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From: rmk4@woodlawn.uchicago.edu (Robert Knippen)
Subject: Re: Danish Numbers (was: Linguistics for Kids)
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Date: Thu, 16 Mar 1995 06:49:06 GMT
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In article <241561598.33328314@inform-bbs.dk>,
OleStig Andersen <OSA@inform-bbs.dk> suggested the following
rationalization of the words for certain numbers in Danish:


>This number system is a relict from a crazy old 20-based system where the
>tens run like this
>
>10 = ti
>20 = tyve
>30 = tredive
>40 = fyrre
>50 = halvtredsindstyve  = halvtredje sinde tyve  = half third times twenty =
>2,5*20
>60 = tresindstyve  = tre sinde tyve  = three times twenty = 3*20
>70 = halvfjerdsindstyve  = halvfjerde sinde tyve  = half fourth times twenty
>= 3,5*20
>80 = firsindstyve  = fire sinde tyve  = four times twenty = 4*20
>90 = halvfemsindstyve  = halvfem sinde tyve  = half fifth times twenty =
>4,5*20
>
>halv = half
>og = and
>sinde/sinds = times

I'm afraid that just like every other attempt I've seen by speakers 
of Danish to explain their number system, this doesn't work.  The 
math simply doesn't work.  "half-third" just doesn't get you 2.5, no 
matter how hard you try.  (at least not logically--more on this later)
In fact, the problem with 50, 70, and 90 is 
just restated in your solution.  The problem is that it isn't clear 
what to do with the occurence
of "halv" in the form.  If it had its normal meaning, _something_ ought
to be halved. Well, the only thing you can halve to get 2.5 is 5, and the 
only thing you can halve to get 50 is one hundred.  Making "half-third"
equal to 2.5 is the same as making "half-sixty" (half three times 20) 
equal to 50, so we haven't gotten anywhere.

The immediate response to this by a Danish speaker is to notice that 
halvtredje "half-third" _is_ the way to say 2.5 in Danish.  So the 
problem really isn't with 50, 70, and 90 at all.  It's with these
strange ways that words for 2.5, 3.5, and 4.5 are formed.  When somebody
explains how half-third (or fourth or fifth) can come to mean 2.5 (or 3.5
or 4.5, respectively), then I'll believe there is some logic to the system.

(note:  I realize that 1/2 times 3 equals 2.5, but we're missing the
word for "times" and we have a form that means "third," not "three.")

>It is not entirely correct that the fullfledged system is used in official
>documents only. In daily life we just say (and write), e.g.
>53 treoghalvtreds, omitting the -indstyve, and
>76 seksoghalvfjerds(indstyve)
>BUT in the ordinal numbers we do the whole chore:
>the fiftythird is den treoghalvtredsindstyvende which cannot be abbreviated!
>the only other alternative is to say number 53, nummer treoghalvtreds.
>
You should also mention that sinde/sinds doesn't seem to mean "times"
in modern Danish (at least as far as I could tell from my Gyldendals--I
had to look in the etymological dictionary to find this use) this makes
the system all the more opaque.

>It might comfort you to know that Danes in general are utterly unaware of the
>"logic" of the system, and no "normal" Dane would be able to explain it. We
>simply learn the numbers without any understanding of their internal
>structure. Consequently the illogicity - or rather the outlandish logic - of
>the system poses absolutely no problems to us.

It does make for some interesting debates sometimes, though.  I've heard
Danes argue about this more than once.  It's something most Danes are aware
of, and many people develop their own rationalizations (I've heard some
real doozies, let me tell you--like one that involved a supposed relic
form for units of 20, something like "snaess").

Bob Knippen
r-knippen@uchicago.edu
