The Magic of Numbers – Serial 4

Number writing systems

According to the history books, various ancient cultures all over the world developed their own number writing systems. In this article we will only take a look the common number writing systems that are in use today and how versatile are each number writing system.

Languages started with voices, then the people in ancient times developed the ability to store ideas by writing. They used an alphabet based on the sounds the voice box can make to write their ideas.

A medium of writing is needed. In ancient times, rocks, tablets, stones and pebbles were use as a medium for writing numbers. People needed better ways to communicate their comparisons or share information intended for a group.

Making sense of size was important for everyday communication in ancient times, separate cultures worldwide developed number writing systems based on their ability to count with their ten fingers.

The basics of a number writing system

A number writing system should always consist of a unique symbol for each numeral. Numerals are part of a language vocabulary and numbers are a shorthand for writing those numeral word.

When we read aloud our counting, we read aloud the numeral based on the language we know. If we read aloud “eight” in English or “huit” in French, we are representing the number character/symbol “8”.

Also it must have a size/magnitude indication system. In the previous chapter we have seen one example of it, called the place value system. Number symbols are meaningless if it is not able to show size.

Just as the 26 Latin alphabet characters can form thousands of words, symbols can be grouped together to create another number, but the symbols must be based on a logical, continuous sequence to reach that grouping, as we have seen in the place value system. We can call this the “number thread”. This enables counting.

Size can be shown by only defining the correct sequence of numerals, as stated in the previous two chapters. Example: When reciting (reading aloud) numerals, “two” must always come after “one” and “six” must come after “five” to indicate something is increasing or moving forward.

The sequence can be reversed, if we want to count backwards. “Six” must come before “five” and “two” must come before “one” if we want to count backwards. Backward counting is called a countdown. It can also mean moving backwards or something is decreasing.

Below we will take an excursion on at least two popular number writing systems, the Roman number writing system and the East Asian number writing system. The characteristics of the Hindu-Arabic number writing system were already discussed in the previous serial. This article will only compare how versatile each number writing system compared to the frequently used Hindu-Arabic number writing system.

The Roman number writing system

Below, the number symbols of the Roman number writing system is based on some of the capital letters of the Latin alphabet. We can call them Roman number symbols, not the popular term “Roman numerals” to avoid semantic confusion with the numeral vocabulary in languages. French numerals are included to show how these number symbols are independent of the language.

The table below contains the numbers one to ten:

Here are the Latin characters that determine the size of a number, so they are important for the size indication system of the Roman number writing system:

Here are examples of large numbers in the Roman number writing system:

As we can see above, the order of size indicated by the numeral assigned to the alphabet letters (example: C). In ascending order, numbers I, V, X, L, C, D, and M indicate the size.

They are usually in front of the smaller numbers. The number of characters used in a number cannot determine size: “CM” might take have two characters only but it is larger than “CXLVII” based on the sequence/continuum of counting.

So the numerals of most languages are independent of number writing systems: The numeral or word “eight” in English or “huit” French can represented by two number writing systems we know: In Hindu-Arabic it is “8” or in Roman number writing system it is “VIII”.

East Asian number writing system

East Asian cultures (Chinese, Japanese and Korean) use Chinese characters as number symbols. They also use the counting rod number writing system which is very similar to the Hindu-Arabic number writing system, due to a similar place value system, but they won’t be discussed here.

Those cultures now use three (3) number writing systems: Hindu -Arabic, Roman and East Asian. To spell out in their language any Hindu-Arabic or Roman numbers, they use East Asian. Hindu-Arabic and Roman were introduced due to the influence of the Western culture.

The Japanese language will be used in this section. The Japanese language uses Chinese characters (kanji) along with its native characters (kana) for writing. Individual Chinese characters have distinct meanings because they are based on pictures, examples:

The character for child (子) depicts a baby with a large head and both arms extended.

The character for write down (記) combines the character for word (言) and winding thread (己). This can be thought of as tying words together in writing.

The character for time and hour (時) is symbolic of the sundial as a reference point to measure time. Japanese readings: ji and toki. It combines the character for sun (日) and temple (寺). The temple is where they kept track of time by looking at the position of the sun in the sky. The sundial will be described in detail on Serial 11.

Just as we spell out in writing the number 178 as “one hundred and forty-eight”, the Japanese people will spell out in writing the Hindu-Arabic number 178 as (百七十八). The romanized version of the Chinese characters are (hyaku-nana-juu-hachi).

So the East Asian number writing system is not independent of Japanese, because they still depend on Chinese number characters to speak any Hindu-Arabic number.

In Mandarin, each Chinese character has a unique sound and meaning, therefore Chinese characters are words in their own right. But the Chinese characters used in Japanese have multiple sounds or readings (maximum four), which are used based on context.

Since spoken words are derived from the combined sounds of vowels and consonants, and in Japanese those sounds are associated with a Chinese character, the East Asian number symbols are numbers and numerals at the same time.

Numerals refer to the sounds associated with the fingers open. All Chinese characters are word symbols because they are based on pictures, while each letter of the Latin alphabet represent individual sounds that can be combined to form words.

So if you learn Japanese, you must learn how to read aloud the Japanese readings of East Asian number writing system.

The East Asian number symbols 1-10 are shown below:

Here are the characters for large numbers. Being large they are important for size presentation:

Here are examples of large numbers in the East Asian number writing system:

As we can see above, the characters 十, 百, 千, 万, 億 and 兆 indicate the size of the number. In this article we will call them the size indicators. The characters 一, 二, 三, 四, 五, 六, 七, 八, and 九 are used to indicate the quantity of those indicators.

Also 億 is ten thousand times bigger than 万. And 兆 is ten thousand times bigger than 億.

The arrangement of the reading is just like the English numerals. The numbers 1-9 are put in front of characters like 十 and 百 to indicate the size, examples:

三十 (thirty) and 五十三 (fifty-three)

This means that the number of characters used in a number cannot determine size directly, we have to look at the size indicators, which is similar to the Roman number writing system.

Other number writing systems

Since ancient times almost every culture in the world has its own number writing system:

1. Ancient Egyptian
2. Babylonian
3. Mesoamerican (Mayans)
4. Thai (also based on the Hindu-Arabic number writing system)
5. Cyrillic (used by the Slavic peoples before they adopted the Hindu-Arabic system)

Why is the Hindu-Arabic number writing system very convenient?

As we can see in the table above, the Roman and East Asian number writing system is not convenient in everyday communication and in mathematics, due to their awkward size presentation system.

They don’t have the place value system used as a size indication system. The size indication system of the Hindu-Arabic number writing system is the place value system. The place value system works like an abacus or a slot machine. The quantity of number characters used in one number is the indicator of size. These two properties make it very convenient to use.

So was selected for everyday practical use in mathematics due to its more efficient and orderly size presentation system.

Just imagine what would life be like when we use the East Asian number writing system or the Roman number writing system in everyday life. It would be inconvenient. The most versatile number writing system is Hindu-Arabic due its place value system, that as mentioned in this article, it is now used in East Asian countries as well.

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