Semester Project

Numbers have been a part of mankind since the beginning. People started by learning to count the things around them, but they didn’t need a method to write their numbers until they learned to write (LeVeque, W Judson and Smith. David Eugene, 2019). As numbers became more and more common, they created a system to represent both small and big numbers, which are known as number systems. As far back as historians have studied, there has been evidence of a system where numbers have “a repeated sign for each group of [ten] followed by another repeated sign for [one]” (Gascoigne, 2021). Number systems are systematized and simplified, to form what is called a base. The number system just referenced is the most common and is called a base ten system.

There were many base systems developed and used throughout the world as time went on. Many people established the counting system that worked for their culture, which meant different things around the world. “The pair system, in which the counting goes “one, two, two and one, two twos, two and two and one,” and so on, is found among the ethnologically oldest tribes of Australia,” and many others in the surrounding islands (LeVeque, W Judson and Smith. David Eugene, 2019). “The Mayans used a base-20 system, called the “vigesimal” system” which is said to come from using their fingers and their toes (The Mayan Numeral System, 2021). In South America they used bases of three and four, or even some use the quinary scale, a base five system, which seems to be used by speakers of Saraveca, found in South America (LeVeque, W Judson and Smith. David Eugene, 2019). In Africa, they use a base six scale a little throughout the top of the northwest, otherwise they use the duodecimal, or base 12, system (LeVeque, W Judson and Smith. David Eugene, 2019). There are many more systems used in different areas around the world, as well as many ways to write the numbers.

Throughout the world people wrote their numbers differently according to their culture. One of the first records of written numbers come from the Egyptians, the records we show around 3000 BC. They used hieroglyphics, little pictures representing words, using a base ten system (J J O'Connor and E F Robertson, 2004). East Asia used a system where they wrote their numbers as ―, =, ≡, etc. for the simple needs they required at the time (LeVeque, W Judson and Smith. David Eugene, 2019). Babylonians used a system of base 60, using only a few symbols to represent all their numbers involving a unit symbol and a ten symbol (J J O'Connor and E F Robertson, 2004). “Around Babylon, clay was abundant, and the people impressed their symbols in damp clay tablets before drying them in the sun or in a kiln, thus forming documents that were practically as permanent as stone” (LeVeque, W Judson and Smith. David Eugene, 2019). The Babylonians also provided a crucial step towards our system today as they introduced a positional system, which means that depending on where the symbol was in the number changed the meaning of that number (Gascoigne, 2021). It is interesting to note that as many other civilizations began to use this positional system. For example the Greeks kept their system which was based on geometry, which lead them to not needing some “clever notation” (LeVeque, W Judson and Smith. David Eugene, 2019). Each ancient community had their own way to write their numbers, and many adapted the use of a positional systems because it helped with arithmetic.

With a positional system occurring around the world in Babylonia the need for a placeholder became more apparent, which we know today as the number zero. The history of this number is unique because it was a concept hard to grasp, and it was discovered in a few different ways. The first way was its use as an “empty place indicator in our place-value number system” (J J O'Connor and E F Robertson, 2004). Both the Babylonians and the Mayans had positional systems containing zero, but neither of these civilizations completely developed the idea of zero, unlike the Hindus who did (LeVeque, W Judson and Smith. David Eugene, 2019).

The second use of zero is using it as a number itself, which is symbolized by 0, which is what the Hindus discovered (J J O'Connor and E F Robertson, 2004; LeVeque, W Judson and Smith. David Eugene, 2019). The Hindus, in India, “used a dot or small circle when the place in a number has no value, and they give this dot a Sanskrit name - sunya, meaning 'empty'” (Gascoigne, 2021). The Indians discovery and use of the number zero influenced many other civilizations around the world in both the way numbers were written but also how arithmetic was done. The Mayans, in Central America, also had discovered this relationship of zero. However, they used this idea before their use of positional systems, and did not have an influence on others at the time (J J O'Connor and E F Robertson, 2004).

The mathematicians in India also were some of the first to use the symbols of numbers that we use today. We can track these numbers throughout history: “the 1, 4, and 6 are found in the Ashoka inscriptions (3rd century BCE); the 2, 4, 6, 7, and 9 appear in the Nana Ghat inscriptions about a century later; and the 2, 3, 4, 5, 6, 7, and 9 in the Nasik caves of the 1st or 2nd century CE” (LeVeque, W Judson and Smith. David Eugene, 2019). These numerals were used in astronomical tables of India and a book was translated into Arabic, which introduced these symbols to the Arabic scholars (LeVeque, W Judson and Smith. David Eugene, 2019). Arabics slowly over time began to use this system as their own, and began to take it around the world while trading. (J J O'Connor and E F Robertson, 2004). Europe was first exposed to these symbols by the Indians, but they were not ready for the change yet. At the time Europeans used the Roman numeral system, which was “maintained for nearly 2,000 years in commerce, in scientific and theological literature, and in belles lettres (a type of writing)” (LeVeque, W Judson and Smith. David Eugene, 2019). So, when the Arabians brought these numbers to them later through trading it took them time to adjust to see the need for this change. This adjustment was because the “concept of place notation proved to be very difficult for medieval Europeans to understand…and the symbols for numbers were also brand new for Europeans” (Why learning numbers was so hard in medieval Europe, 2021). This was the beginning of the wide spread use of the Hindu-Arabic numeral system.

Throughout the course of history, the Hindu-Arabic numeral system became the most used throughout the world. This system is what you see every day, in gas prices, addresses, the clock on your phone, etc. This number system “might be said to be the nearest approach to a universal human language yet devised; they are found in Chinese, Japanese, and Russian scientific journals and in every Western language” (LeVeque, W Judson and Smith. David Eugene, 2019). Though this system is a base ten system, there are exceptions to other base systems used in our world today. We can see evidence of this all around us; “12 occurs as the number of inches in a foot, months in a year, and twice 12 hours in a day, and both the dozen and the gross measure by twelves. In English the base 20 occurs chiefly in the score (“Four score and seven years ago…”); in French it survives in the word quatre-vingts (“four twenties”), for the 80 system and other traces are found in ancient Celtic, Gaelic, Danish, and Welsh. The base 60 system still occurs in measurement of time and angles” (LeVeque, W Judson and Smith. David Eugene, 2019). Overall, many people have been taught throughout their lives about the Hindu-Arabic system and symbols to understand the world around them.

It is interesting to note that many people aren’t aware of this history and don’t acknowledge that their number system has a history and origin. In the United States a survey was done and asked people if the Hindu-Arabic number system should be taught in school, the result was that fifty-six percent of people said that this system should not be taught in school (Felton, 2019). With how much we use this system in everyday life, it’s important to know what it is, and where it came from.