The Origins and History of the Number System
We call them Arabic Numerals, but our numbers actually find their origins in the history of the Hindus of India. They have changed greatly over the centuries, passing first to the Arabs of the Middle East and finally to Europe in the Middle Ages, and are now the most commonly used numbers throughout the world.
The Basis of Our Number System
The number system that we use today is a place value decimal system. What that means is that not only the number but the placement of the number is significant. Take a look at the number 536. It incorporates three numerals: 5, 3 and 6. Because we use a place value system, we know that the 5 does not stand just for 5, it means 500. The 3 stands for 30, and the 6 is in the ones place, is only 6. Rather than writing 500 + 30 + 6, our system allows us to write it just like 536.
Our system is also decimal because it is by increments of 10. We have 10 numerals in our system: 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. We count 1 through 9, then move to the next level with 10. Then we go up to the ones place through 9 before moving to the next 10s place (20). Each place value in the system is ten times the value of the one before it. (Ones, then tens, then hundreds, thousands and so on).
The vital element in making this system work is the development of the concept of zero. Aside from the Maya of Central America, the only group to develop the idea of zero was the Hindu peoples of India.
When precisely the Hindus first began using a place value decimal system which incorporated zero is not certain. They were undoubtedly using such a system in 400 CE, where we first find inscriptions of 0. (The Maya were using 0 before this time, and were the first to use it.)
By the 7th century CE, a fully developed place value decimal system was in place. The Brahmasphutasiddhanta (Opening of the Universe) was composed in 628 CE and demonstrated a full set of Indian numerals including 0.
Although the 0 did not become visible until 400 CE, Indian scripts for numerals first start appearing in the 1st century. There were two significant scripts: the Brahmi and the Kharosthi scripts. It is from the Brahmi script that our numbers originate.
The symbols for 1, 2 and 3 in the Brahmi scripts were initially lines: one line for 1, two lines for 2 and 3 lines for 3, drawn horizontally. Over time these lines began to be connected (and the one line rotated 90 degrees so it would be vertical). When you look at our own 2 and 3 today, you can see how the 2 was initially two lines which get joined with a path through the middle, and the 3 composed of 3 lines connected.
After the number 3, different symbols were used to represent these numbers. Most of the symbols used in the Brahmi script are similar to the numerals that we use today.
Other Numeral Systems
There were other numeral systems developed at the same time as the Hindu numerals and before. For example, the Babylonians and Egyptians had simple systems using tick marks to write their numbers. (1 tick for 1, 5 ticks for 5, and so on).
The Greeks and the Hebrews used letters for numbers. Every letter in the Greek or Hebrew alphabet corresponded to a different number. For example, in Greek, the letter Alpha corresponded to the number 1, and the letter Theta compared to the number 9.
The other numeral system most known to people today is the Roman numeral system. They too used letters for numbers. The numeral conversion with our numerals today looked like this:
- I – 1
- V – 5
- X – 10
- L – 50
- C – 100
- M – 1000
Roman numerals do not use a place-value system. Instead, they write down their numbers from biggest to smallest. Let’s look at an example: 1998, which in Roman numerals we would write MCMXCVIII
We start with M. This stands for 1000. C follows it. Now, this could mean 1100 (1000 + 100). However, there is another M after the C. Because M is larger than C but comes after it, that says the C is working with the second M, rather than the first. (Yes it is a bit confusing!) So the C (100) is subtracted from the M (1000). So far then we have 1000 + 900 (1000-100).
We now move onto the next number, which is X. We could add X to 1900 we have so far. However, we need to look to the next numeral first. It is C, larger than X, so we have to subtract the X from C rather than add it to the MCM. 100 – 10 = 90, so the XC stands for 90. We now have 1990.
Next, we come to the V, which stands for 5. There are no larger numbers after it (they are I’s, 1s). So we add the V and the Is together (5 + 3 1s = 8). Thus you have 1000 + 900 + 90 + 8 = 1998. Quite a bit of work for what is only four numbers in our system!
Fortunately for us, we do not still use the Roman numeral system in common practice today. We use the Hindu system, which gets transmitted to us through the Arabic world of the Middle Ages.
It is uncertain when precisely Hindu numerals first came to the Islamic world of the Middle Ages. The Brahmasphutasiddhanta mentioned above came to Baghdad in the year 776 CE, and was presented before the current Caliph al-Mansur. This book then gets translated into Arabic
Two Muslim mathematicians contributed significantly to the use of Indian numerals: al-Khwarizmi of Persia and al-Kindi, both of whom worked in the first half of the 9th century CE.
Like the Hindus before them, Arabic mathematicians began to change the numerals as well as people use them over time. Before the development of the printing press, everything written had to be written by hand, and thus there was no universal uniformity. Scholars working far apart over long periods of time would eventually change the numerals even unknowingly but directly through a change of handwriting.
Use of Indian numerals in the Muslim world was limited primarily to mathematicians, however. Muslim scientists and astronomers generally used the older Babylonian system of numerals. It was in fact still in use until modern times in the Arabic world. Merchants also used a different numeral system, similar to that of the Greeks and Hebrews.
Arabic Numerals Come to Europe
The use of Arabic numerals in Europe is because of the Italian mathematician Fibonacci. In 1202 he published a book called Liber Acci, which taught Arabic numerals and Algebra and strongly advocated the use of Arabic numerals in society.
Before the time of Fibonacci, the primary numeral system used in Europe was the Roman system discussed above. Acceptance of the Arabic numerals pushed by Fibonacci took time to come, however. In fact, even today the Roman numeral system is still used, primarily in copyright dates for books and movies. This practice has been dying out, however, since it is so much easier to write, for example, 1998 than it is to write MCMXCVIII.
Use of the Hindu-Arabic numerals is now the standard number system throughout the world. With the development of the printing press in the 16th century, the digits have become standardised, and this has only increased with the growth of computers. Our numeral system will be with us for a long time, and it is unlikely that we will be seeing changes any time soon.