大数—big numbers

The fastest supercomputer in Japan is at the RIKEN institute in Kobe and is called the K-computer or kei-computer (京コンピュータ).

kei-computer

With 80,000 8-core processors, using an incredible 10 MW of power, it was the fastest computer in the world when it was built in 2011, and 4 years later it is still the 4th fastest. According to Wikipedia, it uses a “proprietary 6-dimensional torus interconnect called Tofu“.

The reason it’s called “kei” is that 京 kei is the Japanese word for 10 quadrillion (10 to the power of 16). And the fact that Japanese has a word for 10 quadrillion is a fascinating thing in itself. Because 10 quadrillion is a very, very large number. It’s approximately the number of meters light travels in a year: one light year is one kei meters. But it is not the largest number word in Japanese – not by a long shot.

Learners of Japanese will be very familiar with the word 万 man meaning 10,000. 1 man yen is equivalent to about 100 dollars or euros, so when you ask about the price of a nice hotel room, an airfare or a car, or the population of a town or city, you’re likely to hear the word man.

The next number word is 億 oku—100 million. While it’s not as common as man, it still crops up fairly often. 一億円 1 oku yen is equivalent to about a million dollars or euros, so you’ll hear it on the news, talking about company profits or budgets, or even the price of an expensive house or apartment.

In fact, the word 億ション oku-shon is used to mean a luxurious apartment. This is a bit of Japanese wordplay. You see, the Japanese word マンション manshon (from English “mansion”) means a large apartment or apartment building. But wouldn’t it be even more impressive if, instead of a “man-” (10,000) shon, you had an “oku-” (100,000,000) shon?

According to Statistics Japan, the population of Japan is 1億2682万人 — that’s 1 oku 2 thousand six hundred and eighty two man people, or 126.82 million. (That example may give some insight into how confusing it is to translate numbers between Japanese and English, even if you know both languages perfectly, which I don’t. Understanding Japanese numbers is very challenging, calling on mathematical as well as linguistic comprehension skills.)

After 億 oku comes 兆 chou—one trillion. This is a big number, but you’ll still come across it, thanks to the fact that the yen is a relatively low-value unit of currency. National budgets and some large infrastructural projects are measured in 兆円. The new maglev Shinkansen line from Tokyo to Nagoya is expected to cost around 9 chou yen.

So what’s bigger than chou? That’s where we meet our old friend 京 kei, ten quadrillion. And until the kei computer was named, I had never heard this number used in real life. It far exceeds the entire world’s money supply. But in 2011, the kei computer was clocked at a speed 10 petaflops per second, which is 1 kei flops. And that’s where it got its name.

And there’s a whole world of numbers after kei. In the Japanese tradition of recreational mathematics, wasan, a 17th-century arithmetician called Yoshida wrote a textbook, Jinkouki, that starts by setting out the names of large and small numbers. I don’t know whether any numbers larger than kei are ever used nowadays, and I seriously doubt that anyone would understand them.

1 垓 gai is 100 quintillion, or 10 to the power of 20. That’s far more than the number of animals in the world, including all the tiny insects and teeming krill in the sea. After that, the numbers continue to go up in powers of 10,000. For example, 1 穣 jou (10 to the power of 28) is about the number of atoms in my body, and if you wanted to estimate the number of atoms in the whole world, that would be around 百極 a hundred goku.

What’s the largest number name in Japanese? The honour goes to 無量大数 muryoutaisuu which is 10 to the power of 68, and appropriately means uncountable large number.

So where did these absurdly large number names come from? Did Yoshida simply invent them, or was he drawing on an existing tradition? I don’t know for sure, but there seems to be a connection to Sanskrit and Buddhism. Wikipedia tells me that the ancient Indian passion for large numbers extended to naming extraordinarily large numbers. Some of the Japanese number names come from Sanskrit, while the word 恒河沙 gougasha, meaning 10 to the power of 52, refers to the constant sands of the Ganges River.

 

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