Number systems (was: Picto & Dil)

On Monday, April 18, 2005, at 01:36 , Henrik Theiling wrote:

> Hi!
>
> Ray Brown <ray.brown@...> writes:
>> ...
>> In other words, just add the plural ending to the units - just like
>> Schleyer's Volapük! Arie de Jong's reformed Volapük is better than Dil in
>> this matter. He introduced the word _deg_ for 10, and the other tens are
>> formed in the same way as Esperanto (and modern Welsh :) by combining the
>> words for 2, 3, 4 etc with 10, thus:
>> teldeg = 20, kildeg = 30, foldeg = 40 etc.
>
> And what's '200' in this lang?  I suspect it is tel + another special
> word (teltum maybe like in Volapük)?
Yep - same in both versions of Volapük.

>  What's '2000'?  Again tel +
> another special word (maybe 'telmil')?  But '20000' is totally
> different (like 'teldegmil')?
Yep

>  And the next level of base words is 'a
> million', 'a billion', etc? (balion, kelion, ...)?
I have no information about this - I presume that this was left the same
in reformed Volapük. Also I assume _kelion_ was 'billion' in the older
German & British use of 'a million millions', and not the American (and
now IME contemporary British) use of a 'thousand millions'.

> I still don't like this specialised treatment of a few exceptional
> bases (like 10, 100, 1000 in many IE langs and 10, 100, 1000, 10000 in
> most East Asian langs) with a second level of special bases (e.g. a
> million in English or '100 million' in Japanese).  It introduces an
> asymmetry and makes translation of large numbers between, say,
> Japanese and English were hard.  Try translating '123,456,789' from
> English into Japanese.  That's very painful.
I know - but I do not think either Fr Schleyer not Arie de Jong were
familiar with counting in east Asian langs    :)

> My approach that originally for Tyl Sjok uses a base and exponent
> representation.  Much more symmetry there:
>
>    (zero ten) three = 3,
>    (one) ten  three = 30,
>    two   ten  three = 300,
>    three ten  three = 3000,
>    four  ten  three = 30000
>    etc.
>
>    Stuff in () is optional.
>
> It's quite simple to translate between this and English, I think.
> Unfortunately, there is no empirical data about this claim. :-)
>
> (The above number would be
>    'nine ten one two three four five six seven eight nine'
> in Tyl Sjok, BTW.  Erm, with all words directly translated, of
> course. :-))
In other words: 0.123456789e9     :-)
or, in Tyl Sjok:
{exponent} ten {mantissa}

It's neat, but how easy this is the 'person in the street' I don't know -
as you say there is a lack of empirical data   :-)

I guess if the exponent is greater than 9, then we'll have 'ten' expressed
twice, for example
ten one two ten three four five six seven = 0.34567e12

> Errrm, all this is not an auxlang argument for me, but a purely
> artistic, esthetical issue.
So I have understood.

> I only feel that auxlangs, with their
> special design goals, are one class of langs thot should have some
> similar ideas.
They should certainly be aware of the problem if they are supposed to
global. But the prefixes for SI units are based on the 1000 division: ...
pico-, nano-, micro-, mili-, kilo-, mega-, giga- etc and that might
suggest keeping a similar system in an auxlang - but I'll leave that to
that other list  ;)

>  OTOH, I also feel that highly abstract artlangs like
> Ithkuil should do better than natlangs ('better' = 'symmetric')
> instead of using complex but asymmetric number systems.
Conlangs can do all sorts of things with numbers (and indeed some do) -
they do not even have to stick with base 10. Indeed, if I ever get around
to designing an artlang, I suspect I would not use boring ol' base 10   :-
)

Ray
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