Monday, 18 June 2018

Japanese Numbers

The New Job

Nowadays I'm working in medical research. One recent task was to internationalise some UI, then localise it into Japanese. With little in the way of a clue how to do this, but having built up some Audible audiobook credits over the spring months, I decided to take advantage of my three hour daily commute to learn a little about the Japanese language and culture. After all, there's every chance I'll soon have the opportunity to visit Japan on the company ticket, and I'd like to be able to speak to people in their first language, without causing humongous offence. So I bought a couple of Teach Yourself Japanese audiobooks.

Linguistic Regularity

Boy, did they do a job on me. You would never think, looking at the Japanese writing system, reputedly one of the most horrendously complex in the world, that this language could be a clean and tidy, logically lovable, stone fox. But I was soon smitten. I mean, just look at some of these features. There are no singular or plural nouns, there's just the noun. The verb to be, one of the most irregular in my native tongue, doesn't conjugate at all; it's just like I be, you be, he she or it be. Month names are like first month, second month, and so on. Dates are in perfect ANSI order: the greater subdivision always comes first, so it's year-month-day, or yyyy-mm-dd. Ideal for sorting by computer! There are only 47 syllables in the language, and every vowel is always pronounced the same.

Of course that's just the first flush of romance; eventually reality and entropy make themselves heard. There might indeed be so many welcome regularities in Japanese, but then they go and spoil it all by saying something stupid like "there are three levels of formality for every sentence", or "men and women speak with subtly different inflections." This last, together with the fact that most teachers of Japanese are female, has the interesting consequence that male learners usually, unwittingly, start off sounding quite effeminate.

Numeric Logicality

But then there are the numbers. The Japanese counting system is beautifully simple and regular, with very few exceptions in structure and pronunciation. Again, the first idealistic impression is somewhat spoiled by reality, this time by the introduction of "counters". These are little particles which must be appended to numbers, when counting objects. Surprisingly, the particular counter used is often based upon the physical appearance of the thing being counted. Then again, certain numbers cannot be used in counting certain types of thing, but must be substituted with other special purpose counters...

Still, the basic counting system is quite easy to learn, interesting too, and if nothing else can at least be used while you count through the steps of kata in your chosen martial art (mine is press-ups-do). I considered it potentially a big win, both mathematically and scientifically, to count as high as I possibly could using this system. As a study aid I made a little text file, delighted to realise that all the kanji characters and superscript numerals available in unicode were supported in Notepad. Printed out and laminated in A6, it became a pocket reference card. Later in A4 format, it would become a placemat suitable, used in conjunction with a transparent plate, for learning your ichi-ni-san while eating your sushi.

Original Text Version

The version below can be copied to the clipboard as text, then saved in Notepad. Just remember to select one of the Unicode options, such as UTF-8, from the Encoding drop-down list.

0  〇/零  zero/rei  JAPANESE NUMBERS REFERENCE CARD  * Learn these exceptions!

       1            10               100              1,000           10,000
1   一 ichi       十 jū            百 hyaku         千 sen        一万 ichi-man
2   二 ni       二十 ni-jū       二百 ni-hyaku     二千 ni-sen     二万 ni-man
3   三 san      三十 san-jū      三百 san-byaku *  三千 san-zen *  三万 san-man
4   四 yon      四十 yon-jū      四百 yon-hyaku    四千 yon-sen    四万 yon-man
5   五 go       五十 go-jū       五百 go-hyaku     五千 go-sen     五万 go-man
6   六 roku     六十 roku-jū     六百 ro-ppyaku *  六千 roku-sen   六万 roku-man
7   七 nana     七十 nana-jū     七百 nana-hyaku   七千 nana-sen   七万 nana-man
8   八 hachi    八十 hachi-jū    八百 ha-ppyaku *  八千 ha-ssen *  八万 hachi-man
9   九 kyū      九十 kyū-jū      九百 kyū-hyaku    九千 kyū-sen    九万 kyū-man

10⁵ 十万 jū-man       10⁶ 百万 hyaku-man       10⁷ 千万 sen-man

10⁸    10¹²   10¹⁶   10²⁰   10²⁴     10²⁸   10³²   10³⁶   10⁴⁰   10⁴⁴   10⁴⁸
億     兆     京      垓     𥝱/秭    穣     溝      澗     正     載     極
oku    chō    kei    gai    jo/shi   jō     kō     kan    sei    sai   goku

10¹² 一兆 itchō      8x10¹² 八兆 hatchō        10¹³ 十兆 jutchō †
10¹⁶ 一京 ikkei      6x10¹⁶ 六京 rokkei      8x10¹⁶ 八京 hakkei

10¹⁷ 十京 jukkei †     † Multiples of 10:  change -jū to -jutchō or -jukkei
10¹⁸ 百京 hyakkei ‡    ‡ Multiples of 100: change -ku to -kkei

10⁵²⸍⁵⁶       10⁵⁶⸍⁶⁴       10⁶⁰⸍⁷²       10⁶⁴⸍⁸⁰       10⁶⁸⸍⁸⁸
恒河沙         阿僧祇     那由他/那由多     不可思議      無量大数
gōgasha       asōgi        nayuta        fukashigi    muryōtaisū

How It Works

The first thing to do is memorise the top left column, digits 1 to 9, and 10: ichi, ni, san, yon, go, roku, nana, hachi, kyū, jū. Note that the horizontal bar along the top of a vowel just makes it sound "long" - some guides use double vowels for this purpose.

Next, to form the numbers 11 to 19, just use literally ten-one, ten-two, ten-three, etc. So that's jū-ichi, jū-ni, jū-san, etc.

Multiples of ten up to ninety are found in the second column: ni-jū (20) is literally two tens, san-jū (30) three tens, and so on. Intermediate numbers are simply concatenated or added together, so 42 is "four tens two", or yon-jū-ni.

It's a similar story for multiples of 100, found in the third column, although there are three little exceptions to be aware of - more or less subtle variations in pronunciation. I've marked these with asterisks. So although 3 is san and 100 is hyaku, 300 is not san-hyaku but san-byaku; note the hard 'b' sound here, and also the hard 'pp' in 600 (ro-ppyaku instead of roku-hyaku) and 800 (ha-ppyaku rather than hachi-hyaku).

Multiples of 1,000, as seen in the fourth column, also have exceptions marked at 3,000 and 8,000, although there isn't an exception for 6,000, which is just business as usual: roku-sen.

Chinese Roots

Reaching 10,000 there's another little surprise in store, and quite an important one. It might help a bit to think first about English powers of 10. Notice that 100 (one hundred) and 1,000 (one thousand) both begin with the word "one", whereas 10 (ten) and 10,000 (ten thousand) don't. But actually, there is an old English number "myriad", one of whose older meanings is literally ten thousand. We might therefore think of 10,000 as "one myriad", and in fact that's similar to what the Japanese, following on from Chinese tradition, actually do. Ten thousand is best translated into Japanese via "one myriad", hence ichi-man.

With that in mind, column five otherwise proceeds much as before: 20,000 is ni-man (two myriad), 30,000 is san-man, and so on without further exceptions. But we have just passed an important milestone here. Just as our big numbers tend to group themselves into powers of 1,000 such as thousands, millions, billions, trillions, and so on, each time multiplying by 10³ and adding another comma, so the oriental tradition is to partition into powers of 10,000, and groups of four digits. The importance of this structure is reflected in the use of the ichi (one) prefix for 10,000: not just man (myriad), but ichi-man (one myriad).

The same caveat will apply to all subsequent powers of 10,000. But before getting to those, look at the next few powers which are not multiples of 4, and don't need the ichi prefix. As shown immediately below the main table, we already knew how to construct:
  • one hundred thousand (100,000  = 10⁵ = ten myriad = jū-man),
  • one million (1,000,000 = 10⁶ = hundred myriad = hyaku-man), and
  • ten million (10,000,000 = 10⁷ = thousand myriad = sen-man).
Next, we shall alight upon the Big Sequence, the powers of 10⁴ spanning 10⁸ to 10⁴⁸ (one quindecillion!), listed in the second horizontal table.

To Infinity And Beyond (almost)

So, now we avail ourselves of the long line of Powers of Myriad (that's definitely the name of my next witching and wizarding trilogy, watch out JK). We have reached 10⁸ which is labelled oku, but since 8 is a multiple of 4, we have to prepend this with ichi. Thus, 10⁸, or a hundred million, becomes ichi-oku. Two hundred million is ni-oku. And so on.

Things chug along quite nicely until we reach one trillion, or 10¹². Everything we've covered so far leads to the expectation ichi-chō, until we stop and consider the clumsiness of that utterance. Surely that is the reason the wise Japanese have decided to contract it to itchō. Similarly, eight trillion becomes not hachi-chō but hatchō, while ten trillion is not jū-chō but jutchō (with the shorter u).

Similar exceptions apply to the next big multiplier, 10¹⁶ (which becomes not ichi-kei but ikkei), as well as multiples of this by 6, 8, 10 and 100. There is a pattern to the modifications in these cases, codified by the daggered comments in the bottom half of the reference card (or placemat).

Finally, we reach the bottom 3 rows of the card, where the only reliable historical sources contradict each other. In a denouement reminiscent of the war between American and British billions (see Wikipedia for details,, there's a forking schism in which the same terms are used to count, simultaneously and incompatibly, using multiples of 10⁴ and/or 10⁸, into an uncaring infinity. Of limited scientific use admittedly, but why not take advantage of the Creative Commons licence, and print out and laminate your own set of Japanese Numbers placemats?

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