Numbers: Their Tales, Types, and Treasures.

Chapter 3: Numbers in History



Egyptians, and similarly the Greeks and Romans, used an additive principle for writing numerals. That is, the symbols for one, ten, hundred, and so on are repeated as often as necessary to represent a number. Consider, for example, the Roman numeral MCCCXXIII. It has one symbol for “thousand” and repeats the symbol for “hundred” three times, and the symbols “ten” and “one” as often as it is necessary to represent 1323. The same number in Egyptian hieroglyphs is shown in figure 3.8, illustrating the same “additive” method of constructing numerals.


Figure 3.8: Egyptian and Roman additive system.

About three thousand years ago, the Chinese went a step further and developed a multiplicative-additive scheme. In its present form, this method of writing numerals has the number symbols shown in table 3.4:

















Table 3.4: Chinese number symbols.

As with all other Chinese symbols, these signs represent words. They are just written forms of the spoken numbers, not separate kinds of symbols. Hence 七 corresponds to seven rather than 7.

In spoken language, the Chinese use a numeral system, essentially following the construction principle shown in table 2.1 in section 2.9. The written numerals are just the translations into a written form of the spoken number words. Additionally, the verbal scheme uses multiplication and addition at the same time.

Placing one of the symbols for 1 to 9 after one of the symbols representing the powers of 10 implies addition:

十五 = 10 + 5 = 15, 千五 = 1000 + 5 = 1005.

Placing one of the symbols representing the numbers 1 to 9 before the higher units indicates multiplication:

五十 = 5 × 10 = 50, 五千 = 5 × 1000 = 5000.

You can see that the Chinese system is different from our written numeral system, but nevertheless is very similar to our way of pronouncing numerals.

For other Chinese numerals, the principles of addition and multiplication are combined, as we do in spoken language. Hence, it is easy to form longer number words. For example,

5724 = 五千七百二十四
( = five-thousand seven-hundred two-ten four).

For even higher numbers, the Chinese used the symbol for ten thousand as a new unit. Hence, the numeral for five million would have been (using the multiplicative principle)

5,000,000 = 五百万 ( = five-hundred ten-thousands).

We would probably confuse this with 510,000, but it actually denotes a quantity of five hundred “ten-thousands”—that is, 500 × 10,000 = 5,000,000. Similarly, 一万万 would be 1 × 10,000 × 10,000, which is one hundred million. This method of writing numbers is still in use today. We can see that a symbol for zero is absolutely not needed to represent a number unambiguously.