Re: Numbers in Qthen|gai (and in Tyl Sjok) [long]
| From: | Ray Brown <ray.brown@...> |
|---|
| Date: | Sunday, January 9, 2005, 19:45 |
|---|
On Saturday, January 8, 2005, at 09:56 , Henrik Theiling wrote:
[snip]
> 1) Different languages use different widths of blocks of digits
> to encode numbers.
>
> E.g. in English, you have words for 10,100,1000 and then reuse
> the smaller number to form 10000 (ten thousand). For this
> reason, separators are inserted every three digits (as in
> 10,000) to make reading easier. The larger numbers in English
> are all multiples of 1000.
We also of course read figures like 1900 as nineteen hundred; 1524 as
fifteen hundred (and) twenty four. We do not seem to do that with numbers
greater than 1999. for example 2005 is two thousand (and) five.
> In Chinese, Korean and Japanese, however, the major structuring
> uses *four* digits instead of *three* in English. So there is
> a word for 10 (shi), 100 (bai), 1000 (quan), 10000 (wan), and then
> 100000 is encoded as '10 10000' (shi wan). And 1 million
> is '100 10000' (bai wan).
>
> Therefore, it is quite hard to translate large numbers from
> Chinese to English and vice versa.
A good point - especially as the Chinese form about a quarter of the world'
s population and the culture's they have influenced (like Japanese &
Korean) count for even more.
> And there are even more complex systems like Hindi, which uses
> a mixed two and three digit system.
>
> I wanted to make it reasonably easy to use Tyl Sjok regardly of
> your L1 system.
A very valid point, and one which, I must confess, I had not considered.
Most clearly it should be one of things that designers of auxlangs ought
to consider - but IME so rarely do. Certainly it is something I must
consider in reference to Bax and Brx.
> The only chance I saw was to use the smallest
> denominator, i.e., the largest basic number is *ten* in Tyl
> Sjok.
>
> 2) Like in Chinese, I wanted number bases to be very similar to
> units.
>
> I.e. 50 = 5 10 (wu shi) in Mandarin. Here, 10 is the base and 5
> is the coefficient.
Just like the modern Welsh numeral :)
pum deg = 5 10 = 50
chwe deg = 6 10 = 60
saith deg = 7 10 = 70
[snip]
> 3) The system should be usable for science as well, so very large
> and very small numbers should fit into the system without needing
> changes.
Another very valid point.
> 4) The system should feel appropriate and easy to normal speakers.
> This might collide with 3), of course.
>
> I don't know whether I solved 4), but I think I solved the other three
> ones. :-)
>
> So the system I came up with works as this: for each digit of the
> number you want to say, use the sequence 'exponent base coefficient'
> and join them with the word 'and'. Any trivial things can be left out
> (like coefficient = 0 or exponent = 1). E.g:
>
> 500 = 2 10 5 in Tyl Sjok (that is 10^2 * 5 = 100 * 5 = 500)
> 50 = 10 5 (short for 1 10 5)
> 51 = 10 5 and 1
> 520 = 2 10 5 and 10 2
> 502 = 2 10 5 and 2
> 532 = 2 10 5 and 10 3 and 2
>
> The order is 'large exponent before small exponent', like in English,
> Chinese and probably many languages
Very neat! Tho as you remarked above, I do not know how appropriate and
easy this would be for the non-mathematical :)
> (I don't know whether there are
> some that *systematically* reverse the whole sequence of digits
Arabic - and I believe the Semitic languages generally. That is why
although Arabic is written from right to left, the numerals appear to us
occidentals to be written from left to right!
[snip]
> Because this form can become very long and explicit and since the
> exponent typically decreases by one in each step, there is a
> simplified form where you can give coefficients after you first
> defined at what exponent to start. E.g. instead of
> '2 10 5 and 10 3 and 2' you can say:
>
> 532 = 2 10 5 3 2
>
> And
> 520 = 2 10 5 2
>
> As you can see here, you need not give all digits at the end if they
> are zeros.
I wonder, however, the latter would be misunderstood by the
non-mathematical.
>
> You may need zeros now:
>
> 502 = 2 10 5 0 2
>
> If there are too many zeros in a row, you can use a mixed system:
>
> 56,000,023 = 7 10 5 6 and 10 2 3
>
> I hope you are still listening. :-)
Certainly - it is great to have something on topic :)
It is an interesting solution. Do you have any non-mathematical friends
you test the system on?
>
> Different Bases
> ---------------
>
> With this system, you need quite a minimal set of basic words for
> numbers, namely 0 .. 10 for a base 10 system plus the word 'and',
> making 12 basic words.
>
> To add a bit more, Tyl Sjok supports different basis as well. The
> smallest is 2 and the largest native base is 16.
So good for computer geeks as well ;)
>
> Large Numbers
> -------------
>
> For very large numbers, the system is recursively applied. E.g.
>
> 5.000.000.000.000 is 10 1 2 10 5
>
> I.e. the exponent is 12, which is '10 1 2' and then this is put in
> front of the base of 10 which is then multiplied by 5.
Neat - but does it meet '4) The system should feel appropriate and easy
to normal speakers'?
Certainly a neat solution - I just wonder how appropriate & easy it will
feel for 'normal' users? It would be interesting to find the reaction of
any such users.
But it has given me much to think about and it is great to have something
on topic :)
Ray
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