Meet the G that killed me

The standard Japanese counting units go like this:

KanjiPronunciation10 to the power of ...

(There was actually an older system whereby the number of zeros kept increasing at the same rate, so that, for example, a kei was only 10,000,000 instead of 100,000,000,000,000,000,000, but since the Edo period at least things have worked as described in the above table.)

Obviously, going up to one gai is enough for almost any conceivable purpose to which counting might be put. Nerds, however, have always been with us, and nerds crave more, more, more useless definitions. Thanks to the tireless work of these geeks of old, an even more magnificent set of pointlessly vast numbers crowns the standard ones. This is the series as described in in YOSHIDA Mitsuyoshi's 1627 mathematics textbook Jinkouki (『塵劫記』):

KanjiPronunciation10 to the power of ...
* As one character -- can't find this in Unicode, and according to the Iwanami Bunko edition it's probably a mistake on Yoshida's part anyway. But I can't find the correct character (禾市) either.

10 to the power of 48: that's a big number. Surely Yoshida would stop there? But no! He presses on, assigning specific values to various phrases from the Lotus Sutra that were never meant to be treated that way:

   Kanji   Pronunciation10 to the power of ...Meaning
恒河沙gougasha56"Sands of the Ganges"
阿僧祇asougi64Transliteration of Sanskrit word meaning "uncountably large number"
那由他nayuta72Transliteration of Sanskrit word meaning "extremely large amount"
無量大数muryoutaisuu88"Infinitely large number" (oh, the irony)

You'll notice that the number of zeros starts increasing by eights instead of fours at the start of this series. This was, it seems, a quirk of Yoshida's, and nowadays it's more usual to stick with the fours all the way through, so that a fukashigi is only ten to the power of 64.

But, seriously, that's only a trillion times greater than the observed universe's total mass as measured in kilograms (at least according to some site I it-chou-muryoutaisuu'd up just now). What possible use could such a tiny number be? Silly modernizers and their lack of vision.

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Mark S.:

I didn't have any luck with 禾 + 予. But I did find 禾 + 市 (Unicode 25791, GB+ 9639e633). It's in the Hanyu Da Zidian: vol. 4, p. 2601, entry 5. I'll paste the character here, but I doubt it will appear as it should: 𥞑.

If Yoshida had kept going just a little further, to 10 to the 100th, Google might have had yet another alternative to 谷歌 (Gǔgē). But I suppose that wasn't a big priority for a company that didn't use "googol" in the first place.


in chinese, 秭 [zi3] classically means only 10^9 (a far cry from 10^24). i suppose the more advanced a civilization gets, the higher they would like to be able to count. in another couple thousand years, will it then represent 10^50?


Mark S. -- thanks! It didn't come through, but I'm glad it exists. And yeah, I too felt a slight pang of frustration when I realized he didn't quite make it up to the googol...

Andy -- Thanks! That's the other character that the IB edition identifies as the Chinese alternative. As for the 10^9 thing, I guess that's from the older system I mentioned at the top, where the orders magnitudes increased one at a time instead of jumping by 4s:

man = 4oku = 5chou = 6kei = 7gai = 8jo/zi3 = 9


I had been wondering what was after 兆 and 京 in Japanese for a while, but had never bothered to look it up. Beyond this though, I don't really think it's very useful, since only a technical or scientific application would ever use a number that big. Scientists generally use 10^n when numbers get really big, so in Japanese that would just be 十のn乗, if I'm remembering my technical Japanese correctly.

Even very-large-number theoretical mathematics generally uses much more concise ways to write very large numbers, again using a power system. Very large primes are usually expressed as 2^n-1, and the number 9^9^9^9 which is so big we can't even calculate how many digits it has! (Even larger than googolplex, incidentally) This site talks about nomenclature for increasingly larger classes of very large numbers.


Oh yeah, totally useless. And how much more so in Edo times...

Thanks for the link, some really fascinating stuff in there!

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