Unique Japanese

Japanese is not unique. As a human natural language it shares many similarities with every other language in the world, some more than others. But Japanese is unique, as it appears to have no common relatives, sitting as it does in its own language group. There have been various theories as to where it comes from, but none has been conclusive.

Numbers often a good way of determining the origin of a language as their social importance means that they cannot radically change from one generation to the next, and Japanese numbers show some unique properties.

In modern Japanese the Sino-Japanese numbers imported from China have all but replaced the native numbers, but the latter is clinging on for dear life as generic counting words up to ten.

ひとつ、ふたつ、みっつ、よっつ、いつつ、むっつ、やっつ、ここのつ、とお

The older forms were:
ひとつ、ふたつ、みつ、よつ、いつつ、むつ、やつ、ここのつ、とお

Believe it or not, there is a hidden pattern.

Going from one (ひとつ) to two (ふたつ）: hito→huta
Three (みつ) to six (むつ): mi→mu
Four (よつ) to eight (やつ): yo→ya
Numbers are doubled by changing the internal vowels.
Five (いつつ) to ten (とお) doesn't follow the rule, unless you take the stem of five to be つ, so it would be tu→to.

The first recorded person to notice this was a chap called 荻生徂徠 (1666-1728), so as far as we know, until that point nobody had realised that such a rule existed.

Finding the rule opens up new questions:

• Why does changing the vowel lead to doubling?
• Why don't five and ten follow the rule exactly?
• Is the same rule seen elsewhere in the language? 
• Are there any other languages that share the phenomenon?

The pattern is too consistent to ignore, but it is not shared by any other language that Japan has historically had ties with. Mysterious....

Actually, as unique as Japanese may be, the answers to some of these questions are more related to how similar the language is to others than how different it is. Similar phenomena can be seen in all natural languages. But it's still quite amazing that the two times table is hidden in the number system, and that hardly anybody notices.

References
数字とことばの不思議な話　窪薗晴夫 岩田ジュニア新書　（p.2～)
日本語　金田一 岩波新書　（上、p.51～)

Big numbers

Japanese has had the good fortune of inheriting the Chinese number system. The way of building higher numbers is so logical that a learner can pick it up very quickly, and it makes arithmetic much easier for children, because they are already well aware of the concepts of hundreds, tens and units by the time they start school.

Powers of ten, however, are not quite as logical. In fact, the usage of the higher powers are not universally agreed on in the kanji using world. There were 下数, using increments of 10; 中数 using increments of 10,000; and 上数 where each number name was the square of the previous. In Japan 中数 became standard in the 17 century, although apparently remnants of the different systems persist elsewhere.

From 1 to 10,000, each multiple of ten has its own name.
一 いち 1
十 じゅう 10
百 ひゃく 100
千 せん 1,000
万 まん 10,000

Then the numbers go up in multiples of 10,000.
億 おく 100,000,000 (10⁸ a hundred million)
兆 ちょう 1,000,000,000,000 (10¹² a trillion)
京 けい 10,000,000,000,000,000 (10¹⁶ ten quadrillion)

That's about the limit as far as useful numbers go, but they do go much higher!
Even from 兆 (portent, omen) and 京 (capital city) characters are being reused. There isn't always a clear explanation as to why a particular kanji was chosen, as they are most likely phonetic borrowings.

垓 がい　10²⁰ The character means boundary or limit.
禾予(as one Kanji) じょ　10²⁴ The character for this is so rare that it isn't even in the basic JIS character set. The original kanji was 秭, which means 'piling up'. When writing this, I found that I could paste the kanji in the editor, but it wouldn't display on the published post.
穣 じょう　10²⁸ Lush, abundant.
溝 こう　10³² A ditch or narrow waterway.
澗 かん　10³⁶ A mountain stream. Two water related kanji in a row. Is there a pattern coming up? Sadly, no.
正 せい　10⁴⁰ Usually means 'correct', but has a minor meaning of 'long' which could be why it is used.
載 さい　10⁴⁴ Load or carry. Nothing could possibly carry anything this big! It also means write down or print, so is more likely to have the meaning 'something so large it cannot be written'.
極 ごく　10⁴⁸ Limit, extreme. The absolute highest number ever! Hang on a minute....

After that, Buddhism was clearly a major influence.

恒河沙 ごうがしゃ 10⁵² 恒 is a kanji transcription of the Sanskrit name for the Ganges, 河 is river and 沙 means 'sand', so the whole thing is 'the number of grains of sand on the River Ganges'. Quite poetic, really.
阿僧祇 あそぎ 10⁵⁶ From the Sanskrit for 'more than can be counted'
那由他 なゆた 10⁶⁰ From the Sanskrit for 'an extremely high number'
不可思議 ふかしぎ 10⁶⁴ 不可 is 'impossible', 思議 is 'conjecture' or 'guess'. An unimaginably large number!
無量大数 むりょうたいすう 10⁶⁸ Originally two words, 無量 is 'unmeasurably huge' and 大数 is 'a big number'. So together they make an gigantastically meganormous number.

100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

 Still quite a bit smaller than a googolplexian, and slightly less than the total number of atoms in the universe.

Special birthdays

There are some birthdays that have special names in Japanese, although the significance is more often word play (or kanji play) than a significant milestone.

還暦 かんれき is 60 years old. 還 means 'to return' and 暦 means 'calendar'. The Chinese system of naming years after twelve animals is well known, but there is a lesser known cycle of ten 'heavenly stems'. The detail of this is for a different post, but the two systems combine together to create a 60 year cycle. Therefore, after 60 years you have lived through a full cycle, and the calendar returns back to the beginning again.

古希 こき is 70 years old. 古 means 'old', but not an old person, and here means 'long ago'. 希 means 'wish' usually, but it can mean 'rare' which it does here. The original way of writing the kanji with this meaning was 稀, but 稀 is now usually abbreviated to 希. The word comes from a poem: 
酒債は尋常行く処に有り 人生七十古来稀なり
Everywhere I go, a bar tab is common thing for there to be; a man who lives to 70 is a rare thing since long ago.
Basically, the man travels a lot and just as sure as he'll run up a debt in a pub, he'll not run into a man that's over 70.

喜寿 きじゅ is 77. 寿 means '(long) life'. 喜 means 'delight', and in Japan has an abbreviate form that looks like 七十七 (7, 10 and 7: 77) arranged as one character.

傘寿 さんじゅ is 80. 傘 umbrella may seem like a strange choice, but the character can be abbreviated to 仐, which is 八 (8) and 十 (10), hence 80.

米寿 べいじゅ is 88. Why 米, rice? Again it's the character's form. The top two dashes form an inverted 八, the cross is 十 and the bottom two strokes form a second 八. 88!

卒寿 is 90. そつじゅ It's a bit late for graduating, but 卒 (most commonly seen in 卒業) can be abbreviated to 卆, which is 九 (9) and 十 (10).

白寿 はくじゅ is 99. 白, white, isn't abbreviated to anything resembling kanji numbers. If 百 is 100 and 一 is 1, removing 1 from 100 leaves 99; removing 一 from 百 leaves 白. Therefore, 白 means 99. Clearly.

There are special names for other ages as well, but these are the most common ones. One thing to remember is that the ages are normally based on the old method of counting years: a new-born baby is one at birth, and you add a year at the new year. So you're actually 米寿 at 87.