- Rejistanian does a mild example of that: Rejistani numbers have a kind of place value system without the zero:

1, 2, 3, 4, 5, 6, 7, 8, 9, [1](ke), [1](ke)1, [1](ke)2, ... [1](ke)9, 2[ke], ... 9(ke)9, [1](ry), [1](ry)1, [1](ry)2, ... [1](ry)[1]ke, [1](ry)[1]ke1 etc.

angular brackets show an optional component, round brackets indicate a sign in rejistanian, which is not in Unicode.

On 05.03.2013, at 01:44, Matthew George wrote:

> I was thinking about Roman numerals, and how terrible for performing

> mathematics that whole system is. Then it occurred to me that I've never

> encountered a conlang with a system anything like it. Toki Pona's is

> somewhat similar, but much simpler, and is obviously related to that lang's

> design intent. Pretty much all of the other variation I've heard about

> involves numerical bases. But the place-value system, complete with zero,

> is always what people seem to choose.

>

> I haven't looked at all that many systems. Do people ever make clunky,

> irrational, and old-fashioned systems like the Roman numerals? Or are the

> purposes of number systems so practical that most conlangers have no

> interest in making such a complex (no, baroque) method for doing math?

> Most other aspects of conlangs seem to be deliberately elaborated and

> intricate, reflecting how much weirdness is out there and how the

> complexity of a language isn't related to how materially-advanced its

> society is. But historically, most peoples had very basic math skills.

>

> I'd love to see counter-examples to the modern place-value system. Can you

> recommend any?

>

> Matt G. - On 4 March 2013 18:44, Matthew George <matt.msg@...> wrote:
> I was thinking about Roman numerals, and how terrible for performing

Sadly, I cannot provide examples of conlangs with entirely

> mathematics that whole system is. Then it occurred to me that I've never

> encountered a conlang with a system anything like it. Toki Pona's is

> somewhat similar, but much simpler, and is obviously related to that lang's

> design intent. Pretty much all of the other variation I've heard about

> involves numerical bases. But the place-value system, complete with zero,

> is always what people seem to choose.

>

> I haven't looked at all that many systems. Do people ever make clunky,

> irrational, and old-fashioned systems like the Roman numerals? Or are the

> purposes of number systems so practical that most conlangers have no

> interest in making such a complex (no, baroque) method for doing math?

> Most other aspects of conlangs seem to be deliberately elaborated and

> intricate, reflecting how much weirdness is out there and how the

> complexity of a language isn't related to how materially-advanced its

> society is. But historically, most peoples had very basic math skills.

>

> I'd love to see counter-examples to the modern place-value system. Can you

> recommend any?

non-place-value systems. However, Klingon uses a place-value system

that's rather different from what most people are familiar with; it's

got three numerals, but the digits run 1 to 3, not 0 to 2.

Counting goes as follows:

1 - 1

2 - 2

3 - 3 (three ones)

11 - 4 (one three and one ones)

12 - 5 (one three and two ones)

13 - 6 (one three and 3 ones; this is the kind of weird part)

21 - 7 (two threes and one one)

etc.

Most representations are the same as in a regular place value system

with zero, except for powers of the radix, which have one less digit,

eliminating the zero. A mechanical transformation can be done on any

regular place-value system to turn it into a zero-less system like

this.

I came up with a mixed system (intending to use it for Mev Pailom, but

that hasn't worked out very well as of yet) with basic numerals for 1,

2, and 5. Counting goes

1

2

1 and 2

2 2s

5

5 and 1

5 and 2

5 with 2 and 1

5 with 2 2s

2 5s

...

2 and 1 of 5 = 15

...

2 2's of 5 = 20

I don't have any sort of extra-linguistic numeral-only notation for it

yet. And it gets very clumsy when trying to describe numbers much

larger than 80 (2 2s of 2 2s of 5). So it needs a bit work still.

-l.