"Unbelievable" is actually a quantifier? Netizen: It turns out that "100 million" is really a small goal!

The picture shows the inner page of "Mathematical Enlightenment" written by Yuan Dynasty mathematician Zhu Shijie. (Picture provided by the author)

Recently, a video of a mother teaching her children about units of quantity went viral, and many netizens exclaimed that "incredible" is actually a unit of quantity. How big a number does "incredible" represent? It represents 10 to the 120th power, which is 1 followed by 120 zeros. If a person wants to count from 1 to 1 billion, which is 10 to the 9th power, even if he keeps counting without eating or sleeping, it will take about 30 years. The number "incredible" is 10 to the 120th power, and it will take several lifetimes to count it, which is really incredible.

In ancient China, ten thousand was a very large number.

More than 2,000 years ago, the ancient Greek philosopher Pythagoras said, "Everything is number." Coincidentally, at that time, Duke Zhou asked mathematician Shang Gao about numbers and exclaimed, "How great is the word number." How big is the number?

In the oracle bone inscriptions of the Shang Dynasty 3,000 years ago, in addition to one, two, three, four, five, six, seven, eight, and nine, there were already records of the numbers of ten, hundred, thousand, and ten thousand. They are all decimal numbers, and 10,000 is equal to 10 to the fourth power. Xu Yue of the Eastern Han Dynasty recorded the Chinese numerals for quantity very completely in "Records of Numerology" (190 AD). These numerals are ten, hundred, thousand, ten thousand, hundred million, trillion, jing, gai, zi, rang, gou, jian, zheng, zai, and ji. From ten to ten thousand, it is the decimal system. Starting from ten thousand, it is the permadecimal system, that is, ten thousand is one hundred million, one trillion is one trillion, and ten thousand trillion is jing... 100 million is equal to 10 to the eighth power, 1 trillion is equal to 10 to the twelfth power, 1 jing is equal to 10 to the sixteenth power, and 1 ji is equal to 10 to the 48th power.

In ancient China, "ten thousand" was a very large number, so in idioms, there are good words to express "a fortune of ten thousand", "a long and arduous journey", "all-embracing", "a life of ten thousand years"... There are bad words to express "a thousand kinds of idle sorrow", "a heart pierced by thousands of arrows", "a crime of ten thousand deaths"... After the reform and opening up, a new term appeared in China - "ten thousand yuan household", which refers to some wealthy families with an annual income of ten thousand yuan or a deposit of ten thousand yuan in the bank, which was very enviable at the time. With economic development and social progress, people's income has increased and their living standards have improved, and "ten thousand yuan household" is no longer a synonym for wealth.

"Incredible" comes from Buddhism

In 2016, "a small goal of 100 million" was even selected as one of the top ten Internet terms of the year. In ancient Chinese arithmetic, there were many more units of numbers than 100 million. There was a large number unit called "incredible". In the Chinese dictionary, "incredible" means unimaginable, difficult to understand, and also contains the meaning of mystery and beyond common sense.

However, most people would not think that it was a mathematical counting unit in ancient China. What is the origin of this magical counting unit? The decimal units in ancient my country were from one to ten, hundred, thousand, and ten thousand. Ten thousand is one hundred million, which is the ten thousand system. Later, trillion, jing, gai, zi, rang, gou, jian, zheng, zai, and ji were all ten thousand system, as recorded in the "Mathematical Enlightenment" (engraved in Yangzhou in the third year of Dade in the Yuan Dynasty) by Zhu Shijie, a mathematician in the Yuan Dynasty. After "ji", there are ten thousand and ten thousand digits of Ganges sand, asamkhya, nayuta, and inconceivable: "Ten thousand ji is called Ganges sand, ten thousand Ganges sand is called asamkhya, ten thousand asamkhya is called nayuta, and ten thousand nayuta is called inconceivable." These counting units were compiled by Zhu Shijie with reference to the Buddhist classics "Avatamsaka Sutra" and "Sangqi Vinaya". However, after the inconceivable number, there are also infinite numbers, large numbers, Quan Shixiang, Gugol, Gugolplex... What a great number!

The number of numbers in the world is endless, and human beings’ understanding of numbers is also endless. From this point of view, one hundred million is really a small goal!

(The author Wang Yusheng is a member of the National Education Advisory Committee, former director and researcher of the China Science and Technology Museum)