Names for large numbers

Language Log on number delimitation. In the United States, we put commas between every three digits: 123,456,789. In Europe they use periods instead of commas, but in the same places.

In China, they group into sets of four digits instead of three: 1,2345,6789. (I've seen this a few times written with the commas, in English-language texts; it's very disorienting.) The ancient Greeks also did something like this: they referred to "myriad", "myriad myriad", and so on, where "myriad" is 10⁴. ("Myrio-" and "myria-" are also obsolete metric prefixes for 10⁴ and 10^-4 respectively.)

In India, they break into a low-order group of 3 and then groups of 2: 12,34,56,789. This reflects the structure of the language -- certain odd powers of 10 have names, with 10⁵ being "lakh" and 10⁷ being "crore".

In a way, though, we do the same thing, and least if you consider the etymology of the number names thousand, million, billion, trillion, and so on. (By "billion" I mean an American billion, 10⁹.) "Thousand" is somehow special; we're treating the first power of 10³ differently than all the others. The British system, where successive powers of 1000 are named thousand, million, milliard, billion, billiard, trillion, ... is more "logical". But shouldn't "thousand" be "thousard" or something like that? And "billiard" is also a name for that game where you hit the balls with the sticks.

There's also the Knuth -yllion notation, which answers a question that Poser asked: are there systems with groups that double in size? The answer is yes, although I don't think anyone seriously uses this system.