy
Maastricht, The Netherlands
Fan power: I use many fans to cool my airless, New York apartment. One of my
fans has two blades, one has three blades, and two others have five blades.
What considerations determine how many blades a fan has? How does the number
of blades a fan has affect the amount and velocity of the air it moves?
And, as an aside, are the underwater propellers that are used for moving
boats and ships subject to the same considerations?
Arnold Klein
New York