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From: Pierre Abbat <phma@bezitopo.org>
To: lojban@googlegroups.com
Subject: Re: [lojban] numeric bases
Date: Mon, 17 Aug 2015 00:38:38 -0400
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On Friday, August 14, 2015 17:46:34 Ilmen wrote:
> I don't like much the fact that {ju'u} is an operator though; I think it
> would have been better for it to be a digit particle. If mekso operators
> operate on abstract numbers, then {ju'u} should rather be a digit
> particle like {pi'e} or {ji'i}, because it acts at the digit string
> level, before an abstract number is extracted from the symbolic digit
> string.
> 
> First you have a sequence of digit symbols representing the positional
> notation of an abstract number with a set of digits, whose size is the
> number base/radix. In order to extract a number from a digit string, you
> need to know which number radix it is encoded with (the radix may either
> be explicitly part of the number symbolic notation or otherwise be
> inferred from context, for example if there is a previously specified or
> traditional default radix).
> 
> It's why I think the device for indicating the number radix should be
> part of the number symbol (so a PA cmavo) and not some operator that
> would take abstract numbers as an input (such as VUhU cmavo).

I agree.

> As for the default base, I wouldn't much like it to defaults to ten by
> definition, as it wouldn't be culturally neutral (although ten is by far
> the most common number radix nowadays, some cultures do use other
> radices for encoding their numbers). I'd be in favor of adding a cmavo
> of class MAI for specifying the default number radix for the following
> text until another default is given; in lack of any default and explicit
> radix, the number radix would be inferred from context (for example the
> standard default in effect where and when the text has been produced).

As far as I know, the most commonly used base today for general numeration 
outside of computers, and other than 10, is 20, used by 40% of the population 
of Guatemala (whose money has numbers written in base 20), many people in 
Mexico, and a growing number of people in El Salvador. Lojban doesn't have 
digit words for 16 through 19. Mayan languages have teens (e.g. ox-lajuj=thir-
teen), and Nawat has words for 5, 10, and 15 to which 1-4 are added, but maybe 
some other language in the area has unanalysable digits up to 19.

The other commonly used base is 60, only for times and angles. The ancient 
Babylonians used separate symbols for tens and units. I don't know of anyone 
else who used base 60 for general purpose and didn't pick it up from 
Babylonians or Sumerians.

Pierre
-- 
The gostak pelled at the fostin lutt for darfs for her martle plave.
The darfs had smibbed, the lutt was thale, and the pilter had nothing snave.

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