Re: Types of numerals; bases in natlangs.

Henrik Theiling wrote:

>My number system first developed for Tyl Sjok system only uses base
>words up to ten if you use base ten numbers and encodes long numbers
>very efficiently without needing and words for large numbers.  It uses
>a base-exponent notation, just as you write mathematically.  This is
>then applied recursively.  Basically, number work like this:
>
>    Number ::= Exponent Base Sequence_of_digits
>
>Where Exponent is itself a Number. Base is the base word, (often
>enough, this is therefore '10').  Any of the three Exponent, Base and
>Sequence_of_digits may be empty if trivial, but at least one of them
>must be given.
>To understand the system:
>   20 = kjox kul          = '10 2'
>   12 = kjox ling kul     = '10 1 2'
>
>  100 = kul kjox          = '2 10'
>  300 = kul kjox hen      = '2 10 3'
>  120 = kul kjox ling kul = '2 12 1 2'
So Base defaults to 10, Digits defaults to 1 followed by x zeroes, and
Exponent defaults to the number of digits (except a leading 1 does not
count)? So then, 1.2 would be "ling kjox ling kul", right?


>And now:
>
>  3*10^20    = kjox kul kjox hen    = '10 2 10 3'
>  10^300     = kul kjox hen kjox    = '2 10 3 10'
>
>Is this understandable?
Definitely ambiguous. There will be no way to tell where the border between
basal and digital (?) numbers are. "Hen kul" could be either 2^3 (digits
omitted), 3+2 (exponent omitted), 200 (base omitted) or maybe even 32
(exponent and base both omitted?) Even if you disallow digits if the base is
something else than 10, you still get cases like "kjox kul kjox hen" having
an alternative analysis as  "30^20".

OTOH, if Base must always be 10, I don't see why it needs to be specified at
all; you can do with just a marker for "number ends". Expressing it as a
right parenthesis and adding left ones for looks: (((2)25)1997845188) =
1.997845188 * 10^250.

Are there any other instances where Base can be omitted than the natural
numbers 0 thru 9? Will "hen kul" mean anything??

John Vertical

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