We write in base ten or base one thousand or a blend of the two, and we speak in base one thousand.

Consider 999,999,999 : one short of a billion. We say ‘nine hundred ninety-nine million nine hundred ninety-nine thousand nine hundred ninety-nine’. What we say, from a certain intellectual perspective, is not base ten but base one thousand.

If we think of ‘nine hundred ninety-nine’ as the name of a base one thousand numeral, one of nine hundred ninety-nine such numerals with the smallest being ‘one’ and the biggest being ‘nine hundred ninety-nine’ it really does look like base one thousand, albeit with numerals whose names are built up out base ten names. ‘Nine’, ‘ninety-nine’, ‘nine hundred’ , and indeed ‘nine hundred ninety-nine’ are all base ten numbers. But ‘nine hundred ninety-nine thousand’ is base a thousand. And so is ‘ten thousand’.

In base ten that quantity would be called ‘one myriad’, or ‘one’ followed by some other single word that means ten to the power four. In true spoken base ten, each power of ten has its own name. Up to nine thousand nine hundred ninety-nine it’s impossible to tell whether we are speaking base ten, or base one thousand, or base ten thousand for that matter, or any base higher than a thousand. Up to nine thousand nine hundred ninety-nine, it could be base one thousand one. Or base one million. Or base one million and one. As soon as you hear ‘ten thousand’, you know it is base one thousand.

What about how we write ‘base ten numbers’. Well 999,999,999 can be looked at at least two ways. One way is to ignore the commas as mere placeholders. If you were from Mars and watched someone or some machine count in writing 1, 2, 3, 4, … up to 999,999,999 that it was base ten could not be ruled out by you. If on the other hand the commas are taken to be not mere placeholders but separators that indicate where the (three) numerals (aka digits) begin and end, then 999,999,999 being a base one thousand number cannot be ruled out.

In conclusion, when spoken it is unclear what base it is, up to ten thousand whereupon it becomes clear that it is base one thousand, and likewise written long hand. When written as digits with commas (or spaces, or periods i.e. full stops or anything else used in there place) it is unclear which base it is at all times. When written without commas, ‘ 999999999’ it looks like base ten, although it could also technically be any base bigger than base 999,999,999.

That’s unclear, base one thousand, unclear, base one thousand, unclear, and finally more or less clearly base ten. Three unclear cases, two base one thousand cases, and one more or less clearly base ten (and you need to write it without the commas). So there are more ways that is is base one thousand than base ten, overall.

My favorite activity is learning new things.