> 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'?
>
> > Units
> > -----
> >
> > So that's the basic system. I will post the incorporation of
> > units later. If you are interesting, look at
> >
> >
http://www.theiling.de/projects/s2/grammar2.ps.gz
> > or
> >
http://www.theiling.de/projects/s2/grammar2.pdf
> >
> > page 75.
> >
> >
> > Now, Qthen|gai works exactly the same (of course, the number words are
> > totally different). You can see some samples at:
> >
> >
http://www.theiling.de/projects/s7/s_05#06_02
> >
> > If you are still reading, please make some comments! :-)
>
> 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
> ===============================================
>
http://home.freeuk.com/ray.brown
> ray.brown@freeuk.com
> ===============================================
> Anything is possible in the fabulous Celtic twilight,
> which is not so much a twilight of the gods
> as of the reason." [JRRT, "English and Welsh" ]
>