Re: Number systems (was: Picto & Dil)

Hi!

Ray Brown writes in response to me:
>...
> If Greek culture had had a significant effect on western & central
> European culture, I suppose we might have counted in myriads (10000), but
> even their numeric symbols only went up to 999; you then used the same
> ones again, but with a mark to multiply them by 1000 - so I guess the
> number symbols would still have suggested counting in 1000s  :(
BTW: as a friend of mine pointed out after lurking here, putting me
under heavy surveilance (hi!!), the East Asian conlang Baronh (an a
posteriori of purified Ancient Japanese) uses 10^4 as a basis of unit
prefixes.

>...
> So if 'nine ten one two three four five six seven eight nine' =
> 1.23456789e9, then do we just say (with direct translation) 'five ten one
> two three four five six seven eight nine' to denote 1.23456789e5, thus
> eliminating any need for a Tyl Sjok word for point/decimal/comma?
This would be done in the scientific world, but it is one of the
things I find a bit unnatural in daily life, I think.  Maybe with
fixed things like units of money, this would happen.

In normal speech, you'd split the number into two parts and link them
with 'add':

  5 10 1 2 3 4 5 + - 1 10 6 7 8 9

What's common is abbreviation, however, e.g.:

  5000 = 3 10 5

And the above 'add' is also used to skip a lot of zeros:

  500002 = 6 10 5 + 2

> > Hmm -- I don't think it's more complex to count the factors of ten
> > instead of learning several words for a few of them.  The 'person on
> > the street' possibly just uses relatively small number words, and when
> > getting exposed to larger ones, they'd hopefully not be scared away by
> > a different type of number representation, because the one they'd use
> > on the street is just the normal one.
>
> Ooh - but they would IME - it's surprising the number of adults, in the UK
> at least, that just have a mental block when it comes to anything
> unfamiliar with numbers. It would be those brought up with the new system
> that might find it easier, but......
Yeah, sure, same mental block in this country. :-) But for natives in
Tyl Sjok and Qthyng|ai, this would be their everyday system.  They'd
not have to learn a second one for maths.

>... without empirical data, it is guess work. I don't know how we
> could go about getting empirical data. It would certainly be very
> interesting IMO.
:-) I'm not the person to test my conlangs on children...

>...
> I guess not either. But it must be easier than working with a mile of 1760
> yards or 5280 feet  :)
Ough!  That's no good for a metrical person like me. :-)

Anyway, more on the Tyl Sjok system -- you asked, at least
implicitly. :-) Any I think the gory details of the following are not
on the list yet (maybe some bits):

I've included inches and times in the Tyl Sjok system: it can handle
'strange' units.  This is actually the second layer: you'd treat the
super-units of a base unit as exponents and keep the same syntax as
with numbers.  If the multiples are > 16, you have to introduce an
intermediate unit step:

    (1) second     = second
    2 second       = 15 seconds
    3 second       = minute
    4 second       = 15 minutes
    5 second       = hour
    6 second       = half a day
    7 second       = day
    8 second       = week
    9 second       = month
   10 second       = year

The range of the exponent is valid where the unit is multiplied
irregularly, so below 1 seconds, you'd use decimal again and above a
year, you'd also use decimal again.  Also note that you count from 0,
not from one: just like after 9 comes 10, after, January 30 comes
February 0.  This may be confusing when learning Tyl Sjok, I
admit... :-))))

The time now is:

   3:45:31 = 5 second 3 3 0 2 1

For times, the unit will probably be left out, and since you usually
need to start at exponent 6 (half a day), that'd be:

   0 3 3 0 2 1

(Reminds me: program a digital desktop clock in Tyl Sjok, Henrik...)

Nice thing is: a five digit clock is a 12 hour clock while a 24 hour
clock has six digits.  Very natural. :-)

The layering of units and bases can be seen in dates:

   Apr 22, 2005 = 10 second 3 10 2 0 0 5 3 3 1

Here, after 3 10 2 0 0 5, the number's exponent would drop to < 0, but
the unit exponent is still > 0, so it's understood that the next
sub-unit is due now and the following 3 is not taken to be year
2005.3, but Month 3 = April, etc.

You can use whatever unit system you like with Tyl Sjok, there's no
conculture.

Ah, yes: the base by which the smalles unit divides is lexicalised,
because for m, it is probably 10, but for inches, it is probably 2:

   meter 2 1     = 2.1 meters
   meter 2 1 1   = 2.1 meters
   meter 2 1 1 1 = 2.1 meters
   inch  2 1     = 2 + 1/2 = 2.5 inches
   inch  2 1 1   = 2 + 3/4 = 2.75 inches
   inch  2 1 1 1 = 2 + 7/8 = 2.825 inches

> > (In Tyl Sjok, these prefixes just don't exist (by definition :-))).
> > You'd use 1000m instead of 1km.  This holds for whatever unit.)
>
> But 1024b instead of 1Kb   :)
Right! :-)  You'd probably count in hexadecimal then, anyway, so it's:

  1km  =  meter 3 10
  1kB  =  byte  2 16 4

> >> and that might suggest keeping a similar system in an auxlang - but
> >> I'll leave that to that other list ;)
> >
> > Right -- may this be discussed in that place! :-)
>
> They actually _discuss_ things there now, do they (just kidding  :)
:-))  I don't know -- I've never been there.  They used to only shout?

**Henrik

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