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The Sand Reckoner in Your ‘Langs

From:Alex Fink <000024@...>
Date:Sunday, April 5, 2009, 5:55
On Sat, 4 Apr 2009 16:18:49 -0400, Eldin Raigmore <eldin_raigmore@...>

>Questions: >How do you name very-large numbers in your conlangs and natlangs?
Perhaps surprisingly for a math person like me (or perhaps not?) I don't even know how to name vaguely-large numbers in most of my serious conlangs. Pjaukra is base 12 and I don't know the word for 12^3 (_undu_ 12, _sarda_ 12^2). In Sabasasaj I haven't decided whether to use base 120 (subbase 10, though using lots of fractions so not the canonical subbase system) or no exponential base at all but something more irregular, and in particular _phian-tu_ 120 is my largest number word. In A:jat he-Heloun, which is base 10, I have (ASCIIfied) _k@i_ 1, _ro_ or _k@ir^_ 10, _ki:ju_ 100, _(k@i) taihec^_ 1000. 1000 is a unit, so (quoting from ) | These methods go so far as 10^6-1. Beyond that there are no standard | words. There does exist a sequence of names for higher numbers | (syntactically like _taihec^_), namely _motnja_ N:S 'zillion', | _motnja lja`_ lit. 'second zillion', _motnj @lzy_ lit. 'third zillion', | etc. The catch is that different traditions assign them different | values: for some the nth zillion is 10^(6n), for others 10^(4n). | If one wants an unambiguous 'million' one's best recourse is | _aftaihec^ taihec^_ 'thousand thousands'. This is of course inspired by the contrast of the short and long count systems for the English "illion" numbers.
>But IMO successive-squaring is probably more “natural” than the European >method of having a geometric sequence, each new “unit” being a set multiple >of the next smaller one.
I'd disagree, if you use "natural" with the sense it has in "natural language" here. I analyse this pattern of having a geometric sequence as just another exponential base. You'll know of natlangs with base-subbase systems, say base 20 and subbase 5 (so that the numbers less than 20 are formed as 5a+b); so short-count English just has base 1000 and subbase 10. Do you know Donald Knuth's -yllion notation? This is the only instantiation of your suggestion I can think of that I've seen before. But really, big number names are just cumbrous, aren't they? For powers of the base, "ten to the fifteenth" seems an easier way to go than "quadrillion". So when I'm wearing my non-naturalist hat I can't think I'd bother with big number names either; better just a sufficiently lithe way to express exponentiation. (And I probably wouldn't use them in number names as throughgoingly as English does either. For example in my language with Robert Barrington Leigh, which was base 16, no positive powers of the base had names; numbers were purely and simply digit strings. Alright, this is maybe bad in that you might lose count of how long a number is and so not know its order of magnitude, if you care about that.) Alex